Thirty years of atomic and electronic structure determination of surfaces of tetrahedrally coordinated compound semiconductors

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Surface Science North-Holland

299/300

(1994) 469-486

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Thirty years of atomic and electronic structure determination of surfaces of tetrahedrally coordinated compound semiconductors A. Kahn Department of Electrical Engineering, Princeton University, Princeton, NJ 08540, USA Received

20 April

1993; accepted

for publication

13 May 1993

Surface Science has evolved considerably since the early 1960’s. Experimental and theoretical techniques pioneered twenty to thirty years ago have been developed into sophisticated tools which today allow systematic and almost routine determinations of atomic geometries, electronic structures, chemical compositions and surface energies of semiconductor surfaces. In this article, I review the part of the history of this work devoted to tetrahedrally coordinated compound semiconductor surfaces.

1. Introduction

In this article, I examine the evolution of our understanding of atomic geometries and electronic structures of tetrahedrally coordinated compound (TCC) semiconductor surfaces over the past thirty years. The sum of all the work devoted to this subject is considerable and a detailed account of this period would exceed by far the boundaries set by the length of this article. It is therefore with great respect for all experimental and theoretical studies not mentioned herein that I select some examples associated with the most significant advances in the field. The theme of the paper is that remarkable progress has been made in thirty years. The technologies for experimental and theoretical surface investigations have evolved at a pace which was difficult to foresee in the early 1960’s. While early experiments were limited to observations of new surface symmetries and qualitative indications of atomic displacements, today the availability of sophisticated electron and ion diffraction techniques, of tools such as the scanning tunneling microscope, and of advanced energy minimization and electronic structure calculations allows a 0039-6028/94/$07.00 0 1994 - Elsevier SSDI 0039-6028(93)E0327-Q

Science

systematic, almost routine, approach to the quantitative determination of complex surface atomic displacements and associated local and extended electronic structures. This progression and the ever increasing pace of gathering quantitative information on surfaces has led to the recognition and formulation of very general principles which govern TCC surface atomic geometries. The organization of this article is essentially chronological. I identify three decisive periods of the history of surface structure determination and, within each Ijeriod, illustrate the progress made with ground-breaking studies. In Section 2, I review the pioneering work done on polar and non-polar surfaces with electron diffraction and electronic structure measurements in the 1960’s and early 1970’s. This work laid the experimental foundations on which quantitative methods could be developed in the 1970’s. Section 3 is devoted to the second decade (early 1970’s to mid 1980’s), during which quantitative structure determination techniques were fully developed and applied mostly to non-polar semiconductor surfaces, leading to the initial formulation of structural scaling laws and of principles governing the occurrence of surface relaxations. In the final section, I review the period extending from the mid 1980’s to

B.V. All rights reserved

the present. This period is marked by furthcl developments in experimental techniques, in particular scanning tunneling microscopy. and broadcning activity on the structure of polar surfaces of III-V compounds and cleavage surfaces of II-VI and I-VII compounds which led to the confirmation and extension of the principles governing semiconductor surface atomic geometries and electronic structures.

SIDE

VIEW

‘[ill]

0

CATION

0

lNlON

(111)

TOP

VIEW

SURFACE

@ (100)

t [loo]

SURFACE

(b)

2. The early years ( 1960- 1975)

21.1. III-V conlpourlds Investigations of surface atomic geometries of TCC started around 1960 with examinations of ( I 11) surfaces of III-V zincblcndc semiconductors. Studies of cleavage (I IO) III-V surfaces followed rapidly. One may consider the reasons why the (111) surfaces, and not the lower index (100) surfaces, were chosen for these initial studies. The first was probably one of immediate interest. The (111) plane is the cleavage plane for diamond-structure elemental semiconductors. and the comparison between the structure of (111) III-V surfaces and that of Sic I1 I) and Get 111) surfaces investigated in 1959 by Schlier and Farnsworth [l] was a natural path at the onset ot this research. The second reason might have been more practical. The topology of the (111) surface appeared at the time to favor the formation of one dangling bond (DB) per surface atom and the preservation of the tightly bound and closely spaced double layer (Fig. la). Thus, the surface composition, anion or cation, was thought to depend essentially on the crystal orientation. The atomic connectivity on the (100) surface, on the other hand, is more symmetric (Fig. lb). Each surface atom is connected to two second layer atoms and exhibits two DBs. As a consequence. the surface composition can evolve continuously from full anion to full cation, a situation which was considerably more difficult to control with the surface preparation techniques available at the time. Only with the development of molecular beam epitaxy (MBE) pioneered by Cho [2.3] and

(110)

t [1101

SURFACE (c)

Fig. I. Schematic

illustrations

of the zinchlende

ing hide and top views ol the Iruncakd

(100) surface; cated

(c)

in each

indicate

atomic

(I 10) surface.The

CHW by dashed movements

(a)

(I X I)

lines.

compatible

Iatticr

(11I)

Show-

surface: (h)

unit cell is indi-

Arrows

in panel

(c)

with a bond-lcngth-

conserving

relaxation.

