- Email: [email protected]
Semiconductor surface reconstruction
vacuum/volume33/numbers 1O-l S/pages 613 to 619f 1963
0042-207X/63S3.00+ .OO Pergamon Press Ltd
Printed in Great Britain
Semiconductor D J Chadi,
surface
reconstruction
Xerox Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, CA 34304,
USA
A review of the current state of our understanding of some semiconductor surface reconstructions is given. These include the GaAs(l10) surface and the (100) and (17 1) surfaces of Si and Ge. The strong correlation between atomic and electronic structure and the energies involved in structural rearrangements at the surface _I_ “IIYY*YW”* #&rr.rs~J WI_
1. Ilmdlmion
Atomic displacements from ‘ideal’ positions occur on virtually all semiconductor surfaces. The structural rearrangements can (1) keep the surface topology or connectivity unchanged from that of .L:>a.., &..,I. .--:....r,~ ,...z..- I?\ ^I.^___ lLIK L- zur,Wz . ...-r..- r---l--.. UK I&W111 “uI&-LC‘IlII&&PWu WuI_, ,L, r;llaul(c L”pu1”gy but maintain a one-to-one correspondence between the atoms of the reconstructed and the ideal surface and (3) lead to the addition or removal of atoms from the surface resulting in a loss of the oneto-one correspondence with the ideal surface. The relaxed 1 x 1 GaAs( 110) cleavage surface, the dime&d Si( lW)-2 x 1 surface, and adatom, vacancy or terrace-step models for the Si( l l l )-7 x 7 surface provide examples of each of the three types of atomic rearrangementa, respectively. Until recently, it was generally thought that all cleaved surfaces were examples ofthe first type of surface geometry. The most important new development has been the realization that the cleaved Si(l l l)-2 x 1 surface is much better described by a type (2) reconstruction involving a change in the surface topology than by a type (1) buckling reconstruction. In the following sections, a detailed discussion of the various surface reconstructions mentioned above is given. Attention will be given to a presentation of the problems remaining in each case. The relaxation of the GaAs(ll0) surface, its electronic structure and the question of mirror reflection symmetry are discussed in section 2. The 2 x 1 and c-4 x 2 reconstructions of Si and Ge( 100) surfaces are reviewed in section 3. New structural models for the Si(l1 l)-2 x 1 surface, as well as questions related to buckling, spin-polarization and the occurrence of more than one structure at the surface, are discussed in section 4. The cnergetics of an adatom model for the Si(l1 I)-7 x 7 surface are examined in section 5. % GaAs(ll0)
!hrface
The (110) surface structures of all III-V and II-VI semiconductors that have been studied show remarkable similarities tn ~nntbrr nf 1 IfI\ ir nmnna .V nnr ““I _Y”...W.. V‘ tkmr .,.“ow, thr eaa- CP --a Ad a”\* a”, r~rrfmem .,-.....Y nninnur “...y..- s....“..b semiconductor surfaces for the accuracy and confidence with which its surface atomic geometry is known. Each surface unit cell contains a Ga and an As atom as shown in Figure 1. The surface relaxation involves an approximatelyrotational type of
Top
view
side view ideal 1x1
view relaxed Ix
Side
I
Figwe 1. Top and side views of the GaAs(ll0) surface. The tilting of the surfaa GaAs bond is about 27.5”.
atomic displacement (ie, involving very small bond-length changes of ‘c f 1% with the As moving out of the surface plane and with Ga moving closer to bulk atomsles. The total relative displacement of the atoms normal to the surface is 0.650.69 A. Dynamical low-energy-electron diffraction’-” (LEED), as well as theoretical total-energy minimization studies via tightbinding&‘, self-consistent pseudopotentiaL and quantum chemical methods’, predict a tilting of the Ga-As surface bonds by an angle 6 of about 27.5”* 1.5”. The quality of the fit to the LEED data is most sensitive to 6 and relatively insensitive to small uniform displacements of the surface Ga and As atoms along the y diraXion1’3. In fact, an early LEED model’ (referred to as a bond-relaxation mode19) took account of only the normal displacements of the surface atoms and ignored the transverse displacements. This led to large changes in the bond-lengths at the surface, but a n-examination of the model shows that it does give a relatively good value of 0 _ 26.4” for the tilt angle. The energyminimization calculations also show a greater sensitivity to normal displacements than to transverse ones. The rehybridiintinn “. nf “.“.....I nrhit.lr ir nnlv cliahrlv mffa,.td kv . . ..mll ..nifnrm w-1.. .I “...I “.‘O I... J _._.w v, m 0 .wrBu,s Y.I..“,I.I displacement of the surface atoms. The effects of the relaxation on the angular distributions around each surface atom are the most revealing. The surface geometry constrains one angle to near its tetrahedral value of ‘5 109.5”. The other two angles are lr91.5” 613
D J CAadi: Semiconductor surface reconstruction around As and 2 123.5” around Ga These are consistent with the VIEWS of 94.3” and 120” determined from quantum-chemical calculations on GaH, and ASH, moleculeslO. The surface relaxation and rehybridixation reduce the total energy (relative to the unrelaxed surface) by 0.25 to O&V per surface atom’-‘. Up to now all LEED and energy-minimixation studies have assumed that the GaAs(ll0) surface possesses reflection symmetry about yz planes normal to the surface and passing through either surface Ga or As atoms. This has been based on the observation of a mirror symmetric variation of the intensity of LEED spots. But even if mirror symmetry is broken, the LEED pattern can still remain symmetric because of the presence of domains. To test this possibility, new energy-minirnixation calculations were carried out in which all restrictions on atomic displacements were removed. The calculations show two stable structures for the surface, one with a mirror symmetry, the other without. The surface atomic displacements Ax along the xdirection, which lead to a breakdown of the mirror symmetry, are estimated to be about 0.06-0.10 A. ne total-energy vs displacement curve is very Sat in the region O~AxsO.1 A, and its variations are in the meVs per atom range. A similar type of bistabiity has been predicted for bulkGaAs under pressure from theoretical studies of phonon dispersion c~rves~~. The small energy difference suggests that even at low temperatures both types of structures will coexist at the surface. This should help explain the apparent violation of selection rules based on parity observed in recent normal photoemission measurementsr2. The accepted 27” rotational model for the GaAs(l10) surface provides a good description of the measured surface electronic states9*r3. In the absence of relaxation, both filled and empty surface states appear in the fundamental band gap. The 27.5” ‘rotational relaxational’ models remove these states from the gap, in agreement with contact-potential difference measurements’5 and the absence of Fermi-level pinning in the gapr6*“. The relaxation results in only a small charge transfer between the surface Ga and As atoms. Because of strong hybridization between the dangling-bonds, the filled and empty surface states near the valence-band-maximum and conduction-bandminimum have an appreciable mixing of Ga and As derived characters.
3. Si(100) attrfaee The dimer geometry is currently the most generally accepted model for this surface’7-22. Dimerixation leads to a large reduction in the total energy by decreasing the number of dangling-bonds at the surface. The asymmetric dimer geometry which involves inequivalent displacements of the surface atoms forming the dimer is energetically the most favourable20-22. LEED both suggest analyses2L26 and total-energy calculations1e22 that the atomic motions from ideal positions extend several layers into the bulk. The analysis of the experimental data is complicated by the presence of more than one geometry at the surface. StNCtUI’B With 2 X 1, 2 X 2, C@td-2 X 4 (C-2 X 4), c-2 X 2, etC, can be easily created by using asymmetric dimers as building blocks. The energies of all these structures are approximately equal. Experimentally, this leads to problems in preparing a wellordered surfaa”. The phase diagram of the surface has been recently determined by mapping the problem into a twodimensional anisotropic Ising mode12s. 614
There is now a great amount of experimental evidena in favour of the asymmetric dimer geometry. Photoemission measurements29*30 of the surface state density are consistent with those calculated for a dimer geometry. In particular, the non-metallic behaviour and dispersion of the surface band”O is well explained by the asymmetric model 31*32.Ion scattering measurements33*34, combined with Monte Carlo analyses of the scattering from various StNCtURs, provide very strong evidence for the asymmetric dimer geometry and against the symmetric dimer. The theoretical prediction 2o of an indirect bulk to surface band gap of about 0.6 eV is in good agreement with experimental results35*36. The magnitude of the filled to empty surface state splitting is also in good agreement with optical data3’. High resolution infra-red studies of H and H,O chemisorption on the surface ate also consistent with the dimer model. Finally, the best 6t to the LEED data is obtained2”*26 by using the asymmetric dimer geometry. The degree of agreement on the detailed structure of the asymmetric dimer model is not as good as for the GaAs(l10) surface. The LEED studies on the 2 x 1 surface consistently suggest2 ’ a relatively large ‘twisting’ of the dimers (ie, motion along the It j directions where i is normal to the surface and x is along the dimerization direction). Calculations show, however, an increase in the total-energy resulting from this motion. Only structures with larger unit cells are found3s to have Ay#O and only for subsurface atoms and not for the surface dimers. Another problem is that the LEED studies give2s a dimer bond length of 2.5 A, which is larger than the bulk-like 2.35 A length found in tight-binding calculations20 and the molecular-like 2.25 A bondlength found in ab initio self consistent pseudopotential calculations2’. The LEED analysis 25 also gives a smaller asymmetry than the calculations with the exception of quantum-chemical calculations on clusters which predict zero asymmetry for the dimer39. The extent to which the abse.na of band structure effects influence the results of the cluster calculations is not clear, however. Band structure effects could be important in stabilizing the asymmetric dimer relative to the symmetric one through a metal-semiconductor transition’O. The Si(lO0) dimer models are also applicable to the Ge(100) surfaa except for a change in the length scale. Result of recent photoemission results4’ from the 2 x 1 surfaa are in good agreement with the theoretical results calculated for Si. X-ray diffraction measurements at very glancing angles give results consistent with a dimer geometry4’. At low temperatures the surface exhibits a sharp c-4 x 2 LEED pattem42. Ion backscattering expcrimmts are also consistent with the asymmetric dimer mode142.
