A resistance-network analysis of the current gain of junction transistors

The paper describes an investigation concerning the variation of the current gain of homogeneous-base junction transistors with recombination conditions and geometrical shape, using a resistance network as direct analogue. The basic equations which govern the flow of minority carriers in a transistor with a cylindrically symmetrical shape, in the presence of both surface and volume recombination, are established in a form which is directly analogous to a resistance network arrangement as described by Liebmann. The transistor action may then be studied conveniently. In the first instance the steady-state solution has been investigated for a representative model, very much like that of the medium-frequency p-n-p alloyed-junction device, and the dependence of the current gain of the transistor on both recombination and geometrical configuration is established. A large number of measurements on the analogue for both normal and inverse operation of the transistor are illustrated by plotting the common-emitter current-transfer ratio against the various transistor parameters. Additional results showing the distribution of the surface recombination current density over the surface of the base are given. The resistance network permits the solution to be read directly off the analogue and facilitates the extension to other geometries and types of transistor.