Thermal phonon scattering in Li-doped Si

Experimental results are presented for thermal conductivity of Si containing between 5×${10}^{15}$ and 7×${10}^{17}$ Li donors ${\mathrm{cm}}^{-3\mathrm{}}$ in the temperature range 1.2-50 °K, which show that Li donors scatter phonons very effectively at low temperature. The Li donor in Si has an "inverted" ground state in which the lowest level is degenerate and the split-off level is a singlet in contrast with group-V donors. Is is shown that strong scattering of phonons is due to the degenerate lowest state and the small valley-orbit splitting. A theory on the basis of a simple model for the donor ground state is formulated in which possible splitting of the degenerate state is ignored. It can fairly well explain the experimental results for lightly doped samples in the low-temperature region ($T\le 10$°K), without using adjustable parameters. However, it cannot explain the stong scattering of phonons observed at very low temperatures. Discussions of this are given.