4. Si aad ce(ll1)
cleavqge dpces
A. Buckling model. The 2 x 1 reconstructed cleavage surface of Si has aroused new interest as a result of recent experimenta14w5 and theoretical developments 46-52. The buckled modelS3 for the surface in which alternate rows of atoms are raised and lowered was until recently the most widely accepted structure for the surface. Problems in accounting for the experimental data, particulary photoemission data, have led to new StNCtUrd models involving radically different bonding features. A brief review of the evolution of our understanding of the surface structure and a descriptions of the new geometries is given below. The buckled model for the 2 x 1 surface was introduced more than 20 yr ago by Haneman s3. The basic argument in favour of the
D J Chadi: Semiconductor surface reconstruction
model was that by buckling the surface, a net reduction in the total energy would result from the transfer of the dangling-bond dectron of the lowered atom to that of the raised atom. The charge transfer and buckling of the surface would occur only if the intraatomic Coulombic repulsion U were not too large.+ If U were large enough to prevent charge transfer, there would be no reduction in the ‘electronic’ energy; furthermore, the strain energy associated with buckling would raise the total energy so that buckling would become suppressed. Initial calculations54 suggested a small U and gave a large charge transfer for the Haneman model.Tight-binding calculations4*55 based on the assumption of a negligible U also gave a large charge transfer and predicted a strong buckling of the surface. The buckling model accounted fairly wells’ for the surface state optical absorption spectrums6. In addition, electromodulated absorption experiments on the Ge(l1 l)-2 x 1 surface provided evidence for a charge transfer between surface atoms 5’. The calculated surface state electronic %.-.A”58 vuuua
f-‘,I”,
.I.- L..A.l,A 1”5 “UbLIcu
c:,, a(,
4, \ ? - , r..AL,, ,A T& a 1 DUllawz
_.^__ ^I”... r ^.._ A l WG15 aIS” l”U‘l” I”
reasonable agreement with experiment59. The experiments also revealed that the photoemission results were strongly cleavage dependent with the dispersion of the least bound surface state varying by ~0.5 eV from sample to sample5’. High resolution angle-resolved measurements using synchrotron radiation later showed an upward dispersing surface band*-’ along the T-J direction of the Brillouin zone (see inset of Figure 3). An earlier measurement had shown a similar dispersion along the _#~___.:__6*-_a _X,alspcrzacm >:_-__-z_- __.__-_._L I_____rL__ -L_. 1P -A” o~rccuon--. I nc u.0L cv was mucn larger lnan mat calculated for the buckling model which showed at most a flat or a downward dispersing band. Attempts to bring the buckling model into agreement with experiment by varying the amount of buckling were unsuccessfulso. Other problen)s with the buckling model were noticed. Surface core-level shit measurements6’*62 revealed a much smaller core shit (0.4 zeV) than the 5 2.2 eV shift expected from a one electron transfer between surface atoms. The most surprising development, however, was the observation in angle-resolved measurements*’ of two dangling-bond states at the J point of the Brillouin zone split by ~0.55 eV. The danglingbond character of the two states was established by using s- and p-polarized light which gave indication of a predominantly (s + p,) character for the two states. Two different theoretical approaches to the questions of small core-shift and the existence of two distinct dangling-bonds occur at the surface have been pursued. The first approach emphasizes the importance of electronic correlations and spin-polarization effects at the surfaceso-52; the second attributes the two dangling-bond states and the observed cleavage dependence of electronic properties to the occurrence of more than one structure on the same surface4’. The two approaches have led to a deeper understanding of the surface structural and electronic properties of Si and are discussed separately below. be in
B. Spia-polarixatioo and buckling.The atoms on the ideal (111) surfaces of C, Si and GE are separated by second-nearest neighbour or longer distances at the surface. The interaction V between
The requirement is CJC~E~[+[AE~+E,,.~. where E, is the sukce Madelung energy for unit charge transfer between surlaa atoms. ASis the l
self-energy diffcrena between the dangling-bond orbitals on raised and lowered atoms, and Era,,” is the lattia strain energy of subsurlaa atoms
resulting from buckling. t The direction of the quantization axis being arbitrary.
neighbouring dangling-bonds ia therefo* about one order of magnitude smaller than the bonding interactions with the subsurface atoms. It is primarily because of thii weak interaction (relative to the interatomic correlation energy U) between dangling-bonds that spin-polarization effects become important at the surface. In the limit 4V/U> 1 the surface is metallic with a half-filled band of states in the band gap. In the other limit where V/U+ 1, the atomically 1 x 1 surface will have an electronically 2 x 1 unit cell and will be insulating 50-52b3*64.The doubling of the electronic uxiit cell results from spin-polarization, ie, the two dangling-bond electrons of the 2 x 1 cell will have their spins polarized predominantly in the + and - directions, respectiveiyt. The paramagaetic (or non-magnetic)solution is also a selfconsistent solution but with a higher energy than the antiferromagnetic solution. The difference between the two energies is 4V2/U Ab initio selfconsistent pseudopotential calculations based on the local-density-functional formalism, which have been --r---l.. ^>“LKJ=SXLII ..-- ““(1.1ll, :, ,url:..,:..r ,r-.,.*.._.,, y,“~Ln~J __,._ ..+L. ,..c slllsl‘rcl~ pr~rcnua *I.&USJL,YC,Y,(11 “1 c; 0s give an energy difference of 0.04 eV per 2 x 1 cell”. This leads to the estimate: vl/U=O.Ol eV
(1)
which gives Uzl
eV for YzO.1
eV.
0.254.35 eV estimated for the buIk67*68 and is a consequence of the lower screening at the surface. Values of U ranging from z 1 to = 1.2 used in several Hubbard-type models50*63*64 for- the dangling-bond states of the Si( l l l)-2 x 1 surface are consistent with this estimate. A consequence of the large U/V ratio of 3: 10 is that the atomic 1 x 1 surface is stable against small buckling distortions”*“. The reason for this is that the buckling strains the lattice, but very little energy lowering charge transfer between the raised and lowered atoms occurs as a result of the large intra-atomic Coulombic energy U. Self-consistent pseudopotential calculations suggest that the relaxed 1 x 1 surface is stable against all buckling distortions6*’ I The inclusion of intra-atomic correlation eITects into the empirical tight-binding energy-minimization method gives a similar result. Without taking account of Coulombic and spin-polarization effects, these calculations4 give a large charge transfer and predict the buckled surface to be ~0.72 eV (per 2 x 1 unit cell) more stable than the unrelaxed surface having a paramagnetic electronic structure. Spin-polarization reduces the energy of the unrelaxed surface by z0.S eV, thereby decreasing the relative stability of the buckled surface to 0.22 eV. The Hubbard U term raises the buckled surface energy by 2c 1.15 eV and the screened surface Madelung energy lowers it by 5 0.8 eV. Overall, therefore, the buckled energy is (-O-22+ 1.15-0.8) = 0.13 (per 2 x 1 cell) eV higher than for the unrelaxed antiferromagnetic surface. Total energy considerations, therefore, appear to rule out the buckled model. Despite this, the small charge transfer between surface atoms, the observation of two danglingbond states at the Brillouin zone boundary, and the surface optical properties cnn be accounted for reasonably well by the k&led ____-__
mnrlrlsO . -___.
