On the Theory of the A-C. Impedance of a Contact Rectifier

HE a-c. impedance of the rectifying contact between a metal and a semiconductor is measured by superimposing a small a-c. current on a tl-c. bias current. It is generally recognized 1 that an equivalent circuit consists of a parallel resistance and capacitance in series with a resistance as shown in Fig. 1. The parallel components represent the impedance of the barrier layer itself and depend on the d-c. bias current flowing. The series resistance is that of the body of the semiconductor. It has been shown theoretically by Spenke 2 that under quite general conditions the parallel capacitance and resistance are independent of frequency. Unfortunately Spenke's proof is highly mathematical and is also not readily available. The derivation of the impedance relations which is presented here is in some ways more general and gives more physical insight into the problem. The method of analysis which is used is similar to that employed by Miss C. C. Dilworth 3 for the d-c. case. Except for some obvious differences in sign, the theory is the same for n- and p-type semiconductors. 4 We give the theory for the latter because the signs are a little simpler for positively charged holes than for negatively charged conduction electrons. Before the discusssion of the theory of the a-c. impedance, a brief outline of Schottky's theory of the barrier layer will be given. A rough schematic energy level diagram, based on Schottky's theory of the barrier layer at a contact between a metal and a />-type semiconductor, is illustrated in Fig.