Steady-State Simulation of Semiconductor Devices Using Discontinuous Galerkin Methods

Chen, Liang; Bağcı, Hakan

doi:10.1109/access.2020.2967125

Cited by 34 publications

(51 citation statements)

References 77 publications

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“…In this work, we use the trap assisted recombination described by the Shockley-Read-Hall model [22], [30], [31]…”

Section: A Physical and Mathematical Descriptionmentioning

confidence: 99%

“…The bias voltage is applied to the electrodes continuously throughout the operation of the device. Before the optical EM wave excitation is turned on, the device is under a non-equilibrium stationary state [22]. When the EM wave impinges on the device, carriers are generated.…”

Section: A Physical and Mathematical Descriptionmentioning

confidence: 99%

“…The linearized set of equations that needs to be solved at every iteration of this method is discretized using a stationary DG scheme. For details, we refer the reader to [22]. In the rest of this paper, we focus on the time-domain scheme proposed to solve the Maxwell-DD system (10)- (13).…”

Section: B the Multiphysics Dg Solvermentioning

confidence: 99%

“…The surfaces of the nanostructures are modeled as floating potential surfaces for the stationary state simulation (i.e., for solution of the Poisson equation) [22], [52]. Note that in the case of nanostructures being used as electrodes [53], one could use Dirichlet boundary condition with the bias voltage on the surface of the nanostructure.…”

Section: B Plasmonic Pcdmentioning

confidence: 99%

“…Following the two stages of the PCD operation, the semiconductor device is numerically modeled also in two stages: The stationary state is described by a coupled system of the (nonlinear) Poisson equation and the bipolar DD equations. This coupled system is solved iteratively using the Gummel method and the linearized set of equations at each iteration are discretized using (stationary) DG schemes [20]- [22]. The transient stage is described by a nonlinearly coupled system of the time-dependent Maxwell and DD equations.…”

Section: Introductionmentioning

confidence: 99%

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Multiphysics Simulation of Plasmonic Photoconductive Devices Using Discontinuous Galerkin Methods

Chen

Bağcı

2020

IEEE J. Multiscale Multiphys. Comput. Tech.

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Plasmonic nanostructures significantly improve the performance of photoconductive devices (PCDs) in generating terahertz radiation. However, they are geometrically intricate and result in complicated electromagnetic (EM) field and carrier interactions under a bias voltage and upon excitation by an optical EM wave. These lead to new challenges in simulations of plasmonic PCDs, which cannot be addressed by existing numerical frameworks. In this work, a multiphysics framework making use of discontinuous Galerkin (DG) methods is developed to address these challenges. The operation of the PCD is analyzed in stationary and transient states, which are described by coupled systems of the Poisson and stationary driftdiffusion (DD) equations and the time-dependent Maxwell and DD equations, respectively. Both systems are discretized using DG schemes. The nonlinearity of the stationary system is accounted for using the Gummel iterative method while the nonlinear coupling between the time-dependent Maxwell and DD equations is tackled during time integration. The DG-based discretization and the explicit time marching help in handling space and time characteristic scales that are associated with different physical processes and differ by several orders of magnitude. The accuracy and applicability of the resulting multiphysics framework are demonstrated via simulations of conventional and plasmonic PCDs.

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“…In this work, we use the trap assisted recombination described by the Shockley-Read-Hall model [22], [30], [31]…”

Section: A Physical and Mathematical Descriptionmentioning

confidence: 99%

Section: A Physical and Mathematical Descriptionmentioning

confidence: 99%

Section: B the Multiphysics Dg Solvermentioning

confidence: 99%

Section: B Plasmonic Pcdmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multiphysics Simulation of Plasmonic Photoconductive Devices Using Discontinuous Galerkin Methods

Chen

Bağcı

2020

IEEE J. Multiscale Multiphys. Comput. Tech.

