Solution of the Field Problem of the Germanium Gyrator

A mathematical solution is obtained of a two-dimensional boundary-value problem involving flow of electricity in a solid when Hall effect is present, it being assumed that only one type of carrier is involved and that there is no surface recombination. The solution is used to calculate the efficiency of a Hall-effect ``gyrator,'' a four-terminal circuit element which violates the reciprocity law, as function of relative electrode size, shape of boundary, and magnetic field strength. It is also shown how corrections must be applied in measurements of Hall voltage and magnetoresistance in short samples. Some of the results have been checked experimentally with fields up to 22 000 gauss. The calculations have been carried out for much higher fields as well and should prove useful in studies of materials such as indium antimonide which have higher mobilities than germanium.