Determination of semiconductor resistivity by microwave measurements

Direct measurement of the resistivity of semiconductors presents problems which arise from minority-carrier injection at the contacts and the nonohmic behaviour of the contacts. In order to avoid these problems, the resistivity may be measured by microwave methods. The approach presented here was evolved for obtaining the resistivity from the measurement of voltage-standing-wave ratio of a parallel-faced semiconductor sample placed across the open end of a waveguide and backed by a highly conducting surface. The range of sample thickness for which the standing-wave ratio can be measured accurately has been computed for both germanium and silicon samples, of various resistivities, over a wide range of frequency at X and Q bands. Microwave measurements on samples of germanium and silicon of known doping levels have been carried out and crosschecked by direct measurement, using the 4-probe method. A simple empirical rule is given for obtaining the resistivity of any sample of germanium or silicon, of given thickness, which provides a perfect match to waveguide impedance. Conversely, when the order of resistivity is known, the sample thickness which gives a reasonably low standing-wave ratio, at a particular frequency, can be deduced.