Analysis of the lattice thermal resistivity due to the presence of electrons at low temperatures: Application to phosphorus-doped Ge

The temperature-dependence of the extra lattice thermal resistivity of a doped sample due to the presence of electrons has been studied at low temperatures for the first time by analysing the extra lattice thermal resistivity due to electrons of five samples of phosphorus-doped Ge having different carrier concentrations in the range 1.2×10²³–1.1×10²⁴ m^?3 in the temperature range 1–5 K. The variation of the extra lattice thermal resistivity of a doped sample due to electrons with the parameters η^* (the reduced Fermi energy),m ^* (the density of states effective mass),E _D (the deformation potential constant) andn (the carrier concentration) which are responsible for the electron-phonon scattering relaxation rate has also been analysed for the first time in the present study. A distinction has been made between non-peripheral and peripheral phonons in the present analysis. An analytical expression is reported for calculation of an approximate value of the extra lattice thermal resistivity of a doped sample due to the presence of electrons at low temperatures.