22 DEC. 1975

. PHILIPSRESEARCHREPORTS

SUPPLE~M~E~t\b\. \'\otlab.

PHlllPS RESEARCH LABORATORIESPhlllps Res. Repts Suppl. 1975 No. 8PrInIcd In the Ncthcrland.

© N.V. Philips' Gloeilampenfabrieken, Eindhoven, Netherlands, 1975.Articles or illustrations reproduced, in whole or in part, must be

accompanied by full acknowledgement of the source:PHILlPS RESEARCH REPORTS SUPPLEMENTS

BY

iq-,

IMPLANTATION OF BORONIN SILICON*)

w. K. HOFKER

*) Thesis, University of Amsterdam, November 1975.Promotors: Prof. Dr. J. Kistemaker (University of Leiden),

Prof. Dr. J. Bloem (University of Nijmegen).Co-referent: Dr. C. A. J. Ammerlaan.

Philips Res. Repts Suppl. 1975, No. 8.

Abstract

The distribution versus depth of boron implanted in silicon and the corre-sponding electrical activity obtained after annealing are studied. Theboron distributions are measured by secondary-ion mass spectrometry.From an investigation it is concluded that within certain conditions thismethod gives reliable results. Boron distributions implanted at energiesin the range from 30 keY to 800 keY in amorphous and polycrystallinesilicon are analysed. Moments of these distributions are determined bya curve-fitting programme and compared with moments calculated byWinterbon. For the first three moments the agreement is within 15% ifa coefficient of electronic stopping 1·5 times the standard Lindhardvalue is used in the calculations. It is found that these distributions canbe accurately described by distributions of the Pearson system. Borondistributions obtained by implantations along a dense crystallographicdirection in monocrystalline silicon are found to have penetrating tails.After investigation of some possible mechanisms of tail formation it isconcluded that the tails are due to channelling. It was found that thebehaviour of boron during annealing is determined by the properties ofthree boron fractions consisting of precipitated boron, interstitial boronand substitutional boron. The electrical activity of the boron versusdepth is found to be consistent with the three boron fractions. A peculiarredistribution of boron is found which is induced by the implantation ofa high dose of heavy ions and subsequent annealing. Different mech-anisms which may cause the observed effects, such as thermal diffusionwhich is influenced by lattice strain and damage, are discussed.

CONTENTS

1. INTRODUCTION . 1References. . . . . 3

2. THEORETICAL AND EXPERIMENTAL ASPECTS RELATEDTO THE INVESTIGATION OF BORON IMPLANTATIONS INSILICON. . . . . . . . . . . . . . . . . . . . . . . . 42.1. Range distributions in amorphous and polycrystalline solids 42.2. Range distributions in single crystals . 72.3. Implantation damage . . . . . . . . 92.4. Redistribution effects during annealing 112.5. Electrical behaviour of implanted ions. 142.6. Experimental techniques. . . . . . . 16

2.6.1. Ion-implantation equipment. . 162.6.2. The measurement of in-depth distributions of implanted

ionsReferences. . . . . . . . . .

3. THE MEASUREMENT OF RANGE DISTRIBUTIONS OFIMPLANTED IONS WITH SECONDARY-ION MASS SPEC-TROMETRY . . 21Abstract. . . . . . . . . 213.1. Introduction. . . . . 213.2. Principle of the method 213.3. Requirements . . . . 233.4. The instrument. . . . . 243.5. Experimental investigation. 25

3.5.1. The uniformity of the sputtering rate . 253.5.2. Measurement of the sputtering rate. . 273.5.3. Influence of an oxide layer on the surface . 283.5.4. The influence of the residual-gas atmosphere 293.5.5. Effect of damage on the sputtering rate and ion yield. 293.5.6. Contribution of ions from the crater rim . . . . .. 303.5.7. Disturbance of an impurity distribution by the sputtering

process. . . . . . . . . . . . . . . . . . . 313.5.8. The influence ofthe band structure on the ion yield 333.5.9. The linearity of the system . . . . . . . . . . 333.5.10. The measurement of annealed-boron distributions 343.5.11. "Chemical-emission" effects. . . . . . 353.5.12. Transients in the secondary-ion current. . . . . 37

1619

3.5.13. Delay effects in the detection system . . 393.5.14. Calibration of the boron measurements. 39

3.6. Conclusions 39References. . . . . . . . . . . . . . . . . . . 40

4. CONCENTRATION PROFILES OF BORON IMPLANTATIONSIN AMORPHOUS AND POLYCRYSTALLINE SILICON 41Abstract. . . . . . . . . . . . . . 414.1. Introduetion . . . . . . . . . . 414.2. Experimental procedure and results 43

4.2.1. Experimental details . . . 434.2.2. Experimental results . . . 44

4.3. Analysis of the experimental results . 444.3.1. Determination of the moments of the experimental distri-

butions . . . . . . . . . . . . . 444.3.2. Comparison with theoretical results 48

4.4. Discussion and conclusions 52References. . . . . . . . . . . . . . . . . 57

5. CONCENTRATION PROFILES OF BORON IMPLANTATIONSIN MONOCRYSTALLINE SILICON . 58Abstract. . . . . . . . . . . . . . . . . . . . . . . . . .. 585.1. Introduetion . . . . . . . . . . . . . . . . . . . . . .. 585.2. Range distributions of boron implanted along a dense crystallo-

graphic direction . . . . . . . . . . . . . . . . . . . .. 585.3. Comparison of distributions of implantations along open and

dense crystallographic directions . . . . . . . . . . . . .. 625.4. Comparison of boron distributions in monocrystalline and in

amorphous silicon . . . . . . . 645.5. The mechanism of tail formation . 64References. . . . . . . . . . . . . 67

6. INFLUENCE OF ANNEALING ON THE CONCENTRATIONPROFILES OF BORON IMPLANTATIONS IN SILICON 69Abstract. . . . . . . . 696.1. Introduetion . . . . 696.2. Experimental details 706.3. Experimental results 70

6.3.1. Concentration profiles after annealing at different tem-peratures . . . . . . . . . . . . . . . . . . .. 70

6.3.2. Concentration profiles as a function of annealing time 726.3.3. Background-dope measurements. . . . . . . . .. 72

6.3.4. Concentration profiles of an implantation along an opencrystallographic direction . 77

6.4. Discussion. . . . . . . . 776.4.1. General aspects . . . . . 776.4.2. Precipitation effects . . . 786.4.3. Transient diffusion effects. 816.4.4. Profile broadening after prolonged annealing 82

6.5. Conclusions 83References. . . . . . . . . . . . . . . . . . . . . 85

7. BORON IMPLANTATIONS IN SILICON: A COMPARISON OFCHARGE-CARRIER AND BORON CONCENTRATION PRO-FILES .. . . . 86Abstract. . . . . . . . . . . . . . . . . . . . . . . . 867.1. Introduction. . . . . . . . . . . . . . . . . . . . 867.2. The measurement of charge-carrier concentration profiles 86

7.2.1. Theory of the Hall-effect-resistivity measurements 867.2.2. The Hall-effect-sheet-resistivity measurements . 887.2.3. The layer-removal technique 89

7.3. Experimental results . . . . . . . . . . . . . . 907.4. Discussion . . . . . . . . . . . . 95

7.4.1. The region of maximum boron concentration 957.4.2. The tail region of the profile 977.4.3. The profile near the surface . 98

7.5. Conclusions 98References

8. REDISTRIBUTION OF BACKGROUND IMPURITIES IN SILI-CON INDUCED BY ION IMPLANTATION AND ANNEALING 100Abstract8.1. Introduetion8.2. The experimental method8.3. Experimental results . .8.4. Discussion of the peak structure

8.4.1. The peak structure in the boron distribution8.4.2. Mechanism for formation of the peak structure8.4.3. The position of the peak structure . . . . . .8.4.4. The influence of the implantation dose, ion species and

background concentration . . . . . . . . . .8.4.5. The influence of the temperature of implantation8.4.6. The electrical properties of the peak structure

8.5. Discussion of the substructure . . . . . . . . . . . .

99

100100101101107107109112

113115116117

8.6. Discussion of the junction dip . . . . . . . .8.7. The secondary-ion yield of redistributed boron .8.8. ConclusionsReferences

118119120121

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1. INTRODUCTION

When one bombards a solid with a beam of ions, most of the ions penetrateinto the solid and are implanted there. The physical or chemical properties ofthe implanted region may be influenced by the implanted ions and by thecreated damage.Interestin.g applications of ion implantation are found in the semiconductor

field due to the fact that the electrical properties of semiconductors can beconsiderably influenced by ion bombardment. This was first observed by Ohl,who in 1952 1-1) reported that the rectifying properties of silicon point-contactdiodes were changed if the silicon surface was bombarded with gas ions. Inthis case the electrical influence was obtained by the creation of electricallyactive defect centres. A more important and direct way to influence the elec-trical properties of semiconductors is to implant impurities with acceptor- ordonor-type properties such as is the case if elements of group III or V of theperiodic table are implanted in silicon (group IV). This was realized by Shockleywho, in 1954, filed a far-seeing patent on ion implantation in which he alsoanticipated the need of thermal annealing to restore the crystalline propertiesof the bombarded region. Considerable support to research on ion implantationcame at the beginning of the sixties from investigators working on semi-conductor radiation detectors. Their problem was that the introduetion ofelectrically active impurities into silicon or germanium by thermally activateddiffusion - a commonly used semiconductor doping technology - requires ahigh process temperature. By such a process the lifetime of the charge car-riers is spoilt, resulting in bad collection ofthe charge carriers and consequentlyin poor energy-resolving power of the detector. Therefore ion implantationwhich involves a lower process temperature became interesting. Later on otheradvantages of ion implantation were realized, such as a better dose control andan easier in-depth control of impurity distributions, all of which are of impor-tance in electronie-device technology. This stimulated world-wide research onion implantation in industrial as well as in university and governmentallabora-tories.

Research on ion implantation started in our laboratory in 1962 and wasintensified in 1968. We decided in the course of 1970 to start a study on boronimplantations in silicon. Silicon is a widely used substrate material in semi-conductor-device technology, whereas boron, a group-Ill element, is used toobtain p-type electrical conductivity. In viewof the said features of ion implan-tation a study of the various aspects that determine the concentration of thecharge carriers as a function of depth was of special interest. We thereforeinvestigated the as-implanted boron distributions, the annealing behaviour ofsuch distributions and the electrical activity of the boron as a function of depthwhich is obtained after annealing, Several aspects, which are related to these

-2-

subjects, are introduced in chapter 2.The measurement of boron distributions is in these studies very important.

We adopted the method of Secondary-Ion Mass Speetrometry for this purpose.This method requires a careful interpretation and therefore we investigated itsreliability for the special case of the measurement of in-depth profiles of boronin silicon. Results are reported in chapter 3.

Most theories which describe distributions of implanted ions in solids onlyapply to the case that the structure of the solid isnon-crystalline. For such targetsLindhard, Scharff and Schiett 1-2) derived a formalism for the calculation oftherange and range straggling of implanted ions and recently Winterbon 1-3)succeeded in calculating higher moments of range distributions.We investigated boron distributions in non-crystalline silicon and verified

these theoretical calculations. Some results of this investigation together withan analytic description which we developed for experimental boron distribu-tions are given in chapter 4.Implanted-impurity distributions in crystalline solids differ considerably from

those in non-crystalline solids. Often the impurity distributions in crystallinesolids have penetrating tails. This effect is probably due to deep penetration ofthe ions through channels between the regular atomic rows. We observed suchtails on boron distributions. These distributions and a more detailed investiga-tion of the tails are discussed in chapter 5.The implanted layers obtain the desired electrical properties by annealing.

During annealing the implanted boron is thermally activated and thereforeredistributed. Up till now no systematic study of the behaviour of implanted-impurity distributions upon annealing has been done. We decided therefore toinvestigate these annealing effects in more detail. With ion implantation it ispossible to obtain higher boron concentrations than is obtained with thermaldiffusion due to the fact that, in the case of ion implantation, the impurityconcentration is not limited by the solid solubility. It was thus of special interestto us to include in our research the annealing behaviour of the high boronconcentrations reported on in chapter 6.The electrical behaviour of implanted boron as a function of depth for dif-

ferent annealing treatments and implantation doses is investigated by com-paring the boron distributions with the corresponding charge-carrier distri-butions as is discussed in chapter 7. So far such an investigation had not beencarried out on boron for .lack of an adequate method for the measurement ofboron distributions.We observed an interesting redistribution of boron in silicon induced by

implantation and annealing. This effect is found to be most pronounced atthe transition from the implanted to the non-implanted region. Differentmechanisms which may cause this effect such as thermal diffusion which isinfluenced by lattice strain and damage are investigated. This phenomenon,

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which is discussed in the last chapter, provides better understanding of theinteractions between sequential implantations.A part of this report gives a compilation of results which we published earlier

in differentjournals and proceedings 1-4/10). More in detail this concerns someof the results which are described in chapters 3, 5 and 8 and most of the resultsdescribed in chapters 4, 6 and 7..

REFERENCES1-1) R. S. Ohl, Bell Syst. techno J. 31, 104, 1952.1-2) J. Lindhard, M. Scharff and H. E. Sch ie tt, Mat. Fys. Medd. Dan. Vid. Selsk. 33,

no. 14, 1963.1-3) K. B. Winterbon, Rad. Effects 13, 215, 1974.1-4) W. K. Hofker, H. W. Werner, D. P. Oosthoek and H. A. M. de Grefte, Rad.

Effects 17, 83, 1973.1-5) W. K. Hofker, H. W. Werner, D. P. Oosthoek and H. A. M. de Grefte, in

B. L. Crowder (ed.), Proc. int. conf. ion implantation in semiconductors and othermaterials (Yorktown Heights 1972),Plenum Press, New York, 1973,p. 133.

1-6) W. K. Hofker, H. W. Werner, D. P. Oosthoek and H. A. M. de Grefte, Appl.Phys, 2, 265, 1973.

1-7) W. K. Hofker, H. W. Werner, D. P. Oosthoek and N. J. Koeman, AppJ. Phys. 4,125, 1974.

l-B) W. K. Hofker, H. W. Werner, D. P. Oosthoek and N. J. Koeman, Proc. int. conf.ion implantation in semiconductors and other materials (Osaka 1974),in S. Nam ba(ed.), Ion implantation in semiconductors, Plenum Press, New York, 1975, p. 201.

1-9) W. K. Hofker, D. P. Oosthoek, N. J. Koeman and H. A. M. de Grefte, Rad.Effects 24, 223, 1975.

1-10) W. K. Hofker, Rad. Effects, in press.

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2. THEORETICAL AND EXPERIMENTAL ASPECTS RELATED TOTHE INVESTIGATION OF BORON IMPLANTATIONS IN SILICON

2.1. Range distributions in amorphous and polycrystalline solids

Heavy ions which penetrate into matter gradually lose their energy by inter-actions with target atoms and free electrons. One of the first to study thesecollision phenomena was N. Bohr, who published in 1948a classical work onthis subject 2-1). His work was continued by Lindhard and collaborators.Some of their results are summarized in the present work and applied to boronimplantations in silicon.The stopping process of heavy ions of velocity v < vo Z1 where Z1 is the

atomic number of the ion and vo is the Bohr velocity (vo = q2/28011 whereq is the electronic charge, 80 is the permittivity of free space and It is Planck'sconstant) can be described byelastic Coulomb interactions between thescreened nuclear charges of the ion and target atoms and by inelastic inter-actions of the ion and the electrons in the target. Using this concept the ion'saverage energy loss with distance can be expressed in terms of the energy lossper target atom by

dE- = -N [SneE) + Se(E)]dx

(2.1)

where E is the ion energy at point x, SneE) is the nuclear-stopping cross-section, Se(E) is the electronie-stopping cross-section and N is the number oftarget atoms per unit volume. From (2.1) we derive for the total distance Rthat an ion with initial energy Eo travels in coming to rest

1 Eo dE

R = N f SneE) + Se(E)o

(2.2)

The nuclear-stopping cross-section SneE) was calculated by Lindhard,Scharff and Schiett (LSS) 2-2) using classical collision mechanics. In thesecalculations they used a screened interatomie Thomas-Fermi potential VTF(r):

V () - Z Z 2 <PTF(r/aTF) (2.3)Tl' r - 1 2 q ;

4:n; 80 r

where r is the interatomie separation, Z1 and Z2 are the atomic numbers ofincident ion and target atom, respectively, <PTF is the Thomas-Fermi screeningfunction which was numerically calculated and tabulated by Gombas 2-3) andaTF is the Thomas-Fermi screening parameter specified as

(2.4)

-5-I

where ao is the Bohr radius (ao = 80 Jz2/:rc m q2 = 0.529 Á, where m is theelectronic mass).

Figure 2.1 shows the specific energy loss in nuclear collisions versus energywhich resulted from calculations 2-2) by LSS. In order to obtain a universal

o·6/

Nuc/eJr /·-Elecfronic-B(5i)• (5.=0-216 t:"2J

/: <,~//

-21! i /~. i

J> ./ 1 ----1 r---/1 1

[// I 10

o

-0 II

3keV

1 2I

17keV a (5i)

3_t:"2

Fig. 2.1. Nuclear and electronic specific energy losses versus energy expressed in terms of thereduced parameters Band e (based on Lindhard et al.2-2». The curve of the electronic stop-ping represents the case of boron implantation in silicon.

result the energy and range are expressed in dimensionless reduced parameters,which are specified as

M28 = E 4:rc 80 aTF ,z, Z2 q2 (MI +M2)

MIM2e = x N 4:rc aTF2 ,(MI +M2)2

where MI and M2 are the masses of incident ion and target atom, respectively.The electronie-stopping cross-section Se depends on the velocity v of the ions,

that is, Se increases with V at low ion velocities, obtains a maximum at a velocityof the order of VI = Vo Zi2/3 2-2) and decreases again at higher velocities.For boron VI corresponds to an energy of 2·3 MeV. In the present study theenergy of the boron ions is below this level, or 0 < V < VI. In this velocityregion Lindhard et al. derived by using an electron-gas model of energy loss,that electronic stopping occurs proportional to V as specified in reducedparameters by

where

K. = ~ 0·0793 Z//2 Z21/2'(AI + A2)3/2

L _ e (Z//3 + Z22/3)3/4 A13/2 A21/2

(2.5)

(2.6)

(2.7)

(2.8)

-6-

where Çe~ Z11/6 and A denotes the mass number.In fig. 2.1 (de/dg.)e versus e1/2 is shown for boron in silicon (KL = 0·216).

For this case at E = 3 keY nuclear stopping has a maximum value, whereasfor E > 17 keV electronic stopping dominates nuclear stopping.

Using the results of fig. 2.1 in (2.2) R can be calculated. In ion implantation,the most probable penetration depth of the ions measured perpendicularly tothe surface is of interest. This depth is equal to Rp cos (), where Rp is themost probable range as measured in the direction of incidence and () is theangle between this direction and the surface normal. Rp is found by projectionof R on the direction of incidence and is therefore called the projected range(fig.2.2).

ITarget surface

Fig. 2.2. Definition of total range R and projected range Rp for a direction of incidence at anangle IJ to the surface normal.

Lindhard et al.2-2) formulated integral equations for the average projectedrange (x) (or first moment of the range distribution) and the standard de-viation Cf (second moment). Later studies were directed to obtaining moments ofhigher order. In these studies electronic stopping was at first excluded 2-4.5).However, recently Winterbon succeeded in developing a formalism for themoments of an ion distribution where electronic stopping was incorporated 2-6).The tabulated Thomas-Fermi screening function is replaced in this study byan analytical approximation. In fig. 2.3 a result of this study is given, showingrange distributions calculated for different energies (e) and the conditionsM2/M1 = 2 and KL = 0'1, which approximate the case of boron in silicon.The distributions are plotted with equal mean depth (x) and standard devia-tion Cf. It is observed that the skewness of these distributions increases withenergy.The electronie-stopping cross-section is obtained in experiments where one

measures the energy loss of ions passing through a thin foil. In such trans-mission experiments it is found that (de/de)e has a periodic dependence uponZI which is not predicted by LSS theory 2-7.8). This effect is attributed toelectronic shell effects. In this way an experimental electronie-stopping cross-section for boron in silicon is found to be 1·6times the standard LSS value 2-9).This electronie-stopping cross-section can also be derived from range measure-ments as reported in chapter 4 where we found the relation

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t

(x)-cr (x) (x)+cr (x)+2cr-Depth

Fig. 2.3. Range profiles at different energies s with equal mean depth <x) and straggling (J

for KL = 0·1 (KL = coefficient of electronic stopping) and M2/ M1 = 2 (from Winterbon 2-6».

Se = 1'75.10-13 EO'46 eV cm2jatom (E in MeV). (2.9)

Besides the above effect there is in general good correspondence betweenthe experimental and LSS values for (x) and a of the range distributions. Forhigher moments such comparisons were not carried out and therefore we de-cided to do these for boron in silicon. In chapter 4 we describe in which waywe investigated moments up to the fourth of experimental distributions.

2.2. Range distributions in single crystals

Experimentally it is found that energetic ions can penetrate deeply into singlecrystals if they are implanted in a low-index crystallographic direction 2-10).

This effect is due to steering of the ions through open channels between theregular atomic rows and planes and is therefore described as the channellingeffect. An important physical parameter in the study of this effect is the criticalangle for channelling "Peril' If 'Ijl < "Peril, where 'Ijl is the angle between thedirection of incidence of the ions and the channel axis, and if the impact occursoutside a critical distance to the atomic rows (about aTF), then channelling ofthe ions occurs. Using a continuum model for the interatomie interactionpotential along a channel Lindhard 2-11) derived in the case ofaxial channel-ling if E ~ Eo = Zl Z2 q dj2n 80 aTF2 eV:

(2.10)

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and if E« Eo:

(c aTF )1/2

"Perlt~' d V2 "P1

where d is the spacing between atoms along the channel axis and C is a param-eter in the analytical approximation of the Thomas-Fermi screening function(C is of the order of V3).

"Peril is given in table 2-1 for boron in silicon calculated with (2.10) and (2.11)for a number of channel directions and energies. From these results we observethat "Perlt is largest for the (I 1 0) direction and decreases with energy.

(2.11)

TABLE 2-1

Critical angles for channelling of boron in three crystallographic directions ofa silicon target calculated for different implantation energies

channel directionsenergy

(110) (111) (100)(keV)(degrees) (degrees) (degrees)

30 4·7 4·0 3·650 4·1 3·5 3·2100 3·5 3·0 2·7200 2·9 2·5 2·2400 2·1 1·9 1·9800 1·5 1·3 1·2

Experimentally it is found that the maximum range Rmax of well channelledions depends mainly on the crystal direction of the target and on the type andenergy of the ion 2-12). Lattice vibrations, crystal perfection, small mis-alignment and surface layers mainly determine the shape of the range dis-tribution. Rmax is proportional to E1/2 if E is sufficiently high 2-13). Thisresult is characteristic for electronic stopping. At the end of the range de-channelling of the ion occurs. This is caused by the increase of the nuclear-stopping cross-section 2-14) and by the increase of the transverse energy dueto electronic collisions. In transmission experiments Eisen 2-15) measuredelectronie-stopping cross-sections which are proportional to EP with p between0·3 and 0·9, dependent on Zl. The fact that a deviation from velocity propor-tionality is found is less understood.

Ion implantation in a dense (misaligned) crystal direction often results inion distributions which have penetrating exponential tails 2-16). Such tailsmay be caused by scattering of the ions into open crystal directions duringimplantation. Recently Blood et a1.2-17) demonstrated conclusively that tails

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on phosphorus distributions are due to this effect. In the case of implantationof indium and antimony Gamo et al.2-1B) observed exponential tails if im-plantation occurred at 300 oe or higher and no tails if the sample is at a lowertemperature during implantation. Due to this thermal dependence of tailformation they conclude to some type of enhanced thermal diffusion. In boronimplantations in a dense crystal direction we observed small tails which arenot strictly exponential. These tails are due to channelling as we concludefrom measurements which are described in chapter 5.

2.3. Implantation damage

Implantation damage is produced if, in primary or secondary nuclear col-lisions, enough energy is transferred to substrate atoms that they are displacedfrom their lattice sites. The displacement energy of an atom depends on therecoil direction within the crystal lattice. In silicon the threshold energy Edfor such a process is about 14 eV 2-19). The average number of displacementsor Frenkel pairs (vacancy-interstitial pairs) N(E) produced by an ion isestimated according to Kinchin and Pease 2-20):

(2.12)

where En is the part of the ion energy transferred in primary or secondarynuclear collisions. Lindhard et al.2-21) put forward a theoretical discussionof En. Using this theory Thomsen numerically calculated En for different ionspecies and substrate materials 2-22). In order to estimate En for boron ionsin silicon we used his reported data for carbon ions in silicon. With these datain (2.12)we obtain N(E) for different energies Eo as given in table 2-11.Incrystalline silicon N(E) may be different, especially if boron is implanted in alow-index direction. For instance implantation in a <t 10) direction produceshalf the disorder that is created by implantations in a random direction 2-9).

TABLE 2-11Number of Frenkel pairs N(E) created in silicon by a boron ion implantedat an energy of Eo estimated from data for carbon in silicon 2-22)

Eo En N(E)(keY) (keY)

10 6 21030 14 500

100 27 960300 41 1460

1000 54 1930

-10 -

The depth distribution of the concentration of the created Prenkel pairs canbe obtained from moment calculations ofWinterbon, Sigmund and Sanders2-5).In these calculations an analytical approximation of the Thomas-Fermi poten-tial is used and electronic stopping is not taken into account. Prom their resultsfor the average depth (X)D and standard deviation (fD ofthe damage distributionas expressed in the corresponding values for the range distribution, (X)R and (fRrespectively, we derived for boron implantations in silicon:

(2.13)

(2.14)

These results are in reasonable agreement with those obtained by Pavlov etaP-23) using Monte Carlo calculations and given in fig. 2.4. In these calcula-tions electronic stopping is included; however, the less realistic Bohr inter-action potential is used.

ê0/00.s]o.l:;c:lIJg 0·58t

Fig. 2.4. Distributions of boron ions (drawn curves) and vacancies (dashed curves) in siliconafter implantation at 20 keY, 40 keY and 60keY, calculated by the Monte Carlo method. Themaximum concentrations are normalized to unity. The maximum vacancy concentrations arefor a boron dose of 1000 ions cm-2 implanted at 20, 40 and 60 keY: 11.95.109,11.8.109,11·9. 109 cm- 3, respectively (from Pavlov et aJ.2-23».

In the region where the defect concentration is about 0·02 of the atomicdensity, a spontaneous transformation to the amorphous state occurs 2-24).Here we have to consider amorphous in the sense that there is no long-rangecrystallographic ordering, whereas close-range (tetrahedral) ordering may stillexist. If the implanted ion dose is high enough the amorphous zones createdby the individual ions will overlap and a continuous amorphous layer is formed.Such a situation occurs if heavy ions (Z > 10) are implanted at room tem-perature with a dose of 1014 ions cm-2, as verified by optical- and electron-diffraction measurements 2-25). For ions with Z < 10 a continuous amor-

-11-

phous layer is produced at much higher implantation doses. In the first placethis is due to the lower defect concentration as a consequence of the longer rangeand of the smaller fraction of the ion energy which is transferred in nuclearcollisions. More important however is that in the region where no amorphouszone is created, dissolution and erosion of the defect clusters occur due torecombination and out-diffusion of the defects. These effects are already ofinterest at room temperature. This explains why in case of boron implantationin silicon a continuous amorphous layer is obtained at 77 K at a dose of1015 ions cm"? whereas at room temperature a dose of > 1017 ions cm-2 isrequired 2-9). A further consequence of these annealing effects is that thedamage at room temperature is dose-rate-dependent 2-26). An effect whichhas hitherto been less well understood is annealing of the damage due tobombardment with light ions (beam annealing) 2-27.28).

Annealing at high temperatures is required to remove the damage and toensure that the implanted ions move to lattice positions in order to obtainfull benefit of their electrical activity (sec. 2.5). If a continuous amorphouslayer is produced, annealing at 600 "C during a period of 10 min is neededto restore the crystalline properties. In case of isolated amorphous regionsreordering occurs at 300 °C. The reordering of a continuous amorphous layeris initiated at the interface of the amorphous and undamaged regions as hasbeen found from helium back-scattering measurements using the channellingeffect 2-29).It is known from transmission electron-microscopic measurements that even

after annealing at 600 °C or higher many defect clusters are still present 2-30).This is demonstrated in figs 2.5 and 2.6 where are shown typical transmissionelectron micrographs which we made of silicon that is implanted with boron.One observes that after annealing at 800°C (fig. 2.5) the residual damagemainly consists of linear defects and dislocation loops, whereas after annealingat 1000 °C (fig. 2.6) big stacking faults are left.

2.4. Redistribution effects during annealing

During annealing redistribution of the boron will occur due to thermal dif-fusion. Such thermal-diffusion effects have been extensivelystudied for impurityatoms introduced into a solid by the process of thermal diffusion. These redis-tribution effects are adequately described by Fick's laws given in one dimensionby

dCI=-D-

dx'(2.15)

dC d2C-=D--dt dx2

(2.16)

- 12-

Fig. 2.5. Transmission electron micrograph of silicon, implanted with boron at an energy of25 keVand a dose of 1015 ions cm- 2 and annealed at 800°C for 35 min.

Fig. 2.6. Transmission electron micrograph of silicon implanted with boron, at an energy of70 keV and a dose of 1016 ions cm- 2 and annealed at 1000°C for 35 min.

