Specific-heat studies of heavily doped Si:P

Abstract

The extrinsic specific heats of several samples of phosphorus-doped silicon have been measured at temperatures $0.06<T<1.6$ K. The phosphorus concentrations of the samples range from ${N}_{D}=3.5\ifmmode\times\else\texttimes\fi{}{10}^{17} \mathrm{to} 1.05\ifmmode\times\else\texttimes\fi{} {10}^{20}$ donors/${\mathrm{cm}}^{3}$. The results obtained for the semiconducting, amorphous antiferromagnet samples with ${N}_{D}<{N}_{D}^{C}\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{18}$ 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 ${N}_{D}>5.9\ifmmode\times\else\texttimes\fi{}{10}^{18}$ 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 ${m}^{*}=1.06{m}_{0}$. In a dilute metallic sample, having ${N}_{D}=5.9\ifmmode\times\else\texttimes\fi{}{10}^{18}$ 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.