CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application No. 63/416,465 filed on Oct. 14, 2022. The entire contents thereof are incorporated herein by reference.

BACKGROUND OF THE INVENTION

One of the key requirements for controlling an electrometallization process, including, but not limited to electroplating, is the on-line monitoring and on-line control of the concentration of the metallic plating bath constituents. Proper concentration control is essential to ensure the void free and complete filling of the features including, but not limited to vias and trenches, often of complex morphology, optimum deposition rate, mechanical properties, including, but not limited to tensile strength, roughness and hardness, and grain structure of the plated metallic film depending on the needs of the customer. The concentrations of deliberately added bath constituents decrease during the electroplating process due to electrochemical and chemical consumption and/or drag-out. The knowledge of exact concentration levels of deliberately added bath constituents is necessary for maintaining the concentration of deliberately added bath constituents at the target level.

Another important issue is the buildup of additive breakdown products contaminating and affecting the electroplating process. Optimally, real-time monitoring of an electroplating process should be conducted and automatic adjustments to the concentration of the constituents of the electroplating bath should be made to the constituents which are out of spec.

A commonly employed technique in the field of electroplating uses on-line analyzers to monitor the concentration of organic additives in an electroplating bath is referred to as cyclic voltammetric stripping (CVS). The CVS method is based on a cyclic process of the plating and stripping of a metal from a rotating disc electrode. The adsorption of an additive on a surface of an electrode inhibits the rate of metal deposition. This decrease is quantified by measuring the anodic charge by integrating the stripping of a voltammetric peak. The decrease in deposited charge is related to the change in the concentration of the organic additives. The CVS method integrates the multivariate voltammetric response of an anodic peak into a univariate output. A conventional voltammetric apparatus is a first-order instrument that produces an output in the form of a voltammogram, a vector (e.g., first-order tensor). The ultimate output of the CVS is univariate (e.g., zero-order tensor of the zero-order instrument) oxidation charge. The CVS does not benefit from the richness of analytical information contained in the voltammetric response of an anodic peak. The CVS method is focused solely on the anodic oxidation peak totally ignoring the cathodic portion of the multivariate voltammetric response. The multivariate voltammetric response contains analytical information relevant to electroplating process control. The CVS method does not teach how to extract the analytical information from the multivariate voltammetric response of the cathodic portion.

High-Performance Liquid Chromatography (HPLC) is another quantitative analysis technique that is employed to monitor the concentrations of plating bath constituents, especially organic additives. HPLC is a technique in analytical chemistry used to separate, identify, and quantify each constituent in a mixture. HPLC relies on pumps to pass a pressurized liquid solvent containing the sample mixture through a column filled with a solid adsorbent material. The separation principle of HPLC is based on the distribution of the analyte (i.e., sample) between a mobile phase (i.e., eluent) and a stationary phase (i.e., packing material of the column). The pressurized liquid is typically a mixture of solvents including, but not limited to, water, acetonitrile and/or methanol and is referred to as a “mobile phase”. The active constituent of the column (i.e., stationary phase) is typically a granular material made of solid particles (e.g., silica, polymers, etc.), 2-50 μm in size. Depending on the chemical structure of the analyte, the molecules are adsorbed on the column stationary phase while passing through the column. The specific intermolecular interactions between the molecules of a sample and the packing material define their time “on-column.” Hence, different constituents of a sample are eluted at different times. The separation of the sample ingredients is achieved. A detection unit (e.g., including, but not limited to, UV light, fluorescence and refractive index detector) recognizes the analytes after leaving the column. The automatic on-line chromatographic equipment is characterized by high complexity resulting in prohibitively high expenditure cost and intensive maintenance requirements (e.g., including, but not limited to column conditioning, cleaning, and replacing) and having an adverse effect on reliability. Another fundamental drawback of HPLC for the application of monitoring of electroplating solutions is focusing on measurement of concentrations of separated organic constituents individually while missing the highly relevant impact that these constituents have while acting synergistically during the plating process.

Metara's In-Process Mass Spectrometry (IPMS™) (Metara, Inc., Sunnyvale, CA) is a unique metrology tool which provides sophisticated analytical capability and process diagnostics. The tool utilizes an electrospray-ionization time-off-light mass spectrometer (ESI-TOF/MS) for fully automated in-line monitoring of the copper plating process. The unique analytical capability of the IPMS™ enables the detection and quantitative measurement of anionic, cationic, and organic contamination as well as elemental species present as contamination in process solutions. Having an ability to measure breakdown products, an IPMS™ addresses the major weakness of the CVS that ignores breakdown products. The accumulated breakdown products impact the quality of the deposited film and need to be controlled. IPMS™ instruments providing an impressive amount of information related to the deliberately added chemical constituents and the amounts of chemical constituents formed as the breakdown products, during the electroplating process. However, as a weakness that is common to the prior art separation techniques, the IPMS™ instrument fails to connect data about singled-out chemical constituents with the overall performance of the electroplating process that is of the outmost relevance. By design, the plating bath constituents are intended to act in synergy, whose outcome is often empirical and cannot be strictly modelled analytically. Controlling this synergy is driven by data about the plating solution in the solution's entirety. The analytical information obtained by using prior art separation techniques directed to the functional interdependence between bath constituents is lost. The cost of the IPMS™ instrumentation is prohibitively high, increased by the need for complex, robotic sample preparation necessary for the on-line mode.

The Real Time Analyzer (RTA) (Technic, Inc. Cranston, RI) provides an automatic, in situ, on-line monitoring of electrometallization baths. The RTA uses a unique combination of advance electroanalysis (i.e., unlimited plethora of measurement techniques including direct current (DC) and alternating current (AC) voltammetry) with multivariate data compression and relevant information extraction chemometric techniques. The RTA provides information about concentration of electroplating bath constituents and about the comprehensive condition of the electroplating bath so that adjustments, such as controlled replenishment of the electroplating bath constituents, are made to the electroplating bath to ensure proper plating performance. Concentrations of all of the plating bath constituents are measured by the RTA using only electroanalytical techniques. The duration of the RTA analysis to provide information about concentration of all electroplating bath constituents takes less than thirty (30) minutes. The RTA analyzes samples without any pretreatment and the unaltered sample is returned, post analysis, back into the plating tank. The RTA provides early fault detection, such as plating bath contamination due to accumulation of degradation products or the presence of foreign contaminants, and bath “health” diagnosis as discussed in U.S. Pat. No. 7,214,120 (Wikiel et al, 2007), the entire contents of which is incorporated herein. The RTA utilizes electrochemical techniques for the analysis of an electroplating bath solution without pretreating the analyzed sample such as the RTA comprehensively characterizes the electroplating process by mimicking this process in experimental conditions that are almost identical to the condition of the electroplating tank. Any disturbances affecting the plating performance are manifested in RTA voltammetric responses. Deviations from the proper plating pattern are detected to assure consistency of the electroplating process. The process controlled by RTA is enhanced by adding a new capability focused on pattern recognition that goes beyond simple constituent concentration determination.

