thermal oxidation of inp and properties of oxide film

7
Thermal oxidation of InP and properties of oxide film Masafumi Yamaguchi and Kohshi Ando Citation: Journal of Applied Physics 51, 5007 (1980); doi: 10.1063/1.328380 View online: http://dx.doi.org/10.1063/1.328380 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/51/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Thermal desorption of oxides on InP Appl. Phys. Lett. 52, 386 (1988); 10.1063/1.99474 Photoenhanced thermal oxidation of InP J. Appl. Phys. 57, 637 (1985); 10.1063/1.334756 Reply to ’’Comments on ’Thermal oxidation of InP and properties of oxide film’’’ J. Appl. Phys. 53, 1834 (1982); 10.1063/1.330602 Comment on ’’Thermal oxidation of InP and properties of oxide film’’ J. Appl. Phys. 53, 1832 (1982); 10.1063/1.330601 Thermal oxidation of InP J. Appl. Phys. 51, 812 (1980); 10.1063/1.327302 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 137.112.220.156 On: Tue, 16 Dec 2014 16:30:25

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Page 1: Thermal oxidation of InP and properties of oxide film

Thermal oxidation of InP and properties of oxide filmMasafumi Yamaguchi and Kohshi Ando Citation: Journal of Applied Physics 51, 5007 (1980); doi: 10.1063/1.328380 View online: http://dx.doi.org/10.1063/1.328380 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/51/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Thermal desorption of oxides on InP Appl. Phys. Lett. 52, 386 (1988); 10.1063/1.99474 Photoenhanced thermal oxidation of InP J. Appl. Phys. 57, 637 (1985); 10.1063/1.334756 Reply to ’’Comments on ’Thermal oxidation of InP and properties of oxide film’’’ J. Appl. Phys. 53, 1834 (1982); 10.1063/1.330602 Comment on ’’Thermal oxidation of InP and properties of oxide film’’ J. Appl. Phys. 53, 1832 (1982); 10.1063/1.330601 Thermal oxidation of InP J. Appl. Phys. 51, 812 (1980); 10.1063/1.327302

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Page 2: Thermal oxidation of InP and properties of oxide film

Thermal oxidation of InP and properties of oxide film Masafumi Yamaguchi and Kohshi Ando lbaraki Electrical Communication Laboratory, Nippon Telegraph and Telephone Public Corporation, Tokai­mura, Ibaraki-ken 319-11, Japan

(Received 14 January 1980, accepted for publication 28 May 1980)

Thermal oxidation of InP and properties of oxide films have been studied. Surface orientation dependence of the oxidation rate can be explained by orientation dependence of bond density available for reaction with oxygen molecules. The activation energy of the parabolic rate constant is 2.06 eV, which may be attributed to the value for oxygen diffusion through InP oxide. From the electron diffraction and infrared absorption measurements, it is found that the oxide film is composed of poly crystalline InP04 (In20 3 + P20 S) and that oxides thermally grown at high temperatures, above 620 ·C become In rich and form lower oxides, such as In40 2 and In20, owing to phosphorus evaporation. Resistivities of the thermally grown oxide films at room temperature range from 108 to 109 n cm and decrease with an increase in oxidation temperature and time, which may be mainly caused by lack ofP20 s in the oxide film.

PACS numbers: 81.20. - n, 68.40. + e, 73.4O.Qv, 78.65.Jd

I. INTRODUCTION

InP is one of the important semiconductor materials for laser diodes, field effect transistors, solar cells, and so forth. In order to develop InP devices, it is necessary to form insu­lators with good chemical stability, and dielectric and inter­face properties on the InP surface, in view of applications to surface passivation and device fabrication. Especially, it is necessary to examine formation of an interfacial layer, such as natural oxide, in order to construct a low-leakage Schottky barrier diode. 1 In the past, anodic oxidation2

•3 and

chemical oxidation 1 have mainly been studied for forming InP natural oxide films. These natural oxides formed under low-temperature processes are chemically unstable and therefore have several limitations for applications to planar technology for InP. Moreover, InP thermally formed oxides, which may be chemically more stable than the anodic and chemical oxides, have not been reported.4 Therefore, more extensive studies on forming several oxides and insulation films on InP are now requested for establishing the technol­ogy for surface passivation of InP devices, and the planar technology for InP.