projections

on the plane of the figure of two bonds from the

The double lines illustrate

the parallel

Arthur [4,5] in the early 1970’s was the composition of the (100) surface brought under some control, leading to the observation of complex sequences of reconstructions spanning the full range of relative anion-to-cation surface stochiomctry. Haneman performed the first low-energy electron diffraction (LEED) studies of the (11 l)-cation and (111 J-anion surfaces of InSb [61 and GaSb [7] in 1960. These surfaces were prepared by the argon ion bombardment and annealing (IBA) technique developed by Farnsworth ct al. [8], in an experimental apparatus consisting of a vacuum vessel evacuated with a diffusion pump and equipped with molybdenum getters. an off-

471

A. Kahn / Tetrahedrally coordinated compound semiconductor surfaces

axis electron gun, a Faraday cup for LEED intensity measurements and an ion bombardment system. The ultimate pressure achievable at the time was of the order of lo-’ Torr, roughly 20 times higher than pressures routinely obtained in modern ultra-high vacuum (UHV) systems. Haneman established that these polar surfaces, like Si and Ge [l], were reconstructed and identified (2 x 2) reconstructions on both cation and anion surfaces. (Throughout this article, we will use a terminology consistent with the following definition: reconstruction is associated with a space group symmetry different at the surface than in the bulk, leading to the appearance of non-integral beams in diffraction experiments; reluxation designates surface atomic displacements which conserve the symmetry, shape and size of the bulk unit cell, giving rise to a (1 x 1) diffraction pattern.) This work was later expanded by MacRae [9] who benefited from improved vacuum technology (pressure N 5 X 10-i’ Torr) and --showed that the (Ill)-cation and (Ill)-anion surfaces of GaSb and GaAs exhibited --(2 x 2) and (3 x 3) structures, respectively. The (111) surface was found to be considerably less stable under annealing than its (111) counterpart and to decompose easily into (110) facets, a trend confirmed a few years later by Grant and Haas [lo] for InAs. None of the reconstructions observed by Haneman and MacRae were analyzed quantitatively before 1984 [ll]. Yet, very insightful considerations about the atomic geometries already were given in the 1966 paper. MacRae suggested that the reconstructions resulted from the requirement to lower the high energy of these polar surfaces, and proposed a model for the (2 x 2) structure consisting of an ordered array of cation vacancies formed to decrease the polar character of the surface (Fig. 2a). He correctly pointed out the need to saturate the surface DBs and suggested that the remaining surface cations underwent a displacement toward the anion layer accompanied by a rehybridization of surface bonds from tetrahedral sp3 to planar sp2. This prediction was remarkably close to the (Ill)-Ga GaAs structure quantitatively determined by LEED two decades later [ll] (Fig. 2b and Section 3.3).

GaAs(ll1)

- (2x2)

= As 0

=

Ga

Fig. 2. (a) Schematic of the Ga vacancy model proposed by MacRae [9] and confirmed by Tong et al. [ll]. The vacancy creates 12-membered GaAs rings (Section 3.3). tb) Perspective representation of the (2 X 2) reconstructed Gatlll) GaAs surface. The cation vacancies appear in one out of two cation-anion rows in the top atomic plane (after Tong et al.

1111).

2.1.2. II- VI compounds Polar surfaces of II-VI TCC were investigated in the second half of the 1960’s. Surfaces of wurtzite CdS, CdSe and ZnO, and zincblende ZnS were studied first because of their impact on the physics and chemistry of gas adsorption on insulators. Considering long range electrostatic interactions in the crystal, Mark and coworkers 112,131 predicted that these surfaces could be stabilized only through the introduction of a f monolayer of electronic surface charge, obtained via vacancy reconstruction, charged surface states, or large scale reconstruction such as facetting of the surface. The idea of energy-lowering reconstruction ensuring surface charge neutrality was, therefore, already at the forefront for II-VI and III-V polar surfaces alike. It was to be formalized later on by Harrison with the concept of surface auto-compensation [141. The predictions

472

A. Kahn / TetrahedralI) coordinated compound semiconductor .srrrfam

on the wurtzite surfaces were qualitatively confirmed by most LEED observations. Campbell et al. [15] observed (2 x 2) reconstructions on (OOOl)-Cd and (OOOi)-S CdS surfaces prepared by IBA, and (2 X 2) and (4 x 4) reconstructions on the (OOOl)-Cd CdSe surface, compatible with the f monolayer requirement. Chang and Mark [16,17] reported integral diffracted spots for the (OOOllcation surfaces of ZnO and CdS in a pattern exhibiting a six-fold symmetry indicative of a non-ideal termination, a poorly developed tfi x v’%)R30” reconstruction for the (OOOil-S CdS surface and the formations of facets and steps under various annealing conditions. The list of examples which could be cited is long. They would underscore the fact that, at the end of this first decade, the occurrence of reconstruction on polar surfaces of tetrahedrally coordinated III-V and II-VI compounds was recognized as a general phenomenon. Although specific atomic geometries were far beyond the capabilities of experimental and theoretical techniques available at the time, the models proposed to explain the occurrence of these reconstructions already embodied the same concept as the models used today to rationalize reconstructions, namely surface auto-compensation by saturation of surface dangling bonds and minimization of surface energy by the resulting surface relaxations. 2.2. Non-polar cleaclage surfaces 2.2. I. III-V compounds The importance of cleavage surfaces in the history of semiconductor surface physics cannot be overstated. Non-polar surfaces such as the (110) zincblende surface are naturally charge neutral. They offer the combination of a high degree of structural and stoichiometric perfection and the absence of intrinsic surface states in the fundamental energy gap. This latter property, although accepted only in the mid 1970’s, was established by Van Laar and Scheer [18] as early as 1967 and contributed to making the (1101 surface an essential testing ground for experimental and theoretical investigations of surface electronic

