Patent Application: US-62107903-A

Abstract:
the present invention relates generally to any plating solution and methods for monitoring its performance . more specifically , the present invention relates to plating bath and methods for monitoring its plating functionality based on chemometric analysis of voltammetric data obtained for these baths . more particularly , the method of the present invention relates to application of numerous chemometric techniques to describe quantitatively plating bath functionality in order to maintain its proper performance .

Description:
unless otherwise stated , computations were done using the matlab ver . 6 . 0 environment ( the math works , inc ., natick , mass .) with the pls_toolbox ver . 2 . 1 . 1 ( eigenvector research , inc ., manson , wash .). the data of the training set consists of independent variables , voltammograms , and dependent variables , concentrations corresponding to the voltammograms . the number of independent variables , which corresponds to the chosen number of points of the voltammogram taken for the analysis , equals n . the number of dependent variables , in the cases discussed below , equals unity . the number of samples in the training set is m . the original data consists of a matrix of independent variables , x o ( m , n ), and a vector of dependent variables , c o ( m ). the upper index “ o ” denotes original ( means not transformed ). according to the formalism employed throughout the text a bold capital letter denotes a matrix . some matrices are described by two bold letters , the first of which is capital . a bold small case letter ( s ) denotes a vector . the superscript “ t ” and the subscript “− 1 ” denote a transposed matrix / vector and an inverse matrix , respectively . the subscript “ u ” denotes an unknown sample ( s ). preprocessing refers to the transformation of the original data in order to enhance the information representation . after the transformation a variable is referred to as a feature to distinguish it from the original variable . the preprocessing method most commonly applied throughout this paper is the autoscaling to unit variance [ 8 , 9 ] which refers to meancentering followed by dividing by the standard deviation , s j , on a variable by variable basis : x i , j = x i , j o - x j μ s j ( 1 ) where x j μ = ∑ i = 1 m   x i , j o m ( 2 ) and s j = 1 m - 1  ∑ i = 1 m   ( x i , j o - x j μ ) 2 ( 3 ) application of autoscaling transforms original variables x o and c o into features x and c , respectively . if not otherwise stated , all features , both dependent ( c ) and independent ( x ), of the calculations presented below are assumed to be autoscaled to unit variance . independent variables for prediction are being transformed prior the calculations using autoscaling parameters of the training set . predicted concentrations ( dependent variables ) are obtained via retransformation of predicted independent features using autoscaling parameters of the training set . the properly conducted calibration starts with several preparatory steps that were discussed in details by wikiel et al . [ 1 ]. the first step is the determination of the optimal calibration range . the following step aimed at outlier detection within the training set prior regression calculation requires a closer look as it is also used for generation of some statistical parameters applied for outlier detection among unknown samples . the principal component analysis ( pca ) [ 10 , 11 ] method is applied to decompose matrix x ( m , n ) into matrices being outer products of vectors called scores ( s ( m , a )) and loadings ( v ( n , a )), where a is a number of factors capturing most of the total variance . several methods , pair - by - pair nonlinear iterative partial least squares ( nipals ) [ 9 , 12 ], successive average orthogonalization ( sao ) [ 13 ] and that calculating all the principal components at once via the variance co - variance matrix ( jacobi transformation [ 14 , 15 ], householder reduction [ 14 , 15 ]) were used to decompose data matrix x . the results of all methods were practically identical . the pca calculations were done in ms visual basic ( vb ) and were compared to results obtained with matlab singular value decomposition technique to reach full agreement . all computations discussed below connected with outlier detection were done in vb and in matlab mostly in order to verify their correctness . in case of vb programs the nipals method was chosen as optimal ( based mostly on the time factor ) for x matrix decomposition . the regression is calculated using pcr [ 16 - 18 ] and pls [ 8 , 9 , 16 - 19 ] method . both of the regression methods are described in detail in the literature and are commonly used . as stressed by wikiel et al . [ 1 ], it is highly recommended to perform calculations aiming at obtaining the optimal number of factors ( by press [ 8 ]) and eliminating outliers by regression calculation from the training set ( methods based on concentration residuals : f - ratio and studentized concentration residuals versus leverages plot [ 1 , 20 ]) in the iterative sequence . the iteration