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Discontinuous Galerkin Time‐Domain Method in Electromagnetics: From Nanostructure Simulations to Multiphysics Implementations

Dong

Chen

et al. 2022

Advances in Time‐Domain Computational Electromagnetic Methods

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In the last few decades, the discontinuous Galerkin time-domain (DGTD) method has become widely popular in various fields of engineering due the fact that it benefits from computational advantages that come with finite volume and finite element formulations. Similarly, in the field of computational electromagnetics, the superiority of the DGTD method has been quickly recognized after first few works on its formulation and 1 implementation to solve Maxwell equations. With further developments in more recent years, the DGTD method has become one of the preeminent solutions to tackle a wide variety of challenging large scale electromagnetic problems including those that require multiphysics modeling.This chapter starts with a brief introduction to the DGTD method. This introduction provides the fundamentals of numerical flux, discretization techniques that rely on vector and nodal basis functions, and incorporation of absorbing boundary conditions. This is followed by descriptions of a time-domain boundary integral(TDBI) scheme, which replaces absorbing boundary conditions within the DGTD method, and a multi-step time integration technique, which uses different time step sizes for the DGTD and TDBI parts. Numerical results show that both techniques significantly improve the efficiency, accuracy, and stability of the traditional DGTD method. Then, the chapter continues with the applications of the DGTD method to several real-life practical problems. More specifically, it describes various novel techniques developed to enable the application of the DGTD method to electromagnetic analysis of nanostructures and graphene-based devices, and multiphysics simulation of optoelectronic antennas and source generators. For each application, several numerical examples are provided to demonstrate the accuracy, efficiency, and robustness of the developed techniques.

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Explicit Marching‐on‐in‐time Solvers for Second‐kind Time Domain Integral Equations

Chen¹,

Sayed²,

Ülkü³

et al. 2022

Advances in Time‐Domain Computational Electromagnetic Methods

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Time domain methods are often preferred over their frequency domain counterparts for numerical electromagnetic analysis since they can produce broadband data from a single simulation, can account for nonlinearities directly, and often provide immediate physical interpretation of the problem's solution. Among the time domain methods, time domain integral equation (TDIE) solvers have recently found widespread use and they have become an attractive alternative to differential equation solvers such 1 as finite difference time domain schemes and time domain finite element method, especially for open region scattering problems. This is because TDIE solvers do not suffer from numerical phase dispersion, do not require approximate radiation boundary conditions (such as absorbing boundary conditions and perfectly matched layers), and their time step size is not restricted by a Courant-Friedrichs-Lewy-like condition. Almost all traditional TDIE solvers utilize an implicit time marching scheme, i.e., they call for solution of a (sparse) matrix at every iteration. This reduces the computational efficiency under low-frequency excitations and makes the use of TDIE solvers in multiphysics frameworks a challenge. To address these challenges, recently, various explicit marching-on-in-time (MOT) schemes have been developed to solve the second kind TDIEs for perfect electrically conducting and dielectric scatterers. This chapter details the formulation and implementation of these TDIE solvers. These schemes cast the second kind TDIE in the form of an ordinary differential equation (ODE).A classical scheme such as those making use of Rao-Wilton-Glisson and Schubert-Wilton-Glisson basis functions and Nyström integration is used for spatial discretization. Then, a predictor-corrector scheme is used to integrate the spatially discretized ODE systems in time for the expansion coefficients of the unknowns. The explicit TDIE solvers described in this chapter use the same time step size as their implicit counterparts without sacrificing from accuracy and stability of the solution. In addition, they are significantly faster under low-frequency excitations. Numerical results are presented to demonstrate these computational benefits.

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Steady-State Simulation of Semiconductor Devices Using Discontinuous Galerkin Methods

Cited by 34 publications

References 77 publications

Multiphysics Simulation of Plasmonic Photoconductive Devices Using Discontinuous Galerkin Methods

Multiphysics Simulation of Plasmonic Photoconductive Devices Using Discontinuous Galerkin Methods

Discontinuous Galerkin Time‐Domain Method in Electromagnetics: From Nanostructure Simulations to Multiphysics Implementations

Explicit Marching‐on‐in‐time Solvers for Second‐kind Time Domain Integral Equations

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