Low-temperature thermal conductivity of heavily doped n-type Ge

We have theoretically studied the low-temperature thermal conductivity of heavily doped n-type Ge by using an expression of the phonon relaxation rate previously derived by us in which both the intravalley and intervalley relaxation times of the conduction electrons due to ionized impurities have been taken into account. We have measured of a Ge sample doped with 2.78×1018 As cm-3 at 1.2<T<7 K. The following is found: In the temperature region T<1 K, becomes more sensitive to the intervalley relaxation time as T decreases; that is, the dependence of on the impurity species becomes more pronounced. On the other hand, in the temperature region T2 K, depends weakly on the impurity species. This seems to be consistent with the experimental data reported previously and given by us here. Furthermore, the calculated thermal conductivity is quantitatively in fairly good agreement with the experiment. However, there exist some discrepancies between them. A discussion on this is given.