Frozen-in defects in bismuth in relation to its magnetoresistivity and thermoelectric power

An experimental study is presented of effects on the electrical properties of bismuth single crystals of quenching from about 4 K below the melting point (544 K) into liquid nitrogen. Each of the twelve coefficients that describe the low field, magnetoresistivity tensor and the components of the thermoelectric power tensor has been compared in the annealed and quenched sample conditions at 77 K and at room temperature. Pronounced changes in the tensor coefficients at 77 K have been observed following quenching; the anisotropy ratio $\rho _{11}^{0}/\rho _{33}^{0}$ of the zero field resistivity inverts from 0.9446 before quenching to 1.030 after. Quenching effects anneal out on heating to below room temperature. Results are analysed in terms of a two-band, multivalley Fermi surface model to obtain carrier densities and mobilities, the tilt angle of the electron ellipsoids and the Fermi energies and band overlap. Carrier densities at 77 K in both bands are 4.4 $\times $ 10$^{23}$ m$^{-3}$ in the carefully annealed state. Quenching increases both the electron and hole densities, the former to 4.6 $\times $ 10$^{23}$ m$^{-3}$ and the latter to 5.3 $\times $ 10$^{23}$ m$^{-3}$; the separation between the Fermi level and the valence band edge is increased markedly (27%), as is the band overlap (13%). The quenched-in defects show predominantly acceptor-like character. Carrier mobilities in the xy plane are reduced after quenching but those along the z axis are slightly increased.