Electronic properties of delta doped semiconductors

Semiconductors doped at high concentrations in a region with a few atomic layer thickness (10-50 Ao) are called delta-doped semiconductors. The main purpose of this thesis is to solve the Poisson equation in a delta doped region and find the potential profile and use it to solve the Schrödinger equation. The solution of Schrödinger equation provides the energy levels and the electron concentration at each level. The electrons at each level in turn effects the potential obtained from the solution of Poisson equation, the Poisson and Schrödinger equations must be solved in a self-consistent manner. The Poisson/Schrödinger equations are solved in the framework of Hartree and effective mass approximations. The solutions are obtained in a proper combination of analytical and numerical methods. From these solutions the potential profile, the energy levels, the wave functions, the electron concentration at each level are obtained in the delta doped region of the semiconductor. The dependence of these parameters on doping concentration and on the width of doped region are also investigated. The problem is solved again by taking into account the exchange interaction that is neglected in the Hartree approximation.