The analysis of electroplating baths while in use poses immense challenges. The solutions employed in electrometallization are a very complex media whose constituents, by design, are selected and optimized to interact with each other synergistically during the electroplating process in order to achieve the desired structure and physical properties of the deposited metal. The electroplating bath constituents are fundamentally different in their physical and chemical properties and in their concentration levels in the plating solution. The electroplating bath solution is a dynamic medium. The changes to the concentrations of the plating bath constituents occur at various rates during the idle periods and the electroplating process is what causes complications in process control based on monitoring of concentrations of plating bath constituents. Dragout in which electroplating solution is carried out of the electroplating bath as the plated objects are removed, is problematic. Compositional changes, such as the degradation of organic additives that depend upon number of objects being plated and the parameters that are employed in different plating recipes, are also problems affecting the quality of the desired plating. The build-up of by-products from the organic additives in the plating tank over time also adversely impacts the plating performance.

The electroplating processes of copper damascene and Through Silicon Via (TSV) are commonly used in the metallization of silicon wafers in semiconductor manufacturing. Accurate and prompt monitoring of concentration of all bath constituents in the copper damascene and TSV processes is essential to minimize costs and to satisfy process specifications for high-yield manufacturing of integrated circuits. Well-maintained electroplating processes minimize defects in products as well as minimizing production interruptions. The effective defect-free, bottom-up filling of features, such as trenches and vias, by copper electrodeposition, relies on additive systems, including, but not limited to, an accelerator, a suppressor and a leveler that promote bottom-up filling, macro, and minimal over-plating. Suppressors that inhibit electrodeposition are high molecular weight polyether or polyoxyether polymers. Suppressors adsorb (i.e., in the synergistic combination with chloride ions) rapidly, but weakly, at the surface of the object being electroplated with copper. The suppressor-chloride molecular association is subsequently deactivated in competition with accelerators.

The accelerators, such as bis(3-sulfopropyl) disulfide (SPS) (Raschig, Espenhain, DE) or its reduced monomer 3-mercaptopropylsulfonate (MPS) (Sigma Aldrich Chemicals, St. Louis, MO), competitively replace the suppressor-chloride molecular association adsorbed at the electroplated surface. The adsorbed accelerator facilitates the accelerated growth of the copper deposit at the bottom of the feature, such as trenches and vias. Levelers, such as polyethyleneimines (PEI) (Sigma Aldrich Chemicals, St. Louis, MO) or polyvinylpyrrolidones (PVP) (Sigma Aldrich Chemicals, St. Louis, MO) are inhibitors and surface leveling agents that prohibit excessive copper growth of copper deposit above the features, such as trenches and vias.

For on-line monitoring of plating bath constituents used in electroplating processes such as copper damascene and Through Silicon Via, there is a demand for a prompt analytical technique for measuring concentration of plating bath constituents directly in the plating solution without any sample modification or pretreatment processes including, but not limited to, dilution, chemical addition, and masking.

The method to analyze the constituents of an electroplating bath in a single measurement is mass spectrometry (MS). Mass spectrometry produces an impressive amount of information related to the chemical species present in an electroplating bath, including the amount of such constituent in the bath, MS requires significant data interpretation making MS impractical and irrelevant for monitoring electroplating baths during an electroplating process. Additionally, MS as a separation method, shares the same fundamental weakness as chromatographic techniques of being incapable of identifying and investigating the synergistic interactions between the plating bath constituents that is of imperative relevance in defining and monitoring the plating performance.

For electroanalytical methods, the fundamental differences in physical and chemical properties of the electroplating bath constituents require using a highly individualized, separate approaches for each of bath constituents. This individualization requirement involves not only using various parameters of electroanalytical signals for each of the bath constituents, but also individual sample preparation for each constituent (Freitag W O et al., (1983), Plating Surf Fin, 70(10):55-66). Although several bath constituents are analyzed with CVS, each constituent of the electroplating bath is monitored using a different procedure requiring separate hardware and chemicals for sample preparation and frequent standardization. Even if these routines and procedures share the same rotating disk electrode (RDE)-based electroanalytical cell, such a consolidation becomes a bottleneck adversely effecting the analysis of the constituents of the electroplating bath, thus increasing the time required for a complete analysis of the bath. Additionally, a requirement of sample preparation, i.e., aiming to suppress the effect of all constituents with the exception of, constituent to be analyzed, limits the amount of analytical information related to the synergistic interaction between bath constituents that is of critical relevance for the monitoring of the electroplating bath to quantify the electrometallization process performance. Conventional electroanalytical techniques, designed for the zero- and first-order instruments (source), require using strict and limited parameters to define an electroanalytical wave form that limits the analytical information that could be obtained from such qualitatively and quantitatively diverse media, such as a standard electroplating solution.

The parameter-based limitations of conventional electroanalytical techniques adversely affect the general progress of fundamental mechanistic studies, such as the identification of reversibility or quasi-reversibility and contributions from uncompensated resistance and background capacitance. The term “Designer AC Waveform” was introduced by Tan et al. (Tan Y et al. (2009), J Electroanal Chem, 634:11-21). Tan et al. focused mainly on mechanistic studies analyzing comparatively experimental and simulated data concluding that use of a complex multifrequency AC waveform enables the identification of reversibility or quasi-reversibility, and contributions from uncompensated resistance and background capacitance. The major emphasis of Tan et al. was the parametrization of complex reactions, either by heuristically or by Bayesian and machine learning frameworks. Other attempts to “modify” conventional DC and AC electroanalytical waveforms focused on improving methods for determining physicochemical parameters, rather than obtaining practical analytical advantages in form of the concentration values. The prior art requires that the analyte to be well defined so as to be parametrized qualitatively and quantitatively. Analyte stabilization requirements are imperative for mechanistic studies. Analyte stabilization requirements counter the process control conditions especially of such dynamic quantitatively (i.e., depletion of concentration of deliberately added constituents) and qualitatively (i.e., accumulation of a plethora of breakdown products and foreign contaminants) in complex media, such as electroplating solutions.

The demand for a prompt analytical technique capable of measuring all deliberately added bath constituents during an electrometallization process is only met by electroanalytical instrumentation. To meet the demand for a prompt analytical technique capable of measuring all deliberately added bath constituents, the electroanalytical instrumentation must be capable of analyzing the electroplating solution without any pretreatment. To meet the demand for a prompt analytical technique capable of measuring all deliberately added bath constituents, the analyses electroanalytical instrumentation must be capable of analyzing all constituents of the electroplating solution with a single sensor.

