Effects of Modified Collector Boundary Conditions on the Basic Properties of a Transistor

An abrupt p n junction, such as occurs at the collector junction of an n-p-n transistor, is considered. The ratio of nto p-region conductivity is taken to be very high, so that the transition region is restricted almost entirely to the p-region. The electron density distri bution n within the transition region is investigated as a fUnction of the applied r everse bias V , and of the minority carrier electron c current density J which is injected into the transition region from the neutral p region . It is shown that significant departures occur from the conventional solutions in which the presence of current is neglected. In particular , the electron density n c at the plane of injection and the transition region thickness wt' used as collector boundary conditions in the analysis of transistor operation, are shown to be currentdependent . Two cases are considered . In Case I, applicable to transistors with an epitaxial layer under the collector, the electron velocity is assumed much less than the limiting drift velocity. For low injection level, where the minority carrier density n is everywhere less than the equilibrium majority carrier density p , the transition region is p essentially a depletion region and the injected electrons move in an electric field determined uniquely by the applied voltage. It is shown that n ~ J and wt ~ V l/ 2• For high injection level, when n >> p , c c p the transition r egion is essentially an accumulation region, and conditions of ~ space-charge-limited current flow are established for which nc ~ J2/3 and wt ~ Vc 2/3;Jl-/3. In Case II, applicable to most alloy and diffused-base transistors, the electron velocity is assumed equal to the limiting drift velocity throughout the transition region. Mobile carrier depletion at low injection again gives way to accumulation at high injection . The functional relationships remain as for Case I at low injection, but become n ~ J , w ~ V l/ 2;~/2 at high injection . c t c Semi quantitative and detailed quantitative treatments are developed, and normalized graphs of the minority carrier density as a function of distance within the transition region a r e given for various junction voltage s and injected currents .