On discrete random dopant modeling in drift-diffusion simulations: physical meaning of `atomistic' dopants

Sano, Nobuyuki; Matsuzawa, K.; Mukai, M.; Nakayama, Noriaki

doi:10.1016/s0026-2714(01)00138-x

Cited by 98 publications

(60 citation statements)

References 10 publications

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“…However, the resolution of individual charges in "atomistic" simulations using a fine mesh creates problems [33]. Due to the use of Boltzmann or FermiDirac statistics in the classical drift-diffusion approach, the electron concentration follows the electrostatic potential gained from the solution of the Poisson equation.…”

Section: Simulation Approachmentioning

confidence: 99%

“…Attempts to correct these problems in "atomistic" simulations have been made by charge smearing [20], [35] or by splitting of the Coulomb potential into short-and longrange components based on screening considerations [33]. The charge-smearing approach is however purely empirical and can result in a loss of resolution with respect to "atomistic" scale effects.…”

Section: Simulation Approachmentioning

confidence: 99%

“…Particular attention has been paid to the resolution of each individual dopant in the simulation using fine grain discretization and DG quantum corrections for both electrons and holes. This avoids the arbitrary doping smearing [20] and/or the splitting of the Coulomb potential of the individual dopants into long-and short-range components [33].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Simulation Study of Individual and Combined Sources of Intrinsic Parameter Fluctuations in Conventional Nano-MOSFETs

Roy

Brown

Adamu-Lema

et al. 2006

IEEE Trans. Electron Devices

264

117

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Abstract-In this paper, using three-dimensional statistical numerical simulations, the authors study the intrinsic parameter fluctuations introduced by random discrete dopants, line edge roughness (LER), and oxide-thickness variations in realistic bulk MOSFETs scaled to 25, 18, 13, and 9 nm. The scaling is based on a 35 nm MOSFET developed by Toshiba, which has also been used for the calibration of the authors' "atomistic" device simulator. Special attention is paid to the accurate resolution of the individual discrete dopants in the drift-diffusion simulations by introducing density-gradient quantum corrections for both electrons and holes. In the LER simulations, two scenarios have been adopted: In the first one, LER follows the prescriptions of the International Roadmap for Semiconductors; in the second one, LER is kept constant close to the current best values. Combined effects of the different sources of intrinsic parameter fluctuations have also been simulated in the 35 nm reference devices and the results for the standard deviation of the threshold voltage compared to the measured values.

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Section: Simulation Approachmentioning

confidence: 99%

Section: Simulation Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Simulation Study of Individual and Combined Sources of Intrinsic Parameter Fluctuations in Conventional Nano-MOSFETs

Roy

Brown

Adamu-Lema

et al. 2006

IEEE Trans. Electron Devices

264

117

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show abstract

“…Even if microscopic simulations such as the MC method are concerned, the treatment of the electrons and impurities is not straightforward due to, again, the long-range nature of the Coulomb potential. The incorporation of the short range-range Coulomb potential in the MC method has been a long-standing issue [84]. This problem is, in general, avoided by assuming that the electrons and the impurities are always screened by the other carriers so that the short-range part of the Coulomb interaction is effectively suppressed.…”

Section: Theoretical Modelmentioning

confidence: 99%

Monte Carlo Device Simulations

Raleva¹,

Shaik

Hathwar

et al. 2011

Applications of Monte Carlo Method in Science and Engineering

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As semiconductor devices are scaled into nanoscale regime, first velocity saturation starts to limit the carrier mobility due to pronounced intervalley scattering, and when the device dimensions are scaled to 100 nm and below, velocity overshoot (which is a positive effect) starts to dominate the device behavior leading to larger ON-state currents. Alongside with the developments in the semiconductor nanotechnology, in recent years there has been significant progress in physical based modeling of semiconductor devices. First, for devices for which gradual channel approximation can not be used due to the two-dimensional nature of the electrostatic potential and the electric fields driving the carriers from source to drain, drift-diffusion models have been exploited. These models are valid, in general, for large devices in which the fields are not that high so that there is no degradation of the mobility due to the electric field. The validity of the drift-diffusion models can be extended to take into account the velocity saturation effect with the introduction of field-dependent mobility and diffusion coefficients. When velocity overshoot becomes important, drift diffusion model is no longer valid and hydrodynamic model must be used. The hydrodynamic model has been the workhorse for technology development and several high-end commercial device simulators have appeared including Silvaco, Synopsys, Crosslight, etc. The advantages of the hydrodynamic model are that it allows quick simulation runs but the problem is that the amount of the velocity overshoot depends upon the choice of the energy relaxation time. The smaller is the device, the larger is the deviation when using the same set of energy relaxation times. A standard way in calculating the energy relaxation times is to use bulk Monte Carlo simulations. However, the energy relaxation times are material, device geometry and doping dependent parameters, so their determination ahead of time is not possible. To avoid the problem of the proper choice of the energy relaxation times, a direct solution of the Boltzmann Transport Equation (BTE) using the Monte Carlo method is the best method of choice. That is why the focus of this review paper is on explaining basic Monte Carlo device simulator and then the focus will be shifted on the inclusion of various higher order effects that explain particular physical phenomena or processes.The Monte Carlo book chapter is organized as follows. First, the idea behind the Monte Carlo technique is outlined by revoking the path integral method for the solution of the BTE. This approach naturally leads to the free-flight-scatter sequence that is used in solving the BTE using the Monte Carlo method. Various scattering mechanisms relevant for different materials are given to completely specify the collision integral in the BTE. A discussion followed with the presentation of a generic flow-chart for implementing bulk Monte Carlo code is presented. Note that bulk Monte Carlo approach is suitable for the characterization of ma...

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“…16 Screening factor was calculated as 2 Â N 1/3 , where N is arsenic doping concentration. Since all the nanowire FETs had low boron doping concentration in the channel regions, only the arsenic dopants of the source/drain regions were randomized.…”

mentioning

confidence: 99%

Statistical variability study of random dopant fluctuation on gate-all-around inversion-mode silicon nanowire field-effect transistors

Yoon

Rim

Kim

et al. 2015

Applied Physics Letters

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On discrete random dopant modeling in drift-diffusion simulations: physical meaning of `atomistic' dopants

Cited by 98 publications

References 10 publications

Simulation Study of Individual and Combined Sources of Intrinsic Parameter Fluctuations in Conventional Nano-MOSFETs

Simulation Study of Individual and Combined Sources of Intrinsic Parameter Fluctuations in Conventional Nano-MOSFETs

Monte Carlo Device Simulations

Statistical variability study of random dopant fluctuation on gate-all-around inversion-mode silicon nanowire field-effect transistors

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