Static V-I relationships in transistors at high injection levels

Abstract

At high injection levels the static V-I characteristics of p-n junction devices must be modified to account for nonlinear transport mechanisms and for relationships between the injected carrier concentrations and the applied voltages which differ from the familiar low-injection relationships. These carrier-concentration-voltage relationships differ in part because of ohmic voltage drops and in part because of conductivity-modulation effects. It is difficult to explore experimentally the high-level extensions of p-n junction theory in diodes because ohmic drops usually dominate the VI characteristics at high levels. However, these effects can be studied experimentally in a transistor which operates in the avalanche mode, with zero base current, because the ohmic drops can be suppressed. Experimental results are presented which support an analysis of the high-level V-I characteristics of the emitter junction of a transistor. This analysis does not predict an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e^{qV/2kT}</tex> dependence of the junction current at high levels, but yields instead an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e^{qV/(1 \pm m)kT}</tex> dependence, where m is a parameter having a value of about 0.3 in germanium, and V is the applied voltage less the ohmic drops. The plus sign applies for a p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> -n junction while the minus sign holds for an n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> -p junction. In accordance with this theory, complementary n-p-n and p-n-p transistors exhibit markedly different behavior at high injection levels.