Localized versus itinerant electrons at the metal-insulator transition in Si:P

The specific heat C of uncompensated phosphorus-doped silicon with P concentration N between 0.34 and 7.3×${10}^{18}$ ${\mathrm{cm}}^{\mathrm{-}3}$, i.e., in the vicinity of the metal-insulator transition, has been measured over a large range of temperature (0.04 K≤T≤3 K), allowing the unambiguous detection of an anomalous contribution ΔC∼$T^{\alpha }$, with α becoming negative for small N. This is attributed to exchange-coupled clusters. The magnetic-field dependence of C (up to 5.7 T) allows us to deduce the relative contributions of localized and delocalized electrons and gives evidence for interactions and correlations between these.