Abstract
As the economic develops, the production and usage of the energy has become an increasing important issue. Thermoelectric materials are one of the most promising energy material. At the same time, light and low dimension are the ways that technology develops nowadays. For thermoelectric materials, the reduction of the scale can also lead to higher conversion efficiency. We use computational quantum mechanics to simulate thermoelectric materials in nanoscale, and obtain their thermal and electrical properties, and then finally calculate the figure of merit to find out whether it is a good thermoelectric material. In the end, we aim to optimize the figure of merit by changing the composition, structure and doping. As a result of the commercial materials nowadays are rare and expensive, we choose silicon and germanium to set up our model. The study uses Kohn-Sham equation, plane wave basis and self-consistent field to optimize the model. After that, density functional perturbation theory (DFPT) is employed to calculate the phonon dispersion relation and phonon density of states, which can be further analyzed to achieve the group velocity, heat capacity, phonon relaxation time and finally the thermal conductivity. Next, we use density functional theory (DFT) to calculate the band structure and the density of states. Implementing the above parameters into the Boltzmann Transport Equation (BTE) and artificial doping, the electrical properties can be calculated. In conclusion, no matter what the structure the nanowire is, low frequency phonons dominate the heat transfer, while the silicon core germanium shell nanowire leads to the lowest thermal conductivity, and the thermal conductivity decreases with the increasing thickness of the germanium shell at the same nanowire diameter.