Calculation of the internal electric field within doped semiconductors

Abstract

A detailed model for the calculation of the internal potential and electric field profile within doped semiconductors is developed from a first-principles approach and presented in this paper. The model utilizes Poisson's equation and basic Boltzmann statistics to develop a standard nonlinear Poisson–Boltzmann equation (NPBE) for doped semiconductors. The resultant NPBE links the internal electrostatic potential within the doped semiconductor to the doping concentration profile of the semiconductor device under consideration. The NPBE is solved by the application of numerical methods, is general in formulation, supporting multiple simultaneous dopant configurations, and may be applied to any semiconductor type. Calculated results of the electric field profile for various semiconductor dopant structures derived using the model are additionally presented in this paper. The electric field results predicted by the model are shown to be in excellent agreement with those found by other methods. The model may be expanded to accommodate effects involving internal substrate electron–hole pair generation (gemination) caused by photo-ionization for application to and the modeling of solar cell device structures.