On the theory of DC amplification factor of junction transistors

According to Webster's phenomenological theory, the base current consists of three terms arising from 1) surface recombination 2) bulk recombination, and 3) non-unity emitter efficiency. In this paper, the diffusion equation inside the base region of an alloyed transistor is solved, and an analytic expression for the dc amplification factor is presented in terms of arbitrary bulk lifetime and surface-recombination velocity and the geometry of the transistor. The surface-recombination term depends on the distribution of the injected carriers along the emitter-base boundary, and hence, it increases as the emitter current increases on account of the base-resistance bias effect which tends to concentrate the minority carriers near the periphery of the emitter. The falloff in beta at high-emitter current is attributed mainly to an increase in the surface-recombination term, contrary to Webster's theory. A comparison with Webster's theory is made on units having the same bulk property but different surface treatments. Experimental results give strong support to the present theory.