properties during the next twenty years. The two ground-breaking studies outlined below arc therefore among the most important contributions to the physics of TCC surfaces of this first decade. The first was devoted to structure. The (1101 surface consists of equal numbers of anions and cations arranged in zig-zag chains in which each atom is bound to two surface and one second layer atom (Fig. 1~1. As would be discovered later, this topology allows activationless displacements of the surface atoms through bond-lengthconserving rotations of the anion-cation surface bonds (indicated by arrows in Fig. 1~1. MacRac and Gobeli [19] used (1101 surfaces prepared by cleaving in UHV (5 x 10 -I0 Torr) following a technique developed by Lander et al. [20]. Second generation LEED optics with post-acceleration. spherical grids and fluorescent screen, and tracking spot photometer for intensity versus energy measurements were already available for this work. Pointing out the absence of non-integral order beams, MacRae and Gobeli measured the unit cell dimensions to show that these non-polar (1101 surfaces were unreconstructed. They performed the first structure factor analysis of LEED intensities on a specially designed analog computer. They demonstrated that the intensity of the (ho) beams, for h odd, should be very weak for unrelaxed surfaces of GaAs and InSb for which anion and cation scattering factors are almost identical (quasi-forbidden beams). The observation of the contrary was the first evidence of atomic relaxation on (1101 surfaces. The first quantitative LEED structure determination on GaAs(1 lo), performed a decade later [21,22]. confirmed these conclusions. The second set of experiments was devoted to electronic properties. Gobeli and Allen [23] and Van Laar and Scheer [18] performed contact potential difference (CPD) measurements using a vibrating Kelvin probe, and photothreshold measurements to investigate work function and band bending on cleaved GaAs(llO1 as a function of doping density, doping type and temperature. In a remarkably insightful paper, Van Laar and Scheer [18] demonstrated that the Fermi level (E,) could be shifted by 1 eV or more from the

473

A. Kahn / Tetrahedrally coordinated compound semiconductor surfaces

upper to the lower part of the gap at the (110) surface of GaAs by going from n-type to p-type doping. They were first to conclude that, unlike Si(ll1) and Ge(ll1) surfaces [24,25], the (110) GaAs surface could be obtained without significant band bending and was devoid of intrinsic states in the fundamental gap. The two key ingredients of the physics of the (110) zincblende surface, i.e. the occurrence of a surface relaxation and the absence of intrinsic states in the gap, were therefore recognized by 1967, although the structure was still unknown and the link between them had not been established. The exceedingly important result on the absence of gap states unfortunately was challenged incorrectly in the early 1970’s by virtue of experiments flawed by the presence of cleavageinduced surface defects. The controversy which ensued led to several years of uncertainty concerning the electronic properties of GaAs(l10). This subject is reexamined in Section 3.2. Scheer and Van Laar [26] tackled the problem of adsorbate-induced changes in band bending on GaAs(ll0). By depositing Cs on n- and p-GaAs, they showed that E, stabilization resulted from, but did not precede as had been suggested by Spitzer and Mead [27], the adsorption of foreign species on the surface. They correctly postulated that GaAs belonged to a group of semiconductors for which the adsorption of small amounts of any species on the (110) surface created gap states which stabilized E, near midgap, irrespective of doping type. This report was among the first to address the problem of the formation of Schottky barriers, a subject which was to monopolize tremendous research energy during the following twenty years [281. In retrospect, it is clear that the studies of MacRae and Gobeli and of Van Laar and Scheer had a considerable impact on the fundamental understanding of the structure and electronic properties of cleavage surfaces, as well as on the development of LEED, CPD and photoemission techniques. They represent the opening chapter of what was to become the single most successful effort to determine the atomic geometries and electronic structures of compound semiconductor surfaces and interfaces.

2.2.2. II-VI compounds The early 1970’s also were marked by the first structural studies of cleavage (lOi0) and (ll?O) surfaces of II-VI wurtzite compounds. The wurtzite 0010)surface consists of anion-cation dimers with each constituent bound to one atom in the surface and two atoms in the second layer (Fig. 3a). An activationless bond-length-conserving relaxation is obtained by rocking the dimer along its axis (indicated by arrows in panel (a)>. The (1120) surface embodies a more complex chain structure with four atoms per unit cell (Fig. 3b). Each surface atom is bound to two atoms in the chain and one atom in the second layer. The rectangular cell has a glide-plane symmetry resulting in missing diffracted beams in LEED [29]. This seemingly more rigid structure can relax

0 CATKIN

ANION SIDE VIEW

t

I

110ioI

TOP

VIEW

(1070) SURFACE

(1120) SURFACE

W

Fig. 3. Schematic illustrations of the wurtzite lattice showing side and top views of the truncated (a) (1010) surface; (b) (1120) surface. The (1 X 1) unit cells are indicated by dashed lines. Arrows in panel (a) indicate atomic movements compatible with bond-length-conserving bond rotation. The double lines indicate the parallel projections on the plane of the figure of two bonds from the same atoms.

while conserving bond lengths with a puckering of the unit cell (as determined in the late 1980’s). Cleavage initially was reported for the (lOi surface of ZnO and CdS [30]. Shortly thereafter, Mark and coworkers used LEED to determine the unit cell symmetries and to measure diffracted intensities for the two non-polar (1010) and (1120) surfaces of ZnO and CdS [16,29] prepared by IBA. The mirror and glide-plane symmetries of the (lOjO) and (1120) unit cells were shown to be preserved at the surface, confirming the absence of reconstruction noted for the (110) surfaces. Diffracted intensities computed from a singlescattering (“kinematical”) structure factor analysis were compared to experimental data in an effort to assess the existence of surface relaxation. Unlike for the III-V (110) surfaces, however, no compelling evidence for relaxation was found, leaving the relaxation of wurtzite-structure cleavage faces a subject which was to remain without a clear understanding until the late 1980’s (Section 4.2).

