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

Abstract

k,T = Boltzmann's constant and absolute temperature. P o , P v , B o , B v = Network points and corresponding 'cells'. Sv 0 , 8S Q = Volume and area of B o . G v , G o , G s , C o = Conductances and capacitance of analogue components, a, jS, y = Constants of proportionality.m,l = Scaling coefficients. 00 ^ i _ steady-state, and small superposed signal solutions. / 0 , i 1 , 7°, 7 1 = Transistor and analogue currents corresponding to these solutions. Y c , Y b = Admittances of a.c. measuring bridge. SUMMARYThe 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 a 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. 1 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 mediumfrequency 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. LIST OF PRINCIPAL SYMBOLSa cb> u ce> a s> °^ -Current ratios. p e , p b = Resistivities of emitter and base. A»e> L pb = Diffusion lengths of electrons in emitter and holes in base. n c> Pc -Electron and hole concentrations in collector. Pm Pp -Mobilities of electrons and holes. D, D p = Diffusion constant for holes. s, T, r b = Surface recombination velocity and volume lifetime. A e , A c = Areas of emitter and collector. Af, A s = Total and effective areas of recombination surface. £, r) = Radial and axial co-ordinates. £e> £c -Radii of emitter and collector. Ve> Vc -Depths of penetration of emitter and collector. W, W = Junction separation (base width) and wafer thickness. A, B, . . . G = Geometrical code labels. e = Hole charge. t,t -Time and time measured on analogue. p,p = Hole density and its equilibrium value. (f>, (f> = Hole charge density and its equilibrium value. ifj = Excess hole charge density. j , v = Hole current density and hole flow velocity. i, I = Transistor current and analogue current. V e , V c = Potentials of emitter and collector with respect to the base. V = Potential on the analogue.