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Electronic structure of Si(111) surfaces
Surface Science 99 (1980) 13-27 0 North-Holland Publishing Company
ELECTRONIC
STRUCTURE
OF Si(ll1)
SURFACES
G.V. HANSSON, R.Z. BACHRACH, R.S. BAUER, D.J. CHADI and W. GiiPEL Xerox Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, California 94304, USA Received 26 November 1979;accepted
for publication 18 February 1980
We report on new angle-resolved photoemission studies of Si(l1 I) 2 X 1 and 7 X 7 surfaces. The emission from the 2 x 1 surface shows much structure. For normal emission the energy positions are insensitive to the photon energy in the range 19-27 eV. The emission has been interpreted as a probe of the surface density of states, SDOS, including both surface states, resonances and bulk-like states. The SDOS was also calculated as a function of parallei momentum kU for a model of the Si(ll1) 2 X 1 surface obtained from energy minimization considerations. We identify emission from the dangling bond band, which has a positive dispersion of 0.6 eV, and also emission from surface resonances which have some character of the compressed and stretched back bonds. There are also other predicted surface resonances that correspond to experiments peaks which have not been identified in previous work. Except for the dangling bond band, the surface resonances are limited in k,y space, so that it is not possible to follow these resonance bands over all angles. Maximum intensity for the normal emission from the dangling bond is obtained at 23 eV, while the emission from the lowest s-like states monotonically increases towards 30 eV photon energy. When annealing the cleaved 2 X 1 surface to the 7 X 7 reconstructed surface, the spectra broaden significantly. The intensity of the dangling bond decreases and we see a very small metallic edge.
1. Introduction Angle-resolved photoemission has proved to be a very sensitive tool for the study of the electronic structure of solids and solid surfaces [1] . The analysis of the data using direct transitions within the three-step msdel has made it possible to get very detailed information about the bulk electronic structure of materials like the noble metals Au, Ag and Cu [l-3]. For other materials, like Al [4], the bulk direct transitions are not detectable, but the main part of the photoemission comes from the surface. ogle-resolved photoemission spectra (ARPES) in general have features attributable to both bulk and surface photoemission, The intensity of each component varies with photon energy such that the surface photoemission can be either emphasized or suppressed. In this study we have choosen to study the photoemission from Si(ll1) surfaces with photon energies between 20-30 eV, where as we will show the ARPES are dominated by contributions from surface photoemission. It 13
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G. V. Harmon et al. /Electronic
structure of Siflll)
surfaces
has earlier been shown that also for GaAs there is a decrease in the direct transition contributions in this photon energy range [5]. One reason for the surface sensitivity is the very short mean free path of the excited electrons, which means that the emitted electrons are excited within 10 A of the surface [6]. A maximum in the transition probability from the dangling bond surface state of Si(ll1) 2 X 1 at 23 eV also makes the surface contributions more dominant. As it is not possible experimentally to separate surface states from surface resonances, we may sometimes use the term surface state for what are actually surface resonances. The Si(ll1) surface is known to have several possible reconstructions depending on the sample treatment [7,8]. We report measurements of ARPES from cleaved crystals showing 2 X 1 LEED patterns and from annealed crystals having 7 X 7 reconstructed surfaces. Studies of the angle-integrated photoemission first showed the existence of surface states near the valence band edge on both 2 X 1 and 7 X 7 surfaces [9,10]. A more detailed picture of the electronic structure of the 2 X 1 structure was obtained in ARPES studies by Rowe et al. [ 111. The reported emission from the dangling bond band and strong emission from a back bond which showed a clear three-fold symmetry. Emission from the dangling bond band and back bond bands on Si(ll1) 2 X 1 have also been reported by McKinley et al. [12] using 21.2 eV radiation. By studying many cleaves they showed the difficulties in getting reproducible ARPES results from surfaces that are all mirror-like and which show 2 X 1 LEED patterns. This was also seen in our study. The measurements on 2 X 1 surfaces reported here are in good agreement with what were reported as the best cleaves of McKinley et al. [12]. The 7 X 7 electronic structure has been studied by Eastman et al. [13] and by Hansson et al. [14]. Both groups report similar surface states and a clear metallic edge at the Fermi level. Recent synchrotron measurements with higher photon energies by Houzay et al. [15] on the 7 X 7 surface show a much smaller metallic edge. They [ 151 also report a very strong variation of the transition probability from the dangling bond state with a maximum at 53 eV photon energy. Around 25 eV photon energy they report negligible emission from both the dangling bond state and the metallic edge.
2. Experimental The experiments were performed at the Stanford Synchrotron Radiation Laboratory (SSRL), by using the facilities VG ADES-400 photoelectron spectrometer. The angle-resolved photoelectron spectra were measured by a hemi-spherical deflection analyzer that is rotable in the horizontal plane. The analyzer has an angular resolution of 22” and the energy resolution is 1.8%, which corresponds to GO.4 eV in our spectra. The samples were lightly doped silicon crystals (5 X 1Or5 cmF3, boron) that were cleaved in situ at a base pressure of 1 X lo- lo Torr . After the photoemission mea-
G. V. Hansson et al. 1 Electronic structure of Si(1 I I) surfaces
15
surements the surfaces were checked with low-energy electron diffraction (LEED). For the cleaved surfaces used in the photoemission studies the 2 X X LEED patterns were sharp and they showed only one domain of the 2 X 1 reconstruction. There were macroscopic steps distributed over the surfaces even for our best cleaves. Studies in a scanning electron microscope at a resolution of 200 A showed that the macroscopic steps were typically 0.2 X 10” m wide, but they were separated by flat terraces that were -20 X low6 m wide. The stepped regions thus correspond to -1% of the total surface and the strong angle-dependence in the ARPES indicate that the surface roughness on the terraces was ne~i~ble. Some of the cleaved surfaces were converted to the 7 X 7 reconstructed phase by heating the crystals to approximately 700°C.
3. Theory Theoretical aspects relevant to the results and discussion in section 4 are briefly presented here. In angle-resolved photoelectron spectroscopy one measures the energy and direction of emitted electrons. For cases in which hole damping may be neglected the photocurrent at the detector can be written [16].
where the operator
0 is defined by
6(x) = + [A(x) p + p/i(x)]
.
