NON-PARABOLIC HYDRODYNAMIC FORMULATIONS FOR THE SIMULATION OF INHOMOGENEOUS SEMICONDUCTOR-DEVICES

Hydrodynamic models are becoming prevalent design tools for small scal e devices and other devices in which high energy effects can dominate transport. Most current hydrodynamic models use a parabolic band appro ximation to obtain fairly simple conservation equations. Interest in a ccounting for band structure effects in hydrodynamic device simulation has begun to grow since parabolic models cannot fully describe the tr ansport in state of the art devices due to the distribution populating non-parabolic states within the band. This paper presents two differe nt non-parabolic formulations of the hydrodynamic model suitable for t he simulation of inhomogeneous semiconductor devices. The first formul ation uses the Kane dispersion relationship (<(h)over bar k>)(2)/2m = W(1 + alpha W). The second formulation makes use of a power law {(<(h) over bar k>)(2)/2m = xW(y)} for the dispersion relation. Hydrodynamic models which use the first formulation rely on the binomial expansion to obtain moment equations with closed form coefficients. This limits the energy range over which the model is valid. The power law formulat ion readily produces closed form coefficients similar to those obtaine d using the parabolic band approximation. However, the fitting paramet ers (x,y) are only valid over a limited energy range. The physical sig nificance of the band non-parabolicity is discussed as well as the adv antages/disadvantages and approximations of the two non-parabolic mode ls. A companion paper describes device simulations based on the three dispersion relationships; parabolic, Kane dispersion and power law dis persion. Copyright (C) 1996 Elsevier Science Ltd