Analytic light—or radiation—induced pn junction photocurrent solutions to the multidimensional ambipolar diffusion equation

Axness, Carl L.; Kerr, Bert; Wunsch, T.F.

doi:10.1063/1.1769100

Cited by 12 publications

(62 citation statements)

References 7 publications

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“…The expression is a generalization to that derived in reference [9]. We make the following assumptions in the depleted region:…”

Section: Simple Approximation To the Depletion Current For An Abrupt mentioning

confidence: 99%

“…The solution to the problem for a constant minority carrier lifetime (i.e. no neutron pulse) is known [9].…”

Section: Simple Approximation To the Depletion Current For An Abrupt mentioning

confidence: 99%

“…This work suggested the use of finite Fourier sine transforms to solve problems involving the ADE. This SAND report generalizes the solutions of [9] to the particular case where there is a time-dependent change in the carrier lifetime during or after irradiation. Such behavior might be expected for a neutron pulse that is not coincident with a gamma irradiation of the device.…”

Section: Introductionmentioning

confidence: 99%

“…Work by Axness, Kerr, and Wunsch [9] extended the solution to monochromatic light pulses and found an n-dimensional transformation from the ADE to the non-homogeneous heat equation. This work suggested the use of finite Fourier sine transforms to solve problems involving the ADE.…”

Section: Introductionmentioning

confidence: 99%

“…Using the above assumptions, analytic solutions to the ambipolar diffusion equation for the photocurrent response to irradiated 1D pn junction diodes have been developed over the past four decades ( [8], [9], [10], [11], [12], [13]). These photocurrent solutions are applicable under limited boundary conditions with restrictions on the carrier generation rate.…”

Section: Introductionmentioning

confidence: 99%

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Analytic 1D pn junction diode photocurrent solutions following ionizing radiation and including time-dependent changes in the carrier lifetime.

Axness¹,

Keiter²,

Kerr

2011

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Circuit simulation tools (e.g., SPICE [1]) have become invaluable in the development and design of electronic circuits in radiation environments. These codes are often employed to study the effect of many thousands of devices under transient current conditions. Device-scale simulation tools (e.g., MEDICI [2]) are commonly used in the design of individual semiconductor components, but require computing resources that make their incorporation into a circuit code impossible for large-scale circuits. Analytic solutions to the ambipolar diffusion equation, an approximation to the carrier transport equations, may be used to characterize the transient currents at nodes within a circuit simulator. We present new transient 1D excess carrier density and photocurrent density solutions to the ambipolar diffusion equation for low-level radiation pulses that take into account a finite device geometry, ohmic fields outside the depleted region, and an arbitrary change in the carrier lifetime due to neutron irradiation or other effects. The solutions are specifically evaluated for the case of an abrupt change in the carrier lifetime during or after, a step, square, or piecewise linear radiation pulse. Noting slow convergence of the raw Fourier series for certain parameter sets, we use closed-form formulas for some of the infinite sums to produce "partial closed-form" solutions for the above three cases. These "partial closed-form" solutions converge with only a few tens of terms, which enables efficient large-scale circuit simulations.

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“…The expression is a generalization to that derived in reference [9]. We make the following assumptions in the depleted region:…”

Section: Simple Approximation To the Depletion Current For An Abrupt mentioning

confidence: 99%

“…The solution to the problem for a constant minority carrier lifetime (i.e. no neutron pulse) is known [9].…”

Section: Simple Approximation To the Depletion Current For An Abrupt mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analytic 1D pn junction diode photocurrent solutions following ionizing radiation and including time-dependent changes in the carrier lifetime.

Axness¹,

Keiter²,

Kerr

2011

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Development of data‐driven exponential integrators with application to modeling of delay photocurrents

Bochev

Paskaleva

2021

Numerical Methods Partial

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Radiation-induced photocurrent effects represent a threat to microelectronic components operating in space, manmade and terrestrial radiation environments. Analysis of these threats by circuit simulations requires accurate and computationally efficient compact models. Most existing compact models are based on closed form analytic solutions of the governing equations and require empirical assumptions and idealizations that can limit their validity. In this paper we formulate an alternative numerical, data-driven approach that learns a compact model from data representative of the type of measurements one can obtain in an experimental facility. To develop the model we start from a generic discrete-time dynamical system and then use physics knowledge to refine its structure. Numerical studies demonstrate the potential of the model and establish some empirical guidelines for its training.

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Learning compact physics‐aware delayed photocurrent models using dynamic mode decomposition

Hanson

Bochev

Paskaleva

2020

Statistical Analysis

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Radiation-induced photocurrent in semiconductor devices can be simulated using complex physics-based models, which are accurate, but computationally expensive. This presents a challenge for implementing device characteristics in high-level circuit simulations where it is computationally infeasible to evaluate detailed models for multiple individual circuit elements. In this work we demonstrate a procedure for learning compact delayed photocurrent models that are efficient enough to implement in large-scale circuit simulations, but remain faithful to the underlying physics. Our approach utilizes dynamic mode decomposition (DMD), a system identification technique for learning reduced-order discrete-time dynamical systems from time series data based on singular value decomposition. To obtain physics-aware device models, we simulate the excess carrier density induced by radiation pulses by solving numerically the ambipolar diffusion equation, then use the simulated internal state as training data for the DMD algorithm. Our results show that the significantly reduced-order delayed photocurrent models obtained via this method accurately approximate the dynamics of the internal excess carrier density-which can be used to calculate the induced current at the device boundaries-while remaining compact enough to incorporate into larger circuit simulations.

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Analytic light—or radiation—induced pn junction photocurrent solutions to the multidimensional ambipolar diffusion equation

Cited by 12 publications

References 7 publications

Analytic 1D pn junction diode photocurrent solutions following ionizing radiation and including time-dependent changes in the carrier lifetime.

Analytic 1D pn junction diode photocurrent solutions following ionizing radiation and including time-dependent changes in the carrier lifetime.

Development of data‐driven exponential integrators with application to modeling of delay photocurrents

Learning compact physics‐aware delayed photocurrent models using dynamic mode decomposition

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