On the History of the Numerical Methods Solving the Drift Diffusion Model
In 1964 Hermann Gummel published the first numerical solution method for the one-dimensional Drift Diffusion model. In his seminal paper [1] already the nonlinear iteration method and the basics of the discretization method named after him are outlined. Soon after this paper appeared many research g...
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| Format: | Article |
| Language: | English |
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JommPublish
2020-12-01
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| Series: | Journal of Microelectronic Manufacturing |
| Online Access: | http://www.jommpublish.org/p/61/ |
| Summary: | In 1964 Hermann Gummel published the first numerical solution method for the one-dimensional Drift Diffusion model. In his seminal paper [1] already the nonlinear iteration method and the basics of the discretization method named after him are outlined. Soon after this paper appeared many research groups worldwide tried to solve the Drift Diffusion equations in two and more dimensions applying predominantly general finite element discretization methods which were very popular at these days. Due to this a large variety of different codes solving the multidimensional Drift Diffusion equations based on many different space discretization schemes existed in the seventies. However already in the nineties all Drift Diffusion simulators being of importance for semiconductor device design in industry and academia still used Gummel’s nonlinear iteration method but were entirely based on just one specialized space discretization method, which incorporates the basic ideas of the Scharfetter-Gummel discretization scheme [2]. All other codes which were not based on this special space discretization method had nearly vanished already in the nineties and this is still the case today. This paper tries to shed some light on the hidden reasons for this astonishing development. |
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| ISSN: | 2578-3769 |