should stop when the optimal number of factors is calculated and there are no outliers in the training set . having the correct number of factors determined and the outlier - free training set , one can perform the final regression calculation using pls or pcr methods . the outlier - free training set is also used for calculation of parameters like mahalanobis matrix ( equation 9 ), mahalanobis matrix calculated based on the residual augmented scores ( equation 11 ), residual variance ( equation 14 ) or residual sum of squares ( equation 6 ) which are later employed for outlier detection for unknown samples ( equation 17 ). the methods listed - above consist the core of the text presented below . obtained regression equations are used for prediction of carrier and brightener concentrations in samples of copper plating bath ( pc 75 , technic , inc .) contaminated with different concentration of tetra ( ethylene glycol ). predicted concentrations of these two components are presented in table 1 . actual concentrations of both analyzed components were 5 . 0 ml / l , what corresponds to the nominal values for analyzed bath . concentration predictions for both carrier and brightener seem not to be noticeably affected by the presence of contaminant , even for the highest values of contaminant concentration . analyzing these predictions , only the plating bath operator would be unaware of worsening conditions of the bath due to contamination leading to bad plating performance . one should realize that knowledge of the concentrations of components of the plating bath , which can be obtained via calibration and subsequent prediction , may not be sufficient information necessary to control the performance of that bath . the bath contaminants of various origin ( mostly organic additives degradation products ) accumulating in time may significantly impede the bath plating performance . such a situation can take place even if concentrations of deliberately added bath components are within the specification limits . pc 75 carrier , which is a polyglycol ether , undergoes degradation in the plating bath yielding shorter chain polyglycol fractions [ 21 ]. the degradation is difficult to monitor indirectly because is not correlated with amount of electricity flowing through the plating bath . a series of experiments were conducted employing pc 75 plating solution containing nominal concentration of brightener and carrier . the freshly prepared solution produces a uniform , bright deposit . small additions of tetraethylene glycol ( teg , 4 - monomer fragment of polyethylene glycol ) up to 200 ppm produce hull cell panels of acceptable to marginally acceptable appearance . an addition of teg at a level higher than 200 ppm leads to a dull deposit with vertical streaks ( 1b ). below there are presented several approaches applying pca and various versions of mahalanobis distance , simca , f s - ratio methods in order to determine the presence of the contaminant . while looking for a reliable calibration range and channel of the experimental voltammograms one is focused on current responses changing only with the concentration of the calibrated component . this means that the current signal should not be affected by the presence of all other bath components including degradation products and foreign contaminants . this approach was described by wikiel et al . [ 1 ] in the chapter “ determination of the calibration range ”. a completely opposite approach should be applied while picking up ranges and channels whose shape is possibly strongly affected by the presence of contaminants and / or foreign contaminants . the presence of contaminants may change the shape of the voltammogram making it qualitatively and quantitatively different then the voltammograms of the training set . therefore , by applying various chemometric methods one can quantify and detect outlying voltammograms that are affected by contaminants and / or foreign contaminants . in the experiments whose results are presented below , the freshly prepared nominal solutions of the plating bath were deliberately contaminated with tetra ( ethylene glycol ) of various concentration . this component is a possible degradation product of one of organic additives and can accumulate in the plating bath tank over time . the first method one can apply for outlier detection is a graphic approach based on the pca method . in this method the scores for two first principal components are plotted against each other . the scores for pc1 versus pc2 plot are calculated in the following way : the scores for training set are calculated by the pca decomposition of autoscaled training set matrix , x ( m , n ), to scores , s ( m , a ), and eigenvectors , v ( n , a ), for a number of factors a = 2 . the row vector of original unknown sample , x u o , is scaled using parameters of the training set to obtain x u . the scores for unknown sample ( the one suspected to be an outlier ) are calculated by multiplication of matrix of unknown voltammograms by eigenvector matrix of training set : a typical pc2 versus pc1 plot is presented in fig2 . one can notice that the scores