D(T) = Do exp (-QfkT) (2.17)

-13-

where I is the flux density, C is the impurity concentration and D is the diffusioncoefficient, specified by

where k is Boltzmanns' constant and T is the absolute temperature.For boron in silicon, Do is 3 to 10 cm2fs and the activation energy Q is

3·5 to 3·6 eV 2-31). At high boron concentration, D is concentration-depend-ent 2-32). In the case of thermal diffusion the boron atoms are on substitu-tional lattice sites. The diffusion of boron occurs with some type of defectmechanism. Often a mono-vacancy mechanism is assumed. However, the valueof the activation energy for self-diffusion of silicon in silicon calculated withsuch a mechanism, being 3·2-3·4 eV, is much lower than the experimental one(4·8-5·2 eV). Various suggestions have been put forward in explanation ofthis discrepancy. For instance, Hu 2-33) supposes that the models used inthe calculation should be refined. Ghoshtagore 2-34), and Kendall and DeVries 2-35), suggest a di-vacancy mechanism for self-diffusion, whereas Seegerand Chick 2-31) propose an extended interstitial or vacancy mèchanism fordiffusion at high temperatures.In the case of implantation the substrate is left in a state which is far from

equilibrium. A description of the redistribution is now more complicated thanimplied by the expressions (2.15)-(2.17) for the case of thermal diffusion. Forinstance, in the first place D will be time-dependent due to the fact that, in thefirst stage of annealing, defects are released which may enhance the impuritydiffusion. An indication that such an effect may be effective can be deducedfrom measurements on heated silicon substrates bombarded with ions in a glowdischarge 2-36) or with protons 2-37.38). In such experiments the effect ofradiation-enhanced diffusion is clearly observed. A second complicating effectis that in the case of ion implantation the impurity concentration can exceedthe solid solubility. This as contrasted with thermal diffusion, where the solidsolubility limits the impurity concentration. Another difference comes fromthe fact that a fraction of the implanted ions is on interstitial lattice sites. Inchapter 6 we discuss the situation that the second effect results in an immobileboron fraction, whereas the last-mentioned effect causes a fast broadening ofthe boron distribution in the first stage of the annealing process.After implantation of a high dose of heavy ions and a subsequent annealing

process we observed a peculiar redistribution of a boron background dope.This effect may be due to different mechanisms such as by thermal diffusionwhich is influenced by lattice strain and damage caused by the implantation.A study of this effect is of interest for better understanding of the interactionsbetween sequential implantations as discussed in chapter 8.

-14 -

2.5. Electrical behaviour of implanted ions

At room temperature the energy gap Eg between the valence band and con-duction band of silicon is 1·12 eV. Boron, an element of group III ofthe periodicsystem, if on a substitutionallattice site, introduces an acceptor level within theband gap. The electrical behaviour ofthe boron is then described by the reaction

(2.18)

. where BD is neutral boron, B- is negatively charged boron and e+ is a positivefree hole. In case of thermal equilibrium the concentrations of the componentsin (2.18) follow from the condition for neutrality, that is

(2.19)

where n is the free-electron concentration, [B -] is the concentration of nega-tively charged boron and p is the free-hole concentration.

Using the concept of the Fermi level, eq. (2.19) - if non-degeneration isassumed 2-3?) - can be expressed as

(Ee-EF) 1 (N~ +B =N~

e p kT [ ] 1 + 4exp [(Ea-EF)jkT] v pEF-Ev)

kT

(2.20)

where EF is the energy of the Fermi level, Ne is the effective density of statesin the conduction band, Ee is the energy at the bottom of the conduction band,N; is the effective density of states in the valence band, E; is the energy at thetop of the valence band, [B] is the total boron concentration, Ea is the energyof the boron acceptor level, and k is Boltzmann's constant.

The acceptor ionization energy 8a= Ea - E; for boron in silicon is 0·045 eV.From computer calculations it is found from (2.20) with [B] up to 1017 cm-3

that p ~ [B] at room temperature. With 1017 < [B] < 1019 the ionizationof the boron is incomplete. With [B] > 1019 a different situation arises dueto the phenomenon of impurity band conduction 2-40).

When boron is implanted and no annealing has occurred, the situation ismore complicated than that described above. Then the defects which are createdby the implantation introduce deep levels within the band gap of donor- andacceptor-type 2-41). The Fermi level is now near the middle of the band gapand consequently the charge-carrier concentrations are nearly intrinsic.Annealing is required to obtain p-type conduction as is demonstrated by theresults given in fig. 2.7. This figure shows the effective charge-carrier concen-tration N,eff in the implanted surface layer versus the temperature of annealingTann for implantations at an energy of70 keV and doses of 1013, 101\ 1015 and1016 ions cm=", respectively. Annealing was carried out in a nitrogen atmos-

1o"oL------:20.Lo---4-:-:'oc::-o---:::6o~O:----:8::-!:O-=-O--,:=OO~O:-----J

-- Tantl·C)

-15 -

Fig. 2.7. Effective surface concentration of the charge carriers versus annealing temperatureof silicon implanted with boron at an energy of70 keVand doses ofl013, 1014, 1015 and 1016ions cm-2, respectively.

phere during periods of 35 min. N. eff was determined by measuring the sheetHall-effect coefficient R. (see chapter 7) from

1N.eff = --.

qR.(2.21)

The increase in N. eff at annealing temperatures up to Tann= 550 oe is mainlydue to removal of the lattice disorder giving a decrease of compensating deepenergy levels. In the temperature region 550 oe < Tann < 650 oe in some casesa reverse annealing effect is observed. From boron-location measurements usingthe channelling technique with a Bll(p,ex) reaction it is found that this reverseannealing of N. eff is due to a decrease of the substitutional boron frac-tion 2-42.43). This decrease is likely due to interactions of substitutional boronwith defects which are released from the damaged regions. For Tann >: 650 oethe increase in N. eff closely corresponds to the increase in the substitutionalboron fraction. In this temperature region annealing occurs with an activationenergy of about 5 eV 2-44). This energy corresponds to the energy needed forformation and migration of a vacancy and therefore it is suggested that thecreation of substitutional boron occurs by the capture of an interstitial boronatom by a vacancy 2-45). Annealing at temperatures of up to 1100 oe isrequired to make the implanted ions fully electrically active. Then a situation is

-16-

obtained which is similar to the one described at the beginning ofthis section.There is a dependence on depth of the electrical activity of implanted boron,

as we found by comparing boron distributions and corresponding charge-carrierdistributions after annealing, as is discussed in chapter 7 in more detail.

2.6. Experimental techniques

2.6.1. Ion-implantation equipment

In fig. 2.8 a schematic drawing of an ion-implantation system is given. Inthe indicated ion source, gases as supplied, or vapours from solids heated in theion source, are ionized. The ions are extracted from the source by an electro-static field and fed into an analysing magnet. The ions which pass the mass-defining slit are accelerated and fed into the target chamber containing thesamples to be implanted. The X- Y scanning system provides uniform implan-tations for large areas. Dose control is performed by measuring the integrated

High-voltage terminal'yMass-defining slit

M "",_1 ---8-===J1t_, ~~===::.-==-::._:..--=-= -::-=- -::..===== l'l-substrate/////J --- -- I,::::'"

Acceleration- Focussing X and Y fffaday, r Analysing lense system system scanningplates p

I ': ImagnetI, AcceleratiorIlllandil focussing

" lenser~!,~ Extraction .rrllamen lense

Ionsource

Gas inlet

Target chamber

Fig. 2.8. Schematic drawing of an ion-implantation system.

current of the Faraday cup. Figures 2.9a and b show the high-voltage terminaland the beam line with target chamber of a research implantation system ofthe Philips Research Laboratory at Amsterdam. This equipment provides boronimplantations with an energy of up to 500 keY and a beam current of 30 [LA.Ions with an energy of up to 1MeV are obtained by using doubly charged ions.

2.6.2. The measurement of in-depth distributions of implanted ions

The measurement of distributions of implanted ions is commonly performedby implanting a radioactive isotope of the investigated ion species. After theimplantation, the implanted layer is stripped off mechanically 2-46) or chemi-cally 2-10) layer by layer and the removed or remaining radioactivityis measured,giving differential or integral ion distributions. However, no radio-active isotopeof boron èxists. Up till now most information about boron distributions has

-17-

Fig. 2.9a. A 500-kVion-implantation equipment of the Philips Research Laboratory (Amster-dam Department); high-voltage terminal.

been obtained from charge-carrier distributions. These distributions are derivedfrom Hall-effect measurements combined with layer-removal steps 2-47) or fromcapacitance versus voltage characteristics using the junction properties of theimplanted layer or ofSchottky diodes, which are obtained by a metal depositionon the implanted region 2-48). These methods only provide reliable informa-tion about boron distributions if the electrical activation of the boron is com-pleted. Therefore in order to study boron distributions as-implanted or thebehaviour of boron distributions upon annealing, these methods are not useful.

A direct method for the measurement of lOB distributions is provided by thel°B(n,O() 7Li reaction. This method requires a thermal neutron flux and a systemfor the detection of prompt 0( particles. From the energy loss of the 0( particlesin the silicon the depth of the originating boron atoms is found. With such a

a)

- 18-

b)Fig. 2.9b. Beam line with target chamber.

method ZiegIer et al. 2-49) measured a boron distribution within about 10 husing a thermal neutron flux of about 108 cm-2 S-1 from a nuclear reactor.We consider such conditions as rather unpractical and decided therefore toinvestigate the application of Secondary-Ion Mass Speetrometry (SIMS) formeasurements of boron in depth. The application of SIMS for profiling indepth was mentioned earlier by Werner 2-50) and Croset 2-51). However,several aspects of this method, such as the sputtering and ion emission ofimplanted layers are not well understood. We therefore considered an investiga-tion of the reliability of this method for our application necessary. Results ofsuch an investigation are reported in the next chapter.

19

REFERENCES2-1) N. Bohr, Mat. Fys. Medd. Dan. Vid. Selsk. 18, no, 8, 1948.2-2) J. Lindhard, M. Scharffand H. E. Sch ie t t, Mat. Fys. Medd. Dan. Vid. Selsk. 33,

no, 14, 1963.2-3) P. Gombas, Handbuch der Physik, Vol. 36, Springer, Berlin, 1956,p. 109.2-4) J. B. Sanders, Can. J. Phys. 46, 455, 1968. .2-5) K. B. Winterbon, P. Sigmund and J. B. Sanders, Mat. Fys. Medd. Dan. Vid.

Selsk. 37, no, 14, 1970.2-6) K. B. Winterbon, Rad. Effects 13, 215, 1972.2-7) J. H. Ormrod and H. E. Duckworth, Can. J. Phys, 41, 1424,1963.2-8) J. H. Ormrod, J. R. MacDonald and H. E. Duckworth, Can. J. Phys, 43,27.5,

1965.2-9) F. H. Eisen, B. Welch, J. E. Westmoreland and J. W. Mayer, in D. W. Palmer,

M. W. Thompson and P. D. Townsend (eds), Proc. int. conf. on atomic collisions(Brighton 1969), North-Holland Publishing Company, 1970, p. 111.

2-10) J. A. Davies, G. C. Ball, F. Brown and B. Domey, Can. J. Phys. 42, 1070, 1964.2-11) J. Lindhard, Mat. Fys. Medd. Dan. Vid. Selsk. 34, no. 14, 1965.2-12) J. A. Davies, L. Eriksson and J. L. Whitton, Can. J. Phys. 46, 573,1968.2-13) L. Eriksson, J. A. Davies and P. Jespersgärd, Phys. Rev. 161, 219, 1967.2-14) D. V. Morgan (ed.), Channeling, John Wiley, London, 1973, p. 236.2-15) F. H. Eisen, Can. J. Phys. 46,561, 1968.2-16) G. Dearnaley, M. A. Wilkins and P. D. Goode, in I. Ruge and J. Graul (eds),

Proc. 2nd int. conf. on ion implantation in semiconductors (Garmisch-Partenkirchen1971), Springer, Berlin, 1971, p. 439.

2-17) P. Blood, G. Dearnaley and M. A. WiJkins, Rad. Effects 21, 245,1974.2-18) K. Gamo, M. Iwaki, K. Masuda and S. Namba, in I. Ruge and J. Graul (eds),

Proc. 2nd int. conf. on ion implantation in semiconductors (Garmisch-Partenkirchen1971), Springer, Berlin, 1971, p. 459.

2-19) A. Sosin and W. Bauer, in G. J. Dienes (ed.), Studies in radiation effects, GordonBreach, New York, 1969, Vol. 3.

2-20) G. H. Kinchin and R. S. Pease, Rep. Progr. Phys. 18, 2, 1955.2-21) J. Lindhard, V. Nielsen, M. Scharff and P. V. Thomsen, Mat. Fys, Medd. Dan.

Vid. Selsk. 33, no. 10, 1963.2-22) J. W. Mayer, L. Eriksson and J. A. Davies, Ion implantation in semiconductors,

Academic Press, New York, 1970, p. 68.2-23) P. V. Pavlov, D. I. Tetel'baum, E. I. Zorin and V. I. Alekseev, SOy. Phys.-Solid

State 8, 2141, 1967 (translated from Fizika Tverdogo Tela 8, 2679, 1966).2-24) M. L. Swanson, J. R. Parsons and C. W. Hoelke, in J. W. Corbett and G. D.

Watkins (eds), Radiation effects in semiconductors, Gordon and Breach SciencePublishers, London, 1971,p. 359.

2-25) D. J. Mazey, R. S. Nelson and R. S. Barnes, Phil. Mag. 17, 1145, 1968.2-26) F. H. Eisen and B. Welch, Proc. European conf. on ion implantation (Reading 1970),

Peter Peregrinus, Herts, 1970, p. 227.2-27) J. K. Hirvonen, W. L. Brown and P. M. Glotin, in 1. Ruge and J. Gr au l (eds),

Proc. 2nd int. conf. on ion implantation in semiconductors (Garmisch-Partenkirchen1971), Springer, Berlin, 1971, p. 8.

2-28) H. E. Roosendaal, Thesis, University of Amsterdam, 1974.2-29) J. W. Mayer, L. Eriksson, S. T. Picraux and J. A. Davies, Can. J. Phys, 46, 663,

1968.2-30) L. T. Chadderton and F. H. Eisen, Rad. Effects 7, 129, 1971.2-31) A. Seeger and K. P. Chik, Phys, Stat. sol. 29, 455, 1968.2-32) N. D. Thai, J. appl, Phys. 41, 2859, 1970.2-33) S. M. Hu, in D. Shaw (ed.), Atomic diffusion in semiconductors, Plenum Press, Lon-

don, 1973, p. 217.2-34) R. N. Ghoshtagore, Phys. Stat. sol. 20, K89, 1967.2-35) D. L. KendalI and D. B. De Vries, in R. Haberecht and L. Kern (eds), Proc. first

int. conf. on silicon material science (NewYork 1969), Electrochem. Soc., 1969, p. 358.2-36) H. Strack, J. appl. Phys. 34, 2405, 1963.2-37) P. Baruch, C. Constantin, J. C. Pfister and R. Saintesprit, Disc. Faraday Soc.

31, 76, 1961.2-38) R. L. Minear, D. G. Nelson and J. F. Gibbons, J. appl. Phys. 43,3468,1972.2-39) R. A. Smith, Semiconductors, Cambridge University Press, 1959,p. 74.

- 20-

2-40) J. S. Blakemore, Semiconductor statistics, Pergamon Press, Oxford, 1962, p. 166.2-41) I. D. Konozenko, A. K. Semenyuk and V. 1. Khivrich, in J. W. Corbett and

G. D. Watkins (eds), Radiation effects in semiconductors, Gordon and Breach,London, 1971,p. 249.

2-42) J. C. North and W. M. Gibson, Appl. Phys. Letters 16,126,1970.2-43) G. Fladda, K. Bjö r kqvist, L. Eriksson and D. Sigurd, Appl, Phys. Letters 16,

313, 1970.2-44) T. E. Seidel and A. U. MacRae, Rad. Effects 7,1, 1971.2-45) T. E. Seidel and A. U. MacRae, Trans. Met. Soc. A.I.M.E. 245, 491,1969.2-46) J. L. Whitton, J. appl. Phys. 36,3917,1965.2-47) N. G. E. Johansson and J. W. Mayer, Solid State Electronics 13, 317,1970.2-48) T. E. Seidel, in I.Ruge and J. Graul (eds), Proc. 2nd int. conf. on ion implantation

in semiconductors (Garmisch-Partenkirchen 1971),Springer, Berlin, 1971,p. 47.2-49) J. F. Ziegier, G. W. Co Ie and J. E. E. Baglin, J. appl. Phys. 43,3809, 1972.2-50) H. W. Werner, Developments in applied spectroscopy, Plenum Press, 1969, Vol. 7A

p.239.2-51) M. Croset, Rev. Techn.: Thompson-CSF 3,19,1971.

- 21-

3. THE MEASUREMENT OF RANGE DISTRIBUTIONS OF IMPLANTEDIONS WITH SECONDARY-ION MASS SPECTROMETRY

Abstract

The concentration of boron implanted in silicon as a function of depthis measured by using secondary-ion mass spectrometry. In this methodthe silicon substrate is sputtered continuously by ion bombardment andthe secondary-ion current of boron is measured as a function of time.The requirements that must be fulfilled to ensure that this time-depend-ent current represents the true concentration profile have been for-mulated and were checked by a number of experiments. It is foundthat, with certain precautions, secondary-ion mass speetrometry pro-vides a reliable and fast method for the measurement of boron distri-butions.

3.1. Introduetion

For the measurement of the distribution of implanted ions with Secondary-Ion Mass Speetrometry (SIMS) the sample is continuously bombarded withions. In this way atomic layers are removed successively from the substratesurface by sputtering. Part of the sputtered ions pass a mass analyser, whichselects the ions ofthe species, the concentration ofwhich we want toknow. Thecurrent, produced by these ions at the output of the detection system of themass analyser is, under certain conditions, proportional to the concentrationof the investigated element in the substrate and in that case the time dependenceof this current may reflect a concentration profile.

Some basic requirements for the application of this method have beenpublished by several authors 3-1.2) but we were of the opinion that more workwas needed to prove the reliability of this method in the underlying problem ofboron implanted in silicon. The profile distortion, found for instance by Cairnset al. 3-3), due to recoiling collisions or by unequal erosion of the substrate mayinterfere with the measurements. Also, the depth-dependent crystal disorder ascaused by the implantation may give a depth-dependent sputtering rate. Like-wise contaminants on the surface and chemicalor electrical effects may in-fluence the measurement.

We reported on an investigation of the SIMS method as used for the meas-urement of boron in silicon in refs 3-4 and 3-5. In the present study we will addto these data the results of recent investigations.

3.2. Principle of the method

In the sputtering process energetic primary ions penetrate into the target andtransfer energy in collisions to target atoms. Some of the target atoms willobtain a momentum which is directed to the surface. They may escape fromthe target or they will transfer energy to other atoms or particles, which areejected if they are close enough to the surface. The ejected particles consist of

-22-

atoms, molecules or clusters of the matrix and the impurity material. Some ofthe atoms and particles which escape are electrically charged. If we want toknow the distribution of a certain impurity species M in the substrate, thepositively or negatively charged ions of M are analysed and collected. In somecases it may be useful to detect molecular ions which contain the element M(see sec. 3.5.11).

In the following we derive an expression for the collected secondary-ioncurrent. We introduce therefore a coordinate system (x,y,z) with the x-axisparallel to the surface normal and the y- and z-axes in the plane of the targetsurface at t = O.After sputtering for a period t the target surface is indicatedby the coordinates (x' ,y' ,z'). If only single charged positive ions are detectedthen the collected secondary-ion current icon(t) can be expressed by

icou(t) = J jp(x',y',z') SNM(x',y',z') ct 'I'](x',y',z') TdA (3.1)A

wherejp(x',y',z') is the current density of the primary beam at position (x',y',z')of the substrate surface, S is the sputtering yield of the target atoms defined bythe number of sputtered target atoms per incident primary ion, NM(x',y',z') isthe concentration of M at the substrate surface, ct is the secondary-ion yield,defined in this specific case by the fraction of the sputtered atoms of species Mwhich are positively charged, 'I'](x',y' ,z') is the collection efficiencyof secondaryions originating from a position (x',y',z') of the target surface, T is the trans-mission ofthe analysing and detection systems and A is the area ofthe sputteredregion over which the integration is done. We assume that at the region fromwhich ions are extracted (where 'I'](x',y',z') =1= 0) the current density of theprimary beam is independent of place. Then x' depends only on t. Assumingthat the concentration ofM depends only on depth x and ifwe consider ct and Tto be constant, then the expression (3.1) can be simplified as

icou (t) = k1 N(x') (3.2)

where k1 is a constant. With a constant sputtering (erosion) rate x we havet

x' = J x dt = k2 to

(3.3)

where k2 is a constant. With (3.3) the time dependence in (3.2) is transformedlinearly into a depth scale.

A crucial factor in the method is the secondary-ion yield ct. Its value is about10-1_10-3 depending on the experimental conditions. It was found by Slodzianet al.3-6) that oxygen in front of the target enhances the secondary current ofthe positive ions considerably. Such an influence of the oxygen on the second-ary-ion yield is also found in experiments where sputtering occurs with oxygenions instead of with noble-gas ions 3-7) and in experiments where oxide layers

"./..-,

-23 -

are analysed 3-1). According to Andersen 3-8) this effect is due to an increaseof the work function at the target surface caused by the electronegative proper-ties of the oxygen. The increased potential barrier therefore makes neutraliza-tion of ions just outside the surface by electrons from the substrate less prob-able. This model has been criticized by Blaise and Slodzian 3-9) who supposethat the enhancement is caused by the ionic character of the oxygen bonds. Forexample in the case of BZ03 this bond-breaking model can be described by thefollowing reactions:

O'+ e-:(± 0-.

Due to the electronegative character of oxygen, the creation of 0- according to(3.6) promotes the creation of'B" ions according to (3.5). These ions are expulseddirectly from the target. Such so-called '(chemical-emission" effects 3-6) arealso observed if boron precipitation occurs in boron-doped silicon, as will bediscussed in more detail in chapter 6. Due to the many interrelated processes inthese effects a quantitative prediction of their behaviour is as yet not possible.In order to sustain the interpretation of our boron measurements we decidedtherefore to investigate some of these "chemical-emission" effects experimen-tally. For that reason the secondary-ion currents of boron in some boron-siliconcompounds were compared with those of crystalline boron and of boron inboron-doped silicon, as will be discussed in sec. 3.5.11.

3.3. Requirements

To obtain a reliable measurement of impurity distributions according to theexpressions (3.2) and (3.3) the following requirements must be satisfied:(a) The sputtering process should not disturb the impurity profile. This implies

that- heating due to the energy dissipated by the bombarding ions should be

limited,- the recoil energy transferred to impurity atoms residing in the substrate

must be low.(b) The sample must be sputtered uniformly and at a constant rate. This

implies- a uniform current density of the primary-ion beam over the bombarded

area,- a sputtering rate independent of lattice disorder as caused by ion im-

plantation,- a constant or small influence of the chemisorption of gases from the

(3.4)

(3.5)

(3.6)

-24-

residual-gas atmosphere on the sputtering rate.(c) Only ions from the zone that is bombarded homogeneously, should contrib-

ute to the secondary current. This implies that_ the area from which secondary ions are collected must be smaller than

the bombarded area,- material from the rim of the crater should not be redeposited in the

central area of the crater, avoiding the simulation of a higher coneen-tration than is actually present.

(d) The ion current must be proportional to the concentration. This requiresthat the yield for the production of ions is constant and thus independent oflattice disorder and impurity concentration. Moreover, changes in thechemical composition of the surface of the bombarded area should beprevented.

(e) The sensitivity of the instrument must be high enough to avoid interferencefrom any background effects. This implies- high primary-ion current density on the target,- high secondary-ion yield for the element under consideration,- extraction of the ions from as large as possible a region,- a high detection efficiency of the secondary ions.

3.4. The instrumentThe instrument used is the Cameca IMS 300 3-10.11). A schematic diagram of

this instrument is shown in fig. 3.1. A primary-ion beam strikes the surface ofthe target at an angle of 45°. The emitted secondary ions are analysed in amagnetic prism which provides a momentum filtering of the sputtered ions.The energy spread of the emitted ions necessitates energy filtering of the ions inorder to obtain a better mass resolution. This is performed with an electrostaticmirror. The analysed secondary ions are detected by a Daly-type detectionsystem 3-12.13). In such a system the energetic secondary ions release secondaryelectrons from a convertor electrode. The electrons are accelerated and generate

PrifTr1rybeam

I I I ConvertorI I IAnalYSedsecondary-ion beam

Projectionlens

Extradtionlens

Analysing magnet

EIe;;;:öSiäticmirror

Fig. 3.1. A schematic diagram of the Cameca secondary-ion emission mass analyser.

- 25-

in a scintillator flashes of light which are detected with a photomultiplier. Fromexperiments (see e.g. chapter 4) it can be concluded that boron concentrationsdown to 3. 1016 cm-3 can be measured under optimum conditions with thephotomultiplier in a D.e..mode. A gain in sensitivity of at least one order canbe expected when the current is measured in a pulse-counting mode.The stability of the instrument as determined by that of the primary-beam

current and of the analysing and detection systems has been found to be about1% during a measuring run of 10minutes.The energy ofthe primary ions can be adjusted between 3·5 and 6 keY in the

case that positive secondary ions are detected. For negative secondary ions thisenergy is between 10 and 15 keY. In order to limit a possible distortion of theconcentration profile due to recoiling collisions, the energy of the primary ionsshould be as low as possible. However, the sputtering rate decreases also withthe energy. As a compromise between both effects we used in most of thedescribed experiments an energy of the primary ions of 5·5keY.Noble-gas ions or oxygen ions can be used in principle. For our purpose a

primary beam of oxygen ions was used, because the overall sensitivity is then afactor of 20 higher than in the case of argon ions (sec. 3.2). The ion current canbe chosen between 0·5 and 5 fLA.

3.5. Experimental investigation

In view of the requirements stated in sec. 3.3 we report in the next sections asystematic experimental investigation of the method.

3.5.1·. The uniformity of the sputtering rate

The area Ae (fig. 3.2a) of the substrate, from which secondary ions contrib-uting to the output current are collected, has a diameter of about 0·3mm. Thesputtering rate in this area should be uniform. In earlier experiments 3-1.2) thiswas realized by defocussing the ion beam and cutting out the innermost part.The current density in such a system is rather low, resulting in a low sensitivity.We have therefore used a different method in the Cameca instrument. Theprimary beam is focussed to a small cross-section on the target giving a Gaussiancurrent density distribution across the beam. To achievea homogeneous currentdensity distribution across the sample the focussed beam is scanned in twodirections perpendicular to each other. Scanning is done by triangular voltageswitli periods of 0·3 ms and 6 ms for the horizontal and vertical deflections,respectively.For a high sensitivity of the measurement the average current density of the

primary beam on the target should be high, giving a high secondary-ion currentand a good signal-to-noise ratio at the output. It seemsobvious that with a con-stant scanned area a high current density can be achievedbyusing a highprimary-ion current ip. However, this is not the case, as the diameter 0p of the beam

-26 -

ip

\\\\\

a}

/;/f~ ~r;77. / //7";; /pç;j' I ~/ .

l2uc} ISmm

Fig. 3.2. (a) Schematic drawing of the sputtering process; ip: primary-ion beam, is: secondary-ion current, Ae: area from which secondary ions are collected.(b) Typical crater profile in silicon in the plane given by the surface normal and the primary-ion beam.(c) Typical crater profile in silicon in a plane perpendicular to that of fig. 3.2b.

changes with the current. For ip = 0·01!LAwe determined 0p = 30 !Lm and forip = 2!LA we determined 0p = 300 [.Lm. Therefore on a constant scannedarea the dimensions ofthe flat bottom of the crater will decrease when the pri-mary-ion-beam current increases. Agood compromise between the dimensions ofthe flat area and the sensitivity was reached at a beam current of 1·5!LA.Typical crater profiles are given in figs 3.2b and 3.2c. These profiles weremeas-ured with a stylus measuring apparatus (type Talysurf, manufactured byTaylor-Hobson). It is found that with such conditions the variations in thecrater depths in the analysed area are not more than about 3%. By investigatingthe crater bottom with a scanning electron microscope and with a transmissionelectron microscope using the replica technique we observed that the surfacewas flat after the sputtering process within the depth resolutions of both meth-ods. Only some pits were found in the crater bottom, however with such dimen-sions that they will not disturb the measurements in a' significaI].t~way. Theflatness obtained of the crater bottom is somewhat contradictory~t<l the factthat in the sputtering of crystalline materials facets are often fo~hd at thesurface 3-14), which are due to the crystalline structure. The reason why this isnot found in the case of silicon is that the damage caused during sputteringanneals slowly at room temperature, so that in fact sputtering is done on....anamorphous surface structure. Another effectwhich is reported is the appearanceof grooves on the surface when the substrate is bombarded from a non-perpen-dicular direction. Cairns et a1.3-3), using a lOO-keYKr+ bombardment at anincident angle of 45° on silicon, found a severely corrugated surface. The dif-

".

a} O·6mm

- 27-

ference from our results may be due to the fact that in our experiments the totaldose of the primary ions was 2 to 3 orders lower. Besides, we were using a muchlower energy of the primary ions.

