Electronic structure of H chemisorbed on Si(111) surfaces

Solid State Communications,

Vol. 25, pp. 439-441,

ELECTRONIC

STRUCTURE

Pergamon Press

1978.

OF H CHEMISORBED ON Si(ll1)

Printed in Great Britain

SURFACES

F. Yndurain Instituto

de Fisica de1 Estado Solid0 (CSIC and UAM), Universidad Autdnoma,

Cantoblanco,

Madrid, Spain

and E. Louis* Department

of Physics, University

of Illinois, Urbana, IL 6 1801, U.S.A.

(Received 15 July 1977; in revised form 19 September 1977 by L. Hedin)

We study the electronic density of states of hydrogen chemisorbed (111) Si surface. We analyse two situations: one single chemisorbed hydrogen atom in an otherwise clean surface and a complete monolayer of hydrogen chemisorbed at the surface. The method of calculation is based on an extension of the cluster-Bethe lattice approximation developed by the authors to study surfaces. Our results for the monolayer are in good agreement with UPS data, as well as with other theoretical calculations. RECENTLY, various calculations of the electronic density of states of hydrogen chemisorbed semiconductor surfaces have been reported [l-3]. These calculations qualitatively agree with each other and with experimental UPS data [4], although there are some minor discrepancies between tight-binding and self-consistent calculations [2,3]. In this letter we perform a calculation of the electronic density of states corresponding to two situations, namely, a single hydrogen atom and a complete monolayer of hydrogen chemisorbed at the Si (111) 1 x 1 surface. Our calculation is based on the cluster-Bethe lattice approximation [5,6] and deals with a realistic tight-binding Hamiltonian [7]. Due to the local character of our approach, k-space integrations are avoided. The Hamiltonian used in the calculation includes all possible interactions between sp3 orbitals in nearestneighbour atoms [7]. The interaction parameters between Si atoms are fitted to pseudopotential bulk band structure calculations [8]. The Si-H parameters are taken from Pandey’s work, who finds them by fitting the SiH4 and Si, H6 energy levels. In our calculation of the electronic structure of hydrogen chemisorbed at the (111) unreconstructed Si surface, we distinguish two situations: (i) A single hydrogen atom chemisorbed (111) 1 x 1 surface

at the Si

We assume that the hydrogen lies on top of a Si sur-

* Partially supported by the Program of Cultural Cooperation between the U.S.A. and Spain. 439

face atom, whereas the rest of the Si surface is clean. The calculation of the density of states around the atom in which we are interested is done following the extension of the cluster-Bethe lattice approximationrecently developed by the authors [9, lo]. If we label 0 the hydrogen and 1 the Si atom bonded to it, we obtain the following equations for the matrix element of the Green’s function between the hydrogen s-orbital: (E - &f)G,e

= 1 + VH.G,,,, (I)

i Ui -r; - GI,O 9 i i=2 i where UH is the energy of the hydrogen s-orbital. VH is the one-column matrix formed by the Hamiltonian matrix elements between the hydrogen s-orbital and the sp3 orbitals of the Si atom where the hydrogen is absorbed. The (4 x 4) matrices U. and Ui (i = 2,3,4) contain the intra-atomic and inter-atomic interactions between sp3 orbitals, respectively. The matrices 7:” are the free surface transfer matrices defined in [9], and finally the onerow matrix G1,o contains the matrix elements of the Green’s function between the sp3 Si orbitals and the hydrogen s-orbital. Once Goa is known from equation (l), the local density of state at the hydrogen atom is readily obtained Similar equations to (1) can be derived to get the local density of state at the different orbitals. In Figure 1 we show the density of states corresponding to the H-Si pair. We first notice a hydrogeninduced peak at - 4.2 eV [ Ill. Another hydrogeninduced peak appears at - 12 eV at the bottom of the valence band. We also notice that whereas the free (IE--&Gt.o

= VH’. Go,o +

440

ELECTRONIC STRUCTURE

OF H CHEMISORBED ON Si( 111) SURFACES

Vol. 25, No. 7

analysis of each individual local density of states reveals. Experimentally another peak at - 7.0 eV is observed, however our single hydrogen atom calculation does not reproduce this peak. In order to make a more detailed comparison with experiments we now study a more realistic situation: (ii) A monolayer of hydrogen chemisorbed (111) 1 x 1 surface

.OC9

ENERGY

Here we shall be dealing with the monohydride phase, i.e. a single hydrogen on top of each Si surface atom. In this case, and due to the perfect twodimensional periodicity of the system, we perform the calculation using a chemisorbed-surface transfer matrix, as it was done in [9] for the case of the free surface. In Fig. 2 we show the results corresponding to the densities of states associated to the hydrogen layer, the first Si layer and the layer underneath. In order to compare with experiments, we also show the averaged sum of the previous densities of states. Several hydrogen-induced features in the density of states are worth noticing:

WI

Fig. 1. Density of states for a single hydrogen chemisorbed at the (111) surface of Si. The density of states drawn is the sum of the local density of states at the hydrogen atom and that at the surface Si atom where the hydrogen is chemisorbed. The density of state is normalised to one.

