Cluster model electronic structure calculations for the ideal and hydrogen chemisorbed Si (100) surfaces

Solid State Communications, Vol. 18, pp. 563—565, 1976.

Pergamon Press.

Printed in Great Britain

CLUSTER MODEL ELECTRONIC STRUCTURE CALCULATIONS FOR THE IDEAL AND HYDROGEN CHEMISORBED Si (100) SURFACES I.P. Batra, S. Ciraci and I.B. Ortenburger IBM Research Laboratory, San Jose, CA 95193, U.S.A. (Received 26 September 1975, by A. A. Maradudin) The electronic structure of the ideal and hydrogen chemisorbed Si(100) surfaces is calculated using the self-consistent scattered-wave cluster model. The results are presented for total and local density of states. These are compared with experiments and other calculations, where available. RECENT photoemission measurements1 have shown that each atom on the Si(100) surface adsorbs one hydrogen atom just like the Si(1 1 1) surface. In view of the fact that Si(l 11) has a single sp3-type dangling bond per surface atom, but the Si(l00) has two broken bonds per surface atom, this is an unexpected finding, Furthermore, unlike the Si(l 11) surface, the (2 x 1) reconstructed Si(100) surface is stable 1even upon make the hydrostudy genthe chemisorption. These observations of electronic structure of the hydrogen chemisorbed Si(100) surface an important topic of investigation. In addition, the cluster model calculations have not been reported for the ideal Si(100) surface, In this we report theSi(l00) electronic structure ofcommunication, the ideal and H chemisorbed surfaces, calculated using the self-consistent scatteredwave2’3 (SCF—Xa—SW) cluster model. In our calculations, the orbital relaxation effects were included in determining the binding energies of all occupied orbitals by employing the transition state method, Furthermore, to improve the physical realism of the scattered wave cluster model for surface studies of covalent semiconductors, overlapping spheres (sphere radius of 2.54 a.u. for Si and 0.75 a.u. for H) were used. The same value of the exchange factor (a = 0.75) in various regions was chosen. The results are presented for the local as well as total densities of states. A cornparison with experiments and other available calculations In is themade, present work the Si(100) surface is simulated by a cluster consisting of eighteen silicon atoms, whose dangling bonds in the bulk have been saturated by twenty-two hydrogen atoms, Such a cluster, i.e.,Si is shown schematically projected in the z = 0 plane18H22, in Fig. 1. It consists of five layers of silicon atoms along the [100] direction and belongs to C 2~,point group symmetry. The first layer consists of five silicon atoms of which three (shaded circles in Fig. 1) have broken

bonds and are connected to the second layer by two back-bonds each. The two broken bonds of surface atoms play an important role in determining the surface electronic energy structure for the ideal Si(100) surface. As will be made clear later, saturation of each surface atom with a single hydrogen leads to a cluster (Si 18H25) which is suitable for studying hydrogen chemisorption. Prominent features of the surface electronic energy structure of the Si 18H22 cluster are summarized in Fig. 2. Shown here are densities of states generated by assigning to each calculated energy level a Gaussian half-width (a = 0.35 eV). Figures 2 (a) (b) respect4 asand adapted5 to ively, give the local density of states SCF—Xa—SW method for the first and second layer of silicon atoms. Figure 2 (c) shows the total density of states. Since the transition state binding energy scale from the SCF—Xa—SW method has no absolute significance due to the presence of the outer sphere surrounding the entire cluster, the energy scale in Fig. 2. is obtained by approximately locating the Fermi level in the middle of the occupied and unoccupied surface bands. Focussing our attention on the first two layers of the Si 18H22 cluster, we observe five distinct features, A, B, C, D, and E. Energy states producing bands A and B have their charge primarily localized in the first layer and thus are readily recognizable bands, as dis6 Bands C and Esurface have major contricussed by others. butions from the second layer (back-bonds) silicon atoms but are not highly localized, These bands appear as localized surface bands upon relaxation at some 6 States producing the ks-points in other band D have their calculations. wave functions extending to deeper layers.

