chapter 2. semiconductor surface studies

Chapter 2. Semiconductor Surface Studies


Academic and Research Staff

Professor John D. Joannopoulos, Professor Tomas A. Arias, Dr. Karl Brommer

Graduate Students

Rodrigo B. Capaz, Kyeongjae Cho

Technical and Support Staff

Imadiel Ariel

2.1 Introduction

Sponsor

Joint Services Electronics ProgramContract DAAL03-92-C-0001Grant DAAH04-95-1-0038

Understanding the properties of surfaces of solidsand the interactions of atoms and molecules withsurfaces is extremely important both from the tech-nological and academic points of view. The adventof ultrahigh vacuum technology has made micro-scopic studies of well-characterized surfacesystems possible. The way atoms move to reducethe energy of the surface, the number of layers ofatoms involved in this reduction, the electronic andvibrational states that result from this movement,and the final symmetry of the surface layer are allof utmost importance in arriving at a fundamentaland microscopic understanding of the nature ofclean surfaces, chemisorption processes, and theinitial stages of interface formation.

The theoretical problems associated with thesesystems are quite complex. However, we are cur-rently at the forefront of solving the properties ofreal surface systems. In particular, we are contin-uing our efforts to develop new techniques for cal-culating the total ground-state energy of a surfacesystem from "first principles," so that we canprovide accurate theoretical predictions of surfacegeometries and behavior. Our efforts in thisprogram have concentrated in the areas of surfacegrowth, surface reconstruction geometries, struc-tural phase transitions, and chemisorption.

2.2 Chemisorption

In this section we discuss an ab initio theoreticalinvestigation of the electronic surface states and thereactivity of the Si(111)-(7x7) surface recon-struction. The Si(111)-(7x7) reconstruction has a

rich and complex chemistry because it contains adiverse set of dangling bonds. This surface is achallenge for studying surface reactions, because asingle atomic species reconstructs into a large (7x7)unit cell containing nineteen dangling bonds. Thenineteen dangling bonds in the unit cell define nine-teen different reactive sites, each on a silicon atom.Seven are unique, with the other twelve related bysymmetry. It is difficult and challenging to ratio-nalize the dramatic differences in reactivity amongthe different sites on the surface. While this recon-struction has been studied for thirty years, it is onlywith the use of massively parallel computers thatrealistic ab initio studies of its electronic structureare tractable. In particular, we used the ab initiomolecular dynamics scheme that we have devel-oped at MIT for calculating the electronic states andcomputing the relaxed positions of the ions.

The relaxed positions of atoms in the 7x7 unit cellare plotted in figure 1. A top view of the surfacewith the unit cell outlined with dotted lines is shownin figure l a. In this figure, all unique dangling

Figure 1. Si(111)-(7x7) surface dangling bond sites.


bonds are labeled with capital letters. The faultedand unfaulted rest atoms, denoted by shadedcircles labeled A and A' respectively, sit on the topsurface bilayers. There are a total of six restatoms, three on each side of the unit cell. Thelarge black circles labeled B, B', C and C' denoteadatoms sitting on the top of the first surfacebilayer. The six adatoms on each side of the unitcell form triangles. Adatoms at the faulted andunfaulted triangle corners B and B' are chemicallydistinct from adatoms at the triangle centers C andC'. The relative heights of the surface atoms areplotted in figure lb, showing a side view throughthe long diagonal of the cell. It can be seen thatthe rest atoms with the dangling bonds are buckledslightly upward from the positions of other first-layeratoms. In the side view, the depth of the large holeat each corner of the cell is also apparent. Insidethis corner hole sits the nineteenth dangling bondsite, labeled D.

Surface chemisorption will depend on a variety offactors, especially electronic effects dictating theexistence and magnitude and activation barriers, aswell as dissipative channels for the energy of inci-dent reactants, steric constraints, and surface dif-fusion. The close similarity of different danglingbonds sites on the complex Si(111)-(7x7) surfacereconstruction means that most of the commonchemisorption factors are virtually identical amongthe different sites. To determine reactivity we con-struct a theory that is based on two parametersdescribing the electronic surface states: the globalelectronegativity, and the local softness.

