Energy Relaxation Mechanisms in n-InSb at Low Temperatures

Experimental results for the energy relaxation time in n-InSb as a function of electron concentration in the temperature range 1.5–20°K are presented. These values were determined by measuring the response times of bulk InSb mixers. Analytical results for the energy loss rates to the acoustic modes via deformation potential scattering and piezoelectric scattering are given. The effects of degeneracy and screening are considered. Good agreement between theory and experiment is obtained for the low-concentration material (1.5×1013 cm−3) with a piezoelectric constant e14 equal to 3.0×104 dyn1/2/cm and a deformation potential constant E1 less than or equal to 5.0 eV. However, no single set of values for e14 and E1 accurately describes the temperature dependences of the energy relaxation time for all electron concentrations. The usual polar optical phonon scattering treatment is shown to be adequate; however, a careful comparison of the temperature dependence of the energy relaxation time above 14°K strongly suggests that energy relaxation occurs through the simultaneous emission of two acoustic phonons.