Modeling semiconductor devices with position-dependent material parameters

An overview of the transport model describing electron and hole motion and density in solids with position-dependent band structures is presented. This includes materials with nonuniform composition such as graded heterojunctions, and devices with highly doped regions such as the emitter region of bipolar transistors and solar cells. Hot-electron and quantum mechanical effects are not considered. Effects due to carrier degeneracy, changes in the energy-band edges due to spatial variations in electron affinity and bandgap, and spatial variations in the density of states produce terms in the carrier- and current-density equations in addition to those found in the conventional Shockley model. These new terms are discussed. The general energy-band diagram relating the electrostatic potential, electron affinity, and bandgap of a nonuniform semiconductor is given. The current densities are expressed in terms of gradients of quasi-Fermi level and the carrier densities in terms of normalization integrals. The concepts of generalized drift and diffusion are discussed. The transport equations applicable to parabolic bands, nondegenerate material, and the rigid-band model are presented. Various device applications are given. Limitations in the underlying theory and key approximations used in device analysis are discussed