temperature compensation by embedded temperature variation … · 2019. 12. 14. · temperature...

Temperature Compensationby Embedded Temperature Variation Method

foran AC Voltammeric Analyzer of Electroplating Baths

Jaworski et al., 17th ESEAC, Rodos, Greece, June 3-7, 2018

Aleksander Jaworski, Hanna Wikiel and Kazimierz WikielTechnic, Inc., Cranston, RI, USA

2

Typical Copper Plating Bath Composition

Copper Copper Sulfate 0.25-1 mol/L

Acid Sulfuric Acid 0.1-2 mol/l

Chloride Chloride Ion 20-100 ppm

Suppressor

Accelerator

Leveler N+

N+

N+

ppm(s)

Wide (from sub-ppm to g/L)


100s ppm

3

Superfilling Mechanisms of Submicron Featuresadsorption-based, temperature dependent

Strong adsorbing Leveler inhibits plating (by deactivating accelerator) in the field and at the mouth of the feature.Diffusion-Consumption Model

Suppressor: adsorption instantaneous but weak, diffuses slowly, but moderately concentrated: adequate initial supply.

Accelerator: adsorption of moderate pace but strong, diffuses fast, but low concentration: insufficient initial supply, gradual displacement of suppressor, bottom-up platingCurvature Enhanced Accelerator Coverage Model

P.M. Vereecken et al., IBM J. Res. & Dev. Vol. 49 No 1, January 2005, pp.3-18


4Jaworski et al., 17th ESEAC, Rodos, Greece, June 3-7, 2018

P.M. Vereecken at al., IBM J. Res. & Dev. Vol.49 No 1 January 2005, p.3-18

“Simple System”:Cu2+ , H2S04, Cl-, suppressor, accelerator


Multitask Electrochemical Probe


Leveler, NLev

Suppressor,NSupp

Accelerator, NAcc

Temperature o C

0.67 0.50 0.67 19.0

0.67 1.50 0.83 20.0

0.67 1.25 1.00 21.0

0.67 1.00 1.17 22.0

0.67 0.75 1.33 23.0

0.83 1.00 1.33 19.0

0.83 0.75 0.67 20.0

0.83 0.50 0.83 21.0

0.83 1.50 1.00 22.0

0.83 1.25 1.17 23.0

1.00 1.50 1.17 19.0

1.00 1.25 1.33 20.0

1.00 1.00 0.67 21.0

1.00 0.75 0.83 22.0

1.00 0.50 1.00 23.0

1.17 0.75 1.00 19.0

1.17 0.50 1.17 20.0

1.17 1.50 1.33 21.0

1.17 1.25 0.67 22.0

1.17 1.00 0.83 23.0

1.33 1.25 0.83 19.0

1.33 1.00 1.00 20.0

1.33 0.75 1.17 21.0

1.33 0.50 1.33 22.0

1.33 1.50 0.67 23.0

Two Training Sets: at constant temperature and with embedded temperature variation

7

Fundamental Frequency AC Cyclic Voltammogram: Dependence on Leveler Concentration

f=50 Hz, ϕ=0o, A=50 mV, v=50 mV/s, Eini=0.8, Evertex=0 V vs. ECu2+ /Cu


0

0.5

1

1.5

2

2.5

3

3.5

4

0 500 1000 1500

AC

cu

rre

nt

/ m

A

Index point of voltammogram, variable j

0.67 N_lev, CC3

0.83 N_lev, CC8

1.00 N_lev, CC13

1.17 N_lev, CC18

1.33 N_lev, CC23

8

Variable Selection Based on Leveler ImpactRegression analysis of voltammetric data

𝑿 𝐼×𝐽 voltammetric data matrix

𝒄 𝐼×1 leveler concentration vector

𝒕 𝐼×1 temperature

Ƹ𝑐𝑖,𝑗 = 𝛽0,𝑗 + 𝛽1,𝑗𝑥𝑖,𝑗 LSR equation

Ƹ𝑐𝑖,𝑗 = 𝛽0,𝑗 + 𝛽1,𝑗𝑥𝑖,𝑗 + 𝛽2,𝑗𝑡𝑖 trivariate regression eq.

𝑅𝑗2 =

σ𝑖=1𝐼 𝑐𝑖ො𝑐𝑖,𝑗− Τσ𝑖=1

𝐼 𝑐𝑖 σ𝑖=1𝐼 ො𝑐𝑖,𝑗 𝐼

2

σ𝑖=1𝐼 𝑐𝑖

2− ൗσ𝑖=1𝐼 𝑐𝑖

2𝐼 σ𝑖=1

𝐼 ො𝑐𝑖,𝑗2 − ൗσ𝑖=1

𝐼 ො𝑐𝑖,𝑗2

𝐼squared correlation coefficient



0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 500 1000 1500

R2


Training set CC, 21C

Training set CV, no T compensation

Training set CV, with T compensation

Variable Selection Based on Leveler ImpactLeveler calibrations: R2 calculated individually for points of voltammograms of training sets CC and CV


0.5

1

1.5

2

2.5

542 562 582 602 622 642 662

AC

cu

rre

nt

/ m

A


0.67 N_lev, CC3

0.83 N_lev, CC8

1.00 N_lev, CC13

1.17 N_lev, CC18

1.33 N_lev, CC23

Variable Selection Based on Leveler ImpactA selected portion of AC voltammogram for a range corresponding to applied DC potential of 260 to 134 mV vs. E Cu2+ /Cu , respectively recorded at 21°C for different concentrations of leveler additive.


