Theory of Microplasma Instability in Silicon

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Abstract
A statistical theory is presented to explain microplasma instability at the onset of avalanche in reversebiased silicon linearly graded and step junctions. An expression is derived which relates the turnoff probability of the microplasma to the differential resistance of the diode in its conducting state and to other physically measurable diode parameters. Measurements of the turnoff probability as a function of the pulse current are presented for several diodes and are shown to agree well with the derived theory. To explain the turnon probability, three expressions, each involving slightly different approximations, are derived for the probability that a carrier entering the breakdown region will initiate an avalanche. In each case, this probability is found to be proportional to the excess of the applied voltage over a uniquely definable sustaining voltage Vs, in poor agreement with experiment. The various mechanisms which determine the diode's differential impedance in the conducting state are discussed and approximate expressions for the contributions of each mechanism to the differential impedance are derived. Multilevel pulses, previously interpreted as indicating more than one conducting state for a microplasma, are explained in terms of parallel breakdowns of more than one microplasma.

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