The definition of local softness introduced by Yangand Parr for metals was extended to systems with agap to obtain regional softness for the Si(111 )-(7x7)surface reconstruction. Two different classes ofregional softness are calculated, one related to thenucleophilic (acceptor) capacity, and the otherrelated to the electroophilic (acceptor) capacity ofthe surface. Accordingly, an order can be assignedfor the nucleophilic and electrophilic nature of theseven dangling bonds of the surface. From thisanalysis of regional softness, a general qualitativebehavior for the reactivity of this surface recon-struction can emerge.

For our application, we are interested in deter-mining the possible differences in reactivity betweenthe seven types of dangling bonds in the system.To do this we defined a regional reactivity indexassociated with a local region of the surfacethrough spatial integration of the local softness

S =f s(r) dr,

where Qi is the local volume surrounding the dan-gling bond i. As an extension of the physicalmeaning of s(r) we interpret Si as the measure ofthe ability of the dangling bond i to perform chargetransfer. Extrapolating from Politzer, we choose thename charge capacity for this property. Thus, dif-ferences in charge transfer capabilities among thedifferent dangling bonds will be determined entirelythrough Si.

Our calculations of the charge capacity, Si areexhibited in figure 2. An analysis of the values inthis figure shows that the donor and acceptorcapacities follow the order displayed in table 1.Table 2 summarizes the differences in chargecapacity between faulted and unfaulted halves ofthe unit cell.

a) 1.0 .2.6 .2 0 .5 0

(b) .4 .7 0 1.0 .6 .1 1.0

Figure 2. Charge capacity of each unique dangling bondon the 7x7 surface for (a) electrophilic and (b)necleophilic reactants.

Table 1. Charge capacity order for differentsites on the Si(111)-(7x7) reconstruction

Surface donor Corner hole > rest atoms >capacity adatoms

Surface Adatoms > corner hole >acceptor rest atomscapacity

Table 2. Differences in charge capacitybetween faulted and unfaulted halves

As a donor Faulted rest atoms >unfaulted rest atoms

As an acceptor Faulted center adatoms >unfaulted center adatomUnfaulted corner adatoms >faulted corner adatom

General reactivity patterns. According to table 1,electrophilic attaching groups interact with thesurface in the following order: corner hole > restatom > adatoms. The corner hole and rest atom

172 RLE Progress Report Number 137


reactivities are strong, while the adatom reactivity isrelatively weak. The nucleophilic groups interactwith the surface mainly through the adatoms, to alesser extent with corner holes, and most weaklywith the rest atoms. Among the seven differentdangling bonds the corner holes is unique in exhib-iting a strongly active site for electrophilic reactantsas well as exhibiting some reactivity for nucleophilicreactants. Adatoms are more selective towardsnucleopholes. While rest atoms are strongly reac-tive toward electrophilic species, the rest atoms areweakly reactive toward necleophilic species.

We now consider the effects of the stacking fault inthe reactivity of the Si(111)-(7x7) reconstruction.With respect to donor capacity, there is a clear dis-tinction between reactivity at faulted and unfaultedhalves as shown in table 2. Electrophiles shouldprefer to interact with the faulted half of the surface,and in particular with the faulted rest atoms. Withrespect to acceptor capacity, there does not appearas strong a selectivity for one half or the other sincepreferred reactive sites are found on both sides tothe unit cell. If a donor (nucleophile) reacts with thefaulted half, the interaction will be primarily with thefaulted center adatom. If the unfaulted half isselected, the interaction is generally with theunfaulted corner adatom.

Reactions preserving reconstruction. To illustratethe utility of the present approach, we will use it toanalyze some experimental reactivity patters of theSi(111)-(7x7) reconstruction. In particular, table 3displays the reactivity patterns for some attackingcompounds which maintain the reconstruction. Theexperimental information was obtained usinginfrared spectroscopic techniques by Chabal and byscanning tunneling microscopy (STM) by Avourisand colleagues. To classify the reactants asdonors or acceptors, we used an electronegativitycriterion. If the difference in electronegativitybetween the surface and the reactant is negative,then the reactant is the acceptor and the surfacethe donor. If the difference is positive, the roles arereversed. Table 4 shows these differences for aseries of compounds. Electronegativities for thereactants were taken from Pearson's estimations.The surface electronegativity is the work function,4.8 eV.

