Surface states of ternary semiconductor alloys: Effect of alloy fluctuations in one-dimensional models with realistic atoms.

Abstract

Calculations of the local electronic surface densities of states (DOS) of semi-infinite one-dimensional chain models for ternary semiconductor alloys are presented to illustrate the effects of alloy fluctuations on semiconductor surface states. The atoms are modeled with a basis set of s and p levels which produces the correct level mixing and energy-band dispersion.Alloys with randomly occupied cation sites are considered. The embedded-cluster approach is employed to incorporate the alloy effects on states localized near the chain end. The cluster calculations are performed by including the contributions from all possible configurations of a cluster at the end of the semi-infinite chain. These results are compared with results obtained using the coherent-potential approximation (CPA) and the virtual-crystal approximation (VCA). The CPA is implemented with one self-energy appropriate for all cation sites in the bulk and different self-energies for each cation site near the surface. In practice the most accurate CPA results can be obtained by treating only the four cation sites nearest the surface differently from the bulk.Examples which are typical of the weak and strong alloy limits are considered. In the first limit the alloy constituents are similar direct-gap semiconductors. In the strong alloy limit one constituent has an inverted band structure, as HgTe does, and the other is a normal semiconductor such as CdTe. The cluster calculation for the surface DOS is sensitive to fluctuations in the environment local to the chain end. In the weak alloy limit, the surface DOS in the band gap has a bimodal distribution with the peaks located near the energies of the surface states of the constituents. In the strong alloy limit, the HgTe-like constituent of the HgCdTe-like alloy has no surface states while the surface states of the CdTe-like constituent lie above the alloy band gap.As a consequence, the alloy surface DOS has a resonance structure above the band edge and band tailing below the edge. The CPA reproduces qualitatively the structure of the cluster calculations. The VCA predicts well-defined surface-state peaks in the band gap. These peaks are related to the average of the bimodal distribution in the weak alloy limit but cannot be consistently identified with any resonance structure or band tailing in the strong alloy limit.