This paper presents thermal oxidation studies on InP and the properties of the oxide film. Here results of the oxi­dation studies show a dependency upon the surface orienta­tion and oxygen partial pressure. Structural properties of oxide films and electrical properties of InP MOS (metal­oxide-semiconductor) diodes are dependent on oxidation temperature and time.

II. EXPERIMENTALS

InP wafers were cut from undoped liquid-encapsulated Czochralski-grown single crystals of (100), (111)ln, and (11 I)P orientations: The conductivity of all the wafers was n type with carrier concentration around 1016 cm-3

• In the ex­periments, (100) InP wafers were mainly used.

The wafer surfaces were prepared by polishing with 0.05-,um alumina and etching them off with a bromine(2 %)-

methanol solution for 2-3 min. Then the wafers were rinsed in deionized water.

The schematic diagram of the oxidation apparatus is illustrated in Fig. 1. The wafers were completely dried and were put into a quartz tube. After evacuating the tube to a pressure of 10,5 Torr, oxygen gas was introduced into the tube. Thermal oxidation of InP in dry oxygen with a partial pressure from 0.2 to 2 atm was studied at temperatures rang­ing from 450 to 740 ·C for 15 min to 16 h. Temperature was controlled to within ± 2 .c.

Oxide thickness was measured mechanically using sur­face roughness tester DEKT AK of Sloan Instruments Cor­poration after chemical etching through a photoresist mask, and was measured by observation of the cleaved cross sec­tion by a scanning electron microscope.

Crystal structure and composition for oxide film were measured by electron beam diffraction and infrared absorp­tion spectroscopy for oxide/lnP structures.

Current-voltage and capacitance-voltage properties for the oxide films were investigated by measurements on metal­oxide-semiconductor structures. InP substrate contact was made by evaporating looo-A-thick Au,Ge layers and then heat treated at 400 ·C for 5 min in vacuum to form Ohmic contacts to the substrate. One-mm-diam Au field plates on the oxide were formed by evaporating.

Fused quartz tube

(3) Sample , (4) Vacuum system O2 (Diffusion, rotary pump)

(5) Pressure gouge

(6) Valve

FIG. 1. Schematic diagram of the experimental apparatus.

5007 J. Appl. Phys. 51(9), September 1980 0021-8979/80/095007-06$01.10 © 1980 American Institute of Physics 5007

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Page 3: Thermal oxidation of InP and properties of oxide film

5,--------------, P02 = 1 aIm

2

2 5 10 20 50 Oxidation time t (h)

FIG. 2. Thermal oxide film thickness on the InP(IOO) surface as a function of oxidation time in dry oxygen of 1 atm at temperatures from 450 and 740"C.

III. RESULTS AND DISCUSSION

A. Oxidation rate

Figure 2 shows oxide thickness Xo on the InP(l00) sur­face as a function of oxidation time t in 1 atm dry oxygen at temperatures from 450 to 740 ·C. In the temperature range between 450 and 620 ·C, the oxidation follows a parabolic relationship:

x~ =kt=AP~,Dotexp( -Ea/kBT) [cm/sec]. (1)

where k is the parabolic rate constant, A is the reaction rate constant, Po, is the oxygen partial pressure, m is the con­stant, Do is the preexponential factor in the Arrhenius ex­pression for a diffusion coefficient, Ea is the activation ener­gy for diffusion, kB is Boltzmann's constant, and Tis the absolute temperature. At high temperatures, above 680 ·C, the oxide thickness changes irregularly with oxidation time and even decreases with time. Decrease in film thickness is due to the evaporation effect in the oxide growth rate. It was estimated, by scanning electron microscope observation of the cleaved cross section, that the average evaporation rate for oxide film was given by

R e =3.26XI06 exp(-2.88 eV/kBT) [cm/sec]. (2)

It is expected from the thermochemical data5-8 that oxide

film evaporation is caused by thermal decomposition of the P20 5 film and InP substrate. Moreover, it is reasonable that at oxidation temperatures below 620 ·C, oxide film evapora­tion during oxidation is negligible and evaporation above 680 ·C is marked.

