Simulation of electronic states in polycrystalline texture

As many thermoelectrics are in polycrystalline form with grain size down to nanometer scale, the size and boundary effect play important roles in their physical properties. In the paper we develop an approach to simulate the electronic and thermo-electric property of polycrystalline. In the first step, the polycrystalline texture is created from phase field method in a two dimension scale for simplicity. Although there are many ways to create polycrystalline texture, such as Potts model and Voronoi method, the phase field method can produce a polycrystalline texture with continuous grain boundary. After the polycrystalline texture is generated, the grain boundary potential function is created using the order parameters of the phase field. Here we assumed the grain boundary act as a potential barrier. Then the Hamiltonian can be constructed with the near free electron model and the grain boundary potential. Eigen-energies and wave-functions can bee obtained by solving the Schordinger equation numerically. From the energy levels and the wave functions, we found that the ground state electrons are confined at the largest grain. Also we found that larger grains have more opportunity to confine electrons than the small grains, less opportunity for small grains confine electrons unless in the high energy state. A possible way to calculate Seebeck coefficient has been proposed.