A new iteration method for solving the Boltzmann equation has been used to calculate the electron relaxation-time tensor for the metal zinc at high temperature for both one-plane-wave and multiple-plane-wave approximations. The latter calculation shows a nonzero relaxation time right at the Brillouin-zone sections of the Fermi surface. The second-order correction in solving the Boltzmann equation has been estimated and it turns out to be very small. Zinc exhibits considerable elastic anisotropy with acoustic velocities higher for the modes polarized in the basal plane. As a consequence, the electron scattering is smaller for the umklapp processes parallel to this plane and the relaxation time is correspondingly longer for conduction perpendicular to the c axis. On the other hand, the Fermi sphere, which is cut by many Brillouin zones at large angles to the basal plane, is more distorted close to the basal plane than along the c axis. The resulting missing area and reduced electron velocity in the distorted regions compensate quite closely the anisotropy of the relaxation time and give a nearly isotropic conductivity, in good agreement with experiment. Also, this analysis in terms of the relaxation time and the electron velocity is able to afford a qualitative understanding of both the temperature variation of the anisotropy in conductivity and the anisotropy in electromigration measurements.
關聯:
Physical Review B (Solid State) 12(12), pp.5441-5458