3.5.2. Measurement of the sputtering rate

After each measurement of a concentration profile the sputtering rate x isfound from the depth of the crater and the total measuring time. The depth ofthe crater is measured mechanically with a stylus apparatus. In order to increasethe accuracy of the depth measurements we use a diaphragm with an opening

IS

~I ,, \I ,

j \I \I ,I \

\

•• rll~)·.111:11,1111b . ~

1IIIIIIIIIIIilllll[,II/')~ 11111; ·IIIIII'! 111111 i

Fig. 3.3. Ca) Schematic drawing of the sputtering geometry with a diaphragm on the substrate;ip: primary-ion beam, is: secondary-ion current, Ae: area from which secondary ions arecollected .•Cb)Typical crater profile in silicon in the plane given by the surface normal and the primary-ion beam.Cc) Typical crater profile in silicon in a plane perpendicular to that of fig. 3.3b.

diameter of 0·6 mm on the substrate to obtain steeper crater walls (fig. 3.3a)Figures 3.3b and 3.3c give typical crater profiles. An irregularity is observed atthe right-hand side of the bottom of the crater profile of fig. 3.3b. This irreg-ularity, situated outside the area Ae (0 = 0·3 mm) from which the secondaryions are extracted, is a systematic effect. It is caused by particles that are

- 28-

sputtered from the inner side of the diaphragm opening to the crater bottom.This effect was minimized by making the diaphragm from tantalum, which hasa low sputtering yield, by choosing a small thickness for the diaphragm (10 (lm)and by spark-eroding the opening to avoid burrs. Thanks to these precautionsthe variations in the crater depth in the analysed area Ae are less than about 3%.

3.5.3. Influence of an oxide layer on the surface

After cleaning the surface of the silicon substrate by etching, an oxide layergrows on the surface under normal environmental conditions. This layer maygive a. non-linear relationship between crater depth and sputtering time. Thiswas checked by the measurement of crater depths at different sputtering times.In fig. 3.4 the depths of 4 craters made in t, 1,2 and 5 minutes, respectively, areplotted against sputtering time. In this figure we have also inserted the meas-uring results found in profile measurements, i.e. of crater depths in implantedsilicon.The figure shows tbat naturally grown oxide layers do not disturb the linearity

of the sputtering process. This result can be expected from the thickness of the

5000

TO T5 20- Sputtering time (min)

Fig. 3.4. Crater depths as a function of sputtering time. 0: measurements on non-implantedsilicon, .: measurements on implanted silicon.

- 29-

oxide layer (approx. 30 A 3-15» and from the sputtering yield S of fused quartzobtained under krypton bombardment (6-keVB4Kr: S= 1molecule/ion 3-16».

3.5.4. The infiuence of the residual-gas atmosphere

The chemisorption of gases from the residual-gas atmosphere in the targetchamber-on the substrate surface influences the sputtering rate and ion yield.This effect was investigated by sputtering a silicon slice which is homogeneouslydoped with boron (resistivity is 0·01Q cm) and measuring the B+ and Sj3+secondary-ion currents at varying gas pressure. A change in these currents of upto about 50% was found when the gas pressure varied between 10-6 Torr and2. 10-7 Torr. Below a pressure of 2. 10-7 Torr the currents are constantwithin about 3%. Therefore the distribution measurements were done at apressure of< 2. 10-7 Torr.

During the profile measurement the influence of the gas adsorption on thesputtering rate and ion yield was checked by measuring the secondary Sj3+ and11B+ currents as a function of the primary-ion-beam current. In the case of noinfluence there should be a linear relationship between the primary- and second-ary-ion-beam currents near the operatingvalue of the primary-ion-beam current.Itwas found that in general this was the case at a pressure of < 2. 10-7 Torr.This result is in agreement with a value obtained by theory 3-17)that states thatthe formation of surface layers during sputtering can be disregarded if j/Pb > lOBwherej is the primary current density on the target in (.LA/cm2and Pb the back-ground pressure in Torr. From this it follows that at an average current densityof 50 (.LA/cm2,as used in our experiments, the pressure should be < 5. 10-7Torr in order to have no influence of residual-gas adsorption on the secondary-ion yield.

3.5.5. Effect of damage on the sputtering rate and ion yield

The influence on the sputtering rate and ion yield of distributed damagecaused by ion implantation was measured as follows: a silicon slice, homo-geneously doped with natural boron, containing lOB and llB, and implantedwith 11B+ions was sputtered from the implanted side. The 10B+secondary-ioncurrent was measured as a function of time. When the damage exerts no in-fluence, this 10B+current should be constant. We used a sample with bulk con-centration of natural boron of 1020cm-3 corresponding to a lOBconcentrationof about 2. 1019cm-3. The llB+ ions were implanted at an energy of 70 keYwith a dose of 1016 cm-2. It was found that the 10B+ secondary currentwas constant within the measuring accuracy of 2% and that it amounted to(5'2± 0'1).10-16 A.The influence of the implantation damage on the sputtering rate was checked

independently by comparing crater depths in implanted and non-implantedsilicon. In this experiment a silicon slice was implanted through a gridded mask

- 30-

with B+ ions at an energy of 25 keY and a dose of 1015 cm-2• Craters werecreated by bombarding an area which was lying just at the boundary of im-planted and non-implanted silicon. Most of the damage caused by the ionimplantation is found in a zone which extends to a depth smaller than the depthof the maximum boron concentration (sec. 2.3). In order to measure mainly thecontribution from this damage zone we stopped the sputtering process just afterthe top of the 11B current was reached, The crater depths were compared bymeasuring the crater profile over the boundary. On the boundary no step wasfound within the measuring accuracy, indicating that the difference between thesputtering rates can be estimated to be les~ than 10%.In general, damage may have a distinct influence on the sputtering rate as is

described for instance by MacDonald et al.3-18) for germanium where thedamage was caused by Ar+ ions with a dose of 1017 cm-2 and an energy of1 keY. The difference from our results must be due to the much lower defectconcentration caused by the lower dose and lower mass ofthe bombarding ionsin our case.

From our experiments it can be concluded that the damage corresponding todoses of up to 1016 cm- 2 of B+ ions will not disturb the linearity of the meas-urements,

3.5.6. Contribution of ionsfrom the crater rimA distortion of the profile occurs if there is a contribution to the secondary-

ion current by ions from the crater rim. This may be due to a direct parasiticcontribution or it may be that ions from the crater rim are redistributed overthe crater bottom and from there are sputtered and collected. In order to meas-ure this effect we made a device where the rim contribution is excluded. Thisdevice consisted of a silicon slicewith a low boron concentration « 1013 cm=")in which implanted boron spots were made. The spot diameter was chosen tobe 0·6 mm, i.e. smaller than the dimensions of the crater, but larger than thediameter of the sensitive area Ae (fig. 3.2a). This device was made by coveringone side of the silicon slice with a chemically deposited oxide layer with athickness of about 3 !Lm.In the oxide layer on one half of the slice holes with adiameter of 0·6mm were etched, whereas the oxide layer on the other half wasremoved (see inset fig. 3.5). Then this side of the slice was implanted with boronat an energy of 30 keY and a dose of 1015 cm-2• After the implantation theoxide was removed down to a thin layer which was left for identification of theimplanted spots. Boron profiles were measured on the spots and on the uni-formly implanted half of the slice.

Typical results are given in fig. 3.5. Although the results ofthe measurementsare recorded continuously we have given measuring points in this figure. Thesepoints were arbitrarily chosen from the recorded diagram for rescaling to thelog scale of fig. 3.5.

- 31-

o.o•

o

•o'.o.

10~---70.~I---0~.2~--~O~3~--~O~·4~--~O~·5----~_Depth (um)

Fig. 3.5. Concentration profiles of 11B+ implantation in silicon measured by SIMS on areastype-l and -2 (see inset). Implantation energy 30 keY, dose 1015 ions cm-2 (.: area type-I,0: area type-2).

This figure shows that the contribution of ions from the rim to the secondarycurrent can be considered to be insignificant. This result is contradictory to theconclusion of Croset 3-2), who found a strong profile distortion. We supposethat this disagreement is due to his use of a defocussed ion beam instead of afocussed one which we are using.

3.5.7. Disturbance of an impurity distribution by the sputtering process

A boron distribution in silicon may be influenced during the sputteringprocess by recoiling of the boron atoms. Whether this effect interferes with ourmeasurements under experimental conditions was checked first by comparing aboron distribution in a well annealed sample, as measured with SIMS, with acorresponding charge-carrier distribution. The charge-carrier distribution wasmeasured with Hall-effect measurements combined with layer stripping(chapter 7). The implantation was carried out at an energy of 25 keY and a doseof 1015 ions cm:". The samples were annealed at 950 oe for 40 minutes,making about 95 % of the boron atoms to behave as acceptors (sec. 2.5). Forboth distributions see fig. 3.6.

The scale for the concentration found with the SIMS method was calibratedwith a silicon sample homogeneously doped with natural boron in a concen-tration of 1·5. 1019 cm-3, corresponding to a concentration of 1.22.1019 cm-3of 11B.

From the results of fig. 3.6 it can be concluded that the sputtering processdoes not influence the impurity profile beyond accuracy limits.

Secondly this effect was checked by measuring the same boron distributionwith different experimental conditions ofthe primary-ion beam. Figure 3.7 givesthe boron distributions which are obtained with two values of the primary-ion

-32-

~20r--_'-_--r---'----r---'-_~

ro~L---~~----~----~----~~--~~~o 0·' 0·2 0·3 0·4 0·5- Depth (pm)

Fig. 3.6. Comparison of a distribution found by the SIMS method with a charge-carrierdistribution of an annealed silicon sample implanted with boron. B+-ion dose 1015 cm-2,energy 25 keY, annealing was done at 950°C for 40 minutes (. - - -.: boron distribution bySIMS, 0: measuring points for charge-carrier concentrations).

Fig. 3.7. Boron-concentration profiles with two different energies and currents oftheprimary-ion beam.0: Ep = 5·5 keY, ip = 1·5p.A;.: Ep = 3·8 keY, t» = 2·5 [.lA.

1O'7o=-----=!-.:-----::'::-----:~----;;'-;-----:O;;-'.S'0·' 0-2 0·3 0·4-Depih(pm)

- 33-

energy and beam current. The coincidence of both distributions demonstratesthat profile distortion by the primary ions due to energy-dependent boronrecoiling is of no importance in our measurements.The results found by Cairns et al.3-3) show that some influence may be

expected. There it was found that sputtering with lOO-keYKr+ ions gives severedistortion of an antimony distribution in silicon. This was partly explained bythe extra .penetration of the Sb atoms due to recoiling and partly by the cor-rugated erosion of the silicon surface. The disagreement with our results can beexplained by the fact that we are using a relatively low sputtering energy of5·5 keY. Our results are compatible with the results given by Schulz et al.3-19).

3.5.8. The influence of the band structure on the ion yield

In profile measurements the impurity concentration near the surface changesduring the sputtering process. This may result in a changing electronic-energyband structure which may give a changing ion yield. The influence of this effectwas checked by measuring the secondary boron current when sputtering a p-njunction which contains a homogeneous boron concentration. The p-n junctionwas made from a homogeneously boron-doped silicon slice which was im-planted on one side with phosphorus. The boron concentration amounted to1019cm-3 and the Pv-ion implantation was done at 50 keY with a dose of1015 ions cm-2• From thermal probe measurements it was found that the layerwhich is implanted with p+ ions became n-type after annealing at a temperatureof 400°C or higher. When a sample, which was annealed at 400 °C, wassputtered from the implanted side we found that the boron secondary-ion cur-rent was constant (within a measuring accuracy of 5%) with a value thattypically amounted to (1·05 ± 0·05) . 10-16 A. Therefore we can concludethat the differences in the electronic-energy levels near the surface, which aredue to differences in the impurity concentration, do not influence the profilemeasurements beyond accuracy limits.On slices which were annealed at 700 oe distinct deviations of about 20 %

from the average secondary-UB" -ion current were found. These deviationscan be attributed to a redistribution of the boron which is caused by thermaldiffusion of the boron. This effect is discussed in more detail in chapter 8.The fact that in the above results no influence of the electronic-energy band

structure on the ion yield was found is assumed to be due to the creation of anamorphous layer by the sputtering process. The energy levels in such a layerwill be constant due to the dominating effect of the defects.

3.5.9. The linearity of the system

. The output current of the system should be proportional to the boron con-centration. Possible effects which may disturb this behaviour are non-linearitiesin the detection system and in the ion yield. The non-linearities in the ion yield

-34-

-

-

Fig. 3.8. Maximum boron concentration (cm-3) versus implantation dose (cm-2) ofboron fordifferent doses implanted at 30 keY.

may come from the influence of the electronic band structure, as discussed inthe preceding section, and from chemical effects. The linearity of the systemwasinvestigated by implanting known doses of boron in silicon that had beenhomogeneously doped with a known background concentration of boron andby comparing the ratios of the maximum secondary-ion current to that of thesecondary-ion current of the background concentration. Boron was implantedat an energy of 30 keY at doses in the range of 3 . 1013 up to 3 . 1015 ions cm-2•From the results shown in fig. 3.8 it is found that up to a concentration of atleast 3 . 1020 ions cm? the method can be considered to be linear.

3.5.10. The measurement of annealed-boron distributions

It is known from channelling experiments that the location of boron ions inthe silicon lattice depends on the annealing temperature 3-20,21). For instancefor a dose of 1015 ions cm-2 the substitutional boron fraction decreases fromabout 30% in the "as-implanted" case to about 10% after annealing at 600oe.At higher annealing temperatures this fraction increases again. At 1000oeabout all the boron is substitutional. Precipitation of the boron mayalso occuras we observed in samples which were implanted with a boron dose of 1016 ionscm-2 and are annealed at 800-1000 oe (sec. 6.4.2). It is therefore of interest toinvestigate whether the secondary-ion yield depends on the position or phaseof the boron in the silicon lattice. This was done by determining the integratedsecondary boron current, which reflects an apparent total boron dose. If theion yield depends not on the location or phase of the boron an equal apparent

-35 -

total dose will be found after annealing at the different temperatures.For this investigation llB+ ions were implanted at an energy of 70 keY and

a dose of 1016 ions cm-2 in silicon with a homogeneous natural backgroundconcentration of 1·6 . 1019 ions cm-3• With the background dope a direct cali-bration of each SIMS measurement is possible giving a higher accuracy of theapparent dose measurements. The boron distributions are measured of sampleswhich are "as-implanted" and are annealed at 600 oe, 900 oe and 1000 oe,respectively. After subtracting the background dose, we obtained from themeasurements the apparent total doses as given in table 3-1. The relative

TABLE 3-1

Total apparent boron dose after annealing at different temperatures

annealing temperatureCOC)

total apparentboron dose(ions cm-2)

accuracy in these results is within 2%. The average systematic deviation of theapparent doses from the stated implanted dose (1016 ions cm-2) is mainly due.to a systematic inaccuracy in the measurement of the implanted dose. Fromthe results in table 3-1 we observe that the apparent dose after annealing at1000oe is somewhat higher than the doses found after annealing at lowertemperatures. At implantation doses ~ 1015 ions cm? no effects of this kindwere observed. From these results we conclude that the ion yield of substi-tutional boron is similar to that of interstitial boron and to that of small boronprecipitates as occurring at lower implantation doses (~ 1015 ions cm-2) orafter annealing at temperatures up to 900 oe. Excessive boron precipitates orclusters, as found after annealing at 1000oe of a dose of 1016 ions cnr? appearto have a somewhat higher ion yield. In sec. 6.4.2 it is found that this en-hancement is on the average 30%.

3.5.11. "Chemical-emission" effects

The precipitates mentioned in the foregoing section are assumed to consist ofboron-silicon compounds such as SiB4 or SiB6• The enhanced ion yield of theboron precipitates may therefore be due to "chemical-emission" effects whichwe mentioned in sec. 3.2. In order to investigate this in more detail we com-pared the secondary-ion current of boron of the compounds SiB4 and SiB6

no annealing6009001000

1.40.10161.40.10161·41. 10161.58.1016

- 36-

with those of crystalline boron and of boron in boron-doped silicon. This com-parison was done for positive and negative ions by measuring the B+-ion andBO--ion currents, respectively. The conditions for the B+-ion current were asgiven in sec. 3.5.1. The BO--ion measurements were done with a primary beamwith a current of 3 !LAand an ion energy of 14·5keY. The results with corre-sponding 'boron concentrations and sputtering rates are given in tables 3-IIand 3-III. To facilitate the comparison the total efficiency 'YJtot defined as'YJtot = ct 'YJ T (sec. 3.2) is also tabulated. For the cases given in table 3-II 'YJ Tcan be considered to be equal. Therefore we may conclude that if positive ionsare detected, the ion yield of boron in SiB4 and SiB6 is about a factor 30 to50 higher than that of boron in boron-doped silicon. In a similar way we mayconclude from the results given in table 3-II1 that if negative ions are detectedthe difference between the ion yields for the different samples is within accuracy

TABLE 3-II

Boron concentration, sputtering rate, secondary-ion current of B+ ions, andtotal efficiency for boron-doped silicon, SiB4, SiB6 and crystalline boron

substrate boron sputtering secondary-ion totalconcentration rate current efficiency

(cm-3) (A/min) of B+ ions 'YJtot

(A)

Si(B) 1.3.1019 450 5.8.10-16 5·2. 10-6SiB4

I

8.2. 1022 115 4.5.10-11 2.6.10-4SiB6 9.5. 1022 120 3.8.10-11 1·7. 10-4B 1.3.1023 140 6.6.10-11 1·9. 10-4

TABLE 3-II1

Boron concentration, sputtering rate, secondary-ion current of BO- ions andtotal efficiency for boron-doped silicon, SiB4, SiB6 and crystalline boron

substrate boron sputtering secondary-ion totalconcentration rate current efficiency

, (cm-3) (A/min) of'Bf)" ions 'YJtot

(A)

Si(B) 1.3.1019 388 1.3.10-15 1.4.10-4SiB4 8.2. 1022 113 2.5. 10-12 0.7.10-4SiB6 9.5. 1022 106 1.7.10-12 0.7.10-4B 1.3.1023 84 4. 10-12 0.7.10-4

- 37-

limits. The different behaviour between the two cases is likely due to the factthat, in the case of positive ions, charge-exchange effects between the ions andthe substrate are more effective. From the above measurements one may decideto the measurement of negative ions. However, in the measurement of BO- ionsa background secondary-ion current is found which comes from other impuritieswith mass 27, such as aluminium or hydrocarbons, which limits the sensitivityof the boron measurements.

3.5.12. Transients in the secondary-ion current

At the start of a measurement there is a peculiarly shaped transient in thesecondary-ion current. We have studied this transient by investigating thesecondary-ion current of boron that is homogeneously distributed in silicon ata concentration of I·3 . 1019 ions cm- 3. Figure 3.9a shows the start of a boronmeasurement of such a sample. It is observed that after a short current peakthe current drops and then increases to a steady-state value. If the sputtering isinterrupted for 3 minutes and the process is started again the secondary-ioncurrent behaves as shown in fig. 3.9b. If during the interruption the sample isexposed to air then a restarting of the process results in a secondary-ion currentas shown in fig. 3.9c. In this case, too, a current peak is observed. The currentpeak occurs only if the silicon is exposed to air. Therefore we conclude thatthis current peak is due to a change in the surface conditions caused by thisexposure. The main influence will likely come from the oxygen, for, as men-tioned in sec. 3.2, oxygen enhances the ion yield considerably. Besides it is

I Io 1

_ Sputtering time (mir,J

Fig. 3.9. Plots of secondary current of boron versus time of homogeneously boron-dopedsilicon.Ca) Start of the measurement. Cb)Restart of the measurement after an interruption with thesample kept at vacuum conditions. Cc) Restart of the measurement after an interruption withthe sample kept in air.

a)

Î

b)

Ef=

-E

c)

i=

- 38-

known that on a silicon surface in normal environmental conditions an oxidelayer with a thickness of about 20 A is created within a few minutes 3-15).

Therefore we assume that the observed boron current peak is due to an en-hancement in the secondary-ion yield by the oxygen in the surface layer.The drop of the secondary-ion' current which occurs after the current peak

shown in fig. 3.9a mayalso be explained by the influence of the oxygen. Duringthe sputtering process oxygen is implanted in the substrate. Therefore, theoxygen concentration in the substrate depends on the depth and the oxygenconcentration at the surface on the sputtering time. Due to the simultaneouseffects of sputtering and implantation the oxygen concentration at the surfacereaches an equilibrium value after some time. In the results shown in figs3.9b and 3.9c such an equilibrium value has already been obtained.One may try to analyse these results quantitatively 3-22). Therefore we

assume for the implanted oxygen ions a Gaussian range distribution, with anaverage projected range (x ) and a standard deviation a. An x-axis is takennormal to the surface with at x = 0 the position of the surface at the start ofthe sputtering process (t = 0) and at x = x' the position of the surface aftera sputtering period t. The oxygen concentration versus depth, which is im-planted at time t during a period dt is then expressed by

0·4 ((X-X' - (X»)2) IdN(x)= -exp - -dt

a 2 a2 q A(3.7)

where I is the primary beam current, q is the electronic charge, and A is thearea of the sputtered region. If we suppose a constant sputtering rate x thenx' = x t and the oxygen distribution at time t will be

0·4 I ft ((X - x t - (X»)2)N(x, t) = -- exp - dt.

a q A 2 a2o(3.8)

The integral can be expressed in error functions. The oxygen concentration atthe surface Nsurc is found by substituting x = x t giving

I 1 ( x t- (x) (X»)Nsurc(t) = -- - erf + erf-- .2 A q x a V2 a V2

According to a manufacturer's report the primary-ion beam contains about99% O2+ ions and 1% 0+ ions. Both types of ions have an energy of 5·5keY.The primary-ion beam strikes the surface at an angle of 45° with the x-axis.The O2+ ions will split up at the moment of impact into two atoms with eachatom having a primary energy of about 2·8 keV. Because they are in a majority,these ions will determine the surface-loading with oxygen. Their average rangeand range straggling, estimated by extrapolating calculated values 3-23), are67 A and 32 A, respectively. In the direction of the x-axis these quantities are

(3.9)

-39 -

47 A and 22 A, respectively. With these values and with x = 500 A/min in(3.9) we derive that, after a sputtering time of t = 0·2 min, the oxygen concen-tration at the surface has approached its equilibrium value within 2%. Fromfig. 3.9a we observe that the secondary-ion current obtains its steady-statevalue at about t = 0·3 min. The observed discrepancy may be due to a deviationin the ion composition of the primary beam or from a lower sputtering rate ofcrystalline silicon in comparison to that of bombarded silicon. No measuringresults are available to discuss the influence of these effects in more detail.

3.5.13. Delay effects in the detection system

In detection systems incorporating a photomultiplier tube, a high second-ary-ion current causes, after switching off, a temporary increase of the back-ground current due to after-effects in the scintillator and the photomultipliertube. This may be of importance when tails of distributions with a steepgradient in the concentration are to be measured. Typically it was foundthat, after a secondary-ion current of 4. 10-15 A, corresponding to a concen-tration of 1·5. 1020 uB ions cm-3, was switched off, an increase inthe background current of 3 . 10-18 A, corresponding to a concentration of1.1.1017 uB ions cm=", was found. The decay time ofthis signal was about0·7 min. In the measurement of real boron distributions transients in thesecondary-ion current have usually a much smaller gradient. Therefore in thesecases the above-mentioned after-effects will not disturb the distribution meas-urements.

3.5.14. Calibration of the boron measurements

Calibration of the sensitivity of the Secondary-Ion Mass Spectro-meter was carried out with a silicon slice homogeneously doped with boronto a concentration of 1·6. 1019 cm? as determined from Hall-effect meas-urements (chapter 7). This concentration corresponds to a 11B concentrationof 1.3.1019 ions cm-3• The Talysurf apparatus used for the crater-depth'measurements was accurate within 2%. Each profile measurement was com-pleted with a measurement of the Sp+ -ion current in order to check thereproducibility of the measurement and the vacuum conditions.

3.6. Conclusions

The reliability of the measurement of boron distributions in silicon withSIMS has been investigated experimentally. It was found that within accuracylimits of about 5%:- the crystal damage caused by boron implantations up to a dose of 1016 cm-2

implanted at room temperature does not influence the secondary-ion cur-rent, and thus has no influence on either the sputtering rate or the ionyield;

-40-

there is no influence on the secondary-ion yield of the electronic-energylevels in the substrate;

- there is no contribution of ions from the crater edge to the secondary-ioncurrent, either directly or by redistribution to the crater bottom, regardlessof the use of a diaphragm;the energy of the primary ions was low enough not to disturb the concen-tration profile by recoiling effects;

- the sputtering rate is constant when the residual-gas pressure is < 2 . 10-7

Torr.For the interpretation of measurements of boron distributions are the fol-

lowing aspects of further interest:- the first 200 A of an in-depth profile shows a transient in the secondary-ion

current;- the secondary-ion current of 11B+ ions in the compounds SiB4 and SiB6 is

a factor of about 40higher than that of boron that is located at latticepositions in boron-doped silicon (boron concentration about 1019 cm=").

REFERENCES3-1) H. W. Werner, Developments in applied spectroscopy, Plenum Press, 1969, Vol. 7A,

p.239.3-2) M. Croset, Revue technique Thompson-CSF 3, 19, 1971.3-3) J. A. Cairns, D. F. Holloway and R. S. Nelson, Rad. Effects 7,167,1971.3-4) W. K. Hofker, H. W. Werner, D. P. Oosthoek and H. A. M. de Grefte, Rad.

Effects 17, 83, 1973.3-5) W. K. Hofker, H. W. Werner, D. P. Oosthoek and H. A. M. de Grefte, in

B. L. Crowder (ed.), Proc. int. conf. ion implantation in semiconductors and othermaterials (Yorktown Heights 1972), Plenum Press, New York, 1973, p. 133.

_3-6) G. Slodzian and J. Hennequin, C. R. Acad. Sci. Paris 263,1246, 1966.3-7) A. Benninghoven, Z. Naturforschung 22a, 841, 1967.3-8) C. A. Andersen, Int. J. Mass Spectr. Ion Phys. 2, 61, 1969; 3, 413, 1970.3-9) G. Blaise and G. Slodzian, Surface Sci. 40, 708, 1973.3-10) J. M. Rouberol, J. Guernet, P. Deschamps, J. P. Dagnot and J. M. Guyon de

la Berge, in G. Möllenstedt and K. H. Gaukler (eds), Proc. 5th. int. congress onX-ray optics and microanalysis (Tübingen 1968), Springer, 1969, p. 311.

3-11) R. Castaing and G. Slodzian, J. de Microscopie 1,395, 1962.3-12) N. R. Da ly, Rev. sci. Instr. 31, 264, 1960.3-13) H. W. Werner, H. A. M. de Grefte and J. van der Berg, Int. J. Mass. Spectr. Ion

Phys. 8, 459, 1972.3-14) J. J. Ph. Elich, H. E. Roosendaal, H. H. Kersten, D. Onderdelinden, J. Kiste-

maker and J. D. EIen, Rad. Effects 8, 1, 1971.3-15) R. J. Archer, J. chem. Soc. 104, 619, 1957.3-16) A. J. Akishin, S. S. Vasil'ev and L. N. Isaev, Bull. Acad. Sciences USSR Phys,

Series 26, 11, 1379.3-17) G. Carter and J. S. Colligon, Ion bombardment of solids, Heinemann Educational

Books, London, p. 311.3-18) R. J. MacDonald and D. Haneman, J. appl. Phys, 37, 4, 1609, 1966.3-19) F. Schulz, K.Wittmaack and J. Maul, Rad. Effects 18, 211,1973.3-20) G. Fladda, K. Bjö r kqv is t, L. Eriksson and D. Sigurd, Appl. Phys, Letters 16,

313, 1970.3-21) J. C. North and W. M. Gibson, Appl. Phys. Letters 16,126,1970.3-22) J. C. C. Tsai and J. M. Morabito, Surface Sci. 44, 247,1974.3-23) W. S. Johnson and J. F. Gibbons, Projected range statistics in semiconductors,

Stanford University Bookstore, 1969.

- 41-

4. CONCENTRATION PROFILES OF BORON IMPLANTATIONSIN AMORPHOUS AND POLYCRYSTALLINE SILICON

AbstractBoron is implanted in amorphous silicon at energies in the range30-200 keY and in polycrystalline silicon at energies in the range30-800 keY. The boron distributions are measured with secondary-ionmass spectrometry. It was found that with the first four moments ananalytical description of distributions can be given by distributions ofthe Pearson system. The moments are determined by curve-fitting ofPearson distributions to experimental distributions. In this way asysternatic extrapolation of the low-energy distributions outside thesurface is automatically obtained. The moments are compared with themoments calculated by Winterbon and others.

