Carrier dynamical VLSI device simulation

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Abstract
In this paper two and three-dimensional Si MOSFET simulations based on a new carrier dynamical model of transport in semiconductors are presented. The simulation results derive from numerical solution of Poisson's equation, the carrier continuity equation and carrier momentum and energy conservation equations. The modelling equations differ from those used previously in that they assume the carrier distribution is quantified by a perturbation approximation rather being a drifted Maxwellian. Momentum and energy relaxation times are taken as being dependent upon the average carrier energy, which is strictly proportional to temperature in the new transport model. This overcomes the problem, inherent in drift-diffusion-based device simulation, of mobility being modelled as a local electric field-dependent parameter. It is shown that no boundary conditions are needed for the carrier energy conservation equation and that a lattice energy conservation can be easily appended to the carrier dynamical transport model, allowing lattice temperature to be readily calculated. Carrier temperature profiles within MOSFETS are presented, as are lattice temperature profiles for the two-dimensional simulations. It is demonstrated that carrier heating effects can be significant, indicating that carrier diffusion, which is directly proportional to the carrier temperature, may be underestimated by conventional (isothermal carriers and lattice) modelling and simulation techniques. The three-dimensional simulations show that the hottest carriers are not generated in the middle of the channel with respect to the width of a MOSFET.

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