Scattering of Phonons by Electrons in Germanium-Silicon Alloys

Abstract

The theory developed by Ziman for the scattering of phonons by electrons is extended to high temperatures using the formalism of Klemens and Callaway. The theory is applied to the experimental results recently published by Dismukes et al. on the effect of doping on the thermal conductivity of Ge-Si alloys. After subtracting the electronic contribution from the measured thermal conductivity, the resulting lattice conductivity is analyzed. In describing the effect of doping, the deformation potential is the only free parameter; its value is adjusted for each sample to obtain agreement with the experimental data at 500°K, which is close to the Debye temperature. The theory then predicts the correct temperature dependence of the lattice thermal conductivity. The deformation potentials, derived in this manner, are found to be higher for w-type than for p-type material, and to increase with carrier concentration. For lightly doped />-type and w-type material, values of 1.2 and 1.6 eV were obtained, respectively, which compare well with the available literature data.

Phonon Scatterings in the Lattice Thermal Conductivity of Si_(1-x) Ge_x Alloy Nanowires: Theoretical Study

“…Their model treats phonons with the Boltzmann transport equation under a relaxation time approximation. In this model, the contribution of optical modes to thermal resistivity is neglected [27,29]. Thus this model is given by:…”

“…Phonon-alloying scattering: the assumption is made that the lattice disorder due to alloying can be described by point-defect scattering [27]. The relaxation time ( A τ ) for point-defect scattering due to lattice disorder in alloys is given by [24]:…”

“…Steigmeier and Abeles' model [27] of the lattice thermal conductivity (LTC) of bulk alloys, based on the Callaway's model [28], was used in this work. Their model treats phonons with the Boltzmann transport equation under a relaxation time approximation.…”

“…The alloy is assumed to be a random mixture of atoms with different masses and volumes arranged in a lattice. In this case of alloy disorder scattering, Γ represents the disorder parameter and is calculated using the virtual lattice approach given by [27,35]:…”

Effect of Rh Substitution for Co on the Thermoelectric Properties of CoSb<SUB>3</SUB>

“…The alloying can reduce the lattice thermal conductivity by the point defect phonon scattering while giving little influence on the electrical transport, because it does not introduce charge disorder in the crystal lattices. For example, in the systems of Si-Ge alloy, 8) (Zr,Hf)NiSn, 9) and Ti(Co,Rh)Sb, 10) the reduction of the lattice thermal conductivity through the alloy scattering effect have been achieved.…”