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SOLUTION OF THE COUPLED POISSON–SCHRÖDINGER EQUATIONS USING THE MULTIGRID METHOD

✍ Scribed by Eric A. B. Cole; Christopher M. Snowden; TOBIAS BOETTCHER

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
297 KB
Volume
10
Category
Article
ISSN
0894-3370

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✦ Synopsis

This paper presents a multigrid method for numerically solving the coupled Poisson-Schro ¨dinger equations in one dimension for a multilayered HEMT device structure. It is shown that this method produces a good speed-up factor over the non-multigrid approach. This should make it suitable for incorporating into the twodimensional HEMT model involving coupled Poisson, Schro ¨dinger, current continuity and energy transport equations, with the Schro ¨dinger equation being solved in slices perpendicular to the layer structure. The time taken to produce a multigrid solution depends on the size of the coarse grid and on the number of grids used. A method of predicting the time taken for any combination of these values is presented. The method is demonstrated for a 4-layer device.

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