THERMAL CONDUCTIVITY OF SILICON IN THE BOUNDARY SCATTERING REGIME.

Thermal conductivity measurements on high-resistivity single crystals of silicon were made in the phonon boundary-scattering regime. The conductivities of samples with rough surfaces had a nearly T to the 3rd power dependence, in close agreement with the theory of Casimir. The conductivity did not change with different crystallographic rod faces for a given rod axis. However, the conductivity showed a strong dependence upon the crystallographic orientation of the rod axis of the sample, the conductivity of a sample having a 100 rod axis being nearly double that of an equal-sized sample with a 111 rod axis. In silicon, the phonon velocities are anisotropic, but it does not appear that the inclusion of the anisotropy in the Casimir formulation would be sufficient to explain this effect. For both rod axes, the change in conductivity with crystal dimensions is in agreement with the modified size-effect theory of Berman, Simon, and Ziman. For rough samples of rectangular cross-section, the effective diameter is the harmonic mean width rather than the geometric mean usually assumed. However, the conductivity deviates strongly from the T to the 3rd power law below 1.7K. Highly polished surfaces gave a large increase in conductivity, indicating largely specular reflection of the phonons. The temperature dependence was much less than cubic, indicating that the amount of specularity is wavelength dependent. Very smooth surfaces had a diffuseness f 0.10 at 1.5K in the theory of Berman, Simon and Ziman, and confirmed the predicted large dependence of conductivity upon the ratio of crystal radius to length. Author