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Scaling Analysis of Roughness Scaling Analysis of Roughness During Silver ElectrodepositionDuring Silver Electrodeposition
David G. Fostera,b and Jacob Jornéa
aDepartment of Chemical Engineering University of Rochester, Rochester NY 14727
bEastman Kodak Company, Rochester, NY 14650
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Silver ElectrodepositionSilver Electrodeposition
• Successfully done for many years• Majority of information remains empirical• Solutions evolve to better environmental
positions, silver electrodeposition has changed
• Previous work described the differences in plating silver from sodium and ammonium thiosulfate solutions
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Electrolytic Silver RecoveryElectrolytic Silver Recovery
At the Cathode:[Ag(S2O3)2]3- + e- Ago + 2S2O3
2-
S2O32- + 8e- + 8H+ 2HS- + 3H2O
2SO3 2- + 4H+ + 2e- S2O4
2- + 2H2OAt the Anode:SO3
2- + H2O 2H+ + SO42- + 2e-
S2O32- + H2O 2H+ + SO4
2- + 2e- + S
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Surface Roughness EvaluationSurface Roughness Evaluation
Roughness: important consideration in evaluating deposit quality
1. AFM images of surface topography
2. Scaling analysis
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AFM Flow CellFluid Cell
O-Ring
Silver Wire attachedwith silver epoxy
Vapor Deposited SilverSubstrate (workingelectrode)
Inlet Port
Silver Wire ReferenceElectrode
Silver WireCounterElectrode
Outlet Port
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Ammonium Thiosulfate Sodium Thiosulfate
0.20 C 0.20 C
0.45C 0.45 C
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Scaling Analysis
[ ][ ]2),(),( yxHyxH −=σ
rms of self-affine surfaces scales as: σ(L,t) = Lαf(t/Lα/β)
where the function f(t/Lα/β) is defined so that:σ ∝ Lα for t/Lα/β >> 1
σ ∝ tβ for t/Lα/β << 1
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Surface Roughness: roughness exponent400
α = slope
Expectedsaturationα = roughness exponent
• characterizes the roughness of the interface
• calculated by determining the slope of the log-log plot of the rms height vs length scale plot before saturation
β = growth exponent• characterizes the time-
dependent dynamics of the roughening surface
• calculated by determining the slope of the saturation rms height versus deposition time
rms h
eigh
t (nm
)
40040
4000 40000
Length (nm)
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Rms Roughness vs Length
100 1000 10000 100000
Length (nm)
10
100
1000
rms r
ough
ness
(nm
)
0.45 C0.40 C0.35 C0.30 C0.25 C0.20 C
100 1000 10000 100000
Length (nm)
10
100
1000
rms r
oug h
ness
( nm
)0.45 C0.40 C0.35 C0.30 C0.25 C0.20 C
Ammonium Sodium
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Roughness vs. Deposition Time
• Surfaces plated from ammonium thiosulfate always rougher
• Slope of sodium slightly higher
βNH4 < βNa
400 4000
Deposition time (sec)
50
500
satu
ratio
n rm
s (nm
)
ammoniumsodium
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Scaling Analysis ResultsSOLUTION GROWTH
EXPONENT, βROUGHNESSEXPONENT, α
SATURATEDRMS HEIGHT
AT 0.35 CAmmoniumthiosulfate
0.71 0.62 ± 0.05 188.9
Sodiumthiosulfate
0.88 0.36 ± 0.03 131.2
Surface Diffusion 0.25 1.0
Surface Diffusionand Step Growth
0.20 0.67
KPZ Equation 0.25 0.39
Ballistic 0.23 0.30
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Surface Diffusion and Step Growth
• Adatoms on the surface move toward the growing asperity
• Ions in solution, move toward the top of the asperity
Silver adatom on the surface
Silver ion in solution
Silver metal
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Silver Growth on Top of AsperityDeposition from Ammonium Thiosulfate Solution
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Leveling Mechanisms
• Erosion/dissolution of asperity
• Filling in of surface valleys
Adatom
Erosion
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Ammonium vs SodiumAmmonium Thiosulfate Sodium Thiosulfate
NaNaNH4NH4
Plating from Ammonium system• rougher surface• slows down surface diffusion
Plating from Sodium system• smoother surfaces • slows/blocks step growth
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Conclusions• Scaling analysis is a useful tool in describing surface
growth of silver electrodeposited surfaces• Silver electrodeposition from ammonium thiosulfate is
dominated by surface diffusion and step growth• Silver electrodeposition from sodium thiosulfate is
dominated by erosion of asperities and filling in a surface recesses
• The poor agreement with the experimentally obtained values for β with those of the continuum models suggests that there are effects going on experimentally that the models do not account for.
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Future Work
• Further examination of sodium and ammonium differences in plating other metals
• Modeling work to better understand the differences between experimental and continuum models
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Acknowledgment
We gratefully acknowledgeEastman Kodak Companyfor supporting this research.