Oxide films formed below 620 ·C are transparent and uniform, and are dissolved in lOH20 + HCI solution at a rate of 50 A/sec. The opaque and inhomogeneous films formed above 680 ·C are not dissolved in that solution and contain a lot of pits formed by evaporation of the oxide and InP substrate.

5008 J. Appl. Phys., Vol. 51, No.9, September 1980

fOtl".------______ --,

<) Q) C/)

~ l.>

-c E C/)

5 l.>

Q)

"010' ...

P02 = 1 aIm

t.O 1.2 1.3 1.4

( K-1 )

t "­o

><

FIG. 3. Arrhenius plot of parabolic rate constant in dry O2 of I atm for InP(IOO), (lll)P, and (lll)ln surfaces.

In Fig. 3, the logarithm of the parabolic rate constant k is plotted against the reciprocal of the absolute temperature in dry O2 oft atm for InP(lOO), (lIl)P, and (llI)ln surfaces. The oxidation rate on the InP (1II)P surface is larger than that on the (1 (0) surface and is almost the same as that on the (llI)ln surface. The parabolic rate constants k for (lOO) and (111) surfaces are presented by

k (100) = 4.8 X 10-2 exp( -2.06 eV /kB T) [cm2/sec], (3)

k (Ill) = 8.8 X 10-2 exp( -2.06 eV /kB T) [cm2/sec]. (4)

For both the (100) and (111) surfaces, the activation energy is 2.06 eV and is considered to be that for diffusion of oxygen

l.> 5 r------------------, ~ ] 2

5 L.---I._--'-_--'-__ '--I--I. ___ '-----'

005 Of 02 05 2 5 10 Partial pressure Po! (aIm)

FIG. 4. Effect of oxygen partial pressure on parabolic rate constant for InP(I00) surface at oxidation temperature of 620"C.

M. Yamaguchi and K. Ando 5008

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Page 4: Thermal oxidation of InP and properties of oxide film

Q) o c

20~------------------------------,

.810 -'E (II c

~

InP

, ! 1085 940

OL-~~~--~~~--~~~~~~~

1500 1000 500 Wave number (em-t )

FIG. 5. Infrared absorption spectrum for thermally grown oxide films on InP(lOO). Oxidation condition is at 740"C for 1 h in dry 0, at 1 atm.

through the InP oxide. The surface orientation dependence of k originates from a difference in the reaction rate constant, that is, simply surface orientation dependence9 of bond den­sity Nb (cm-2) available for reaction with oxygen molecules:

Nb(lII)/Nb(I00) = y'3

k (111)lk (100) = 1.83 ± 0.1.

Figure 4 shows the effect of oxygen partial pressure on the parabolic rate constant of the InP(I00) surface at an oxidation temperature of 620·C. The parabolic rate con­stant should be proportional to the partial pressure Po, if the oxidation theory reported by Deal and Grove lO is obeyed. However, in this study, k is proportional to the square root of the oxygen partial pressure. This dependence may be due to complicated oxidation kinetics, such as linear-parabolic re­lationship 11 accompanied by the evaporation of the oxide film and InP substrate. Moreover, at the same partial pres­sure of oxygen, the oxidation rate in air is smaller than that in dry O2, This must originate from the suppression effect of oxidation by N2 as observed in thermal oxidation ofSi (Ref. 12) and evaporation of the oxide film and InP.

B. Structural properties of thermally grown oxide film

Structural properties of thermally grown oxide films on InP substrates were examined by electron diffraction and infrared absorption spectroscopy.

The electron beam diffraction patterns of all the oxide films thermally grown at temperatures between 450 and 740 ·C revealed polycrystalline structures. Oxide films grown at 450 and 500 ·C are mostly composed of polycrys­talline InP04 (In20:~ + P20 S)' and those at 560 and 620·C are mostly In20 3• Moreover, the oxide films grown above 680 ·C are mostly composed of In20 3 and In. This suggests that the oxide films thermally grown at high temperatures, above 560 ·C, become In rich and phosphorus is vaporized

5009 J. Appl. Phys., Vol. 51, No.9, September 1980

from the InP surface during oxidation. According to the thermochemical data,7.8 the dissociation vapor pressure of P 20 S is much larger than that ofIn20 3, and thus it is expect­ed that mainly thermal decomposition of P 20S in the oxide film occurs. At the same time, thermal decomposition ofInP occurs at high temperatures above 680 ·C, and the surface of the InP oxide becomes In rich caused by evaporation of phosphorus.

