Thermomagnetic effects in semiconductors and semimetals

The principal thermomagnetic effects in semiconductors and semimetals are discussed, with emphasis on the physical processes which affect the transport coefficients. The Seebeck, Nernst, Righi-Leduc, Peltier, Ettingshausen and magnetothermal resistance coefficients are defined and the Kelvin-Onsager relations between the coefficients are discussed. The Boltzmann equation for electrons is discussed rather briefly, with some comments on its limitations, and references to more rigorous treatments, especially in high magnetic fields. The Boltzmann equation is used to discuss the symmetry of the thermomagnetic effects, and explicit formulae are given for spherical energy bands within the relaxation time approximation. It is emphasized that if the density of states is non-parabolic the thermomagnetic coefficients are particularly affected. Experimental results in extrinsic semiconductors are reviewed. Phonon drag effects are discussed qualitatively for both lightly and heavily doped semiconductors. Formulae are given for the ambipolar effects in an intrinsic semiconductor or semimetal, and the use of the Ettingshausen and Peltier effects to obtain useful cooling at low temperatures is discussed. The practical achievements which have been obtained so far are given.