Spectral limits for disordered semiconductors and their interfaces

A spectral limit theorem is proved for semiconducting systems without crystal periodicity, generalizing earlier theorems involving model Hamiltonians for amorphous semiconductors and substitutional alloys. The theorem treats the combined effects of substitutional chemical disorder, bond-strength fluctuations, and noncrystalline topology. The allowed one-electron spectrum is shown to be contained in the union of the one-electron spectra associated with a collection of hypothetical bulk Hamiltonians corresponding to the various bond types in the system. Applications to simple models representative of the AlxGa1-xAs-GaAs interface, the Si grain boundary, and amorphous Si and GaAs are discussed.