Figure 5 shows the infrared absorption spectrum of thermally grown oxide film on InP. According to the in­

frared absorption spectra of In20 3 and P 20S powder and their data in Refs. 13-17, several absorption peaks of the oxide film were assigned as follows: 1155 cm-I-asymmetric stretching vibration ofP02 ; 1085 cm-I-asymmetric or sym­metric stretching vibration of In02; 1015 cm-I-symmetric stretching vibration ofP02 or P03; 940 cm-I-unknown; 745 em-I-asymmetric stretching vibration ofIn20; and 565 and 535 em-I-symmetric stretching vibration ofIn40 2•

Figure 6 shows oxidation temperature dependence of aXejJ1xO for thermally grown oxide films. aXeIT is given by the following relationship

aXeIT = In(1o/l), (5)

where a is the absorption coefficient for remarked absorp­tion line, XeIT is the effective film thickness for remarked ox­ide composition, 10 is the optical transmittance at the wave number region without oxide absorption, and 1 is the optical transmittance at the absorption band. In Fig. 6, aXelf is nor­malized to the oxide film thickness Xo, and the value of aXelf/xO is considered to correspond with the effective oxide molecule number or oxide film thickness for the remarked

t = Ih

.. .-----.. /745"," t

I =16h

Oxidation temperature (oG)

FIG. 6. Oxidation temperature dependence ofaxdf /xo for thermal oxide film on InP(lOO).

M. Yamaguchi and K. Ando 5009

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Page 5: Thermal oxidation of InP and properties of oxide film

Id2r-----------------__________ ~ forward .

Xo' OA BOOA

I08~ ____ ~ ____ ~ ____ ~ ____ ~ __ ~ o 05 10 1.5 2.0 2.5

V d12 (VII2)

FIG. 7. Typical I ~ v' V characteristics for InP MOS diodes possessing thermal oxide films of various thicknesses. Oxidation temperatures are be­low 620·C.

oxide composition. Absorption intensities for P02 (1015 cm- I

) and In02 (1085 cm- I) lines decrease with an increase in

oxidation temperature, and the decreasing rate for the P02

absorption line is larger than that for the In021ine. At oxida­tion temperatures above 560-620 °C, the absorption intensi­ties for In20(745 cm- I

) and In40l535 cm- I) lines remark­

ably increase with an increase in oxidation temperature. These results are consistent with the electron diffraction data described above, and suggest that oxide films thermally grown at high temperatures above 560-620 ·C become In rich and phosphorus is vaporized from the InP surface dur­ing oxidation, and then change into low-grade oxides, such as In20 and In402' According to the thermochemical data,S In20] vapor pressure at about 1000 K is expected to be 10-11

_

10-10 atm. Therefore it is reasonable that at high tempera­tures, above about 620 ·C, In20 3 starts to change into low­grade oxides, such as In20 and In402'

C. Electrical properties of InP MOS diodes

1. Current-voltage characteristics

Figure 7 shows typical I-v V characteristics for InP MOS diodes possessing thermally grown oxide films in var­ious thicknesses. A current flow mechanism through an ox­ide film, thermally grown below 620 ·C, of thickness below 1000 A can be explained by Schottky emission (field-en­hanced thermionic emission over an interfacial barrier), as­suming the dielectric constant Eox for the oxide is 9.2,

J, =A*Texp{-q[¢b -(qEI411'Eox )1/2]lkBT}, (6)

where Js is the Schottky current density, A * is the effective Richardson constant, ¢b is the barrier height, and E is the electric field.

5010 J. Appl. Phys., Vol. 51, No.9, September 1980

109r---------------------______ --,

____ *560°C

* /0 o 450:C ~S<::::::)<. 6 200 C 500 C

A 6800C

1 2 3 4 5 (Oxidation time )'12 tlt2 ( h'~)

FIG. 8. Oxidation temperature and time dependence of resistivities forther­mal oxide films.