Wnwrvrr __.e.._‘“.,
thr rknno . ..w mwnll ““UP . ..* “,nyC
nf “a
thm LYI
..wfm.a eY..O-
band dispersion cannot he brought into agreement with experiment. This disagreement, together with the results from total-energy calculations, make the acceptance of the buckled model for the Si(lll)-2 x 1 surface difficult. 615
D J Chadi: Semiconductor surface reconstruction
C Ge(lll)-I x 1. An important recent development is the discovery6a*69 of a 1 x 1 LEED pattern on Ge(lll) surfaces cleaved at temperatures near 4 K. Similar experiments on Si are found to lead to a 2 x 1 pattem64. The Ge(lll)-1 x 1 LEED pattern is sharp and stable; it is not clear yet whether it corresponds to an atomically ordered surface. If ordered, the electronic structure should have an antiferromagnetic ordering with a 2 x 1 periodicity (even though the atomic periodicity is 1 x 1). As discussed above, this structure is stable against buckling distortions. It should be metastable50*51 against distortions leading to the n-bonded chain structure described in section D. The activation barrier for this transformation has been calculated*’ to beabout 0.1 eV atom- r. The transition rate to the lower energy 2 x 1 structure would be, therefore, nearly zero at 4 K, consistent with the experimental observations. Since Si and Ge have similar properties, it has been suggested that despite the lack of a 1 x 1 LEED pattern on Si( 111) surfaces at low temperatures, the surface probably contains a two-phase structure consisting of 1 x 1 and 2 x 1 ordered areas6**69. More experiments are needed to reveal the nature of the atomic structure of surfaces cleaved at low temperatures. The similarities, if any, between the low and high temperature 1 x 1 structures need to be also investigated. D. New sbuctural models. A new ‘chain’ model for the Si( Ill)-2 x 1 surface was recently proposed by Pandey6*46. The n-bonded chain model offers an explanation for the stability of the 2 x 1 surface relative to the relaxed 1 x 1 surface”*47*4s.The formation of the chain starting from the 1 x 1 surface involves bond-breaking and rebonding. The reconstruction leaves the density of dangling bonds constant but moves the dangling-bonds closer to each other such that the interactions become of the neatest-neighbour type* The distortions leading to the n-bonded chain structure4’ are shown in Figure 2. Figures 2(a) and (b) show the top and side
views of the chain-model, respectively; Figure 2 shows the side view of a 1 x 1 surface. The positions of atoms before and after reconstruction can be compared by matching atoms with the same number in Figures 2(b) and (c). The reconstruction involves a shear distortion of the surface double layer along the long axis of the unit cell accompanied by breaking l-5 bonds in Figure 2(c) and formation of 43 bonds in Figure 2(b). The reconstruction changes the topology of the surface, resulting in the formation of alternating 5- and 7-fold rings of atoms. The necessity of extra bond breaking in creating the chain structure raises the question of whether the cleavage process supplies sufficient-energy for this purpose. The measured cleavage energy ‘O of Si of about 1240 erg cm2 corresponding to about 1: 1 eV per surface atom on each of the two surfaces resulting from cleavage may appear to be too small to account for the additional breaking of bonds between atoms 1 and 5 in Figure 2(c). Northrup and Cohen have shown*‘, however, that this is not the case. By calculating the total energy for eight different configurations intermediate between a buckled 2 x 1 surface and the chain model, they find an activation barrier of about ~0.1 eV atom- * This is a much smaller energy than might be expected from bond energies in bulk Si. It demonstrates that the cleavage process can supply sufficient energy to create the chain structure. The energy of the n-bonded chain structure is ~0.4 eV atom-l lower than the ‘1 x 1’ structure having an antiferromagnetic spin arrangement. The stability of the chain arises primarily from the strong x-bonding interactions which more than compensate for the large angular strains in the structure,. The magnitude of the n-bonding interaction in the bulk is z 1.05 eV. The interaction at the surface is expected to be reduced from this value because the surface atoms are not all at the same height above the surface, and the dangling-bonds do not all point in the same direction. The measured dispersion of the upper surface state seen in angleresolved measurements is described well by the equation E(k)=const
(0)
+2V2 cos 2nk-,/ci+(2V,
cos nk)?
where V, z -0.63
eV
is the tight-binding Hamiltonian neighbour dangling-bonds,
(3) matrix element between nearest-
V2z +0.13 eV is the second-nearest-neighbour 2s, z 0.20 eV
5
Figure 2. The top and side views of the n-bonded chain model for the Si(lll)-2 x 1 surface are shown in (a) and (b). The side view of the ideal surface is shown in (c). The numbering on the atoms shows the changes in bonding occurring as a result of the reconstruction. 616
(2)
(4) interaction
and (5)
represents the difference in the self-energies (or diagonal matrix elements) of the two dangling-bonds in the unit cell. The reduced wavevector k in equation (2) corresponds to the projection of the actual wavevector along the F-J direction of the Brillouin zone (Figure 2) with k = f corresponding to J and k =0 to f. The large value of V, (i.e., 2V,/U> 1) makes spin-polarization e5ects much weaker for the chain model than for the ideal 1 x 1 surface. A comparison of the surface band dispersion obtained from equation (3) to the experimental data is shown in Figure 3. Unlike the case of the buckling model, the chain structure provides a very good description for the surface band dispersion. Recent angleresolved photoemission measurements” on the Ge( 11l)- 2 x 1 surface also give a dispersive band similar to that of Si. Previous angle-integrated measurements give evidence for one72*‘3 or
D J Chsdi: Semiconductor surface reconstruction 4
F?Ll 3
(0)
2
1.0 -
2 P
0.5
-1.0
-iJ
-i K
I F
2
3
I
4
3
3
tb)
-
Surfacewave
I
I
5
i?
vector
Figure 3. Surface energy-band dispersion for the n-bonded chain model. The tight-binding result from equation (2) is shown as the solid line; the
experimental results of references 4345 by 0, x, and 0, respectively.
Figure 4. The top and side views of the n-bonded molecular model for the Si(l1 l)-2 x 1 surface are shown in (a) and (b). The atomic positions in the
ideal 1 x 1 surface confisuration are shown in (cb
two’3 surface states near the valence-band-maximum depending on the annealing temperature. Electronic transitions between filled and empty surface states near the J-K’ line of the Brillouin zone give rise to a large peak in the joint-density-of-state which should correspond to the mainpeak measured in the optical reflectivity spectrums6*s’. The optical absorption is predicted to be maximum for electric field polarization parallel to the short axis of the real space unit cell and nearly zero for polarization along the long axis of the cell. For the buckling model, an opposite anisotropy with a 3 : 1 ratio for the absorption intensity has been predicted50. Tests of polarization dependence of the surface optical absorption or the surface photovoltage” should, therefore, prove very useful in distinguishing between different surfaa structures. The n-bonded chain model provides a satisfactory explanation for the stability and dispersion of the upper surface state band of the 2 x I surface. As mentioned before, however, the photoemission experiments indicate the presence of another nearly dispersionless dangling-bond band at the surface. This state cannot be explained by the chain model. If intrinsic, it would imply the existence of a second structure at the surface. This possibility is attractive in that it would also account for the strong cleavage dependence of the surface electronic states measured by photoemission. It would be interesting if surfaces with predominantly one type of structure having only one of the two dangling-bond bands could be prepared. The presence of more than one structure at the surface makes the analysis of LEED data very dimcult. In fact, a recent LEED study finds the chain model (unlike the buckling modeI) to be in poor agreement with the experimental data76. A reconstruction that involves the same types of atomic distortions as those involved in generating the n-bonded mode149 shown in Figure 4. The shear distortion of the top double layer of atoms leading to rebonding occurs at 120” with respect to the long axis of the unit instead of parallel to it as is the case for the chain model. The model consists of a dimerized pair of atoms (atoms 1