(2)
The wave function Qf needed to calculate the matrix elements is a time-reversed LEED function. A full calculation of the photocurrent from eq. (1) is practically impossible. The way to relate the ARPES to the surface and/or bulk electronic structure has rather been to discuss different mechanisms contributing to the matrix element for the photoe~ssion process 1171. A most useful approximation is contained in the three-step model. This applies to direct (k conserving) transitions between bulk electronic states, followed by the transport of the excited electron to and though the surface, during which the parallel momentum k~ is conserved. This three-step model has been used to determine the bulk-band structure of many metals and semiconductors. The initial energy of a direct transition will in general be dependent upon the photon energy, which can make the direct transitions easily recognizable if a continuous photon energy source is used. Over limited photon energy regions a direct transition peak can appear stationary due to very flat initial state bands or final state band gaps [ 18,191. For the direct transition model to work well the mean-free path should be long, since strong scattering in the final state will relax the k conservation rule,
16
G. V. Hansson et al. /Electronic
structure of Si(lliJ
surfaces
which results in broadening of the peaks. There is now experimental evidence that the matrix element for excitation from surface states can also have resonances that correspond to the direct transitions in the bulk [ZO] . This means that these surface states have to be localized over a larger number of layers than just the surfa\ce layer. Surface effects can enter through the operator 8 in eq. (1). These are often separated into the effect of the surface potential V, and the effect of the varying vector potential at the surface, &4/8z. All mechanisms for photoemission give rise to a kn conservation transition rule when applied to a perfect crystal face, i.e. an electron emitted with parallel momentum kl has been excited from an initial state with parallel momentum kn + GJ, where GJ is a reciprocal lattice vector (or the nullvector) of the surface unit cell. Since the mean free path of the excited electrons in our experiment is of the order of 5 A [6], we do not expect the three-step model to work. This is verified by our experiment. We interpret our data as emission from the surface whether the states involved are surface states, surface resonances or bulk-like in character. To make a detailed comparison between theory and experiment we have calculated the surface density of states, SDOS as function of k, along different directions in the surface Brillouin zone. Fig. I a shows the uppermost double-layer of a Si( 111) surface. For the generally accepted description of the 2 X 1 reconstruction the alternate rows in the surface layer are raised and lowered [7]. The corresponding change in the surface Brillouin -__ zone is shown in fig. lb. We also show the line in the extended zone scheme, FKM, along which the electronic structure has been investigated in some detail in our experiments and calculations. The geometry of the 2 X 1 reconstructed surface used in our calculation was chosen as to mini~ze the total energy of the electron-ion system (211. The atomic displacements from the unrelaxed positions are given in table I. The electronic structure was then calculated for a 12-layer slab with a 2 X 1 reconstructed top surface. The bottom surface was kept unrelaxed to avoid coupling between surface states (resonances) on the two surfaces. The calculation was performed using the tight-binding approximation, with the parameters for nearest neighbour and second nearest nei~bour interactions according to Pandey-__and Phillips 1221. The electronic states were calculated in 15 points along the FKM line in k space. At each k/l point we obtained 48 occupied bands that could be investigated with respect to orbital content and localization on each of the atoms in the slab, For the surface density of state curves presented in this paper we summed the density of states over the four uppermost atoms in the 12-layer slab, i.e. for the top doublelayer of the 2 X 1 structure. A problem in a comparison between theory and experiment is to relate the energy scales to a common origin. The calculation refers all energies to the bulk valence band edge, E,, which is not detectable in our experiment. The experimental ARPES are instead measured relative to the Fermi level EF. To get a common scale we assume that Eli - E,= 0.35 eV, which has been determined in other experiments 1231. The uncertainty in this value is a.1 5 eV [24].
G. V. Hansson et al. /Electronic
structure of S/ill)
surfaces
17
Fig. 1. (a) Top view of the Si(l11) 2 X 1 surface. Atoms 1 and 2 are the raised and lowered atoms in the top layer and atoms 3 and 4 are in the second layer. (b) The surface Brillouin zone for the 2 X 1 reconstruction (rectangles) super-imposed on the 1 X 1 surface Brillouin zone (hexagons).
Table 1 Atomic displacements from unrelaxed positions for the 2 X 1 reconstructed (Ill) surface of Si; i is the surface normal and p is parallel to the surface projection of a vector from atom 2 to atom 4 in fig. 1 Atom 1
Atom 2
Atom 3
Atom 4
A.z (19)
0.31
AY (A)
0.00
-0.44 0.06
0.00 -0.13
0.00 0.09
-
--
18
G. V. Harmon et al. /Electronic
structure
of Si(l I I)
surfaces
4. Results and discussion The angle-resolved photoemission results are presented in this section along with a discussion of the interpretation. We start with the Si(ll1) 2 X 1 surface and analyze the normal emission as a function of photon energy. This is followed by studies of the emission as function of polar angle. In the normal emission one probes the I’L line in the bulk Brillouin zone and the r point of the surface Brillouin zone. For off-normal emission one probes the surface electronic structure as function of kl. Finally we report some results from studies of the Si(ll1) 7 X 7 surface. 4.1. Normal emission from Si(ll1)
2 X1
To experimentally separate the surface and bulk contributions to the photoemission current is generally a difficult task. One case for which a clear identification of a bulk contribution is possible is when the initial energy of a transition, Ei(ki), is varying with photon energy [ 171. In this way it has been shown that the major contributions from Si( 111) 7 X 7 in the photon energy range 7-l 2 eV are due to direct transitions in the bulk [14]. With the continuous radiation of the synchrotron source we can choose to work at higher photon energies where the mean free path of the excited electrons is minimized thus increasing the relative portion of emission from the surface electronic structure. Because the final states are very strongly damped in the bulk, at these energies, a model with direct transitions between Bloch states may not be applicable. The electron escape depth from a Si(ll1) surface has been determined to be 4-7 ,& for electrons excited to 17-140 eV above the Fermi level [6]. This means that the majority of the electrons originate from the first two double layers (6.3 ,&separation). Fig. 2 shows examples of the photoemission in the normal direction from Si(ll1) 2 X 1 for different photon energies. In the range 19 to 27 eV there is very little dispersion of the peaks. The peak energy positions as well as the lack of dispersion over this photon energy range cannot be explained by direct transitions between bulk states. Disregarding the 10.5 eV spectrum which contains contributions from direct transitions, we see that the only changes in the spectra are intensity variations. There is a strong increase of the low energy peak of the spectra, H, which is due to the increased cross section for transitions from the low lying states, which have predominantly s-character. One can compare our results to angle-resolved photoemission measurements on Cu(l10). For this system the direct transition model can be used even for excitation to highly damped final states in final state band gaps [18,19]. The main conclusions from those studies are that a reduction of the emission intensity occurs and the initial density of states near the symmetry point of the band gap in the bulk electronic structure is probed. This means that the peak positions do not vary with photon energy over the region of the final state band gap. Since there are no band
G. V. Hailsson et al. /Electronic
19
structure af si(Il I} surfaces
Si (1111 2 x 1 icJ = 0 Ai = 4P,
p-polarization
a
-12
-lQ
-6 INITIAL
-6 ENERGY BELOW E,
-4
-2
tev)
Fig. 2. Photoemission spectra measured normal to the Si(ll1) 2 X 1 surface (i.e., @= 0) are compared with the calculated surface density of states fox states with kl = 0. The experimental spectra were measured relative to the Fermi level, which is assumed to be 0.35 eV above the valence baud edge.
