Hot-Electron—Phonon Interaction in the Nonparabolic Conduction Band of Degenerate InSb at 4.2 K

Adopting the Kane model of the nonparabolic conduction band of InSb, calculations of the energy-loss rates of the electrons to acoustic modes via deformation potential and piezoelectric coupling and to polar optical modes are performed. Use is made of matrix elements which take into account p-function admixture and static screening of the electron-phonon interaction. The applicability of this theoretical approach to experiments at 4.2 K in strongly degenerate n-InSb is examined. Measurements of the electric-field-dependent amplitudes of the Shubnikov---de Haas effect with B∥j are used to determine the dependence of the electron temperature on the electric field up to 1.7 V/cm. Theoretical values of the energy-loss rates are found on averaging over the Fermi distribution at an elevated electron temperature Tₑ. A combination of deformation-potential scattering and piezoelectric scattering accounts for the energy-loss rate below Tₑ=12 K. A value of the deformation-potential constant of 6.9 ±{} 0.4 eV is used to fit the calculated energy-loss rates to the experimental data. Above Tₑ=24 K, polar-optical-phonon scattering is the dominant mechanism. Between 12 and 24 K, there remains a difference between experiment and theory which is attributed to a two-phonon-scattering process.