Semiconductor Device Modelling for Heterojunctions Structures With Mixed Finite Elements

Hecht, Frédéric; Marrocco, A.; Caquot, E.; Filoche, Marcel

doi:10.1108/eb051718

Cited by 7 publications

(3 citation statements)

References 3 publications

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“…We obtain the quasi-Fermi energy ϕ. We recall that mixed finite elements schemes for the drift-diffusion in the quasi-Fermi energy formulation have been used in [15,16].…”

Section: Algorithm Approachmentioning

confidence: 99%

A Hybrid Classical-Quantum Transport Model for the Simulation of Carbon Nanotube Transistors

Jourdana¹,

Pietra²

2014

SIAM J. Sci. Comput.

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In this paper, we propose a hybrid classical-quantum approach to study the electron transport in strongly confined nanostructures. The device domain is made of an active zone (where quantum effects are strong) sandwiched between two electron reservoirs (where the transport is considered highly collisional). A one dimensional effective mass Schrödinger system is coupled with a drift-diffusion model, both taking into account the peculiarities due to the strong confinement and to the two dimensional transversal crystal structure. Interface conditions are built preserving the continuity of the total current. Self-consistent computations are performed coupling the hybrid transport equations with the resolution of a Poisson equation in the whole three dimensional domain. To illustrate this hybrid strategy, we present simulations of a gate-all-around single-walled Carbon Nanotube Field-Effect Transistor.

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“…We obtain the quasi-Fermi energy ϕ. We recall that mixed finite elements schemes for the drift-diffusion in the quasi-Fermi energy formulation have been used in [15,16].…”

Section: Algorithm Approachmentioning

confidence: 99%

A Hybrid Classical-Quantum Transport Model for the Simulation of Carbon Nanotube Transistors

Jourdana¹,

Pietra²

2014

SIAM J. Sci. Comput.

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“…This has been described in detail in [64, pp 57-70]. Here we consider the simple case of problem (113) with a(x) = exp(−ψ(x)) for some function ψ, f as in (118), and u l = u r = 1. Taking the same basis functions as in [62], the discretized system is of the form…”

Section: Practical Considerationsmentioning

confidence: 99%

“…Similar combinations of methods, using the finite element method only for the discretization of Poisson's equation to obtain a global representation of the electric field, have also been described for other types of semiconductor device simulations. In [113], a combination of a mixed finite element method with an alternating direction implicit (ADI) method is presented for the modelling of semiconductor heterojunction structures. In [114], a standard quadratic finite element method is combined with a particle simulation method, such as the Monte Carlo method.…”

Section: Miscellaneousmentioning

confidence: 99%

Application of finite element methods to the simulation of semiconductor devices

1999

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In this paper a survey is presented of the use of finite element methods for the simulation of the behaviour of semiconductor devices. Both ordinary and mixed finite element methods are considered. We indicate how the various mathematical models of semiconductor device behaviour can be obtained from the Boltzmann transport equation and the appropriate closing relations. The drift-diffusion and hydrodynamic models are discussed in more detail. Some mathematical properties of the resulting nonlinear systems of partial differential equations are identified, and general considerations regarding their numerical approximations are discussed. Ordinary finite element methods of standard and non-standard type are introduced by means of one-dimensional illustrative examples. Both types of finite element method are then extended to two-dimensional problems and some practical issues regarding the corresponding discrete linear systems are discussed. The possibility of using special non-uniform fitted meshes is noted. Mixed finite element methods of standard and non-standard type are described for both one-and two-dimensional problems. The coefficient matrices of the linear systems corresponding to some methods of non-standard type are monotone. Ordinary and mixed finite element methods of both types are applied to the equations of the stationary drift-diffusion model in two dimensions. Some promising directions for future research are described.

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A comparison of formulations and non-linear solvers for computational modelling of semiconductor devices

Pérez-Escudero,

Codony,

Arias

et al. 2024

Comput Mech

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The drift-diffusion formulation, modelling semiconductor materials in terms of carrier densities and electric potential, is considered together with an alternative formulation in terms of dimensionless logarithmic quantities. Stability of both formulations in presence of sharp variations with a Galerkin Finite Element discretisation is assessed in two realistic problems: a p-n junction and an n-MOSFET device. The robustness with respect to the initial guess and the computational efficiency of the Newton-Raphson and Gummel non-linear solvers are also compared.

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Semiconductor Device Modelling for Heterojunctions Structures With Mixed Finite Elements

Cited by 7 publications

References 3 publications

A Hybrid Classical-Quantum Transport Model for the Simulation of Carbon Nanotube Transistors

A Hybrid Classical-Quantum Transport Model for the Simulation of Carbon Nanotube Transistors

Application of finite element methods to the simulation of semiconductor devices

A comparison of formulations and non-linear solvers for computational modelling of semiconductor devices

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