Chapter 4. Semiconductor Surface Studies

Chapter 4. Semiconductor Surface Studies

Academic and Research Staff

Professor John D. Joannopoulos, Dr. Tomas A. Arias, Dr. Robert D. Meade

Graduate Students

Rodrigo B. Capaz, Kyeongjae Cho, Jing Wang

Technical and Support Staff

Imadiel Ariel

4.1 Introduction

SponsorsJoint Services Electronics Program

Contract DAAL03-92-C-0001

Understanding the properties of the surfaces ofsolids and the interactions of atoms and moleculeswith surfaces has been of extreme importance bothfrom a technological and an academic point of view.The advent of ultrahigh vacuum technology hasmade microscopic studies of well-characterizedsurface systems possible. The way atoms move toreduce the energy of the surface, the number oflayers of atoms involved in this reduction, the elec-tronic and vibrational states that result from thismovement, and the final symmetry of the surfacelayer are all of utmost importance in arriving at afundamental and microscopic understanding of thenature of clean surfaces, chemisorption processes,and the initial 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.

4.2 Defects on Surfaces

Real surfaces typically contain a variety ofimperfections that can be important in determiningtheir electronic and chemical behavior. A partic-ularly interesting system is the vicinal Si(100)surface. The Si(100) surface has been an object ofintensive study for the last three decades in partbecause it is technologically important in semicon-ductor industry, and in part because its recon-structions are simple enough to be tractable totheoretical investigations.

Although much is understood about the electronicand structural properties of Si(100), there has beenrelatively little work done to study the nature ofintrinsic defects on this surface. Interestingly,scanning-tunneling-microscopy (STM) images ofthis surface consistently show the presence of alarge number of what appear to be missing dimersor dimer vacancies (DV). In fact, a typical STMimage of this surface exhibits three striking fea-tures. The first is the very large number of missingdimers present on the surface. The second is thatthe missing dimer defects tend to congregate intosmall clusters, and the third is that the clustersappear to form distinctive complexes that dominateover others. These results are summarized for atypical image (which had about 22,000 dimer sitesin total) in figure 1. The data shown here are froma surface annealed at 7000C and "flashed" up to1100C for several minutes. The STM image,however, is taken at room temperature after thesample has cooled down. The STM image there-fore represents a quasi-equilibrium "snap-shot" atsome freezing-in temperature below 7000C.

In order to unravel this striking behavior, we com-bined ab-initio total energy calculations of the ener-getics of over 20 defect complexes with statisticalmechanical and kinetic arguments to construct ameaningful and realistic theory of this system.Examples of some of the defects and defect com-plexes studied are shown in figures 2-4. In figure 5

Chapter 4. Semiconductor Surface Studies

Figure 1. The total number and fraction of various DV,DV clusters, and DV cluster complexes on the surface.

2.74 A 2 34 A

I I f(a)

2.29 2.40A

I / II(b)

Figure 2. Total energy and restoring force as a surfacedimer penetrates the bulk to attempt to form an interstitialdimer. (a) Schematic diagram illustrating three stages ofthe penetration process. Open circles represent thesurface atoms and shaded circles, bulk atoms. (b) Theforce and formation energy of the dimer as a function ofpenetration depth. Note the absence of a metastableinterstitial-dimer configuration.

we summarize the results of our total energy calcu-lations for some of the most important defects anddefect complexes.

Let us now address the problem of predicting thedistribution of DV clusters and complexes on the Si

(a)

(b)

Figure 3. Two stable configurations of the 2-DV basedcluster complexes. (a) The stable configuration for(1+2)-DV: the unrebonded side of the 2-DV cluster linkswith a rebonded 1-DV. (b) The stable configuration of the(1+2+1)-DV: two rebonded 1-DVs link to either side of the2-DV cluster. The symbols are the same as in figure 2.

surface. The first phase in the analysis of thedefect distribution is to determine whether thekinetics of the anneal at 800-11000C are sufficientto establish a thermal distribution among thedefects or whether some trace remains of the initialdistribution form cleavage. The kinetic pathwayswhich contribute to the distribution after the initialanneal must have barriers sufficiently low that theymay be expected to be traversed during the timescale of the anneal. Taking the waiting time for atransition event to be on the order of 1 minute, theattempt rate to be near the Si optic phonon fre-quency (the final answer is not sensitive to thesevalues as we eventually take a logarithm), and theprobability of a successful traversal to be theBoltzmann factor, we conclude the maximum barrierheight for allowed paths in this experiment is 4.0 eVat the peak anneal temperature.

