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

The thermal conductivity K of single crystals of silicon has been measured from 3 to 1580^ and of single crystals of germanium from 3 to 1190^. These measurements have been made using a steady-state, radial heat flow apparatus for T>300^K and a steady-state, longitudinal flow apparatus for T<300^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^ for Ge and 1000^ 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. 60. 1 eV for Si and 0. 260. 08 eV for Ge.