and 2 in Figures 4a and b) per unit cell. Self-consistent pseudopotential calculations76 and one-electron tight-binding calculations predict a much lower energy for the chain than for the ‘molecule’. However, the energy of the molecule is stabilized appreciably by configuration interaction mixing49 and the energy of the n-bonded molecular and chain structures are expected to be very close in Si The calculated = 0.6 eV-wide surface band for the molecular structure is not, however, in agreement with the dispersionless band seen in photoemission measurements”*45. It is interesting to note that other structures, in particular a chain structure involving only S-fold rings of atoms at the surfaa, can be created’ ‘I. At this stage, we have to conclude that despite impressive progress in understanding of reconstruction on (111) surfaces, much more remains to be done both experimentally and theoretically. 5. Adatoms Surface reconstruction and relaxations can lower the surface energy in one of several different ways. On the GaAs( 110) surface, the atomic motions result in rehybridization making Ga atoms more sp2 and As atoms more p3 bonded. On the Si( 111) - 2 x 1 surface, the total energy is lowered by a rebonding which brings the dangling-bonds closer to each other such that they interact via nearest instead of second-nearest neighbor interactions. One expects that a third mechanism for lowering the total energy is the reduction in the surfaa dangling-bond density. The bonding of two three-fold coordinated Si atoms would release about 2.4 eV in energy if no bond-length and angular strains are involved. This is a much larger energy than those involved in the reconstructions which have been considered up to now. Simple ways of reducing the surface dangling-bond density are known. The major problem, however, at least for small unit cells, is that it is nearly 617
D J Chedi: Semiconductor surface reconstruction
impossible to avoid large, angular strains which more than offset the energy gains resulting from having fewer dangling-bonds. A particularly simple adatom model is the Harrison model’e. For a (111) surface, it essentially involves one extra atom for every three surface atoms. Each adatom is bonded to three surface atoms. In this way, the only dangling-bonds are on the adatom, and a factor of three reduction in dangling-bond density is achieved. On a surface such as Si( 11l), there are two inequivalent positions where the adatom can be placed. It can be positioned above a second layer atom of the substrate, or on a ‘hollow’ site. Both configurations give rise to large bond angle deviations from the ideal 109.5” tetrahedral angle. In the first configuration bond angles of 180” and 424 and in the second bond angles of 180” and -z 72” result. The ‘hollow’ site configuration is appreciably lower in energy than the’on top’geometry; but it still has a high surface energy and is me&stable. The binding energy of the adatom to the surface is calculated to be ~2.8 eV which is equivalent to an average energy of0.93 eV per bond. This is only ~40% of the bulk bond energy of -2.4 eV. The total energy would be reduced by (2 x 2.4 - 2.8) eV or 2 eV by transferring the adatom into the bulk. Even though the tight-bonding calculations somewhat underestimate the binding energy (because of the neglect of d-states), they do not support the preliminary interpretation of recent very elegant vacuum tunnelling measurements on the Si(lll)-7 x 7 surface reconstruction in terms of a simple adatom model”. More complicated structures involving adatoms in which the deviations from perfect tetrahedral bonding are smaller cannot be ruled out. 6. Coacluaions The short review of surface reconstruction on GaAs(l10). Si and
Ge(100) and (111) surfaces presented above demonstrates that much has been accomplished in the last five years and that even more remains to be done for a better understanding of even the ‘simplest’ reconstructions on well-studied semiconductor surfaces. This is particularly true for the cleaved surfaces of C, Si and Ge, where at this time a single structural model cannot account for all experimental data Studies of the similarities and differences in the surface properties of these materials should prove fruitful for identifying the various mechanisms leading to surface reconstruction on cleaved and hopefully annealed surfaces. Acknowledgements
This work is supported in part by the US Office of Naval Research through Contract No NOOO14-82-C-0244. References
’ R J Meyer, C B Duke, A Paton, A Kahn, E So, J L Yeh and P Mark, Phys Rev B, 19, 5194 (1979). ’ S Y Tong, A R Lubinsky, B J Mrstik and M A Van Hove, Phys Rev B, 17, 3303 (1978) ’ C B Duke, J Vat Sci Techno) (to be published). ’ D J Chadi, Phys Rev Letr, 41, 1062 (iO78). ’ D J Chadi. Phvs Reu B. 19.2074 (1979). ’ K C Pandey, ihys Reu.Lett, 49,223 (1982). ’ J A Barton, WA Goddard and T C McGill, .I Vat Sci Technol, 16.1178 (1979) * A Kahn, G Cisneros, M Bonn, P Mark and C B Duke, Surjace Sci, 71, 387 (19781 9 D j Chdi, Phys Rev B, 18, 1800 (1978). to CA Swarts WA Goddard and T C McGill, J Vat Sci Technol, 17,982 (1980). ’ I1 K Kunc and R M Martin, Phys Rm B, 24,231l (1981). 618
I2 F Cenino (unpublished). “J R Cbelikowsky and h4 L Cohen, Phys Reu B, 20.4150 (1979)
t4 D J Chadii J Vat Sci Technol, IS.1244 (1978). ” JvanLaarandAHuijaer,.J VacSci Tech&, 13,769(1976);ibid,14,893 (1977) ‘6WESl)iar,PW(3hKPEGngory,TSuktgawaMdIABebelole,J J’uc Sci TecJmol, 13,233 (1976); ibid,14,885 (1977). ” W Gudat and D E Eastman, J Vat Sci Techno/, 13,831 (1976). ‘s J A Atmelbaum G A BaraR and D R Hamann. Phvs RN B, 14, 588 (1976). -I9 J A Appelbaumand D R Hamann, Slajbee Sci. 74.21 (1978). lo D J Chadi. Phvs Rev Lerr. 43.43 (1979). ” M T Yin and hl L Cohen, Phys l&u B,‘U, 2303 (1981) 21 W S Venvoerd, Surface Sci 103,404 (1981) )’ S Y Tong and A L Maldondo, Sta$hce Sri, 7B, 459 (1978). ‘* F Jona, H D Shih, D W Jepson and P M Marcus, J Phys C, 12, L455 (1979). ” W S Yang, F Jona and P M Marcus, Sohi State Cammun, 43,847 (1982L js S J.White, DC Frost and K A R Mitchell, Solid State Canmun, 42,763 (1982);GJRJoncaandBWHoUand.SolidSrureCnmmun.46.651(19833. ” M J Cardillo and G E Becker, P&s Rev B, il. 1497 (1980). **J Ihm and J D Joannopoulos, J vat Sci Technor (to be published). 29JERoweandHIbach.PhvsReuLQrr.32.421(1974):JERoweandSB Christman. J Vat Sci T&h&, 17, 220’(1<801 . ‘. ‘O F J Himpsel and D E Eastman, J Vat Sci Technol, 16, 1297 (1979). ‘t M A Bowen. J D Dow and R E Allen. Phvs Reu B. 2.6.7083 (1982). ‘* A Mazur and J Pollmann, Phys Rev i, Xi 7086 (1982). ” L C Feldman, P J Silverman and I Stensgaard, Nucl /astrum Methods, 168, 589 (1980); I Stensgaard et al, Surfice Sci, 102, 1 (1981). ‘* R M Tromp, R G Smeenk and F W Saris, Solid Stare Commun. 39,755 (1981); and Su&ce Sci (to be published). ” WMiinch,PKokeandSKrueger,J VucSciTechnol,19,313(1981);W Miinch and P Koke, Solid State Commun, 36, 1007 (1980). ‘I’ Y J Chabal, S B Christman, E E Chaban and M T Yin (to be published). ” P E WietetIga, M J Sparnaay and A van Sihhouf St&ce Sci, 99.59 (1980). 3* D J Chadi, J Vat Sci Te&al16,1290 (1979); J Appl Optics,19.3971 (1980). ‘9 A Redondo and W A Goddard, J Vat Sci Technol, 21,344 (1982). *OJ G Nelson, W J Gignac, R S Williams, S Robay, J Tobin and D A Shirley, Phys Rev (to be published). ” P Eisenberger and W C Morra, Phys Rm Lerr, 46, 1081 (1981). 42 L C Feldman (to be published). 43 F J Himpael, P Heinmann and D E Eastman, Phys Rev B, 24,2003 (1981). u R I G Uhrberg, G V Hansson, J M Nicholls and S A Flodstrijm, Phys Rev Lerr, 48, 1032 (1982). ” F Houzay, G Guichar, R Pinchaux, G Jemquel, F Solal, A Barsky, P Steiner and Y PetroB, Surjace Sci (to be published). 46 K C Pandey, Phys Ra, Lerr, 47, 1913 (1981) *’ J E Northrup and M L Cohen, Phys Rev Left, 49, 1349 (1982). 4n J E Northrup and M L Cohen, J pat Sci Technol, 21,333 (1982). 49 D J Chadi. Phvs Rev B. 26.4762 (1982). so R Dei Sole’and
D J Chadi: Semiconductor
surface reconstruction
” S Brannan, J Stohr, R Jacgar and J E Rowe, Phys Ret Lerr, 451414 (1980). CQM Lanoo and G Allan, Srufaee Sci, 115, L137 (1982). 6’C B Duke and W K Ford, Sugiie Sci. 111, L165 (1981)
6’ M T Yin and M L Cohan, Phys Reu Len, 45, 1005 (1980). 66 G A BaraB, E 0 Kane and M Schluter, Phys Rev LPtr,43,956 (1979) “I W B Jackson, Solid Stare Commun, 44,477 (1982). ‘s V YU Aristov, N I Goiovko, V A Grazhulis, Yu A Cksipyan and V 1 Talyanskii, Su&ce Sci, 117,204 (1982); V Y Aristov, 1 E Batov and V A Grarhulis, Surface Sci (to he published). e9 D Hancman and R 2 Bachrach, J Yac Sci Technol, 21,337 (1982); and Phys Reu i3.27 (to be published). “J J Gilman, .I Appl Phys, 31,2208 (1960).
