Decay of injected electron-hole plasmas in p-type InSb

William P. Robbins, Betsy Ancker-Johnson

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The decay of high-density (4×1014-1012 cm -3) injected electron-hole plasmas in pure p-InSb (p 0≈1014 cm-3) at 77 K is investigated in detail by means of a double-pulse technique that determines the decay of the plasma conductivity. The decay curves show two distinct modes: a high-density mode (>1013 cm-3) characterized by rapid decay and a low-density mode (<1013 cm-3) of relatively slow decay. The high-density mode is dominated by electrons and lasts for a period of time ranging from several hundred nanoseconds to only a few tens of nanoseconds depending on sample size. The effective time constants in the high-density mode decrease as the plasma density is reduced. This is true whether the reduction is accomplished by letting decay proceed in time or by starting decay at a lower initial density. This trend is observed independent of sample cross section and surface conditions, factors that do affect, however, the magnitude of the time constants. An electron trapping mechanism in the sample bulk accounts for this density-dependent effective plasma lifetime. The maximum high-density lifetime allowed by the trapping mechanism is T∞=0.9 μsec (accurate to within a factor of 2), but the observed time constants are generally smaller because of surface recombination. Since the measurements show no evidence of hyperbolic decay, a characteristic of radiative recombination, and since the theoretical radiative lifetime is much larger than the measured lifetimes, it is concluded that radiative recombination is not important in this decay process. When the low-density mode controls, the shape of the decay curves becomes independent of the initial plasma density. All curves in a family obtained from a sample of given size and surface condition have the same time constant. In the low-density mode the plasma is a one-component plasma composed of holes, the electrons having been bound in traps or returned to the valence band. In large cross-section samples (≥1×1 mm2), the holes decay with the well-known hole lifetime, 1-2 μsec. In both decay modes, surface recombination must be considered. This mechanism causes the measured time constants to be less than would be predicted on the basis of bulk recombination alone, and, in addition, it causes the measured lifetimes to decrease as the sample size is reduced or when the surface recombination velocity of small samples (<0.4×0.4 mm2) is increased. In the high-density mode the observed dependence of the initial time constant on the sample size is in agreement with an approximate theoretical treatment of surface recombination. This work, both theory and experiment, yields a value of the ambipolar diffusion length of 0.14 mm.

Original languageEnglish (US)
Pages (from-to)5776-5791
Number of pages16
JournalJournal of Applied Physics
Issue number13
StatePublished - 1971


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