Thermal Conductivity of Silicon and Germanium from 3°K to the Melting Point

TLDR

The authors measured Si and Ge thermal conductivity from 3 K to the melting point using steady‑state radial flow above 300 K and longitudinal flow below 300 K, achieving ~5 % accuracy, and calculated phonon conductivity from boundary, isotope, three‑ and four‑phonon scattering relaxation times, which agreed with the measurements. Phonons dominate the thermal conductivity of Si and Ge at all temperatures, with calculated phonon contributions matching measurements, while above 700 K (Ge) and 1000 K (Si) electrons contribute, accounting for 40 % of K at the melting points, and the electronic K yields thermal band gaps of 0.6 ± 0.1 eV for Si and 0.26 ± 0.08 eV for Ge.

Abstract

The thermal conductivity $K$ of single crystals of silicon has been measured from 3 to 1580\ifmmode^\circ\else\textdegree\fi{}K and of single crystals of germanium from 3 to 1190\ifmmode^\circ\else\textdegree\fi{}K. These measurements have been made using a steady-state, radial heat flow apparatus for $T>300\ifmmode^\circ\else\textdegree\fi{}$K and a steady-state, longitudinal flow apparatus for $T<300\ifmmode^\circ\else\textdegree\fi{}$K to give absolute $K$ values. This radial flow technique eliminates thermal radiation losses at high temperatures. The accuracy of both the low-temperature apparatus and the high-temperature apparatus is approximately \ifmmode\pm\else\textpm\fi{}5%. Some special experimental techniques in using the high-temperature apparatus are briefly considered. At all temperatures the major contribution to $K$ in Si and Ge is produced by phonons. The phonon thermal conductivity has been calculated from a combination of the relaxation times for boundary, isotope, three-phonon, and four-phonon scattering, and was found to agree with the experimental measurements. Above 700\ifmmode^\circ\else\textdegree\fi{}K for Ge and 1000\ifmmode^\circ\else\textdegree\fi{}K for Si an electronic contribution to $K$ occurs, which agrees quite well with the theoretical estimates. At the respective melting points of Si and Ge, electrons and holes are responsible for 40% of the total $K$ and phonons are responsible for 60%. The measured electronic $K$ yields values for the thermal band gap at the melting point of 0.6\ifmmode\pm\else\textpm\fi{}0.1 eV for Si and 0.26\ifmmode\pm\else\textpm\fi{}0.08 eV for Ge.