Concept of the Effective Mass and Minimal Thermal Conductivity of Superlattices

The periodic potential and its symmetry determine the energy band structure and as a consequence the effective masses of semiconductors. Superlattices do have a lower symmetry than the materials they are made of and they do have an additional long-range periodicity. Therefore the effective masses of superlattices should be a propertie of the superlattices itself and different of the one of its constituents. An increase of the Seebeck coefficient in the cross-plane direction, i.e. in the direction of growth of the superlattice, due to the filtering of electrons having energy below the Fermi level is expectable and an increase of the figure of merit may be attainable. In this article, the effective mass of an electron in a one dimensional rectangular periodic potential is derived in the tigh t-binding limit. The effective mass is found to be related to the energy band width calculated with the Kronig-Penney Model and the periodicity of the superlattice. The dependence of the figure of merit Z on the effective masse for a single conduction band and one type of charge carrier is discussed for bulk materials. The discussion is also done with the figure of merit derived by Dresselhaus for electrons in stacked quantum wells. Finally, the concept of minimal thermal conductivity of solid is reviewed and a method is proposed to compute the thermal conductivity of superlattices. The method of calculation proposed for the electronic and thermal properties suggest the possibility to derive a figure of merit which is much more related to the structure of the superlattices (periodicity, he ight of the energy barrier, interatomic distance and scattering mechanisms) and less related to the bulk material properties of the constituents