Interaction with hydrogen. According to table 4, Hcan be classified as an acceptor species withrespect to the surface. Hydrogen is one of themost electronegative of the neutral reactants listedin this table. From table 4 it is clear that the cornerhole atoms are the most reactive sites in this case,and this is in complete agreement with the exper-iments of Chabal et al. summarized in table 3.

Interaction with Pd, Ag,4, these metal atomsrespect to the surface.

and Li. According to tableare electron donors with

Thus, our theoretical calcu-lations suggest that they should interact primarilywith adatoms and specifically with faulted centeradatoms. This is again consistent with the exper-imental evidence summarized in table 3.

Interaction with NH3, H20, and PH3. These mole-cules dissociate on the surface into anions OH-,(NH2)-, and (PH2)- and the cation H+. From table 4,all of the dissociation products except the protonare donors. The proton is clearly a strong acceptor.By assuming that the dissociation process takesplace in the initial step of the reaction withoutinducing large changes in the chemical potential ofthe surface, we determine the order of preferentialreactivity as corner hole atoms, then rest atoms,and last adatoms. Table 3 shows that the predictedreactivity order of rest atoms and adatoms agreeswith experimental STM data. Our calculations alsopredict that the corner hole site is the most reactive.This remains to be detected experimentally, butmay be difficult due to the depth of the corner holebelow the adatom and rest atom layers.

Interaction with 02. From table 4, the 02 moleculeis an electron acceptor with respect to the Sisurface. Therefore, it should prefer to interact withthe faulted half of the unit cell. Our calculationspredict that the corner hole is the preferred reactionsite, followed by rest atoms and adatoms. Thepreference for the faulted half agrees with STMexperiments. Room temperature experiments haveshown that 02 is a molecular precursor which thendissociates and reacts preferentially with corneradatoms compared to center adatoms. While theregional softness of the isolated Si surface explainsthe preference for the faulted half by the molecularprecursor, the presence of 02 on the surfacechanges the local softness sufficiently to require

173

Table 3. Experimental studies of chemicalreactivity of the Si(111)-(7x7) reconstruction

Reactant Method Reactivity

H Spec- The most active site istroscopy the corner hole atom

Pd, Ag, STM The faulted half is pre-Li ferred and reactants are

believed to bond prima-rily to rest atoms andcenter adatoms

NH3, H20, STM Rest atoms > centerPH 3 adatoms > corner

adatoms


recomputation of local softness to analyze reactivityafter dissociation.

Table 4. Relative electronegativity of reactants

Reactant Electronegativity dif-ference (eV)

Li 1.8

Ag 0.4

Pd 0.3

PH3 0.7

H -2.4

NH 3 2.2

H20 1.7

Radicals (anions)

NH 2 -1.3

OH -2.7

PH2 -0.7

Acceptors

As -0.5

Au -1.0

Pt -0.8

Metal cations <0.0

Halgen atoms <0.0

BF 3 -1.4

H2 -1.9

02 -1.5

Donors

Ga 1.6

Pb 0.9

Al 1.6

Ti 1.3

Alkaline Metals >0.0

Predicted interactions. Based on the success ofour reactivity analysis as demonstrated in the pre-ceding example, we attempt to predict the reactivityassociated with a number of atoms and moleculesthat yet remain to be studied. By using Pearson's


electronegativity tables and the work function of thesurface, we can classify a great variety of atomsand molecules as donors or acceptors with respectto the Si(111)-(7x7) reconstruction. Selectedexamples are presented in table 5 including predic-tions of possible reaction patterns. Theseexamples were chosen to illustrate the interaction ofboth acceptors and donors with the surface,including both hard and soft chemical reactants.The predictions assume non dissociative inter-actions and that surface reconstruction is main-tained.