BRIEF SUMMARY OF THE INVENTION

The present invention is directed to methods for monitoring the constituents of any electrolyte. More specifically, the present invention relates to methods for monitoring the constituents of a plating bath contained therein based on novel second-order, consolidated voltammetric waveforms developed with variance and chemometric analysis of voltammetric data obtained for this bath. More particularly, the method of the present invention relates to the development of voltammetric consolidated designer waveforms by implementing of analysis of variance. Subsequently, chemometric techniques of data compression and relevant information extraction are simultaneously applied to build a quantitative calibration model using voltammetric data obtained with consolidated designer waveforms.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

FIG. 1 is a schematic rendering of the apparatus designed to monitor an electroplating bath composition.

FIG. 2 is a flow chart of the steps undertaken by the apparatus designed to monitor an electroplating bath composition.

FIG. 3 is a graphical representation of the AC Multi-frequency Component of a Designer Waveform generated by the apparatus designed to monitor an electroplating bath composition.

FIG. 4 is a graphical representation of the DC Component of a Consolidated Designer Waveform generated by the apparatus designed to monitor an electroplating bath composition.

FIG. 5 are a series of 3D plots resulting from the F-factor analysis performed by the apparatus designed to monitor an electroplating bath composition.

FIG. 6 are a series of contour plots resulting from the F-factor analysis performed by the apparatus designed to monitor an electroplating bath composition.

FIG. 7 is a graph of combined contour plots resulting from the F-factor analysis performed by the apparatus designed to monitor an electroplating bath composition and

FIG. 8 is a flow diagram illustrating DC Adsorptive Stripping Voltammetry (AdSV).

DETAILED DESCRIPTION OF THE INVENTION
Definitions of Terms

Additive breakdown products, as used herein, the term “additive breakdown products”, refers to deliberately not adding plating bath constituents formed by the degradation of the deliberately to the bath constituents. Breakdown products are created by electrochemical and/or chemical reactions during electroplating and/or idling (no electroplating) periods. Additive breakdown products form unintended constituents in the electroplating bath. Some of the additive breakdown products may still be electrochemically active, contributing therefore to the outcome of the electro-metallization process.

Adsorption, as used herein the term “adsorption,” refers to the process by which a solid retains molecules of a gas or liquid or solute as a thin film.

Analysis of variance (ANOVA), as used herein, the term “analysis of variance (ANOVA),” refers to a statistics analysis tool that splits an observed aggregate variability found inside a data set into two parts: systematic factors and random factors. The systematic factors have a statistical influence on the given data set, while the random factors do not. Analysts use the ANOVA test to determine the influence that independent variables have on the dependent variable in a regression study.

Analytical method development range, as used herein, the term “analytical method development range,” refers to a range of concentration values of deliberately added bath constituents covered by the method intended for process control. The range of analytical model development needs include the process control range and be wider than process control range.

Analytical output, as used herein, the term “analytical output,” refers to quantitative results of an analysis. With respect to the analyzer used for a plating process control in particular, the term generally refers to the concentrations of deliberately added bath constituents.

Anodic peak, as used herein, the term “anodic peak,” refers to the portion of a voltammogram that corresponds to potentials from an equilibrium potential to the maximum applied oxidation potential. The equilibrium potential, also referred to open circuit potential, is an electrical potential of a working electrode measured against a reference electrode when there is no current flowing through the working electrode.

Anodic portion of voltammogram, as used herein, refers to the portion of a voltammogram that corresponds to the potentials of an equilibrium potential to the maximum applied oxidation potential. The equilibrium potential, also called an open circuit potential, is an electrical potential of a working electrode measured against a reference electrode when there is no current flowing through the working electrode.

Artefact, as used herein, the term “artefact” refers to something observed in a scientific investigation or experiment that is not naturally present but occurs as a result of the preparative or investigative procedure.

Automatic replenishment system, as used herein, the term “automatic replenishment system,” refers to a system that maintains the concentrations of deliberately added components found in a plating bath at constant target level by dosing those components when said components become depleted.

Background capacitance, as used herein, the term “background capacitance,” refers to measuring the ability of an electrical double layer to store electrical charge as a capacitor. The electrical double layer is the structure of charge accumulation and charge separation that always occurs at the interface when an electrode is immersed into an electrolyte solution. The excess charge on the electrode surface is compensated by an accumulation of excess ions of the opposite charge in the solution. The amount of charge is a function of the electrode potential. This structure behaves essentially as a capacitor. There are several theoretical models that describe the structure of the double layer. The three most commonly used ones are the Helmholtz model, the Gouy-Chapman model, and the Gouy-Chapman-Stern model.

Band broadening, as used herein, the term “band broadening” refers to describing the overall dispersion or widening of a sample peak as it passes through a separation system. Band broadening in chromatography, including HPLC, is a result of several effects, including but not limited to, the diffusion of solutes between the mobile phase and stationary phases.

Bayesian framework, as used herein, the term “Bayesian framework,” refers to an approach of parameter optimization that provides a posterior probability distribution for a parameter derived from the observed data and a prior probability distribution for that parameter. The posterior distribution forms the basis for statistical inference. Using modern day high-speed computers, Bayesian methods are coupled with simulation-based Monte-Carlo techniques that utilize efficient algorithms such as Gibbs sampling, the Metropolis-Hastings algorithm, and Approximate Bayesian Computation. This has revolutionized the ability to fit complex mathematical models to experimental data in fields as disparate as astronomy and systems biology. Crucially, these techniques provide the means not only to provide estimates of key parameters of interest but also to quantify the uncertainty associated with these parameters. Accordingly, rather than point estimates, probability distributions of each parameter are provided.

Calibration training set matrix, as used herein, the term “calibration training set matrix,” refers to a combination of the concentrations of the deliberately added bath constituents of the calibration training set. The concentrations of each of the deliberately added bath constituents are varied within an analytical method development range for each of the deliberately added bath constituents.

Cathodic peak, as used herein and in science of voltammetry and related techniques, the term “cathodic peak” refers to the maximum value of the faradaic current during a single potential sweep toward the reduction potentials applied to the working electrode.

Cathodic portion of a voltammogram, as used herein, the term “cathodic portion of a voltammogram,” refers to the portion of the voltammogram that corresponds to “potentials” from an equilibrium potential to the maximum applied reduction potential. The equilibrium potential, also referred to as open circuit potential, is an electrical potential of a working electrode measured against a reference electrode when there is no current flowing through the working electrode.

Chemometric[s], the terms “chemometric” or “chemometrics,” as used herein, refer to the application of statistics to the analysis of chemical data and design of chemical experiments and simulations.

Chemometric techniques, the term “chemometric techniques,” as used herein, refers to chemometric, i.e. “the science of extracting information from chemical systems by data-driven means,” methods used for multivariate data compression and relevant information extraction including, but not limited to, Principal Component Analysis (PCA), Partial Least Squares (PLS) (used for two-way data), Hierarchical PCA (HPCA), Hierarchical PLS (HPLS), Consensus PCA (CPCA), Multi-Block PLS (MBPLS) (used for two-way data sets arranged in the hierarchy), Parallel Factor Analysis (PARAFAC), Multi-linear PLS (N-PLS) Direct Trilinear Decomposition (DTLD) (used for three-way data sets).