In figure 6, we show the pathways whose energybarriers we find to be near or less than the 4.0-eVcutoff. Note the defects we have considered in thiswork form a connected Markov chain which is tiedto the sink and the source of DVs by diffusion ofsingle DVs to the step edges. Therefore, theannealing process will be sufficient to remove alltraces of the DV distribution of DV clusters andcomplexes.

After the initial anneal is completed, the sample isthen cooled to room temperature before being scru-tinized by the STM. Understanding the behavior ofthe distribution during this process requires a moredetailed look at the transitions between the DV

182 RLE Progress Report Number 136

Chapter 4. Semiconductor Surface Studies

Figure 4. (a) The nearly degenerate stable and (b)metastable configurations of the (1+3+1)-DV cluster com-plexes. The symbols are the same as in figure 2.

defects. Three broad groups make up these transi-tions. The first group, indicated by the solid lines infigure 6, have relatively low energy barriers. Thesetransitions all involve processes whereby an iso-lated dimer vacancy can migrate to an adjacentsite. Using our estimates of the three basic typesof second-layer rebonds, we find that all thetransitons in this class traverse barriers of about 2.5eV.

The second class of transition, indicated by thedashed lines in figure 6, have significantly higherbarriers because they can occur only by disturbingthe strong second-layer rebonding adjacent to themoving dimer. The barrier heights for these transi-tions are more difficult to estimate quantitatively, butour bond counting puts them in the range of 3.5-4.0eV. The broken solid line in figure 6 represents anexample of a third class of transition which webelieve to be rare despite its energy barrier being inthe first class. This is the transition by which theDV on the far right of the (1+2+1)-DV complexstretched in figure 5 migrates to the left, leavingbehind a (1+2)-DV complex. This motion aloneresults in a high-energy metastable (1+2)-DVcomplex which can decay into the stable (1+2)-DVcomplex only by the independent migration of bothsecond-layer rebonds across the 2-DV cluster. Thisparticular transition therefore requires three inde-pendent motions to occur in concert (the initialdimer migration plus the migration of the rebonds),and so we suggest in our model that the attemptfrequency for this transition may be so muchreduced from the optic phonon frequency that thispathway is not relevant in the system.

We are now ready to understand the system'sbehavior as it cools from the anneal. As thesystem cools, the higher-energy transitions rapidlybecome inaccessible to the system, severing the

Figure 5. The formation energy (in eV) of DV, DV clus-ters, and DV cluster complexes. The second column illus-trates the second-layer rebonding. The third column isthe formation energy from the ab initio calculation, thefourth column the Keating correction, and the fifth andsixth columns are corrected formation energy per struc-ture or per dimer, respectively.

Markov chain into two disconnected parts byremoving the dashed pathways shown in figure 6.As a consequence, the system of complexes com-prising the upper part of the chain in the figureloses thermal contact with the rest of the system asthe temperature drops below 900-11000C (corre-sponding to 3.5-4.0 eV). Although low barrier tran-sitions among these complexes continue to occurdown to about 5700C (the freeze-in temperature forthe lower barrier transitions by the familiar kineticargument), they cannot change the total number ofthese complexes, which will remain fixed as thesystem cools. These transitions, however, willaffect the relative distribution among those com-plexes, which will track the surface temperaturedown to the lower freeze-in temperature.

The lower part of the chain, however, remains incontact with the DV source and the sink at the stepedges through lower-energy single DV migrationsand thus remains in overall thermal equilibrium withthe surface until the lower freeze-in temperature.