20
G. V. Hansson et al. /Electronic
structure of Sifl I I) surfaces
gaps in the final state band structure along FL in silicon in the probed energy region, we cannot attribute the lack of dispersion to that mechanism. Also the experimental peak positions do not correspond to maxima in the bulk density of states. The important point for the further discussion is that the emitted electrons come from the uppermost surface layers and that the direct transition model cannot explain the data. We compare in fig. 2, the normal emission spectra to the calculated occupied surface density of states, for states with k( = 0, r. The SDOS is summed over the four uppermost atoms constituting the top reconstructed double-layer. Featured in the SDOS curve is the dangling bond state (a) which is more than 75% localized on the top double-layer, An “ideal” bulk state would have approximately l/6 = 17% of its charge in each double-layer, since the slab geometry used in the calculation is built of six double-layers. Except for the dangling bond state at -0.5 eV there are no states with kl = 0 which have a localization greater than 30% on the top doublelayer. The double-peak (d) near -7 eV has weak character of a surface resonance, while the states giving rise to peaks b (-2.7 eV) and c (4.4 eV) are very bulk-like. The experimental spectra show structures at -0.7 (A), -2.6 (B), -4.4 (C) and -6.7 eV (D) which are in very good agreement with the theoretical SDOS. The experimental peak H at -11.3 eV that appears at higher photon energies corresponds to a maximum in the SDOS at -11 .O eV (h). One can question, however, the significance of peaks c and h in the SDOS since they are of the order of the variations in the SDOS due to the finite size of the slab used. More significant is the minimum in the SDOS near -5 eV, which corresponds to the minimum at N -4.8 eV in the spectra. It is comforting that the energy positions of the four largest features in the experimental spectra and the calculated SDOS are in such a good agreement. The most important omission in such a simple comparison is of course the matrix element effects for the different transitions. To avoid the possibility that some matrix elements are identical to zero due to symmetry, we measured the photoemission with the light coming in at 45” from the normal in the (2ii) plane which is not a mirror plane. Large effects of the matrix elements can still be seen in the intensity variations with photon energy of the emission from the predominantly s-like states near -11 eV and also for the surface resonance at -0.7 eV which has maximum intensity at 23 eV photon energy. This low binding energy surface resonance is the dangling bond with mostly pZ but also significant s-character, that is localized primarily on the raised atom (No. 1 in fig. 1) of the outer reconstructed surface layer. All other occupied states with kl= 0 are quite evenly distributed over the four atoms in the top double-layer. Thus, we are not able to distinguish any stretched or shortened back bonds at T. The studies by Parke et al. [ 121 on a large number of cleaves have shown the difficulties to get reproducible results on different cleaves. Even within the set of cleaves showing mirror-like surfaces, the peak positions may vary by up to 0.5 eV. Using 21.2 eV radiation they obtained spectra that are in good agreement with ours
G. V. Hansson et al. /Electronic
structure of Si(l1 I) surfaces
21
with respect to the spectral shape and the energy positions of the dangling bond peak and -6.7 eV peak. For peaks in the region -1 to -5 eV below the valence band edge (Ev) they measured peak positions varying around our values with average positions that are slightly lower than our reported values. 4.2. Off-normal emission from Si(ll1)
2 Xl
The polar angle variation of the emission in the (2ii) plane is shown in fig. 3. The corresponding line in the 2D k space is presented in fig. 1. The emission from the dangling bond state is increased at off-normal emission and has a maximum intensity at about 25”. This is consistent with the incorporation of emission from a state with a high degree of p,-content, since the theoretical maximum for emission from a pure p,-orbital to a plane wave with an A-vector 45” from the z-direction is 22.5” from the z-axis [25]. Note also the positive 0.6 eV dispersion for the dangling bond emission, with the band maximum between K and M at 0.0 + 0.1 eV relative to the valence band maximum. The dispersion is very anisotropic. Along the I’J’ direction we find a flat dangling bond band, while states closer to Tare higher in energy. In the original paper by Traum, Rowe and Smith a positive dispersion of 0.6 eV was also reported for the weak shoulder, that later has been interpreted as the dangling bond. Thus both experiments, although performed along different directions, show a positive dispersion for the dangling bond surface state. Unlike the results on GaAs [5], we see no direct transitions from the uppermost of the bulk valence bands. These would show a negative dispersion for the photon energies used, in disagreement with the experimental results. For initial states in the range -1 to -5 eV a complex variation of the emission with the polar angle is observed and it is not possible to follow any surface resonance band over all angles. As will be discussed in more detail later there is a continuous appearing and disappearing of peaks. The strongest feature in the spectra is a peak, G, at about -6.6 eV that appears around a polar angle of 35’. The parallel momentum kl of these electrons in the extended-zone scheme corresponds to states near the I? point of the 1 X 1 surface Brillouin zone. For the unreconstructed surface, the states in the surface layer at the K point are all surface states. From our SDOS calculation we expect to see strong features in the spectra probing near the K’point also for the reconstructed surface. The surface density of states has been calculated as function of k# to facilitate a comparison between experiment and the calculated surface electronic structure. Fig. 4 shows SDOS curves calculated along the Kh4 direction in the extended-zone scheme. The grid of points in the Brillouin zone used in the calculations was a factor of two more dense than showed in fig. 4. Cross hatched regions correspond to surface resonances (states) that are more than 30% localized in the uppermost double-layer, cf. 17% average per double layer for a bulk state. For all kj values we get the strongly localized dangling bond state, but it has a much smaller dispersion
22
G. V. Hansson et al. /Electronic
I
I
I
I
I
structure of Si(il I) surfaces
I 1
Si (111) 2 x 1 hv = 20.0 eV
0; = 49,
I -10
I
I
I
-8
-6
-4
INITIAL
ENERGY
BELOW
p-polarization
1
-2 E,
(eV)
/I 0
EF
Fig. 3. Photoemission spectra as function of the polar angle e measured in the (2ii) plane of Si(ll1) 2 X I. _ The spectra were measured relative to the Fermi level, which is assumed to be 0.35 eV above the valence band edge.
G. V. Harmon et al. /Electronic
-12
%-10
-8 INITIAL
-6
structure of Sill 1 I) surfaces
-4
-2
23
0
ENERGY BELOW E,(eV)
Fig. 4. Surface density of states in the top double-layer as function of parallel momentum, kl, in the rKM direction. Indicated by shading are also the surface resonances (states) that are more than 30% localized in the top double-layer.
than the experimental peak. The strongest feature in the theoretical curves is a number of surface states that appear near the K point in good agreement with experiment. Another striking feature of the theoretical curves is that except for the dangling bond, it is not possible to follow any surface resonance band over the whole k, region. In the experimental spectra there is strong emission at -2.7 eV close to normal emission, 6 < lo”, (B), but also at high angles 19> SO0 (E). Peak B corresponds to the peak b in the SDOS, which only contains bulk-like states. This interpretation is
24
G. V. Hansson et al. /Electronic
I
structure of Si(i1 lj surfaces
I Sitlll)
-.
I
I
-ck
\
2 X 1
0
-a-
-c
-iyj-•
_--
r
2x1
K
B. L. edge
i%
T;/,
Fig. 5. Experimental and calculated surface electronic band structure along the rKM direction. Filled circles correspond to strong peaks and open circles are weaker structures in the experimental spectra. The continuous curves show the energy positions of the strongest peaks in the calculated SDOS, while the dashed curves correspond to weaker but still significant peaks.