of the training set are clustered . for the contaminated samples , the distance from the training set cluster increases with the increase in contaminant concentration , starting from 5 ppm . one can notice that the sample containing 1 ppm of contaminant , due to its location within the training set cluster , would not be detected as an outlier on this voltammogram yet . however , the sample containing 5 ppm of contaminant is already outside the training set cluster . another approach is based on projection of residual sum of squares for both training set and unknown samples versus principal component . the residuals for the training set are calculated quite straightforwardly : the autoscaled training set matrix , x , is decomposed by pca to scores ( s ) and eigenvectors ( v ) for a number of factors of a . the training set matrix is reconstructed using calculated scores and eigenvectors : for each i - th sample from the training set the residual sum of squares , also called q - residuals , is calculated employing the following formula : rs i = ∑ j = 1 n   ( x i , j - x i , j ) 2 ( 6 ) calculation of the residuals for unknown samples is a little more complex . for each unknown sample the following procedure should be applied : the autoscaled training set matrix , x , is being decomposed to scores ( s ) and eigenvectors ( v ) for a certain number of factors of a . unknown sample vector , x u o ( n ), is being scaled using parameters from the training set to obtain x u ( n ). the vector of residuals for unknown sample is calculated using equation : where i ( n , n ) is an identity matrix . the identity matrix is always square and contains ones on the diagonal and zeros everywhere else . the residual sum of squares ( q residuals ) for the unknown sample is calculated from the following expression : rp u = ∑ j = 1 n   e u , j 2 ( 8 ) the projection of the residual sum of squares for both training set and unknown samples versus first principal component is shown in fig3 . one can notice much bigger quantitative selectivity of q residuals versus pc1 projection than that of pc2 versus pc1 . the vertical width of the training set cluster is much smaller relative to the vertical distance of the outliers from the training set cluster in fig3 than in fig2 . outliers can also be predicted quantitatively ( purely numerically not graphically ) using several of versions of mahalanobis distance method coupled with pca : regular md / pca ( also called md ) and mahalanobis distance by principal component analysis with residuals ( md / pca / r ; also called mdr ). the procedure for prediction of squared mahalanobis distance value in unknown samples in md / pca is presented below : autoscaled matrix x ( m , n ) is decomposed by pca to principal components ( scores ), s , and loadings ( eigenvectors ), v . the mahalanobis matrix is calculated for the training set via the following equation : unknown sample vector , x u o ( n ), is being scaled using parameters from the training set to obtain x u ( n ). the squared mahalanobis distance for unknown sample is calculated using the following equation : values of mahalanobis distance for unknown samples are compared with that for the training set . in table 2 are listed d u values obtained from data of different voltammograms for various concentration of the contaminant . for comparison , the largest acceptable values of d for corresponding training sets are presented . one can notice that the sensitivity of md / pca method depends strongly on the kind of analyzed voltammogram ( its waveform ). some voltammograms ( mc1 , ch2 ; s4 , ch6 ; cr2 , ch3 ) are particularly sensitive to presence of contaminant , and d u value increases with increasing concentration of the contaminant . however , there are also voltammograms that seem not to be affected by the presence of contaminant ( cuac ch5 ). it is noticeable that the sensitivity of outlier detection by mahalanobis distance can be much higher than a simple functional test of hull cell panel plating . in example 2 , for up to 200 ppm of teg there was no obvious effect of this compound on the hull cell panel plating performance . in table 2 , one can easily notice that the significant electrochemical effect ( expressed as mahalanobis distance ) can be detected at the presence of teg as low as 5 ppm . for each i - th sample from the training set the residual sum of squares is calculated employing the equation 6 . the result is a column vector rs ( m ). the column vector rs is appended as the a + 1 st column to the matrix of scores s ( m , a ). this creates a residual augmented scores matrix , t ( m , a + 1 ). the i - th row of matrix t is the vector t i . unknown sample vector , x u o ( n ), is scaled using parameters from the training set to obtain x u ( n ). scores for unknown sample , row vector s u ( a ), are calculated using equation 4 . the column vector of residuals for the unknown sample , e u , is calculated employing equation 7 . squared sum residuals of the unknown sample , rp u , is computed according to the equation 8 . the scalar rp u is appended as the a + 1 st value in the row vector s u ( a ). this creates a residual augmented scores vector , t u ( a + 1 ). the square mahalanobis distance is predicted for the unknown sample applying the following expression : in table 3 there are listed dr u values obtained from same data used to calculate d u in table 2 . qualitatively the performance of md / pca / r is similar to that of md / pca in cases of mc1 , ch2 ( 180 - 280 ), cr2 ch3 ( 300 - 1200 ), and s4 ch6 ( 200 - 250 ). the voltammogram cuac - ch5 remains insensitive to contaminant concentration throughout whole range of teg concentrations while analyzed with md / pca ( table 2 , column 5 ). in contrast , md / pca / r detects outliers from the level of teg concentration of 5 ppm while analyzing the same data set ( table 3 , column 5 ). comparing the performance of md / pca and md / pca / r presented in tables 2 and 3 , one can conclude that the latter method has much higher resolution that the former one . the simca ( simple modeling of class analogy ) [ 8 ] method can also be applied for checking whether the unknown sample is a typical category member or is very distant from the model ( training set ) and therefore should be considered an outlier to that model . the procedure for outlier detection by simca is following : autoscaled matrix x ( m , n ) is decomposed by pca to principal components ( scores ), s , and loadings ( eigenvectors ), v . the matrix of residuals for the training set is calculated from the following expression : the residual variance for training set x is calculated using the following equation : rv 0 2 = ∑ i = 1 m   ∑ j = 1 n   e i , j 2 ( m - a - 1 )  ( n - a ) ( 14 ) the vector of unknown sample , x u ( n ), is being scaled using parameters from the training set . the vector of residuals for unknown sample , e u ( n ), is calculated using equation 7 . the predicted residual variance for x u normalized with respect to rv 0 2 is computed employing the following expression : rv u 2 = ∑ j = 1 n  e u , j 2 ( n - a )  rv 0 2 ( 15 ) in the following text , the results of predicted residuals variance normalized with respect to residual variance in the training set will be referred as simca . the procedure described above was used for outlier detection ( table 4 ) for the same data files as that of table 3 . comparing table 3 to table 4 , one can easily notice that simca performs very similarly both qualitatively and quantitatively to md / pca / r . therefore these two techniques can be applied equivalently for outlier detection for ac / dc voltammograms . another approach for detecting the outliers due to contamination in unknown samples is the f - ratio method based on residuals calculated for independent features , f s ratio . first , the f s - ratios are computed for the training set in order to determine the maximal acceptable value of f s - ratio [ 19 ] for the prediction : f i s = ( m - 1 )  rs i ∑ j ≠ i   rs j ( 16 ) then the f s - ratios for unknown sample are calculated using the following equation [ 19 ]: f u s = ( m )  rp u ∑ j = 1 m   rs j ( 17 ) the results of calculation of f s - ratios for some voltammograms are presented in table 5 . results in table 5 are analogous both qualitatively and quantitatively to those in tables 3 and 4 . it suggests that in considered cases mahalanobis distance values in case of md / pca / r method are determined in greater degree by residuals than by scores . the above examples ( 1 - 8 ) were focused on a copper plating bath with deliberately added teg , which simulates a possible breakdown product of organic additives . some studies were conducted in order to determine the fault detection ability of several chemometric outlier detection techniques to detect problems caused by other factors . the training set consisted of 25 solutions of a copper pc75 bath ( technic , inc .) prepared according to 5 - component , 5 - level linear orthogonal array . the concentration ranges for copper , acid , chloride , carrier and brightener were 14 - 20 g / l , 140 - 200 g / l , 30 - 80 ppm , 3 . 0 - 8 . 0 ml / l and 3 . 0 - 8 . 0 ml / l , respectively . additionally , the training set contained 9 solutions having copper , acid and chloride on the nominal level of 17 . 5 g / l , 175 g / l and 55 ppm , respectively . the concentrations of carrier and brightener were varied within the calibration ranges according to 2 - component , 3 - level full factorial array . the last solution of the training set contained all the five components on their nominal level , which for carrier and brightener is 6 ml / l and 5 ml / l , respectively . each solution of the training set was analyzed in duplicate . the outlying scans were generated using nominal solution with one experimental parameter being varied out of calibration conditions at a time . the nominal temperature for copper pc75 bath is 25 ° c . in order to generate the outliers due to temperature , the voltammetric data was collected for the pc75 bath solution of nominal composition at various temperatures : 6 , 15 , 30 , 40 and 50 ° c . four afore - mentioned outlier detection techniques were applied for shape analysis of the voltammogram ( dq21cu , channel 2 , 200 - 1000 , 3 factors ). this voltammogram was chosen because its shape is sensitive to changes in the bath induced by various factors . the obtained results are presented in fig4 . the maximal acceptable value of the outlier detection parameters obtained by crossvalidation within the training set were 3 . 