The Atomic Heat of Silicon below 100°K

Abstract

The atomic heat of Si containing less than 0.01 percent $P$-type impurities has been measured between 1°K and 100°K. Below 5°K, the atomic heat can be represented by the sum of a cubic term with Debye $\theta =658\mathrm{}$°K, and a linear term equal to that of a highly degenerate "hole gas" with concentration about ${10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$. This is also the hole concentration calculated from Hall constant measurements on this material. The Debye $\theta$ calculated from elastic constants is 653°K, using a simplified procedure (described in Appendix II) based on the Hopf-Lechner method. The atomic heat is in reasonable agreement with measurements of Nernst and Schwers above 20°K, and of Anderson above 60°K. Above 5°K, $\theta$ decreases to a minimum of 456°K at $T=40\mathrm{}$°K and then rises to 580°K at $T=100\mathrm{}$°K.