consistent with the results of Parke et al., who have shown that peak B remains strong also after a change in reconstruction from 2 X 1 to 1 X 1. The peak E at high angles corresponds to the SDOS peak e, which has some contributions from the stretched (weakened) back bonds. Around 45” there is a very sharp peak (F) at -4.5 eV that disappears very quickly with increasing angle. This is in good agreement with the surface resonance, f, calculated to be at -4.2 eV. The last large feature in the spectra, peak G near -6.5 eV, is also in quite good agreement with either of two calculated surface resonances, g and i. A comparison between experimental peak positions and peaks in the SDOS is given in fig. 5. The curves show peaks in the SDOS that are significantly above the variations due to the finite slab size. The filled dots are strong peaks in the spectra and the open rings are weaker structures. For the dangling bond band the center of gravity in the experiment is well described by our calculation. The dispersion, however, is much stronger than any calculation has given [26-281. We have calculated
G. V. Hansson et al. /Electronic
structure of Si(ll1)
surfaces
25
the dispersion for several different reconstructions and have not been able to get a significantly better agreement with the experiment. The dispersion of this dangling bond band as calculated by both the self-consistent pseudopotential [27] and tight-binding methods [28,29] is much smaller (or in the case of the pseudopotential results of opposite sign) than that observed experimentally on our samples. The energy positions of most of the smaller but still significant features in the spectra can also be interpreted as emission from maxima in the SDOS. Exceptions are the shoulder at -1.5 eV in the 0’ spectrum and the small peak at -3.4 eV in the 40’ spectrum which is in between two calculated surface resonances. Knowing that the experimental peak positions can vary by up to 0.5 eV for different cleaves we think that the overall agreement between the experiment and the SDOS calculation is quite good. It is possible that some of the minor structures are from direct transitions in the bulk, although we have not been able to identify any. For the dangling bond we have calculated the localization on the uppermost double-layer to be between 70% and 90% for different k# values. The dangling bond states have up to 53% of their total charge in p,-orbitals localized on the raised surface atom and their s-content is 20% or less. A 70% localization was also calculated for the surface state g at -7.1 eV, which has 50% s-character in the top layer and 20% px, pY in the second layer. These two surface resonances are identified as the two strongest peaks in the experimental photoemission spectra. For the intermediate region -1 to -5 eV there are a number of surface resonances, some of which can be interpreted as the compressed and stretched back bonds respectively. The band dispersing from -2.9 to -4 eV near the K point can be characterized as the stretched back bond band. The states in that band are localized more on the raised surface atom and the second layer atoms than on the lowered surface atoms. This is also true for the surface resonance band near -2.7 eV between K and fi. The compressed back bond is seen as a very weakly localized surface resonance band about 1 eV below the stretched back bond band. The relative positions of the compressed and stretched back bonds are consistent with the calculation by Pandey and Phillips [28]. Although we use the same tight binding parameters as Pandey and Phillips [22], the detailed results of our calculation are different from theirs for two reasons. First we do not use the same 2 X 1 reconstruction geometry and secondly we scale the interaction parameters with distance d as (do/d)*, while they use a exp@(de - d)) scaling. do is the ideal bulk nearest neighbour distance. We also want to point out that the agreement between Pandey and Phillips’ surface resonance bands [28] and the experiments reported by Parke et al. [12] (fig. 2 in ref. [12]) is partly due to an error in the plotting of the theoretical energy bands taken from Pandey and Phillips’ paper [28]. 4.3. Si(IlI)
7 X7
Some of the cleaved 2 X 1 surfaces were converted to the 7 X7 reconstructed phase by heating to about 7OO’C and slow cooling to room temperature. This
26
G. V. Hanson
et al. /Electronic
structure of Si(ll Ij surfaces
results in a considerable broadening of the photoemission spectra. There is also a much weaker angle dependence, as is expected due to the increased surface scattering at a 7 X 7 compared to a 2 X 1 reconstructed surface. The strongest effect is however the decrease of the dangling bond emission. This is in agreement with recent measurements by Houzay et al. 1151 who have made a study of the emission from Si(l11) 7 X 7 over a wide range of photon energies, 20-80 eV. They find that the emission from the dangling bond is not detectable at 20 eV photon energy but the emission intensity has a sharp maximum at 53 eV photon energy. Thus the disappearance of the emission from the dangling bond does not mean that the state has disappeared. Eastman et al. [13] have reported emission from the dangling bond (at -0.9 eV relative to EF) from 10 up to 25 eV photon energy. It thus appears that emission from the dangling bond in some experimental configurations is minimized near 20 eV but that it is detected in other measurements. It is not clear whether the polarization direction of the light or different sample preparation techniques is the origin of the inconsistency of the experiments. The same discrepancies between experiments are also present for the magnitude of the metallic edge. The experiments by Houzay et al. [ 151 agree with ours that the metallic edge is very small (close to detection limit), while the measurements by Eastman et al. 1131 and also low photon energy data by Hansson et al. [14] show a very clear metallic edge. Further experiments are planned to resolve these differences.
5. Conclusions Angle-resolved photoemission from Si(ll1) surfaces at photon energies of 20-30 eV probes electronic states very near the surface. The details of the electronic structure depend on the reconstruction of the surface. We have found good agreement between peaks in the ARPES and maxima in the calculated surface density of states for an energy minimized model of the 2 X 1 surface. In particular we have found that the two states with the strongest surface localization correspond to the largest features in the ex~rimental spectra, From our study of the electronic structure as function of parallel momentum we conclude that the surface states and surface resonances cannot be characterized as pure dangling bonds and back bonds. Our calculations show that the surface localization of surface resonances vary strongly, and this behaviour is confirmed in our experiments. It is known that the reproducibility of photoemission results on cleaved surfaces even with good 2 X 1 LEED patterns is a problem, i.e. the electronic structure is very sensitive to the details of the reconstruction. Having that in mind we think the agreement between our experiment and our calculation is good. A further study of how the geometrical configuration affects the surface electronic structure is planned. The goal for future studies would be to determine properties of the reconstruction by using angle-resolved photoemission.
G. V. Hansson et al. /Electronic
structure of Si(l II) surfaces
27
Acknowledgements We wish to thank R. Gutcheck, who participated in the data collection process. Some of the materials incorporated in this work were developed at the Stanford Synchrotron Radiation Laboratory which is supported by the National Science Foundation (under contract DMR77-27489), in cooperation with SLAC and the Department of Energy.
