Anisotropic diffusion of copper into bismuth telluride

Abstract

Bismuth telluride (Bi 2Te 3) has a layer structure (…--Te -Bi -Te -Bi -Te --Te -Bi -Te -Bi -Te --Te …) and readily cleaves perpendicular to the c-axis of the rhombohedral crystal. A marked difference has been found between the penetration of radioactive copper parallel to and perpendicular to the cleavage planes in Bi 2T e3. D ∥=D 0 exp−( E kT )=0.0034 exp(−0.21 eV kT) , D⊥=0.071 exp(−0.80 eV kT ) . At room temperature, D ∥1̃0 −6cm 2/sec, while extrapolated D⊥ is more than eight decades lower at ∼3 × 10 −15cm 2/sec . Minute cracks, except perhaps on an atomic scale, are not believed responsible for the fast parallel diffusion. The fast parallel diffusion can be rationalized on the basis that in this direction, between adjacent tellurium layers the copper moves through a region of relatively weak electrostatic bonding forces and large layer spacing. In any other direction, covalent and ionic bonding between tellurium and bismuth atoms would make penetration more difficult. Zener's theory is shown to give a reasonable fit to the D 0 values, requiring a negligible entropy term for parallel diffusion and a small entropy term, approximately the Boltzmann factor k, for perpendicular diffusion.