Temperature Compensation by Embedded Temperature Variation Method - PowerPoint PPT Presentation

Temperature Compensation by Embedded Temperature Variation Method for an AC Voltammeric Analyzer of Electroplating Baths Aleksander Jaworski, Hanna Wikiel and Kazimierz Wikiel Technic, Inc., Cranston, RI, USA Jaworski et al., 17th ESEAC, Rodos, Greece, June 3-7, 2018

Typical Copper Plating Bath Composition Copper Copper Sulfate 0.25-1 mol/L Sulfuric Acid 0.1-2 mol/l Acid Chloride Ion 20-100 ppm Chloride 100s ppm Suppressor ppm(s) Accelerator Wide (from sub-ppm to g/L) N + N Leveler + N + Jaworski et al., 17th ESEAC, Rodos, Greece, June 3-7, 2018 2

Superfilling Mechanisms of Submicron Features adsorption-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 plating Curvature Enhanced Accelerator Coverage Model P.M. Vereecken et al., IBM J. Res. & Dev. Vol. 49 No 1, January 2005, pp.3-18 Jaworski et al., 17th ESEAC, Rodos, Greece, June 3-7, 2018 3

“Simple System ”: Cu 2+ , H 2 S0 4 , Cl - , suppressor, accelerator P.M. Vereecken at al., IBM J. Res. & Dev. Vol.49 No 1 January 2005, p.3-18 Jaworski et al., 17th ESEAC, Rodos, Greece, June 3-7, 2018 4

Multitask Electrochemical Probe Jaworski et al., 17th ESEAC, Rodos, Greece, June 3-7, 2018 5

Temperature o C Leveler, Suppressor, Accelerator, N Lev N Supp N Acc 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 Two Training Sets: 0.83 1.00 1.33 19.0 at constant temperature 0.83 0.75 0.67 20.0 0.83 0.50 0.83 21.0 and with embedded 0.83 1.50 1.00 22.0 0.83 1.25 1.17 23.0 temperature variation 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 Jaworski et al., 17th ESEAC, Rodos, Greece, June 3-7, 2018 1.33 1.50 0.67 23.0 6

Fundamental Frequency AC Cyclic Voltammogram: Dependence on Leveler Concentration f =50 Hz, ϕ =0 o , A=50 mV, v=50 mV/s, E ini =0.8, E vertex =0 V vs. E Cu2+ /Cu 4 3.5 3 0.67 N_lev, CC3 AC current / mA 0.83 N_lev, CC8 2.5 1.00 N_lev, CC13 2 1.17 N_lev, CC18 1.5 1.33 N_lev, CC23 1 0.5 0 0 500 1000 1500 Index point of voltammogram, variable j Jaworski et al., 17th ESEAC, Rodos, Greece, June 3-7, 2018 7

Ƹ Ƹ Variable Selection Based on Leveler Impact Regression analysis of voltammetric data 𝒀 𝐽×𝐾 voltammetric data matrix 𝒅 𝐽×1 leveler concentration vector 𝒖 𝐽×1 temperature 𝑑 𝑗,𝑘 = 𝛾 0,𝑘 + 𝛾 1,𝑘 𝑦 𝑗,𝑘 LSR equation 𝑑 𝑗,𝑘 = 𝛾 0,𝑘 + 𝛾 1,𝑘 𝑦 𝑗,𝑘 + 𝛾 2,𝑘 𝑢 𝑗 trivariate regression eq. 2 𝐽 𝐽 𝐽 2 = σ𝑗=1 𝑑𝑗ො σ𝑗=1 𝑑𝑗 σ𝑗=1 ො Τ 𝑑𝑗,𝑘− 𝑑𝑗,𝑘 𝐽 𝑆 squared correlation coefficient 𝑘 2 2 𝐽 2− 𝐽 𝐽 2 − 𝐽 σ𝑗=1 𝑑𝑗 σ𝑗=1 𝑑𝑗 ൗ 𝐽 σ𝑗=1 𝑑𝑗,𝑘 ො σ𝑗=1 ො 𝑑𝑗,𝑘 ൗ 𝐽 Jaworski et al., 17th ESEAC, Rodos, Greece, June 3-7, 2018 8

Variable Selection Based on Leveler Impact Leveler calibrations: R 2 calculated individually for points of voltammograms of training sets CC and CV 1 0.9 0.8 0.7 0.6 R 2 Training set CC, 21C 0.5 Training set CV, no T compensation 0.4 Training set CV, with T compensation 0.3 0.2 0.1 0 0 500 1000 1500 Index point of voltammogram, variable j Jaworski et al., 17th ESEAC, Rodos, Greece, June 3-7, 2018 9

