A numerical method for a transient quantum drift-diffusion model arising in semiconductor devices

This paper describes a numerical method for a transient quantum drift-diffusion model arising in semiconductor devices. The discretization method is presented with emphasis on adaptive time discretization. An adaptive time step algorithm is constructed by introducing the derivative of the free energy of the system, which has an essential property to understand the carrier behavior of the time-dependent problems. The algorithm is verified with switching characteristics of one-dimensional n⁺–n–n⁺ silicon diodes. It is shown that the time step is adapted to the switching characteristics. The new algorithm significantly reduces the total number of time steps.