Leveler, NLev

Suppressor,NSupp

Accelerator, NAcc

Temperature o C

0.67 0.50 0.67 19.0

0.67 1.50 0.83 20.0

0.67 1.25 1.00 21.0

0.67 1.00 1.17 22.0

0.67 0.75 1.33 23.0

0.83 1.00 1.33 19.0

0.83 0.75 0.67 20.0

0.83 0.50 0.83 21.0

0.83 1.50 1.00 22.0

0.83 1.25 1.17 23.0

1.00 1.50 1.17 19.0

1.00 1.25 1.33 20.0

1.00 1.00 0.67 21.0

1.00 0.75 0.83 22.0

1.00 0.50 1.00 23.0

1.17 0.75 1.00 19.0

1.17 0.50 1.17 20.0

1.17 1.50 1.33 21.0

1.17 1.25 0.67 22.0

1.17 1.00 0.83 23.0

1.33 1.25 0.83 19.0

1.33 1.00 1.00 20.0

1.33 0.75 1.17 21.0

1.33 0.50 1.33 22.0

1.33 1.50 0.67 23.0

Variable Selection Based on Temperature Impact

Five subsets of the training set with parametrized leveler concentration

12

Variable Selection Based on Temperature Impact Relationship between temperature and univariate voltammetric data

within 1/5 subsets of the training set

Ƹ𝑡𝑖 = 𝛼0,𝑗 + 𝛼1,𝑗𝑥𝑖,𝑗 regression equation

𝑅𝑡,𝑗2 =

σ𝑖=1𝐼/5

𝑡𝑖 Ƹ𝑡𝑖,𝑗 − σ𝑖=1𝐼/5

𝑡𝑖 ൗσ𝑖=1𝐼/5 Ƹ𝑡𝑖,𝑗 Τ𝐼 5

σ𝑖=1𝐼/5

𝑡𝑖2 − ൗσ

𝑖=1𝐼/5

𝑡𝑖2

Τ𝐼 5 σ𝑖=1𝐼/5 Ƹ𝑡𝑖,𝑗

2 − ൗσ𝑖=1𝐼/5 Ƹ𝑡𝑖,𝑗

2Τ𝐼 5

squared correlation coefficient


13

Variable Selection Based on Temperature ImpactSquared correlation coefficients between selfpredicted and actual temperature values calculated individually for

each point of voltammogram, subsets of matrix CV with parametrized leveler concentration


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 500 1000 1500

R2


0.67 N_lev

0.83 N_Lev

1.00 N_Lev

1.17 N_Lev

1.33 N_Lev

14

Variable Selection Based on Temperature ImpactAC voltammogram for leveler, selected range 542-668, dependence on temperature at parametrized

leveler concentration of 1.33 N_Lev


0.5

0.7

0.9

1.1

1.3

1.5

1.7

542 562 582 602 622 642 662

AC

cu

rre

nt

/ m

A


19.0 C

20.0 C

21.0 C

22.0 C

23.0 C

15

Calibration Calculation by Principal Component Regression (PCR)

𝑿 = 𝑺𝑽𝑇 + 𝑬 PCA decomposition into scores S and loadings V𝜷 = 𝑺𝑇𝑺 −1𝑺𝑇𝒄 Inverse Least Squares Regression on scoresƸ𝑐𝑢 = 𝒙𝑢𝑽𝜷 Regression equation

𝑺𝑡 = 𝑺 𝒕 PCA scores augmented with temperature𝜷𝑡 = 𝑺𝑡

𝑇𝑺𝑡−1𝑺𝑡

𝑇𝒄 Inverse Least Squares Regression on scores augmented with temperature

Ƹ𝑐𝑢 = 𝒙𝑢𝑽 𝑡𝑢 𝜷𝑡 Regression equation with embedded temperature variance



0.60

0.80

1.00

1.20

1.40

1 2 3 4 5 6 7 8

22.5o C

0.60

0.80

1.00

1.20

1.40

1 2 3 4 5 6 7 8

21.5o C

0.60

0.80

1.00

1.20

1.40

1 2 3 4 5 6 7 8

20.5o C

0.60

0.80

1.00

1.20

1.40

1 2 3 4 5 6 7 8

19.5o C

n Actual n Model at 21o C n Embedded temp. var.

No

rmal

ized

leve

ler

con

c. N

_lev

Prediction of Leveler Concentration in Validation Set Samples

17

Conclusions


General, rigorous routine for the development of the analytical method using a chemometric model with temperature variation embedded in regression is introduced for exemplary determination of leveler additive concentration by AC voltammetry.

Chemometrics is critical in mitigating the adverse effect of temperature variation on accuracy of concentration prediction by an on-line AC voltammetric analyzer.

Accurate calibration can be calculated for experimental conditions where hard-models do not exist.

Chemometrics promotes an interest in AC-based electroanalytical techniques for industrial applications.

temperature compensation by embedded temperature variation … · 2019. 12. 14. · temperature...

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