Low current density regions in InP MOS diodes pos­sessing oxide films above 1000 A can be attributed to Schottky emission, assuming Eox is 8.3; high current density regions can be explained by the Poole-Frenkel mechanism 1M

(thermionic emisson from localized coulombic traps in the oxide), assuming Eox is 7.6,

JFP =CEexp{-q[¢b -(qEI11'Eox)I/Z]/kBT}, (7)

where C is a constant. The electric conduction mechanism through oxide films thermally grown above 680·C can most­ly be attributed to Ohmic conduction, which is caused by evaporation of the P 205 and InP substrate.

Figure 8 shows oxidation temperature and time depen­dence of resistivities for thermally grown oxide films. Oxide resistivities were roughly estimated from J- V characteristics for InP MOS diodes at J = 10-4 A/cm2

• Resistivites for ox­ide films thermally grown below 560·C range from 108 to 109 n cm, but those grown above 620 ·C decrease with an increase in oxidation temperature. This reflects that the ox­ide films thermally grown at high temperatures become In

C/Cox 1.0

Cox =224x167 F/cm~

x 0 = 400 A

o -I 0 1 2 3

Applied gate voltage Vo (V)

FIG. 9. Typical capacitance-voltage characteristics for InP MOS diode measured at 1 MHz. Oxidation condition is at 500 ·C for 4 h in dry 0, at I atm. The dashed line shows a theoretical C- V curve.

M. Yamaguchi and K. Ando 5010

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Page 6: Thermal oxidation of InP and properties of oxide film

rich by lack of P 205 and change into low-grade oxides, such as In20 and In40 2, as described above.

At current densities of 10-6 and 10-5 A/cm2, oxide film

resistivities were on the order of 109 n cm.

2. Capacitance-voltage characteristics

Figure 9 shows a typical capacitance normalized to Cox versus applied gate voltage V G curve measured at 1 MHz. Using a 1 X 1016 cm-3 carrier density and the dielectric ca­pacitance Cox value obtained from the capacitance asymp­tote for positive bias, a theoretical capacitance curve neglect­ing the effect of surface states was calculated and is also plotted as the dashed line in Fig. 9:

C(V) (8)

where Csc (V) is semiconductor space-charge capacitance. 19

Although the hysteresis is relatively small, the clockwise hysteresis which is caused by carrier injection20 is observed in the C- V curve.

Figure 10 shows changes in flat-band voltage VFB for InP MaS diodes as a function of oxide film thickness. The flat-band voltage proportionally increases with an increase in oxide film thickness. Surface charge density N FB at the flat band is about 1.3 X 1011 cm-2, obtained from the following relationship:

NFB = Cox VFBlq. (9)

In the case of MaS structures composed of oxide films ther­mally grown at the temperatures above 620'e, N FB increases with an increase in oxidation temperature, and is (3.5-4.5) X 1011 cm-2. This effect may be attributed to an increase in the phosphorus and oxygen vacancy, and excess In at the oxide-lnP interface.

Figure 11 shows energy level distribution for surface state density Ns determined from Terman's method,21 using the following relationship:

10r---------------------------~

> .. IL

> Q)

01

E g "t:l c: o £ 0.1 o

lL.. o

o 500. 560°C • 620°(, x 680°C t:. 7400C

103 104

o Oxide thickness Xo (A )

FIG. 10. Changes in flat-band voltage for InP MOS diode as a function of oxide film thickness.

5011 J. Appl. Phys., Vol. 51, No.9, September 1980

SI0r-------------------~ Q)

':IE u ..

Q

-01 EF(O) 0 t Energy level (eV)

02! Conduction Bond

FIG. II. Energy level distribution for surface state density, determined from Terman's method.

(10)

where.1 Vis the voltage difference between the experimental curve and theoretical C- V curve, and tPs is the surface potential.

Ns has two peaks: one energy level is at 0.075 eV below the conduction band Ec ofInP, and the other is at 0.16 eV below Ec. The level of Ec - 0.16 e V may be attributed to the phosphorus vacancy level (0.16 ± 0.03) eV as observed in the photoluminescence measurement. 22 Origin of the Ec - 0.075 eV level is not clear, but oxygen and its vacancy, and excess In are presumed to be the source of this interface state.

Moreover, the dielectric constant for InP oxide, ob­tained from C- V characteristics at 1 MHz, was 10.3 ± 1.