Chromatography detector, the term “chromatography detector, as used herein, refers to a device used in chromatography, including but not limited to HPLC, to detect components of a mixture being eluted off the chromatography column. There are two general types of detectors: destructive and non-destructive. The destructive detectors perform continuous transformation of the column effluent (burning, evaporation or mixing with reagents) with subsequent measurement of some physical property of the resulting material (plasma, aerosol, or reaction mixture). The non-destructive detectors directly measure some property of the column eluent (e.g., UV absorption) and thus afford greater analyte recovery.

Common time domain, the term “common time domain,” as used herein, refers to the time in which physical signals that utilize multiple parameters are measured concurrently instead of using a sequence of measurements as performed using a conventional voltammetric approach. The influence of various parameters on the physical signal (AC current) can be determined and viewed for the same time of the consolidated experiment.

Completeness of filling, the term “completeness of filling,” as used herein, refers to measuring the filling of the features of the substrate (often of complex morphology) with the metallic deposit.

Complex Designer Voltammetry (CDV), the term “complex designer voltammetry” and/or its acronym “CDV,” refer to a voltammetric technique using a Consolidated Designer Waveform.

Consolidated Designer Waveform (CDW), the term “consolidated designer waveform” and/or its acronym “CDW,” refer to a multi-frequency, variable amplitude waveform in which several AC sinusoidal potential perturbations, each of different frequency and amplitude, are superimposed on the DC potential ramps. CDW is not available in “off-the-shelf” voltammetric instruments and requires use of custom-made hardware and/or software.

Copper Damascene, the term “copper damascene,” as used herein, refers to the process of electrodeposition of thin deposits of copper onto patterned silicon wafers to form copper interconnects. In this process, the underlying silicon oxide insulating layer is patterned with open trenches where a conductor should be. A thick coating of copper that significantly overfills the trenches is deposited on the insulator and chemical-mechanical planarization (CMP) is used to remove the copper (referred to in the art as overburden) that extends above the top of the insulating layer. Copper sunken within the trenches of the insulating layer is not removed and becomes the patterned conductor. The most common electrolytes are copper sulfate and sulfuric acid that are kept at or near room temperature. Bright coatings are obtained through the use of addition agents that refine the grain size and level the surface morphology. The electrolytes used in “damascene interconnects” possess multiple organic additives to induce super-filling or bottom-up feature deposition, resulting in the void-free deposition in features of sizes ranging from nano- to micrometers, and with aspect ratios greater than one.

Counter electrode, the term “counter electrode,” (also referred to an “auxiliary electrode”) as used herein, refers to an electrode in a three-electrode cell that is used only to make an electrical connection to the electrolyte so that a current can be applied to the working electrode. The processes occurring on the counter electrode are unimportant, it is usually made of inert materials (e.g., noble metals or carbon/graphite) to avoid its dissolution. This is the case for cells used for research or for electroanalytical purposes. For many practically used cells, the processes occurring on both electrodes can be very important.

Data acquisition (DAQ), the term “data acquisition” and its acronym “DAQ,” refers to the process (HW & SW) of measuring an electrical or physical phenomenon, e.g., voltage, current, temperature, pressure, or sound. A DAQ system consists of sensors, DAQ measurement hardware, and a computer with programmable software.

Data contraction by integration, the term “data contraction by integration,” as used herein, refers to reducing the dimension of data by integrating a multivariate signal. Usually conducted to simplify the interpretation of the multivariate signal, often at the expense of losing the advantages of higher order instruments reducing the order of the instrument.

Deliberately added bath constituents, the term “deliberately added bath constituents,” as used herein, refers to bath components, exhibiting known synergistic action that are mixed in a controlled manner in order to ensure proper performance of the electrometallization process. For copper electrometallization processes common to the semiconductor industry, the deliberately added bath constituents usually include, but not always, copper ion, an acid (e.g., sulfuric or methanesulphonic acid), chloride, an accelerator, a suppressor and/or a leveler.

Deposition rate, the term “deposition rate,” as used herein, refers to the velocity with which the thickness of the deposited metallic layer increases over time during the electrometallization process. The deposition rate is expressed in units of length (e.g., nanometers) per time (e.g., seconds).

Diagnostic portion of a voltammogram, the term “diagnostic portion of a voltammogram, refers to a range of neighboring variables of a voltammetric waveform whose corresponding current response obtained for an electroplating solution exhibits high correlation with the concentration uniquely of one deliberately added bath constituent while being not affected by varying concentrations of all other bath constituents.

Drag out, the term “drag out,” as used herein, refers to the unintended removal of bath constituents from the electroplating bath solution, as the drops of electroplating solution become attached to the electroplated parts (e.g., wafers in semiconductor manufacturing) and are thereafter removed from the electroplating chambers along with the electroplated parts.

Early fault detection, the term “early fault detection,” as used herein, refers to an effective strategy used to determine and solve problems arising in a manufacturing process such as electroplating process. The operating status of the equipment or process (e.g., use of an electroplating solution) is monitored in real time. The early fault detection strategy can incorporate chemometric outlier detection techniques.

Electrochemical analysis and/or electroanalytical techniques, the terms “electrochemical analysis” and “electroanalytical techniques,” as used herein interchangeably, refer to a class of techniques in analytical chemistry that study an analyte by measuring the potential (in volts) and/or current (in amperes) in an electrochemical cell containing the analyte. These methods can be broken down into several categories depending on which aspects of the cell are controlled and which are measured. The three main categories are potentiometry (i.e., the difference in electrode potentials is measured), coulometry (i.e., the cell's current is measured over time), and voltammetry (i.e., the cell's current is measured while actively altering the cell's potential).

Electrochemical (or electrochemically) activity, the term “electrochemical (or electrochemically) activity,” as used herein refers to the property of constituent of the electrometallization solution regarding the participation of the constituent in the electrometallization process. The participation is direct if the constituent is involved in the charge transfer process. The participation is indirect, if the constituent is contributing to the plating process without engaging directly in the charge transfer for instance by forming a complex with other constituents that are involved in the charger transfer process.

Electrochemical cell, the term “electrochemical cell,” as used herein refers to a device that converts chemical energy into electrical energy or vice versa when a chemical reaction is occurring in the cell. Typically, it consists of two metal electrodes immersed into an aqueous solution (e.g., electrolyte) with electrode reactions occurring at the electrode-solution surfaces.

