On the formation of periodic electric field domains in p-Si/SiGe quantum cascade structures

Biased semiconductor quantum well cascade structures, as are nowadays used in intersubband infrared photodetectors and lasers, are well known to be susceptible to the formation of electric field domains. The homogeneous electric field in a structure is broken, due to charge redistribution over individual wells and the appearance of the associated space-charge contribution to the potential. In this work we consider the formation of stationary periodic domains in p-type Si/SiGe cascade structures. Hole transport is described via scattering between quantized subbands in subsequent wells, as calculated using the 6/spl times/6 k.p method which accounts for the full anisotropy of heavy hole and light hole subbands. The scattering mechanisms taken into account are deformation potential (acoustic and optical phonons), alloy disorder, and carrier-carrier scattering. In order to find the possibility of domain formation the hole scattering rates between all pairs of states in subsequent wells in a homogeneous cascade are calculated, as a function of the electric field, taking the carrier heating (thermal self-consistency) into account. These are then used (via interpolation) to solve a system of rate equations for the subband populations in each quantum well, coupled with the discretized Poisson equation. In order to avoid use of contact boundary conditions, for which no experimental data is presently available, we use periodic boundary conditions, in which the electric field distribution in a long homogeneous cascade is assumed to break into an arbitrary number of periodic segments. This is a generalization of the period-doubling model described in (Ryzhii et al. (2000).