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. Applied magnetic field is taken into account. The general transport equations derived hold without explicit reference to detailed trapping and recombination statistics. Modified ambipolar diffusivity, drift velocity, and lifetime function, which depend on two phenomenological differential "trapping ratios," apply in the steady state. The same diffusion length is shown to hold for both carriers, and a general "diffusion-length lifetime" is defined. Mass-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, and a restriction from detailed balance to which they are subject is derived. Found widely useful is "capture concentration," the concentration of centers at equilibrium that are occupied times the fraction unoccupied. 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 corresponding to the Shockley-Read electron and hole lifetimes, and that for recombination centers in the presence of (nonrecombinative) traps; linear and nonlinear steady-state and transient photoconductivity; the photomagnetoelectric effect; and drift of an injected pulse. The small- and large-signal nonlinearities that may occur with saturation of deep traps provide a single-level model for superlinearity. Photomagnetoelectric 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. With solutions of one type obtained for drift of an injected pulse, multiple trapping ultimately results in Gaussian mobile-carrier distributions which spread as if through diffusion and which drift at a fraction of the ambipolar velocity. With solutions of another type, related to reverse drift is the occurrence of local regions of mobile-carrier depletion which may in practice extend over appreciable distances.