"We develop a selfconsistent solution of the Schroedinger and Poisson equations in semiconductor heterostructures with arbitrary doping profiles and layer geometries. An algorithm for this nonlinear problem is presented in a multiband k.P framework for the electronic band structure using the finite element method. The discretized functional integrals associated with the Schroedinger and Poisson equations are used in a variational approach. The finite element formulation allows us to evaluate functional derivatives needed to linearize Poissonâ€™s equation in a natural manner. Illustrative examples are presented using a number of heterostructures including single quantum wells, an asymmetric double quantum well, p-i-n-i superlattices and trilayer superlattices."
Worcester Polytechnic Institute
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Moussa, Jonathan Edward, "The Schroedinger-Poisson Selfconsistency in Layered Quantum Semiconductor Structures" (2003). Masters Theses (All Theses, All Years). 1094.
heterostructure, semiconductor, quantum engineering, self consistency, Semiconductors, Poisson's equation, Quantum theory