4.1. Introduction

In an earlier investigation 4-1) we demonstrated that the concentrationprofiles of boron in amorphous silicon differ considerably from those incrystalline silicon. The distribution profiles in amorphous silicon are ratherskew, with a steep slope on the penetrating side, whereas those in crystallinesilicon have a penetrating tail as will be discussed in the next chapter in moredetail.In this chapter the first topic of interest will be a study of the characteristics

of boron distributions in amorphous and polycrystalline silicon as a functionof implantation energy. Therefore we measured boron distributions which wereimplanted at energies in the range from 30 to 800 keY. It was also of interestto investigate whether the distributions obtained are predicted by theory. Wedetermined therefore the first four moments of the measured distributions, viz.average range, standard deviation, skewness and kurtosis, and compared themwith moments calculated by Winterbon 4-2). Further we derived an analyticaldescription of experimental boron distributions. With such a description, borondistributions for one energy or for more arbitrary energies in succession, as areused often in practice, can be approximated analytically, thus facilitating thestudy and application of such distributions.Some results relevant to this work are available. Several authors'4-3,4) have

determined the most probable projected range and standard deviation of ex-perimental distributions in crystalline silicon and compared them with theoreti-cal ones. However, theoretical calculations consider distributions in non-crystal-line solids. Moreover, the calculated ranges concern the average range insteadof the most probable range. Besides, the energy range of implantations in theseinvestigations is rather limited. So far no results on moments higher than thesecond one are available for distributions of boron or any other ion species.With regard to the analytical description' of distributions in amorphous

silicon, Gibbons and Mylroie proposed describing them by joined half Gaussian

-42-

distributions 4-5). For the part of the distribution on the surface side, such adescription leads to a serious misfit as can be verified by considering the concaveshape on log scale of the distributions we found for implantation energies above200 keY (fig. 4.1h).The amorphous silicon layers needed in our experiments were obtained by

bombarding silicon substrates with Ne+ ions. In this way amorphous siliconlayers ar~ produced with a thickness of about 0·7 (.Lm.These layers are thickenough to stop B+ ions which are implanted with an energy of up to200 keY 4-6). To enable similar distributions to be studied at higher energies,boron was implanted in polycrystalline silicon layers (grain size < 300 A).These layers, with a thickness of about 2 (.Lm,are made by a chemical deposi-tion process. They are grown in such a way that the properties of amorphoussilicon for the boron stopping process are closely simulated. This was verifiedby comparing boron distributions in both types of layer implanted at the sameenergy.

To analyse the boron distributions and describe them analytically the methodof moments was chosen. The use of moments facilitates comparison of theexperimental results with theoretical results derived from LSS theory 4-7).These moments are calculated numerically. Therefore their physical relationwith the implantation energy or parameters of the stopping process is notobvious. However, a more direct way of describing an implanted distributionis not yet available.

LSS theory refers to an infinite medium. The boron in the negative part ofa theoretical distribution corresponds in practice to boron which is reflectedat the surface. This effect is mainly of importance at implantation energieslower than 200 keY. To obtain comparable experimental and theoreticalmoments for,these energies as well, the moments should be derived from borondistributions which are extrapolated outside the surface. Instead of calculatingthe moments directly from the distributions we introduced the determinationof moments by a curve-fitting procedure. With a computer programme atheoretical distribution using moments as parameters is fitted by trial and errorto an experimental distribution. The moments giving the best fit are the momentsof the experimental distribution, as was verified by direct computation of themoments from the experimental distributions. Series expansions such as theEdgeworth or Gram Charlier series are often used to construct distributionsfrom their moments 4-8). Unfortunately, these series expansions requiremoments of up to a high order to fit an experimental distribution. Vfe there-fore looked around for another method and found the class of Pearson dis-tributions to be more suitable for our purpose. Accurate fitting to an experi-mental distribution is found to be possible with only four moments, as waschecked at the high-energy distributions (energy 200 keY or higher). From thisresult we derive an argument for using these distributions additionally for

"'_

-43 -

analysing the low-energy distributions, where the tail outside the surface is infact unknown. We believe that in this way we have reduced the arbitrarycharacter of the extrapolation procedure referred to above.The moments obtained were compared with theoretical moments calculated

by Winterbon, who developed a formalism for moment calculation based onLSS theory, using an analytical expression for the Thomas-Fermi cross-sectionand incorporating electronic stopping 4-9). Comparison was also made withresults obtained from Mylroie and Gibbons 4-10), who extended a computa-tional procedure of Brice to calculate the third moment.For comparison of the experimental and theoretical results the densities of

amorphous and polycrystalline silicon are needed. One method which isproposed to determine these densities is by measuring the layer thickness by aconventional technique and the areal density in the layer (in atoms/cm") by anuclear back-scattering technique 4-11). We, however, used another methodand obtained these densities relative to that of monocrystalline silicon by com-paring the mode depths (depth of maximum concentration or most probableprojected range) of boron distributions implanted at equal energies in amor-phous, polycrystalline and monocrystalline silicon.

4.2. Experimental procedure and results

4.2.1. Experimental details

In order to create a homogeneous amorphous layer in silicon a numberof 2°Ne+-ion bombardments with different energies and doses were appliedsuccessively. The required energies and doses were obtained using experi-mental results reported by Feldman and Rodgers 4-12), who at an energy of250 keY found a damage distribution which is saturated at a dose of1·4. 1015 2°Ne+ ions cm-2 and has a standard deviation of half the modedepth of the damage distribution. Use was also made of the consideration thatthe neon dose which gives saturation of the damage is roughly independent ofthe bombarding energy. Using the theoretical relation 4-8) (X)R/(X)D = 1,2,where (X)R and (X)D are the mode depths ofthe ion and damage distributions,respectively, the following energies and doses for the successive bombardmentswere calculated to give a reasonably uniform (approx. 10%) amorphousnessover a depth ofO·7 {Lm:380 keY, 2·5. 1015ions cm-2; 140 keY, 1015ions cm-2;70 keY, 1015ions cm-2; 40 keY, 1015 ions cm-2. In fact, no crystalline prop-erties could be detected in the surface layer when the bombarded zone wasinvestigated with proton back-scattering.The polycrystalline silicon layers were obtained by chemical vapour deposi-

tion from an SiH4-H2 mixture at a temperature of 680°C and a growth rateof 300 A/min on a p-type substrate which had a resistivity of 0·01ncm. Theaverage grain size was estimated to be 300 A. The low substrate resistivity was

/

.,

-44-

necessary to prevent disturbance of the SIMS measurements by electricalcharging of the substrate surface by the primary-ion beam.

Boron implantations in the amorphous layers were applied at a dose of1015 ions cm-2 and an energy of 30, 50, 70, 100, 150 and 200 keY, respectively.The polycrystalline layers were implanted with a dose of 1015 ions cm-2 andan energy of 30, 50, 70, 100, 200, 300, 400, 600 and 800 keY, respectively.During the bombardment the targets were water-cooled to limit annealing ofthe amorphous layers. In the same implantation runs monocrystalline siliconslices, cut perpendicularly to a (763) direction, were implanted in a direc-tion normal to the surface. These implantations, performed in a dense crystaldirection, were used to determine the density of the amorphous and poly-crystalline layers relative to that of crystalline silicon. The accelerating voltagèof the implantation equipment was calibrated with an accuracy of 0·2%.The profile measurements were done with SIMS as described in chapter 3.

It was found that the standard deviation in the mode depth was 2%. Thesystematic error in the mode depth is embodied mainly in the measurementof the depth of the crater which is formed during the sputtering process. Thedepth measurements were calibrated with an accuracy of 1% by Tolanskyinterferometry. We measured the secondary-ion current ofboron in amorphousand polycrystalline layers which were homogeneously doped with boron. Thecurrent was found to be constant within accuracy limits. Therefore the sput-tering rate in these layers is constant, reflecting a homogeneous structure ofthese layers.

4.2.2. Experimental results

Figures 4.1a and 4.1b givethe measured boron distributions in the amorphousand the polycrystalline silicon layers, respectively. The small tails, which areobserved on the distributions (e.g. fig. 4.Jb: 200-keV and 3OO-keVdistributions)are due to a background current of the SIMS apparatus. Table 4-1 shows themode depths of the distributions. It also lists the mode depths of the boronimplantations in crystalline silicon.

4.3. Analysis of the experimental results

4.3.1. Determination of the moments of the experimental distributions

The moments of the measured distributions were, as mentioned in the intro-duction, determined by a curve-fitting procedure using Pearson distributions.The Pearson distributions are based on the differential equation 4-13.14)

df(x) (x-a)f(x)(4.1)

dx s, + b, X + b2 x2

wheref(x) is the frequency function. The distributions based on this equation

ft (average range <x» f xf(x) dx, (4.2)

-45 -

Fig. 4.la. Experimental boron distributions in amorphous silicon obtained by implantingdoses of 1015 11B+ ions cm- 2 at energies of 30, 50, 70, 100 and 200 keV, respectively.

have a single mode (at x = a) and a smooth contact with the x-axis at theextremities (df(x)fdx = 0 at fex) = 0). They are therefore very suitable fordescribing implanted-ion distributions. The four constants can be expressedin the first four moments of I(x). It will be shown later that an adequatedescription of an experimental distribution can be given with four moments.The four moments are defined as

-00

a (standard deviation)(

00 )1/2_~ (x - <x»2/(x) dx , (4.3)

f (x- <x»3/(x) dxY1 (skewness, dimensionless): -00

(4.4)

f (x-<x»4/(x)dx{32 (kurtosis, dimensionless) -00

(4.5)

-46 -

-.s 102°1-t l..lt.....·~............J:: r lie ~ ,/ ~ ,," ~ .....-\ ..........:ij , ,. \ t \ ' ,JO; -~ ~g t J, ~ '/ X JI~ \ / \8 :/ \)1 /\ ~\ ~\ / \

t10'9 I; I l \ • I ,,~I , ,

I- : / 1/ ~ / ~" \ \ / \f ; {I' / ,~ , \" '~I I' X " ~ ~ l \I I / ~ 'I ,'~ , '" ,~l • '\_.\ ,\ " \ ".' ,I .( , .( , '"" , ~' , I , ~. i

10'8 ~ ./ ,,~j. ~ I" I '

,- .. ""'1 ' I / I '..0''' l ~,,~\ \ ..... I \/ ,," " ~ ",," \ ~ ,.. ,," ~, \ ..' \.......... \J, ~., ~\ \ ,.' • ..' ,., ~, ~ I

10'7 ... :.... ~ ~ /." ~.... '" \ ~o ~ H N N ffl ~ M ~ ffl

_ Depth (pm)

-

-

2·0

Fig. 4.lh. Experimental boron distributions in polycrystalline silicon obtained by implantingdoses of 1015 llB+ ions cm-2 at energies of70, 100,200,300,400 and 800 keY, respectively.

TABLE 4-1

Mode depths of distributions of boron implanted at different energies inamorphous, polycrystalline and monocrystalline silicon

energymode depths CA)

CkeV) amorphous Si polycrystalline crystalline SiSi

30 1170 1170 112050 1870 1900 188070 2610 2510 2440100 3510 3390 3360150 4870200 5830 5965 5720300 7870 7680400 9600 9700600 12950 12300800 15725 15030

-47 -eo

with the condition: J I(x) dx = 1.-<Xl

In these definitions is ft the moment about x = 0 and the other momentsare about x = (x), where the x-axis is parallel to the direction of the ionbeam and x = 0 is at the surface. The symbols Yl and fJ2 correspond to thoseused in ref. 4-13. Yl is a measure of the skewness of the distribution. If Yl isnegative, the slope on the penetrating side of the distribution is the steepest.fJ2 describes whether the distributions are sharply peaked or flat-topped.Peaked distributions with heavy tails have relatively high values of fJ2' Withthese definitions the following expressions are obtained for a, bo, bI and b2in the four moments:

a = -Yl (] (fJ2 + 3)JA, (4.6)

bo = -a2 (4fJ2 - 3 YI2)JA, (4.7)

bI = a, (4.8)

b2 = -(2 fJ2 - 3 Y12 - 6)JA, (4.9)

where A = 10 fJ2 - 12 Yl2 - 18. (4.10)

The solutions of (4.1) are 4-15)

(4.11)

(4.12)

-48 -

(4.13)

A computer programme was compiled giving these solutions for a certain setof moments fJ" a, Y1 and (J2. Further this programme was extended to generatea graphical display off(x) for such a set of moments on a storage display unit.The set of moments which gives the closest fit of f(x) to the experimentaldistribution comprises the first four moments of this distribution. With someexperience it was found that a close fit could be obtained after 5 to 10 trials.The tolerances in the moment determination are found to be different for thedifferent distributions. For the distributions in the high-energy range thesetolerances are: ± 2% for fJ" ± 5% for a, ± 10% for Y1 and ± 20% for {J2·For distributions in the low-energy range these tolerances are: ± 1% for fJ"± 2% for a, ± 3% for Y1 and ± 5% for {J2. Some examples of this fittingprocedure are given in fig. 4.2. Table 4-II lists the moments of the experimentaldistributions that were obtained in this way.

4.3.2. Comparison with theoretical results

To compare the experimental moments with moments derived from theorythe densities of the amorphous and polycrystalline silicon layers relative tothat of crystalline silicon have to be known. They are obtained by comparingthe mode depths as given in table 4-1. The mode depths in amorphous andpolycrystalline silicon are equal within accuracy limits (± 2%). The ratio ofthese mode depths to those in crystalline silicon is found to be 1·04 on theaverage and consequently the density of the amorphous and polycrystallinelayers areproportionally smaller. This value corresponds reasonably to resultsgiven in refs 4-16 and 4-17 obtained by other methods.The values of the average ranges and standard deviations as given in table 4-Il,

transformed to the density of crystalline silicon, are shown versus energy infigs 4.3 and 4.4. Figures 4.5 and 4.6 give the values from table 4-11 for skewnessand kurtosis versus energy. Figure 4.3 also indicates the theoretical values ofthe average ranges (x) as calculated by Winterbon for different values of theelectronie-stopping coefficient K, i.e. for K = 1·4 KL' 1·5 KL and 1·6 KL>respectively, with KL the so-called Lindhard value 4-18) of the electronic-stopping coefficient (sec. 2.1, eq. (2.8)). It will be seen from fig. 4.3 that thereis considerable agreement between the experimental and theoretical values forK = 1·5 KL. The corresponding calculated values for standard deviation,skewness and kurtosis versus energy are therefore indicated for this value of Kin figs 4.4, 4.5 and 4.6.

-49 -

1021

:::. :::. :::.~ ~ Ol

"'"C C C

'" Q ~

/·4 l'S 2·0- Depth (pm)

Fig. 4.2. Experimental boron distributions (0) and matched Pearson distributions (-).

TABLE 4-II

The average range (x), standard deviation a, skewness "1 and kurtosis (32 ofdistributions of boron implanted at different energies in amorphous and poly-crystalline silicon

target material energy (x) a Yl (32(keV) (A) (A)

amorphous Si 30 1015 425 -0·55 3·6amorphous Si 50 1645 570 -1·0 5·5amorphous Si 70 2330 680 -1,0 5·3amorphous Si 100 3150 790 -1,3 7·0amorphous Si 150 4420 960 -2·05 15amorphous Si 200 5340 1060 -2,4 22

polycrystalline Si 70 2260 700 -1·0 5·5po1ycrystalline Si 100 3100 845 -1,3 7·5polycrystalline Si 200 5560 1080 -2·15 17·5polycrystalline Si 300 7355 1160 -2,25 19polycrystalline Si 400 9020 1270 -2,75 32polycrystalline Si 600 12375 1295 -2·6 28polycrystalline Si 800 15150 1465 -3,3 60

t03f-

- 50-

'I

Experimental:Q: amorphous siliconx: polycrysfalline silicon

1

-

-

Fig. 4.3. Experimental average ranges ofboron distributions in amorphous and polycrystallinesilicon and ranges calculated by Winterbon using different electronie-stopping coefficients Kversus energy.

The theoretical results of Mylroie and Gibbons 4-10) for the average range,standard deviation and skewness, calculated using formalisms from LSS theorywith K = 1·59 KL' correspond closely to the values of Winterbon and are there-fore not indicated in the figures.From the results given in fig. 4.3 it will be observed that there are small

systematic differences between the experimental and theoretical ranges. Thesedifferences are thought to be due to special effects in the electronie-stoppingprocess owing to the fact that at energies higher than about 20 keV electronicstopping predominates over nuclear stopping. In order to find some energy-dependent relation for these deviations we analysed the experimental andcalculated ranges on a differential basis very similar to the method used inref. 4-19. Differences in average ranges (x) for energies El and E2 differingby not more than about 15%, obtained from a smoothed curve drawn throughthe experimental range values, were compared therefore with correspondingcalculated (x) values. For certain values of K/KL there is a correspondencebetween the calculated and experimental range differences. These values of

-51-

Experimental,s' amorphous siliconx' polycrystall ine silicon

Calculated, K=l·SKL(WinterbonJ

Fig. 4.4. Experimental standard deviations of boron distributions in amorphous and poly-crystalline silicon and corresponding theoretical values calculated by Winterbon for K =1·5 KL' versus energy.

K/KL' in some cases found by interpolating the tabulated values of Winterbon,were used to calculate the behaviour of the electronie-stopping cross-section Seversus energy. Because Winterbon used the velocity-proportional electronic-stopping relation, the Se value at the average energy (El +E2)/2 can be foundwith

(4.14)

These calculated values of Se versus energy are given in fig. 4.7. The hatchedregion indicates the accuracy limits. This figure also shows the electronic-stopping cross-section versus energy proposed by Eisen 4-20):

Se = 2·06. 10-13 EO'S eV cm2jatom. (4.15)

Also shown in the figure ,is an approximation of our results given by

- 52-

Experimental:-la 0: amorphous silicon

x: polycrystalline silicon

l:l xIl>

~ X

Il>

~

t -1.0~

-0.~LO--~-L-~~~~'~0~2--~-L-~~~~m3-Energy (keV)

Fig. 4.5. Experimental values of the skewness of boron distributions in amorphous and poly-crystalline silicon and corresponding theoretical values, calculated by Winterbon for K =1·5 KL' versus energy.

Se = 1·75. 10-13 £0.46 eY cm2/atom. (4.16)

The average value of Se, shown by the curve in fig. 4.7 can be assumed to beproportional to EP with p being energy-dependent, e.g. in the high-energyregion (800 keY) p = 0·3.

4.4. Discussion and conclusions

From the results given in fig. 4.2 it is found that the experimental borondistributions obtained by implantations in the energy range 30 to 800 keY inamorphous and polycrystalline targets can be described analytically with con-siderable accuracy by Pearson distributions. It was possible therefore to usethe latter distributions in a fitting procedure to determine the average range,standard deviation, skewness and kurtosis of the boron distributions. An ad-vantage of this method over direct calculation of the moments is that a system-atic extrapolation of the low-energy distributions outside the surface isautomatically obtained.

The similarity of the distributions in amorphous and polycrystalline siliconat energies of 70, 100 and 200 keY, which is also reflected by the corresponding

- 53-

102 Experlrnenitü.O' amorphous siliconx: polycrystalline silicon x

.~x0.... x...

~ 0

tx

x0

la/;j

Calculated, K=I·SKL(W irderbon}

11=0----~~~~~~~ro~2----~~--~~~~/O-3

- Energy (keV)Fig. 4.6. Experimental values of the kurtosis of boron distributions in amorphous and poly-crystalline silicon and corresponding theoretical values calculated by Winter bon for K =1·5 KL. versus energy.

moments in table 4-II, proves that the polycrystalline silicon layers used in thisstudy can be considered to be amorphous in respect of the boron stopping proc-ess in the energy range which includes the specified energies. At higher energiesthe ranges become relatively larger compared with the average diameter of thecrystal grains in the polycrystalline silicon layers. Therefore we may surely con-sider the polycrystaIIine layers to be amorphous in the high-energy region. Thedistributions in these layers can thus be compared with theoretical results de-rived from LSS theory for amorphous targets. Distributions at implantationenergies in the range from 30 to 800 keV could then be used for verifyingtheoretical calculations.There are different types of Pearson distributions, which are distinguished

by the value of" = b12/4bob2 4-13). Calculating x for the moments given intable 4-II, or for moments that are obtained by interpolation, it is found that" is about 0·6. This value of" is within the range 0 < " < 1 giving imaginaryroots of bo + bI X + b2 x2 in the Pearson differential equation. The distri-butions satisfying 0 < " < 1 are the so-called type-IV Pearson distributions.They are unimodal and have unlimited ranges in both directions. With theo-retical moments, however, which can be obtained from figs 4.4 to 4.6, a valueof" is often found outside the above limits. In that case bo + bI X + b2 x2

- 54-

c:.g

]~ 1·0

b

"".S;

g:1ji.I,!s.::,utij

t 0.1 L--_-''---'-___.--'--'--L-L-'-'-.--_-'-_-'----L..-'-.1....1_._._j10 102 103

_ £nergy(keV)

Fig. 4.7. Electronie-stopping cross-section Se versus energy for boron in amorphous andpolycrystalline silicon obtained by comparing experimental ranges and ranges calculated byWinterbon. The estimated accuracy limits are indicated by shading. Also shown in the figureare curves corresponding to Se = 2·06. 10-13 EO.s and Se = 1·75. 10-13 EO.46 presentingthe Eisen value of the electronie-stopping cross-section 4-20) and an approximated valueof our calculated Se versus energy curve, respectively.

has real roots, limiting the applicability of the Pearson distributions consider-ably.It was found that the experimental values of average range and standard

deviation correspond reasonably well to values calculated using an electronic-stopping coefficient of 1·5 KL (figs 4.3 and 4.4). The use of an electronic-stopping coefficient different from KL is explained by the fact that LSS theorydoes not account for Z, oscillations observed 4-21). For the skewness the cor-respondence between experimental and calculated values is somewhat less good(fig. 4.5). For the kurtosis a discrepancy is found which increases from 30%at the lower energies to over 100% at 800 keV (fig. 4.6) and is outside theaccuracy limits with which the concentration profiles are measured or themoments are determined. This discrepancy is due to different tails of Pearsontype-IV distributions and theoretical Winterbon distributions which is explainedas follows. Pearson's type-IV distributions are usually written as

(X2)-m

f(x) = kp 1 + a2

exp [-11 arctan (x/a)] (4.17)

wheref(x) is the frequency function with parameters kp, a, m and 11.At high

- 55-

values of Ix!. f(x) tends asymptotically to Ixl-2m. Of the fitting Pearson dis-tributions -m changes from about -10 at 30 keY to about -3 at 800 keY.However, the tails of the distributions according to Winterbon's calculationstend asymptotically to an exponential function such as exp (-Ä.lxlp) for somepower p > 1 4-22). In this case the slopes of the tails will be steeper and thismay result in a lower value of the moments, especially of the fourth. We havechecked this by replacing the tails of the Pearson distributions by exponentialfunctions and by calculating the moments of these adapted distributions directly.The level of the truncation was chosen at 10-3 of the maximum value. Thislevel represents the lowest boron concentration measured.The exponential functions were of the type A exp [-,1. (x - XO)2] and were

fitted at the matching point as to value and first and second derivatives. Themoment calculation was extended down to a concentration level of 10-11 ofthe maximum value. In figs 4.8a, band c the results are given for the secondmoment (standard deviation), third moment (skewness) and fourth moment(kurtosis). The figures also show the theoretical moments of Winterbon, cal-culated with an electronie-stopping coefficient K = 1·5KL, Comparing theseresults with those given in figs 4.4 to 4.6 we observe that for the fourth momentthe discrepancy between the experimental and theoretical values has indeedbeen reduced. This improvement is most important at the higher energies. 0 Thisis due to the fact that at these energies the value of Iml is rather low. For thesecond and third moments no distinct improvement is obtained due to the factthat these moments are less sensitive for the tail at low concentrations. Theseresults prove that the method of extrapolating the tails of the experimentaldistributions outside the measured region has a marked influence on the fourthmoment. We conclude therefore that the discrepancy between the calculatedand experimental values, as shown in fig. 4.6, is within the accuracy limits withwhich the fourth moment of the experimental distribution has been determined.A more accurate determination of the fourth moment requires improvedmeasuring techniques which extend the boron measurements to lower concen-trations and reduce the need for extensive extrapolation.The approximation of the electronie-stopping cross-section versus energy was

as given by (4.16) between the value Se= 2·06 . 10-13 EOoS as proposed byEisen 4-20) and the value Se = 1·70. 10-13 E004 eV cmê/atom as given byWittmaack, Maul and Schulz 4-19). A deviation of the electronie-stoppingcross-section from velocity proportionality has also been found by others usingdifferent particles and targets 4-23). In transmission experiments on boron,well channelled through silicon along a <1 1 0) crystal direction, Eisen 4-24)obtained an energy dependence of Se of E(0.49±0003). It will be observed thatthis result includes our approximation. In greater detail we found the energydependence of Se at an energy of about 800 keY to be proportional to EO·3.

Existing formalisms are assumed to be useful for ion velocities up to Vo Z12/3,

- 56-

......::g_c:

IOJ.g......~{l1:>....gc:.e11)

a} t T02

!:lOlc:~-T'O~ - Calculated K=T·SKLt (Winterbon)

Experimental:Q: amorphous siliconXI polycrystalline silicon

b} -O·T

TO.~11)0.......~

tc} 1

TO 102. 10J_Energy (keV)

Fig. 4.8. Comparison of moments calculated by Winterbon with those obtained by directcalculation of Pearson distributions which fit the experimental distributions. At concentra-tions below the measured ones the tails of the Pearson distribution were truncated andreplaced by matched exponential functions. (a) Standard deviation; (b) skewness; (c) kurtosis.

where Z, is the atomic number of the ion and Vo the Bohr velocity. In the case'of B+ ions this velocity corresponds to an energy of 2·3 MeV. The above-mentioned energy dependence at 800 keV seems therefore rather exceptional.We consider, however, that before definite conclusions can be drawn about thisbehaviour, verification of our results is needed by more-direct measurements,for instance by energy measurements of the kind performed in transmissionexperiments.

, ,

- 57-

REFERENCES4-1) W. K. Hofker, H. W. Werner, D. P. Oosthoek and H. A. M. de Grefte, in

B. L. Crowder (ed.), Proc. int. conf. on ion implantation in semiconductors and othermaterials (Yorktown Heights 1972), Plenum Press, New York, 1973, p. 133.

4-2) K. B. Winterbon, Private communication.4-3) T. E. Seidel, in I. Ruge and J. Graul (eds), Proc. 2nd int. conf. onionimplantation

in semiconductors (Garmisch-Partenkirchen 1971), Springer, Berlin, 1971, p. 47.4-4) G. Schwarz, M. Trapp, R. Schimko, B. Butzke and K. Rogge, Phys. Stat. sol.

(a) 17, 653, 1973.,.4-5) J. F. Gibbons and S. Mylroie, Appl. Phys. Letters 22,568,1973.4-6) W. S. Johnson and .J. F. Gibbons, Projected range statistics in semiconductors,

Stanford University Book Store, 1969.4-7) J. Lindhard, M. Scharff and H. E. Sch ie tt, Mat. Fys. Medd. Dan. Vid. Selsk. 33,

no. 14, 1963.4-8) K. B. Winterbon, P. Sigmund and J. B. Sanders, Mat. Fys. Medd. Dan. Vid.

Selsk. 37, no. 14, 1970.4-9) K. B. Winterbon, Rad. Effects 13, 215, 1972.4-10) S. Mylroie and J. F. Gibbons, in B. L. Crowder (ed.), Proc. int. conf. on ion

implantation in semiconductors and other materials (Yorktown Heights 1972),Plenum Press, New York, 1973, p. 243.

4-11) M. H. Brodsky, D. Kaplan and J. F. Zie gier, Appl. Phys. Letters 21, 305, 1972.4-12) L. C. Feldman and J. W. Rodgers, J. appl. Phys. 41,3776, 1970.4-13) M. G. KendalI and A. Stuart, The advanced theory of statistics, Charles Griffin,

London, 1958, vo!. 1, p. 148.4-14) W. P. Elderton, Frequency curves and correlation, Cambridge University Press,

1953, 4th ed.4-15) M. Abramowitz and I. A. Stegun (eds), Handbook of mathematical functions,

Dover Pub!., 1970, p. 12.4-16) K. N. Tu, P. Chaudhari, K. Lal, B. L. Crowder and S. I. Tan, J. appl. Phys. 43,

4262,1972.4-17) J. F. Zie gier and M. H. Brodsky, J. app!. Phys. 44, 188, 1973.4-18) J. Lindhard and M. Scharff, Phys. Rev. 124, 128, 1961.4-19) K. Wittmaack, J. Maul and F. Schulz, in B. L. Crowder (ed.), Proc. int. conf.

on ion implantation in semiconductors and other materials (Yorktown Heights 1972),Plenum Press, New York, 1973, p. 119.

4-20) F. H. Eisen, B. Welch, J. E. Westmoreland and J. W. Mayer, in D. W. Palmet,M. W. Thompson and P. D. Townsend (eds), Proc. int. conf. on atomic collisions(Brighton 1969), North-Holland Publishing Company, 1970, p. 111.

4-21) See e.g.: J. W. Mayer, L. Eriksson and J. A. Davies, Ion implantation in semi-conductors, Academic Press, New York, 1970, p. 27.

4-22) K. B. Winterbon, Rad. Effects 15, 73, 1972.4-23) B. Fastrup, A. Borup and P. Hvelplund, Can. J. Phys, 46, 489,1968.4-24) F. H. Eisen, Can. J. Phys. 46, 561, 1968.

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5. CONCENTRATION PROFILES OF BORON IMPLANTATIONSIN MONOCRYSTALLINE SILICON

AbstractDistributions of boron implantations along dense and open crystallo-graphic directions are investigated. It is observed that distributions ofboron implantations along a .dense crystallographic direction showpenetrating tails with small humps. The mechanism of tail formationis investigated. From implantations done at 77 K we inferred that theprocess of thermal diffusion does not contribute significantly to the tailformation. The same is true for ionization-enhanced diffusion as wasverified experimentally. From these results and from arguments derivedfrom further experimental results we conclude that the tails on the borondistributions are mainly due to steering of the ions into and channellingalong low-index crystallographic directions and planes.

