Thermoelectric Figure of Merit of Two-Dimensional Materials in a Magnetic Field

A theoretical treatment on the effect of a magnetic field on the thermoelectric figure of merit ZT for two-dimensional (2D) materials is presented. The figure of merit is a function of three transport coefficients: the electrical conductivity, the Seebeck coefficient or thermopower, and the total thermal conductivity. The total thermal conductivity consists of contribution from electrons and phonons to energy transport. For any magnetic field, in twoor three-dimensions, the limiting factor in ZT is the phonon contribution to the thermal conductivity. The phonon thermal conductivity is an intrinsic property which cannot e changed without significantly changing the other properties of the material. The other coefficients can be optimized relative to each other by varying the chemical potential by doping and by the application of a magnetic field. The figure of merit was investigated at various ranges of magnetic field. The ranges of a magnetic field can be categorized into three regions: the low-field or semiclassical case, the quantum or Landau-level case, and the high-field case. The low-field case is treated in the context of the relaxation time approximation of the semiclassical Boltzmann equation. The Landau-level case is treated first by the ad hoc extension of the semiclassical equations by using magnetically-quantized density of states; secondly, by the Born approximation for Landau-level broadening. The high-field case is qualified by the ground state Landau-level being much greater than the Fermi energy; this case can be treated semiclassically. Various approximations are used for the various cases to provide analytical results and to simplify numerical calculation. Under conditions of Landau-level quantization, an effect referred to as carrier dumping occurs. This results in carrier pockets with low cyclotron effective masses emptying into pockets with high cyclotron effect mass. This effect is due to the pinning of the Fermi energy to the nearest Landau-level. This can result significant increases in ZT by dumping all the carriers into a pocket with the most favorable orientation. Two thermoelectric materials, bismuth and bismuth telluride, are used as test cases for the application of the theory presented. The quantitatively favorable with respect to the current state of experimental knowledge. Thesis Supervisor: Mildred Dresselhaus Title: Institute Professor Acknowledgments I'd like to thank Mom and Dad for their support in my education, my brother Mark for his help, and my sister Camille. I am deeply grateful to Professor Dresselhaus for supporting my work and supervising this thesis. I'd also like to thank Lyndon Hicks for his help in the research and guiding of this thesis.