Generalized equations for the steady-state analysis of inhomogeneous semiconductor devices

Abstract

The generalized equations for the study of the steady-state charge transport in inhomogeneous semiconductor devices are reviewed and extended to take into account the effects of strong electric fields. Inhomogeneous semiconductors are assumed to have the position-dependent band structure which may occur in heterojunctions, graded-bandgap, and nonuniformally doped semiconductors. The generalized equations for the electron and hole current densities are derived by using the exact solution of the Boltzmann transport equation in relaxation time approximation. In semiconductors with parabolic band structure, cubic symmetry and wave-vector-independent relaxation time, these equations reduce to useful form for the modelling of semiconductor devices. The generalized expressions for the electric current densities and nonequilibrium electron and hole densities are expressed in the conventional form used for nondegenerate semiconductors at constant temperature. As a application of these generalized equations a general expression for the photovoltage of solar cell is derived. It is shown that in addition to already known sources of the photovoltage, obtained from the first-order solution of the Boltzmann transport equation, the photovoltage can also arise from the gradients of both the photoelectric field, and the equilibrium densities and mobilities of electrons and holes.