关于p-n合金结中少数载流者的注射理论

本文用一维模型计算了p-n合金结中少数载流者的一般注射理论。这里假设复合率是与注入载流者的密度成正比。首先,我们讨论了大注射和小注射的两种极端情况,这样得到的结果被用作零级近似解来计算p-n结中注入少数载流者的分布情况。用逐步近似的方法我们得到了注射效率和注射强度(即注入少数载流者的密度与原有多数载流者的密度之比)间的解析关系。在同样的基础上也得到了通过结的总电流密度和注射强度间的类似关系。这理论的结果表明;对一个平常的合金结晶体三极管来说,当发射极电流增加时,发射极的注射效率逐渐下降。在很大的注射强度下,注射效率趋近于极限值1/(1+b),其中b是电子迁移率与空穴迁移率之比。对一个具有很低注射效率的p-n合金结来说,在注射电流小的时候,注射效率是正比于通过结的总电流;当往射电流很大时,注射效率趋近于极限值1/(1+b)。理论结果还表明,在小注射情下,通过p-n合金结的总电流是正比于注射强度;而在大注射情况下,它是正比于注射强度的平方。

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

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.