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

Abstract

The thermal conductivity $K$ of single crystals of silicon has been measured from 3 to 1580°K and of single crystals of germanium from 3 to 1190°K. These measurements have been made using a steady-state, radial heat flow apparatus for $T>\mathrm{}300\mathrm{}°$K and a steady-state, longitudinal flow apparatus for $T<\mathrm{}300\mathrm{}°$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 ±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°K for Ge and 1000°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±0.1 eV for Si and 0.26±0.08 eV for Ge.