Specific-heat studies of heavily doped Si:P

The extrinsic specific heats of several samples of phosphorus-doped silicon have been measured at temperatures $0.06<T<\mathrm{}1.6\mathrm{}$ K. The phosphorus concentrations of the samples range from $N_D=3.5\mathrm{}\times {10}^{17} \mathrm{to} 1.05\times {10}^{20}$ donors/${\mathrm{cm}}^3$. The results obtained for the semiconducting, amorphous antiferromagnet samples with $N_D<N_D^C\sim 3\times {10}^{18}$ donors/${\mathrm{cm}}^3$ compare favorably with expectations on the basis of a short-range-order-dominated cluster theory. No evidence was found for the existence of specific-heat anomalies which would be associated with ordering in these materials. Our more concentrated metallic samples (i.e., with $N_D>5.9\mathrm{}\times {10}^{18}$ donors/${\mathrm{cm}}^3$) exhibited specific heats which were equal to, within experimental error, the theoretical values anticipated from a rigid conduction band characterized by the accepted density-of-states effective mass $m^{*}=1.06\mathrm{}{m}_0$. In a dilute metallic sample, having $N_D=5.9\mathrm{}\times {10}^{18}$ donors/${\mathrm{cm}}^3$, deviations from the rigid-band results were observed. These deviations were quantitatively explained in inhomogeneity-model terms in a manner consistent with earlier interpretations of the spin-susceptibility and Hall-carrier-density data. Ambiguities in this description are discussed and related to other experiments and the alternative Brinkman-Rice-like interpretation of these results.