The equivalent circuit model in solid-state electronics—III: Conduction and displacement currents

Abstract

The equilibrium and nonequilibrium equivalent circuits of a single and a multiple energy level recombination centers were developed in parts I and II. This paper extends the analysis to include the nonequilibrium case arising from a d.c. steady state conduction current in the semiconductor structure. Application is made to minority carrier small signal transport in both homogeneous and heterogeneous semiconductors at low steady state levels ( P « N in n- type sample) . Samples containing p- n junctions are not included but the effect of static, built-in electric field on the signal propagation is considered. In an extrinsic sample, it is shown that the nonequilibrium equivalent circuit is identical to the equilibrium case for considering carrier trapping, recombination and generation at the defect or impurity centers if the recombination conductances and capacitances are defined in terms of the steady-state carrier concentrations. The conditions on the properties of the imperfection centers and the frequency range in which trapping, recombination or generation event dominates at the centers are discussed in detail. It is shown that the effective small-signal minority carrier lifetime, τ p in n-type semiconductor, is a complex variable due to the charge storage or trapping effect at the centers. In addition, τ p is positional dependent due to the spatial variation of the steady state carrier concentrations. The small-signal lifetime, τ p , is substantially different from the steady state lifetime τ pSS which is commonly used in high-frequency, lumped-model device analysis. For strongly extrinsic samples with low concentration of recombination centers, the usual approximation, τ p ⋍ τ pSS ⋍ τ p0 = 1/c pN TT , is valid. The lump model approximation to a specimen of length W is rigorously derived for minority carrier transport. It is shown that the commonly used stored-charge lump model is valid only at low frequency and zero recombination when the sample is geometrically divided into two or more lumps. For finite recombination, the effective length of each lump is shorter than at zero recombination and the sum of the length of each lump is less than the physical length of the sample.