The effect of interface roughness on multilayer heterostructures

Semiconductor devices which utilize the quantum confinement of charge carriers inherently employ material layers thin enough that even monolayer interface roughness has an effect on performance. We present a method for including the effect of interface roughness on the calculation of electron energy levels and wavefunctions by solving Schrödinger's equation across the interface between semiconductor layers. Interface roughness is approximated by considering a supplementary interface in addition to the idealized perfectly flat interface. The position of the second interface is considered to be a probabilistic distribution with a mean corresponding to the position of the perfect case. Using Green's theorem and the appropriate reciprocity relations, we deduce a correction to the reflection and transmission probabilities of an electron incident upon a rough material interface. The procedure is presented in terms of a transfer matrix algorithm to facilitate use in existing electron reflection transmission probability models. Examples are given of the calculation of the effect of interface roughness in resonant tunneling diodes and multiquantum barriers. We also discuss how this model is applicable to a range of physical mechanisms that result in roughness at the interface of two semiconductor materials.