Effect of phonon focusing on the temperature dependence of thermal conductivity of silicon

The effect of phonon focusing on the temperature dependence of thermal conductivity (T) of single crystalline silicon is studied at temperatures from 3 to 40K in the frame of generalized Callaway theory. Thermal conductivity has been calculated for silicon samples in the form of finite length rectangular rods with different orientations of long axis and side faces. To evaluate the phonon scattering rate due to diffuse boundary scattering, the analytical expressions derived recently by us were utilized. Theoretical results representing the dependence of (T) on temperature and sample orientation are in agreement with experimental data. Contributions of different phonon polarizations to the thermal conductivity have been analyzed. The transverse phonon branches are most important as expected, the slow transverse mode being the most prominent in the formation of conductivity anisotropy. The phonon dispersion was found to have a weak effect on the calculated (T) at these temperatures.