Electrochemical Impedance Spectroscopy (EIS), the term “electrochemical impedance spectroscopy” and its acronym “EIS,” as used interchangeably herein, refer to a powerful tool for examining processes that occur at electrode surfaces. A small amplitude ac (i.e., sinusoidal) excitation signal (i.e., potential or current), covering a wide range of frequencies, is applied to the system under investigation and the response (i.e., a current or voltage or another signal of interest) is measured. Due to the small amplitude of the excitation signal, the measurement can be carried out without significantly disturbing the properties being measured. Due to the wide range of frequencies used, the complex sequence of coupled processes including but not limited to, electron transfer, mass transport and chemical reaction, can often be separated and investigated with a single measurement. Electrochemical impedance spectroscopy is routinely used in electrode kinetics and mechanism investigations and in the characterization of batteries, fuel cells, and corrosion phenomena.

Electrode, the term “electrode,” as used herein refers to two electronically conducting parts of an electrochemical cell, e.g., anode and cathode. An electrode may be simple metallic structures (e.g., rods, sheets) or much more complicated, composite structures. The electrodes in a rechargeable battery may also “contain” chemicals being converted during its operation.

Electrometallization process and/or Electroplating process, the terms “electrometallization process” and “Electroplating process,” as used herein interchangeably, refer to a process of depositing a layer of metal on a substrate (often of complex morphology) by means of electrodeposition, i.e., the reduction of metal ions from a plating solution onto a substrate that acts as a cathode, or more precisely, the process of producing a thin, metallic coating on the surface on another metal (or any other conductor, e.g., graphite). The metal substrate to be coated acts as the cathode in an electrolytic cell where the cations of the electrolyte are the positive ions of the metal to be coated on the surface. When a current is applied, an electrode reaction occurring on the cathode is the reduction of the metal ions to metal. For example, gold ions in solution can be discharged from the solution to form a thin gold coating on a less expensive metal to produce “costume” jewelry. Similarly, a chromium coating is often applied to steel surfaces to make them more “rust resistant”. Electroplating is also used in the production of integrated circuits on computer chips and for other modern electronic instrumentation. The anode material can either be the metal to be deposited (in this case the electrode reaction is an electro-dissolution that continuously supplies the metal ions) or the anode can be an inert material and the anodic reaction is oxygen evolution causing the plating solution to eventually be depleted of metal ions.

Electroplating solution and/or Electroplating bath and/or Plating Bath, the terms “electroplating solution,” “electroplating bath” and “plating bath,” as used interchangeably herein, refer to a liquid mixture of several chemical constituents used in an electroplating process.

Empirical platform, the term “empirical platform,” as used herein, refers to use of an analytical instrument to implement unconventional analytical techniques, intended to be conceptualized by the user without traditional constraints on experimental parameter selection.

Factor analysis, the term “factor analysis,” as used herein, refers to a method of quantifying the utility of a variable of a voltammetric waveform to determine the concentration of a deliberately added bath constituent. The factor analysis indicators include, but are not limited to, relative F-ratio, relative Mean Square, and Factor Effect.

Fast Fourier Transform (FFT), the term “fast Fourier transform” and its acronym “FFT,” both interchangeably refer to an algorithm that computes the discrete Fourier transform (DFT) of a sequence. Fourier analysis converts a signal from its original domain (e.g., time) to a representation in the frequency domain. The DFT is obtained by decomposing a sequence of values into components of different frequencies.

Features, the term “features,” as used herein, refers to geometric shapes of the substrate intended to be filled with the metallic deposit during the electrometallization process. In the case of semiconductor manufacturing applications, “features” may be in the form of trenches and vias having dimensions that vary from micrometers to single digit nanometers.

First-order instrument (also known as a first-order tensor), the term “first-order instrument,” as used herein, refers to an instrument capable of generating multiple measurements for one sample that can be put into an ordered array referred to as a vector of data (e.g., typical voltammogram).

Foreign contamination, the term “foreign contamination,” as used herein, refers to the unintentional entering into an electroplating bath of a substance that is neither a deliberately added nor a degradation product of any of the deliberately added bath constituents. The presence of foreign contaminant in the electroplating solution may adversely impact the plating performance of the electroplating solution.

Frequency domain data, the term “frequency domain data,” as used herein, refers to data consisting of physical signals or mathematical functions expressed in reference to frequency. A frequency domain graph displays how much of the signal exists within a given frequency band concerning a range of frequencies.

Frequent standardization, the term “frequent standardization,” as used herein, refers to the least frequency with which the standardization routine needs to be performed on the process control analytical equipment in order to assess that master calibration analytical model implemented on that instrument retains the requested accuracy and reproducibility. The implementation of standardization routines is an undesired interference of process control as it interrupts the continuous process monitoring. Therefore, it is imperative to minimize the frequency of standardization by designing process control analyzers of high consistency and stability in time.

Fundamental frequency, the term “fundamental frequency,” as used herein, refers to the lowest frequency of a periodic waveform. In AC Voltammetry, the lowest frequency of a periodic current response is equal to the voltage perturbation frequency.

Grand average, the term “grand average,” as used herein, refers to the mean of the means of several subgroups, provided the subgroups have the same number of data points.

Harmonic frequency, the term “harmonic frequency,” as used herein, refers to the integer multiple of the fundamental frequency.

Heuristic framework, the term “heuristic framework,” as used herein, refers to the general cognitive framework humans rely on regularly to quickly reach a solution. Heuristic frameworks are commonly implemented for parameter estimation undertaken by the experimenter visually comparing experimental data and deciding which combination of values gives the best fit. Heuristic frameworks often lead to problem solution, but are not guaranteed to succeed and can be distinguished from algorithms that are methods or procedures that will always produce a solution sooner or later.

Higher-harmonic time domain signals, the term “higher-harmonic time domain signals,” as used herein, refers to a component of the physical signal (AC current) in a time domain obtained by Inverse Fast Fourier Transform (IFFT) for a selected frequency corresponding to the harmonic frequency of any of the waveforms used for generating the original physical signal. The FFT followed by IFFT are used for deconvoluting from the original consolidated signal only the portion associated with selected higher-harmonic frequency.

Inverse Fast Fourier Transform (IFFT), the term “Inverse Fast Fourier Transform” and its acronym “IFFT,” as used herein, interchangeably refer to an algorithm that computes the inverse discrete Fourier transform (IDFT) by converting the signal in the frequency domain back to the original domain (e.g., time).

Machine learning framework, the term “machine learning framework,” as used herein, refers to an automatic method of data analysis based on the idea that systems can continually learn from data, identify patterns and make decisions with minimal human intervention. The basic principle of machine learning is to train the machine to do what humans can do. An important and probably the most difficult step in applying machine learning to the recognition of a particular mechanism (e.g., the electrode reaction mechanism studied with voltammetry) within a given set of possible mechanisms is the extensive training needed. During this computationally demanding process, the machine is trained on a set of data with known classifications. A well-considered training data set allows the machine to classify new input cases with superior efficiency compared with human experts and update its knowledge during practice to improve its efficiency and accuracy.

