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An experimental and theoretical investigation of the statistics of avalanche breakdown in silicon Drews, Reinhold Eldor

Abstract

Measurements are made on Si p - n junctions under reverse bias in the unstable avalanche breakdown region to determine the statistics of the current pulses, and their effect on the measured mean current - mean voltage characteristics. It is found that the slope and shape of the measured mean current - mean voltage is not unique, but depends on the external resistance in series with the power supply. The mean current - mean voltage characteristics are also found to display turnover, with the voltage at turnover and the magnitude of the maximum negative resistance both increasing with increasing resistance R. Measurements are also made to determine the relation between the current pulse amplitude I₁ and the voltage V₁ across the diode during the avalanche. The results show that over the range where data are available, a linear relation exists between reverse voltage and current pulse amplitude. The intersection of this line with the voltage axis is defined as the breakdown voltage V[subscript B], and its slope is the conductance denoted by g. A simple model consisting of a random switch in series with a two terminal device having the property that for V₁ < V[subscript B], I₁ = 0 and for V₁ > V[subscript B], I₁ = g(V₁- V[subscript B]) is proposed. An avalanche initiation transition probability which increases monotonically with increasing voltage in excess of V[subscript B], and an extinction transition probability which decreases monotonically with increasing excess voltage are postulated. The experimentally derived probability functions satisfy the chosen theoretical functional dependence on excess voltage to within experimental error. Assuming that the "switching" process is Markoffian, an expression for the fraction of the time during which the avalanche occurs is derived. Using this relation and the pulse amplitude data, a theoretical mean current - mean voltage characteristic is obtained which is in good agreement with the experimental curve. The predicted mean pulse rate curve is also experimentally verified. Illumination experiments show that the initiation transition probability is directly proportional to the number of carriers entering the avalanche region; the discharge probability for an electron entering the avalanche region is independent of illumination and carrier density in the breakdown region. The apparent predominance of a form of "surface leakage" in the reverse current makes it impossible to obtain data regarding the discharge probability per incoming electron from temperature variation experiments. Measurements of the spectral density of the current fluctuations over a wide range of frequency confirms the simple form S[subscript I](ω) = S[subscript I](0) / (1 + ω²τ²) associated with a Markoffian process.

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