Table 5. Theoretical predictions of the chemicalreactivity of the Si(111)-(7x7) reconstruction

Reactant Reactivity

Acceptors: As, Au, Pt, Corner hole > restmetal cations, atoms > adatomshalogens, BF3, H2

Faulted rest atom >unfaulted rest atom

Donors: Ga, Pb, Al, Adatoms > cornerTi, Ca, alkaline holes > rest atomsmetals

Faulted centeradatoms > faultedcorner adatoms

2.3 Cross-sectional ScanningTunneling MicroscopyScanning tunneling microscopy (STM) provides animage of the structure of a surface at atomic resol-ution. This STM image is generated by an electrontunneling between the STM tip and a surface atomunder the tip as a result of the overlap between thetip and surface wave functions. Consequently, thetip and the surface may in certain cases interactsignificantly during the process of an STM meas-urement. The conventional theories of STM,however, are based on a first order perturbationapproximation which does not include the tip-surface interaction. STM images are then inter-preted simply as a convolution of the tip wavefunction and the surface wave function. Althoughthis interpretation is a very useful approximation formany applications, there may exist systems forwhich the tip-surface interaction and the surfacedynamics play a crucial role in the STM measure-ment process.

In this section we describe ab initio total energypseudopotential calculations to demonstrate thatthe Si(100) surface is an example of a system forwhich STM does not provide a direct mapping of


the surface atomic structure and that a conventionalinterpretation of the STM images is not appropriate.Typically, a room temperature STM image of theSi(100) surface shows the majority of dimers inwhat appear to be unbuckled, symmetric configura-tions. Such configurations are in disagreement withthe theoretical predictions of buckled, asymmetricdimer configurations. One might expect that thisdiscrepancy could reasonably be resolved byarguing that thermal fluctuations in the asymmetricdimer configurations will create an averaged or"symmetric" image. Such thermal fluctuations havebeen predicted to be present on the surface in theabsence of a tip. In the presence of a tip, however,we propose that a different mechanism is opera-tional. Specifically, we demonstrate that the tip-surface interactions are significant enough to flipand bind an asymmetric dimer to the tip. As the tipis then moved along the surface, dimers are flippedtracking the tip and create what appears to be asymmetric image in the scan.

In our calculations, we allowed the tip to vary inthe range 4.5 to 5.2 A above the atoms in the out-ermost surface layer. As shown in figure 3 even forthe shortest tip-surface distance of 4.5 A, thesurface is not greatly perturbed by the presence ofthe tip, and no new bonds are formed betweenthem. Nevertheless, as we discuss in the nextsection, there is enough interaction between tip andsurface to significantly alter the dynamics of thesurface dimers.

Figure 3. This plot shows a cross section of the totalcharge density of the tip-surface system with the tipdirectly above an upper dimer atom. The buckling angleof the dimer, the position of the apex tip atom, and thecharge density distributions of the tip and the dimer arenot significantly changed by the tip-surface interaction,but the intereaction energy is significant. (- 0.57 eV).

Interaction energies. The tip-surface interactionenergy is calculated by combining three separately

calculated energies: E(tip), E(surface), andE(tip+surface). The results of our calculations for atip restricted to lie directly above a surface atom aresummarized in figure 4. For the configurationshown on the left panel, the tip lies 5.2 A above thelower dimer atom, and the interaction energy is-0.37 eV. The panel at the center of the figurerefers to a symmetric dimer configuration that corre-sponds to the "saddle point" or static barrier config-uration for flipping the buckled dimer. In theabsence of the tip, the barrier is calculated to be0.08 eV in good agreement with 0.09 eV asobtained by Dabrowski and Scheffler. In the pres-ence of the tip, the barrier for an up flip of thebuckled dimer is found to be 0.1 eV. The oppositebarrier, corresponding to a down flip of the buckleddimer is obtained from the right panel of figure 4and is found to be 0.3 eV. Note that the interactionenergy in the latter case is correspondingly large at-0.57 eV and the distance between tip and dimeratom is 4.5 A.

0=-17 9o0 e=17

Dimer Buckling Angle

Figure 4. Total energy (in eV) of a tip-surface system asa function of surface-dimer buckling angle. The tip(shown schematically as a triangle with filled circles) issituated directly above a surface-dimer atom (opencircles). The results at and above the horizontal dashedline correspond to E(tip) + E(surface). Note that thebarrier for flipping from one asymmetric dimer configura-tion to the other is about 0.08 eV. The panels below thedashed line correspond to the fully interacting tip-surfacesystem. In this case the horizontal bars correspond toE(tip + surface). Note that the barriers for up flip anddown flip are 0.1 and 0.3 eV, respectively.

