I Conditions at a reverse-biased p-n junction in the presence of collected current II Effects of modified collector boundary conditions on the basic properties of a transistor

Abstract

An abrupt p-n junction, such as occurs at the collector junction of an n-p-n transistor, is considered. The ratio of n- to 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 distribution n within the transition region is investigated as a function of the applied reverse bias V_c , and of the minority carrier electron 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 w_t, used as collector boundary conditions in the analysis of transistor operation, are shown to be current-dependent. 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_p, the transition region is a 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 w_t ∝ V_c^(l/2). For high injection level, hen n >> p_p, the transition region is essentially an accumulation region, and conditions of space-charge-limited current flow are established for which n_c ∝ J^(2/3) and w_t ∝ V_c^(2/3/(J^(l-/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_c ∝ J , w_t ∝ V_c^(l/2/J^(1/2)) at high injection. 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 are given for various junction voltages and injected currents.