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The orbital character of the surface bands is interesting. In the ideal bulk each this atomtohas 3-type orbitals, and ifconfiguration one extrapolated a four sp

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STRUCTURE CALCULATIONS FOR Si(lOO) SURFACES 12

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Vol. 18, No. 5

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surface states of Si(100). Large and small circles correspond to Si and saturating H atoms, respectively. Shaded circles are the atoms which have unsaturated bonds. The numbers in the positive quadrant indicate the layers formed by the atoms in the cluster. 1 = surface layer, 2 = second layer, etc. Numbers with the prime are for the layers of saturating H atoms,

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Fig. 2. Local and total densities of states for the Si(l00) surface. Solid lines are for the ideal and dotted lines for the hydrogen chemisorbed Si(100) surfaces using cluster model. Tight-binding results for the ideal Si(l00) surface shown by dash—dots are taken from reference 7.

surface atom of Si(lOO), one would expect two dangling bonds per surface atom, However, we find that the two dangling bonds interact with each other in the surface environment and produce two new bonds. One of these lies in the surface (primarily p~-type)and the other perpendicular to the surface (primarily ps-type). Our calculations show that the ps-type orbitals have lower energy and are responsible for the occupied surface band B. The unoccupied surface band, A, primarily consists of the p~-typeorbitals. These results are agree6’7 in Since the ment with other theoretical investigations. surface dangling bonds have assumed a different hybridization state from the bulk even for the ideal surface, it is possible that the back bonds are also affected, giving rise to bands C and E. In fact, we find that the band c is produced from back bonding states having primarily

calculations, the broad features of the bulk as well as surface-like structures compare well. The tight-binding local densities of states calculated at the first and second layer have comparatively more structure because of the better description of energy bands in an infinitely large system. In the cluster method the fine Structure is smoothed out through the finite size of the cluster and the Gaussian broadening. Also, the density of states corresponding to the X 1 point of the Brillouin zone does not vanish in the cluster method. This is an artifact of the Gaussian broadening. On the other hand, the cluster method provides a better estimate of the upper valence band width than the tight-binding calculations, In the latter, the second-neighbor approximation cannot des-

p~ p,.~character and E from a primarily bonding combination of s-type orbitals. C 8~’ and Of E correspond to course, states S2 and S3 of the Si(l 11) surface, producing bands C and E will become highly localized on back bonds upon surface relaxation, In the ultraviolet photoemission experiments one expects to see similar total density of states to that shown in Fig. 2 (c). The distribution resembles the bulk density of states hut has some additional structure due to the surface effects, The only prominent surface structure is the surface band B. Of course, the band A is unoccupied and may not be easily observable, A comparison of our results with the local and total densities7 of states calculated using the tight-binding is carried out in Figs. 2 (a—c). In spite of the method normalizations of the intensities in both different

cribe the minima of the ~ band. Let us nowondiscuss theineffect chemisorption Si(100) termsofofthe thehydrogen Si 18H25 cluster. The cluster is obtained from the cluster Si18l-122 by placing one hydrogen atom on each shaded (see Fig. I) Si atom. The Si—H bond distance is taken from the SiH4 molecule. The densities of states corresponding to this new system are shown by dotted lines in Figs. 2 (a—c). The most important effect can be seen by examining the local density of states for the first layer of Si atoms with and without hydrogen atoms, as shown in Fig. 2(a). Notice that the peak B of the ideal Si(l00) surface has lost some intensity, but the peak C has gainedupon somechemisorption. and has become considerably more ened In addition, band A is broadnow partially occupied, and thus the work function is

Vol. 18, No. 5

STRUCTURE CALCULATIONS FOR Si(100) SURFACES

slightly reduced upon H chemisorption. Note, however, that the peak A and in fact the entire curve of the H chemisorbed Si(l00) have been shifted down due to the alignment of the Fermi energy as the zero level, These results can be understood physically as follows. The presence of hydrogen with its additional electron forces the charge from the occupied ps-states (region B) to higher lying pr-surface states (region A) and forms an

