The relationship between the built-in potential and the energy bands in a heterojunction device is defined using the Anderson model. Based on this model, Poisson's equation for a nonhomogeneous semiconductor device in thermal equilibrium is derived and solved analytically for the special case of a doubly intrinsic abrupt heterojunction. Several numerical methods of solving Poisson's equation for general cases are explored to find the most efficient method. The validity of the chosen numerical method is tested against both the analytical solution for a Ge/GaAs doubly intrinsic diode and recently published results from similar numerical simulation studies. A p-i-n superlattice device is then analyzed, and the resulting numerical solutions of the electrostatic potential, electric field, carrier concentration, charge density, and energy band profiles are given. These results are utilized by other simulation software which yields the resonant energy levels in the conduction band of the p-i-n superlattice and their associated probability density functions.
Brown, Harold K.
Master of Science (M.S.)
College of Engineering
Electrical Engineering and Communication Sciences
Length of Campus-only Access
Masters Thesis (Open Access)
Dissertations, Academic -- Engineering; Engineering -- Dissertations, Academic
Rollins, Norman Todd, "Numerical solutions of poisson's equation in a superlatice device" (1988). Retrospective Theses and Dissertations. 4332.