39 , 4 . 26 , 3 . 72 and 3 . 95 for md / pca , md / pca / r , simca and f s ratio , respectively . one can notice much larger sensitivity for the methods utilizing q residuals in comparison to md / pca . the scale of the response for md / pca / r , simca and f s ratio is one order of magnitude larger than that of md / pca while maximal acceptable values for all three techniques are very close to each other . in contrary to sensitive md / pca / r , simca and f s ratio , the md / pca was not able to detect outliers at 30 ° c . and barely detected outliers at 15 ° c . in order to generate the outliers due to the copper concentration being out - of - calibration - range , the voltammetric data was collected for the pc75 bath solution with the copper content of 2 , 5 , 8 , 12 , 22 and 25 g / l . the concentrations of all other components and experimental conditions were nominal . the training data set is the same as in example 9 . the values of following chemometric parameters : md / pca , md / pca / r , simca and f s ratio , are presented in fig5 . the shapes of voltammograms obtained for the copper concentration closest to the lower and upper calibration limit , namely 12 and 22 g / l , respectively , do not differ enough from that of the training set to be detected as outliers . as mentioned above , the shape of the dq21cu voltammogram within the range of 200 - 1000 changes with the concentrations of other than copper components too . at first glance this may seem disadvantageous , but on the other hand the dq21cu voltammogram can guard the plating bath from disturbances of various origins simultaneously . in order to generate the outliers due to the brightener concentration being out - of - calibration - range , the voltammetric data was collected for the pc75 bath solution with the brightener content of 0 , 0 . 5 , 1 . 5 , 10 , 15 and 20 ml / l . the concentrations of all other components and experimental conditions were nominal . the training data set is the same as in example 9 . the values of following chemometric parameters : md / pca , md / pca / r , simca and f s ratio , are presented in fig6 . one can easily notice much higher discriminative power of all q residuals based techniques in comparison to md / pca . the md / pca / r , simca and f s - ratio methods proved to be capable to detect as outliers any solution containing brightener at the level different than that of the calibration range . all of the examples discussed above deal with the outlier detection in the artificially ( in controlled manner ) prepared outlying samples . this example focuses on a real - life example of the industrial plating solution contaminated with hydrogen peroxide . this kind of contamination is quite common in the industrial electroplating where hydrogen peroxide is used to oxidize all organic components ( mostly degradation products ) accumulated in the used plating bath and / or for plating tank cleaning ( leaching ). excess of hydrogen peroxide is supposed to decompose to water and oxygen , but some small amount of h 2 o 2 may remain in the plating solution impeding its plating performance . the deformation of the voltammogram due to the presence of h 2 o 2 contamination is apparent in fig7 where voltammograms recorded for contaminated and training set solutions are compared . in this case the training set was composed of several tens of industrially recorded voltammograms . they consisted of a representative sample covering all concentration variations allowed by process control requirements . all four outlier detection chemometric techniques , md / pca , md / pca / r , simca and f s ratio ( range 15 - 25 s , 3 factors ) easily detect voltammograms recorded for the contaminated bath as shown in the table 6 . moffat et al . [ 4 - 7 ] correlated the formation of the hysteretic shape of the cyclic current vs . potential response obtained in a copper plating bath with the capability of superconformal electrodeposition . they proposed using the extent of this phenomenon to monitor and explore additive consumption and efficiency . fig8 shows cyclic voltammograms obtained in pc75 copper plating bath with various concentration of pc75 brightener . the small hysteris loop can be observed in solutions with brightener concentration as low as 0 . 5 ml / l ( 10 % of the nominal concentration ). when the concentration of brightener increases , the size of this hysteretic loop is growing as well . hysteresis formation were observed ( fig8 ) for pc75 bath solutions when the brightener concentration was significantly below lower calibration limit ( 3 ml / l ). all other concentrations were at their nominal level . the calculation of md / pca , md / pca / r , simca and f s ratio was employed to check whether it is possible to quantify the hysteresis loop effect ( size ). the training set was the same as in examples 9 , 10 and 11 . results obtained from the calculations are presented in fig9 . for all outlier detection techniques the voltammograms recorded for brightener concentration 2 . 