Theory of transient build-up in avalanche transistors

It is found that an avalanche transistor biased into the negative resistance range will deliver an exponentially increasing current into a capacitor connected between the emitter and collector. For a uniform base layer of width W, minority carrier diffusion constant D, emitter efficiency γ, collector capacitor Cc, load capacitor C, and avalanche multiplication M, the current builds up as exp λ t where $\lambda = (D/W^{2}) [cosh^{-1} \gamma MC/(C+C_{c})]^{2}-\nu$ where v is the reciprocal of the minority carrier lifetime. The time required for a voltage drop from near breakdown voltage to about 89% of breakdown voltage is about W2/4D provided Cc/C < 1 and γ is nearly unity; the rate of drop of voltage is substantially equal to 2VBD/(n + 1)W2 after the voltage has dropped from near VB to below 90% VB where n is the exponent in 1/M = 1-(VC/VB)n. If the ratio of C/Cc is too small, the collector voltage will not “bottom,” i.e., drop to the base voltage; means of estimating the critical size of the capacitor are given. The analysis is based on an integral equation involving stored minority carrier charge in the base layer, which may be useful in other transient problems of transistors.