Department of Mathematics, UCI

Computer simulations of charge transport in semiconductor devices (like diodes and micro-chips) are used by the semiconductor industry as a tool for reducing the cost of developing new devices and new process technologies. At the scale of micron or sub-micron, the semiconductor Boltzmann equation is the most exact model. In order to alleviate computing load, macroscopic models have been derived, assuming that the state of the electron gas is described by certain averaged quantities. These models take similar forms as those in fluid mechanics, and we may apply CFD techniques to probe this promising field of academic importance and commercial value.

We shall present some of our recent results. First, by simulating a hydrodynamic model, we demonstrate the (direct) applicability of CFD techniques. Secondly, the continuing trend of scaling-down and speed-up makes the modeling and computing of quantum effect and transient behavior among the top issues in semiconductor research. Careful numerical tests helped identifying well-posedness problem in a quantum hydrodynamic (QHD) model. Viscous QHD model derived from a Wigner Fokker-Planck equation yields more reliable numerical results, and demonstrate interesting nonlinear phenomena, such as negative differential resistance and hysteresis.