scholarly journals Existence of Weak Solutions to a Class of Degenerate Semiconductor Equations Modeling Avalanche Generation

2009 ◽  
Vol 2009 ◽  
pp. 1-22
Author(s):  
Bin Wu
Keyword(s):  
Weak Solutions ◽  
Semiconductor Device ◽  
Mixed Boundary ◽  
Drift Diffusion Model ◽  
Degenerate Semiconductor ◽  
Drift Diffusion ◽  
Diffusion Term ◽  
Existence Of Weak Solutions ◽  
Semiconductor Equations ◽  
Avalanche Generation

We consider the drift-diffusion model with avalanche generation for evolution in time of electron and hole densitiesn,pcoupled with the electrostatic potentialψin a semiconductor device. We also assume that the diffusion term is degenerate. The existence of local weak solutions to this Dirichlet-Neumann mixed boundary value problem is obtained.

ON THE EXISTENCE OF WEAK SOLUTIONS TO THE STATIONARY SEMICONDUCTOR EQUATIONS: THE CURRENT DRIVEN CASE

1999 ◽  
Vol 09 (01) ◽  
pp. 111-126
Author(s):  
J. NAUMANN
Keyword(s):  
Weak Solution ◽  
Semiconductor Device ◽  
Mixed Boundary ◽  
Diffusion Equations ◽  
Total Current ◽  
Mixed Boundary Value Problem ◽  
Drift Diffusion ◽  
Weak Formulation ◽  
Existence Of Weak Solutions ◽  
Semiconductor Equations

This paper is concerned with the stationary drift-diffusion equations of a semiconductor device where along a part of the device boundary the total current flux is prescribed. We introduce the weak formulation of this mixed boundary value problem and prove the existence of a weak solution.

ON THE EXISTENCE OF WEAK SOLUTIONS TO A SYSTEM OF STATIONARY SEMICONDUCTOR EQUATIONS WITH AVALANCHE GENERATION

1994 ◽  
Vol 04 (02) ◽  
pp. 273-289 ◽  
Author(s):  
J. FREHSE ◽  
J. NAUMANN
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Impact Ionization ◽  
Mixed Boundary ◽  
Diffusion Equations ◽  
Mixed Boundary Value Problem ◽  
Drift Diffusion ◽  
Existence Of Weak Solutions ◽  
Semiconductor Equations ◽  
Avalanche Generation

This paper is concerned with the stationary drift-diffusion equations of semiconductor theory involving recombination-generation of carriers due to particle transition, and pure generation by impact ionization (avalanche generation). We establish the existence of a weak solution to the mixed boundary value problem for the system of PDEs under consideration. In the proof we combine an approximation argument with some estimates based on a positivity property of the recombination-generation term.

scholarly journals Bounded weak solutions to a matrix drift–diffusion model for spin-coherent electron transport in semiconductors

2015 ◽  
Vol 25 (05) ◽  
pp. 929-958 ◽  
Author(s):  
Ansgar Jüngel ◽  
Claudia Negulescu ◽  
Polina Shpartko
Keyword(s):  
Diffusion Model ◽  
Weak Solutions ◽  
Spin Vector ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Vector Density ◽  
Cross Diffusion ◽  
Electron Density Matrix ◽  
Finite Volume Discretization ◽  
Bounded Weak Solutions

The global-in-time existence and uniqueness of bounded weak solutions to a spinorial matrix drift–diffusion model for semiconductors is proved. Developing the electron density matrix in the Pauli basis, the coefficients (charge density and spin-vector density) satisfy a parabolic 4 × 4 cross-diffusion system. The key idea of the existence proof is to work with different variables: the spin-up and spin-down densities as well as the parallel and perpendicular components of the spin-vector density with respect to the precession vector. In these variables, the diffusion matrix becomes diagonal. The proofs of the L∞ estimates are based on Stampacchia truncation as well as Moser- and Alikakos-type iteration arguments. The monotonicity of the entropy (or free energy) is also proved. Numerical experiments in one-space dimension using a finite-volume discretization indicate that the entropy decays exponentially fast to the equilibrium state.

The Global Existence and Semiclassical Limit of Weak Solutions to Multidimensional Quantum Drift-diffusion Model

2007 ◽  
Vol 7 (4) ◽  
Author(s):  
Xiuqing Chen
Keyword(s):  
Diffusion Model ◽  
Weak Solutions ◽  
Semiclassical Limit ◽  
Periodic Boundary Conditions ◽  
Drift Diffusion Model ◽  
Global Weak Solutions ◽  
Drift Diffusion ◽  
Initial Value ◽  
Fourth Order Parabolic System ◽  
Entropy Estimate

AbstractWe establish the global weak solutions to quantum drift-diffusion model, a fourth order parabolic system, in two or there space dimensions with large initial value and periodic boundary conditions and furthermore obtain the semiclassical limit by entropy estimate and compactness argument.

scholarly journals Additive Decomposition Applied to the Semiconductor Drift-Diffusion Model

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 393-399
Author(s):  
Elizabeth J. Brauer ◽  
Marek Turowski ◽  
James M. McDonough
Keyword(s):  
Diffusion Model ◽  
Large Scale ◽  
Semiconductor Device ◽  
Stokes Equations ◽  
Numerical Technique ◽  
Small Scale ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Additive Decomposition ◽  
Scale Grid

A new numerical method for semiconductor device simulation is presented. The additive decomposition method has been successfully applied to Burgers' and Navier-Stokes equations governing turbulent fluid flow by decomposing the equations into large-scale and small-scale parts without averaging. The additive decomposition (AD) technique is well suited to problems with a large range of time and/or space scales, for example, thermal-electrical simulation of power semiconductor devices with large physical size. Furthermore, AD adds a level of parallelization for improved computational efficiency. The new numerical technique has been tested on the 1-D drift-diffusion model of a p-i-n diode for reverse and forward biases. Distributions of φ, n and p have been calculated using the AD method on a coarse large-scale grid and then in parallel small-scale grid sections. The AD results agreed well with the results obtained with a traditional one-grid approach, while potentially reducing memory requirements with the new method.

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