Abstract: Electronic structure of Si and Ge surfaces—clean and with chemisorbed layers
Authors: Appelbaum Joel A. , Hamann D. R. 
Published: July 2002

Practical techniques have been developed for performing self−consistent calculations of the electronic structure of solid surfaces. The method exploits the fact that the disturbance produced by the surface is significant only in the first few atomic layers, and that beyond this the potential may be assumed to be identical to that of the bulk solid. The charge density in the surface region is calculated by numerically solving Schroedinger’s equation for the surface region tails of the bulk wavefunctions and for bound surface states. The self−consistent surface region potential is constructed using a fitted model potential for the ion cores, the exact Hartree potential, and a local approximation for the exchange and correlation potential.
The calculations outlined above have been carried out for the Si(lll) surface. An inward relaxation of the surface atom plane of 0.34 Å is suggested by empirical chemical considerations, and the consequences of this and several other amounts of relaxation were explored. In all cases, a band of surface states was found within the absolute energy gap whose charge has a clear ’’dangling bond’’ character. Its shape was dependent on relaxation, going from sp3 to pz with increasing relaxation. A major qualitative difference found in going from 0.17 to 0.34 Å was the appearance of two additional bands of surface states below the valence bands and in internal gaps. These states are clearly identified with the strengthened bonds between the first and second layers, and contribute structure to the surface density of states, which has recently been verified in spectroscopic measurements. The calculated workfunction and surface Fermi level pinning are in excellent agreement with experiment.
Similar calculations have been carried out for Ge(lll). The main difference from the Si results is a change in the nature of the energy vs parallel momentum relation for the dangling bond surface state. A second energy minimum appears which has a charge distribution that is not dangling bond−like, and that could participate in chemisorption bonds to second layer Ge atoms.
The theoretical methods employed are also suitable for treating ordered adsorbed overlayers. H chemisorbed on Si(lll) has been studied, and a single fully occupied band of surface states has been found to lie in internal energy gaps of the valence band, 4−7 eV below the valence band maximum. The charge density contributed by this band is concentrated in the Si−H bond. Spectroscopic structure associated with this band of surface states has been seen experimentally. Another chemisorption system studied was Al substitutionally adsorbed on Si(lll), one of several structures which has been observed for this system. Since Al in this position has its valence requirements satisfied, a filled−band (saturated bond) picture might have been anticipated. Instead, three partially occupied bands of surface states have been found, indicating a metallic surface. This is especially remarkable considering that the Al atoms are 3.84 Å apart, compared to 2.86 Å in Al metal. A consequence of this result is the possibility that adsorbed metal films only a few layers thick may provide an adequate model of semiconductor metal interfaces which is suitable for study on an atomic scale by our methods.