References [l] [2] [3]
[4] [S] [6]
[7] [8] [9] [lo] [l l] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]
For a review, see B. Feuerbacher, B. Fitton and R.F. Willis, Eds., Photoemission and the Electronic Properties of Surfaces (Wiley, London, 1978). J.A. Knapp, F.J. Himpsel and D.E. Eastman, Phys. Rev. B19 (1979) 4952. P.S. Wehner, R.S. Williams, S.D. Kevan, D. Denley and D.A. Shirley, Phys. Rev. B19 (1979) 6164; G.V. Hansson and S.A. Flodstrom, Phys. Rev. B18 (1978) 1572. G.V. Hansson and S.A. Flodstrom, Phys. Rev. B18 (1978) 1562. T.C. Chiang, J.A. Knapp, D.E. Eastman and M. Aono, Solid State Commun. 31 (1979) 917. LT. McGovern, A.W. Parke and R.H. Williams, Solid State Commun. 26 (1978) 21; R.S. Bauer, J.C. McMenamin, R.Z. Bachrach, A. Bianconi, L. Johansson and H. Petersen, in: Institute of Physics Conf. Series, No. 43 (1979) p. 797 ; CM. Garner, I. Lindau, C.Y. Su, P. Pianetta and W.E. Spicer, Phys. Rev. B19 (1979) 3944. For a review, see W. Gudat and D.E. Eastman, ref. [l ] ch. 11, and references therein. D.J. Chadi, R.S. Bauer, R.H. Williams, G.V. Hansson, R.Z. Bachrach, J.M. Mikkelsen, F. Houzay, G.M. Guichar, R. Pinchaux and Y. Petroff, Phys. Rev. Letters 44 (1980) 799. D.E. Eastman and W.D. Grobman, Phys. Rev. Letters 28 (1972) 1378. L.F. Wagner and W.E. Spicer, Phys. Rev. Letters 28 (1972) 1381. J.E. Rowe, M.M. Traum and N.V. Smith, Phys. Rev. Letters 33 (1974) 1333. A.W. Parke, A. McKinley and R.H. Williams, J. Phys. Cl1 (1978) L993; A. McKinley, R.H. Williams and A.W. Parke, J. Phys. Cl 2 (1979) 2447. D.E. Eastman, F.J. Himpsel, J.A. Knapp and K.C. Pandey, in: Institute of Physics Conf. Series No. 43 (1979) 1059. G.V. Hansson, R.I.G. Uhrberg and S.A. Flodstrom, Surface Sci. 89 (1979) 159. F. Houzay, G.M. Guichar, R. Pinchaux and Y. Petroff, to be published. P.J. Feibehnan and D.E. Eastman, Phys. Rev. BlO (1974) 4932. B. Feuerbacher and R.F. Wills, J. Phys. C9 (1976) 169, and references therein. P.O. Nilsson and N. Dahlback, Solid State Commun. 29 (1979) 303. E. Dietz and F.J. Himpsel, Solid State Commun. 30 (1979) 235. S. Louis, P. Thiry, R. Pinchaux, Y. Petroff, D. Chandesrir and J. Leconte, to be published. D.J. Chadi, Phys. Rev. Letters 41 (1978) 1062. K.C. Pandey and J.C. Phillips, Phys. Rev. B13 (1976) 750. M. Erbudak and T.E. Fischer, Phys. Rev. Letters 29 (1972) 732. C. Sebenne, D. Bolment, G.M. Guichar and M. Balkanski, Phys. Rev. B12 (1975) 3280. P.K. Larsen, N.V. Smith, M. Schliiter, H.H. Farrell, K.M. Ho and M.L. Cohen, Phys. Rev. B17 (1978) 2612. S. Ciraci and I.P. Batra, Solid State Commun. 18 (1976) 1149. M. Schliiter, J.R. Chelikowsky, S.G. Louie and M.L. Cohen, Phys. Rev. B12 (1975) 4200. K.C. Pandey and J.C. Phillips, Phys. Rev. Letters 34 (1975) 1450. K.C. Pandey, calculations reported in the review article by D.E. Eastman, J. Vacuum Sci. Technol. 17 (1980) 492.
ELECTRONIC
STRUCTURE
OF Si(ll1)
SURFACES
G.V. HANSSON, R.Z. BACHRACH, R.S. BAUER, D.J. CHADI and W. GiiPEL Xerox Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, California 94304, USA Received 26 November 1979;accepted
for publication 18 February 1980
We report on new angle-resolved photoemission studies of Si(l1 I) 2 X 1 and 7 X 7 surfaces. The emission from the 2 x 1 surface shows much structure. For normal emission the energy positions are insensitive to the photon energy in the range 19-27 eV. The emission has been interpreted as a probe of the surface density of states, SDOS, including both surface states, resonances and bulk-like states. The SDOS was also calculated as a function of parallei momentum kU for a model of the Si(ll1) 2 X 1 surface obtained from energy minimization considerations. We identify emission from the dangling bond band, which has a positive dispersion of 0.6 eV, and also emission from surface resonances which have some character of the compressed and stretched back bonds. There are also other predicted surface resonances that correspond to experiments peaks which have not been identified in previous work. Except for the dangling bond band, the surface resonances are limited in k,y space, so that it is not possible to follow these resonance bands over all angles. Maximum intensity for the normal emission from the dangling bond is obtained at 23 eV, while the emission from the lowest s-like states monotonically increases towards 30 eV photon energy. When annealing the cleaved 2 X 1 surface to the 7 X 7 reconstructed surface, the spectra broaden significantly. The intensity of the dangling bond decreases and we see a very small metallic edge.
1. Introduction Angle-resolved photoemission has proved to be a very sensitive tool for the study of the electronic structure of solids and solid surfaces [1] . The analysis of the data using direct transitions within the three-step msdel has made it possible to get very detailed information about the bulk electronic structure of materials like the noble metals Au, Ag and Cu [l-3]. For other materials, like Al [4], the bulk direct transitions are not detectable, but the main part of the photoemission comes from the surface. ogle-resolved photoemission spectra (ARPES) in general have features attributable to both bulk and surface photoemission, The intensity of each component varies with photon energy such that the surface photoemission can be either emphasized or suppressed. In this study we have choosen to study the photoemission from Si(ll1) surfaces with photon energies between 20-30 eV, where as we will show the ARPES are dominated by contributions from surface photoemission. It 13
14
G. V. Harmon et al. /Electronic
structure of Siflll)
surfaces
has earlier been shown that also for GaAs there is a decrease in the direct transition contributions in this photon energy range [5]. One reason for the surface sensitivity is the very short mean free path of the excited electrons, which means that the emitted electrons are excited within 10 A of the surface [6]. A maximum in the transition probability from the dangling bond surface state of Si(ll1) 2 X 1 at 23 eV also makes the surface contributions more dominant. As it is not possible experimentally to separate surface states from surface resonances, we may sometimes use the term surface state for what are actually surface resonances. The Si(ll1) surface is known to have several possible reconstructions depending on the sample treatment [7,8]. We report measurements of ARPES from cleaved crystals showing 2 X 1 LEED patterns and from annealed crystals having 7 X 7 reconstructed surfaces. Studies of the angle-integrated photoemission first showed the existence of surface states near the valence band edge on both 2 X 1 and 7 X 7 surfaces [9,10]. A more detailed picture of the electronic structure of the 2 X 1 structure was obtained in ARPES studies by Rowe et al. [ 111. The reported emission from the dangling bond band and strong emission from a back bond which showed a clear three-fold symmetry. Emission from the dangling bond band and back bond bands on Si(ll1) 2 X 1 have also been reported by McKinley et al. [12] using 21.2 eV radiation. By studying many cleaves they showed the difficulties in getting reproducible ARPES results from surfaces that are all mirror-like and which show 2 X 1 LEED patterns. This was also seen in our study. The measurements on 2 X 1 surfaces reported here are in good agreement with what were reported as the best cleaves of McKinley et al. [12]. The 7 X 7 electronic structure has been studied by Eastman et al. [13] and by Hansson et al. [14]. Both groups report similar surface states and a clear metallic edge at the Fermi level. Recent synchrotron measurements with higher photon energies by Houzay et al. [15] on the 7 X 7 surface show a much smaller metallic edge. They [ 151 also report a very strong variation of the transition probability from the dangling bond state with a maximum at 53 eV photon energy. Around 25 eV photon energy they report negligible emission from both the dangling bond state and the metallic edge.
2. Experimental The experiments were performed at the Stanford Synchrotron Radiation Laboratory (SSRL), by using the facilities VG ADES-400 photoelectron spectrometer. The angle-resolved photoelectron spectra were measured by a hemi-spherical deflection analyzer that is rotable in the horizontal plane. The analyzer has an angular resolution of 22” and the energy resolution is 1.8%, which corresponds to GO.4 eV in our spectra. The samples were lightly doped silicon crystals (5 X 1Or5 cmF3, boron) that were cleaved in situ at a base pressure of 1 X lo- lo Torr . After the photoemission mea-
G. V. Hansson et al. 1 Electronic structure of Si(1 I I) surfaces
15
surements the surfaces were checked with low-energy electron diffraction (LEED). For the cleaved surfaces used in the photoemission studies the 2 X X LEED patterns were sharp and they showed only one domain of the 2 X 1 reconstruction. There were macroscopic steps distributed over the surfaces even for our best cleaves. Studies in a scanning electron microscope at a resolution of 200 A showed that the macroscopic steps were typically 0.2 X 10” m wide, but they were separated by flat terraces that were -20 X low6 m wide. The stepped regions thus correspond to -1% of the total surface and the strong angle-dependence in the ARPES indicate that the surface roughness on the terraces was ne~i~ble. Some of the cleaved surfaces were converted to the 7 X 7 reconstructed phase by heating the crystals to approximately 700°C.
