Transient Response of Double Injection in a Semiconductor of Finite Cross Section

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Abstract
The transient response of the current to an applied voltage step is analyzed for a structure exhibiting double‐injection behavior, subject to the condition that both initial and final states are describable by the same double‐injection regime. The analysis is carried out for both the one‐dimensional case (no surface recombination) and the case of a two‐dimensional slab (surface recombination included). For the one‐dimensional case, the response is an Ohmic current step followed by an exponential decay with a time constant equal to the high level, common lifetime. For the two‐dimensional case the response is similar, except that the decay following the current step is described by a sum of exponential decays with time constants determined by the transverse modes of the system. The time constant for the longest lived mode is not equal to the effective lifetime found by Hiroto et al. for the steady‐state case, but may differ from it by as much as 23.4%. The high level photoconductive decay is also analyzed for the two‐dimensional case. Two types of initial excitation are considered, a steady state excitation abruptly terminated and a brief flash of light abruptly terminated. In both cases the light is allowed to have an arbitrary penetration depth. A comparison of the results shows that the decay from a voltage step invariably gives less interference from the higher modes and in general is a more attractive method of measuring the high level lifetime. Experimental results on a silicon p—π—n structure illustrating the above are also given.