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An energy transport model has been numerically implemented in the device simulator HFIELDS. The transport parameters for the standard hydrodynamic model and the energy transport model are calibrated by means of DAMOCLES, a two‐dimensional Monte Carlo Boltzmann equation solver. We analyse the relative merits of these two models by comparing their predictions of the energy and velocity distributions for a bipolar transistor and a ballistic diode. In the cases presented, the hydrodynamic model is found to agree with the Monte Carlo results more closely than the energy transport model.

A discretization technique is proposed for the multi‐dimensional, steady‐state hydrodynamic model of semiconductor devices, and a derivation of the model's appropriate boundary conditions is given. The model includes the complete balance equations for charge, momentum and energy, coupled with Poisson's equation, thus accounting for both diffusion and convection phenomena. The technique, like the Scharfetter—Gummel scheme for the simpler drift‐diffusion model, provides an efficient method for solving the hydrodynamic equations, allowing for a more detailed investigation of carrier dynamics in semiconductor devices.

Some results concerning the well‐posedness of the hydrodynamic model of semiconductor devices in two dimensions are given. We show the non‐ellipticity of the stationary model; give representations which exhibit its elliptic and hyperbolic components, and obtain some appropriate boundary conditions from an examination of the time‐dependent problem.

We propose a modified discretization for the current continuity equation in the hydromodel for semiconductors. It combines ease of implementation within existing codes and robustness, even for extremely short devices. Some computational results for one and two dimensional structures are given.

Application of the waveform relaxation algorithm to the differential‐algebraic equations generated by problems in circuit and semiconductor device simulation have demonstrated that the method often contracts uniformly in time. In addition, instabilities in the underlying multirate integration method have not been observed. In this paper, it is proved that multirate A‐stability and waveform relaxation uniform contractivity are connected, and use the result to show that the first and second‐order backward‐difference based multirate methods are A‐stable when applied to block diagonally‐dominant problems.

We discuss the device applications of a new impact ionization model. This model is based on a new formulation of the impact ionization rate for bulk semiconductors, derived from solvable high‐field Boltzmann transport equations. The model inputs are relaxation times which simulate the dominant electron‐phonon scatterings and are calibrated by realistic Monte Carlo simulations. Our impact ionization model is shown to be physically motivated and is easily implemented in the standard hydrodynamic device simulators HFIELDS and FIELDAY. An efficient numerical scheme is used to simulate three thin‐base silicon bipolar transistors. Results based on this impact ionization model are found to agree well with the experimental multiplication factors over a large range of applied voltages. These results are contrasted with the more phenomenological treatment of Scholl and Quade which is shown to be a low‐field limit of our model.

A numerical implementation of a discretization scheme of the hydrodynamic model for submicron devices is described and applied to a one‐dimensional ballistic diode. The performance of the numerical method and the physical results of the simulation for different biases and lattice temperatures, and a brief comparison to Monte Carlo simulations, are also given.

This paper presents a new discretization technique of the hydrodynamic energy balance model based on a finite‐element formulation. The concept of heat source lumping is introduced, and the thermal conductivity model includes the effect of varying both carrier concentrations and temperatures. The energy balance equation is formulated to account for kinetic energy as a convective flow. The new discretization method has the advantage that it allows for assembling the functions out of elementary variables available over elements instead of along element links. Therefore, theoretically, calculation of the Jacobian should be three times faster than by the classic method. Results are given for three examples. The method suffers from mathematical instabilities, but provides a good basis for future work to solve these problems.

The effects of viscosity, previously neglected in electronic device stimulations, are studied using a non‐standard hydrodynamic model, following Anile and Pennisi. Results are compared with those of Gardner.

A mathematical analysis of the time‐dependent multi‐dimensional Hydrodynamic model is performed to determine the well‐posed boundary conditions for semiconductor device simulation. The number of independent boundary conditions that need to be specified at electrical contacts of a semi‐conductor device are derived. Using the classical energy method, a mathematical relation among the physical parameters is established to define the well‐posed boundary conditions for the problem. Several possible sets of boundary conditions are given to illustrate the proper boundary conditions. Natural boundary conditions that can be specified are obtained from the boundary integrals of the weak‐form finite element formulations. An example is included to illustrate the importance of well‐posedness of the boundary conditions for device simulation.