Three-dimensional concentration dependent diffusions and simultaneous chemical reactions in chemically-amplified photoresists are simulated. Fickian, a linearly increasing diffusivity and an exponentially increasing diffusivity due to free volume increase with T-BOC are considered. Two different grid to processor mappings are proposed in implementing the simulator on massively parallel processo...

The effect of optically generated reverse saturation current on the series resistance and negative resistance properties of single drift region (nnp) X band Si IMPATT diodes under (i) punch through, (ii) exact and (iii) undepleted field distributions have been studied. Simulation following Gummel-Blue approach [1] indicates an overall degradation of microwave properties with an increase of seri...

The mathematical semiconductor device model, consisting of the potential equation and the current continuity subsystem for the carriers, is studied from the standpoint of its decoupling fixed point map and the numerical approximate fixed point map. Variational principles will be discussed for this process and for discretizations achieved by use of generalized splines. By the choice of trial spa...

In this paper, we develop and study a fully implicit positive finite volume scheme that allows an accurate approximation of the nonlinear highly anisotropic convection-diffusion equations on almost arbitrary girds. The key idea is to relate oscillatory fluxes, including convective ones, normal monotonic diffusive flux thanks technique used in Scharfetter-Gummel discretizations. Then, obtain two...

We study a generalized Gummel iteration for the solution of an abstract optimal semiconductor design problem, which covers a wide range of semiconductor models. The algorithm is exploiting the special structure of the KKT system and can be interpreted as a descent algorithm for an appropriately defined cost functional. This allows for a convergence proof which does not need the assumption of sm...

The stationary energy-transport equations for semiconductors in three space dimensions are numerically discretized. The physical variables are the electron density, the energy density, and the electric potential. Physically motivated mixed Dirichlet-Neumann boundary conditions are employed. The numerical approximation is based on an hybridized mixed finite-element method using Raviart-Thomas el...

We present a derivation of exponential shape functions for the convection diffusion problem. The shape functions are defined for triangular elements and can be regarded as an extension of the one-dimensional Scharfetter-Gummel discretization scheme to two dimensions. The shape function varies exponentially in the direction of the element field vector and linearly in the direction orthogonal to ...

In this study, we present a numerical scheme to solve the drift-diffusion traffic flow model under the steady state. The drift-diffusion traffic flow model consists of a continuity equation and a nonlinear Poisson equation. The continuity equation describes the propagation of density along the road, and the Poisson equation describes the interaction among vehicles. The system equations cannot b...

The p–n junction i–u characteristic model is decisive for the accuracy enhancement of calibration-free temperature measurement. In this paper, we give a survey of adapted physically-based p–n junction i–u characteristic models, such as the Ebers–Moll2, the Ebers–Moll3, and the Gummel–Poon model. Furthermore, we build new models through polynomial extensions to the fundamental Shockley model. Th...