3. Theory Theoretical aspects relevant to the results and discussion in section 4 are briefly presented here. In angle-resolved photoelectron spectroscopy one measures the energy and direction of emitted electrons. For cases in which hole damping may be neglected the photocurrent at the detector can be written [16].
where the operator
0 is defined by
6(x) = + [A(x) p + p/i(x)]
.
(2)
The wave function Qf needed to calculate the matrix elements is a time-reversed LEED function. A full calculation of the photocurrent from eq. (1) is practically impossible. The way to relate the ARPES to the surface and/or bulk electronic structure has rather been to discuss different mechanisms contributing to the matrix element for the photoe~ssion process 1171. A most useful approximation is contained in the three-step model. This applies to direct (k conserving) transitions between bulk electronic states, followed by the transport of the excited electron to and though the surface, during which the parallel momentum k~ is conserved. This three-step model has been used to determine the bulk-band structure of many metals and semiconductors. The initial energy of a direct transition will in general be dependent upon the photon energy, which can make the direct transitions easily recognizable if a continuous photon energy source is used. Over limited photon energy regions a direct transition peak can appear stationary due to very flat initial state bands or final state band gaps [ 18,191. For the direct transition model to work well the mean-free path should be long, since strong scattering in the final state will relax the k conservation rule,
16
G. V. Hansson et al. /Electronic
structure of Si(lliJ
surfaces
which results in broadening of the peaks. There is now experimental evidence that the matrix element for excitation from surface states can also have resonances that correspond to the direct transitions in the bulk [ZO] . This means that these surface states have to be localized over a larger number of layers than just the surfa\ce layer. Surface effects can enter through the operator 8 in eq. (1). These are often separated into the effect of the surface potential V, and the effect of the varying vector potential at the surface, &4/8z. All mechanisms for photoemission give rise to a kn conservation transition rule when applied to a perfect crystal face, i.e. an electron emitted with parallel momentum kl has been excited from an initial state with parallel momentum kn + GJ, where GJ is a reciprocal lattice vector (or the nullvector) of the surface unit cell. Since the mean free path of the excited electrons in our experiment is of the order of 5 A [6], we do not expect the three-step model to work. This is verified by our experiment. We interpret our data as emission from the surface whether the states involved are surface states, surface resonances or bulk-like in character. To make a detailed comparison between theory and experiment we have calculated the surface density of states, SDOS as function of k, along different directions in the surface Brillouin zone. Fig. I a shows the uppermost double-layer of a Si( 111) surface. For the generally accepted description of the 2 X 1 reconstruction the alternate rows in the surface layer are raised and lowered [7]. The corresponding change in the surface Brillouin -__ zone is shown in fig. lb. We also show the line in the extended zone scheme, FKM, along which the electronic structure has been investigated in some detail in our experiments and calculations. The geometry of the 2 X 1 reconstructed surface used in our calculation was chosen as to mini~ze the total energy of the electron-ion system (211. The atomic displacements from the unrelaxed positions are given in table I. The electronic structure was then calculated for a 12-layer slab with a 2 X 1 reconstructed top surface. The bottom surface was kept unrelaxed to avoid coupling between surface states (resonances) on the two surfaces. The calculation was performed using the tight-binding approximation, with the parameters for nearest neighbour and second nearest nei~bour interactions according to Pandey-__and Phillips 1221. The electronic states were calculated in 15 points along the FKM line in k space. At each k/l point we obtained 48 occupied bands that could be investigated with respect to orbital content and localization on each of the atoms in the slab, For the surface density of state curves presented in this paper we summed the density of states over the four uppermost atoms in the 12-layer slab, i.e. for the top doublelayer of the 2 X 1 structure. A problem in a comparison between theory and experiment is to relate the energy scales to a common origin. The calculation refers all energies to the bulk valence band edge, E,, which is not detectable in our experiment. The experimental ARPES are instead measured relative to the Fermi level EF. To get a common scale we assume that Eli - E,= 0.35 eV, which has been determined in other experiments 1231. The uncertainty in this value is a.1 5 eV [24].
G. V. Hansson et al. /Electronic
structure of S/ill)
surfaces
17
Fig. 1. (a) Top view of the Si(l11) 2 X 1 surface. Atoms 1 and 2 are the raised and lowered atoms in the top layer and atoms 3 and 4 are in the second layer. (b) The surface Brillouin zone for the 2 X 1 reconstruction (rectangles) super-imposed on the 1 X 1 surface Brillouin zone (hexagons).
Table 1 Atomic displacements from unrelaxed positions for the 2 X 1 reconstructed (Ill) surface of Si; i is the surface normal and p is parallel to the surface projection of a vector from atom 2 to atom 4 in fig. 1 Atom 1
Atom 2
Atom 3
Atom 4
A.z (19)
0.31
AY (A)
0.00
-0.44 0.06
0.00 -0.13
0.00 0.09
-
--
18
G. V. Harmon et al. /Electronic
structure
of Si(l I I)
surfaces
4. Results and discussion The angle-resolved photoemission results are presented in this section along with a discussion of the interpretation. We start with the Si(ll1) 2 X 1 surface and analyze the normal emission as a function of photon energy. This is followed by studies of the emission as function of polar angle. In the normal emission one probes the I’L line in the bulk Brillouin zone and the r point of the surface Brillouin zone. For off-normal emission one probes the surface electronic structure as function of kl. Finally we report some results from studies of the Si(ll1) 7 X 7 surface. 4.1. Normal emission from Si(ll1)
2 X1
To experimentally separate the surface and bulk contributions to the photoemission current is generally a difficult task. One case for which a clear identification of a bulk contribution is possible is when the initial energy of a transition, Ei(ki), is varying with photon energy [ 171. In this way it has been shown that the major contributions from Si( 111) 7 X 7 in the photon energy range 7-l 2 eV are due to direct transitions in the bulk [14]. With the continuous radiation of the synchrotron source we can choose to work at higher photon energies where the mean free path of the excited electrons is minimized thus increasing the relative portion of emission from the surface electronic structure. Because the final states are very strongly damped in the bulk, at these energies, a model with direct transitions between Bloch states may not be applicable. The electron escape depth from a Si(ll1) surface has been determined to be 4-7 ,& for electrons excited to 17-140 eV above the Fermi level [6]. This means that the majority of the electrons originate from the first two double layers (6.3 ,&separation). Fig. 2 shows examples of the photoemission in the normal direction from Si(ll1) 2 X 1 for different photon energies. In the range 19 to 27 eV there is very little dispersion of the peaks. The peak energy positions as well as the lack of dispersion over this photon energy range cannot be explained by direct transitions between bulk states. Disregarding the 10.5 eV spectrum which contains contributions from direct transitions, we see that the only changes in the spectra are intensity variations. There is a strong increase of the low energy peak of the spectra, H, which is due to the increased cross section for transitions from the low lying states, which have predominantly s-character. One can compare our results to angle-resolved photoemission measurements on Cu(l10). For this system the direct transition model can be used even for excitation to highly damped final states in final state band gaps [18,19]. The main conclusions from those studies are that a reduction of the emission intensity occurs and the initial density of states near the symmetry point of the band gap in the bulk electronic structure is probed. This means that the peak positions do not vary with photon energy over the region of the final state band gap. Since there are no band
G. V. Hailsson et al. /Electronic
19
structure af si(Il I} surfaces
Si (1111 2 x 1 icJ = 0 Ai = 4P,
p-polarization
a
-12
-lQ
-6 INITIAL
-6 ENERGY BELOW E,
-4
-2
tev)
Fig. 2. Photoemission spectra measured normal to the Si(ll1) 2 X 1 surface (i.e., @= 0) are compared with the calculated surface density of states fox states with kl = 0. The experimental spectra were measured relative to the Fermi level, which is assumed to be 0.35 eV above the valence baud edge.