3. The development

years (1975-1985)

3.1. The techniques Experimental and theoretical techniques for studying surface atomic and electronic structures were undergoing very rapid progress throughout the 1970’s. Maturing UHV technologies were driving operating pressures down to levels where surface cleanliness could be maintained for days (high lo-” Torr range). Ultraviolet photoemission spectroscopy (UPS) for valence band and shallow core level spectroscopy was becoming increasingly widespread with the availability of gas discharge sources coupled to UHV systems [31381. Angle resolved photoemission spectroscopy (ARPES) for band structure mapping followed in the mid 1970’s [39-411. Finally, synchrotron storage rings providing photon wave-length tunability in ranges extending from the UV to the X-ray became accessible to surface scientists. Several techniques utilizing photon energy scanning were developed: partial yield spectroscopy (PYS) [42] and constant initial state (CIS) spectroscopy [43], which probe empty states below and above the

vacuum level, respectively; constant final state (CFS) spectroscopy [43]. which probes the initial density of filled states. Tunability also increased the power of discrimination between bulk and surface effects by allowing continuous variation of the escape depth of photoemitted electrons [281. The structure determination techniques also wcrc improved during this period. Most of the LEED computational formalisms were in place in the mid 1970’s [44-471. Yet. structure determinations were hindered by the prohibitive computing time and cost associated with multiple scattering analyses. Techniques to reduce the effect of multiple scattering by averaging methods [48-Sl] were developed to perform LEED intensity analyses with considerably less computer intensive single scattering computations. The best known of thcsc averaging schemes, i.e. the constant momentum transfer averaging (CMTA) technique [48.49], was successfully applied to the ( 110) surfaces of &As [S2] and InSb [S3] and was instrumental in rcvealing the multi-layer relaxations present at these surfaces. The averaging techniques became obsolete at the end of the 1970’s when faster computers and streamlined LEED codes decreased the computing cost. Efforts were then devoted to improving the reliability of the technique by using improved scattering potentials [54,SS] and reliability factors to systemize comparisons between experimental and calculated intensities [S&58]. By the early 1980’s LEED had become a powerful technique for the determination of surface atomic geometries, and was to remain without contest the most prolific tool for semiconductor surface structure determination during the next decade. Techniques involving atom [59,60] and ion [61.62] scattering were developed in the 1970’s and played a significant role in the quest for semiconductor surface structures. The former were instrumental in providing data charge densities associated with atomic positions. The latter were applied more directly to structure determination because of the simple modeling of the classical high energy ion-atom scattering process. Medium energy (- 100 keV) and high energy (- 1 MeV) channeling and blocking configura-

A. Kahn / Tetrahedrally coordinated compound semiconductor surfaces

tions were used very successfully to obtain atomic registry and displacements on a number of III-V surfaces [63-661. Finally, theoretical models for minimization of ground-state energy were also developed in the 1970’s and applied with great success to the determination of atomic geometries and electronic structures of TCC. In all these models, the total energy is expressed and minimized as a function of structural variables and the surface electronic structure is a by-product extracted from the charge density and surface state energies corresponding to the total minimum energy. Calculations involving quantum chemistry of clusters [67,68], tight binding energy models (TBE) [69-721

and pseudo-potential phed to a number of and provided valuable mechanisms operating

475

methods [73,74] were apIII-V and II-VI surfaces insight into the relaxation at these surfaces.

3.2. The zincblende (110) surface 3.2.1. GaAs(ll0) Progress in the determination of surface atomic structures and electronic properties during the second decade can best be reviewed against this background of emerging techniques by examining the case of (110) surfaces. Reviews of this subject have been given by Kahn [75] and Duke [76]. The history of GaAs(ll0) has demonstrated better

1.0

l110lGaAs:BR

Modd

0.5

-1s

-2.5 -

-2.5 -3.0

-

-2.0 -

-2.0

-3.0 -

;I

-3.5 -4.0 4.5

-

-5.0 -5.5 -6.0 4.5:

Fig. 4. Surface

bands

of GaAs(l10)

calculated for the unrelaxed surface and for bond relaxation vertical shear of the top layer (after Chadi [91]).

