On the Variation of Junction-Transistor Current-Amplification Factor with Emitter Current

Abstract

Existing theories of the junction transistor fail to predict the very significant variation of current-amplification factor, α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cb</sub> , as the emitter current is varied. This variation has been very troublesome in power transistors, particularly at high emitter currents where the α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cb</sub> fall-off may be so severe as to limit usefulness. At low currents, α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">cb</sub> also drops off, an effect of importance in very low-power applications. By taking into account modification of the base region by the injected charge carriers, an explanation is found for the observed variation. Electric fields in the base region decrease the mean transit time for minority carriers on their way to the collector. This reduces the effect of surface recombination and increases current-amplification factor as the emitter current rises. Another effect, however, is in the opposite direction; this second effect is due to an increase in conductivity of the base material which increases the rate of volume recombination and also lowers emitter efficiency. The combination of these effects yields calculated curves which show a maximum and agree well with experiment. The work is applicable to both p-n-p and n-p-n types, and it is shown that the latter is inherently less sensitive to emitter current density.