‘I J M Nicholls, G V Hansson, R I G Uhrkrg and S A Flodstriim, Phys Rev B, 27 (to be published). 72 G M Guichar, G A Garry and C A Scbcnnc, Surface Sci, 85,326 (1979). ‘J T Murotani, K Fuiiwara and N Nishiiima. Pkys RPDB, 12.2424 (1975). ‘4 J Assman and W Mdnch, Sur$xe S& 99; 36 (1980). ” R Fader. Solid Stare Cummun 45. 51 119831 76 0 H N&n, R M Ma&n, D J Chadi &d K i&c, J Vat Sci Technol (to be published). ” D J Chadi (to be published) ‘* W A Harrison, Surface Sci, 55, 1 (1976). ‘9 G Binnig, H Rohrcr, Ch Gcrmcr and E Wcibcl, Phys Rev Len. 49.57 (1982)
619
0042-207X/63S3.00+ .OO Pergamon Press Ltd
Printed in Great Britain
Semiconductor D J Chadi,
surface
reconstruction
Xerox Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, CA 34304,
USA
A review of the current state of our understanding of some semiconductor surface reconstructions is given. These include the GaAs(l10) surface and the (100) and (17 1) surfaces of Si and Ge. The strong correlation between atomic and electronic structure and the energies involved in structural rearrangements at the surface _I_ “IIYY*YW”* #&rr.rs~J WI_
1. Ilmdlmion
Atomic displacements from ‘ideal’ positions occur on virtually all semiconductor surfaces. The structural rearrangements can (1) keep the surface topology or connectivity unchanged from that of .L:>a.., &..,I. .--:....r,~ ,...z..- I?\ ^I.^___ lLIK L- zur,Wz . ...-r..- r---l--.. UK I&W111 “uI&-LC‘IlII&&PWu WuI_, ,L, r;llaul(c L”pu1”gy but maintain a one-to-one correspondence between the atoms of the reconstructed and the ideal surface and (3) lead to the addition or removal of atoms from the surface resulting in a loss of the oneto-one correspondence with the ideal surface. The relaxed 1 x 1 GaAs( 110) cleavage surface, the dime&d Si( lW)-2 x 1 surface, and adatom, vacancy or terrace-step models for the Si( l l l )-7 x 7 surface provide examples of each of the three types of atomic rearrangementa, respectively. Until recently, it was generally thought that all cleaved surfaces were examples ofthe first type of surface geometry. The most important new development has been the realization that the cleaved Si(l l l)-2 x 1 surface is much better described by a type (2) reconstruction involving a change in the surface topology than by a type (1) buckling reconstruction. In the following sections, a detailed discussion of the various surface reconstructions mentioned above is given. Attention will be given to a presentation of the problems remaining in each case. The relaxation of the GaAs(ll0) surface, its electronic structure and the question of mirror reflection symmetry are discussed in section 2. The 2 x 1 and c-4 x 2 reconstructions of Si and Ge( 100) surfaces are reviewed in section 3. New structural models for the Si(l1 l)-2 x 1 surface, as well as questions related to buckling, spin-polarization and the occurrence of more than one structure at the surface, are discussed in section 4. The cnergetics of an adatom model for the Si(l1 I)-7 x 7 surface are examined in section 5. % GaAs(ll0)
!hrface
The (110) surface structures of all III-V and II-VI semiconductors that have been studied show remarkable similarities tn ~nntbrr nf 1 IfI\ ir nmnna .V nnr ““I _Y”...W.. V‘ tkmr .,.“ow, thr eaa- CP --a Ad a”\* a”, r~rrfmem .,-.....Y nninnur “...y..- s....“..b semiconductor surfaces for the accuracy and confidence with which its surface atomic geometry is known. Each surface unit cell contains a Ga and an As atom as shown in Figure 1. The surface relaxation involves an approximatelyrotational type of
Top
view
side view ideal 1x1
view relaxed Ix
Side
I
Figwe 1. Top and side views of the GaAs(ll0) surface. The tilting of the surfaa GaAs bond is about 27.5”.
atomic displacement (ie, involving very small bond-length changes of ‘c f 1% with the As moving out of the surface plane and with Ga moving closer to bulk atomsles. The total relative displacement of the atoms normal to the surface is 0.650.69 A. Dynamical low-energy-electron diffraction’-” (LEED), as well as theoretical total-energy minimization studies via tightbinding&‘, self-consistent pseudopotentiaL and quantum chemical methods’, predict a tilting of the Ga-As surface bonds by an angle 6 of about 27.5”* 1.5”. The quality of the fit to the LEED data is most sensitive to 6 and relatively insensitive to small uniform displacements of the surface Ga and As atoms along the y diraXion1’3. In fact, an early LEED model’ (referred to as a bond-relaxation mode19) took account of only the normal displacements of the surface atoms and ignored the transverse displacements. This led to large changes in the bond-lengths at the surface, but a n-examination of the model shows that it does give a relatively good value of 0 _ 26.4” for the tilt angle. The energyminimization calculations also show a greater sensitivity to normal displacements than to transverse ones. The rehybridiintinn “. nf “.“.....I nrhit.lr ir nnlv cliahrlv mffa,.td kv . . ..mll ..nifnrm w-1.. .I “...I “.‘O I... J _._.w v, m 0 .wrBu,s Y.I..“,I.I displacement of the surface atoms. The effects of the relaxation on the angular distributions around each surface atom are the most revealing. The surface geometry constrains one angle to near its tetrahedral value of ‘5 109.5”. The other two angles are lr91.5” 613
D J CAadi: Semiconductor surface reconstruction around As and 2 123.5” around Ga These are consistent with the VIEWS of 94.3” and 120” determined from quantum-chemical calculations on GaH, and ASH, moleculeslO. The surface relaxation and rehybridixation reduce the total energy (relative to the unrelaxed surface) by 0.25 to O&V per surface atom’-‘. Up to now all LEED and energy-minimixation studies have assumed that the GaAs(ll0) surface possesses reflection symmetry about yz planes normal to the surface and passing through either surface Ga or As atoms. This has been based on the observation of a mirror symmetric variation of the intensity of LEED spots. But even if mirror symmetry is broken, the LEED pattern can still remain symmetric because of the presence of domains. To test this possibility, new energy-minirnixation calculations were carried out in which all restrictions on atomic displacements were removed. The calculations show two stable structures for the surface, one with a mirror symmetry, the other without. The surface atomic displacements Ax along the xdirection, which lead to a breakdown of the mirror symmetry, are estimated to be about 0.06-0.10 A. ne total-energy vs displacement curve is very Sat in the region O~AxsO.1 A, and its variations are in the meVs per atom range. A similar type of bistabiity has been predicted for bulkGaAs under pressure from theoretical studies of phonon dispersion c~rves~~. The small energy difference suggests that even at low temperatures both types of structures will coexist at the surface. This should help explain the apparent violation of selection rules based on parity observed in recent normal photoemission measurementsr2. The accepted 27” rotational model for the GaAs(l10) surface provides a good description of the measured surface electronic states9*r3. In the absence of relaxation, both filled and empty surface states appear in the fundamental band gap. The 27.5” ‘rotational relaxational’ models remove these states from the gap, in agreement with contact-potential difference measurements’5 and the absence of Fermi-level pinning in the gapr6*“. The relaxation results in only a small charge transfer between the surface Ga and As atoms. Because of strong hybridization between the dangling-bonds, the filled and empty surface states near the valence-band-maximum and conduction-bandminimum have an appreciable mixing of Ga and As derived characters.
3. Si(100) attrfaee The dimer geometry is currently the most generally accepted model for this surface’7-22. Dimerixation leads to a large reduction in the total energy by decreasing the number of dangling-bonds at the surface. The asymmetric dimer geometry which involves inequivalent displacements of the surface atoms forming the dimer is energetically the most favourable20-22. LEED both suggest analyses2L26 and total-energy calculations1e22 that the atomic motions from ideal positions extend several layers into the bulk. The analysis of the experimental data is complicated by the presence of more than one geometry at the surface. StNCtUI’B With 2 X 1, 2 X 2, C@td-2 X 4 (C-2 X 4), c-2 X 2, etC, can be easily created by using asymmetric dimers as building blocks. The energies of all these structures are approximately equal. Experimentally, this leads to problems in preparing a wellordered surfaa”. The phase diagram of the surface has been recently determined by mapping the problem into a twodimensional anisotropic Ising mode12s. 614
There is now a great amount of experimental evidena in favour of the asymmetric dimer geometry. Photoemission measurements29*30 of the surface state density are consistent with those calculated for a dimer geometry. In particular, the non-metallic behaviour and dispersion of the surface band”O is well explained by the asymmetric model 31*32.Ion scattering measurements33*34, combined with Monte Carlo analyses of the scattering from various StNCtURs, provide very strong evidence for the asymmetric dimer geometry and against the symmetric dimer. The theoretical prediction 2o of an indirect bulk to surface band gap of about 0.6 eV is in good agreement with experimental results35*36. The magnitude of the filled to empty surface state splitting is also in good agreement with optical data3’. High resolution infra-red studies of H and H,O chemisorption on the surface ate also consistent with the dimer model. Finally, the best 6t to the LEED data is obtained2”*26 by using the asymmetric dimer geometry. The degree of agreement on the detailed structure of the asymmetric dimer model is not as good as for the GaAs(l10) surface. The LEED studies on the 2 x 1 surface consistently suggest2 ’ a relatively large ‘twisting’ of the dimers (ie, motion along the It j directions where i is normal to the surface and x is along the dimerization direction). Calculations show, however, an increase in the total-energy resulting from this motion. Only structures with larger unit cells are found3s to have Ay#O and only for subsurface atoms and not for the surface dimers. Another problem is that the LEED studies give2s a dimer bond length of 2.5 A, which is larger than the bulk-like 2.35 A length found in tight-binding calculations20 and the molecular-like 2.25 A bondlength found in ab initio self consistent pseudopotential calculations2’. The LEED analysis 25 also gives a smaller asymmetry than the calculations with the exception of quantum-chemical calculations on clusters which predict zero asymmetry for the dimer39. The extent to which the abse.na of band structure effects influence the results of the cluster calculations is not clear, however. Band structure effects could be important in stabilizing the asymmetric dimer relative to the symmetric one through a metal-semiconductor transition’O. The Si(lO0) dimer models are also applicable to the Ge(100) surfaa except for a change in the length scale. Result of recent photoemission results4’ from the 2 x 1 surfaa are in good agreement with the theoretical results calculated for Si. X-ray diffraction measurements at very glancing angles give results consistent with a dimer geometry4’. At low temperatures the surface exhibits a sharp c-4 x 2 LEED pattem42. Ion backscattering expcrimmts are also consistent with the asymmetric dimer mode142.
