New PDF release: Advanced scientific computing (B673)

By Meglicki Z.

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5 Newton’s Method Newton’s method is a coupled procedure which solves the equations simultaneously, through a generalization of the Newton–Raphson method for determining the roots of an equation. We rewrite Eqs. 10) in the residual form Wv (V, n, p) = 0 Wn (V, n, p) = 0 W p (V, n, p) = 0. 33) δp which is obtained by Taylor expansion. 34) where k indicates the iteration number. In practice, a relaxation approach is also applied to avoid excessive variations of the solutions at each iteration step.

01 μm. L. condition necessary to resolve correctly a purely drift process on this mesh requires t ≤ x/v = 10−15 s. As calculated earlier, this value is not too far from typical values of the dielectric relaxation time in practical semiconductor structures. cls July 24, 2006 16:23 THE DRIFT–DIFFUSION EQUATIONS AND THEIR NUMERICAL SOLUTION 47 When dealing with unipolar devices, as often used in many microwave applications, it is possible to formulate very simple time-dependent DD models, which can be solved with straightforward finite-difference techniques and are suitable for small student projects.

49) can be used for both transient or steady-state conditions if the simulation is run until δn/δt = 0. A basic simple algorithm consists of the following steps 1. Guess the carrier distribution n(x). 2. Solve Poisson’s equation to obtain the field distribution. 3. Compute one iteration of the discretized continuity equation with time step and D(E) are updated according to the local field value. t. v(E) 4. Check for convergence. If convergence is obtained, stop. Otherwise, go back to step (2) updating the charge distribution.

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Advanced scientific computing (B673) by Meglicki Z.

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