The Effects of Junction Shape and Surface Recombination on Transistor Current Gain-Part II

Previous work demonstrated the importance of surface recombination and junction shape on the transistor current amplification factor ¿ by means of a two-dimensional conducting paper analog. This is now extended theoretically and experimentally to other cases which are also of practical importance. Exact analytical solutions have been obtained for the collector-to-base current amplification factor, ¿cb, for plane-parallel (grown junction) transistors of rectangular and round cross section including surface and volume recombination. For the case in which the surface recombination velocity s is small and the volume lifetime ¿ is large, these equations reduce to s T a0cb (_ j_ f+ L) VK Ir) where K and T are geometrical constants simply related to the base width W and the cross-sectional area. The range of validity of this equation has been investigated. For the more complex geometries usually found in alloy transistors, ¿cb is found to be of the form: = Lc - L)-1 ± F(T, S)] (K T)[] where K and T are again geometrical constants. F(¿, s) is a small positive correction term which goes to zero as s approaches zero and ¿ approaches infinity. Although the constants K and T are not readily evaluated analytically, in most practical cases volume recombination can be neglected, and then By means of a three-dimensional electrolytic conductance analog, K and f(s) have been evaluated for various geometries typical of alloy junction transistors.