DESIGN THEORY OF JUNCTION TRANSISTORS 1277 



when the unit is biased. In normal operation for the p-n-p transistor 

 shown, the emitter is biased positive with respect to the base so that a 

 current of holes is injected into the base from the emitter. The collector 

 is biased negative with respect to the base so that the holes dilTusing 

 across the base from the emitter are collected whenever they reach the 

 edge of the collector depletion layer. 



In the analysis each of the three major regions is assumed to have a 

 uniform resistivity, p; a diffusion constant for minority carriers, I), 

 which is a measure of the speed with which injected carriers will diffuse; 

 and a lifetime for minority carriers, r. This lifetime is the average time 

 which a minority carrier remains free before recombining with a majority 

 carrier. The minority carrier density in each region is assumed to have a 

 thermal equilibrium value in the absence of appHed potentials. The 

 density is increased or decreased exponentially from this value by the 

 applied potentials. The base layer is assumed to have a thickness, w, 

 which is dependent on the collector voltage Vc . An increase of collector 

 voltage increases the collector depletion region thickness, Xm , thus de- 

 creasing the base thickness. The rate at which base thickness changes 

 with collector voltage is determined by the nature of the transition 

 from base to collector. For gradual transitions, the rate of the transition 

 is important, while for abrupt or step transitions the rate of change of 

 base thickness with collector voltage is determined by the base region 

 and collector region resistivities. 



Determination of the diffusion currents from minority carrier density 

 gradients requires determination of minority carrier densities everywhere 

 in the three principal regions of Fig. 1. These are obtained by solving a 

 continuity equation for carrier flow in each region, subject to the applied 

 junction potentials and other assumptions described above. It must be 

 pointed out that, in normal operation, there may be a significant flow 

 of electrons to the emitter and from the collector in the p-n-p transis- 

 tor of Fig. 1. Small signal ac diffusion currents are determined by as- 

 suming small signal variations of the junction voltages and discarding 

 all but first-order ac terms from the diffusion currents. 



Results of the analysis are given in Section 3.0, and the analysis 

 appears in Appendix A. 



24 Depletion Layer Capacitances 



In a p-n junction with no bias potential applied, there is a tendency 

 for holes to diffuse into the n-region and for electrons to diffuse into the 

 p-region. This creates a slight unbalance of charge in the two regions 