4. Si aad ce(ll1)
cleavqge dpces
A. Buckling model. The 2 x 1 reconstructed cleavage surface of Si has aroused new interest as a result of recent experimenta14w5 and theoretical developments 46-52. The buckled modelS3 for the surface in which alternate rows of atoms are raised and lowered was until recently the most widely accepted structure for the surface. Problems in accounting for the experimental data, particulary photoemission data, have led to new StNCtUrd models involving radically different bonding features. A brief review of the evolution of our understanding of the surface structure and a descriptions of the new geometries is given below. The buckled model for the 2 x 1 surface was introduced more than 20 yr ago by Haneman s3. The basic argument in favour of the
D J Chadi: Semiconductor surface reconstruction
model was that by buckling the surface, a net reduction in the total energy would result from the transfer of the dangling-bond dectron of the lowered atom to that of the raised atom. The charge transfer and buckling of the surface would occur only if the intraatomic Coulombic repulsion U were not too large.+ If U were large enough to prevent charge transfer, there would be no reduction in the ‘electronic’ energy; furthermore, the strain energy associated with buckling would raise the total energy so that buckling would become suppressed. Initial calculations54 suggested a small U and gave a large charge transfer for the Haneman model.Tight-binding calculations4*55 based on the assumption of a negligible U also gave a large charge transfer and predicted a strong buckling of the surface. The buckling model accounted fairly wells’ for the surface state optical absorption spectrums6. In addition, electromodulated absorption experiments on the Ge(l1 l)-2 x 1 surface provided evidence for a charge transfer between surface atoms 5’. The calculated surface state electronic %.-.A”58 vuuua
f-‘,I”,
.I.- L..A.l,A 1”5 “UbLIcu
c:,, a(,
4, \ ? - , r..AL,, ,A T& a 1 DUllawz
_.^__ ^I”... r ^.._ A l WG15 aIS” l”U‘l” I”
reasonable agreement with experiment59. The experiments also revealed that the photoemission results were strongly cleavage dependent with the dispersion of the least bound surface state varying by ~0.5 eV from sample to sample5’. High resolution angle-resolved measurements using synchrotron radiation later showed an upward dispersing surface band*-’ along the T-J direction of the Brillouin zone (see inset of Figure 3). An earlier measurement had shown a similar dispersion along the _#~___.:__6*-_a _X,alspcrzacm >:_-__-z_- __.__-_._L I_____rL__ -L_. 1P -A” o~rccuon--. I nc u.0L cv was mucn larger lnan mat calculated for the buckling model which showed at most a flat or a downward dispersing band. Attempts to bring the buckling model into agreement with experiment by varying the amount of buckling were unsuccessfulso. Other problen)s with the buckling model were noticed. Surface core-level shit measurements6’*62 revealed a much smaller core shit (0.4 zeV) than the 5 2.2 eV shift expected from a one electron transfer between surface atoms. The most surprising development, however, was the observation in angle-resolved measurements*’ of two dangling-bond states at the J point of the Brillouin zone split by ~0.55 eV. The danglingbond character of the two states was established by using s- and p-polarized light which gave indication of a predominantly (s + p,) character for the two states. Two different theoretical approaches to the questions of small core-shift and the existence of two distinct dangling-bonds occur at the surface have been pursued. The first approach emphasizes the importance of electronic correlations and spin-polarization effects at the surfaceso-52; the second attributes the two dangling-bond states and the observed cleavage dependence of electronic properties to the occurrence of more than one structure on the same surface4’. The two approaches have led to a deeper understanding of the surface structural and electronic properties of Si and are discussed separately below. be in
B. Spia-polarixatioo and buckling.The atoms on the ideal (111) surfaces of C, Si and GE are separated by second-nearest neighbour or longer distances at the surface. The interaction V between
The requirement is CJC~E~[+[AE~+E,,.~. where E, is the sukce Madelung energy for unit charge transfer between surlaa atoms. ASis the l
self-energy diffcrena between the dangling-bond orbitals on raised and lowered atoms, and Era,,” is the lattia strain energy of subsurlaa atoms
resulting from buckling. t The direction of the quantization axis being arbitrary.
neighbouring dangling-bonds ia therefo* about one order of magnitude smaller than the bonding interactions with the subsurface atoms. It is primarily because of thii weak interaction (relative to the interatomic correlation energy U) between dangling-bonds that spin-polarization effects become important at the surface. In the limit 4V/U> 1 the surface is metallic with a half-filled band of states in the band gap. In the other limit where V/U+ 1, the atomically 1 x 1 surface will have an electronically 2 x 1 unit cell and will be insulating 50-52b3*64.The doubling of the electronic uxiit cell results from spin-polarization, ie, the two dangling-bond electrons of the 2 x 1 cell will have their spins polarized predominantly in the + and - directions, respectiveiyt. The paramagaetic (or non-magnetic)solution is also a selfconsistent solution but with a higher energy than the antiferromagnetic solution. The difference between the two energies is 4V2/U Ab initio selfconsistent pseudopotential calculations based on the local-density-functional formalism, which have been --r---l.. ^>“LKJ=SXLII ..-- ““(1.1ll, :, ,url:..,:..r ,r-.,.*.._.,, y,“~Ln~J __,._ ..+L. ,..c slllsl‘rcl~ pr~rcnua *I.&USJL,YC,Y,(11 “1 c; 0s give an energy difference of 0.04 eV per 2 x 1 cell”. This leads to the estimate: vl/U=O.Ol eV
(1)
which gives Uzl
eV for YzO.1
eV.
0.254.35 eV estimated for the buIk67*68 and is a consequence of the lower screening at the surface. Values of U ranging from z 1 to = 1.2 used in several Hubbard-type models50*63*64 for- the dangling-bond states of the Si( l l l)-2 x 1 surface are consistent with this estimate. A consequence of the large U/V ratio of 3: 10 is that the atomic 1 x 1 surface is stable against small buckling distortions”*“. The reason for this is that the buckling strains the lattice, but very little energy lowering charge transfer between the raised and lowered atoms occurs as a result of the large intra-atomic Coulombic energy U. Self-consistent pseudopotential calculations suggest that the relaxed 1 x 1 surface is stable against all buckling distortions6*’ I The inclusion of intra-atomic correlation eITects into the empirical tight-binding energy-minimization method gives a similar result. Without taking account of Coulombic and spin-polarization effects, these calculations4 give a large charge transfer and predict the buckled surface to be ~0.72 eV (per 2 x 1 unit cell) more stable than the unrelaxed surface having a paramagnetic electronic structure. Spin-polarization reduces the energy of the unrelaxed surface by z0.S eV, thereby decreasing the relative stability of the buckled surface to 0.22 eV. The Hubbard U term raises the buckled surface energy by 2c 1.15 eV and the screened surface Madelung energy lowers it by 5 0.8 eV. Overall, therefore, the buckled energy is (-O-22+ 1.15-0.8) = 0.13 (per 2 x 1 cell) eV higher than for the unrelaxed antiferromagnetic surface. Total energy considerations, therefore, appear to rule out the buckled model. Despite this, the small charge transfer between surface atoms, the observation of two danglingbond states at the Brillouin zone boundary, and the surface optical properties cnn be accounted for reasonably well by the k&led ____-__
mnrlrlsO . -___.
