Effects of modified collector boundary conditions on the basic properties of a transistor

Abstract

Effects due to modified collector boundary conditions in an n-p-n alloy-junction transistor are investigated. The modified boundary conditions differ from those conventionally employed in that the minority carrier density n c at the base side of the collector transition region increases with collector current J, and the transition region thickness w t decreases with increasing collector current when high-level injection into the collector transition region occurs. One of the two major objections to the conventional assumptions, namely that zero carrier density at the collector junction would require infinite carrier velocity, is thereby removed. The particular performance properties examined are the collector current J vs. base-emitter voltage V transfer characteristic, and the d.c. current gain β vs. collector current J characteristic. Derivation of these two characteristics is first reviewed for the conventional collector boundary conditions, partly as a tutorial exposition of the charge-control method of analysis, and partly as a foundation for the following derivations with the modified collector boundary conditions. It is shown that the second major objection to the conventional assumptions, namely that charge neutrality would not be maintained in the “neutral” base region at high-level injection, is eliminated in the modified solution. The modified solution predicts that the J vs. V and the β vs. J characteristics differ from the conventional results by only small degrees which, in a practical transistor, will certainly be masked by many effects not represented in the simple model considered. It is concluded, therefore, that the conventional analysis and results do in fact predict with good accuracy the performance of a transistor, within the limitations of the model, and that the major benefit of the modified collector boundary conditions is to remove two untenable assumptions and restore confidence in the conventional analysis.