A Modification of the Theory of the Variation of Junction Transistor Current Gain with Operating Point and Frequency†

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Abstract
A modified solution is discussod of the continuity equation for minority carrier flow in junction transistors, obtained by adhering strictly to the space-charge neutrality approximation and applying alternative boundary conditions which differ from those usually taken principally in that a finite minority carrier density is permitted at the collector. An extension of the modified analysis to a.e. conditions is given, and a comparatively short working formula for the intrinsic short-circuit a.c. gain is determined as a function of operating point and frequency. The common-base cut-off frequency f αs evaluated, and the maximum in the variation of the f αwith emitter current, which has been observed experimentally, is associated with reduced d.c. emitter efficiency at high levels and is related to the corresponding fall-off in d.c. alpha. Experimental results are presented to show that, for a transistor with given cut-off frequency, both the electrical and metallurgical base widths are smaller than is normally supposed, and yet ∂W/∂V is larger than normally supposed as evidenced by measurements of punch-throught voltage V p . A theoretical explanation of both effects is offered.