Reduced Dimensionality and Thermoelectric Power Factor of PbTe Ballistic Nanostructures

We theoretically investigate the dimensionality dependence of the thermoelectric power factor of semiconductor nanostructures. A finite size model is used which allows the continuous crossover between quasi-1D, 2D and 3D structures. Results for PbTe nanowires in the ballistic transport regime are shown as a function of the nanowire width, and temperature. An effective gain with the use of lower dimensional structures is estimated with the ratio of the power factor maximum obtained for the bulk (3D) with that obtained by summing the power factor from all nanowires filling the same space, with varying packing. The Landauer formalism and the envelope-function approximation based on a four-band k.p model for the bulk are used. At room temperature, we estimate some gain only with very small wires, independently of the packing. However, as the temperature is reduced, the gain increases significantly, at temperatures inversely proportional to the wire width.