Mass spectrometry, the term “mass spectrometry,” as used herein, refers to an analytical laboratory technique used to separate the components of a sample by their mass and electrical charge. The instrument used in mass spectrometry is called a mass spectrometer. It produces a mass spectrum that plots the mass-to-charge (m/z) ratio of compounds in a mixture.

Mechanical properties of deposit, the term “mechanical properties of deposit,” as used herein, refers to those physical properties that a material exhibits upon the application of forces including, but not limited to, tensile strength, roughness, hardness and grain size.

Mitigation of band broadening, the term “mitigation of band broadening,” as used herein in the art of chromatography, refers to mitigating band broadening using small packing diameter (with respect to a stationary phase), small column diameter, optimum flowrate of mobile phase, optimum temperature, variation in solvent composition and/or liquid stationary phase. The process minimizes the thickness of a plating layer.

Molecular association, the term “molecular association,” as used herein, refers to a molecular entity formed by loose bonding involving two or more component molecular entities (e.g., ionic or uncharged), or the corresponding chemical species. The bonding between the components is normally weaker than in a covalent bond.

Morphology, the term “morphology,” as used herein, refers to an external structure of a substrate consisting of features intended to be filled in by an electrometallization process. Morphology that combines features, differing in dimensions and shapes, is referred to as a “complex morphology.” A simple morphology is featureless (i.e., flat area) or is an external structure of a limited number of simple features.

Multi-frequency waveform, the term “multi-frequency waveform,” as used herein, refers to a waveform obtained by consolidation of a several periodic waveforms, each of different frequency. The frequency of each of these waveforms is not the harmonic frequency of any of the other consolidated waveforms.

Multivariate data compression, the term “multivariate data compression,” as used herein, refers to the processing of data using Principal Component Analysis (PCA) or other chemometric techniques designed to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables referred to factors. The purpose of PCA is to derive a relatively small number of components that can account for the variability found in a relatively large number of measures.

Out of spec, the term “out of spec,” as used herein, refers to the values of process control parameters that are beyond ranges optimized for the process. The purpose of process control involving monitoring and replenishment systems is to maintain the process control parameters within the optimized ranges.

Potentiostat, the term “potentiostat,” as used herein, refers to an electronic instrument (i.e., hardware) required to perform voltammetric (i.e., electrochemical) measurements. The system functions by maintaining the potential of the working electrode at a constant level with respect to the reference electrode by adjusting the current at a counter (i.e., auxiliary) electrode. A potentiostat controls voltage and measures the resulting current. The Control Amplifier outputs power to the counter electrode (also referred to as an “auxiliary electrode”). A feedback loop is established to control the cell potential between the reference and working electrode. This voltage is measured by the input electrometer having a high impedance. The current is thereafter measured between the working and counter electrodes while this potential is maintained at the working electrode and reference electrode. This system functions by maintaining the potential of the working electrode at a constant level with respect to the reference electrode by adjusting the current at an auxiliary electrode. The core electronic component of a potentiostat is an operational amplifier (i.e., op-amp). When part of the op-amp output signal is fed into itself, it creates a feedback mechanism. Feedback is the mechanism by which a potentiostat controls the potential of a working electrode.

Process control range, the term “process control range,” as used herein, refers to a range of values within which process parameters should be maintained as a condition for ensuring a proper outcome of the process. The “process control range” is determined by optimization of the process. Exemplary process control ranges that should be maintained, are the Low and High concentration limits of electroplating bath constituents.

Polyvinylidene difluoride (PVDF), the term “polyvinylidene difluoride” and its abbreviation “PVDF,” interchangeably refer to a highly non-reactive thermoplastic fluoropolymer produced by the polymerization of vinylidene difluoride. PVDF is a specialty plastic used in applications requiring the highest purity, as well as resistance to solvents, acids and hydrocarbons.

Ramp, the term “ramp,” as used herein, refers to a DC potential linearly changed in time with a constant scan rate expressed in mV/s applied to the electrode in voltammetric measurement of resulting current.

Reference electrode, the term “reference electrode,” as used herein refers to an electrode that has a well-known and stable equilibrium electrode potential. A reference electrode is used as a reference point against which the potential of other electrodes, typically a working electrode or measuring electrode, is measured in an electrochemical cell. In principle, a reference electrode can be any electrode fulfilling the above requirements. In practice, there are a few commonly used (and usually commercially available) electrode assemblies that have an electrode potential independent of the electrolyte used in the cell. Common reference electrodes, include, but are not limited to, silver/silver-chloride electrodes, calomel electrodes and hydrogen electrodes.

Repetitions of analysis, the term “repetitions of analysis,” as used herein, refers an assessment of the repeatability of a series of experiments, so as to assess reproducibility of said experiments.

Replicate information, the term “replicate information,” as used herein, refers to information about the contribution of repeatability or reproducibility to the total variance.

Sample pretreatment, the term “sample pretreatment,” as used herein, refers to, in general, methods of sample preparation in analytical chemistry, referring to the means that a sample is treated prior to its analyses. Preparation is a very important step in most analytical techniques because the techniques are often not responsive to the analyte directly or in the analyte in situ form, or the results are distorted by interfering species. Sample preparations may involve, but are not limited to, dissolution, extraction, reaction with some chemical species, pulverizing, treatment with a chelating agent, masking, filtering, dilution, sub-sampling, or many other techniques. Treatment is performed to prepare the sample into a form ready for analysis by specified analytical equipment. Sample preparation techniques include, but are not limited to, pulverization, dissolution, chemical digestion with acid or alkali, sample extraction, sample sanitization and sample pre-concentration.

Scaling, the term “scaling,” as used herein, refers to a common pre-processing method that centers the variables of the data using the mean of the training set variables followed by division of each variable by the standard deviation of that variable obtained for the training set data.

Second-order instrument, the term “second-order instrument,” as used herein, refers to an instrument that generates a matrix (i.e., a second-order tensor) of data per sample.

Solitary measurement, the term “solitary measurement,” as used herein, refers to a measurement conducted as an execution of a single, complex, consolidated, and multi-parameter scan, as opposed to a sequence of numerous scans each of different parameters.

Target composition, the term “target composition,” as used herein, refers to the concentration values of all deliberately added bath constituents corresponding to the optimum electroplating performance of the plating bath. The “target composition” is within the process control range, usually at the center of the process control range.

Tensor, the term “tensor,” as used herein, refers a generalized multidimensional array. Specifically, a zero-order tensor is a scalar, first-order tensor is a vector, second-order array is a matrix.

Three-electrode cell, the term “three-electrode cell,” as used herein, refers to device having three electrodes that converts chemical energy into electrical energy or vice versa when a chemical reaction is occurring in the cell. Typically, “a three-electrode cell” consists of three electrodes: a working, a counter (also known as auxiliary) and a reference electrode, immersed into an aqueous solution (e.g., electrolyte) with electrode reactions occurring at the electrode-solution surfaces of working and counter electrodes.