(BR) model

embodying

a 0.65 A

476

A. Kuhn / Tetruhedraliy

coordinated

than any other during these thirty years the arduous process of ensuring convergence between all aspects of a same physical system and, as such, is worth a concise review. In spite of the 1967 CPD and photothreshold work by Van Laar and Scheer [18], the absence of intrinsic states in the gap of GaAs(llO) was still being debated in the early 1970’s. Using similar techniques, Dinan et al. [77] concluded that a band of acceptor states overlapping with the conduction band was extending - 0.8 eV down into the gap. This result was confirmed at the time by several PES [78-801 and PYS [81,82] measurements on GaAs. Acceptor states were also found in the upper part of the gap on InP, but not on GaSb [83]. The level of confusion was heightened when surface state calculations performed for the unrelaxed geometry confirmed these results [84861. The fundamental problem with these calculations was, of course, the utilization of an inappropriate atomic structure. The situation was resolved by four key experiments presented in 1976. First, Van Laar and Huijser confirmed their claims for GaAs and InAs, but indicated the presence of acceptor states in the upper part of the GaP gap [87]. Second, Spicer et al. [@I, using synchrotron radiation PES, showed that the states previously reported in the GaAs gap were extrinsic and related to cleavage defects. Third, Duke et al. [21,22] reported the first multiple scattering analysis of GaAs(ll0) LEED data, which identified the surface atomic geometry as consisting of a bondlength-conserving rotation relaxation (“rotational relaxation”) of the surface with the As (Ga) moving up (down) with respect to the truncated surface plane. The introduction of this geometry, and refined versions thereof, in theoretical calculations of the surface electronic structure [89-931 immediately produced shifts of the anion- and cation-dangling bond states back into the valence and conduction bands, respectively, in agreement with the new experimental results (Fig. 4). Finally, Gudat and Eastman 1941 reconciled the PYS [81,821 and electron energy loss spectroscopy (EELS) [95] data, which appeared to support the presence of empty states in the GaAs(ll0) gap, with the new CPD and PES results. They applied

compound semiconductor surfaces

Zincblende (110)

11w

(a) -+

0

Anion

(1

Cation

[OOl]

,; tiioj

Fig. 5. (a) Perspective representation of the relaxed (1 IO) surface of zincblende TCC (after Duke [7h]); (b) Schematic of the structure showing first and second layer relaxations and the bond rotation angle w.

an exciton binding energy correction to the Ga 3d-to-empty-state transition measured in PYS and EELS, and showed that it corresponded to a final (empty) state energy in the conduction band, in agreement with the hypothesis of a gap free of intrinsic states. Subsequent LEED analyses of the GaAs(l10) structure introduced bond length relaxations [96,97] and second layer counter-rotation (As down, Ga up) [52,98-1001 (Fig. 5). This structure was repeatedly challenged in the late 1970’s and early 1980’s on the basis of comparisons between calculated and measured UPS spectra [101,1021, inverse photoemission spectroscopy measurements [103,104], and high energy ion channeling experiments [105,106]. To resolve these issues, refinement analyses of the LEED data were performed [107] with improved scattering potentials

A. Kahn / Tetrahedrally coordinated compound semiconductor surfaces

[54,55] and the sensitivity and accuracy of LEED for determining atomic displacements perpendicular or parallel to the surface were re-evaluated [108]. The GaAs structure determined by Meyer et al. [loo] was confirmed with only minor modifications by each of these re-evaluations. 3.2.2. Principles governing surface atomic relaxations

In the years following this GaAs period, the atomic geometries of the (110) surfaces of most III-V and II-VI compounds were determined via LEED and ion scattering. They included AlP [109], AlAs [llO], GaP [108,111], GaSb [112,113], InP [114,115,116], InAs [117,118], InSb [119], ZnS [120,121], ZnSe [122], ZnTe [1231 and CdTe [124]. All these surfaces were found to exhibit a large top layer distortion corresponding approximately to a bond-length-conserving activationless rotation relaxation with an angle w = 29” f 3” and varying top contraction and second layer relaxation. For bond-length-conserving relaxations, o and Ail, the top layer vertical shear defined in Fig. 5, are simply related by A, I = (a,/4) sin w. These structures were in good agreement with predictions based on quantum chemical calculations [125,126] or TBE minimization calculations [69,70,127]. Further, they produced equally good agreement between calculations of anion-derived filled surface state dispersion and ARPES measurements on GaAs [128-1301, InP [131], ZnSe [132] or CdTe [133], and calculations of cationderived empty surfaces states and inverse photoemission measurements on GaAs [134] and GaP [135] (Ga-derived empty state overlapping with the gap for the latter). By the mid 1980’s, the cleavage (110) surfaces of zincblende compounds constituted a thoroughly investigated set of surfaces on which an unprecedented level of convergence had been obtained between theoretical, experimental, structural and electronic data. The availability of this extensive set of structural data and the realization that the gap of most III-V and II-VI (110) surfaces was free of intrinsic states led to the recognition of a number of general rules. First, as a lesson from the GaAs story, the direct link between the elimination of DB states from the band gap (except for GaP)

