The low field magnetoresistivity tensor and the Fermi surface of arsenic

Abstract

Measurements are presented, at selected temperatures between 305 and 77 $^\circ$K, of the twelve coefficients that define the low-field magnetoresistivity tensor of arsenic. A two-carrier multivalley ellipsoidal model of the energy bands is invoked to determine carrier densities and mobilities and tilt angles of the Fermi ellipsoids. In agreement with recent theoretical calculations and measurements of the de Haas-van Alphen effect, the electrons are sited in pockets tilted at +82$^\circ$ to the trigonal axis and holes in pockets tilted at +40$^\circ$. Equal carrier densities are essentially temperature independent, ranging from 1$\cdot$9 x 10$^{20}$ cm$^{-3}$ at 77 $^\circ$K to 2$\cdot$1 x 10$^{20}$ cm$^{-3}$ at 305 $^\circ$K. Carrier mobility temperature dependences are close to T$^{-1\cdot7}$, considerably greater than the expected T$^{-1\cdot0}$, probably owing to intervalley scattering. Experimental techniques and a new method of computation are described.