In figure 7 we confirm the predictions of our theorywith a plot of our calculated defect energies, E,,against - In(ng), where n is the experimentallyobserved defect density. We choose this scaling sothat Boltzmann distributed data appear as straight

Chapter 4. Semiconductor Surface Studies

Figure 6. Illustration of the Markov chain formed by theprincipal DV defects and the primary pathways amongthem. Dashed lines represent transitions with relativelylarge energy barriers (-3.5-4.0 eV) which cease to be rel-evant around 900-11000C, while solid lines representtransitions of lower energy near 2.5 eV, which essentiallyshut off around 5700C. The transition with the brokensolid line also has a barrier near 2.5 eV, but it isexpected to be forbidden by a low attempt frequency.

lines. Our model predicts all of the salient featuresof this plot. First, the data from the experiment areclearly clustered in two-groupings correspondingexactly to the severed halves of the Markov chain.Second, the lower group, containing the defectswhich remain in thermal contact with the steps, fallsnicely along the predicted 5700C Boltzmann dis-tribution. The (1+2)-Dv complex appears to fallsomewhat above the rest of this grouping, probablyas a result of the favorable elastic interactionbetween the stress field of the constituent 1- and2-DV clusters, which raises the barrier to decay byroughly 0.2 eV, corresponding to a 600C increase inthe freeze-in temperature. Next, the center of thesecond grouping lies, as expected, within the900-1100C Boltzmann distributions, but thegrouping exhibits a relative temperature, or slope,observably less than 9000C and more in line withthat of the lower freeze-in temperature of 5700C.This final feature is the direct result of the mainte-nance of local thermal equilibrium among thesedefects after they have lost thermal contact with therest of the system.

1+3-+1-DV~ b +3--VDb.,"

1+3+1-DV(a) ..

( +2-DV 1

2-DV

I-DV

f O-~D

184 RLE Progress Report Number 136

1.4

1.2 1 l0TC

1

0.,,_

S0.4

0.2

0 2 4 6 8 10

In (q/n,)

Figure 7. Plot of the ab initio formation energy of eachdefect vs. the logarithm of the experimental defectdensity, ni, normalized by appropriate degeneracy factors,g,. Data with absolute Boltzmann distribution at 570, 900,and 11000 C fall along the straight lines indicated in thefigure which pass through the origin. A relative Boltzmanndistribution (see text for definition and discussion) at5700C is sketched through the data clustered at the topof the figure. Note that the two groupings of data corre-spond exactly to the severed parts of the Markov chain infigure 6.

4.3 Cross-sectional ScanningTunneling MicroscopyCross-sectional Scanning Tunneling Microscopy(X-STM) is a potentially powerful experimental toolfor investigating interface structure in heteroepitaxialgrowth. An unfortunate problem with STM,however, has been the unambiguous identificationof chemical species when several types of atomsare present in a variety of bonding configurations.For example, there are two serious questions whicharise when considering an experiment using X-STMto investigate the initial stages of growth in anactual heteroepitaxial system such as GaAs on Si.First, it is not obvious that the isolated Ga and Asatoms on the surface of a Si substrate could beuniquely identified, either by the contrast they pro-duced in an X-STM image (induced by charge-density fluctuations) or by changes in the I-Vsignature of the tunneling current in the vicinity ofsuch atoms. Second, the interactions between thecharge-density fluctuations from the cleaved surfaceof the bulk and the growth Si-doped surface andtheir impact on the resultant X-STM image are notwell-understood. For these two reasons, we havechosen to take a simplified approach as a first stepin our investigation of the initial stages ofheteorpitaxy of GaAs on Si. We have chosen firstto examine, by theoretical methods, the chemicalinteractions taking place in the vicinity of a plane ofimpurity atoms embedded in a host crystal, and topredict whether or not unambiguous chemical iden-tification can be performed on an isolated impurity

Chapter 4. Semiconductor Surface Studies

atom in such a system. By choosing thisprototypical "embedded-surface" approach, we caneliminate the additional complications provided bythe growth surface. Because we are interested inthe atomic interactions between Ga, As and Si, forthis work we have chosen to examine the use of Siatoms to dope a GaAs crystal. Doping of semicon-ducting materials, in which dopant atoms are inten-tionally confined to a single atomic plane in the hostcrystal, has been widely applied to the explorationof quantum effects in two-dimensional structures(where the doping profiles can be narrower than thede Broglie wavelength of electrons in the material),and has also led to important technological devel-opments such as high mobility transistors, non-alloyed contacts, Schottky-gate transistors, anddoping superlattice devices such as spatial lightmodulators and lasers.