20
G. V. Hansson et al. /Electronic
structure of Sifl I I) surfaces
gaps in the final state band structure along FL in silicon in the probed energy region, we cannot attribute the lack of dispersion to that mechanism. Also the experimental peak positions do not correspond to maxima in the bulk density of states. The important point for the further discussion is that the emitted electrons come from the uppermost surface layers and that the direct transition model cannot explain the data. We compare in fig. 2, the normal emission spectra to the calculated occupied surface density of states, for states with k( = 0, r. The SDOS is summed over the four uppermost atoms constituting the top reconstructed double-layer. Featured in the SDOS curve is the dangling bond state (a) which is more than 75% localized on the top double-layer, An “ideal” bulk state would have approximately l/6 = 17% of its charge in each double-layer, since the slab geometry used in the calculation is built of six double-layers. Except for the dangling bond state at -0.5 eV there are no states with kl = 0 which have a localization greater than 30% on the top doublelayer. The double-peak (d) near -7 eV has weak character of a surface resonance, while the states giving rise to peaks b (-2.7 eV) and c (4.4 eV) are very bulk-like. The experimental spectra show structures at -0.7 (A), -2.6 (B), -4.4 (C) and -6.7 eV (D) which are in very good agreement with the theoretical SDOS. The experimental peak H at -11.3 eV that appears at higher photon energies corresponds to a maximum in the SDOS at -11 .O eV (h). One can question, however, the significance of peaks c and h in the SDOS since they are of the order of the variations in the SDOS due to the finite size of the slab used. More significant is the minimum in the SDOS near -5 eV, which corresponds to the minimum at N -4.8 eV in the spectra. It is comforting that the energy positions of the four largest features in the experimental spectra and the calculated SDOS are in such a good agreement. The most important omission in such a simple comparison is of course the matrix element effects for the different transitions. To avoid the possibility that some matrix elements are identical to zero due to symmetry, we measured the photoemission with the light coming in at 45” from the normal in the (2ii) plane which is not a mirror plane. Large effects of the matrix elements can still be seen in the intensity variations with photon energy of the emission from the predominantly s-like states near -11 eV and also for the surface resonance at -0.7 eV which has maximum intensity at 23 eV photon energy. This low binding energy surface resonance is the dangling bond with mostly pZ but also significant s-character, that is localized primarily on the raised atom (No. 1 in fig. 1) of the outer reconstructed surface layer. All other occupied states with kl= 0 are quite evenly distributed over the four atoms in the top double-layer. Thus, we are not able to distinguish any stretched or shortened back bonds at T. The studies by Parke et al. [ 121 on a large number of cleaves have shown the difficulties to get reproducible results on different cleaves. Even within the set of cleaves showing mirror-like surfaces, the peak positions may vary by up to 0.5 eV. Using 21.2 eV radiation they obtained spectra that are in good agreement with ours
G. V. Hansson et al. /Electronic
structure of Si(l1 I) surfaces
21
with respect to the spectral shape and the energy positions of the dangling bond peak and -6.7 eV peak. For peaks in the region -1 to -5 eV below the valence band edge (Ev) they measured peak positions varying around our values with average positions that are slightly lower than our reported values. 4.2. Off-normal emission from Si(ll1)
2 Xl
The polar angle variation of the emission in the (2ii) plane is shown in fig. 3. The corresponding line in the 2D k space is presented in fig. 1. The emission from the dangling bond state is increased at off-normal emission and has a maximum intensity at about 25”. This is consistent with the incorporation of emission from a state with a high degree of p,-content, since the theoretical maximum for emission from a pure p,-orbital to a plane wave with an A-vector 45” from the z-direction is 22.5” from the z-axis [25]. Note also the positive 0.6 eV dispersion for the dangling bond emission, with the band maximum between K and M at 0.0 + 0.1 eV relative to the valence band maximum. The dispersion is very anisotropic. Along the I’J’ direction we find a flat dangling bond band, while states closer to Tare higher in energy. In the original paper by Traum, Rowe and Smith a positive dispersion of 0.6 eV was also reported for the weak shoulder, that later has been interpreted as the dangling bond. Thus both experiments, although performed along different directions, show a positive dispersion for the dangling bond surface state. Unlike the results on GaAs [5], we see no direct transitions from the uppermost of the bulk valence bands. These would show a negative dispersion for the photon energies used, in disagreement with the experimental results. For initial states in the range -1 to -5 eV a complex variation of the emission with the polar angle is observed and it is not possible to follow any surface resonance band over all angles. As will be discussed in more detail later there is a continuous appearing and disappearing of peaks. The strongest feature in the spectra is a peak, G, at about -6.6 eV that appears around a polar angle of 35’. The parallel momentum kl of these electrons in the extended-zone scheme corresponds to states near the I? point of the 1 X 1 surface Brillouin zone. For the unreconstructed surface, the states in the surface layer at the K point are all surface states. From our SDOS calculation we expect to see strong features in the spectra probing near the K’point also for the reconstructed surface. The surface density of states has been calculated as function of k# to facilitate a comparison between experiment and the calculated surface electronic structure. Fig. 4 shows SDOS curves calculated along the Kh4 direction in the extended-zone scheme. The grid of points in the Brillouin zone used in the calculations was a factor of two more dense than showed in fig. 4. Cross hatched regions correspond to surface resonances (states) that are more than 30% localized in the uppermost double-layer, cf. 17% average per double layer for a bulk state. For all kj values we get the strongly localized dangling bond state, but it has a much smaller dispersion
22
G. V. Hansson et al. /Electronic
I
I
I
I
I
structure of Si(il I) surfaces
I 1
Si (111) 2 x 1 hv = 20.0 eV
0; = 49,
I -10
I
I
I
-8
-6
-4
INITIAL
ENERGY
BELOW
p-polarization
1
-2 E,
(eV)
/I 0
EF
Fig. 3. Photoemission spectra as function of the polar angle e measured in the (2ii) plane of Si(ll1) 2 X I. _ The spectra were measured relative to the Fermi level, which is assumed to be 0.35 eV above the valence band edge.
