Quantification of Sodium‐Ion Migration in Silicon Nitride by Flatband‐Potential Monitoring at Device‐Operating Temperatures

Gastrow, Guillaume von; Martínez-Lorán, Erick; Scharf, Jonathan; Clenney, Jacob; Meier, Rico; Bandaru, Prabhakar R.; Bertoni, Mariana I.; Fenning, David P.

doi:10.1002/pssa.202000212

Cited by 2 publications

(9 citation statements)

References 25 publications

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“…As expected from the boundary conditions, we do not see depletion at the metal gate interface, in contrast to the closed system described in Section 4.1. We observe that, when

t < τ_{c}

, the numerical solution behaves identically to the approximation at short times given by the analytical solution to a pure diffusion problem with a moving reference frame, [ 47 ]

\begin{matrix} C (x, t) = \frac{C_{normals}}{2 B} [erfc (\frac{x - μ E t}{2 \sqrt{D t}}) \\ + erfc (- \frac{x - 2 L + μ E t}{2 \sqrt{D t}})] \end{matrix}

…”

Section: Resultsmentioning

confidence: 91%

“…The corresponding concentration profiles as a function of time are shown in Figure 3 , where the drift‐diffusion time is indicated in color scale. Figures 3a,b illustrate the transport kinetics at short times as modeled using the analytical approximation described by Gastrow et al [ 47 ] Figures 3c,d show the numerical solution to PNP coupled system with a constant source and a closed boundary at the semiconductor interface. The characteristic length for electric field assisted diffusion is given by the diffusion length plus the distance the ions move due to drift

L_{normalc} = 2 \sqrt{D t} + μ E t

…”

Section: Resultsmentioning

confidence: 99%

“…Three different values of h were used:

10^{- 8} cm {normals}^{- 1}

shown in cyan,

10^{- 10} cm {normals}^{- 1}

shown in blue, and

10^{- 12} cm {normals}^{- 1}

shown in magenta. For reference, the green circles indicate experimental data taken using the TraC‐BTS method [ 47 ] at

85^{\circ} C

.…”

Section: Resultsmentioning

confidence: 99%

“…Simulated kinetics of

{Na}^{+}

transport for low ion concentration relative to the applied bias. a) Simulated

{Na}^{+}

concentration profiles as a function of time (in color scale) using the analytical approximation from von Gastrow et al, [ 47 ] which yields a complementary error function solution (labeled as ERF) as shown in Equation (17) and b) its corresponding

Δ V_{FB}

as a function of time. c) Simulated

{Na}^{+}

concentration profiles as a function of time using the FEM solution to Equation (1) and (2) (PNP), and its corresponding

Δ V_{FB}

as a function of time.…”

Section: Resultsmentioning

confidence: 99%

“…The flatband voltage shift

Δ V_{FB}

was extracted as described in our previous work. [ 47 ]

Q_{s}

is estimated from

Δ V_{FB}

Q_{s} = ε Δ V_{FB} / L

.…”

Section: Methodsmentioning

confidence: 99%

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A Poisson–Nernst–Planck Model of Ion Transport and Interface Segregation in Metal–Insulator–Semiconductor Structures and Solar Cells

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Clenney

et al. 2021

Physica Status Solidi (b)

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The presence of trace alkali ions, especially sodium (Na þ ), in semiconductor devices has long been identified as a cause of device instability due to ion-drift-induced voltage screening under operating temperatures and applied potentials. [1][2][3][4][5] In the last decade, it has been established that sodium contamination in silicon photovoltaic (PV) modules leads to a catastrophic power loss known as potential-induced degradation (PID), [6][7][8][9] which can lead to failure within a timescale of a few hours to several days under accelerated testing. [10][11][12][13][14][15] A critical component of PID is the transport of Na ions across the dielectric-Si interface, ultimately leading to shunting of the p-n junction. In contrast, the possibility of harnessing ion transport in dielectrics has attracted increasing interest for applications in neuromorphic computing. [16][17][18] Establishing rigorous models for these ion transport phenomena is a necessary step toward comprehensive control of mobile ions in established and novel semiconductor device architectures.Historically, electrostatic models of mobile charges in metal-insulatorsemiconductor (MIS) structures have had some success in reproducing phenomenological effects. [4,[19][20][21] Among these models, Snow et al. [19] proposed an analytical approximation to ion transport in MIS structures, which adequately describes electrostatic measurements of the image

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“…As expected from the boundary conditions, we do not see depletion at the metal gate interface, in contrast to the closed system described in Section 4.1. We observe that, when

t < τ_{c}

, the numerical solution behaves identically to the approximation at short times given by the analytical solution to a pure diffusion problem with a moving reference frame, [ 47 ]