Semiconductor device simulation is a useful tool for predicting the behavior of semiconductor devices prior to their actual fabrication and thus can be used to reduce greatly the cost and time of device development cycle. Two approaches to device simulation have been used frequently. The first is the analytical approach which involves the use of simplified assumptions on both the device geometry and the mathematical models [1, 2]. In this approach, a device is usually treated as a one-dimensional structure having a piecewise constant impurity doping concentration. The structure is further separated into quasi-neutral and space-charge regions which have different physical characteristics. Local solutions of the two adjacent regions are then linked using the boundary conditions, leading to closed-form expressions applicable for simulating the device terminal characteristics. The other approach, called the numerical approach, solves directly and numerically the fundamental semiconductor device equations such as the Poisson equation, electron and hole continuity equations, and electron and hole current equations [3, 4, 5]. Realistic device structures and all relevant device physics can be incorporated into such an approach, but with the expense of more extensive computational time and development of numerical algorithm. The analytical approach was discussed in details in Chapter 1, and the numerical approach will be the focus of this chapter.
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