Effective potential for moment-method simulation of quantum devices

In the simulation of submicron devices, complete quantum descriptions can be extremely computationally intensive, and reduced descriptions are desirable. One such description utilizes a few low-order moments of the momentum distribution that are defined by the Wigner function. Two major difficulties occur in applying this moment method: (i) An independent calculation is required to find quantum mechanically accurate initial conditions. (ii) For a system in a mixed state, the hierarchy of time evolution equations for the moments does not close. We describe an approach to solve these problems. The initial distribution is determined in equilibrium by means of a new effective potential, chosen for its ability to treat the sharp potential features which occur in heterostructures. It accurately describes barrier penetration and repulsion, as well as quantum broadening of the momentum distribution. The moment equation hierarchy is closed at the level of the second-moment time evolution equation, using a closure that is exact for a shifted Fermi distribution. Band-bending is included by simultaneous self-consistent determination of all the moments.