The Multidimensional Bipolar Quantum Drift-diffusion Model

2008 ◽  
Vol 8 (4) ◽  
Author(s):  
Xiuqing Chen ◽  
Yingchun Guo
Keyword(s):  
Weak Solution ◽  
Diffusion Model ◽  
Semiclassical Limit ◽  
Global Weak Solution ◽  
Mean Value ◽  
Doping Profile ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
New Methods ◽  
Fourth Order Parabolic System

AbstractWe investigate the bipolar quantum drift-diffusion model, a fourth order parabolic system, in two or there space dimensions. First, we establish the global weak solution with large initial value and periodic boundary conditions. Then we show the semiclassical limit by using new methods based on delicate interpolation estimates and compactness argument. Furthermore, when the doping profile is a constant, we find that the weak solution approaches its mean value exponentially as time increases to infinity.

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.

On the Multidimensional Bipolar Isothermal Quantum Drift-Diffusion Model

2012 ◽  
Vol 466-467 ◽  
pp. 186-190
Author(s):  
Jian Wei Dong
Keyword(s):  
Diffusion Model ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Mean Value ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
Initial Value ◽  
Inequality Technique ◽  
Entropy Estimate ◽  
Three Space

The bipolar isothermal quantum drift-diffusion model in two or three space dimensions with initial value and periodic boundary conditions is investigated. The global existence of weak solution to the problem is obtained by using semi-discretizing in time and entropy estimate. Furthermore, it is shown that the solution to the problem exponentially approaches its mean value as time increases to infinity by using a series of inequality technique.

scholarly journals On the recovery of the doping profile in an time-dependent drift-diffusion model

2014 ◽  
Vol 22 (2) ◽  
pp. 253-274
Author(s):  
Bin Wu ◽  
Zewen Wang
Keyword(s):  
Inverse Problem ◽  
Diffusion Model ◽  
Electric Potential ◽  
Parabolic Equations ◽  
Time Dependent ◽  
Doping Profile ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
System Of Parabolic Equations ◽  
Theoretical Results

AbstractWe consider an inverse problem arising from an time-dependent drift-diffusion model in semiconductor devices, which is formulated in terms of a system of parabolic equations for the electron and hole densities and the Poisson equation for the electric potential. This inverse problem aims to identify the doping profile from the final overdetermination data of the electric potential. By using the Schauder’s fixed point theorem in suitable Sobolev space, the existence of this inverse problem are obtained. Moreover by means of Gronwall inequality, we prove the uniqueness of this inverse problem for small measurement time. For this nonlinear inverse problem, our theoretical results guarantee the solvability for the proposed physical model.

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