Nonlinear Galvanomagnetic Effect ofn-Type InSb in the Quantum Limit

Nonlinear galvanomagnetic effects in $n$-type InSb in the quantum limit were studied, using uncompensated samples with an impurity concentration of 1.1×${10}^{14}$ atoms/${\mathrm{cm}}^3$. The nonlinear characteristics observed at 1.5°K and in transverse magnetic fields above 2 kG are caused by the heating of conduction electrons under conditions where the frequency of collisions with ionized impurities is much larger than that with acoustic phonons. The ratio of the frequency of collision with ionized impurities to that with acoustic phonons is about 4×${10}^4$. The carrier heating begins to have a large effect near the electric field $E_1$, which is given by ($\frac{\mathrm{sB}}{c}$)${\left(\frac{{\tau }_{\mathrm{im}}}{{\tau }_{\mathrm{ph}}}\right)}^{\frac{1}{2}}$. The value of $E_1$ at 10 kG is about 0.1 V/cm. The electric field $E_2$ which raises the electron energy so that quantum conditions are not satisfied is proportional to $0.11B^{\frac{1}{2}}{\alpha }^{\frac{1}{2}}{E}_1$ where $\alpha$ is about 4. Observations on compensated samples, where freeze-out effects are seen, and on samples of greater impurity concentration, where Shubnikov-de Haas oscillations are seen, are also discussed.