Recovering doping profiles in semiconductor devices with the Boltzmann–Poisson model

Cheng, Yingda; Gamba, Irene M.; Ren, Kui

doi:10.1016/j.jcp.2011.01.034

Cited by 26 publications

(26 citation statements)

References 64 publications

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“…Theorem 1. Let T > 0 and define Σ as in (9). Assume J , J k are Lipschitz continuous, have at most linear asymptotic growth and have sufficiently high derivatives.…”

Section: Stochastic Gradient Descent Methodsmentioning

confidence: 99%

Online learning in optical tomography: a stochastic approach

Chen

Liu

2018

Inverse Problems

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We study the inverse problem of radiative transfer equation (RTE) using stochastic gradient descent method (SGD) in this paper. Mathematically, optical tomography amounts to recovering the optical parameters in RTE using the incoming-outgoing pair of light intensity. We formulate it as a PDE-constraint optimization problem, where the mismatch of computed and measured outgoing data is minimized with same initial data and RTE constraint. The memory and computation cost it requires, however, is typically prohibitive, especially in high dimensional space. Smart iterative solvers that only use partial information in each step is called for thereafter. Stochastic gradient descent method is an online learning algorithm that randomly selects data for minimizing the mismatch. It requires minimum memory and computation, and advances fast, therefore perfectly serves the purpose. In this paper we formulate the problem, in both nonlinear and its linearized setting, apply SGD algorithm and analyze the convergence performance.

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“…Theorem 1. Let T > 0 and define Σ as in (9). Assume J , J k are Lipschitz continuous, have at most linear asymptotic growth and have sufficiently high derivatives.…”

Section: Stochastic Gradient Descent Methodsmentioning

confidence: 99%

Online learning in optical tomography: a stochastic approach

Chen

Liu

2018

Inverse Problems

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“…The modeling of transport of free conduction electrons and holes in semiconductor devices has been well studied in recent decades [1,31,35,41,44,61,77,79]. Many different models have been proposed, such as the Boltzmann-Poisson system [6,13,17,20,27,43,44,60,67,74], the energy transport system [23,30,44] and the drift-diffusion-Poisson system [2,14,22,21,44,61,73,75,80,83,84]. For the purpose of computational efficiency, we employ the reaction-drift-diffusion-Poisson model in this work.…”

Section: Transport Of Electrons and Holesmentioning

confidence: 99%

On the Modeling and Simulation of Reaction-Transfer Dynamics in Semiconductor-Electrolyte Solar Cells

He¹,

Gamba²,

Lee³

et al. 2015

SIAM J. Appl. Math.

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The mathematical modeling and numerical simulation of semiconductor-electrolyte systems play important roles in the design of high-performance semiconductor-liquid junction solar cells. In this work, we propose a macroscopic mathematical model, a system of nonlinear partial differential equations, for the complete description of charge transfer dynamics in such systems. The model consists of a reaction-drift-diffusion-Poisson system that models the transport of electrons and holes in the semiconductor region and an equivalent system that describes the transport of reductants and oxidants, as well as other charged species, in the electrolyte region. The coupling between the semiconductor and the electrolyte is modeled through a set of interfacial reaction and current balance conditions. We present some numerical simulations to illustrate the quantitative behavior of the semiconductor-electrolyte system in both dark and illuminated environments. We show numerically that one can replace the electrolyte region in the system with a Schottky contact only when the bulk reductant-oxidant pair density is extremely high. Otherwise, such replacement gives significantly inaccurate description of the real dynamics of the semiconductor-electrolyte system.

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“…However, a long standing challenge of the reconstruction process centers around the stability issue. If the injected photons carry low energy, the resulting images are very blurred, and the reconstruction is typically unstable [9,10,17,18,29,31]. This phenomenon is the so-called diffuse optical tomography, especially when the injected light is near-infrared.…”

Section: Introductionmentioning

confidence: 99%

On diffusive scaling in acousto-optic imaging

Chung

Lai²,

Qin³

2020

Preprint

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Acousto-optic imaging (AOI) is a hybrid imaging process. By perturbing the to-bereconstructed tissues with acoustic waves, one introduces the interaction between the acoustic and optical waves, leading to a more stable reconstruction of the optical properties. The mathematical model was described in [25], with the radiative transfer equation serving as the forward model for the optical transport. In this paper we investigate the stability of the reconstruction. In particular, we are interested in how the stability depends on the Knudsen number, Kn, a quantity that measures the intensity of the scattering effect of photon particles in a media. Our analysis shows that as Kn decreases to zero, photons scatter more frequently, and since information is lost, the reconstruction becomes harder. To counter this effect, devices need to be constructed so that laser beam is highly concentrated. We will give a quantitative error bound, and explicitly show that such concentration has an exponential dependence on Kn. Numerical evidence will be provided to verify the proof.

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Recovering doping profiles in semiconductor devices with the Boltzmann–Poisson model

Cited by 26 publications

References 64 publications

Online learning in optical tomography: a stochastic approach

Online learning in optical tomography: a stochastic approach

On the Modeling and Simulation of Reaction-Transfer Dynamics in Semiconductor-Electrolyte Solar Cells

On diffusive scaling in acousto-optic imaging

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