Implications. For a given value of energy barrierEb, the average time that a dimer spends in oneasymmetric configuration before flipping to the otheris simply


Tb = 10- 13eEkBT,

where the phonon frequency is estimated to be1013 sec - 1. During an STM measurement, an STMtip typically stays 2 x 10-3 sec tSTM above asurface atom, and therefore the relative values ofTb and tSTM will determine the nature of the STMimage. In the absence of interactions between theSTM tip and the surface, a buckled dimer is in asymmetric potential well as shown in the uppercurve of figure 4, and the energy barrier for flipping(0.08-0.09 eV) is small enough that at room temper-ature the dimer can flip up and down very fre-quently (Tb = 2 x 10 12 sec). This would lead to asymmetric STM image that is the average of up-flipand down-flop configurations.

In the presence of interactions between the STM tipand surface, a buckled dimer is an asymmetricpotential well as shown in the lower curve of figure4 and Tb is different for the down-flip and the up-flipconfigurations. At room temperature, Tb'S are shortenough (Tdown = 5 x 10 12 sec and Tup = 1.3 x 10-8sec) that, in principle, the dimer can flip up anddown freely, and thermal equilibrium between twolocal energy minima of the asymmetric potential isreached during the STM imaging time. Therefore,the dimer spends different amounts of time in eachlocal energy minimum, and the ratio of the times isgiven by the Boltzmann factor of the difference oftwo local minimum energies (4 x 10-4). Conse-quently, the dimer stays in the up-flip configurationexcept for intermittent rapid round trips to the down-flip configuration. For all practical purposes, there-fore, one is always measuring a dimer in the up-flipposition as the tip moves along the surface. Theresulting image is then deceptively that of a "sym-metric" dimer.

2.4 Publications

Arias, T., and J.D. Joannopoulos. "Electron Trap-ping and Impurity Segregation at Grain Bounda-ries." Phys. Rev. B 49: 4525 (1994).

Arias, T., and J.D. Joannopoulos. "Ab-initio Theoryof Dislocation Interactions." Phys. Rev. Lett. 73:680 (1994).

Brommer, K., M. Calvan, A. Dal Pino, and J.D.Joannopoulos. "Theory of Adorption of Atomsand Molecules on Si(111)-(7x7)." Sur. Sci. 314:57 (1994).

Capaz, R., A. Dal Pino, and J.D. Joannopoulos."Identification of the Migration Path of InterstitialCarbon in Si." Phys. Rev. B 50: 7439 (1994).

Cho, K., and J.D. Joannopoulos. "The DevilishWorld of Surfaces." Proceedings of the TeraflopComputer Conference, Baton Rouge, 1994.

Devenyi, A., K. Cho, T. Arias, and J.D.Joannopoulos. "Adaptive Riemannian Metric forAll-Electron Calculations." Phys. Rev. B 49:13373 (1994).

Fan, S., A. Devenyi, R. Meade, and J.D.Joannopoulos. "Guided Modes in PeriodicDielectic Materials." J. Opt. Soc. Am. (1995) inpress.

Fan, S., P. Villeneuve, R. Meade, and J.D.Joannopoulos. "Design of 3D Photonic Crystalsat Submicron Lengthscales." Appl. Phys. Lett.65: 1466 (1994).

Joannopoulos, J.D., "Ab-initio StatisticalMechanics." Proceedings of the QTRM Confer-ence, Berkeley, California, 1994.

Larrabee, J., V. Baisley, R. Huffman, R.and J.D. Joannopoulos. "Detectivity ofPhotodiode." Proceedings of the SPIEence, San Diego, California, 1994.

Meade,a UB-BConfer-

Meade, R., A. Devenyi, J.D. Joannopoulos, O.Alerhand, D. Smith, and K. Kash. "Novel Appli-cations of Photonic Band Gap Materials." J.Appl. Phys. 75: 4753 (1994).

Mucciolo, E., R. Capas, B. Altshuler, and J.D.Joannopoulos. "Manifestation of QuantumChaos in Electronic Band Structures." Phys.Rev. B 50: 8254 (1994).

Winn, J., R. Meade, and J.D. Joannopoulos. "TwoDimensional Photonic Band Gap Materials." J.Opt. 41: 257 (1994).


chapter 2. semiconductor surface studies

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