Determination of Energy Relaxation Time of Hot Carriers in n-Type Germanium from Measurements of Millimeter-Wave Complex Conductivity

A formula for calculating the electron temperature TO and the energy relaxation time τe from the measured values of microwave complex conductivity is derived from the momentum and energy transport equations. This formula is applicable to the semiconductors of one-valley model even when the usual assumptions such as ωτm1 and (TO-TL)/τedτe/dTO1 are not valid, where τm and TL are the momentum relaxation time and the lattice temperature, respectively. The microwave measurements for n-Ge are also carried out at frequencies of 33.73 GHz and 67.5 GHz, and τm, τe and TO as a function of applied dc field are evaluated at 300 K and 78 K. The energy relaxation time in n-Ge is of the order of 10-12 sec and τe(300 K)<τe(78 K). The quantity ωτe is found to be large enough to cause strong relaxation effects. It is to be noted that τe and TO are obtained at 78 K where the relation ωτm≥1 holds.