5 ml / l and lower are considered outlying . these results leave no doubt about the advantages of numerical versus visual approach for plating bath monitoring based on analysis of voltammetric data . one may notice that for this particular data there is no significant benefit in using q residuals based methods in comparison to md / pca . human error can also be a cause of plating bath malfunctioning . early detection of such malfunctioning can minimize production losses . in fig1 there is shown a real - life industrial example of dc - voltammetric scan deformation caused by improperly replenished additives in the copper plating bath . the deformated voltammograms are compared to the proper ones belonging to the industrial training set . the prediction results obtained via calculation using md / pca , md / pca / r , simca and f s ratio for deformated voltammograms for the temporal range of 20 - 45 s , using 3 factors are presented in table 7 . the sensitivity of the q residual based techniques is much bigger than that of pca / md in this case . it is mainly due to large qualitative difference between outlying and training set voltammograms within the temporal range taken for calculations . accumulation of degradation products in a plating bath in time depends on the way the bath is used and maintained . therefore the temporal factor is insufficient to determine whether the plating bath solution is already worn and contaminated with degradation products to a degree affecting plating performance . a real - life industrial example supporting the above statement is presented in fig1 . the concentration of all of bath components ( copper cubath sc , enthone ) in baths a and b were maintained constant over time by replenishments administered based on the bath analyses . the md / pca parameters were calculated from voltammograms recorded over a period of several weeks for two plating baths , a and b . these md / pca parameters were the measure of the accumulation of the degradation products in both baths . as it was determined empirically for that dc voltammogram of that bath , the plating performance is satisfactory as long as md / pca value does not exceed 6 . one may notice that a regularly administered feed and bleed procedure prevents the accumulation of the degradation products over time ( bath b ). on the other hand , passive consumption alone is sufficient to contaminate bath with degradation products beyond acceptable limits ( bath a ). determinant analysis of the shapes of voltammograms can warn the plating bath operator not only about the problems in the plating solution but also about the malfunctioning of the bath analyzer itself . as long as recorded voltammograms pass the chemometric scan qualifier tests the operator is in the comfortable situation of knowing that both plating solution and the bath analyzer are performing well . the voltammetric system can record not only the dc and ac - current components but also the potential applied to the working electrode . the differences in applied potentials among various voltammograms of the training set are minimal and so is the tolerance of the outlier detection techniques . an industrial example of faulty data acquisition causing the recorded applied potential data to be partially substituted by current data is shown in fig1 . the faulty data is compared to several proper potential data sets taken from the industrial training set . the range taken for outlier detection is 80 - 120 and number of factors equals two . outlier detection parameters obtained by md / pca , md / pca / r , simca and f s ratio are presented in table 7 . the aforementioned low tolerance of the determinant techniques is evident in the relatively ( to previous examples ) low value of the maximal outlier detection parameters from the crossvalidation within the training set . tremendous qualitative differences between outlying curves and that of the training set make the effect of q residuals to be dominant in md / pca / r , simca and f s ratio results . the following background documents are cited herein . to the extent necessary for a full and complete understanding of this invention , the disclosures of these documents are hereby incorporated herein by reference : [ 1 ] provisional patent application serial no . 60 / 397 , 120 , filed jul . 19 , 2002 as attorney docket no . 004522 / 00009 . 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[ 20 ] draper , n . r . and smith , h . applied regression analysis , 3 rd ed ., wiley , new york , 1998 . [ 22 ] shah , n . k . and gemperline , p . j . ; anal . chem ., 62 , ( 1992 ), 465 . the present invention has been described in detail , including the preferred embodiments thereof . however , it will be appreciated that those skilled in the art , upon consideration of the present disclosure , may make modifications and / or improvements on this invention and still be within the scope of this invention as set forth in the following claims .