TY - JOUR A1 - Schubert, Martin J. W. A1 - Höfflinger, Bernd A1 - Zingg, René P. T1 - An Analytical Model for Strongly Inverted and Accumulated Silicon Films T2 - Solid-State Electronics N2 - 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). Y1 - 2021 UR - https://opus4.kobv.de/opus4-oth-regensburg/frontdoor/index/index/docId/1163 VL - 33 IS - 12 SP - 1553 EP - 1567 PB - Elsevier ER -