Numerical analysis of thermoelectric phenomenon by boltzmann transport equation with discretization of all wave-number spaces

By the development of micro fabrication technology, further smaller-size electronic devices will be available. In such a smaller device, non equilibrium state might be appeared for careers in metal and/or semiconductor that constitute the device. In such a situation the device performance estimation by the macroscopic transport equations that assume quasi-equilibrium distribution is difficult. Against the background of this difficulty. we are developing a numerical simulation based on Boltzmann transport equation (BTE), which can analyze thermal and electric phenomena even when the state is far from equilibrium. In this paper, we numerically analyzed heat flux and thermoelectric voltage for simple one dimensional system by solving BTE with discretization of all wave number spaces. The calculation result of heat flux agreed with the value estimated from Fourier's law.