(a) A peak at - - 4.4 eV (see Fig. 2). This peak is also present in the case of a single hydrogen atom (see Fig. 1). It essentially corresponds to the hydrogen s-orbital and appears at the energy region where the bulk band structure displays a gap [ 1 ] and the p and sp parts of the spectrum decouple [7]. (b) A peak at - - 7.0 eV [see Figs. 2(a) and (d)]. This peak is not present in the previous situation (a

surface dangling bond is almost completely’washed out, the atomic [9, lo] free surface state at - - 8.6 eV remains essentially unchanged. The peak at - 4.3 eV is in good agreement with other calculations [l-3], as well as with experiments [4]. The states associated to this peak are mostly localised at the hydrogen atom, as the

i

; cx z g

at the Si

t

.I2 .I0 .08 .06 .04 .02 .oo

-13

-II

-9

-7

-5

-3

-I ENERGY

kV)

Fig. 2. Local densities of state (normalised to one) of a hydrogen monolayer chemisorbed at the (111) surface of Si. (a) Local density of states at the hydrogen atom. (b) Local density of states at the Si surface layer. (c) Local density of states at the second Si layer. (d) Weighted sum of the above densities of states (solid line) and bulk Bethe lattice density of states (broken line).

Vol. 25, No. 7

ELECTRONIC

STRUCTURE

OF H CHEMISORBED

single hydrogen adsorbed). It is clearly due to the interaction between the hydrogen atoms through the substrate. Pandey’s tight-binding calculation [ 11, and self-consistent calculations by Appelbaum and Hamann [2] and by Ho et al. [3] also reproduce this feature. The long-range character of the state associated with the peak at - - 7.0 eV is in agreement with experimental findings [ 121. (c) There is an enhancement of the p-like peak at - - 2.5 eV. Although this result is in agreement with both theory [3] and experiment [4], our results do not give enough support to its existence due to the weakness of this feature [Fig. 2(d)]. (d) A peak at - - 9.7 eV [see Figs. 2(a), 2(b) and 2(d)]. The origin of this peak is the interaction of the free surface atomic state [9] at - - 8.6 eV with the hydrogen s-orbital. This peak has never been discussed in the literature. (e) The bottom of the valence band shows a piling up of density of states [Fig. 2(d)]. It is difficult to assess whether this is a real effect or it is due to the presence of the band edge. However, the fact that a peak at - - 12 eV is present in the case of a single hydrogen (Fig. 1) suggests the possible relevance of this feature. (f) It is interesting to notice that the main free surface state (i.e. dangling bond state at the gap and atomic state at - - 8.6 eV) disappear upon absorption of a monolayer of hydrogen. This is in accordance with a simple interpretation of the peaks at - - 4.4 eV and * - 9.7 eV in Fig. 2(d). The free surface dangling bond is, essentially, a p-like state [IO] localised mostly in the surface layer. If we assume this state to be a p-orbital completely localised in the surface layer and calculate the energy levels of the corresponding Si-H pair, we get

ON Si(ll1)

441

SURFACES

a state at -4.89 eV close to the value obtained in the full calculation [Fig. 2(d)]. In the same way the free surface state [lo] at - 8.6 eV is an atomic-like s-orbital almost decoupled from the rest of the crystal [ 131. Then a Si-H pair calculation for this state gives an energy level at - 10.35 eV, close to the above reported position (- 9.7 eV). The reason why this peak at - 9.7 eV has never been observed experimentally is twofold: first, matrix elements are small [ 1] and second it is very close in energy to a bulk crystal peak [ 131. In conclusion, our calculation reproduces fairly well the experimental results and reveals the existence of a hydrogen-induced peak in the density of states at - - 9.7 eV which has never been discussed in the literature. Our method to calculate the density of states has several appealing characteristics: (i) Avoids k-space integration. This is an important advantage in the study of surfaces, where the calculations are lengthy and a good sampling of the Brillouin zone is difficult and expensive. (ii) We deal with an infinite system. We then avoid the presence of the back surface in the calculations of slabs. We also avoid the two-dimensional logarithmic singularities in the density of states due to the discreteness of the spectrum at each fixed value of the momentum parallel to the surface when dealing with slabs. (iii) The method allows us to study the whole range of coverage, from a single atom to a complete monolayer of hydrogen. (iv) The extension of the method to the study of more complex systems, such as hydrogen chemisorbed on Si stepped surfaces [9], is fairly simple.

REFERENCES 1.

PANDEY K.C., Phys. Rev. B14,1557

2.

APPELBAUM J.A. & HAMANN D.R., Rev. Mod. Phys. 48,479

3.

HO K. M., COHEN M.L. & SCHLUTER M., Phys. Rev. B15,3888

4.

SAKURAI T. & HAGSTRUM H.D., Phys. Rev. B12,5349

5.

JOANNOPOULOS

J. & YNDURAIN

6.

JOANNOPOULOS

J. & COHEN M.L., Solid State Phys. 31,71

(1976).

7.

RAJAN V.T. & YNDURAIN

F., Solid State. Commun. 20,309

(1975).

8.

JOANNOPOULOS

9.

LOUIS E. & YNDURAIN

F., Solid State. Commun. 22,147 F., Phys. Rev. B16, 1542 (1977).

J., Unpublished

(1976). (1976). (1977).

(1975).

F., Phys. Rev. BlO, 5164 (1974).

Ph.D. thesis, University of California,

Berkeley.

(1977).

10.

LOUIS E. & YNDURAIN

11.

The origin of energies is taken at the top of the bulk crystal valence band (see [7] and [9] ).

12.

APPELBAUM J.A., HAGSTRUM H.D., HAMANN D.R. & SAKURAI T., Surf Sci. 58,479

13.

FALICOV L.M. & YNDURAIN

F.,J. Phys. C: Solid State Phys. 8,1563

(1975).

(1976).