Optical Absorption Due to Space-Charge-Induced Localized States

Abstract

A self-consistent model of the space-charge potential in narrow, degenerate accumulation regions at a planar semiconductor interface is constructed and applied to evaluate the binding energies and wave functions of quantized, localized states for motion normal to the interface. The model attributes the space-charge potential entirely to charge trapped in the two-dimensional energy bands associated with the localized states. Expressions are derived for the contributions to the absorption coefficient due to vertical transitions among the two-dimensional bands and due to interband transitions in which either the initial or final state is localized near the interface. The results of numerical calculations are presented for $n$-type accumulation regions in GaAs and at the (100) surface of silicon. Experimental observation of the structure in the absorption coefficient at infrared frequencies appears to be practical, and would provide a direct observation of quantization effects in narrow accumulation or inversion channels at semiconductor surfaces.