Nonlinear response of electron-phonon interaction inn-type nondegenerate piezoelectric semiconductors

The nonlinear response of the electron-phonon interaction in nondegenerate piezoelectric semiconductors such asn-type InSb in the presence of a dc magnetic fieldB directed along the propagation of acoustic waves has been studied by using a quantum mechanical treatment. The effect of electron scattering in solids has been taken into consideration, so the electron relaxation time cannot be neglected. The nonlinear nature of the energy band is corrected for, using the Heisenberg equation of motion. It is found that the nonlinear response is proportional to a nonlinear longitudinal conductivity tensor _zzz when acoustic waves propagate parallel to the [111] direction for both piezoelectric and deformation-potential couplings. Numerical calculations for _zzz of n-type InSb at low temperatures are presented. Results show that the nonlinear response decreases rapidly with the sound frequency, and decreases slowly with the dc magnetic field and temperature. Therefore, the electron relaxation time and the nonparabolicity of energy bands play important roles for the electron-phonon interaction due to the piezoelectric and deformation-potential couplings in the microwave region.