The results of our calculations of the electronicstructure of the clean and doped GaAs(1 10)cleaved surface, and associated theoretical X-STMimages at varying bias voltages, have led to severalinteresting predictions, including: (1) Si does notbehave as a conventional donor on the surface; (2)the electronic state associate with Si lies deep inthe gap and is very localized on the surface; (3) atnegative bias voltages, the signature of the Si atomhas enhanced intensity at 3rd-nearest neighborsites; and (4) for positive bias, the signature of Siwould be that of a missing atom on the surface (I)The latter result is shown in figure 8. These predic-tions have recently been experimentally confirmedby Professor E. Weber's group at the University ofCalifornia at Berkeley.

4.4 Publications

Arias, T., and J.D. Joannopoulos. "The View ofGrain Boundaries and Segregation from theComputational Leading Edge." Electrochem.Soc. Proc., 1993.

Brommer, K., B. Larson, M. Needels, and J.D.Joannopoulos. "Modeling Large Surface Recon-structions on the Connection Machine." J. Appl.Phys. 32: 1360 (1993).

Brommer, K., B. Larson, M. Needels, and J.D.Joannopoulos. "Implementation of the Car-Parrinello Algorithm for Ab-Initio Total EnergyCalculations on a Massively Parallel Computer."Computers in Phys. 7(3): 350 (1993).

Cho, K., T. Arias, and J.D. Joannopoulos."Wavelets in Electronic Structure Calculations."Phys. Rev. Lett. 71: 1808 (1993).

Figure 8. Theoretical positive-bias X-STM image of theGaAs (110) surface with a Si impurity. What appers to bea missing Ga atom is in fact the signature of the Si atom.

Cho, K., J.D. Joannopoulos, and L. Kleinman."Constant Temperature Molecular Dynamicswith Momentum Conservation." Phys. Rev. E47: 3145 (1993).

Dal Pino, A., Jr.,Joannopoulos.Segregation atPhys. 98: 1606

M. Galvan, T. Arias, and J.D."Chemical Softness and ImpurityGrain Boundaries." J. Chem.

(1993).

Dal Pino, A., Jr., A. Rappe, and"Ab-Initio Investigation ofDefects in Silicon." Phys.(1993).

J.D. Joannopoulos.Carbon Related

Rev. B 47: 12554

Galvan, M., A. Dal Pino, Jr., J. Wang, and J.D.Joannopoulos. "Local Softness, STM andSurface Reactivity." J. Phys. Chem. Lett. 97:783 (1993).

Galvan, M., A. Dal Pino, Jr., andJoannopoulos. "Hardness and SoftnessAb-initio Study of Polyatomic Systems."Rev. Lett. 70: 21 (1993).

J.D.in thePhys.

Meade, R., A. Rappe, K. Brommer, and J.D.Joannopoulos. "Accurate Theoretical Analysisof Photonic Band-Gap Materials." Phys. Rev. B48: 8434 (1993).

Meade, R., A. Rappe, K. Brommer, and J.D.Joannopoulos. "The Nature of the PhotonicBand Gap." J. Opt. Soc. Am. B 10: 328 (1993).

Chapter 4. Semiconductor Surface Studies

Robertson, W., G. Arjavalingam, R. Meade, K.Brommer, A. Rappe, and J.D. Joannopoulos."Observation of Surface Photons on PeriodicDielectric Arrays." Opt. Lett. 18: 528 (1993).

Robertson, W., G. Arjavalingam, R. Meade, K.Brommer, A. Rappe, and J.D. Joannopoulos."Measurement of the Photo Dispersion Relationin 2D Ordered Dielectric Arrays." J. Opt. Soc.Am. B 10: 322 (1993).

Wang, J., T. Arias, and J.D. Joannopoulos. "DimerVacancies and Dimer Vacancy Complexes onSi(100)." Phys. Rev. B 47: 10497 (1993).

Wang, J., T. Arias, J.D. Joannopoulos, G. Turner,and 0. Alerhand. "STM Signatures and Chem-ical Identifications of the (110) Surface ofd-doped GaAs." Phys. Rev. B 47: 10326(1993).

186 RLE Progress Report Number 136