471

and the surface relaxation was established. The charge redistribution resulting from the relaxation was producing filled anion-derived surface and back bonding states and empty cation-derived surface states, making the surface naturally auto-compensated. In the process, the surface state energies were shifted away from the gap into the valence band and conduction band (Fig. 4). The energy gained in the process was sufficient to drive the relaxation. Second, it was realized that, unlike originally proposed [22,136], these atomic geometries did not scale with the bulk ionicity nor depend specifically on the reduced-coordination (or small molecule) chemistry of the surface anion and cation species. An early interpretation of the relaxation mechanism had attributed the GaAs bond rotation to the requirement of moving the three-fold coordinated surface As and Ga atoms into configurations more compatible with their small molecule configurations, namely pyramidal p bonding for As and planar sp’ bonding for Ga. On the count of this picture, high ionicity II-VI compounds with different small molecule cation and anion chemistries should have exhibited different surface relaxations. In fact, isoelectronic compounds with very different ionicities [137], such as ZnSe and GaAs, or CdTe and InSb, were found to exhibit identical relaxations within the accuracy of the structure analyses. Finally, it was established that the principal parameter of these atomic structures, i.e. the top layer vertical shear A II scaled linearly with the bulk structural parameters (Fig. 6a), leaving the bond rotation angle w approximately constant for all compounds investigated [ 1381. This combination of rules led to the conclusion that the atomic relaxation of these surfaces was driven primarily by the electronic energy gained upon bond rotation, the very nature of the relaxation being dictated by the specific surface topology. The concept of a universal relaxation mechanism for TCC surfaces was emerging. The extension of this concept to other types of surfaces, however, required the recognition that non-polar surfaces, on which the redistribution of charges between equal numbers of anion and cation DBs occurs naturally, are ideal candidates for activa-

A. Kuhn / Tetrahedrally coordinated compound semiconductor surfuces

47x

5.0

5.2

5.4

5.6

5.8

6.0

6.2

6.4

6.6

a,(A)

(a) 08

07

06

05

Iv

(a)

zno

L

30

I

35

40

..

I

...-1 45

a,tab lb)

Fig. 6. Correlation obtained from LEED structure determinations between A, i and lattice constant a,, for (a) the (110) surfaces of zincblende compounds (Section 3.2; Duke 11381); (b) the (lOi0) and (1120) surfaces of wurtzite compounds (Section 4.2: after Duke [193]).

tionless energy-lowering relaxations. Polar surfaces, on the other hand, require reconstructions to create a non-polar environment upon which charge exchange between anion and cation DBs can take place and an energy lowering relaxation can be applied. Such transformations were indeed observed on (111) surfaces (next section1 and, to the best of our present understanding, on the (100) surfaces (Section 4.1). 3.3. Polar surfaces The atomic geometry of the (2 X 2) (Ill)-cation surfaces of GaAs [11,1391, GaP ]1401 and InSb [141] was investigated at the end of this second decade. LEED and X-ray structure determinations produced structures consisting of a f

monolayer of cation vacancies with relaxation of the remaining top layer atoms toward the second layer and lateral displacement of the second layer As to form quasi-planar twelve-membered As-Ga rings, in good agreement with the motif suggested by MacRae [9] (Fig. 21. Interestingly, the local As-Ga configuration and electronic structure in the ring were found to be similar to those of on the (110) surface chain, as confirmed by TBE minimization calculations [142] and ARPES data [143,144]. The reconstruction was here again driven by the lowering of the electronic state energy. The resulting surface was auto-compensated, in agreement with Harrison’s criterion of stability [14]. Finally, the end of this second decade was also marked by attempts to determine atomic structures of the (100) surface. Considerable work had been devoted since the early 1970’s to establishing the relationship between atomic reconstruction and surface stoichiometry on this surface [4,5,145-1481. The (100) phase diagram, however, is still under debate in 1993. Photoemission experiments were performed on the (2 x 4) [1491 and c(4 x 4) [150,1511 reconstructions. Larsen et al. suggested that the latter was due to symmetric dimers of As adsorbed on top of an As-terminated surface, in contrast with the total energy minimization calculation by Chadi et al. [1521 which suggested a combination of symmetric and asymmetric dimers in the As-layer (no chemisorption). The c(4 x 4) and other reconstructions of the (100) surfaces were to be extensively studied and their structure partially resolved with the help of scanning tunneling microscopy (STM) during the next decade (Section 4.1).

4. The maturity years (1985-1993) The last eight years of work on TCC semiconductor surfaces were marked by extraordinary new possibilities offered by the development of scanning tunneling microscopy (STM) and related techniques. Through real space visualization of intricate atomic arrangements in large unit cells and simultaneous measurements of electronic properties of these surfaces with atomic resolu-

A. Kahn / Tetrahedrally coordinated compound semiconductor surfaces

tion, STM opened entirely new avenues for semiconductor surface studies. The most important and spectacular applications to compound semiconductors have been to the determination of atomic arrangements on the (100) III-V surfaces. Structure determinations by LEED and total energy minimization calculations also were extended to non-polar surfaces of zincblende I-VII and wurtzite II-VI compounds. The confirmation of the structural mechanisms and scaling laws uncovered with previous investigations (Section 3) led in the early 1990’s to extensions of the principles on atomic and electronic structures of TCC surfaces. 4.1. Polar surfaces The technologically important (100) surfaces of III-V and II-VI compounds have been studied since the early 1970’s. Several surface phases obtained during MBE growth [2-5,153] as a function of As versus Ga flux or after growth [146,148,1541 had been identified prior to 1980. Yet, their precise As versus Ga compositions were still under debate in the early 1980’s. In order of decreasing As/Ga surface concentration, the most commonly observed reconstructions were the c(4 X 4), (2 x 4)x(2 x 81, (1 x 61, (4 X 6) and (4 X 2)-~$8 X 2). The shear size of the unit cells and the uncertainty of the corresponding surface compositions were impeding quantitative structure determinations, although the proliferation of MBE growth systems linked to PES and electron diffraction techniques in the 1980’s was giving impetus to the study of these complex reconstructions. Chadi used TBE minimization [155] to derive the As-stabilized (2 X 4) structure based on two different arrangements of symmetric As dimers and missing dimer rows in the top layer. Good agreement was obtained between the surface states calculated with this structure and photoemission results [149]. No surface states were found in the energy gap for this structure. A similar As dimer arrangement was also proposed by Farrell et al. [156] based on electron diffraction studies. The calculation also predicted the ~(2 X 8) structure, which is a small perturbation