Si—H bond with p~-orbitalsin lower lying energies. There is an enhancement of intensity in C and D regions (i.e. about 4 and 7 eV below EF) upon hydrogen chemisorption as is in fact observed”9’10”2’13 in hydrogen chemisorbed Si(l 11). Notice that unlike the Si(l 11) surface, the chemisorption of hydrogen does not deplete

565

ideal surface contains an even number of electrons, while that of the chemisorbed surface contains an odd number. Since the effect is small, no differentiation between spin up and spin down electrons was made. Finally, we would like to briefly discuss the (2 x 1) reconstruction mechanism and to speculate upon the effect of the hydrogen chemisorption on the reconstructed surface. According to the Schlier and Farns4 model of the (2 x 1) reconstruction pairs of worth’

surface atoms in each row become closer to each other,

and all of the surface atoms are relaxed inward, In this case, the overlap of p~-orbitalsbelonging to the band A increases, and they produce a band which locates A at lower energies; therefore, A becomes occupied. On the

all the dangling bond surface states from the Si(100) surface, Furthermore, as pointed out elsewhere10’12 for the Si(l 11) surface, the additional structures in the densities of states Si 18H25 are not associated with a single band due to the Si—H bond. These features are

other hand, the occupied band B of the pa-type orbitals in ideal Si(l00) rises in energy. The hydrogen chemisorption on (2 x 1)-Si(l00) occurs through pa-type

also evident when one compares the total density of states in Fig. 2 (c). Notice also that the model for the

surface therefore should not induce any structural changes, in agreement with experimental findings.

orbitals, leaving p~-bondingstates essentially unaltered. The chemisorption of hydrogen on the Si(100) (2 x 1)

REFERENCES 1.

IBACH H. & ROWE J.E., Surf Sci. 43, 481 (1974).

2.

JOHNSON K.H., J. Chem. Phys. 45, 3085 (1966); SLATER J.C. & JOHNSON K.H., Phys. Rev. B5, 844 (1972); JOHNSON K.H., SMITH F.C., Jr.,Phys. Rev. B5, 831 (1972). SLATER J.C., Adv. Quantum Chem. 6, 1 (1972); also see, SLATER J .C. & JOHNSON K.H., Physics Today 27, 34(1974). FRIEDEL J.,Adv. Phys. 3,446(1954); HAYDOCK R., HEINE V. & KELLY M.J.,J. Phys. CS, 2845 (1972). See for example, BATRA I.P. and BRUNDLE C., Surf Sci. (to be published).

3. 4.

5. 6.

PANDEY K.C. & PHILLIPS J.C., Phys. Rev. Lett. 32, 1433 (1974); APPELBAUM J.A., BARAFF GA. & HAMANN D.R.,Phys. Rev. BlI, 3822 (1975).

7.

ORTENBURGER I.B. & BATRA I.P., Bull. Am. Phys. Soc. 1120; ORTENBURGER I.B., CIRACI S. & BATRA I.P. (to be published in Phys. Rev.).

8.

APPELBAUM J.A. & HAMANN D.R.,Phys. Rev. Lett. 31, 106 (1973) and 32, 225 (1974).

9. 10,

BATRA I.P. & CIRACI S.,Phys. Rev. Lett. 34, 1337 (1975). CIRACI S. & BATRA I.P., Solid State Commun. 16, 1375 (1975).

11.

SCHLUTER M., CHELIKOWSKY J.R., LOUIE S.G. & COHEN M.L., Phys. Rev. Lett. 34, 1385 (1975).

12.

APPELBAUM J.A. & HAMANN D.R.,Phys. Rev. Lett, 34, 806 (1975).

13. 14.

HAGSTRUM H.D. & SAKURAI T., Bull. Am. Phys. Soc. 20, 303 (1975). SCHLIER R.E. & FARNSWORTH H.E.,J. Chem. Phys. 30,917 (1959).