Microwave Hall measurements in the intermediate conductivity regime using a bimodal cavity

We study the Hall signal which arises from the resistive unbalance of a bimodal microwave cavity when a sample sits in a magnetic field. When the sample conductivity exceeds a certain value determined by its depolarization factor, screening currents are dominant and the simple expressions used by earlier investigators are no longer valid. We suggest new equations using the samples' depolarization factors which are analogous to the quasistatic approximation for cavity perturbation techniques. Experimental tests of these equations are carried out with six n-type Si samples with resistivities varying from 300 to 0.1 Ωcm. A systematic variation of the measured Hall mobility with resistivity is found in agreement with published dc values. However, our values are consistently 40% higher. The change in sign of the Hall signal when the samples screening currents dominate the induced currents is experimentally confirmed. We also discuss two major defects which prevent ideal balancing of the cavity and suggest corrective measures.