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Measurements of the low-temperature specific heat of phosphorus-doped silicon for densities near the metal-insulator transition show an enhancement over the conduction-band itinerant-electron value. The enhancement increases toward lower temperatures but is less than that found for the spin susceptibility. The data are compared with various theoretical models; the large ratio of the spin susceptibility to specific heat indicates the presence of localized spin excitations in the metallic phase as the metalinsulator transition is approached. PACS numbers: 71.30.+h, 65.40.Em, 71.55.Jv The simple and well-understood microscopic physics of shallow impurities in semiconductors, such as phosphorus-doped silicon (Si:P), makes these systems especially attractive for a study of the metal-insulator (MI) transition in disordered systems. 1 In the insulating phase at low phosphorus concentrations, n, the donor electrons are bound to the phosphorus nuclei in a hydrogenic Is state. The Coulomb interactions between the electrons on different donors lead to an effective antiferromagnetic Heisenberg exchange interaction between the electron spins. The random locations of the donor nuclei lead to large variations in the magnitude of the exchange interaction. The resulting Heisenberg spin-y antiferromagnet was modeled successfully by Bhatt and Lee 2 where they showed that pairs of spins gradually condense into singlets with falling temperature according to a highly correlated, hierarchical scheme. The experimental data are consistent with such a model even close to the critical density n c , at sufficiently low temperatures. 3 " 6 In the metallic phase the electrons delocalize and well above the MI transition (n^2n c ) their interactions can be adequately described in terms of a disordered Fermi liquid. However, in the critical regime just above n c (n c ;S n < 2n c ) we have, at the moment, only a qualitative understanding of the electronic properties. Even though temperature and magnetic field dependences of the electrical conductivity in this dirty-metal regime are in reasonable agreement with the perturbative expansion of the scaling theories, 7 " 11 the critical conductivity exponent 0.5 remains poorly understood. The electron spin susceptibility 12 " 15 and specific heat 16 ' 17 are observed to be greatly enhanced over the expected degenerate-electron values. Such trends are predicted by the Brinkman-Rice treatment 18 for interacting electrons near the MI transition in a Hubbard model without disorder, as well as by the scaling theory of interacting electrons in disordered media. 10,11 Alternatively, an enhancement in the spin susceptibility is obtained if one assumes localized or nearly localized magnetic moments in the metallic phase just above n C9 similar to those in the n

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