Low-temperature magneto-phonon conductivity of lightly doped Si

Abstract

The relative importance of the elastic and inelastic phonon scattering by shallow acceptors to the low-temperature magneto-thermal conductivity of boron-doped Si is studied in the present paper. It is shown that in the temperature range 1-5 K and for magnetic fields up to 55 kG the elastic scattering makes the major contribution towards phonon resistivity. The magnetic field removes the degeneracy of the ground state and the phonon conductivity first falls as the level splittings become comparable to the dominant phonon energies ($\ensuremath{\sim}4{k}_{B}T$) and then rises rapidly when the splittings become $\ensuremath{\gg}{k}_{B}T$. These features are reflected in our calculations. The discrepancy between theory and experiment regarding the absolute values of the ratio [$\frac{\ensuremath{\kappa}(H)}{\ensuremath{\kappa}(H=0)}$] still remains unresolved with the present magnetic-level structure and $g$ values.