G. V. Harmon et al. /Electronic
-12
%-10
-8 INITIAL
-6
structure of Sill 1 I) surfaces
-4
-2
23
0
ENERGY BELOW E,(eV)
Fig. 4. Surface density of states in the top double-layer as function of parallel momentum, kl, in the rKM direction. Indicated by shading are also the surface resonances (states) that are more than 30% localized in the top double-layer.
than the experimental peak. The strongest feature in the theoretical curves is a number of surface states that appear near the K point in good agreement with experiment. Another striking feature of the theoretical curves is that except for the dangling bond, it is not possible to follow any surface resonance band over the whole k, region. In the experimental spectra there is strong emission at -2.7 eV close to normal emission, 6 < lo”, (B), but also at high angles 19> SO0 (E). Peak B corresponds to the peak b in the SDOS, which only contains bulk-like states. This interpretation is
24
G. V. Hansson et al. /Electronic
I
structure of Si(i1 lj surfaces
I Sitlll)
-.
I
I
-ck
\
2 X 1
0
-a-
-c
-iyj-•
_--
r
2x1
K
B. L. edge
i%
T;/,
Fig. 5. Experimental and calculated surface electronic band structure along the rKM direction. Filled circles correspond to strong peaks and open circles are weaker structures in the experimental spectra. The continuous curves show the energy positions of the strongest peaks in the calculated SDOS, while the dashed curves correspond to weaker but still significant peaks.
consistent with the results of Parke et al., who have shown that peak B remains strong also after a change in reconstruction from 2 X 1 to 1 X 1. The peak E at high angles corresponds to the SDOS peak e, which has some contributions from the stretched (weakened) back bonds. Around 45” there is a very sharp peak (F) at -4.5 eV that disappears very quickly with increasing angle. This is in good agreement with the surface resonance, f, calculated to be at -4.2 eV. The last large feature in the spectra, peak G near -6.5 eV, is also in quite good agreement with either of two calculated surface resonances, g and i. A comparison between experimental peak positions and peaks in the SDOS is given in fig. 5. The curves show peaks in the SDOS that are significantly above the variations due to the finite slab size. The filled dots are strong peaks in the spectra and the open rings are weaker structures. For the dangling bond band the center of gravity in the experiment is well described by our calculation. The dispersion, however, is much stronger than any calculation has given [26-281. We have calculated
G. V. Hansson et al. /Electronic
structure of Si(ll1)
surfaces
25
the dispersion for several different reconstructions and have not been able to get a significantly better agreement with the experiment. The dispersion of this dangling bond band as calculated by both the self-consistent pseudopotential [27] and tight-binding methods [28,29] is much smaller (or in the case of the pseudopotential results of opposite sign) than that observed experimentally on our samples. The energy positions of most of the smaller but still significant features in the spectra can also be interpreted as emission from maxima in the SDOS. Exceptions are the shoulder at -1.5 eV in the 0’ spectrum and the small peak at -3.4 eV in the 40’ spectrum which is in between two calculated surface resonances. Knowing that the experimental peak positions can vary by up to 0.5 eV for different cleaves we think that the overall agreement between the experiment and the SDOS calculation is quite good. It is possible that some of the minor structures are from direct transitions in the bulk, although we have not been able to identify any. For the dangling bond we have calculated the localization on the uppermost double-layer to be between 70% and 90% for different k# values. The dangling bond states have up to 53% of their total charge in p,-orbitals localized on the raised surface atom and their s-content is 20% or less. A 70% localization was also calculated for the surface state g at -7.1 eV, which has 50% s-character in the top layer and 20% px, pY in the second layer. These two surface resonances are identified as the two strongest peaks in the experimental photoemission spectra. For the intermediate region -1 to -5 eV there are a number of surface resonances, some of which can be interpreted as the compressed and stretched back bonds respectively. The band dispersing from -2.9 to -4 eV near the K point can be characterized as the stretched back bond band. The states in that band are localized more on the raised surface atom and the second layer atoms than on the lowered surface atoms. This is also true for the surface resonance band near -2.7 eV between K and fi. The compressed back bond is seen as a very weakly localized surface resonance band about 1 eV below the stretched back bond band. The relative positions of the compressed and stretched back bonds are consistent with the calculation by Pandey and Phillips [28]. Although we use the same tight binding parameters as Pandey and Phillips [22], the detailed results of our calculation are different from theirs for two reasons. First we do not use the same 2 X 1 reconstruction geometry and secondly we scale the interaction parameters with distance d as (do/d)*, while they use a exp@(de - d)) scaling. do is the ideal bulk nearest neighbour distance. We also want to point out that the agreement between Pandey and Phillips’ surface resonance bands [28] and the experiments reported by Parke et al. [12] (fig. 2 in ref. [12]) is partly due to an error in the plotting of the theoretical energy bands taken from Pandey and Phillips’ paper [28]. 4.3. Si(IlI)
7 X7
Some of the cleaved 2 X 1 surfaces were converted to the 7 X7 reconstructed phase by heating to about 7OO’C and slow cooling to room temperature. This
26
G. V. Hanson
et al. /Electronic
structure of Si(ll Ij surfaces
results in a considerable broadening of the photoemission spectra. There is also a much weaker angle dependence, as is expected due to the increased surface scattering at a 7 X 7 compared to a 2 X 1 reconstructed surface. The strongest effect is however the decrease of the dangling bond emission. This is in agreement with recent measurements by Houzay et al. 1151 who have made a study of the emission from Si(l11) 7 X 7 over a wide range of photon energies, 20-80 eV. They find that the emission from the dangling bond is not detectable at 20 eV photon energy but the emission intensity has a sharp maximum at 53 eV photon energy. Thus the disappearance of the emission from the dangling bond does not mean that the state has disappeared. Eastman et al. [13] have reported emission from the dangling bond (at -0.9 eV relative to EF) from 10 up to 25 eV photon energy. It thus appears that emission from the dangling bond in some experimental configurations is minimized near 20 eV but that it is detected in other measurements. It is not clear whether the polarization direction of the light or different sample preparation techniques is the origin of the inconsistency of the experiments. The same discrepancies between experiments are also present for the magnitude of the metallic edge. The experiments by Houzay et al. [ 151 agree with ours that the metallic edge is very small (close to detection limit), while the measurements by Eastman et al. 1131 and also low photon energy data by Hansson et al. [14] show a very clear metallic edge. Further experiments are planned to resolve these differences.
5. Conclusions Angle-resolved photoemission from Si(ll1) surfaces at photon energies of 20-30 eV probes electronic states very near the surface. The details of the electronic structure depend on the reconstruction of the surface. We have found good agreement between peaks in the ARPES and maxima in the calculated surface density of states for an energy minimized model of the 2 X 1 surface. In particular we have found that the two states with the strongest surface localization correspond to the largest features in the ex~rimental spectra, From our study of the electronic structure as function of parallel momentum we conclude that the surface states and surface resonances cannot be characterized as pure dangling bonds and back bonds. Our calculations show that the surface localization of surface resonances vary strongly, and this behaviour is confirmed in our experiments. It is known that the reproducibility of photoemission results on cleaved surfaces even with good 2 X 1 LEED patterns is a problem, i.e. the electronic structure is very sensitive to the details of the reconstruction. Having that in mind we think the agreement between our experiment and our calculation is good. A further study of how the geometrical configuration affects the surface electronic structure is planned. The goal for future studies would be to determine properties of the reconstruction by using angle-resolved photoemission.
G. V. Hansson et al. /Electronic
structure of Si(l II) surfaces
27
Acknowledgements We wish to thank R. Gutcheck, who participated in the data collection process. Some of the materials incorporated in this work were developed at the Stanford Synchrotron Radiation Laboratory which is supported by the National Science Foundation (under contract DMR77-27489), in cooperation with SLAC and the Department of Energy.
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