Through silicon via (TSV), the term “through silicon via” and its acronym “TSV,” in the art of electrical engineering, refer interchangeably to a through-silicon via (TSV) or through-chip via that is a vertical electrical connection (via) that passes completely through a silicon wafer or die. TSVs are formed by electrodepositing of conductor, e.g., copper. TSVs are high-performance interconnect techniques used as an alternative to wire-bond and flip chips to create 3D packages and 3D integrated circuits. Compared to alternatives such as package-on-package, the interconnect and device density is substantially higher, and the length of the connections becomes shorter.

Time domain data, the term “time domain data,” as used herein refers to data consisting of physical signals, or mathematical functions expressed in reference to time. Also, in the time domain, the signal or function's value is understood for all real numbers at various separate instances in the case of discrete-time or the case of continuous-time. A time-domain graph displays the changes in a signal over a span of time.

Training set, the term “training set,” as used herein, refers to a data set used for building a predictive model. The training set is used to construct or train a model. When the model is a regression or a calibration model, a “training set” is also called a calibration set.

Trench, the term “trench,” as used herein, refers to a longitudinal morphological feature of greater depth than width (i.e., high aspect ratio) on a substrate intended to be filled with a metal deposit during an electrometallization process.

Uncompensated resistance, the term “uncompensated resistance,” as used herein, refers to the part of the solution resistance that is not automatically compensated for by the electronic control instrumentation like most of the potentiostats. The “uncompensated resistance” causes the electrical potential difference between the two ends of a conducting phase during a current flow. “Uncompensated resistance” is the product of the current (i) and the resistance (R) of the conductor. In electrochemistry, “uncompensated resistance” refers to the solution iR drop or to the ohmic loss in an electrochemical cell.

Via, the term “via,” as used herein, refers to an electrical connection between metal layers in a circuit board. Essentially, a “via” is a small hole that traverses two or more adjacent layers; the hole is plated with metal that forms electrical connection through the insulation that separates two copper layers.

Void, the term “void,” as used herein, refers to a defect in an electrometallization process. A “void” is a closed space surrounded by a deposit, but not filled with the deposit. A void is the outcome of an incorrectly conducted electrometallization that adversely and uncontrollably impacts the properties of a metal deposit.

Voltammetry, the term “voltammetry,” as used herein, refers to an electrochemical measuring technique used for electrochemical analysis, for the determination of the kinetics and mechanism of electrode reactions, and for corrosion studies. “Voltammetry” is a family of techniques with the common characteristics that the potential of the working electrode is controlled by a potentiostat, and the current flowing through the electrode is measured. Types of Voltammetries (typically “built-in” into commercially available voltammetric instruments—potentiostats) are listed below:

- a. DC Linear Scan Voltammetry (LSV)—voltammetric technique with the applied DC potential linearly scanned in time.
- b. DC Cyclic Voltammetry (CV)—is a DC Linear Scan Voltammetry with the scan continued in the reverse direction at the end of the first scan, this cycle can be repeated a number of times.
- c. Alternating Current Voltammetry (ACV)—voltammetric technique involves the application of a sinusoidally oscillating voltage to an electrochemical cell. The AC voltage is often combined with either a steady DC signal or voltage sweep.
- d. DC Staircase Voltammetry (SCV)—voltammetric technique in which the DC potential sweep is a series of stair steps. The current is measured at the end of each potential change, right before the next, so that the contribution to the current signal from the capacitive charging current is reduced.
- e. Square Wave Voltammetry (SWV)—voltammetric technique in which the current at a (usually stationary) working electrode is measured while the potential between the working electrode and a reference electrode is pulsed forward and backward at a constant frequency. The DC potential waveform may be viewed as a superposition of a regular Square Wave onto an underlying staircase; in this sense, Square Wave Voltammetry can be considered a modification of Staircase Voltammetry. In Square Wave Voltammetry, the current is sampled at two times—once at the end of the forward potential pulse and again at the end of the reverse potential pulse (in both cases immediately before the potential direction is reversed).
- f. Normal Pulse Voltammetry (NPV)—voltammetric technique in which the waveform is a series of pulses that are increasing in potential amplitude. The way in which the current is measured at each pulse aids in minimizing the measurement of background (charging) current. Related pulse-type methods include Differential Pulse Voltammetry (DPV) and Square Wave Voltammetry (SWV).
- g. Differential Pulse Voltammetry (DPV)—voltammetric technique in which short DC potential pulses are superimposed on a linear ramp. Current is measured before the application of the pulse and at the end of each pulse, and the difference between the currents is calculated. This procedure effectively reduces the background current due to the DC ramp, and thus this procedure results in a Faradaic current free of most capacitive current. The major advantage of DPV is low capacitive current, which leads to high sensitivity.
- h. Chronoamperometry (CA)—a time-dependent technique where a square-wave DC potential is applied to the working electrode. The DC current of the electrode, measured as a function of time, fluctuates according to the diffusion of an analyte from the bulk solution toward the sensor surface. Chronoamperometry can therefore be used to measure current-time dependence for the diffusion-controlled process occurring at an electrode.
- i. DC Anodic Stripping Voltammetry (ASV)—A quantitative, analytical method for trace analysis of metal cations. The analyte is deposited (electroplated) onto the working electrode during a deposition step, and then oxidized during the stripping step. The current is measured during the stripping step.
- j. DC Cathodic Stripping Voltammetry (CSV)—A quantitative, analytical method for trace analysis of anions. A positive potential is applied, oxidizing the mercury electrode and forming insoluble precipitates of the anions. A negative potential then reduces (strips) the deposited film into solution.
- k. DC Adsorptive Stripping Voltammetry (AdSV)—A quantitative, analytical method for trace analysis. The analyte is deposited simply by adsorption on the electrode surface (i.e., no electrolysis), then electrolyzed to give the analytical signal.
- l. Rotating disc electrode (RDE)—An electrode used in the study of the kinetics and mechanism of electrode reactions and in electroanalysis for ensuring a known and controllable flow of solution over the electrode. The flow control is achieved by using a flat disc electrode (inlaid in an insulator) that is rotated in the solution resulting in a defined hydrodynamic boundary layer. The current may be calculated using the Levich equation.

Voltammogram, the term “voltammogram,” as used herein, refers to a graphical representation of the results of a voltammetric measurement.

Working electrode, the term “working electrode,” as used herein, refers to the electrode in a three-electrode cell where “the action is”. The kinetics and mechanism of the electrode reaction may be under investigation, or the reaction occurring on the working electrode may be used to perform an electrochemical analysis of the electrolyte solution. A “working electrode” can serve either as an anode or a cathode depending on the applied polarity. One of the electrodes in some “classical two-electrode” cells can also be considered a “working” (also referred to as a “measuring”, “indicator”, or “sensing”) electrode, i.e., in a potentiometric electroanalytical setup where the potential of the measuring electrode (as against a reference electrode) is a measure of the concentration of a species in the solution.

