Numerical analysis of thermoelectric properties of bismuth under magnetic field

We study the anisotropic thermoelectric properties of bismuth associated with many-valley bandstructure in magnetic field. In order to obtain the thermoelectric properties of anisotropic materials under a magnetic field, we numerically solved the Boltzmann equation in tensor form. The magnetic field dependences of Seebeck coefficient tensor and conductivity tensor are calculated in various directions of magnetic field. The ratio of effective mass along the longest axis and the shortest axis of each ellipsoid is sensitive for the magnetic field effect of thermoelectric properties. The thermoelectric properties of bismuth under magnetic field are calculated varying relaxation time and Fermi energy, which concern purity of bismuth sample. The lower relaxation time, which corresponds to neutral impurity concentration, makes the optimum strength of magnetic field higher. The higher Fermi energy corresponding to doping impurity causes larger magneto-Seebeck coefficient.