419

of the (2 X 4) structure, to be slightly more stable than the (2 x 4). The unambiguous confirmation of the As dimer structure of the (2 x 4)-~$2 x 8) surface was first obtained by Pashley et al. [157] using STM. These GaAs surfaces were prepared by sublimation of an encapsulating As cap pre-deposited in the MBE growth chamber [158]. Rows of As-dimer arranged in (2 x 4) or c(2 x 8) unit cells with one missing dimer per cell were identified at the time. Biegelsen et al. [159] later expanded on these results by examining the c(4 X 41, c(2 x 81, (2 x 6) and ~(8 X 2) MBE surfaces grown in-situ. The As-saturated c(4 X 4) structure was found to correspond to sets of three As dimers adsorbed on a monolayer of As, in agreement with the suggestion of Larsen et al. [150]. The (2 X 4) unit cell was found to consist of a mix of two and three As dimers per cell with one or two missing rows. Finally, the Ga-rich c(8 x 2) structure was attributed to groups of two Ga-dimers in the top layer (Fig. 7). The details of some of these atomic arrangements have remained controversial. Distribution of areas with one versus two missing As-dimers in the (2 X 4M2 X 8) structure have been observed [157,1601. Cation-anion mixing in the top layer has been suggested [161] and the relationship between structure and stoichiometry has not been completely resolved. Kinetics is thought to play a crucial role in the formation of these surfaces. Finally, the detailed geometry of the dimers, recently investigated [1621, must be addressed with experimental techniques. It remains, however, that the basic anion or cation dimer building block of these reconstructions, predicted by theory in 1987 [155], was unambiguously confirmed by STM. The formation of dimers is consistent with one of the guiding principles governing these semiconductor surfaces, namely the requirement to saturate DBs and to lower the energy of the surface by transforming them into bonding states. Furthermore, the STM data on the distribution of dimers and missing dimers inside the unit cell have led to the demonstration that most of these surfaces are in compliance with the principle of dangling bond saturation and surface auto-compensation 11631.The application of this principle

A. Kahn / Tetrahedrally coordinated compound semiconductor surfaces

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using electron counting techniques has since been recognized as a simple but powerful way to catalogue possible surface atomic arrangements and compositions for TCC semiconductors. Work function and surface dipole measurement results compatible with charge transfers imposed by auto-compensation have been recently obtained on the c(4 x 4) c(2 X 8) and c(8 X 2) GaAs(lOO) surfaces [164,1651. Scanning tunneling spectroscopy (STS) provided key measurements for unraveling the electronic properties of the (100) surface. Pinning of E, near midgap on n-type (100) GaAs had been observed by PES for a range of reconstructions [ 166- 1681, although theory predicted no intrinsic gap states [ 1551. Pashley and Haberern using STM and STS found the charged acceptor-like pinning centers to be due to kink-defects in the rows of As-dimers on Si-doped GaAs [ 169,170], each carrying a single negative electron charge [1711. Studies on the (100) surface of GaAs and other compounds are expected to continue in the 1990’s. The atomic geometries of most of the observed phases remain to be determined quantitatively. Band bending on clean p-type GaAs surfaces is not understood, and recent PES investigations suggest that highly doped surfaces might exhibit very small band bending [172]. The newly developed capability to perform high resolution STM at high temperature [173,174] should also provide in the years to come information on ad-atom and vacancy diffusion crucial for epitaxial growth. STM imaging was also essential in developing the complex structure models for the (2 X 2) and v’?? x v% As(ll1) surfaces of GaAs [175]. A motif consisting of adatom As trimers bound to the complete As ---layer was inferred from images of the (2 x 2) (111) surface. A similar (2 X 2) trimer arrangement was --proposed for both (2 X 2) (11 1)-Ga and (2 X 2) (Ill)-As on the basis of total energy minimization calculation [176,1771, but the cation vacancy model [ill remains at

Fig. 7. Models of the ~(4 X 4), (2 X4&(2X 8) and (4 X 2)-~(8 X 2) structures derived from STM studies (after Biegelsen et al.

11591).

481

A. Kahn / Tetrahedrally coordinated compound semiconductor surfaces

present the accepted one for the (111) surface. A complex distribution of large Ga-As rings resulting from rearrangements of the top bilayer was deduced from the STM observations of the m X I/B structure.

