The low field, magnetoresistivity tensor and the fermi surface of arsenic

Abstract

A technique has been developed for growing large, strain-free, single crystals of the rhombohedral (ɑ) semimetallic form of arsenic from vapour phase. Previously, only small crystals have been obtained: large crystals can only be grown when the deposition temperature is above a critical value of 700ºc. Temperature fluctuations must be kept within 0.2ºC to prevent the development of severe mosaic structure. Dislocations have been examined by etching techniques. Due to the 'puckered layer' structure of arsenic, either trigonal or hexagonal pits may be produced at the same site of emergence of dislocations on the (lll) cleavage plane: the etch determines the pit shape. Galvanomagnetic effects in arsenic have been studied for the low-field condition µH<<1 by systematically measuring the twelve coefficients that define the isothermal magnetoresistivity tensor to second order in magnetic field, at selected temperatures between 77ºK and 305ºK. Because the effects are small, their measurement requires certain experimental refinements: the measuring system has a resolution of 10 (^-9)v: electronic systems have been designed to stabilize .a sample current of 5 amps, to 1 in 10^ and the sample temperature to 0.001 K.A two carrier, multivalley ellipsoidal model of the energy bands of arsenic is invoked to interpret the galvanomagnetic measurements and so determine carrier densities and mobilities and tilt angles of the Fermi ellipsoids. To solve the consequent twelve equations in nine unknowns, a new method of computation, incorporating a least-mean-squares criterion, has been devised. The electrons are sited in pockets tilted at +82 to the trigonal axis and holes in pockets tilted at +40º ; equal carrier densities are essentially temperature independent, ranging from 1.9x10(^20)cm.(^-3)at 77 ºK to 2.1x10(^20) cm.(^-3) at 305ºK. These findings are in close agreement to recent theoretical calculations and measurements of the de Haas-van Alphen effect. Carrier mobility~1 7temperature dependences are close to T(^-1.7) , considerably greater than the expected T(^-1.0)probably owing to intervalley scattering. A measurement of the two components of the thermoelectric-power tensor has shown that S(_33) is negative, not positive, as reported previously.