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An extension of the Scharfetter‐Gummel discretization scheme is presented which is designed for electrothermal semiconductor device equations including avalanche generation terms. The scheme makes explicit use of the exponential character of solutions, and reduces to the standard Scharfetter‐Gummel scheme in the isothermal non‐avalanche case.

In the past decade, very effective techniques for the solution of the drift‐diffusion equations have been developed. This has enabled the simulation of a large variety of semiconductor devices in a robust and efficient way. However, the rapid development and miniaturization of devices necessitate the use of extended physical models in order to still provide an accurate description of device performance. In order to guarantee a similar degree of robustness and efficiency for these extended models, new algorithms have to be developed. In this paper we will present a number of advanced numerical techniques which have been developed for this purpose.

The package CURRY offers a wide range of built‐in facilities for 2D device modelling of a large variety of structures such as MOS, bipolar and charge coupled devices. These capabilities will be illustrated on the transport of a charge package in a charge coupled device and on the simulation of the ESD ( Electro‐Static Discharge) in an MOS transistor. The CURRY package can also be used as a high quality kernel to which the user may add his own extensions by adding small pieces of Fortran code. The flexibility of this setup will be shown in the computation of the threshold voltage of an MOS transistor, in the computation of the I‐V curve of a diode in avalanche breakdown and in the computation of the open collector voltage of a bipolar transistor.

Model order reduction (MOR) has been widely used in the electric networks but little has been done to reduce higher index differential algebraic equations (DAEs). The paper aims to discuss these issues.

Most methods first do an index reduction before reducing a higher DAE but this can lead to a loss of physical properties of the system.

The paper presents a MOR method for DAEs called the index-aware MOR (IMOR) which can reduce a DAE while preserving its physical properties such as the index. The feasibility of this method is tested on real-life electric networks.

MOR has been widely used to reduce large systems from electric networks but little has been done to reduce higher index DAEs. Most methods first do an index reduction before reducing a large system of DAEs but this can lead to a loss of physical properties of the system. The paper presents a MOR method for DAEs called the IMOR which can reduce a DAE while preserving its physical properties such as the index. The feasibility of this method is tested on real-life electric networks.

Imperfections in manufacturing processes may cause unwanted connections (faults) that are added to the nominal, “golden”, design of an electronic circuit. By fault simulation one simulates all situations. Normally this leads to a large list of simulations in which for each defect a steady-state (direct current (DC)) solution is determined followed by a transient simulation. The purpose of this paper is to improve the robustness and the efficiency of these simulations.

Determining the DC solution can be very hard. For this the authors present an adaptive time-domain source stepping procedure that can deal with controlled sources. The method can easily be combined with existing pseudo-transient procedures. The method is robust and efficient. In the subsequent transient simulation the solution of a fault is compared to a golden, fault-free, solution. A strategy is developed to efficiently simulate the faulty solutions until their moment of detection.

The paper fully exploits the hierarchical structure of the circuit in the simulation process to bypass parts of the circuit that appear to be unaffected by the fault. Accurate prediction and efficient solution procedures lead to fast fault simulation.

The fast fault simulation helps to store a database with detectable deviations for each fault. If such a detectable output “matches” a result of a product that has been returned because of malfunctioning it helps to identify the subcircuit that may contain the real fault. One aims to detect as much as possible candidate faults. Because of the many options the simulations must be very efficient.

A new quantum effect device which is capable of highly coherent electron emission is theoretically proposed and analysed. The new device works by using the potential induced accumulation layer at a heterointerface to produce dimensionally reduced electrons. These electrons tunnel through a heterobarrier ensuring that their energy is quantised in the direction of propagation. To avoid the problem of unquantised three dimensional electrons dominating the current the two dimensional electrons that tunnel through the barrier are replenished by electrons from two side contacts. A self‐consistent model is used to analyse the performance of the device and it is found that the new device performs very well, producing electrons with a very narrow energy spread in the direction of propagation. The current density/coherency combination is easily controlled by the applied bias and the device also offers the potential for ultra fast switching through the transition between coherent and incoherent states.

Implicit one‐step methods for the system of differential equations arising from a space discretisation of the semiconductor equations are considered. It is shown that mere spectral conditions like A‐stability or L‐stability do not give a reliable answer to the behaviour of the numerical solution. Rather, positivity arguments for the corresponding rational matrix functions play an important role.

Two new mixed finite element schemes for discretizing current continuity equations are presented. Together with the good features of the already‐known mixed scheme (current preservation and good approximation of sharp shapes), they provide M‐matrices, even when a zero order term is present in the equations.

A computer program for the solution of the single carrier semiconductor equations in GaAs has been developed to simulate charge storage and transfer in GaAs charge‐coupled devices. An uncoupled Newton method is used to solve the steady state problem, and a stable, uncoupled method is used for the transient solution. Using transient simulation, the transfer of a charge packet from well to well can be simulated over time. By comparing the size of the charge packet before and after the transfer, information on the charge transfer inefficency can be derived.

In this paper we carry out a conditioning analysis for the steady state semiconductor device problem. We consider various quasilinearizations as well as Gummel‐type iterations and obtain stability bounds which may allow ill‐conditioning in general. These bounds are exponential in the potential variation, and are sharp e.g. for a thyristor. But for devices where each smooth subdomain has an Ohmic contact, e.g. a pn‐diode, moderate bounds guaranteeing well‐conditioning are obtained. Moreover, the analysis suggests how various row and column scalings should be applied in order for the measured condition numbers of the linearized discrete problem to correspond more realistically to the true loss of significant digits in the calculations.