ON THE THEORY OF INJECTION OF MINORITY CARRIERS IN p-n ALLOY JUNCTIONS

Abstract

A general theory of injection of minority carriers in p-n alloy junctions was developed by using one-dimensional model. It was assumed that the recombination rate is proportional to the density of injected carriers. Two extreme cases of low injection levels and high injection levels were first considered, and the result of which was then used as the zero-order approximation in calculating the distribution of the injected minority carriers in p-n junctions. By the method of successive approximation, an analytical expression for the relationship between the injection efficiency and the injection level (i. e. the ratio of the density of injected minority carriers to that of original majority carriers) was obtained. A similar expression for the relationship between the total current density flowing through the junction and the injection level was developed on the same basis. The results of the present theory show that for an ordinary alloy junction transistor, the injection efficiency of the emitter decreases gradually as the emitter current increases. At very highinjection levels, the injection efficiency approaches a limiting value of 1/(1+b) , where6 is the ratio of electron mobility to hole mobility. For a p-n alloy junction with very low injection efficiency, the injection efficiency is proportional to the total current flowing through the junction when the injection current is small, and itapproaches a limiting value of 1/(1+b) as the injection current becomes very large. Itwas also shown that for low injection levels, the total current flowing through a p-n alloy junction is proportional to the injection level, while for high injection levels, it is proportional to the square of the injection level.