Electron-phonon interaction inP-doped silicon at low temperatures

Thermal conduction in doped single-crystal silicon films

“…This indicates the possibility of additional imperfections in these samples. 6,24 A nominal value of A x ϭ11.75ϫ10 Ϫ45 s 3 yields reasonable agreement with the data. This coefficient is about ten times larger than the coefficients of scattering rates due to isotopes, A isotopes ϭ1.32 ϫ10 Ϫ45 s 3 , and lattice distortion, A ␦R ϭ2.66ϫ10 Ϫ45 s 3 .…”

“…5 The thermal conductivity data for lightly doped samples was fit using Eqs. ͑8͒ and ͑13͒ and the shear deformation parameter, ⌶ u,elec ϭ9 eV, at temperatures below 20 K. The reported values in the literature are ⌶ u,elec ϭ10 eV, 6,24 ⌶ u,elec ϭ8Ϯ0.3 eV, 43 ⌶ u,elec ϭ8.6Ϯ0.2 eV, 44 and ⌶ u,elec ϭ9.5 eV. 45 The thermal conductivity data for heavily doped samples are fitted using the dilatation deformation potential, E D ͑see Table I͒.…”

“…This approach was developed by Callaway 23 and refined for silicon by Holland, 18 who used a more detailed description of the phonon dispersion relations in this material to better capture the temperature dependence of the thermal conductivity. The present work modifies the model of Holland 18 to account for the increase in the phonon-scattering rate due to mass differences between the substitutional impurities and the host atom, 19 phononelectron scattering, 20,21,24 and the small separation between the layer boundaries. 1 The appropriate scattering rates for phonon-impurity and phonon-free electrons ͑holes͒ are presented in Sec.…”

“…33,34 For concentrations below 2.5ϫ10 17 cm Ϫ3 , all the electrons are in the bound state. 24 The inhomogeneity model proposed by Mikohsiba 35 describes the electron behavior in the intermediate region for concentrations between 2.5 ϫ10 17 and 3ϫ10 18 cm Ϫ3 . The availability of free electrons below 30 K may seem counterintuitive due to carrier freeze out.…”

“…This can be explained by the overlap of the donor and conduction bands in degenerate semiconductors. 36,37 Radhakrishnan, Sharma, and Singh 24 showed that the variation of thermal conductivity with temperature of phosphorus-doped silicon can be explained by applying the theories of phonon scattering on electrons in the localizedbound and in the metallic states. For low concentrations, the impurity forms isolated states and does not merge into the conduction band.…”