5.1. Introduction

Distributions of boron that is implanted into monocrystalline silicon has sofar been studied mainly from the corresponding charge-carrier distributions.In such investigations Seidel 5-1) found that if boron is implanted along a low-index axis or between low-index planes a much deeper penetration of the boronoccurred than if boron is implanted along a dense crystallographic direction.Bader and Kalbitzer 5-2) investigated low-energy (6-keV) boron implantationsalong open crystallographic directions. They obtained charge-carrier distribu-tions with tails which were much smaller than those observed on phosphorusdistributions.

In this chapter we discuss investigations into distributions of boron implantedalong open and dense directions by measuring the boron distributions withSIMS. Annealing, which was required in the above-mentioned studies, isavoided here. In earlier investigations 5-3;4), of which some results are recapit-ulated in this chapter, we observed that, if boron is implanted along a densecrystallographic direction, the distributions have penetrating tails with smallhumps. It is of interest to study the mechanism which causes these tails. Thismechanism may be channelling or may be some sort of enhanced diffusion.Experiments which exclude diffusion as the prevailing mechanism are describedin the last section of this chapter.

5.2. Range distributions of boron implanted along a dense crystallographic, direction

As is found in implantations of phosphorus 5-5.6) and boron 5-1) (see alsosec. 5.3) channelling of heavy ions occurs mainly along low-index directionssuch as (110), (I 11), (10 0) or between low-index planes such as {110}.In determining a direction of implantation that decreases the chance ofchannelling, the critical angle ofchannelling in these directions (sec. 2.2) andplanes should be taken into account. Also of interest is the divergency of the

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ion beam over the sample. Bearing these aspects in mind we have chosen a(763) direction as the nominal direction of implantation. This direction hasangles of about 18°, 19° and 44° with the nearest (I 11), (110) and (10 0)directions, respectively. The silicon slices were cut normal (within 0·5°) to a(763) direction from a p-type monocrystal, which was grown using thefloating-zone process. The slices were polished by chemical-mechanical means.They were implanted in a direction perpendicular to the surface (within ± 1°)at energies in the range of 30 keY up to 800 keY (within 0·2%) at a dose of1015 ions cm-2•Figures 5.1a and b show the distributions measured. These distributions have

a distinct tail towards larger depth values. In these tails small humps can bedistinguished. In fig. 5.2 one of the distributions (70 keV) is replotted on alinear scale. In this figure is also indicated a Gaussian distribution with a mode(Rp) and a full width at half of the maximum height (FWHM) which are equalto those of the 70-keV distribution. From the close fitting of both distributionswe conclude that the standard deviation a of the experimental distribution canbe approximated by

a = FWHM/2·36.This value is accurate to within 5% as was checked by direct calculation of a.Values of a of the experimental distributions which are derived with (5.1) andthe corresponding values of R; versus energy are given in fig. 5.3. This figurealso shows the results which Seidel obtained from charge-carrier distributionsof low-dose implantations after annealing at 850oe for periods of 30 minutes.There is a reasonable agreement between his and our results in spite of thefact that in Seidel's results some thermal diffusion of the boron has occurred.In fig. 5.3 are also indicated the depths of the humps in the tails versus energy

which we estimated from the measured distributions. These depth values areroughly proportional to EO.s. This leads us to the supposition that these humpsare due to some type of channelling because in the case of channelling thepenetration depth varies proportionally to EO's (sec. 2.2). We assume thereforethat the humps and tails are caused by a preferential penetration of ions whichare scattered in the surface layer and are steered into channels in low-indexdirections which are nearest to the direction of incidence. In the case above wesuppose that channelling occurs along the nearest (I 1 I) and (I 1 0) direc-tions.The tails we found on implanted-boron distributions are smaller than those

on phosphorus distributions 5-7). If we accept the above-mentioned scatter-ing and channelling mechanisms then one of the reasons will be that in therelevant energy range the critical angle for channelling is proportional to Z11/4

«2.20), (2.11)) with the consequence that boron has a smaller probability ofbeing steered into channels than phosphorus (e.g. in a (110) direction for50-keV boron "Perlt = 4'1° and for 50-keV phosphorus "Perlt = 5'3°).

(5.1)

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Fig. 5.1. Distributions of boron implanted along a (7 6 3) direction at different energiesand a dose of 1015 ions cm-2• (a) Implantation at energies 30, 50 and 70 keY. (b) Implan-tation at energies 50, 100, 200, 300, 400, 600 and 800 keY.

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0·2 0·3 0·' 0·5 0·6_Depth (pm)

Fig. 5.2. Boron concentration profile (implantation energy 70 keY and dose 1015 ions cm-2)and a Gaussian distribution with equal mode and full width at half of the maximum height.Boron distribution 0-0, Gaussian distribution - - .

210 10':--_J--'L....L...L.L.1...l..':10~2;----'---'-...1...i...u..~103

- Energy(k_eV)

Fig. 5.3. Most probable projected range (Rp) and standard deviation (0') of experimental borondistributions implanted at energies in the range 30-800 keY and a dose of 1015 ions cm-2•These results are compared with measurements at energies in the range 30-300 keY ofSeidel 5-1). For some energies the depths of the humps in the tails of the distributions arealso indicated.

ox

Experimental : Rp and aSeidel : Rp rind aDepths of humps In the tolls

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5.3. Comparison of distributions of implantations along open and dense crystallo-graphic directions

Figure 5.4 gives typical distributions of 70-keV implantations in a (I 1 0)and a (763) direction. On the first one two maxima are observed. Themaximum closest to the surface is caused by ions which are scattered by sur-face atoms and by displaced atoms in the damaged surface layer. The second

ro~~----~~--~~----~~----~----~~--~0·2 0·4. 0·6 0·8 '·0- Depth (IJm)

Fig. 5.4. Boron concentration profiles of implantations along two different crystal directions<763> and <1 10>. Implantation energy 70 keY, dose 1015 ions cm-2•

maximum comes from well channelled ions which lost their energy mainly inelectronic collisions. One observes that the hump in the (763) distributionis less deep than the second maximum in the (I 1 0) distribution. Acceptingthe scattering and steering mechanisms mentioned in the last section we canestimate the depth of the hump in the (763) distribution relative to themaximum in the (I 1 0) distribution. The (I 1 0) direction has an angle of18° with the (763) direction. For the calculation we will assume that thehump in the (7 6 3) distribution is caused by ions which are scattered into(11 0) channels. The energy El of the ions after scattering can be calculated,assuming a two-particle interaction, from

El = Eo {I - (1 - IX) sin" (OI2)} (5.2)

where Eo is the initial energy of the ions, IX= [(A - 1)/(A + 1)]2 withA = M2IMI' and 0 is the scattering angle in the centre-of-mass system.The angle 0 can be calculated from the scattering angle cp in the laboratorysystem with

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A sin 8tan cp = ;

1+ A cos ()

with cp = 180 we obtain El = 0·96Eo. The depth d2 of the hump in the(763) distribution expressed in the depth dl of the second maximum in the'(I 10) distribution is

With dl = 0·75 !Lm we obtain d2 = 0·7 !Lm. Experimentally is found:d2 = 0·65 !Lm(fig. 5.3). The discrepancy between the experimental and cal-culated values can be explained from the fact that in the calculation no accountis taken of further nuclear- and electronic-energy losses before scattering inthe concerning direction occurred. That such an effect may be of interest fol-lows from computer calculations of boron-ion channelling by Eltekov etal.5-8). They calculated the distributions of boron implanted along a (I 1 1)direction and in a direction which has only an angle of 10 with this direction, 'and found in the latter case a distinct shift of the distribution to smaller depths.It is interesting to compare the measured maximum ion range of well chan-

nelled boron with the maximum range which can be calculated, supposing onlyelectronic stopping to occur. For the calculation we use data which Eisen 5-9)obtained from transmission experiments. He determined for boron ions whichchannel with a velocity of 1·5. 108 cmfs along a (110) axis of silicon anelectronie-stopping cross-section Se = (3·56± 0·11) . 10-14 eV cmê/atom anda corresponding energy dependence proportional to EP with p = 0·49 ± 0·03.Ifwe write

(dE) = -N s; EPdx e

we obtain, disregarding nuclear stopping:

1 Eo dE 1 Eo1-PRmax = N Ko f EP = N Ko 1 - p

o

where Eo is the energy of implantation. The coefficient Ko is derived from

With Se = (3·56 ± 0.11).10-14 and E = 130 keY (corresponding to a veloc-ity of 1.5.108 cmfs of the boron ions) we obtain Ko = (1·0± 0.03).10-16•With this value, p = 0·49± 0·03 and Eo = 70 keY in (5.6) we find Rmax =1·23± 0·35 !Lm.Experimentally we found: Rmax = 1·03± 0·06 !Lmwhich value is within

the calculated range. This confirms the statement that the deep penetrationof the ions is due to reduced nuclear and electronic stopping.

(5.3)

(5.4)

(5.5)

(5.6)

(5.7)

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5.4. Comparison of boron distributions in monocrystalline and in amorphoussilicon

Figure 5.5 shows distributions of boron implanted at an energy of 30 and70 keY in amorphous silicon (chapter 4) and a distribution of boron that isimplanted at 70 keV in monocrystalline silicon. From these results we con-clude that the crystallinity of the silicon is a condition for tail formation.

T

Fig. 5.5. Concentration profiles ofboron implanted in amorphous silicon (implantation energy30 and 70 keY, dose 1015 ions cm-2). A distribution of boron implanted along a <763)direction implanted at 70 keY and a dose of 1015 ions cm-2 is given for comparison (x).

5.5. The mechanism of tail formation

In the foregoing sections we explained the tail on the distribution as beingcaused by a preferential deep penetration of the ions due to the effects of steeringinto and channelling along open crystallographic directions. A strong argumentfor such a mechanism is derived from the observed EO'5 dependence of thehump position as is discussed in sec. 5.2. A further argument follows from theresults in sec. 5.3 where we found that the maximum range of boron implantedin a (I 1 0) direction corresponds to the range calculated with electronic stop-ping. Therefore the second maximum in a well channelled distribution can beattributed to channelling.The distributions of other ion species implanted in silicon often have more-

pronounced tails, as we discussed already in sec. 5.2 for the case ofphosphorus.For that case Blood et al.5-10) found conclusively, from the transmission ofphosphorus through thinned silicon, that the tail on a phosphorus distributionis due to channelling.· It would be very interesting to do a similar experimentfor boron, but such an experiment is more difficult for boron due to the smaller

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tails and the less sensitive detection methods which are available for boron.Some more results on distributions of implanted ions in silicon are available.For instance Gamo et al.5-11) observed exponential tails on distributions ofindium when the temperature of implantation is ;;;::300 oe. At a temperatureof implantation of 100oe or 200 oe such a tail was not found. A similar resultwas obtained by Iwaki et al. 5-12) for arsenic implanted in silicon. Interstitialdiffusion was considered to be the probable mechanism for the formation ofthese tails.As said at the beginning of this section we assume that the tail on the boron

distributions is caused by channelling. To strengthen this assumption we willconsider a possible contribution to the tail formation by the process of diffusion.In the first place therefore we will discuss the thermal diffusion of substitutionaland interstitial boron. In the second place we will consider an athermal diffusionprocess as proposed by Bourgoin 5-13), in which the alternate capture of elec-trons and holes at interstitial lattice sites serves to drive an interstitial fromone equilibrium configuration in the lattice to another.Thermal diffusion of substitutional boron in silicon requires heating of the

substrate at > 800 oe for it to be significant. With the substrate at room tem-perature, as is the case in our experiments, we can therefore exclude thismechanism. Thermal diffusion of boron may be enhanced if defects are createdsuch as by a proton bombardment 5-14,15,16). However, in this case alsoheating of the substrate at ;;;::600 oe is needed to obtain some effect. We con-clude therefore that thermal diffusion of substitutional boron enhanced bydefects which are created during the implantation can only result in an in-significant effect in our case.Thermal diffusion of interstitial boron may occur at room temperature if we

consider the interstitial diffusion of an ion with a comparable radius, such aslithium 5-17). At 77 K the mobility of lithium is very low, as is found inlithium-drifted deviceswhich are used for nuclear-radiation detection. To studytherefore the possibility ofthermal interstitial diffusion as a cause oftail forma-tion in the case of boron, we investigated boron distributions which were im-planted at 77 K. From sec. 5.4 it is known that in amorphous silicon the tailformation does not occur. Therefore in order to reduce a possible diffusion ofthe boron at 77 K or during the profile measurement at room temperature theboron implantation at 77 K was promptly followed by a neon bombardmentat 77 K to render the silicon amorphous. In fig. 5.6 a typical boron distributionimplanted in this way is compared with a distribution of a boron implantationthat is not followed by a neon bombardment. In both cases a tail is found.The spur on the tail in the neon-bombarded slice may be caused by recoiling ofthe boron during the neon bombardment. From this experiment we concludethat the tail is already formed at 77 K and therefore, thermal diffusion as acause of tail formation can be excluded.

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•o•o.

o.o."-

0·0 .0.0 0

10'7!-_~:--_-,::-_----::-,-::-_-'- • .._o _0~0~ _ ___J

o 0·1 0·2 0·3 0·4 0·5-Depth (pm)

Fig. 5.6. Distributions of boron implanted along a <7 6 3> direction at 77 K. 0: Boron im-plantation (energy 25 keY, dose 1015 ions cm-2) followed by neon implantation (energy140keY, dose 1015 ions cm-2) •• : Boron implantation (energy 25 keY, dose 1015 ions cm-2).

Next we will consider ionization-enhanced diffusion of interstitials as a causeof tail formation. Such a process may be effective during the implantation dueto the concentration of electrons and holes which are created in electronic col-lisions.After the implantation, a fraction of about 50% of the boron is at sub-stitutionallattice sites 5-18,19). This number decreases to a value of about 20%after annealing at 600 oe. One may therefore expect that, if the process ofionization-enhanced diffusion is effective, a change in the boron distributionmay occur if in the boron-doped layer a concentration of electron-hole pairs(e.-h. pairs) is formed which is comparable with the concentration which isformed there during the implantation. We have checked this effect by investigat-ing a possible change in boron distributions due to e.-h. pairs formed by anelectron bombardment. For this experiment boron ions with an energy of70 keY and a dose of 1015 ions cm-2 were implanted in silicon which has aresistivity of 15000 Q cm and a lifetime of the charge carriers of l" ~ 1 ms.Samples as-implanted and samples after annealing at 600oe were bombardedwith electrons at energies of 5, 10 and 20 keY. The maximum ranges of elec-trons at these energies are 0·5 urn, 1 (Lmand 2 (Lm,respectively 5-20). Theseranges cover completely the maximum range of boron ions of 70 keV which is0·7 (Lm.The required electron doses are obtained with the following consider-ations. In the case of a boron ion with an energy of 70 keV about 50 keV isdissipated in electronic collisions (table 2-11). The average energy for creatingan e.-h. pair in silicon is highly independent of the type of the ionizingparticle and amounts to 3·6± 0·1 eV 5-21). The number of e.-h. pairs createdby a boron ion of 70 keY is therefore about 1·4. 104 and thus at a total

-67 -

dose of 1015 boron ions cm=" 1·4. 1019 e.-h. pairs cm-2 are created. From theobservation that in X-ray detection with silicon detectors there is a linearrelationship between the number of e.-h. pairs versus energy down to an energyof 5 keY 5-22) we derive the conclusion that for the bombarding electrons theaverage ionization energy can be assumed to be 3·6 eV. To create at each ofthe specified electron energies of 5, 10 and 20 keY a comparable number ofe.-h. pairs as during the boron implantation, the required electron doses shouldbe 1016, 5. 1015 and 2·5 . 1015 electrons cm-2, respectively. In fact, we useddoses which are one order higher. The radiation periods were chosen similarto those of the boron implantation (about 0·5 h).From the boron distributions which were measured before and after the

electron bombardment we observed that this bombardment had not influencedthe boron distributions within accuracy limits (5%). We conclude therefore thatthe process of ionization-enhanced diffusion makes no significant contributionto the tail formation.

Summarizing the above results we conclude that diffusion is not the causeof tail formation. Add to this the arguments which were mentioned at thebeginning of this section and we may conclude that the tails on the borondistributions are formed mainly by the effects of steering and channelling ofthe boron ions.

REFERENCES5-1) T. E. Seidel, in I. Ruge and J. Graul (eds), Proc. 2nd int. conf. on ion implantation

in semiconductors (Garmisch-Partenkirchen 1971), Springer, Berlin, 1971, p. 47.5-2) R. Bader and S. Kalbitzer, Rad. Effects 6, 211,1970.5-3) W. K. Hofker, H. W. Werner, D. P. Oosthoek and H. A. M. de Grefte, Rad.

Effects 17, 83, 1973.5-4) W. K. Hofker, H. W. Werner, D. P. Oosthoek and H. A. M. de Grefte, in

B. L. Crowder (ed.), Proc. int. conf. on ion implantation in semiconductors andother materials (Yorktown Heights 1972), Plenum Press, New York, 1973, p. 133.

5-5) G. Dearnaley, J. H. Freeman, G. Gard and M. A. Wilkins, Can. J. Phys. 46,587, 1968.

5-6) R. A. Moline and G. W. Reutlinger, in I. Ruge and J. Graul (eds), Proc. 2ndint. conf. on ion implantation in semiconductors (Garmisch-Partenkirchen 1971),Springer, Berlin, 1971, p. 58.

5-7) G. Dearnaley, M.A. Wilkins and P.D. Goode, in I. Ruge and J. Graul (eds),Proc. 2nd int. conf. on ion implantation in semiconductors (Garmisch-Partenkirchen1971), Springer, Berlin, 1971, p. 439.

5-8) V. A. Eltekov, D. S. Karpuzov, Yu. V. Mar tyn enko, E. A. Rubakha, V. A.Simonov and V. E. Yurasova, in L. T. Chadderton (ed.), Proc. int. conf. onatomic collisions in solids (IV), (Gausdal 1971), Gordon and Breach, London, 1972,p.113.

5-9) F. H. Eisen, Can. J. Phys. 46, 561, 1968. .5-10) P. Blood, G. Dearnaley and M. A. Wilkins, Rad. Effects 21, 245, 1974.5-11) K. Gamo, M. Iwaki, K. Masuda and S. Namba, in I.Ruge and J. Graul (eds),

Proc. 2nd int. conf. on ion implantation in semiconductors (Garmisch-Partenkirchen1971), Springer, Berlin, 1971, p. 459.

5-12) M. Iwaki, K. Gamo, K. Masuda, S. Namba, S. Ishihara and I. Kimura, inB. L. Crowder (ed.), Proc. int. conf. on ion implantation in semiconductors and othermaterials (Yorktown Heights 1972), Plenum Press, New York, 1973, p, 111.

5-13) J. C. Bourgoin and J. W. Corbett, Phys, Lett. 38A, 135, 1972.5-14) H. Strack, J. appl. Phys, 34, 2405, 1963.

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5-15) P. Baruch, C. Constantin, J. C. Pfister and R. Saintesprit, Disc. Faraday Soc.31, 76, 1961.

5-16) R. L. Minear, D. G. Nelson and J. F. Gibbons, J. appl. Phys, 43, 3468, '1972.5-17) E. M. Peil, J. appl. Phys. 31, 291, 1960.5-18) G. Fladda, K. Bj ö r qv is t, L. Eriksson and D. Sigurd, Appl, Phys. Letters 16

313, 1970.5-19) J. C. North and W. M. Gibson, Appl, Phys. Letters 16, 126,1970.5-20) Landolt-Börnstein, Zahlenwerke und Funktionen, Band 11,Teil6, Springer, Berlin,

1959, p. 1016.5-21) G. Bertolini and A. Coche, Semiconductor detectors, North-Holland Publishing

Company, Amsterdam, 1968, p. 85.5-22) R. L.Heath, Gamma ray spectrum catalogue, vol. 2 of 2, 3rd edition, 1974,ANCR-

1000-2.

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6. INFLUENCE OF ANNEALING ON THE CONCENTRATION PRO-FILES OF BORON IMPLANTATIONS IN SILICON

Abstract

The influence of annealing on the concentration profiles of boron im-planted into silicon with doses of 1014 ions cm-2 up to 1016 ions cm-2and an energy of 70 keV is studied. The broadening of the concentrationprofiles during annealing is described as a superposition of the effectsof a relatively immobile and a mobile boron fraction. The properties ofthe immobile boron fraction are studied by measuring the influence ofa boron implantation on the distribution of a homogeneous boronbackground dope. From these experiments it is concluded that the im-mobile boron fraction consists of boron precipitates, The properties ofthe mobile fraction are studied from concentration profiles that areobtained after annealing for different periods at the same temperature.It is found that during the initial stage of the annealing process a fastbroadening ofthe profile occurs, which is assumed to be due to an inter-stitial-type boron diffusion. After prolonged annealing the much slowersubstitutional-type diffusion prevails, due to trapping of the interstitialboron atoms by vacancies. Excessive boron precipitation, obtained atannealing of a high dose, such as 1016 ions cm-2, at about 1000 oe,appears to give some increase ofthe ion yield in the SIMS measurements.

6.1. Introduction

Annealing is necessary to remove crystal damage caused by the implantationand to bring dopant ions to substitutionallattice sites, both effectsbeing require-ments for an adequate electrical behaviour of the implanted layer. The behav-iour during annealing of a concentration profile obtained by ion implantationdiffers from the case where the semiconductor is doped by the process of ther-mal diffusion. As said in sec. 2.4 one difference is that crystal damage causedby the implantation may influence the diffusion rate. Another is that theimpurity concentration, as implanted, is not limited by the solid solubility.A third effect is that a considerable fraction of the implanted boron is at inter-stitiallattice sites. Some studies on this subject have been made. Wagner 6-1),for instance, has determined diffusion coefficients in crystalline silicon fromcharge-carrier concentration profiles, obtained after prolonged annealing athigh temperatures. His results are in agreement with those known from thermaldiffusion of boron into silicon. We, however, observed a profile broadeningafter annealing at temperatures as low as 700 oe, which was much bigger thanwas found in the case of thermal diffusion 6-2).In this chapter the effects mentioned above are studied in more detail.

Special attention is paid to high-dose implantations. Annealing was mostlydone isochronously, but in order to study certain transient effects, as caused,for instance, by radiation damage, the annealing time was varied. Whereasmost implantations were done in a dense crystallographic direction, one caseof an implantation in an open direction was studied in order to see whether the

-70-

smaller crystal damage in this case gives a different annealing behaviour of theconcentration profiles ..

From studies on boron-implanted silicon using a transmission electronmicroscope it is known that defects are observed at annealing temperatures inthe range 700-900 "C, These defects are assumed to be correlated with boronprecipitates 6-3.4). In this chapter we prove that precipitation of the boron doesoccur. This is shown in an experiment where boron was implanted in siliconcontaining a homogeneous background dope of boron in natural isotopicabundance (natural boron). As it may be expected that boron of the back-ground dope will behave similarly to implanted boron, it was of interest toinvestigate the distribution of the background dope at different annealingtemperatures. This was done by measuring the concentration of the lOB com-ponent of the background as a function of depth if 11B was implanted or viceversa. We observed a peculiar redistribution of the background dope which weexplain by the effect of boron precipitation, as is reported in sec. 6.4.2.

6.2. Experimental details

The silicon slices are cut from a single crystal with a resistivity of 16500 Q cm,perpendicularly to a (7 6 3) direction (to within 0'5°) (chapter 5), unless other-wise stated. Implantations were carried out at a voltage of 70 kV ± 2% atroom temperature. The angle of incidence with respect to the substrate surfacewas 90° ± 1°.

Annealing up to a temperature of 1000 oe was carried out in a nitrogenatmosphere. For annealing above 1000 "C quartz capsules filled with argon ata pressure of 150 Torr were used in order to limit evaporation of the silicon.Each capsule contained two identical implanted silicon slices,which were placedon top of each other with the implanted sides face to face, in order to diminishout-diffusion.

From profile measurements on slices annealed at 1000 oe it appears thatidentical results are obtained if these slices are annealed in nitrogen, either bareor protected with a chemically deposited oxide layer, or are annealed in cap-sules as described above. The temperature in the furnace was kept constant towithin ± 4 oe. Annealing was done isochronously, that is for periods of 35minutes and, for each annealing temperature, a separate sample was usedunless otherwise stated. This period should be considered as the effectiveannealing time at the stated temperature (to within 4 0C); it does not includethe heating-up and cooling-down periods.

6.3. Experimental results

6.3.1. Concentration profiles after annealing at different temperatures

Figures 6.1, 6.2 and 6.3 give boron distributions in isochronously annealed

-71-

Annealing temperature\.... \"'/_)!.\

,,1 '~\J' '~"'--+-+~'+-'" \ ,

X."K-X;3~ +..' .,-+.... J{ ~?:-"X ...x, ...~~

+" p';' ""'-x..' ,... ,, : "'x. ~~'+ril '''',If." ,.......

II ,t ,,~\"Xt-~.w...'i \ \~\x'x..

I/{ I \ '\ \ "X..

,/ Y, \' ~\ 'x..,/ \ ~ \ ~i \ \'ti{ \ """x...

~\\~\ "'x,\ '.a, \. x".~ \ \ \ <,

\ \ \ \ X'. \m, +, "11.,

"'\ "\ \ \. :)(".~\\~'\ +\ -,\ \ \n +, \c~\ \ \ '\\~, v >, '>\

\\' 'x.10'7D~---~D'-':-2-----:DL'4:---...l.....___:~:---"':'__---:f::::----:;'_-I~'D:-----:I'-'!'2

- Depth (pm)

Fig. 6.1. Concentration profiles of a boron implantation with a dose of 1014 ions cm-2 andan energy of 70 keY before and after annealing. Annealing duration: 35 min.

<;)' no annealing,.: 7DDoem: 8DDoeol : 9DDoe+ :1DDDoex, nDDoe

Annealing temperature<;): no annealingv: 7DDoem, 8DDoe.. ,9DDoe+,IDDDoex: nDDoe

1

Fig. 6.2. Concentration profiles of a boron implantation with a dose of 1015 ions cm-2and an energy of 70 keY before and after annealing. Annealing duration: 35 min.

-72-

Annealing temperatureGl .no annealinglil. BOOoC.. :900oC+ :1000oCx :1100oC

Fig. 6.3. Concentration profiles of a boron implantation with a dose of 1016 ions cm-2and an energy of 70 keY before and after annealing. Annealing duration: 35 min.

samples implanted with doses of 1014, 1015 and 1016 ions cm-2, respectively.The annealing temperatures were chosen in the range 700 oe up to 1100 oe.6.3.2. Concentration profiles as afunction of annealing time

To investigate the influence of the duration of the annealing process onthe concentration profiles, the samples implanted with doses of 1014 and1016 ions cm? and annealed at 800 oe, 900 oe and 1000 oe, respectively, wereadditionally annealed at these temperatures. It is found that within accuracylimits, during a second annealing stage of a period of 35 minutes at 800 oe nofurther change in the concentration profile occurs.

Results ofthe measurements after annealing at 900 oe and 1000oe are givenin figs 6.4 to 6.7.The influence of prolonged annealing is found from fig. 6.8 for the case of

an implantation dose of 1015 ions cm-2 and an annealing period of 21 hoursat 800 oe.6.3.3. Background-dope measurements

Boron was implanted into silicon at doses of1016, 1015 and 2. 1014 ions cm=",respectively. The natural-boron background concentrations were chosen inrelation to the implanted dose that is 2. 1020, 1019 and 5. 1018 atoms cm=",

,~~\

\~~

11.'\~~

~"~~~\\\\\~\..\\'~\\\

'10\"\+,\ '\ \" .10'7~--~----~-- __ L-__~~ __~ __~L- __ -L ~ L-__ --J

o 0·2 D-4. 0'6 0'8 1'0-Depth (pm)

Fig. 6.4. Concentration profiles of a boron implantation with a dose of 1014 ions cm-2and an energy of 70 keY, annealed one, two and four times at 900°C. Each annealing periodis of 35 min duration.

Fig. 6.5. Concentration profiles of a boron implantation with a dose of 1014 ions cm-2and an energy of 70 keY, annealed one and two times at 1000oC. Each annealing period isof 35 min duration.

--73 -

c : no annealingOl' Ix at 900°Cv :2xat 900 °C+ :4xat 900 °C

AMealingo : no annealing'" lx at 10000C'" ,2x.at 1000°C

-74-

Annealingo ,no annealing""lxat900oe.It.,2xat900oe+ , 3xat 9000e

- Depth (pm)

Fig. 6.6. Concentration profiles of a boron implantation with a dose of 1016 ions cm-2and an energy of 70 keY, annealed one, two and three times at 900°C. Each annealingperiod is of 35 min duration.

1021~--~ __ ~--~---r---r--~--~--~--.---r- __ -'---'---.-~

~;;::'~:::::::~.::::..",.. ...... ......iD" '.. ... ....

Q"... "', '+"+" ..

-, '\, , .•,>.,' ..

iD \ ''\\ \ '+,D, ''. \~. \ \,\ \ +,~ '. \., \ '

" \ '\\ \ 'tD, '. ' ...,'~ \\ \

10'7~__~ __~~~ __~~ __~ __~~-L __ ~~ __ ~ __ ~ __ _C~__ ~~ __ ~~~ __ ~\~·__ ~

o 0·6 o-s 1'0 1·2 1-4 1'6- Depth (pm)

Fig. 6.7. Concentration profiles of a boron implantation with a dose of 1016 ions cm-2and an energy of 70 keY, annealed one, two and three times at 1000oC. Each annealingperiod is of 35 min duration.

o , no annealingIll' Ix oriooo»:A ,2x at 1000oe• , 3x at 1000oe

I~\\I~'

,11 '\\,"fl 'I,--I' ~,..-t i-' \ ...,

;f .~.'\.- ,. ~ ," \ -,J ,~ ~\ ". '"~.~, '-\ .. ''\ \ -,\ ' ", .., \,'\ \ ...'. ' \• ., 4..