Wnwrvrr __.e.._‘“.,
thr rknno . ..w mwnll ““UP . ..* “,nyC
nf “a
thm LYI
..wfm.a eY..O-
band dispersion cannot he brought into agreement with experiment. This disagreement, together with the results from total-energy calculations, make the acceptance of the buckled model for the Si(lll)-2 x 1 surface difficult. 615
D J Chadi: Semiconductor surface reconstruction
C Ge(lll)-I x 1. An important recent development is the discovery6a*69 of a 1 x 1 LEED pattern on Ge(lll) surfaces cleaved at temperatures near 4 K. Similar experiments on Si are found to lead to a 2 x 1 pattem64. The Ge(lll)-1 x 1 LEED pattern is sharp and stable; it is not clear yet whether it corresponds to an atomically ordered surface. If ordered, the electronic structure should have an antiferromagnetic ordering with a 2 x 1 periodicity (even though the atomic periodicity is 1 x 1). As discussed above, this structure is stable against buckling distortions. It should be metastable50*51 against distortions leading to the n-bonded chain structure described in section D. The activation barrier for this transformation has been calculated*’ to beabout 0.1 eV atom- r. The transition rate to the lower energy 2 x 1 structure would be, therefore, nearly zero at 4 K, consistent with the experimental observations. Since Si and Ge have similar properties, it has been suggested that despite the lack of a 1 x 1 LEED pattern on Si( 111) surfaces at low temperatures, the surface probably contains a two-phase structure consisting of 1 x 1 and 2 x 1 ordered areas6**69. More experiments are needed to reveal the nature of the atomic structure of surfaces cleaved at low temperatures. The similarities, if any, between the low and high temperature 1 x 1 structures need to be also investigated. D. New sbuctural models. A new ‘chain’ model for the Si( Ill)-2 x 1 surface was recently proposed by Pandey6*46. The n-bonded chain model offers an explanation for the stability of the 2 x 1 surface relative to the relaxed 1 x 1 surface”*47*4s.The formation of the chain starting from the 1 x 1 surface involves bond-breaking and rebonding. The reconstruction leaves the density of dangling bonds constant but moves the dangling-bonds closer to each other such that the interactions become of the neatest-neighbour type* The distortions leading to the n-bonded chain structure4’ are shown in Figure 2. Figures 2(a) and (b) show the top and side
views of the chain-model, respectively; Figure 2 shows the side view of a 1 x 1 surface. The positions of atoms before and after reconstruction can be compared by matching atoms with the same number in Figures 2(b) and (c). The reconstruction involves a shear distortion of the surface double layer along the long axis of the unit cell accompanied by breaking l-5 bonds in Figure 2(c) and formation of 43 bonds in Figure 2(b). The reconstruction changes the topology of the surface, resulting in the formation of alternating 5- and 7-fold rings of atoms. The necessity of extra bond breaking in creating the chain structure raises the question of whether the cleavage process supplies sufficient-energy for this purpose. The measured cleavage energy ‘O of Si of about 1240 erg cm2 corresponding to about 1: 1 eV per surface atom on each of the two surfaces resulting from cleavage may appear to be too small to account for the additional breaking of bonds between atoms 1 and 5 in Figure 2(c). Northrup and Cohen have shown*‘, however, that this is not the case. By calculating the total energy for eight different configurations intermediate between a buckled 2 x 1 surface and the chain model, they find an activation barrier of about ~0.1 eV atom- * This is a much smaller energy than might be expected from bond energies in bulk Si. It demonstrates that the cleavage process can supply sufficient energy to create the chain structure. The energy of the n-bonded chain structure is ~0.4 eV atom-l lower than the ‘1 x 1’ structure having an antiferromagnetic spin arrangement. The stability of the chain arises primarily from the strong x-bonding interactions which more than compensate for the large angular strains in the structure,. The magnitude of the n-bonding interaction in the bulk is z 1.05 eV. The interaction at the surface is expected to be reduced from this value because the surface atoms are not all at the same height above the surface, and the dangling-bonds do not all point in the same direction. The measured dispersion of the upper surface state seen in angleresolved measurements is described well by the equation E(k)=const
(0)
+2V2 cos 2nk-,/ci+(2V,
cos nk)?
where V, z -0.63
eV
is the tight-binding Hamiltonian neighbour dangling-bonds,
(3) matrix element between nearest-
V2z +0.13 eV is the second-nearest-neighbour 2s, z 0.20 eV
5
Figure 2. The top and side views of the n-bonded chain model for the Si(lll)-2 x 1 surface are shown in (a) and (b). The side view of the ideal surface is shown in (c). The numbering on the atoms shows the changes in bonding occurring as a result of the reconstruction. 616
(2)
(4) interaction
and (5)
represents the difference in the self-energies (or diagonal matrix elements) of the two dangling-bonds in the unit cell. The reduced wavevector k in equation (2) corresponds to the projection of the actual wavevector along the F-J direction of the Brillouin zone (Figure 2) with k = f corresponding to J and k =0 to f. The large value of V, (i.e., 2V,/U> 1) makes spin-polarization e5ects much weaker for the chain model than for the ideal 1 x 1 surface. A comparison of the surface band dispersion obtained from equation (3) to the experimental data is shown in Figure 3. Unlike the case of the buckling model, the chain structure provides a very good description for the surface band dispersion. Recent angleresolved photoemission measurements” on the Ge( 11l)- 2 x 1 surface also give a dispersive band similar to that of Si. Previous angle-integrated measurements give evidence for one72*‘3 or
D J Chsdi: Semiconductor surface reconstruction 4
F?Ll 3
(0)
2
1.0 -
2 P
0.5
-1.0
-iJ
-i K
I F
2
3
I
4
3
3
tb)
-
Surfacewave
I
I
5
i?
vector
Figure 3. Surface energy-band dispersion for the n-bonded chain model. The tight-binding result from equation (2) is shown as the solid line; the
experimental results of references 4345 by 0, x, and 0, respectively.
Figure 4. The top and side views of the n-bonded molecular model for the Si(l1 l)-2 x 1 surface are shown in (a) and (b). The atomic positions in the
ideal 1 x 1 surface confisuration are shown in (cb
two’3 surface states near the valence-band-maximum depending on the annealing temperature. Electronic transitions between filled and empty surface states near the J-K’ line of the Brillouin zone give rise to a large peak in the joint-density-of-state which should correspond to the mainpeak measured in the optical reflectivity spectrums6*s’. The optical absorption is predicted to be maximum for electric field polarization parallel to the short axis of the real space unit cell and nearly zero for polarization along the long axis of the cell. For the buckling model, an opposite anisotropy with a 3 : 1 ratio for the absorption intensity has been predicted50. Tests of polarization dependence of the surface optical absorption or the surface photovoltage” should, therefore, prove very useful in distinguishing between different surfaa structures. The n-bonded chain model provides a satisfactory explanation for the stability and dispersion of the upper surface state band of the 2 x I surface. As mentioned before, however, the photoemission experiments indicate the presence of another nearly dispersionless dangling-bond band at the surface. This state cannot be explained by the chain model. If intrinsic, it would imply the existence of a second structure at the surface. This possibility is attractive in that it would also account for the strong cleavage dependence of the surface electronic states measured by photoemission. It would be interesting if surfaces with predominantly one type of structure having only one of the two dangling-bond bands could be prepared. The presence of more than one structure at the surface makes the analysis of LEED data very dimcult. In fact, a recent LEED study finds the chain model (unlike the buckling modeI) to be in poor agreement with the experimental data76. A reconstruction that involves the same types of atomic distortions as those involved in generating the n-bonded mode149 shown in Figure 4. The shear distortion of the top double layer of atoms leading to rebonding occurs at 120” with respect to the long axis of the unit instead of parallel to it as is the case for the chain model. The model consists of a dimerized pair of atoms (atoms 1
