Simulation of field-assisted ion exchange in glass regarding the space-charge density and pseudo-mixed-alkali effect

Daniel Schaeffer; Daniel Klenkert; Julian Stauch; Felix Brand; Wolfgang Foss; Julian Schwietering; Philipp Wachholz; Maria Kufner

doi:10.1364/AO.427171

Applied Optics
Vol. 60,
Issue 22,
pp. 6632-6638
(2021)
•https://doi.org/10.1364/AO.427171

Simulation of field-assisted ion exchange in glass regarding the space-charge density and pseudo-mixed-alkali effect

Daniel Schaeffer, Daniel Klenkert, Julian Stauch, Felix Brand, Wolfgang Foss, Julian Schwietering, Philipp Wachholz, and Maria Kufner

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Daniel Schaeffer, Daniel Klenkert, Julian Stauch, Felix Brand, Wolfgang Foss, Julian Schwietering, Philipp Wachholz, and Maria Kufner, "Simulation of field-assisted ion exchange in glass regarding the space-charge density and pseudo-mixed-alkali effect," Appl. Opt. 60, 6632-6638 (2021)

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Abstract

A model is proposed to describe the field-assisted molten salt ion exchange of ${{\rm Na}^ +}$ with ${{\rm Ag}^ +}$ in glass. It accounts for the buildup of space-charge zones and for the pseudo-mixed-alkali effect. Simulations in 1D proved to be consistent with experimental results. The 1D model has been expanded to 2D, making it suitable for simulating the fabrication of channel waveguides. Using a first-order approximation, a good agreement between the simulations and the experimental data can be achieved.

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Corrections

Daniel Schaeffer, Daniel Klenkert, Julian Stauch, Felix Brand, Wolfgang Foss, Julian Schwietering, Philipp Wachholz, and Maria Kufner, "Simulation of field-assisted ion exchange in glass regarding the space-charge density and pseudo-mixed-alkali effect: erratum," Appl. Opt. 62, 5202-5202 (2023)
https://opg.optica.org/ao/abstract.cfm?uri=ao-62-19-5202

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Supplementary Material (9)

Name	Description
Data File 1	2D refractive index profile measured with refracted near field apparatus. Ion exchange conducted at 305°C for 180 min, external voltage: 0 V.
Data File 2	2D refractive index profile measured with refracted near field apparatus. Ion exchange conducted at 305°C for 180 min, external voltage: 15 V.
Data File 3	2D refractive index profile measured with refracted near field apparatus. Ion exchange conducted at 305°C for 180 min, external voltage: 30 V.
Data File 4	2D refractive index profile measured with refracted near field apparatus. Ion exchange conducted at 305°C for 180 min, external voltage: 45 V.
Data File 5	2D refractive index profile measured with refracted near field apparatus. Ion exchange conducted at 275°C for 180 min, external voltage: 0 V.
Data File 6	2D refractive index profile measured with refracted near field apparatus. Ion exchange conducted at 275°C for 180 min, external voltage: 15 V.
Data File 7	2D refractive index profile measured with refracted near field apparatus. Ion exchange conducted at 275°C for 180 min, external voltage: 30 V.
Data File 8	2D refractive index profile measured with refracted near field apparatus. Ion exchange conducted at 275°C for 180 min, external voltage: 45 V.
Data File 9	2D refractive index profile measured with refracted near field apparatus. Ion exchange conducted at 290°C for 180 min, external voltage: 0 V.

Data Availability

Data underlying the results presented in this paper are available in Data Files 1–9.

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Surface	Top, $x = 0$	Bottom, $x = d$
${A g}^{+}$ concentration	$c_{A g} = 1$	$c_{A g} = 1$
${N a}^{+}$ concentration	$c_{N a} = 0$	$c_{N a} = 0$
Electric potential	$φ = 0$	$φ = - V_{0}$

Surface	Top, $x = 0$	Bottom, $x = a$
${A g}^{+}$ concentration	$c_{A g} = 1$	$c_{A g} = 0$
${N a}^{+}$ concentration	$c_{N a} = 0$	$c_{N a} = 1$
Electric potential	$φ = 0$	$φ = - V_{0} \frac{a}{d}$

Constant	Value
$D_{0, N a} (m^{2} s^{- 1})$	$(3.88 \pm 0.19) \cdot 10^{- 7}$
$D_{0, A g} (m^{2} s^{- 1})$	$(1.94 \pm 0.10) \cdot 10^{- 7}$
$b_{N a}$	$(- 0.05 \pm 0.03)$
$b_{A g}$	$(1.25 \pm 0.03)$
$T_{0} (K)$	10710

Surface	Top, masked	Top, mask opening	Bottom
${A g}^{+}$ concentration	$\frac{\partial}{\partial n} c_{A g} = 0$	$c_{A g} = 1$	$c_{A g} = 0$
${N a}^{+}$ concentration	$\frac{\partial}{\partial n} c_{N a} = 0$	$c_{N a} = 0$	$c_{N a} = 1$
Electric potential	$φ = 0$	$φ = 0$	$φ = - V_{0} \frac{a}{d}$

Surface	Top, $x = 0$	Bottom, $x = d$
${A g}^{+}$ concentration	$c_{A g} = 1$	$c_{A g} = 1$
${N a}^{+}$ concentration	$c_{N a} = 0$	$c_{N a} = 0$
Electric potential	$φ = 0$	$φ = - V_{0}$

Abstract

Corrections

Supplementary Material (9)

Data Availability

Cited By

Figures (7)

Tables (5)

Equations (8)

Applied Optics