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Fast Optimal Design of Semiconductor Devices
 SIAM J. Appl. Math
, 2003
"... This paper presents a new approach to the design of semiconductor devices, which leads to fast optimization methods whose numerical effort is of the same order as a single forward simulation of the underlying model, the stationary driftdiffusion system. The design goal we investigate is to increase ..."
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This paper presents a new approach to the design of semiconductor devices, which leads to fast optimization methods whose numerical effort is of the same order as a single forward simulation of the underlying model, the stationary driftdiffusion system. The design goal we investigate is to increase the outflow current on a contact for fixed applied voltage, the natural design variable is the doping profile.
Inverse problems related to ion channel selectivity
 SIAM JOURNAL ON APPLIED MATHEMATICS
, 2007
"... Ion channels control many biological processes in cells and consequently a large amount of research is devoted to this topic. Great progress in the understanding of channel function has been made recently using advanced mathematical modeling and simulation. This paper investigates another interesti ..."
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Cited by 3 (0 self)
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Ion channels control many biological processes in cells and consequently a large amount of research is devoted to this topic. Great progress in the understanding of channel function has been made recently using advanced mathematical modeling and simulation. This paper investigates another interesting mathematical topic, namely inverse problems, in connection with ion channels. We concentrate on problems that arise when we try to determine (‘identify’) one of the structural features of a channel its permanent charge from measurements of its function, namely current voltage curves in many solutions. We also try to design channels with desirable properties for example with particular selectivity properties using the methods of inverse problems. The use of mathematical methods of identification will help in the design of efficient experiments to determine the properties of ion channels. Closely related mathematical methods will allow the rational design of ion channels useful in many applications, technological and medical. We also discuss certain mathematical issues arising in these inverse problems, such as their illposedness and the choice of regularization techniques, as well as challenges in their numerical solution. The Ltype calcium channel is studied with the methods of inverse problems to see how mathematics can aid in the analysis of existing ion channels and the design of new ones.
Optimization models for semiconductor dopant profiling
, 2007
"... Design of semiconductor devices is an important and challenging task in modern microelectronics, which is more and more carried out via mathematical optimization with models for the device behavior. The design variable (and correspondingly the unknown in the associated optimization problems) is the ..."
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Cited by 2 (0 self)
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Design of semiconductor devices is an important and challenging task in modern microelectronics, which is more and more carried out via mathematical optimization with models for the device behavior. The design variable (and correspondingly the unknown in the associated optimization problems) is the
MATHEMATICAL TOOLS IN OPTIMAL SEMICONDUCTOR DESIGN BY
"... This paper intends to give a comprehensive overview on the basic mathematical tools which are presently used in optimal semiconductor design. Focusing on the drift diffusion model for semiconductor devices we collect available results concerning the solvability of design problems and present for the ..."
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This paper intends to give a comprehensive overview on the basic mathematical tools which are presently used in optimal semiconductor design. Focusing on the drift diffusion model for semiconductor devices we collect available results concerning the solvability of design problems and present for the first time results on the uniqueness of optimal designs. We discuss the construction of descent algorithms employing the adjoint state and investigate their numerical performance. The feasibility of this approach is underlined by various numerical examples. 1.
Finite Element Solution of Optimal Control Problems Arising in Semiconductor Modeling
"... Abstract. Optimal design, parameter estimation, and inverse problems arising in the modeling of semiconductor devices lead to optimization problems constrained by systems of PDEs. We study the impact of different state equation discretizations on optimization problems whose objective functionals inv ..."
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Abstract. Optimal design, parameter estimation, and inverse problems arising in the modeling of semiconductor devices lead to optimization problems constrained by systems of PDEs. We study the impact of different state equation discretizations on optimization problems whose objective functionals involve flux terms. Galerkin methods, in which the flux is a derived quantity, are compared with mixed Galerkin discretizations where the flux is approximated directly. Our results show that the latter approach leads to more robust and accurate solutions of the optimization problem, especially for highly heterogeneous materials with large jumps in material properties. 1
A COMPARATIVE STUDY OF GALERKIN AND MIXED GALERKIN METHODS IN OPTIMAL CONTROL PROBLEMS WITH APPLICATIONS TO SEMICONDUCTOR MODELING
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OPTIMAL CONTROL OF THE STATIONARY QUANTUM DRIFTDIFFUSION MODEL IN THE SEMICLASSICAL LIMIT
"... Abstract. We consider an optimal control problem of the quantum driftdiffusion equation. The existence and uniqueness of solutions to the state system is shown. The control problem is then formulated as a constrained optimization problem and the existence of a minimizer is proven. The adjoint equat ..."
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Abstract. We consider an optimal control problem of the quantum driftdiffusion equation. The existence and uniqueness of solutions to the state system is shown. The control problem is then formulated as a constrained optimization problem and the existence of a minimizer is proven. The adjoint equations are derived and allow for an easy calculation of the gradient of the reduced cost functional. The existence and uniqueness of solutions for the adjoint system is also investigated. Numerical results for different cost functionals show the feasibility of our approach. 1.