The Adiabatic Hall Effect in Semiconductors

Abstract

Calculations are carried out to determine the relative difference between the isothermal and adiabatic Hall coefficients of typical semiconductors. The isothermal Hall effect requires a constant temperature in the plane of the electric current flow and Hall field, whereas the adiabatic Hall effect is defined by the alternative requirements that the temperature gradient be zero in the direction of the electric current flow and the heat current be zero in the direction of the Hall field. The relative difference $\frac{(R_a-R_i)}{R_i}$ is studied for the (1) classical impurity semiconductor, (2) degenerate semiconductor, and (3) classical semiconductor at high temperatures. For the thermal and electrical conductivities characteristic of silicon and germanium, the relative differences are found to be of the order one percent or less, thus indicating that it usually is not necessary to distinguish between the isothermal and adiabatic conditions in interpreting measured Hall values. Tabulated values are presented in such form that the relative difference may be readily calculated for any semiconducting sample of known electrical conductivity, thermal conductivity, and variation of carrier density with temperature.