(lOTO)

Wurtzite

4.2. Non-polar surfaces STM and STS were extensively applied to (110) zincblende surfaces in the late 1980’s [178,179]. Although these studies confirmed the spatial relationship between structure and electronic surface states, their impact on the field was smaller than in the case of polar surfaces given the high level of understanding of the (110) surface prior to these experiments. A more important role was, and still is, played in the area of adsorption on these surfaces, in particular with respect to problems related to the formation of Schottky barriers [180,181]. Quantitative structure determinations of TCC surfaces were extended after 1987 to the cleavage surfaces of wurtzite II-VI compounds and, more recently, to the (1101 surface of highly ionic zincblende I-VII compounds. LEED and low energy positron diffraction (LEPD) structure determinations were performed on the (lOi surface of CdSe [182-1841 and to the (1120) surfaces of CdS [185] and CdSe [183,184,186,187], and TBE minimization calculations were applied to the two cleavage faces of Cd& CdSe, ZnO, ZnS and ZnSe [188-1921. These structure determinations extended to the II-VI wurtzite surfaces the relaxation principles developed for the zincblende surfaces. First, all surfaces were found to relax with large surface distortions. On the (lOi surfaces, dimer tilt angles between 17” and 23” were identified, depending on the structure determination technique (Fig. 8). Bond length contractions in the top layer also were suggested by the energy minimization calculations [188-1921. On the (11201 surfaces, extensive puckering of the chain with rotation angles of the cation-anion-cation planes of the order of 30” were determined (Fig. 9). A two-angle rotation relaxation has been described by Kahn et al. [185] for this surface. On both

Fig. 8. Perspective representation of the relaxed (1OiO) surface of wurtzite TCC (after Duke [193])

surfaces, the relaxations were found to bring anions and cations in local configurations similar to those found on the (110) surface. A detailed review of these structures was given by Duke [193]. Second, like on (110) surfaces, these activationless relaxations were found to be driven by a lowering of the surface state energy. The TBE calculations [188-1921, in accord with ARPES data [194], predicted a significant lowering of the anion-derived filled surface state energy below the valence band maximum on both surfaces upon relaxation (Fig. 101. Finally, the top layer vertical shear, like A, I on the (110) surface, was shown to depend linearly on bulk parameters, thus conWurtzite

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A. Kuhn / Tetrohedrally coordinated compound semiconductor surfaces

482

Fig. 10. Surface electronic band structure of CdSe(lOi0). Solid lines and dashed lines are surface state and surface resonance dispersion curves, respectively, calculated for the relaxed geometry. The dot-dashed curve is the calculated S, state dispersion for the unrelaxed geometry. The squares represent ARPES data [194] (after Wang et al. [189]).

scaling laws formulated for the zincblende surfaces (Fig. 6b). The latest chapter in this history of TCC surfaces was recently written with the study of the (110) surfaces of the zincblende I-VII comfirming

pounds CuCl and CuBr. The spectroscopic ionicities of these compounds are among the highest in the zincblende group (second only to AgI and CuI), and their structure determination was to provide a stringent test on the recently renewed claim that surface relaxations should depend on compound ionicity. Contrary to the theoretical predictions of a strong dependence on ionicity by Tsai et al. [195], however, LEED studies of CuCl [196] and CuBr [197] produced (110) relaxations with top layer vertical shears compatible with covalent compounds (Fig. 11). Although an increase in surface bond-length contractions was detected in these ionic materials [196-1981, the results confirmed the lack of primary role of ionicity in determining the main relaxation parameters of cleavage surfaces. By demonstrating an invariance of the (110) surface structure for compounds with drastically different bulk electronic properties and chemistry, these results emphasized the universal aspect of TCC surface relaxations driven by electronic energy and guided by surface topology.

the

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5. Synopsis The body of work reviewed strong, although incomplete,

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ionicity [137]; (0) Fig. 11. Normalized zincblende (110) first-layer vertical shear, A, I /a,,, as a function of compound spectroscopic correspond to structures experimentally determined by LEED; ( n ) correspond to the theoretical prediction of ionicity dependence by Tsai et al. [195]. The solid line is the best least-squares fit to the experimental values (after Kahn et al. [196]).

A. Kahn / Tetrahedrally coordinated compound semiconductor surfaces

tremendous growth and progress made over the past thirty years in the field of Surface Science in general, and in determination of atomic geometry and electronic ‘properties in particular. The development of sophisticated experimental and theoretical techniques has produced a detailed understanding of many of these surfaces at the microscopic level. More important, the accumulation of knowledge over these thirty years has led to the recognition that deep structural and electronic commonalities exist between seemingly very different surfaces, whether polar or non-polar, III-V, II-VI, or I-VII, zincblende or wurtzite. These commonalities on surface auto-compensation, energy lowering relaxation or reconstruction mechanisms, and universal scaling laws have now been formally expressed in terms of principles which are believed to govern most semiconductor surfaces. As Surface Science embarks on its fourth decade, these principles will guide future studies of elemental as well as compound semiconductor surfaces, and will be tested critically by the ever increasing atomic-level understanding of these surfaces. Acknowledgements

The author is greatly indebted to Dr. C.B. Duke for many years of a wonderful collaboration on the determination of many of the surface structures mentioned in this article. Support from (DMR-90the National Science Foundation 18521) is also gratefully acknowledged. References [l] R.E. Schlier and H.E. Farnsworth, J. Chem. Phys. 30 (1959) 917. [2] A.Y. Cho, J. Appl. Phys. 41 (1970) 2780. [3] A.Y. Cho, J. Appl. Phys. 42 (1971) 1074. [4] J.R. Arthur, Surf. Sci. 43 (1974) 449. [5] A.Y. Cho and J.R. Arthur, Progress in Solid State Chemistry, 10 (1975) 1.57. [6] D. Haneman, J. Phys. Chem. Solids 14 (1960) 162. [7] D. Haneman, Proceedings of the International Conference on Semiconductor Physics, Prague, 1960 (Publishing House of the Czechoslovak Academy of Sciences, Prague 1961)

181H.E.

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