\,,_ \ ~.\ '-t 'l>.,\ \ ~\ ' \, b, l.~ '"10'7

0);-------"J\;-----;f-;-----"Oh.6:--=.--=--0;!-·8=-----:-:!1.0

- Depth (pm)Fig. 6.8. Concentration profiles of a boron implantation with a dose of 1015 ions cm-2and an energy of 70 keY for the cases: not annealed, annealed for 35 min and annealedfor 21 h at 800°C.

-75-

,020r-------,-----,- -,- -,- ---,

Annealinge ,no annealing.. , 35min at 800°C.. , 21h at 800°C

respectively, in order to facilitate comparison of the results. The slices were cutperpendicularly to a (1 1 1> direction and were implanted in a direction tilted14° to this axis. The samples were annealed at 300°C, 500 °C, 700°C, 900 °C,1000°C and 1100°C. One sample implanted with 1016 ions cm-2 was leftunannealed.In the case of the implantation dose of 1016 ions cm-2, llB+ ions were

implanted and the lOB isotope of the background dope was measured. At thelower doses, 10B+ ions were implanted and the liB isotope of the backgroundwas measured in order to avoid interference of the lOB+ and 30SP+ secondary-ion currents at these lower concentration levels.

Only those results are reproduced where distinct redistributions in the back-ground dope occurred. Figure 6.9 gives the concentration of lOB of the back-ground as a function of depth for the case of an implantation dose of 1016ions cm-2• Figures 6.10 and 6.11 givetheconcentration of liB ofthe backgroundas a function of depth for implantation doses of 1015 and 2 . 1014 ions cm-2,respectively.

Out-diffusion of boron to the surface may have influenced the back-ground dope level. In order to estimate the relative importance of this effecton the above measurements, the out-diffusion was determined from a back-ground dope profile of a silicon slice with a natural-boron concentration of

-76 -

1::~"'T=I~_:~'_' ~~ I..:!Ta!!!nn!!.:"':':1~10::::10~D,:::,c-j1

t ::l=A--- --------------------T~·,mm 'e

î '''[~,~----cT,,~nn!!..=-9-0-0-DC-------1101~

102f Tann= BOODC flOIsC: : :~ I I I ~

o W H H ~ M ~ ~ H- Depth (pm)

Fig. 6.9 Concentration of the lOB component of the boron background as a function ofdepth after implantation of llB with a dose of 1016 ions cm-2 and an energy of 70 keY,annealed at different temperatures Tonn•

o O~ 0·4. 0·5 D-'!-Depth (p.m.'

Fig. 6.10. Concentration of the llB component of the boron background as a function ofdepth after implantation of lOB with a dose of 1015 ions cm-2 and an energy of 70 keY,annealed at different temperatures Tonn•

10'9~~---- !ann=700DC

I I I I I I I

-

t ----- ----------to'S

tot J,J=--,--~~~~.~I I

o 0·2 0·4 0·5 0·8-Depth (pm)

Fig. 6.11. Concentration of the llB component of the boron background as a function ofdepth after implantation of lOB with a dose of 2.1014 ions cm-2 and an energy of 70 keY,annealed at different temperatures T.nn•

-77-

1020 ions cm- 3,which was annealed at 1000°C.The dose of out-diffusion is foundto amount to 5. 1013 lOB ions cm-2•

6.3.4. Concentration profiles of an implantation along an open crystallographicdirection

Figure 6.12 gives the concentration profiles of an implantation with a dose of1015 ions cm"? as implanted and when annealed at 800 oe and 900 oe, respec-tively. The silicon was grown by the floating-zone process and had a resistivityof 1000 .Q cm. The slices were cut perpendicularly to a (I 10) axis.

6.4. Discussion

6.4.1. General aspects

From the concentration profiles as given in figs 6.1 to 6.8 it is observed thatthe profile broadening due to annealing occurs in an irregular way. At low andintermediate temperatures the profile broadening in the tails of the profileappears to be much bigger than in the region ofmaximum boron concentration.This general behaviour can be considered to be due to the effectsof a relativelyimmobile boron fraction (situated in the region of maximum boron concen-tration) and a mobile fraction.At different doses the influence of the two fractions on the profiles is observed

at different temperatures. At high doses such as at a dose of 1016 ions cm? andafter annealing at an intermediate temperature (1000 "C) this behaviour is

· .......\\, ............ "

" A., À,

"'. ..l., \

\ ....~ '~

~~,

~

\.,,~\~'.,

10'7 o!:--,---:::'o.2::----'--~O·'-;-4-..---O-:::',6:::---,---:!-;:-,L------:-':l,O;:----'--71,2::---L-"'''''-71,4.';--,--:-'l,6'

-Depth (pm)Fig. 6.12. Concentration profiles of a boron implantation in a (1 10) direction before andafter annealing. Dose 1015 ions cm-zo Implantation energy 70 keY.

6.4.2. Precipitation effects

The immobile boron fraction mentioned in the preceding section consists ofprecipitated boron. This can be shown from the results given in figs 6.9 to 6.11.After annealing at temperatures in the range 700-1000 oe an increase of theboron background concentration is found at the mean depth of the implantedions, whereas in the neighbouring regions there is some decrease. From thisresult it is derived that boron has diffused to the area of high concentration,proving a strong tendency to precipitation of boron in this area.

Precipitation of the boron background in the implantation region can becaused by the following mechanism: Firstly it is supposed that silicon inter-stitials that are created during the implantation and are mobilized during theannealing process displace background boron from the substitutional lattice

-78 -

Annealing temperature",no annealing"'. eoo»:•• 900°C

'.io\\

~\...

lo

clearly observed (fig. 6.7). At a lower dose such as 1015 ions cm-2 this behav-iour is observed at 800 oe (fig. 6.8).

After annealing at high temperatures the immobile fraction disappearsresulting in a smooth broadening of the profile. This is observed e.g. at a highdose (1016 ions cm-2) after annealing at 1100oe (fig. 6.3). At lower doses(1014 ions cm-2) the same effect is already observed at 900 oe (fig. 6.1). In thefollowing sections the different aspects of this profile broadening will bediscussed in more detail.

-79 -

sites to interstitiallattice sites according to.the displacement mechanism sug-gested by Watkins 6-5). Secondly it is supposed that at a high concentration ofthese interstitials these will precipitate in cluster formation.The first supposition is supported by the boron-location measurements of

Fladda 6-6) and North 6-7) who found a decrease of the substitutional-boronfraction after annealing at 600°C and gave a similar explanation.The second supposition is sustained by transmission electron-microscopic

observations showing that the granular appearance of boron-implanted siliconis dissolved at increasing annealing temperatures into linear and loop defects,which are considered to be correlated with precipitates 6-3.4).

The displacement mechanism mentioned above can also be used to explainthe diffusion of the boron of the background dope (substitutional) to the precip-itation area. From the results given in figs 6.9 to 6.11 it can be derived thatthis diffusion occurs at a rate that is higher than is found in normal substitu-tional diffusion processes. An explanation of this effect may be that siliconinterstitials that diffuse from the implantation area, displace substitutionalbackground boron to interstitiallattice sites. Subsequently these boron inter-stitials diffuse to the implantatioh area and precipitate there or they mayrecombine with vacancies and become substitutional again.The precipitation effect of the boron background as well as of the implanted

boron is very pronounecd at the high implantation doses, such as at a dose of1016 ions cm-2 annealed at 1000°C (figs 6.9 and 6.7). A reason for thiseffect is that the maximum boron concentration at this implantation doseof about 1021 atoms cm-3 is higher than the boron solid solubility at 1000 °C:2. 1020 atoms cm-3 6-8). •

After annealing at 1100 °C no peak is found (fig.6.3). This means that dueto the relatively high diffusion coefficient of boron at 1100 °C the maximumboron concentration decreases below the level of the solid solubility so that theprecipitates are dissolved.This result is confirmed by the measurement given in fig. 6.9 where only a

small irregularity in the background is found at 1100°C.These precipitates might be boron compounds such as BN or SixB)Ior may

be pure boron. At the depth at which the peak occurred investigations intothe presence of boron compounds were carried out, by means of SIMS meas-urements. No evidence for compound formation was found within the limits ofdetection.Formation ofBN could be possible because annealing was done in a nitrogen

atmosphere. However, profile measurements on samples that were annealed inargon gave similar peaks in the profile and thus BN formation was consideredunlikely.

From transmission electron micrographs and diffraction patterns of precip-itates of boron implanted in silicon there are indications of the formation of

- 80-

SiB6, as is reported by Karatsyuba et al.6-9).Some information about the kind of precipitates mayalso be derived by

considering the ion yield of the boron in the region where precipitation occurs.To investigate this aspect we integrated the boron distributions as shown in:fig.6.9 to a depth where a constant concentration is reached. In the case ofequal ion yields of precipitated and substitutional boron this integrated boronconcentration should be equal to that of the original background concentrationintegrated to the same depth.This indeed is found to be the case, if annealing is done at temperatures up

to 900 oe. However, after annealing at 1000 oe the integrated boron concen-tration is found to be higher than the integral of the original background dope.This is attributed to an increase of the secondary-ion yield, caused by thereplacement of substitutional boron by boron precipitates or clusters. For thiscase an estimate of the increase in the boron-ion yield can be made. This isobtained from the results given in :fig.6.9 by assuming that the ion yield in thearea where precipitation occurred, has increased to the same amount. Moreover,the dose of the original background dope was corrected for the dose of out-diffusion as found in sec. 6.3.3.In this way it was calculated that the ion yield, in the area where precipitation

occurs, is enhanced by 30%. An enhanced ion yield was also reported in sec.3.5.11 where we observed for SiB4 or SiB6 a much higher ion yield ofthe boronthan of boron on substitutional lattice sites in silicon. From the similarity inthese results we derive a further argument to suppose that the precipitatesconsist for some part of boron-silicon phases.A consequepce of the enhanced ion yield in the region of maximum

boron concentration is that the boron distribution, as presented in :fig. 6.7for Tann = 1000 oe, will differ from the real boron distribution. The dose in thepeak ofthis distribution should be lowered by about 30% as is calculated above.This was checked by applying such a correction factor to the distribution as

mentioned in sec. 3.5.10 where after annealing at 1000 oe the apparent totaldose was calculated (table 3-1). Now, with a correction applied, the corre-spondenee ofthe total apparent doses as given in table 3-I for different annealingtemperatures is found to be within 4%.A further check on this effect is obtained if we make use of the fact that the

secondary-ion current of BO- ions is about the same for boron in boron-siliconcompounds and for boron in boron-doped silicon (sec. 3.5.11). Indeed, if werepeat the measurement of the boron distribution presented in :fig.6.7 forTarin = 1000 oe by detecting BO- ions we :finda distribution with a peak heightwhich is about 30 % lower than is shown.·At doses < 1016 ions cm-2 or at annealing temperatures < 1000 oe no

increase of the ion yield was found, although in these cases, too, precipitationofthe boron occurred (:figs6.10 and 6.11). We do not understand this difference

- 81-

but perhaps an excessive clustering of the boron precipitates in the high-dosecase annealed at 1000oe is a requirement for this effect.

6.4.3. Transient diffusion effects

The mobile boron fraction gives profile broadening at relatively low anneal-ing temperatures (figs 6.1 to 6.3). At the lower doses this appears to occur at700 oe whereas at the higher doses this effect is observed at somewhat higherannealing temperatures, such as 800oe. More evidence on this diffusionprocess is obtained from profile measurements carried out after different anneal-ing times. A general observation from the results given in figs 6.4 to 6.8 is thatthe diffusion rate is high at the beginning of the annealing process.One reason for such an effect may be an enhancement of the substitutional-

type diffusion process by vacancies released during removal of the crystalimplantation damage.Another reason may be that the interstitial fraction of the implanted dose is

responsible for this behaviour. The mechanism would then be an interstitial-type diffusion process at the beginning of the annealing period. The fast profilebroadening will be stopped either by a transition of the boron to substitu-tionallattice sites or by trapping of the boron at defects.In order to verify both suppositions, the annealing behaviour of an implanta-

tion in an open crystallographic direction is of interest because the crystaldamage is relatively small in the case of a channelled implantation, as wasfound from back-scattering measurements 6-10). In this way the probability ofdiffusion being enhanced by vacancies is reduced. Yet, as appears from fig. 6.12,the channelled implantation, too, shows a high diffusion rate. A diffusionprocess enhanced according to the first-mentioned supposition seems thereforeunlikely.Some evidence about the diffusion mechanism can also be obtained from a

comparison of a boron concentration profile and a corresponding charge-carrier concentration profile as determined from electrical measurements. Asis reported in chapter 7, we conclude from a divergency between the tails ofthe two profiles that there is boron on interstitial lattice sites. Thus thisresult also gives some support to the supposition that the initial profile broaden-ing is due to an interstitial-type diffusion. However, more-definite argumentsare needed, possibly from detailed boron-lattice-location measurements.The initial profile broadening is temperature-dependent. This is observed

from fig. 6.1 where it appears that the implantation profile that was annealedat 800 oe appears to have a somewhat larger width than the one that wasannealed at 900 oe. This means, accepting the above-mentioned diffusionmechanism, that the interstitial diffusion range. decreases with the annealingtemperature in the low-dose case.

- 82-

6.4.4. Profile broadening after prolonged annealing

It is expected that after prolonged annealing or at high annealing temperaturesthe profile broadening will occur with a similar diffusion coefficient as is foundin normal thermal diffusion processes.

In order to verify this, the diffusion coefficients were determined for theimplantation doses of 1014 and 1015 ions cm-2 at different annealing tempera-tures. This was done by calculating a concentration profile N(x, t) from anexperimental unannealed profile as a function of depth x and annealing time tusing the formula 6-11)

1 Joo (-(~ - X)2 -(~ + X)2)N(x, t) = N(~, 0) exp + exp M (6.1)

2 (n D t)1/2 4 D t 4 D to

where N(~, 0) is the initial distribution and D is the diffusion coefficient.Several profiles were calculated assuming, in turn, different values for the

diffusion coefficient. The diffusion coefficient was then taken as that value forwhich optimum fitting between the calculated concentration profile and theexperimental annealed one was obtained. D is found in this way with an ac-curacy of about 10%.Formula (6.1) applies to the case where the surface of the substrate can be

considered as a reflecting boundary for the boron atoms. This assumption isjustified by the small dose that is found to diffuse to the surface (sec. 6.3.3).Calculations were done numerically using the Hermite-Gauss quadratureformula.The diffusion coefficients D that were calculated for annealing temperatures

of 900 to 1100 °C are given in columns 2 and 3 of table 6-1. The fifth columngives diffusion coefficients that were derived (partly. by extrapolation) fromresults obtained by Kurtz 6-12) using a p-n-junction method on thermallydiffused layers.Our diffusion coefficients at 1100 °C correspond to those given by Kurtz but

at 900 and 1000 °C our values are higher. The discrepancy at 900 and 1000 °Cis explained by the greater influence of the initial fast diffusion as mentioned inthe previous section. This was checked by using in formula (6.1) for N(~, 0) adistribution which had been already annealed for a period of 35 minutes and byfitting N(x, t) to a profile that was annealed 4 times for 35 minutes. Theseresults are given in the fourth column of table 6-1.A better agreement with thevalues of Kurtz is now obtained.

In the fourth column, also, a value of D for annealing at 800°C is given.This value is derived from concentration profiles that are obtained after anneal:ing for periods of 35 minutes and 21 hours at 800°C (fig. 6.8). In this case a

~ 83-

TABLE 6-1

Diffusion coefficients as a function of the annealing temperature calculatedfrom annealed profiles with the use of an initial distribution N(~, 0) that is notannealed and annealed, respectively. For comparison diffusion coefficientsderived from the results of Kurtz 6-12) are given

D (cm" S-l)anneal-

N(;, 0): not annealeding N(~, 0): from Kurtz ..temp. distribution annealed

CC) dose: dose: distribution

1014 ions ern"? 1015 ions cm-2

800 1'5.10-15 5·2 . 10-16 (extrapol.)

900 1.7 . 10-14 1.4.10-14 1.4.10-15 1·3 . 10-15 (extrapol.)

1000 4.8.10-14 5.2. 10-14 1.8. 10-14 1.7 . 10-14

1100 1.9.10-13 1.5.10-13 1.7.10-13

good correspondence to the measured profile was obtained by assuming animmobile fraction of 80 % and a mobile fraction of 20 % of the total dose(fig.6.13).

From these results it is concluded that at doses of 1014 and 1015 ions cm-2

after the initial fast diffusion process a substitutional-type diffusion prevails,as is found in thermal diffusion of boron into silicon.

At high implantation doses, such as at a dose of 1016 ions cm-2, the shapesof the tails of the profiles that are obtained after annealing at 1000 or 1100 oediffer considerably from those of the more or less Gaussian tails that werefound at the lower doses. However, they are in agreement with those found athigh-dose thermal diffusion of boron into silicon 6-8). They are typical forcases where the boron concentration is limited by the boron solubility and aredue to a concentration-dependent diffusion rate. Similar shapes were foundfrom calculations e.g. by Thai 6-13).

(1) From the profiles obtained after annealing, it is observed that a relativelyimmobile boron fraction exists in the region of high boron concentration.From an investigation. of the influence of a boron implantation on a boron

6.5. Conclusions

The profile broadening during annealing is determined by three groups ofboron atoms, each with its own mobility.

- 84-

1020r---~r---~----~-----r----r----~----.-----r-----r----'lil ,35min annealed at 800 oe.. ,21 h annealed at 800 oe

_ , calculated

\\

'Ia\

\",'s,'...'~

'~'ot.".'.,

-\."m,

.,, "Ill" :\,"\.,

la 17!;----__JL..._---t:;-- __ -L -;!-; -'- __ --:f::- .l...'.::.'" --~l::-----L..._----:-lo ~ N H ~- Depth (pm)

Fig, 6.13. Concentration profile of a boron implantation (dose 1015 ions cm-2, energy70 keY) annealed for 21 h at 800 oe in comparison with a profile that was calculated froman experimental profile that was obtained after annealing for 35 min. The calculation wasperformed with an immobile boron fraction of 80% and it mobile boron fraction of 20 %of the total dose.

background dope it was concluded that this immobile fraction consists ofboron precipitates that were created during the annealing process.At lower doses (1014 to 1015 ions cm=") the influence of the precipitates on

the annealing behaviour is observed at 800°C (fig. 6.8) whereas at 900°C theseprecipitates are dissolved.At high doses (1016 ions cm-2) excessive precipitation occurs due to the fact

that the implanted-boron concentration exceeds the solid solubility. Theseboron precipitates are best observed after annealing at about 1000°C. Theyare responsible for the peaks in the profiles given in fig. 6.7. The ion yield of theboron in these peaks is on average 30% higher than of boron on substitutionallattice sites. Due to the thermal diffusion of boron from the area of high con-centration, erosion of the precipitates occurs. Complete dissolution is obtainedwhen the maximum concentration level comes below that of the boron solidsolubility. This situation is reached after annealing at 1100 °C for 35 min as isobserved in fig. 6.3. The boron precipitates are assumed to be formed byclustering of boron interstitials and to consist of boron-silicon compounds.

(2) At the beginning of the annealing process the mobile boron fraction showsa fast diffusion effect. This is assumed to be due to the diffusion of boron inter-

- 85

stitials. This process stops after a diffusion range of about 0·1 {Lmeither bytrapping at defects or by a transition to substitutionallattice sites.The boron interstitials are formed during the implantation or may be created

during the annealing process by the displacement of substitutional boron bysilicon interstitials (mechanism suggested by Watkins).This fast diffusion effect during the intitial stage of the annealing process is

best observed on profiles that are obtained after successive annealing periodsat the same temperature (figs 6.4 to 6.8).

(3) After the fast broadening of the profile the diffusion rate is slowed down.From the concentration profiles obtained after prolonged annealing diffusioncoefficients were derived that agree with those found from studies on thermaldiffusion of boron in silicon. From this fact it is concluded that, after the initialbroadening, a substitutional-type diffusion prevails. In the case of high doses,such as at 1016 ions cm=", the diffusion process is strongly concentration-dependent.

REFERENCES6-1) S. Wagner, J. electrochem. Soc., solid State Scienceand Technology 119, 1570, 1972.6-2) W. K. Hofker, H. W. Werner, D. P. Oosthoek and H. A. M. de Grefte, in

B. L. Crowder (ed.), Proc. int. conf. on ion implantation in semiconductors and othermaterials (Yorktown Heights 1972), Plenum Press, New York, 1973, p. 133.

6-3) R. W. Bicknell and R. M. Allen, Rad. Effects 6, 45, 1970.6-4) L. T. Chadderton and F. H. Eisen, Rad. Effects 7, 129, 1971.6-5) G. D. Watkins, Proc. 7th int. conf. on the physics of semiconductors (Paris-Royau-

mont 1964),Academic Press Inc., New York, 1964,vol. 3, p. 97.6-6) G. Fladda, K. Björkqvist, L. Eriksson and D. Sigurd, Appl, Phys. Letters 16,

313, 1970.6-7) J. C. North and W. M. Gibson, Appl. Phys. Letters 16, 126, 1970.6-8) G. L. Vick and K. M. Whittle, J. electrochem. Soc., solid State Science and Tech-

nology 116, 1142, 1969.6-9) A. P. Karatsyuba, V. I. Kur in ny, S. V. Rytehkova, T. P. Timashova and

V. V. Yudin, Proc. int. conf. on radiation damage and defects in semiconductors(Reading 1972), Inst. of Physics, London-Bristol, 1973, p. 81.

6-10) F. H. Eisen, B. Welch, J. E. Westmoreland and J. W. Mayer, in D. W. Palmer,M. W. Thompson and P. D. Townsend (eds), Proc. int. conf. on atomie collisionphenomena in solids (Brighton 1969), North-Holland Publishing Co., Amsterdam,p. 111.

6-11) B. I. Boltaks, Diffusion in solids, Infosearch Ltd., London, 1963, p. 102.6-12) A. D. Kurtz and R. Yee, J. appl. Phys, 31, 303, 1960.6-13) N. D. Thai, J. appl. Phys, 41, 2859, 1970.

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7. BORON IMPLANTATIONS IN SILICON: A COMPARISON OFCHARGE-CARRIER AND BORON CONCENTRATION PROFILES

AbstractThe concentration profiles of boron implanted in silicon were measuredusing secondary-ion mass spectrometry. The accompanying charge-carrier profiles were determined by Hall-effect-sheet-resistivity measure-ments combined with layer removal by anodic oxidation and etching.From a mutual comparison of these profiles an electrically inactiveboron fraction is found to exist in the region of maximum boron con-centration. This fraction can be correlated with boron precipitates. Inhigh-dose implantations the precipitates still exist after annealing at1000oC. In the tail of the profile a small electrically inactive boronfraction is observed. This fraction is correlated with fast-diffusing inter-stitial boron. Near the surface a charge-carrier peak is found that canbe correlated with the damage caused by the implantation. The inter-pretation of the observed electrical effects is facilitated by investigationson boron concentration profiles of layers implanted with different dosesand annealed in accordance with different time-temperature schedules.

7.1. Introduction

Information on the electrical behaviour of implanted ions can be obtainedby comparing the concentration profiles of the impurities with those of thecharge carriers. In this chapter this is discussed for the case of boron implantedin silicon. With SIMS we measured concentration profiles of boron implantedat doses of 1014, 1015, 1016 ions cm-2 and at an energy of70 keY. These sam-ples were annealed at 800, 900 and 1000oe in order to correlate the electricaleffects with the typical aspects found in the concentration profiles after anneal-ing in this temperature region, as is reported in chapter 6.The electrical profiles were obtained with Hall-effect-resistivity meas-

urements combined with stripping of the implanted layer by anodic oxidation.Sectioning by anodic stripping of implanted layers has been studied by severalauthors 7-1.2.3). However, we came to the conclusion that for a reliable fittingof the SIMS profile to the electrical profile, the influence of the implantationdamage and the boron concentration on the thickness of the removed layersneeded further investigation. Details of this work are given in sec. 7.2.

7.2. The measurement of charge-carrier conncetration profiles

7.2.1. Theory of the Hall-effect-resistivity measurements

The sheet conductivity as and the Hall-effect voltage from which the sheetHall coefficient R, is derived have been measured. For a layer with a chargeconcentration inhomogeneous in depth (x) and one charge-carrier type pre-dominating, these values can be expressed in the depth-dependent charge-carrier concentration p(x) and the concentratien-dependent relaxation time of

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the charge carriers 't'p(x) as 7-4)

q2o's(x) = - J p(x') ('t'ix') dx',

mpx

1 f p(x') ('t'/(x') dx'R.(x) = __ x _

q ( co )2/ p(x') ('t'ix') dx'

where q is the electronic charge, ('t'p(x') and ('t'/(x') are the respectiveweighted averages of 't'ix') and 't'/(x') over the Maxwell-Boltzmann distri-bution at position x' and mp is the effective mass of a hole.

By differentiation of these equations the following expressions are found forthe Hall mobility f-lH and the electrical-charge concentration p(x):

q ('t'/(x) d[R.(x) O'/(x)]fdxf-lH(X)= - = ,

mp ('t'p(x) dO'.(x)fdx

1 ('t'/(x) [dO'.(x)fdx)]2p(x) = - --- ------

q ('t'p(X)2 d[R.(x) O's2(x)]fdx

The Hall factor r = ('t'/(x)f{'t'p(x))2 = f-lHff-lc is found experimentally undernon-degenerate conditions on Ga-doped silicon to be R:J 0'77-5). For thedegenerate case r ~ 1 is derived by theoretical considerations 7-6). For con-venience we use the approximation r = 1 in the following calculations.

In the case of finite thickness of the removed layer (zlz), the average valuesfor f-lH and p in the ith layer are

and

(R, 0'/), - (R, O's2),+ 1(PH)' = -------

(O's)'- (0'.)1+ 1

1 1 [(O's)'- (O's)'+1r(p),=- -- .

q (zlx), (R. 0'/), - (R; 0'/)'+1

With the relative errors in zlx : Cl1,in as : Cl2and in R. :Cl3it can be derivedfor the relative error in (P), that

In this expression the coefficients

(7.1)

(7.2)

(7.3)

(7.4)

(7.5)

(7.6)

-·88 -

were calculated for the profile measurements given in sec. 7.3.On average it was found that the value of these coefficients may be as high

as 40 at the first steps of the measurement, whereas at the tail of the profile thevalue was about 1. The relative errors (2CT definition) <51, <52 and <53 were foundfrom repeated measurements to be 1, 0'15 and 0'5%, respectively. Consequentlythe relative error at the first steps in the measurement can be as high as 50%.In the results given in sec. 7.3 for a single case, the error in the concentrationis indicated by error bars (fig. 7.2b). The nominal values of (P)l and (}tH)l givenin the figures 7.2-7.6 were calculated from values of CT. and R. derived fromsmooth curves drawn through the measuring points of CT. and R. in order toreduce the error mentioned above.

For the interpretation of the charge-carrier distributions we assume thatboron on substitutional lattice sites is ionized at room temperature. This istrue for a non-degenerate case if the boron concentration is < 1017 cm-3 aswe derived from computer calculations (ionization energy of boron: 0·045 eV).Also in the case of degeneracy, occurring at boron concentrations> 1019, complete ionization can be expected. In the region of concentrations> 1017 cm-3 and < 1019 cm-3 the ionization may be incomplete. However,we verified by calculations that in this region the boron fraction that is notionized, is relatively small due to a decrease of the boron ionization energy withthe concentration 7-7).

7.2.2. The-Hall effect-sheet-resistivity measurements

Boron implantations were done in silicon with a high resistivity (approx.16000n cm) providing adequate insulation of the implanted layer. This waspreferred to the often used p-n-junction insulation of the measured layerbecause problems inherent in the p-n-junction method, such as depletion effectsand leakage-current problems 7-8) were prevented, particularly in the meas-urement of the tail of the profile. The annealing treatment caused some decreasein bulk resistivity. However, this effectwas small enough to have no effect on thedetection sensitivity. The contacts on the sample were' applied in the Van derPauw configuration (fig. 7.1a). The dimensions of the sample were large incomparison with the diffusion length of the minority charge carriers, which, ifinjected at the contacts, will have a small effect on the measurement.After each layer-removal step a low and reproducible surface-state concen-

tration was obtained by rinsing the slice in methanol and waiting for 1 h beforethe measurements were performed. The surface-state concentration amountedto 5 . 1010 charge carriers/cm", making it possible to measure charge-carrierconcentrations as low as 1016 cm=".

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The Hall-effect-resistivity measurement apparatus was automatically con-trolled to measure the Hall-effect voltage with two polarities of the magneticfield, two polarities of the current and at two different contact pairs (MO andNP, fig. 7.1a). By averaging the 8 Hall-effect voltages obtained, not only are theinfluence of misalignment, thermo-electric and contact effects minimized, butalso that of possible inhomogeneities in the implanted layer. Similarly theVan der Pauw resistances are measured with two current polarities and at twodifferent contact pairs (MN and MP, fig. 7.1a).