Variable Selection Based on Leveler Impact A selected portion of AC voltammogram for a range corresponding to applied DC potential of 260 to 134 mV vs. E Cu 2+ /Cu , respectively recorded at 21°C for different concentrations of leveler additive. 2.5 2 AC current / mA 0.67 N_lev, CC3 0.83 N_lev, CC8 1.5 1.00 N_lev, CC13 1.17 N_lev, CC18 1 1.33 N_lev, CC23 0.5 542 562 582 602 622 642 662 Index point of voltammogram, variable j Jaworski et al., 17th ESEAC, Rodos, Greece, June 3-7, 2018 10

Temperature o C Leveler, Suppressor, Accelerator, N Lev N Supp N Acc 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 Variable Selection 0.67 0.75 1.33 23.0 0.83 1.00 1.33 19.0 Based on 0.83 0.75 0.67 20.0 0.83 0.50 0.83 21.0 Temperature 0.83 1.50 1.00 22.0 0.83 1.25 1.17 23.0 Impact 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 Five subsets of the 1.00 0.50 1.00 23.0 1.17 0.75 1.00 19.0 training set with 1.17 0.50 1.17 20.0 parametrized leveler 1.17 1.50 1.33 21.0 1.17 1.25 0.67 22.0 concentration 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 Jaworski et al., 17th ESEAC, Rodos, Greece, June 3-7, 2018 1.33 1.50 0.67 23.0 11

Ƹ Variable Selection Based on Temperature Impact Relationship between temperature and univariate voltammetric data within 1/5 subsets of the training set 𝑢 𝑗 = 𝛽 0,𝑘 + 𝛽 1,𝑘 𝑦 𝑗,𝑘 regression equation 𝐽/5 𝑢 𝑗 Ƹ 𝐽/5 𝑢 𝑗 𝐽/5 Ƹ σ 𝑗=1 𝑢 𝑗,𝑘 − σ 𝑗=1 σ 𝑗=1 Τ 𝑢 𝑗,𝑘 ൗ 𝐽 5 2 = 𝑆 𝑢,𝑘 2 2 𝐽/5 𝑢 𝑗 𝐽/5 𝑢 𝑗 𝐽/5 Ƹ 𝐽/5 Ƹ 2 − 2 − σ 𝑗=1 σ 𝑗=1 Τ σ 𝑗=1 σ 𝑗=1 Τ ൗ 𝐽 5 𝑢 𝑗,𝑘 𝑢 𝑗,𝑘 ൗ 𝐽 5 squared correlation coefficient Jaworski et al., 17th ESEAC, Rodos, Greece, June 3-7, 2018 12

Variable Selection Based on Temperature Impact Squared correlation coefficients between selfpredicted and actual temperature values calculated individually for each point of voltammogram, subsets of matrix CV with parametrized leveler concentration 1 0.9 0.8 0.7 0.67 N_lev 0.6 R 2 0.83 N_Lev 0.5 1.00 N_Lev 0.4 1.17 N_Lev 0.3 0.2 1.33 N_Lev 0.1 0 0 500 1000 1500 Index point of voltammogram, variable j Jaworski et al., 17th ESEAC, Rodos, Greece, June 3-7, 2018 13

Variable Selection Based on Temperature Impact AC voltammogram for leveler, selected range 542-668, dependence on temperature at parametrized leveler concentration of 1.33 N_Lev 1.7 1.5 AC current / mA 1.3 19.0 C 20.0 C 1.1 21.0 C 0.9 22.0 C 23.0 C 0.7 0.5 542 562 582 602 622 642 662 Index point of voltammogram, variable j Jaworski et al., 17th ESEAC, Rodos, Greece, June 3-7, 2018 14

Ƹ Ƹ Calibration Calculation by Principal Component Regression (PCR) 𝒀 = 𝑻𝑾 𝑈 + 𝑭 PCA decomposition into scores S and loadings V 𝜸 = 𝑻 𝑈 𝑻 −1 𝑻 𝑈 𝒅 Inverse Least Squares Regression on scores 𝑑 𝑣 = 𝒚 𝑣 𝑾𝜸 Regression equation 𝑻 𝑢 = 𝑻 𝒖 PCA scores augmented with temperature 𝑈 𝑻 𝑢 −1 𝑻 𝑢 𝑈 𝒅 𝜸 𝑢 = 𝑻 𝑢 Inverse Least Squares Regression on scores augmented with temperature 𝑑 𝑣 = 𝒚 𝑣 𝑾 𝑢 𝑣 𝜸 𝑢 Regression equation with embedded temperature variance Jaworski et al., 17th ESEAC, Rodos, Greece, June 3-7, 2018 15

Prediction of Leveler Concentration in Validation Set Samples 22.5 o C 21.5 o C 1.40 1.40 1.20 1.20 1.00 1.00 Normalized leveler conc. N_lev 0.80 0.80 0.60 0.60 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 n Model at 21 o C n Embedded temp. var. n Actual 20.5 o C 19.5 o C 1.40 1.40 1.20 1.20 1.00 1.00 0.80 0.80 0.60 0.60 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 Jaworski et al., 17th ESEAC, Rodos, Greece, June 3-7, 2018 16

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