Analysis of Multicarrier Galvanomagnetic Data for Graphite

Abstract

The magnetic-field-dependent data of Soule for the Hall effect and magnetoresistance in graphite have been analyzed using a multicarrier model. An improved mode of analysis is used, in which the magnetoconductivity tensor elements are computed as functions of magnetic field strength from experimental data, and then fitted to simple formulas. The formulas represent solutions to the Boltzmann equation in the classical (nonoscillatory) range. The effects of electrons and holes are separated by applying a Kramers-Kronig type relation. The results, which agree with band-model predictions within 20 to 50%, are that there are 2.9\ifmmode\times\else\texttimes\fi{}${10}^{18}$ holes and electrons per ${\mathrm{cm}}^{3}$ in pure graphite at 4.2\ifmmode^\circ\else\textdegree\fi{}K, and 7.0\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ each at 300\ifmmode^\circ\else\textdegree\fi{}K. The mobilities range from about 9\ifmmode\times\else\texttimes\fi{}${10}^{5}$ ${\mathrm{cm}}^{2}$/volt sec at 4.2\ifmmode^\circ\else\textdegree\fi{}K to 1.0\ifmmode\times\else\texttimes\fi{}${10}^{4}$ ${\mathrm{cm}}^{2}$/volt sec at 300\ifmmode^\circ\else\textdegree\fi{}K, with the hole-to-electron mobility ratio being 1.2 and 0.9 at the two temperatures. In addition, at room temperatures there are about 6\ifmmode\times\else\texttimes\fi{}${10}^{14}$ minority holes per ${\mathrm{cm}}^{3}$ with a mobility of 15\ifmmode\times\else\texttimes\fi{}${10}^{5}$ ${\mathrm{cm}}^{2}$/volt sec and 5\ifmmode\times\else\texttimes\fi{}${10}^{14}$ minority electrons per ${\mathrm{cm}}^{3}$ with a mobility 4\ifmmode\times\else\texttimes\fi{}${10}^{5}$ ${\mathrm{cm}}^{2}$/volt sec. The relaxation times for the majority carriers are distributed over a range of a factor of four. The average relaxation times are consistent with those deduced from cyclotron resonance experiments.