Region for SINSmeasurements

Ion-irrplanted region

Contacts:I) implanted with 8(70keV, IO,scm2)

2)Al evaporatedand baked (520OC)

a)

Light

ruunPt electrode

b)

Fig. 7.1. (a) Silicon sample with electric contacts. (b) Set-up for anodic oxidation.

In a single case (fig. 7.2b) the SIMS measurements and the electrical meas-urements were performed on the same slice. In this case a separate implantedregion on the slice was reserved for the SIMS measurements (fig. 7.1a).

7.2.3. The layer-removal technique

Preferably, the thickness of the removed layer should be independent of theboron concentration and of the crystal damage caused by the boron implanta-tion. The relative influence of these effects was investigated by implanting asilicon slice through a gridded mask and by measuring the difference in heightwhich may arise between the implanted and the non-implanted regions duringthe layer-removal process. After several trials it was found that the method of

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anodic oxidation in a bath of composition N-methyl acetamide, KN03 andH20 with weight ratios 100 : 1 : 2 followed by removal of the oxide layer ina buffered etch (HF 48 %, NH4F in volume ratio 1 : 10) was the most suitable.Therefore this bath, introduced by Schrnidt and Michel 7-9) and discussed inrefs 7-3 and 7-10, was investigated by us in more detail.

Other oxidation treatments investigated, such as oxidation inH3B03-Na2B4077-2), in boiling HN03, or in H202 followed by etching, ordirect etching in HN03 and 0'5% HF, were found to show a distinct influenceof the crystal damage on the removed-layer thickness and were dropped forthat reason.

Anodic oxidation was done in a set-up shown in fig. 7.lb. An importantfeature of this unit is that the rear contact is made by a mercury bath making itpossible to achieve a good electrical and thermal contact during the anodicoxidation process, whereas during the Hall-effect-resistivity measurements thiscontact is automatically removed' as required to prevent short-circuiting of thehigh-ohmic substrate. The rear side of the silicon sample was lapped. Thisimproves not only the electrical contact during the anodic oxidation process,but also gives a low electrical-surface-charge density 7-11). Anodic oxidationis performed with a stabilized current-voltage supply. The process starts witha stabilized current density of, typically, 6 mA cm-2 but as soon as an ad-justed voltage of, typically, 140 V is reached, this voltage is stabilized whereasthe current decreases. We terminate the process as soon as the current dropsbelow 5% of the original value. The thickness of the oxide layer has thenreached a saturation value typical of the material investigated. With thisprocess a uniform oxide layer is formed. For each oxidation step a fresh bathwas used to prefent differences in the removed-layer thickness due to changesin the water content as a consequence of the hygroscopic nature of the bath.

Crystal damage caused by boron implantations was not found to influencethe thickness of the removed layer. The boron concentration, however, hassome influence, as was measured on silicon samples which were homogeneouslydoped with boron. It was found that the thickness of the removed layers in thecase of silicon with a boron concentration of 1020 atoms cm- 3 was about 10%less than of silicon with a boron concentration of 1012 atoms cm-3. An averagethickness of the removed layer was determined therefore for each profile meas-urement. This thickness was found by first measuring the thickness of layersremoved from non-implanted silicon (typically 405 A ± 4%) and then correct-ing this value for the influence of the boron. This correction was found bymeasuring the height difference between the implanted and non-implantedregions (fig. 7.1a) of a stripped sample after a profile measurement was finished.

7.3. Experimental results

Figures 7.2, 7.3 and 7.4 give the concentration profiles of boron and the

Fig. 7.2. Concentration profiles of boron (dots) and corresponding charge-carrier profiles(circles with dots) obtained after annealing at different temperatures T.nn• Implantation dose1014 ions cm-2, implantation energy 70 keY.(a) T.nn = 800°C. Points indicated by cross in circle are measured using thin-layer stripping(anodic-oxidation voltage 30 V). (b) T.nn = 900°C. The measuring points of the charge-carrier concentration are provided with error bars. (c) T.nn = 1000 °C.

- 91-

10'8

I I

~ -

f -l- .... 7äm=800oC.e ••0·~0 00

.$'"0 .e ••

~ «; . -a· •0 •.0 ..

l- . -0 ...

