Thermal conductivity of pure monoisotopic silicon

Abstract

The thermal conductivity of pure monoisotopic silicon is estimated by two methods, which give similar results. One estimate, based on the observed thermal conductivity of monoisotopic germanium, yields a maximum of 66 W · cm⁻¹ · K⁻¹ at 22 K. The other estimate, based on measurements of natural silicon and on the theoretical isotope scattering rate, yields 75 W · cm⁻¹ · K⁻¹ at 22 K, an increase of only 45% over the natural crystal. These values are for crystals of approximately 0.5 cm diameter; smaller crystals yield lower values of the maximum conductivity and smaller isotope effects. Silicon cooled to liquid hydrogen temperature seems promising for high-irradiance laser mirrors. The small gain obtained by using monoisotopic silicon would be substantially greater in cases when the generated phonon distribution is athermal and weighted to higher frequencies. The effective heat transport could then be increased by as much as a factor 60 through the use of monoisotopic silicon.