and 2 in Figures 4a and b) per unit cell. Self-consistent pseudopotential calculations76 and one-electron tight-binding calculations predict a much lower energy for the chain than for the ‘molecule’. However, the energy of the molecule is stabilized appreciably by configuration interaction mixing49 and the energy of the n-bonded molecular and chain structures are expected to be very close in Si The calculated = 0.6 eV-wide surface band for the molecular structure is not, however, in agreement with the dispersionless band seen in photoemission measurements”*45. It is interesting to note that other structures, in particular a chain structure involving only S-fold rings of atoms at the surfaa, can be created’ ‘I. At this stage, we have to conclude that despite impressive progress in understanding of reconstruction on (111) surfaces, much more remains to be done both experimentally and theoretically. 5. Adatoms Surface reconstruction and relaxations can lower the surface energy in one of several different ways. On the GaAs( 110) surface, the atomic motions result in rehybridization making Ga atoms more sp2 and As atoms more p3 bonded. On the Si( 111) - 2 x 1 surface, the total energy is lowered by a rebonding which brings the dangling-bonds closer to each other such that they interact via nearest instead of second-nearest neighbor interactions. One expects that a third mechanism for lowering the total energy is the reduction in the surfaa dangling-bond density. The bonding of two three-fold coordinated Si atoms would release about 2.4 eV in energy if no bond-length and angular strains are involved. This is a much larger energy than those involved in the reconstructions which have been considered up to now. Simple ways of reducing the surface dangling-bond density are known. The major problem, however, at least for small unit cells, is that it is nearly 617
D J Chedi: Semiconductor surface reconstruction
impossible to avoid large, angular strains which more than offset the energy gains resulting from having fewer dangling-bonds. A particularly simple adatom model is the Harrison model’e. For a (111) surface, it essentially involves one extra atom for every three surface atoms. Each adatom is bonded to three surface atoms. In this way, the only dangling-bonds are on the adatom, and a factor of three reduction in dangling-bond density is achieved. On a surface such as Si( 11l), there are two inequivalent positions where the adatom can be placed. It can be positioned above a second layer atom of the substrate, or on a ‘hollow’ site. Both configurations give rise to large bond angle deviations from the ideal 109.5” tetrahedral angle. In the first configuration bond angles of 180” and 424 and in the second bond angles of 180” and -z 72” result. The ‘hollow’ site configuration is appreciably lower in energy than the’on top’geometry; but it still has a high surface energy and is me&stable. The binding energy of the adatom to the surface is calculated to be ~2.8 eV which is equivalent to an average energy of0.93 eV per bond. This is only ~40% of the bulk bond energy of -2.4 eV. The total energy would be reduced by (2 x 2.4 - 2.8) eV or 2 eV by transferring the adatom into the bulk. Even though the tight-bonding calculations somewhat underestimate the binding energy (because of the neglect of d-states), they do not support the preliminary interpretation of recent very elegant vacuum tunnelling measurements on the Si(lll)-7 x 7 surface reconstruction in terms of a simple adatom model”. More complicated structures involving adatoms in which the deviations from perfect tetrahedral bonding are smaller cannot be ruled out. 6. Coacluaions The short review of surface reconstruction on GaAs(l10). Si and
Ge(100) and (111) surfaces presented above demonstrates that much has been accomplished in the last five years and that even more remains to be done for a better understanding of even the ‘simplest’ reconstructions on well-studied semiconductor surfaces. This is particularly true for the cleaved surfaces of C, Si and Ge, where at this time a single structural model cannot account for all experimental data Studies of the similarities and differences in the surface properties of these materials should prove fruitful for identifying the various mechanisms leading to surface reconstruction on cleaved and hopefully annealed surfaces. Acknowledgements
This work is supported in part by the US Office of Naval Research through Contract No NOOO14-82-C-0244. References
’ R J Meyer, C B Duke, A Paton, A Kahn, E So, J L Yeh and P Mark, Phys Rev B, 19, 5194 (1979). ’ S Y Tong, A R Lubinsky, B J Mrstik and M A Van Hove, Phys Rev B, 17, 3303 (1978) ’ C B Duke, J Vat Sci Techno) (to be published). ’ D J Chadi, Phys Rev Letr, 41, 1062 (iO78). ’ D J Chadi. Phvs Reu B. 19.2074 (1979). ’ K C Pandey, ihys Reu.Lett, 49,223 (1982). ’ J A Barton, WA Goddard and T C McGill, .I Vat Sci Technol, 16.1178 (1979) * A Kahn, G Cisneros, M Bonn, P Mark and C B Duke, Surjace Sci, 71, 387 (19781 9 D j Chdi, Phys Rev B, 18, 1800 (1978). to CA Swarts WA Goddard and T C McGill, J Vat Sci Technol, 17,982 (1980). ’ I1 K Kunc and R M Martin, Phys Rm B, 24,231l (1981). 618
I2 F Cenino (unpublished). “J R Cbelikowsky and h4 L Cohen, Phys Reu B, 20.4150 (1979)
t4 D J Chadii J Vat Sci Technol, IS.1244 (1978). ” JvanLaarandAHuijaer,.J VacSci Tech&, 13,769(1976);ibid,14,893 (1977) ‘6WESl)iar,PW(3hKPEGngory,TSuktgawaMdIABebelole,J J’uc Sci TecJmol, 13,233 (1976); ibid,14,885 (1977). ” W Gudat and D E Eastman, J Vat Sci Techno/, 13,831 (1976). ‘s J A Atmelbaum G A BaraR and D R Hamann. Phvs RN B, 14, 588 (1976). -I9 J A Appelbaumand D R Hamann, Slajbee Sci. 74.21 (1978). lo D J Chadi. Phvs Rev Lerr. 43.43 (1979). ” M T Yin and hl L Cohen, Phys l&u B,‘U, 2303 (1981) 21 W S Venvoerd, Surface Sci 103,404 (1981) )’ S Y Tong and A L Maldondo, Sta$hce Sri, 7B, 459 (1978). ‘* F Jona, H D Shih, D W Jepson and P M Marcus, J Phys C, 12, L455 (1979). ” W S Yang, F Jona and P M Marcus, Sohi State Cammun, 43,847 (1982L js S J.White, DC Frost and K A R Mitchell, Solid State Canmun, 42,763 (1982);GJRJoncaandBWHoUand.SolidSrureCnmmun.46.651(19833. ” M J Cardillo and G E Becker, P&s Rev B, il. 1497 (1980). **J Ihm and J D Joannopoulos, J vat Sci Technor (to be published). 29JERoweandHIbach.PhvsReuLQrr.32.421(1974):JERoweandSB Christman. J Vat Sci T&h&, 17, 220’(1<801 . ‘. ‘O F J Himpsel and D E Eastman, J Vat Sci Technol, 16, 1297 (1979). ‘t M A Bowen. J D Dow and R E Allen. Phvs Reu B. 2.6.7083 (1982). ‘* A Mazur and J Pollmann, Phys Rev i, Xi 7086 (1982). ” L C Feldman, P J Silverman and I Stensgaard, Nucl /astrum Methods, 168, 589 (1980); I Stensgaard et al, Surfice Sci, 102, 1 (1981). ‘* R M Tromp, R G Smeenk and F W Saris, Solid Stare Commun. 39,755 (1981); and Su&ce Sci (to be published). ” WMiinch,PKokeandSKrueger,J VucSciTechnol,19,313(1981);W Miinch and P Koke, Solid State Commun, 36, 1007 (1980). ‘I’ Y J Chabal, S B Christman, E E Chaban and M T Yin (to be published). ” P E WietetIga, M J Sparnaay and A van Sihhouf St&ce Sci, 99.59 (1980). 3* D J Chadi, J Vat Sci Te&al16,1290 (1979); J Appl Optics,19.3971 (1980). ‘9 A Redondo and W A Goddard, J Vat Sci Technol, 21,344 (1982). *OJ G Nelson, W J Gignac, R S Williams, S Robay, J Tobin and D A Shirley, Phys Rev (to be published). ” P Eisenberger and W C Morra, Phys Rm Lerr, 46, 1081 (1981). 42 L C Feldman (to be published). 43 F J Himpael, P Heinmann and D E Eastman, Phys Rev B, 24,2003 (1981). u R I G Uhrberg, G V Hansson, J M Nicholls and S A Flodstrijm, Phys Rev Lerr, 48, 1032 (1982). ” F Houzay, G Guichar, R Pinchaux, G Jemquel, F Solal, A Barsky, P Steiner and Y PetroB, Surjace Sci (to be published). 46 K C Pandey, Phys Ra, Lerr, 47, 1913 (1981) *’ J E Northrup and M L Cohen, Phys Rev Left, 49, 1349 (1982). 4n J E Northrup and M L Cohen, J pat Sci Technol, 21,333 (1982). 49 D J Chadi. Phvs Rev B. 26.4762 (1982). so R Dei Sole’and
D J Chadi: Semiconductor
surface reconstruction
” S Brannan, J Stohr, R Jacgar and J E Rowe, Phys Ret Lerr, 451414 (1980). CQM Lanoo and G Allan, Srufaee Sci, 115, L137 (1982). 6’C B Duke and W K Ford, Sugiie Sci. 111, L165 (1981)
6’ M T Yin and M L Cohan, Phys Reu Len, 45, 1005 (1980). 66 G A BaraB, E 0 Kane and M Schluter, Phys Rev LPtr,43,956 (1979) “I W B Jackson, Solid Stare Commun, 44,477 (1982). ‘s V YU Aristov, N I Goiovko, V A Grazhulis, Yu A Cksipyan and V 1 Talyanskii, Su&ce Sci, 117,204 (1982); V Y Aristov, 1 E Batov and V A Grarhulis, Surface Sci (to he published). e9 D Hancman and R 2 Bachrach, J Yac Sci Technol, 21,337 (1982); and Phys Reu i3.27 (to be published). “J J Gilman, .I Appl Phys, 31,2208 (1960).
‘I J M Nicholls, G V Hansson, R I G Uhrkrg and S A Flodstriim, Phys Rev B, 27 (to be published). 72 G M Guichar, G A Garry and C A Scbcnnc, Surface Sci, 85,326 (1979). ‘J T Murotani, K Fuiiwara and N Nishiiima. Pkys RPDB, 12.2424 (1975). ‘4 J Assman and W Mdnch, Sur$xe S& 99; 36 (1980). ” R Fader. Solid Stare Cummun 45. 51 119831 76 0 H N&n, R M Ma&n, D J Chadi &d K i&c, J Vat Sci Technol (to be published). ” D J Chadi (to be published) ‘* W A Harrison, Surface Sci, 55, 1 (1976). ‘9 G Binnig, H Rohrcr, Ch Gcrmcr and E Wcibcl, Phys Rev Len. 49.57 (1982)
619