I I I I

~~~~~? 'ti- 7änn=900oCf . . ~l'l. .~ -.~.~.~.I- ~.. -..

~ .I I I

.··0·0·&·00·d~o 0t1. Tann =TOOOoc

ta Ill.~ -.0.e.

0-.I- 0. -....

I c}

a}

b}

0'2 0'6 0-8---Depth (pm)

T'O

-

- 92-

1020' ,......-,---,--,--,---,.---y---.--,---r--r--,...

-

-(;) .

;;;- .(;) ,

IEo ,~

c:: 10'7 I- -:g_gc:: oculJ a)8 10'6

••~·0·è.,ë·(;) <i1~.G 0 7änn=9000C

1019 ~~ 0, -/!l,Q

'qQ,

10'8 r- e. -0,,o ," ,

10'7 r-,, -

o

10'5 I I Ib)

-

-' ....,

10'6 !---'---f:::---''----;}-;---'----;:!L;;-----1-----,-f:::---'--;J,;----l c)o 0'2 0'4 0·6 0'8 1'0- Depth(pm)

Fig. 7.3. Concentration profiles of boron (dots) and corresponding charge-carrier profiles(circles with dots) obtained after annealing at different temperatures T.nn• Implantation dose1015 ions cm-2, implantation energy 70 keY.(a) T.nn = 800 -c, (b) T.nn = 900°C. (c) Tann = 1000oC.

- 93-

1010 ee

o 0o..'e Tann=80o"C

o 0 0 o1019 t- " .

co 0 ö.

" ."."'0

o

e

10'0"Gm =9000C

1019 t-

."10'" l-

"e'""

" .

"

-

-

-

-

-

-

-

1016 I---'---'-----'--l---'---'----~_l_ _ _'__ _'____..__I b)

. 16 L_-'---:!'::----'--:!-.;--~-_f:,---~__,f::_--.---:':__-'--____:' c)10 ij 0-2 0,' 0·6 0'8 1·0 1'2

-Deplh(pm)

Fig. 7.4. Concentration profiles of boron (dots) and corrrsponding charge-carrier profiles(circles with dots) obtained after annealing at different temperatures Tann• Implantation dose1016 ions cm-z, implantation energy 70 keY.(a) Tann = 800°C. (b) Tann = 900°C. (c) Tann = 1000oC.

.'

10'0

e.<l.Q.o.o·o 0 0 0 ~<> 0 0

.•• '. ~.~ !J.o 0

". ~.~ p." Tann=IOOOoC'D'0

1019 t-

o ;10'"l-

-

-

-

-

- 94-

corresponding profiles of the charge carriers as measured on slices, implantedwith doses of 1014, 1015 and 1016 ions cm"? and annealed at 800, 900 and1000 oe. The implantations were carried out at room temperature with animplantation energy of 70 keY ± 2% along a (763) crystal direction. Thisdirection was chosen to diminish the chance of channelling. The implantationsin this direction were facilitated by cutting the slices perpendicular to thisdirection. Annealing was done in a nitrogen atmosphere for 35minutes.

Figure 7.5 gives the concentration profiles for implantations in a (I 1 0)crystal direction. Annealing was done at 800 oe and 900 oe.

Figure 7.6~givesa collection of the Hall mobilities found in the above-men-

1020 r----,.-..,,---r-....-,--,--.--,........---.----,.----....--.----,.---.---,

............... . ..... -

-e ..e

. -

-

-

10'7 !- .. -o

Fig. 7.5. Concentration profiles of boron (dots) and the corresponding charge-carrier profiles(circles with dots) after implantation in a (1 10) direction. Implantation was performed ata dose of 1015 ions cm-2 and an energy of 70 keY.(a) Annealing temperature 800°C .. (b) Annealing temperature 900°C.

- 95-

tioned measurements as a function of the charge-carrier concentration. Forcomparison, the Hall mobility of the holes, as found from measurements onhomogeneously doped p-type silicon 7-12), is also indicated in this figure.

The systematic deviations between the charge-carrier and the boron distri-butions observed in the different regions of the distributions will be discussedin the following sections.

lr1,r----r----.--.,--,-.,---,----.-.-r-.--.,----,--.-,-,.--.,---.,

101O

!,,17;----'----''--..L_..L...!,0'''s,----L...---'--''-''-j-l;O'"'9 -..L_---'---'L...J.-10L,;;--.L_-...J

---- Charge-carrier concentration (cm-J)

Fig. 7.6. The Hall mobilities found in the profile measurements given in figs 7.2 to 7.5 as afunction of the charge-carrier concentration. The measuring points indicated by figures con-cern mobilities in the surface region of the profiles. In the figure the Hall mobility derivedfrom bulk data is indicated 7_12).

7.4. Discussion

7.4.1. The region of maximum boron concentration

The integrated electrical charges obtained from the profile measurementsmentioned above are given in table 7-1.

From this table it is found that, after annealing at 800 oe, the integral relativeelectrical activity, defined as the integrated electrical charge related to theimplanted ion dose, decreases with this dose. It is also found that at a dose of1016 ions cm-2 annealed at 900 oe or 1000 oe no complete electrical activity isobtained. The charge-carrier doses as given in table 7-1 exceed the implantedboron dose in some cases. This may be due to the fact that the Hall factor rdeviates from 1, whereas a deviation in the implantation-dose measurementmayalso be of influence. Furthermore electrically active states near the surfaceform a part of the integrated electrical charge (see sec. 7.4.3).

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TABLE 7-1

Total electrical charge-carrier concentration (cm=") as a function of implanta-tion dose (cm="), annealing temperature (Tann) and implantation direction

implanted implantation total electrical dose (cm=")boron dose direction(ions cm=ê) Tann = 800 oe Tann = 900 oe Tann = 1000oe

,

1014 (763) 1·4 . 1014 1·2 · 1014 1·1 . 1014

1015 (763) 0·26. 1015 1·1 · 1015 0·97 . 1O~51016 (763) 0·17 . 1016 0·43. 1016 0·91 . 10161015 (110) 0·40. 1015 1·2 · 1015

By comparing the charge-carrier distributions with the corresponding borondistributions as given in figs 7.2-7.5 it is found that a large deviation betweenthe boron and the charge-carrier distributions is found in the region of maximumboron concentration. Therefore we conclude that a relatively low concentrationof electrically active centres exists in this region. This is very pronounced for ahigh dose such as 1016 ions cm-2 annealed at 900 oe or 1000oe (figs 7.4b and7.4c). A similar effect, although on a smaller scale, is observed at a lower dosesuch as 1014 ions cm-2 annealed at 800 oe (fig. 7.2a).In chapter 6 we postulated a model to explain the effects observed on the

boron distributions as measured by SIMS. Here we will use the same model toexplain the electrical behaviour.

From the results presented in figs 7.2-7.4 it is observed that the electricallyinactive boron fraction in the region of maximum concentration coincides withthe immobile boron fraction mentioned in sec. 6.4.2. Therefore we can correlatethis electrically inactive fraction with boron precipitates.

From the figures it is also observed that the difference between the charge-carrier and the boron concentrations in the region of maximum boron concen-tration increases with the implantation dose. This is attributed to the fact that,in the region of high boron concentration, the phenomenon of precipitationprevails over the process in which boron atoms become substitutional due tovacancy trapping. The high probability of the precipitation process can beunderstood from the following rough consideration.

Suppose a precipitant requires n boron atoms. The .probability of formationof precipitants will in that case be proportional to [B]" where [B] is the boronconcentration relative to the atom concentration of the matrix. For precipitants

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consisting of boron-silicon compounds, such as SiB4 or SiB6, n will be 4 or 6,respectively. Consequently, the concentration of precipitants will increasestrongly with the boron concentration. This is also due to the fact that theprobability of the competing process, trapping of the boron atoms by vacancies,is not increased at high boron concentrations.

For the doses of 1014 and 1015 ions cm-2 almost all the boron atomsare electrically active after annealing at 900°C (figs 7.2b and 7.3b). Thisis not the case at a dose of 1016 ions cm-2 (fig. 7.4b). At this dose theelectrically inactive boron found after annealing at 900 or 1000 °C is due tothe implanted-boron concentration exceeding the boron solid solubility insilicon (at 1000 °C: 2 . 1020 ions cm-3 7-14)). The rate at which the precipitatesare dissolved is, in this case, determined by the thermal diffusion velocity ofthe boron from the area of precipitation. Annealing for either a longer periodor at a higher temperature is required in order to fully activate the boron.The boron concentration profiles of implantations along a (1 1 0) direction

show two maxima (figs7.5a and 7.5b) as can be expected from the channellingeffect (sec. 5.3). From the profiles offig. 7.5 it is found that the relative electricalactivity at the two maxima is about the same. From this result it can be con-cluded that the crystal damage caused by the implantation and which isexpected to be larger in the neighbourhood of the first maximum does notaffect the electrical-activation process much. This may be understood from thefact that the damage in the case of an implantation in a channelling direction isrelatively small 7-15). In the second place the way in which stopping is effectedappears to be of no great influence. This may be understood from the fact thatalso in the case of channelling dechannelling occurs due to nuclear collisionsat the end of the particle range. Consequently it can be expected that at bothmaxima the position of the boron atoms will be similar. Atomic-locationexperiments are needed to verify this more thoroughly.

7.4.2. The tail region of the profile

It is observed from figs 7.2 to 7.5 that the charge-carrier profiles in the caseof annealing at 800 °C extend to somewhat slighter depth values than do theboron profiles. Furthermore it is found that the concentration gradient of thecharge-carrier profiles in the deeper tail region aftér annealing at 800 or 900 oeis somewhat higher than of the boron distributions.A check was carried out to see whether this effect is to be attributed to a low

resolution in depth of the SIMS method. This was done by measuring theprofile of a steep, shallow, thermally diffused boron layer (diffusion was carriedout at 900 oe for 5 minutes). Itwas found that a difference in concentration bya factor of 10 occurring to within 200 A could be recorded. In our case we aredealing with slopes which are 5 times less steep. Consequently, such a limitationof the SIMS method could not be of influence in our case. Therefore we con-

- 98-

elude that the effects mentioned above are due to boron atoms that are elec-trically inactive. We assume that these boron atoms belong to the mobile frac-tion that causes the fast broadening of the profile during the annealing process,resulting in the shoulders of the profiles as discussed in sec. 6.4.3. The argumentfor this assumption is that the high mobility as well as the electrical inactivityof the boron atoms can both be attributed to the same effect, that is to aninterstitiallattice location of the boron atoms. From the results given in figs 7.2to 7.4 it is observed that the electrical inactivity in the tail region is a relativelysmall effect, especially for the samples annealed at 900°C or 1000 °C. This isexplained by the fact that during annealing for 35 minutes most of the boronatoms in the tail region moved to substitutionallattice sites (sec. 6.4.4).

7.4.3. The profile near the surface.

After annealing a dose of 1014 ions cm-2 at 800°C the charge-carrier con-centration near the surface exceeds the boron concentration (fig. 7.2a). It isverified by stripping off thin layers (voltage of the anodic oxidation process:30 V) that this effect extends over a region of about 600A near the surface. Inthis region the mobility of the charge carriers is low (point 1 in fig. 7.6). Afterannealing at 1000°C this effect has disappeared (fig.7.2c). At a dose of1015 ions cm-2 a similar effect is observed (fig. 7.3a). This is also the case witha dose of 1016 ions cm-2; however, after annealing at 1000 °C the increase inthe charge-carrier concentration has not completely disappeared (fig. 7.4). Thecorresponding mobilities are given in fig. 7.6, point 2 for a dose of 1015 ions cm-2annealed at 800°C, and points 3 and 4 for a dose of 1016 ions cm-2 annealed at800 and 900°C, respectively. With a channelled implantation this effect isrelatively small (fig. 7.5).From these observations we conclude that this effect is correlated with

crystal damage caused by the implantation. Electrically active defects entailedin implantation damage may cause the observed electrical activity near thesurface. We assume that these defect clusters are collected at the surface andextend locally into the interior of the silicon. The large number of neutral andcharged scattering centres (which may exceed the effective charge-carrier con-centration due to compensation effects) explains the low mobility in this region.It is expected that more-definite information about this effect can be obtained

from charge-carrier-distribution measurements performed on samples that areannealed at temperatures lower than 800°C.

7.5. Conclusions

By comparing the boron and charge-carrier concentration profiles it is foundthat the relative electrical activity in the region of maximum boron concentra-tion depends on the dose. In this region, for instance, the relative electricalactivity of a dose of 1014 ions cm? annealed at 900 °C is about 100% and that

-99 -

of a dose of 1016 ions cm-2 annealed at the same temperature or at 1000 oe isabout 10%. The electrically inactive boron fraction is correlated with animmobile boron fraction, consisting of boron precipitates.A limited electrical activity is also found in the tail region of the profile,

particularly if annealing occurred at 800 oe. This electrically inactive boronfraction is correlated with a residue of a rapidly diffusing boron fraction. Theassumption, made in sec. 6.4.3, that the high mobility of these boron atoms isdue to an interstitial lattice position of these atoms is consistent with theelectrical behaviour observed.Near the surface the charge-carrier concentration exceeds the boron concen-

tration, especially if annealing occurred at 800°C. Channelled implantationsshow this effect to a smaller extent. This effect is correlated with the damageintroduced by the implantation. It is assumed that electrically active defects areaccumulated locally in the surface region.For the charge-carrier-distribution measurements the reliability of the

anodic-sectioning technique was checked. The damage introduced by theimplantation was found to exert no influence on the thickness of the removedlayers. However, the boron concentration does have an influence. For this pur-pose correction to the average layer thickness was applied at each profile meas-urement. Electrical insulation of the implanted layer was done by implantingboron in high-ohmic silicon. This necessitated the construction of a new anodic-oxidation bath, mercury being used for the rear electrical contact.

REFERENCES7-1) A. Manara, A. Os t id ic h, G. Pedroli and G. Restelli, Thin solid Films 8, 359,

1971.7-2) M. A. Wilkins, AERE Rept. 5875, 1968.7-3) J. A. Davies, G. C. Ball, F. Brown and B. Domey, Can. J. Phys. 42,1070, 1964.7-4) R. L. Petritz, Phys, Rev. 110, 6, 1254, 1958.7-5) K. B. Wolfstirn, J. Phys, Chem. Solids 16, 279, 1960.7-6) V. I. Fistul', Heavily doped semiconductors, Plenum Press, New York, 1968, p. 77.7-7) G. L. Pearson and J. Bardeen, Phys, Rev. 75, 865, 1949.7-8) W. J. Patrick, Solid-State Electronics 9, 203, 1966.7-9) P. F. Schmidt and W. Michel, J. electrochem. Soc. 104, 230, 1957.7-10) E. F. Duffek, C. Mylroie and E. A. Benjamina, J. electrochem. Soc. 111, 1042,

1964.7-11) D. Colman and D. L. KendalI, J. appl. Phys. 40, 4662, 1969.7-12) H. F. Wolf, Silicon semiconductor data, Pergamon Press, 1969, p. 89.7-13) T. E. Seidel and A. M. MacRae, Trans. met. Soc. AIME 245, 491, 1969.7-14) G. L. Vick and K. M. Whittle, J. electrochem. Soc., solid-State Science and

Technology 116, 1142, 1969.7-15) F. H. Eisen, B. Welch, J. E. Westmoreland and J. W. Mayer, in D. W. Palmer,

M. W. Thompson and P. D. Townsend (eds), Proc. int. conf. on atomic collisionsphenomena in solids (Brighton 1969), North-Holland Publishing Company, Amster-dam, 1969, p. 111.

100 - .

8. REDISTRffiUTION OF BACKGROUND IMPURITIES IN SILICONINDUCED BY ION IMPLANTATION AND ANNEALING

AbstractWe observed that an initially homogeneous boron distribution in siliconcan be modified by subsequent ion implantation with different ions,followed by annealing. We investigated these redistribution effects bymeasuring boron distributions obtained under different conditions,For this purpose the implanted ion species, the annealing temperature,the crystallographic direction of the surface plane and the backgrounddope concentration are varied. The redistribution of a phosphorusbackground dope was also investigated. We conclude that the redistri-bution effects observed in the boron and phosphorus background dopesafter annealing at temperatures of about 800 oe are mainly due tothermal diffusion which is enhanced by the elastic-stress fields and strainin a crystal lattice containing implanted ions and defect structures.Redistribution effects observed after annealing at a temperature ofabout 1000 oe, which were induced by implantation of donor-type ionssuch as arsenic, phosphorus and antimony, are caused by the internalelectric junction field.

8.1. Introduetion

Redistribution effects of impurities induced by ion bombardment or ionimplantation have often been investigated with the substrate kept at an elevatedtemperature during the irradiation process 8-1.2.3). In these investigations thebombardment is by means of light ions, such as protons. The observed effectsare explained by thermal diffusion, which is enhanced by excess vacanciesproduced.

In the present investigation the experimental situation is different in the sensethat during the implantation the substrate is kept at room temperature. Anotherdifference is that we implanted mainly heavy ions such as Ar", p+ and As+ ions,etc. After the implantation the sample is annealed and the distribution of thebackground is measured. By comparing this distribution with the original one,the redistribution effect is found.A study like this is of interest for the understanding of problems in electronic-

device technology such as those encountered in the case of double doping.This investigation is an extension of the work reported in sec. 6.3.3 where we

described the redistribution of a boron background which is induced by aboron implantation.We investigated the influence of the implanted ion species, the annealing

temperature, the concentration ofthe background dope and the crystallographicdirection of the substrate. Most of the experiments are performed with siliconcontaining a boron background. In order to see whether redistribution effectscan be expected with other background impurities as well, the redistribution ofa phosphorus background is also investigated.

- 101 -

8.2. The experimental method

Both the boron and the phosphorus concentrations are measured as a func-tion of depth with SIMS. The results of the boron measurements should beconsidered with some caution due to the fact that precipitation enhances theion yield (sec. 6.4.2). The results in this chapter have not been corrected forthis effect.In case of the measurement of phosphorus concentration profiles, sputtering

is carried out with a primary beam of O2+ ions, while the secondary Pr-ioricurrent is measured. The energy of the primary ions is 14·5keY. This energy ishigher than the energy which is used in the boron measurements (5'5 keY, seesec. 3.4). However, the sputtering yield is lower due to an unfavourable electric-field configuration resulting in a smaller angle between the primary-ion beamand the surface normal. Because of the high energy of the primary ions somedistortion of the concentration profile may occur due to recoiling effects.The measurements in this paper, however, are not so critical as to lead tomisinterpretations.

8.3. Experimental results

In a first experiment the influence of an implantation of the inert-gas ionsAr+ and Ne+ on a boron background was investigated. Implantation of inert-gas ions is of interest because chemical interactions between the implanted ionsand the substrate or the background impurities are unlikely. The ions wereimplanted at an energy of 70 keY and a dose of 1016 ions cm-2 in silicon slicescut perpendicular to a (I 00) direction. The silicon was Czochralsky-grownand homogeneously doped with natural boron. The concentration of the llBisotope in the boron dope was 1,3.1019 ions cm-3• Implantation occurred ina random direction in order to prevent channelling. Annealing was performedat temperatures up to 1000 °C in a nitrogen atmosphere for a period of 35minutes.For the Ar+ -ion implantation the results obtained at annealing temperatures

(Tann) in the range of 600-900 °C are shown in fig. 8.1. At lower annealingtemperatures no redistribution effects are found. In the Ne+ case effects similarto those caused by the Ar+ -ion implantation are observed only after annealingat 700°C and 800 °C.For the argon implantation a peculiar peak structure in the boron distribution

is found at a depth of about 1500 A for Tann = 700 °C and Tann = 800°C(fig. 8.1). For the implanted Ar+ ions the projected range is 700 A with astandard deviation of 200 A 8-4). It can be concluded therefore that the peakstructure is situated at the transition from the implanted to the non-implantedregion at an impurity concentration of about 10- 3 times the maximum concen-tration of the argon. On both sides of the peak structure a regular pattern is

- 102-

2·0

I

ld5 ions cm-2Ar+ 70keV

,~ Tann=6000C, ~, ,·3

.-......~ \ _Ol .... , -, '0- ./ , - - - -, 11 ' ....,,~ •""11 I ~

J' I I Tann=7000C,.... ",\ ...., ,I1

iJ1 'e' \.~', I , ...., ·l '.. _ ...-. _ ...., ,

~Iil.;"

,'t :'""·' : I, ,

I ~I I

f'\,,II , I

.. j I, ,

7änn =8000C\.j • , .5 '. , . \

\ I \ r..iJ .' I ._....::: ;, " ..._.........................., ,, I, ·, •, ,

\

I,I,,,II

Tann=9000CII 1',I I 'I'3~,....""'''' 1If. ......... __ -e~..eA ....

I I I I

ZO

1·

3·0

2·5

2·0

1·5

1,0

o 0-2 OoJ 0'4. 0·5- Depth (IJm)

Fig. 8.1. 11B concentration versus depth after Ar+ -ion implantation (energy 70 keV, dose1016 ions cm-2) and annealing at different temperatures Tann• The substrate surface is per-pendicular to a <I 00> crystaIIographic direction.

0·1

observed. From spot to spot on the same slice and from slice to slice the borondistributions reproduce in detail.The dependence on the crystallographic direction of the implanted surface

was studied by implanting Ar+ ions at an energy of 70 keV and a dose of1016 ions cm-2 in silicon slices, which were cut perpendicular (to within 0'2°)to(110), (I 11), (100) and (763) directions, respectively. The silicon ishomogeneously doped with a liB concentration of 1.3.1019 cm=". Theredistribution effects in the slices with surfaces perpendicular to the directions(I 1 I), (110) and (763) are quite similar. One of them is reproduced infig. 8.2. This figure also shows the boron distribution found in the silicon slice

-103 -

Tonn= BOa oeAr' 70 keV 10'6ions cm-2

2·0§

<Ill>

1·0

o 0·1 0·2 0'3 G-I. 0·5- Depth (pm)

Fig. 8.2. llB concentration versus depth after Ar+-ion implantation (energy 70 keY, dose1016 ions cm-2) in silicon with the surface plane perpendicular to a (I 1 I) and a (I 00)direction, respectively. Annealing was at 800°C.

with the surface normal in the (I 00) direction. This distribution shows apeculiar substructure between the surface and the peak structure which differsconsiderably from the others.We investigated the influence of the concentration of the boron background

on the redistribution effects by implanting Ar+ ions in silicon, having a 10 timeslower boron concentration than that in the foregoing experiments. Similarredistribution effects were obtained, which suggests that the level of the boronconcentration is not important.In order to see whether redistribution of background impurities, other than

boron, can be expected as well, the influence of an Ar+-ion implantation on aphosphorus background was also investigated. The phosphorus backgroundwas obtained by implantation (energy 70 keY, dose 5. 1015 ions cm-2) andannealing at 1000 °C.Figure 8.3 shows the phosphorus distribution before and after an Ar+ -ion

implantation (energy 70 keY, dose 1015 ions cm=) and subsequent annealingat 700°C. It is observed that, in this case too, redistribution of the backgroundoccurs, but the profile is smoother than is found in the case of a boron back-ground.

s,...c:~t:J

~ 5CI1IJc:8

t

- 104-

1or------.-------r------r------.------~iAr+ 70keV,""I'I •I \

~...... - \, ..... I 1f '._e' ;

t \: \

,/ \'o=:>~I

Tann=7000C

°O~----~O~~5~----~~~1-----O~.~~----~O~~----~~~~5- Depth (p.m)

Fig. 8.3. 31P concentration versus depth before (drawn curve) and after (dashed curve) Ar+-ion implantation (energy 70 keY, dose 1015 ions cm-2) and annealing at 700 oe.

Returning again to boron, the influence of an As+ -ion and p+ -ion implanta-tion on a boron background was investigated in a further experiment. Theseion species were chosen in view of their special interest to electronie-devicetechnology. Figures 8.4 and 8.5 show the distributions after an As+-ion andP+-ion implantation (energy 70 keY, dose 1016 ions cm-2) in homogeneouslyboron-doped silicon. In the case of the p+-ion implantation the phosphorus con-centration profile was measured too. From the results given in fig. 8.5 oneobserves for Tann = 800 oe a peak structure in the boron distribution at thetransition from the implanted to the non-implanted region as in the first-mentioned experiment where the redistribution was induced by an Ar+-ionimplantation. From the distributions in fig. 8.4, which are obtained forTann = 900, 950, 1000 and 1050 oe, respectively, one observes that the peakstructure disappears and a separate dip in the boron distribution develops.The position of this dip with respect to the surface increases with the tempera-ture of annealing. This contrasts with the position of the peak structurewhich is independent of the temperature of annealing. The dip is similar to theone Ziegier et al.8-5) found on a device where boron and arsenic werediffused at 1000 oe.In order to study whether the electrical properties of the implanted ions

influence the shape of the peak structure, Sb+ ions and In+ ions are implanted.These ions have a comparable mass and ion radius. Their mechanical behaviourwill therefore be comparable. However, after annealing at 600 oe, their elec-trical charges are opposite, Sb+ ions being donor-type and In+ ions beingacceptor-type, as was verified with a hot-point measurement 8-6). From thesimilar distributions obtained at Tann = 800 oe, shown in fig. 8.6, we observe

o 0·2 oe 0·6 0·8 1-0- Depth (IJm )

Fig. 8.4. llB concentration versus depth after 7~As+-ion implantation (energy 70 keY, dose1016 ions cm-2) and annealing at different temperatures T.nn• The substrate surface is per-pendicular to a (Ill) crystallographic direction.

- 105-

Tann= 6000e1-5

Tann = 700 oe

2'5

2·0

Tann = 800 oe

"'......2·0'E.u

Tann = 900coe

,::::CXl 0.5

Tann= 9S0oe.

Tann = 1000 oe

1·0

0·5

-106 -

"3

3'10+ 70 keV 10'6 ions cm-2

~'B Tann = 600 oe......_,3 'J .'",~ \

700 oen Tann =......--.._/\__8

V·-I",~ 1 j

3'10_1 n~ 11IIIril~II 'E'llt- Tann = 800 Oe_.~I~"\f '....-..--,....~,x\

"p, x

r1I1I1

I1I!

T 11\ 'EJ. -i?." \ Tann = 850 Oe... .

\_... ....--,;~

l·,I ~E

Tann = 900 Oe._.~J "\ ........0, ........

'", '.........'f'o..,. 'EI "'.-It-.... \ T 1000 Oe'- ann =....

" .?..,/.........-........

1·5

1·01·5

0·2 0·4 0'6 0·8_ Depth t um )

Fig. 8.5. llB concentration versus depth after 31P+_ion implantation (energy 70 keY, dose1016ions cm-2) and annealing at different temperatures Tonn• In the figure the concentrationprofile of 31p is indicated, too. The substrate surface is perpendicular to a (111) crystallo-graphic direction.

o 1·0

1·0

2·0

1·5........ "3'e:u 1.0~~

_IJ..... 2·5'"t]s"'co 2.0c:s,g 1·5

~ "3s(..) 1·0

"3

1'0

1·5

"3

1·0

that the influence of the mechanical properties of the implanted ions predom-inates over the electrical properties at that annealing temperature.

In order to study possible systematic effects in the complicated distribu-

0'5 ~[...__"___,L_ _ _'___..L_, _ _,___.,L__-'-_....L'_-''----l

o 0·2 0'4 0·6 0'8

- Depth (firn)

Fig. 8.6. 11B concentration versus depth after implantation of antimony and indium, re-spectively, and subsequent annealing. Energy of implantation is 300 keY, implantation doseis 1015 ions cm-2, temperature of annealing (Tann) is 800°C. The substrate surface is per-pendicular to a (111) crystallographic direction.

- 107

.'2'0

""f' 11" ,I" "I I ,I

-.. I I I 1

~E 1'5 - t\ : i: ~ ,"...lJ N .'....... ~ " 1 1 '.

0) I ".-.' ~--l-,~, _-S2, -}i' ' .

:~;:OJ 2.0 -

Tann = 800 oe

.""

c.!;!ti.l::cQJ

1·5l.Jc8

1 1·0

":~~, , '~ 1 :', •

...... ~ I I I' ," 'O.,

~ .. -." '}_./~ r "1-'---. I ,r-.,.--.,-_-=- ••r-- .............-.-.o--..-----I/ ~ ~ l ... _..I "

1+ ' :~

Tann '" 800 oe

1'0

tions observed we investigated the redistribution of boron for some more im-planted ion species such as N+, 0+, Si+ and Kr+ ions. Some profilesobtained after annealing at 800 oe are shown in fig. 8.7. From the results shownin this figure and those shown in fig. 8.6 one observes that the peak structureoften has two peaks. In some cases such a structure is also found after annealingat 700 oe (e.g. Si+),In the next sections we will discuss some aspects of the measured distribution

profiles. Firstly we will discuss the peak structure situated at the transition fromthe implanted to the non-impla~ted region, secondly the substructure in theredistribution profile lying between the surface and the peak structure andthirdly the dip in the boron distribution, which separates from the peak struc-ture and moves to a larger depth at higher temperatures of annealing (fig. 8.4for Tann > 900°C).

8.4. Discussion of the peak structure

8.4.1. The peak structure in the boron distribution

The peak structure which one observes after annealing at temperatures in therange from 700 oe to 900 oe often consists of a thin region depleted of boron

-108 -

70 keV 1O'6ions cm-2

Tonn = 800 oe

70 keV 1016ions cm-2

Tann = 800 oe

70 keV 1O'5ions cm-2

Tann = 800 oe

2,0 u 1, J\1\ • \ 1\., 1 .', I ,.0 "\ 8' '6'\.j 0_0'· \, Kr+ 300 ke V 10 ions cm-, " .'I' .., Tann = 800 e

I 1\/ •uv >,,,3 1-------+, f-, ---'-''''"--------1

I·

t

1·5

1-0

o 0·2 D·" 0·6 0·8 1·0_ Depth t um }

Fig. 8.7. 11B concentration versus depth after implantation of nitrogen, oxygen, silicon and .krypton, respectively, and subsequent annealing. Energy of implantation is 70 keY fornitrogen, oxygen and silicon, and 300keYfor krypton. The implantation dose isl016 Ionscmr ê

and temperature of annealing (Tann) is 800oe. The substrate surface is perpendicular to a(l11) crystallographic direction.

having a hump in the boron concentration on both sides (see e.g. figs 8.6 and8.7). Obviously boron has diffused from a thin layer which is parallel to thesurface to neighbouring regions which have somewhat smaller and largerdepths. It is very unlikely that such a flow in two opposite directions is due tothe influence of internal electric fields. This consideration is in agreement

- 109-

with the results shown in fig. 8.6 where we found that implanted ions of donor-and acceptor-type cause similar redistributions. It seems therefore more likelythat the peak structures are due to the crystal properties which are non-uniformin depth after the implantation. Such properties may be the stress and damagein the lattice. In the next section we will develop a mechanism for formation ofsuch a peak structure based upon these properties. In further sections we willdiscuss some experimental verifications of the mechanism proposed.

8.4.2. Mechanism for formation of the peak structure

The peak structures shown in figs 8.1 to 8.7 are produced at implantationdoses çe 1015 ions cm=". At these doses a continuous amorphous layer isformed. The formation of such a layer starts at a depth of maximum defectconcentration. Mostly this depth is somewhat smaller than the projected rangeof the ions. While the implantation is going on, the thickness of the implantedlayer increases by growth in both directions.

Let us consider the stresses in such an implanted layer. It is known fromstudies by Gerward 8-7), who used X-ray interferometry and X-ray-diffractiontopography and from investigations of BerNisse 8-8), who studied the curva-ture of a substrate due to the implantation, that the stress in an implanted layerincreases with the dose. At a certain dose the stress reaches a maximum,whereas at higher doses the stress decreases again. The reduction in stresscoincides with the onset of the production of an amorphous layer. Thenstress relief obviously occurs due to elastic-plastic transitions. This leads to amarked elevation of the irradiated part of the surface 8-9). One may concludefrom these facts that, in the regionjust outside the amorphous region, the defectconcentration will induce just the maximum value of stress. The stress will beinfluenced by the annealing process. Hardly any experimental results are avail-able on the stress in implanted and annealed silicon. However, we mayassume that after recrystallization of the amorphous layer this region will showrelatively little stress, because firstly, the regrowth occurs epitaxially from thesubstrate which provides a low-energy location of the implanted ions andsecondly, the density of the silicon increases (sec. 4.3.2). In the region justoutside the amorphous region we may expect the stress to be influenced to amuch smaller extent by the annealing process. This explains why we observeda marked curvature (radius 130 cm) of the substrate surface of a silicon sample(thickness 30 (Lm) which was implanted with Ar+ ions (dose 1016 ions cm=>,energy 70 keV), after annealing at 800 oe. Summarizing this discussion aboutstress we conclude that before annealing there is a thin layer of maximum stressjust outside the amorphous region. After annealing the stress in this layerdecreases but remains higher than that in the neighbouring regions. In orderto explain from this behaviour the peak structures with the two-sided up-hill diffu-sion of the boron we suggest that during the annealing process an enhanced

- 110-

thermal diffusion of the boron takes place from the thin layer of high stress tothe' neighbouring regions of low stress. Such enhanced-diffusion effects are alsofou"nd in plastically deformed silic~n 8-10). For the process of stress-enhanceddiffusion we propose the following mechanism. We assume that in the regionof maximum stress during the implantation or during the annealing processsubstitutional boron moves to interstitial lattice positions in order to obtainstress relief. During annealing the distribution of the interstitial boron is widenedby thermal diffusion. This results in a doubly peaked distribution of the totalboron concentration (that is, substitutional and interstitial boron, as meas-ured with SIMS), which has the same features as most of the peak structuresobserved. Interstitial boron is not stable, because it is trapped by vacancies,and becomes substitutional again, as was discussed in sec. 4.3.2 to explainthe transient diffusion process. The smaller peak structures found at higherannealing temperatures (~ 900°C) therefore are explained, according to thismodel, by a return flow of the substitutional boron. Such an interstitial-substi-tutional process has been recently proposed independently by Baruch etal.8-11) to describe redistribution effects in proton-irradiated hot substrates.If we assume that the production of interstitial boron is finished at the startof the diffusion process then the process is qualitatively expressed by theequations:

(jNt(x, t) (j2N,(x, t)---- = D, - kl Nt(x, t),

()t bx2

(jNs(x, t) (j2Ns(x, t)---- = D, + kl Nt(x, t),

bt bx2

(8.1)

(8.2)

coJ [Nt(x, t) + Ns(x, t)] dx = k2, (8.3)

-co

where Nt(x, t) and Ns(x,t) are the concentrations of interstitial and substituti-onal boron, respectively, as a function of depthxand time t,D, andDj are the diffu-sion coefficients ofinterstitial and substitutional boron, and k1 and k2 are con-stants. The term k1 Nt(x, t) ineqs (8.1) and (8.2)is introduced to describe the tran-sition of interstitial boron to substitutional boron by vacancy trapping. From eqs(8.1) to (8.3) Nt(x, t) and Ns(x, t) can be calculated if the distribution of inter-stitial boron at t = 0, that is Nt(x, 0), is known. With the initial conditions:

Nt(x, 0) = 0 for x =1= xps (8.4)and

co(8.5)

-co

- 111-

and assuming the diffusion process to dominate the process of vacancy trapping(kl = 0) the distributions N,(x, t) and Ns(x, t) are:

N,(x, t) = Q exp [- (xp. - x)2/4 D, t], (8.6)2 (n D, rv=

Ns(x, t) = No - Q exp [- (xp. - x)2/4 D, t], (8.7)2 (n o, t)1/2

where No is the boron concentration before implantation. As an example, someresults calculated with eqs (8.6) and (8.7) are shown in fig. 8.8. In fig. 8.8a are

"'-.. a)'sIJ~~

c: 1·00:;::_gc:<IJIJc:8

I0 0·1 0·2 0·3 0·4__. Depth (pm)

b)-r-Oe:IJ~ 13

~

c: 1·0.~è1:<IJIJc:8

t0 0·1 0·2 0·3 0·4--.. Depth ( pm)

Fig. 8.8. Formation of a peak structure by a substitutional-interstitial diffusion mechanism.Figure 8.8a shows the substitutional-boron concentration N, and interstitial-boron concen-tration N, versus depth after diffusion has occurred. Figure 8.8h shows the total concentra-tion (Ns + N,) versus depth.

- 112-

shown N, and N, versus depth, and in :fig.8.8b (N, + N,) versus depth cal-culated with t = 2100 s (corresponding to the annealing period used in theexperiments of sec. 8.3), D, = 0·5 . 10-15 cmê s-1, D, = 0·5 . 1016 cm" s-1,Q = 2·0. 1013 atoms, No = 1·3 . 1019 cm-3 and xps = 0'2 !Lm.The values ofD, and D, are obtained by extrapolation of results shown in table 6-1. Thedistribution shown in :fig.8.8b is less sharply peaked than the peak structuresshown in :figs8.6 and 8.7. This is partly due to the fact that trapping is nottaken into account in the calculations. We should have obtained a sharper-peakedstructure if D, and D, in the example had been given values closer to oneanother than those derived from the results in table 6-1.

8.4.3. The position of the peak structure

One concludes from the mechanism described that the position of thecentre of the peak structure is just outside the amorphous zone. In order to. check the proposed mechanism we will compare the experimental position ofthe centre of the peak structure with the calculated depth of the boundary ofthe amorphous zone for different ion species.

In table 8-1 the depth Xps ofthe estimated centre ofthe peak structure is givenas measured for ions which are implanted at an energy of 70 keV and a dose of1016 ions cm=".

TABLE 8-1

Comparison of the experimental depth of the peak structure Xps with the cal-culated depth of the boundary of the amorphous layer x, for different ionspecies. The implantation energy is 70 keY, the dose is 1016ions cm-2 and thetemperature of annealing is 800 °C. The values of Xps and Xa are also givenrelative to the projected range Rp of the ions

depth of the centre of depth ofimplanted atomic the peak structure the amorphous layer

ion number Xps xps/Rp Xa xa/RpCA) CA)

14N+ 7 2200 1-1 2380 1·2

160+ 8 2200 1·3 2200 1·3

2°Ne+ 10 2200 1·6 1850 1·4

31p+ 15 1800 2·1 1300 1'5

4°Ar+ 18 1460 2·1 1110 1·6

75As+ 33 1100 2·6 732 1·7

121Sb+ 51 900 2·6 590 1·7

- 113-

The position of the boundary of the amorphous zone is calculated by assum-ing a Gaussian distribution of the defects. The mode and standard deviation ofthe defect distributions are derived from graphs calculated by Winterbonet al.8-12). In these calculations electronic stopping is not taken into accountand a power approximation for the interaction potential is used in the nuclearstopping process. We used the graphs calculated for an energy-independentnuclear cross-section. The critical implantation dose derlt for production of anamorphous silicon layer is obtained from results of Dennis et al.B-13) who basedtheir calculations on a semi-empirical theory developed by Morehead et al.8-14).For an implantation dose of 1016 ions cm-2 the depth of the boundary of theamorphous zone Xa is found by calculating the abscissa of the Gaussian distri-bution at an ordinate which is a factor derlt/1016 below the maximum. Weare interested only in the abscissa with the largest depth. Figure 8.9 shows theprinciple of the method for the case of As+ ions implanted in silicon at anenergy of 70 keY and a dose of 1016 ions cm-2• The critical dose derlt forAs+ ions is 2. )014 ions cm-2. In table 8-1 the values of Xa calculated for dif-ferent ion species are given. In order to facilitate the comparison of the exper-imental and theoretical results the values for Xps and Xa relative to the corre-sponding projected range Rp of the ions 8-4) are also shown. One observes fromthe results shown in table 8-1 that xps/Rp and xa/Rp both increase with theatomic number of the implanted ions. Furthermore, there is a reasonable agree-ment between xps and Xa, in particular for ions with Z < 10. For ions withZ >10 this agreement is not as good, which may be due to the approximationsused in the calculation of the defect distributions. Summarizing we may con-clude that the results in this section give some support to the proposed dam-age and stress mechanisms. More-definite conclusions could be drawn ifmore-accurate data about Xa were available such as could be obtained by themethod of light-ion back-scattering combined with the channelling effect.

8.4.4. The influence of the implantation dose, ion species and background con-centration

We found that a critical implantation dose was required for formation of thepeak structure. For instance at a dose of 10160+ ions cm-2, implanted at anenergy of 70 keV, a sharp doubly peaked structure is formed (fig. 8.7), whereasthis is not the case at a dose of 1015 ions cm-2• According to the data ofDennis et al.8-13) the critical dose for formation of amorphous silicon by 0+ions is about 4. 1015 ions cm-2. Therefore the dose for formation of a peakstructure and that for formation of an amorphous layer are of the sameorder. This fact provides one more argument in favour of the proposed mech-anism.Moreover it is important to consider the ratio of the maximum to the mini-

mum boron concentration in a peak structure. Being largely independent of

-114 -

E= 70 keV )

III

~::..ei....~ dcrif.

-2cm

c:ê_gc:<IJ..,c:o..,

t0·1

Rp

~Xa

Depth I jlm)

Fig. 8.9. Graphical display of the determination of the boundary Xa of the amorphous zoneproduced by arsenic ions which are implanted at an energy of 70 keY and a dose of1016 ions cm-2• The critical implantation dose for the formation of an amorphous layer is2.1014 ions cm=". The distribution of the defects is calculated using data of Winterbonet al.8-12). In the figure is also indicated the projected range Rp of the implanted arsenicions 8-4).

experimental conditions, such as different ion species, implantation doses (ifexceeding a critical dose) and concentrations of the background dope, this ratiois (3 ± 1).The relatively small variations in this ratio are in agreement with theproposed mechanism, since we may expect that the stress just outside theamorphous region will be independent of the conditions by which the amor-phous layer is produced.

-115 -

8.4.5. The infiuence of the temperature of implantation

The formation of an amorphous layer is strongly dependent on the tempera-ture of the silicon during the implantation process (sec. 2.3). According to theproposed mechanism one expects therefore that the formation of the peakstructure will also depend on the temperature of implantation. We have checkedthis by implanting N+ ions in silicon which is homogeneously doped withboron. The temperature dependence of the critical dose for formation of anamorphous layer can be estimated from the semi-empirical results of Moreheadet al.8-14). They derived for this critical dose dcrlt(T) at a temperature T theexpression

dodcrlt(T) = -------------

[1 - k' exp (-U/kT)/(dE/dx)o1/2F

where k' and U are constants (k' = 115keV/fLm,U = 0·06 eV), (dE/dx)o is theenergy-independent nuclear-energy loss per unit path length and do is the doserequired to yield an amorphous layer in the absence of vacancy out-diffusion.One can estimate do as

ENdo = ions cm-2,

(dE/dx)o

where Ë is the effectiveenergy, required to displace a target lattice atom and Nis the volume density of the target atoms. For N+ -ion implantation we cal-culated with eqs (8.6) and (8.7) the values of dcrlt(T) as a function of T. Theresults are shown in table 8-II. With the help of these data we prepared thefollowing experiment. N+ ions were implanted at an energy of 70 keY and adose of 1016 ions cm-2 into silicon at temperatures of (-160 ± 10) °C,

TABLE 8-II

Calculated critical dose for formation of an amorphous layer for differenttemperatures of implantation T for nitrogen implanted at an energy of 70 keYand a dose of 1016 ions cm-2

T dcrlt(T)(K) (N+ ions cm")

100 8·7 . 1014

150 1·0 . 1015

200 1·7 . 1015

250 5·0. 1015

300 2.2.1017

(8.6)

(8.7)

- 116-

(15 ± 2) "C, (200 ± 4) "C and (300 ± 6) °C. After the implantation the sam-ples were annealed at temperatures of 800°C and 900 °C, respectively. Accord-ing to the data of table 8-II one expects a peak structure at an implantationtemperature of -160°C but not if implantation occurs at a temperature aboveroom temperature such as, for instance, at 200 °C. The experimental results werefound to correspond to this prediction which provides another argument infavour of the proposed stress mechanism.

8.4.6. The electrical properties of the peak structure

The electrical properties of the boron at the position of the peak structuremay provide additional evidence on the mechanism of its formation. Weinvestigated therefore the charge-carrier distribution in a boron backgroundwhich was redistributed by an argon implantation. The charge-carrier distri-bution was measured using the experimental procedure described in sec. 7.2.In order to measure small differences in the electrical-charge concentration thetotal number of acceptors per unit area in the sample should be relatively small.A homogeneous boron background, as used in the foregoing sections of thischapter, cannot be used therefore in the present experiment. This problem wasavoided by producing a boron background by implantation and annealing.Boron was implanted at an energy of 70 keY and at a dose of 1015 ions cm-2

in silicon with an acceptor concentration of 1012 cm-3. The silicon was cutperpendicular to a (763) crystallographic direction. The implanted samplewas annealed at 1000 °C for a period of 35 min in order to obtain therequired electrical properties of the implanted layer. Subsequently Ar+ ionswere implanted at an energy of 70 keY and at a dose of 1016 ions cm-2• Afterthis the sample was annealed at a temperature of 800°C. In order to detectpossible steep gradients in the charge-carrier distribution the thickness of thesilicon layers which are removed successively after each measuring step shouldbe ~ 100 Á. This was achieved by reducing the voltage for anodic oxidationfrom 140 V to 30 V, which resulted in a removed layer thickness of about100 Á per step. The expressions (7.5) and (7.6) which are used to calculate thecharge-carrier distributions in chapter 7 result in too high a relative error in pin the present experiment, due to the small differentials in (Is and R, (1/ (7.7).We preferred therefore to use the expression

(8.8)

. where for the hole mobility !LIl an average estimated value is used. In thisexperiment we found a dip in the charge-carrier distribution at a depth cor-responding to the position of the peak structure. In principle it should bepossible to draw conclusions from the results of this experiment on the substitu-

- 117-

tional-interstitial process of up-hill diffusion, mentioned in sec.8.4.2. However,the dominating influence of charged defects obscured details in the charge-carrier distributions, with the consequence that no more conclusions could bedrawn about that process.

8.5. Discussion of the substructure

In this section we will discuss the part of the redistribution profile which issituated between the surface and the peak structure. This so-called substructureis lying in the region which is amorphous after the implantation process. Itmight be assumed that during the recrystallization process which occurs at about600°C, redistribution of the boron occurs by selective segregation. However,only slight redistribution effects are found after annealing at 600 °C, whichsuggests that this effect is not significant in this case.It is known from transmission-electron-microscope and electron-diffraction

measurements that after annealing of implanted silicon at temperatures in therange 600-1OOO°Cmany lattice irregularities, such as, for instance, loops, stackingfaults, linear defects, etc., are still observed (figs 2.5 and 2.6). The dimen-sions and configurations of these defect structures are strongly dependent onthe temperature of annealing. Moreover, there will be clusters of vacancies orclusters of implanted ions. This was inferred from the results of the followingexperiment.We measured the surface elevation of a silicon sample, which is implanted

with a dose of 1016 Ar+ ions cm-2 at an energy of 300 keY. Before annealingthe elevation is (135 ± 25) A. After annealing at 500°C, 700 °C and 900°Cthe elevation still amounts to (110 ± 25) A. Although amorphous silicon hasa densitywhich is about4 % smaller than that ofmonocrystalline silicon (sec. 4.3.2)no marked decrease in the surface elevation is found. Presumably vacancyclusters are formed. Probably argon bubbles are also created during the anneal-ing process suchas arefound in metals S-15). From the above results one mayconclude that after annealing there is a layer which is highly non-uniform. Weassume therefore that during the annealing process at temperatures of700 °C andhigher the substructure of the boron distribution is produced by a diffusion ofthe boron to the above-mentioned inhomogeneities followed by precipitation.

The boron distributions in slices which have their surface normal to a(I 00) axis show a peculiar substructure if implanted with argon (figs 8.1 and8.2). From this substructure we conclude that argon and boron atoms precip-itate preferentially in discrete {lOO} planes. The reproducibility of thesedistributions indicates that these layered precipitates have a fixed position withrespect to the surface. So far, no experimental evidence of such a behaviour inimplanted layers has been found by others. However, Schwuttke S-16) usinginfrared transmission microscopy observed, after quenching of silicon that wasdoped with copper at 1300°C, plate-like copper precipitates which grow only

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in {lOO} planes. The periodic structure may be attributed to the Liesegangphenomenon 8-17). However, at present we have no explanation for the pre-ferred creation of vacancy clusters, argon bubbles or boron precipitates in{lOO} crystallographic planes.

8.6. Discussion of the junction dip

If arsenic is implanted in silicon doped with boron, one observes a dip in theboron distribution after annealing at a temperature of ~ 900 oe. The distanceto the surface of the dip increases with the temperature of annealing (fig. 8.4).A similar effect, although less pronounced, is observed if phosphorus (fig. 8.5)or antimony is implanted. It is rather obvious to assume that this dip is causedby the internal electric field at the junction. The shift of the dip to a larger depthat higher annealing temperatures is explained by a corresponding shift of thejunction as a consequence of the broadening of the arsenic distribution bythermal diffusion. The interaction of an internal electric field on a concentrationprofile was studied by Hu et al.8-18). Based on these calculations Fair 8-19,20)

explained the retarded base diffusion in silicon n-p-n structures with arsenicemitters. Ziegier et al. 8-5) observed a dip in the boron distributions afterarsenic was introduced by thermal diffusion at a temperature of about 1000 oe.They concluded from calculations that the internal electric field does not ac-count for all the details in the boron distribution. They refined the mechanismtherefore by postulating that boron is trapped by pairing with the arsenicdonors.We investigated our experimental results in some detail.Firstly one observes from the distributions shown in fig. 8.4 for Tann ~ 900 oe

that the current direction of boron acceptors corresponds to the polarity of theinternal electric field at the p-n junction.

Secondly we measured the depth of the junction Xj by lapping and stain-ing 8-21) and compared this depth with the depth of the bottom of the dip Xd'

The results, measured at samples which are implanted with arsenic and phos-phorus are shown in table 8-II1for different temperatures of annealing. One ob-serves a reasonable agreement between the positions of the junctions and the dips.Thirdly we investigated whether an arsenic implantation produces a dip in

a boron distribution if the boron-doped layer is made n-type by a phosphorusimplantation. We started in this experiment with silicon doped with boron ata concentration of 1.3.1019 cm-3• p+ ions were implanted at an energy of200 keY and at a dose of 1016 ions cm:". In order to avoid redistribution oftheboron, implantation was done at a temperature of 500 oe. After the implanta-tion the sample is annealed at 1050 oe. From a hot-point measurement wefound that an n-type layer was produced. Subsequently we implanted As+ ionsat an energy of 70 keY and at a dose of 1016 ions cm-2• Then the sample wasannealed at a temperature of 1000oe and the boron distribution was measured.

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TABLE 8-IIl

Comparison of the depth of the junction Xj with the depth of the bottom of thejunction dip Xd for arsenic and phosphorus implanted at an energy of 70 keYand a dose of 1016 ions cm-z, annealed at different temperatures

implantedtemperature

Xj Xd

ionof annealing

(A) (A)CC)7sAs+ 1000 3700 3450

1050 5200 570031p+ 850 2800 3200

900 3800 4700

1000 7700 7000

No dip is found in the boron distribution.From these three results we conclude that the dip in the boron distributions,

induced by arsenic, phosphorus or antimony implantations followed by anneal-ing at a temperature ~ 900°C, is caused by the internal electric field at thejunction. The structure ofthe dip which is obtained after an arsenic implantationdiffers from that obtained after a phosphorus implantation. One observes fromthe results shown in figs 8.4 and 8.5 that the dip in the case of an arsenic im-plantation is more sharply structured with a hump on the side of the arsenicdistribution. We attribute this difference to the lower diffusivity of arsenicin comparison to that of phosphorus.

8.7. The secondary-ion yield of redistributed boron

From most of the results shown in the figures 8.1 to 8.6 one observes thatthe average value of the boron concentration in the redistribution profile ishigher than the value of the initial homogeneous boron concentration. Theincrease in the apparent concentration of redistributed boron is most pro-nounced after implantation of neon, argon, krypton, nitrogen and oxygen. Itincreases with the temperature of annealing and is on the average 20 % abovethe initial value. If instead of the secondary-ion current of B+ ions the second-ary-ion current of BO- ions is measured (sec. 3.5.11) no increase in the appar-ent boron concentration is found. The difference between the two cases is moststriking in the region of the substructure. However, the peculiar features in theredistribution profile are similar in both cases. The increase in the apparent

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....average boron concentration due to the implantation of arsenic, phosphorus,indium, antimony and silicon is relatively small (about 5%). From the resultthat this effect is greatest in the case of implanted gas ions we assume thatthis effect depends on the solubility of the implanted ions. Obviously theion clusters produced during recrystallization of the amorphous layer causethe precipitation of boron and this enhances the secondary-ion yield, as wefound in preceding investigations (see for instance secs 3.5.10 and 6.4.2). Thesmaller effect in case of an arsenic, phosphorus, indium, antimony and siliconimplantation may be due to the fact that these ions readily occupy substi-tutionallattice positions during the recrystallization process.

8.8. Conclusions

Three aspects which one observes in boron redistributions induced byimplantation and annealing are investigated.

Firstly, we studied a peak structure in the boron distribution, which is situatedat the transition of the implanted to the non-implanted region. Often thisstructure consists of a region depleted of boron with a peak on both sides. Weconclude that the peak struct~re is caused by the stress induced by the implantedions. This stress has a maximum value in a region just outside the amor-phous layer produced by the implantation. We explain the observed up-hilldiffusion by assuming that thermal diffusion, enhanced by stress, occurs fromthe strained region to neighbouring regions with lower stress. For the mech-anism of enhanced diffusion we assume that in order to obtain stress reliefboron moves from substitutional to interstitial lattice positions. As a conse-quence of the different diffusivities of substitutional boron and interstitial .boron a peak structure with two peaks results. From this study one may con-clude that if for practical reasons these peak structures have to be minimized,as may be required in the case of double doping, it is recommended that theimplantation which does most damage to be done first. Then the substrateshould be annealed before the next implantation is performed.

Secondly, we discussed the so-called substructure in the redistributionprofile. This substructure is the part of the boron distribution between thesurface and the peak structure and is therefore just within the region madeamorphous by the implantation. It is argued that this substructure is causedby inhomogeneities such as vacancy clusters or clusters of implanted ions inthis layer, which are left behind after recrystallization.Thirdly, we observe a dip in the boron distribution after the implantation of

n-type dopants such as arsenic, phosphorus and antimony. This dip coincideswith the position of the junction. It does not occur if the boron-doped layer ismade n-type by a special compensating phosphorus implantation. We concludetherefore that this dip is caused by the interaction of the internal .electric fieldat the junction. In the case of an arsenic implantation the dip is sharply struc-

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tured due to the relatively low diffusivity of arsenic.

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