Theory of Current-Carrier Transport and Photoconductivity in Semiconductors with Trapping

Abstract

Fundamental differential equations are derived under the unrestricted approximation of electrical neutrality that admits trapping. Extension is made for applied magnetic field. The transport equations derived hold without explicit reference to detailed trapping and recombination statistics. Modified ambipolar diffusivity, drift velocity and lifetime function apply in the steady state. The same diffusion length is shown to hold for both carriers, and a general “diffusion-length lifetime” is defined. Atass-action statistics are considered for cases of (one or) two energy levels. Certain “effective” — rather than physically proper — electron and hole capture and release frequencies or times that apply to concentration increments are defined. Criteria are given for minority-carrier trapping, recombination and majority-carrier trapping, and for “shallow” and “deep” traps. Applications of the formulation include: the diffusion-length lifetime for the Shock-ley-Read electron and hole lifetimes; linear and nonlinear steady-state and transient photoconductivity; negative photoconductivity; the photoconductive decay observed by Hornbeck and Haynes in p-type silicon; the photomagnctoelcctric effect; and drift of an injected pulse. Photomagnetoeleclric current is found to be decreased by minority-carrier trapping, through an increase in diffusion length. A simple general criterion is given for the local direction of drift of a concentration disturbance. With trapping, there may be “reverse drift,” whose direction is normally that for the opposite conductivity type, and also local regions of carrier depletion that may extend in practice over appreciable distances.