Absolute Spin Susceptibilities and Other ESR Parameters of Heavily Dopedn-Type Silicon. II. A Unified Treatment

Abstract

Spin susceptibility, $g$-value, and ESR linewidth data are presented for (Si:P) samples having impurity concentrations ${10}^{18}<N_D<{10}^{19}$ ${\mathrm{d}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{s}/\mathrm{c}\mathrm{m}}^3$. These results and those previously obtained for $N_D>{10}^{19}$ ${\mathrm{d}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{s}/\mathrm{c}\mathrm{m}}^3$ samples are compared with the predictions of alternative simple models of the semiconductor-metal transition in heavily doped semiconductor materials. At low concentrations ($N_D<3\mathrm{}\times {10}^{18}$ ${\mathrm{d}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{s}/\mathrm{c}\mathrm{m}}^3$) our samples behave as semiconductors in transport experiments and are characterized by Curie-Weiss-law spin susceptibilities. Near the upper limit of our sample impurity concentration range ($N_D\sim {10}^{20}$ ${\mathrm{d}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{s}/\mathrm{c}\mathrm{m}}^3$), transport measurements indicate metallic properties and spin susceptibilities which follow the Pauli-law expression with an effective mass which is slightly smaller than that usually associated with the silicon conduction band. A good representation of the experimental spin susceptibilities of samples having intermediate impurity concentrations can be achieved through an expression which is the sum of two terms: one of which is of the Curie-Weiss form and the other of the Pauli type. An analysis of previously published Hall carrier-density data is offered which would appear to allow the identification of these two components with nonconducting (or partially localized) and conducting extrinsic electrons, respectively. The inferred presence of partially localized electrons even in samples with $N_D>{10}^{19}$ ${\mathrm{d}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{s}/\mathrm{c}\mathrm{m}}^3$ is discussed with respect to previously published magnetoresistance and Knight-shift data.