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An Analytical Model for Strongly Inverted and Accumulated Silicon Films

  • An analytical model for the spatial distribution of potential, electric field and carrier densities is presented, assuming uniform doping density and constant quasi-Fermi potentials in the direction of modeling. Starting from the current relations a differential equation respecting two-dimensional effects is developed and solved approximately by decomposition in three regions with different preconditions: (a) flatband region, (b) constant spacecharge density and (c) strong inversion or accumulation. Inaccuracies arise mainly from violated preconditions at the interfaces between the different regions. Two-dimensional effects are respected in the analytical model of (b) only but they influence region (c) by means of boundary conditions at the interface of (b) and (c). The investigations of this paper are focused to region (c). This part of our model is identical to the model of Hauser and Littlejohn[1]. They integrated a simplified form of the semiconductor-Poisson equation twice but were restricted to one-dimensional applications and thermal equilibrium. Our derivation allows for large electric fields and current densities perpendicular to the direction of modeling. From analytical considerations confirmed by numerical experiments we suggest preference to the gradual channel condition, with x and y defined according to Fig. 1. This definition allows the potentials to vary significantly with respect to y. We found that this holds for the quasi-Fermi potentials also. Furthermore an empirical model for the maximum width of strong-inversion layers in uniformly doped silicon films is presented in eqn (46).

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Metadaten
Author:Martin J. W. Schubert, Bernd Höfflinger, René P. Zingg
DOI:https://doi.org/10.1016/0038-1101(90)90136-3
Parent Title (English):Solid-State Electronics
Publisher:Elsevier
Document Type:Article
Language:English
Year of first Publication:1990
Release Date:2021/04/01
Volume:33
Issue:12
First Page:1553
Last Page:1567
Institutes:Fakultät Elektro- und Informationstechnik
Fakultät Elektro- und Informationstechnik / Labor Elektronik
Publication:Externe Publikationen
research focus:Produktion und Systeme
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