IV. CONCLUSION

Thermal oxidation of InP has been studied and the fol­lowing results have been obtained experimentally.

(1) The parabolic oxidation relationship is observed for a low-temperature range (45(}-620 'C). The oxide film ther­mally grown in this temperature range is transparent and is easily etched by lOH20 + Hel solution. The orientation de­pendence of the growth rate is observed and the order is (lll)P = (111)ln > (100), which can be explained by orien­tation dependence of available bond density. The activation energy is about 2.06 eV, which may be attributed to the value for diffusivity of oxygen through InP oxide. The oxide growth rate is proportional to the square root of the oxygen partial pressure.

(2) The oxidation for a high-temperature range (68(}-740 'c) results in a nonuniform and opaque oxide, which is little etched by IOH20 + Hel solution.

(3) The thermally grown oxide, which is polycrystal­line, is mostly composed of InP04 for a low-temperature range (45(}-500 'e), and the oxide is mostly composed of In203 for a high-temperature range. The electron diffraction and infrared absorption data suggest that the oxide film for a high-temperature range becomes In rich and low-grade ox-

M. Yamaguchi and K. Ando 5011

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Page 7: Thermal oxidation of InP and properties of oxide film

ide such as In40 2 and In20, which is caused by the evapora­tion of phosphorus.

(4) Flows of Schottky emission current and Poole-Fren­kel current through the oxide film are observed, whereby resistivity of the oxide ranges from 108 to 109 fl cm. The resistivity of the oxide decreases with an increase in oxida­tion temperature for a high-temperature range, above 620°C, which is caused by the formation of a low-grade ox­ide and the evaporation of phosphorus.

(5) Surface charge density is 1.3 X 1011 cm-2 for a low­temperature range oxide film. For a high-temperature range, surface charge density is (3.5-4.5) X 1011 cm-2

• Energy distri­bution in surface state density, determined from Terman's method, indicates the existence of interface states Ec -0.075 eV and Ec -0.16 eV, which may be attributed to

phosphorus vacancy and so on.

ACKNOWLEDGMENTS

The authors express their sincere thanks to Dr. N. Nii­zeki, Dr. H. Takata, Dr. K. Kudo, and Mr. C. Uemura for their valuable suggestion and encouragement, and to Mr. S. Shinoyama for supplying the InP single crystals in this work.

5012 J. Appl. Phys., Vol. 51, No.9, September 1980

10. Wada and A. Majerfeld, Electron. Lett. 14,125 (1978). 2D. L. Lile and D. A. Collins, App!. Phys. Lett. 28,554 (1976). 'C. W. Wilmsen and R. W. Kee, J. Vac. Sci. Techno!. 14,953 (1977). 4c. W. Wilmsen and R. W. Kee, J. Vac. Sci. Techno!. 15, 1513 (1978). 51. Barin and O. Knacke, Thermochemical Properties of Inorganic Sub­stances (Springer-Verlag, Berlin, 1977), Supplement.

"JANAF Tables (NBS, Washington, DC, 1971). 70. Kubaschewski, E. L. Evans, and C. B. Alcock, Metallurgical Thermo­chemistry (Pergamon, Oxford, 1967), p. 415.

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( 1975). I3R. Roy and M. W. Shafer, J. Phys. Chern. 54, 372 (1954). 14A. J. Hinchcliffe and J. S. Ogden, J. Phys. Chern. 77, 2573 (1973). "L. W. Daasch and D. C. Smith, Ana!' Chern. 23, 853 (1951). 16E. E. Bery, Spectrochimica Acta 24A, 1727 (1968). 17 A. C. Chapman and L. E. Thirlwell, Spectrochimica Acta 20, 937 (1964). 1Xy. Mita, J. Phys. Soc. Jpn. 20, 1822 (1963). 19 A. S. Grove, B. E. Deal, E. H. Snow, and C. T. Sah, Solid State Electron. 8,

145 (1965). 2uH. H. Wieder, J. Vac. Sci. Techno!. IS, 1498 (1978). 21L. M. Terman, Solid State Electron. 5, 285 (1962). nJ. B. Mullin, A. Royle, B. W. Straughan, P. 1. Tufton, and E. W. Williams,

J. Cryst. Growth 13/14,640 (1972).

M. Yamaguchi and K. Ando 5012

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