Magneto-Seebeck and Nernst effects in porous semiconductors with hierarchically distributed nano-to micro-scale pores

Abstract The objective of this work is to study the magneto-Seebeck and transverse Nernst-Ettingshausen effects in semiconductors with spherical hollow pores of varying diameter from micrometers down to nanometers. The change in the magneto-Seebeck and Nernst coefficients due to the porosity is examined using a model based on the Gamma distribution of the pore sizes. Sound analytical expressions are found for the coefficients under both isothermal and adiabatic conditions in the presence of weak and strong non-quantizing magnetic fields. It is shown that the porosity leads to the decrease in the magneto-Seebeck coefficient in absolute value as compared with bulk material in both weak and strong fields. In contrast to that, the Nernst coefficient increases linearly with increasing porosity in strong fields while decreases by hyperbolic law in weak fields. The change in the coefficients is the greater the less is the average pore diameter.