Zero-order instrument, the term “zero-order instrument,” as used herein, refers to an instrument that generates a single datum per sample, for instance pH meter.

Discussion

Electrochemical analyzers are the most common metrology tools used to monitor electroplating process, as analyzers measure physicochemical processes of an electrodeposition procedure. The Technic RTA metrology tool (Technic, Inc., Cranston, RI) analyzes plating solution samples without the need for any pretreatment of the constituents of an electroplating bath utilizing the actual electrodeposition process. Traditional electroanalytical techniques use zero-order instruments and first-order instruments that deliver the analytical output in the form of a scalar or a vector. Recently, Technic, Inc. (Cranston, RI) developed and commercialized Real Time Analyzer 3D (RTA3D™), a unique electrochemical second-order analyzer purposefully designed for a plating process control. FIG. 1 illustrates a block diagram of an analyzer with a closed loop bath circulation in which the plating tank 6 solution samples are analyzed by a sensor 5 without requiring any sample pretreatment in which the sample is returned in an unaltered state back to the plating tank. The sensor 5 is a compact flow-through electrochemical cell, i.e., the electrode compartment of a Multi-Task Electrochemical Probe™ (MTEP™ 5) (Technic, Inc., Cranston, RI). The MTEP™ 5 is easily installed within 5 to 10 minutes without interfering with ongoing production (and integrated with the plating tool if needed). The short installation time is imperativefor the continuity of semiconductor manufacturing characterized by high monetary value¹. The electrode compartment of MTEP™ 5 is a conventional 3-electrode cell consisting of a Pt-wire working electrode, a Pt-foil counter electrode, and a freshly electroplated metal for instance Cu for copper damascene and TSV processes from an analyzed plating solution sample deposited on the Pt wire as a reference electrode. The electrode system is built into the PTFE housing. The volume of the inner compartment containing the analyzed plating solution is about 20 mL. ¹Equipment installation causes disruption in the continuous production resulting in monetary losses. The objection of the instant invention is to minimize disruptions caused by equipment installation.

Circulation of the analyzed solution (i.e., in situ plating bath solution without any sample pre-treatment) inside the MTEP™ 5 is achieved by utilizing a software-controlled diaphragm pump. It is of fundamental importance that the MTEP™ 5 is capable of analyzing plating bath constituents using electroanalysis. The MTEP™ 5 is connected with cables to the RTA3D™ consisting of the electronic modules such as potentiostat 4, Designer Waveform Generator 1, and DAQ module 3. The PC 2 controls electronic modules of the RTA3D™ and the diaphragm pump 5a (Technic, Inc., Cranston, RI). The PC 2 controls electronic modules of the RTA3D using custom-designed software (Technic, Inc., Cranston, RI). The digital parameters of the voltammetric waveform are entered into the PC 2. The PC2 transfers the parameters of the voltammetric waveform to the Designer Waveform Generator 1. The Designer Waveform is applied to the sensor 5 via potentiostat 4 module. The current response to the voltammetric waveform perturbation is recorded by the DAQ 3 module and read and processed numerically by the PC 2.

The RTA3D™ is a multi-order instrument. The RTA3D™ is capable of executing the following first-order instrument conventional voltammetric technique. Additionally, the RTA3D™ is designed as a second-order instrument capable of superimposing a periodic potential perturbation resulting from numerous sine curves over any custom-designed DC potential including those of conventional voltammetric techniques.

The Potentiostat™ 4 (Technic, Inc., Cranston, RI) is a highly flexible electroanalytical instrument that directs the MTEP™ 5 to generate any waveform (a galvanostatic may be used in place of the Potentiostat™ 4) received from the Designer Waveform Generator 1. and collecting an output signal from the DAQ 3 to be recorded on the PC 2. The computer-controlled 2 versatile Designer Waveform Generator 1 electroanalytical system is capable of superimposing a periodic potential perturbation resulting from numerous sine curves over any custom-designed DC potential including those of conventional DC voltammetric techniques for example a DC Cyclic Voltammetry, DC Linear Scan Voltammetry, DC Anodic Stripping Voltammetry, DC Linear Scan Voltammetry, DC Adsorptive Stripping Voltammetry, DC Cyclic Voltammetric Stripping, DC Staircase Voltammetry, Normal Pulse Voltammetry, Reverse Pulse Voltammetry, DC Cathodic Stripping Voltammetry, Differential Pulse Voltammetry, Square Wave Voltammetry and Chronoamperometry. These conventional DC voltammetric techniques are the output of first-order instruments. After collection by the DAQ 3, the experimental data is interrogated by the signal processing software installed in the PC 2 that utilizes the Fast Fourier Transformation (FFT). The FFT algorithm initially converts the time-domain data into a frequency domain. The data is separated based on the multiple fundamental frequencies and the fundamental frequencies harmonics. Next, an inverse FFT algorithm is applied to each selected constituent to generate a DC, multiple fundamental, and their higher-harmonic time-domain signals. This AC voltammetric analyzer is capable of executing multi-frequency and variable amplitude designer waveforms. The AC voltammetric analyzer is a second-order instrument designed to generate multi-way data with a common time domain without compromising the duration of the electroplating process as do first-order instruments. The AC voltammetric analyzer is designed to produce any form of a DC potential waveform (also those being a combination of conventional DC voltammetric techniques) with superimposed multiple potential perturbations.

The AC voltammetric analyzer is designed as an empirical platform for introducing multi-frequency designer waveforms consisting of consolidated various DC ramps. The large number of electroanalytical parameters, such as initial potential of DC potential ramp, vertex potential of DC potential ramp, end potential of DC potential ramp, scan rate, several frequencies of AC potential perturbations, several amplitudes of AC potential perturbations, is integrated into a single waveform on a second-order AC voltammetric analyzer. The resultant multivariable electroanalytical output contains diagnostic portions of voltammogram for each of the bath constituents. Accordingly, a single electroanalytical measurement to determine the concentrations of the constituents of an electroplating bath even when the constituents of the bath are present in the bath in different concentration and the constituents in the bath are chemically distinct. The consolidation of relevant analytical information about all bath constituents into a single multivariate voltammetric output results in a shortening of the total time of analysis.

Method Development

The novel method for monitoring an electroplating bath during an electrodeposition process comprises two distinct steps: construct a Consolidated Designer Waveform (CDW), i.e., a consolidated multi-frequency voltammetric followed by Calibration to create a robust master calibration analytical model. See FIG. 2

To establish a proof of concept that the method discussed herein is effective an actual plating bath used for Cu damascene processes in the semiconductor manufacturing is used. Applicant avers that the method to monitor an electroplating bath during a plating process as discussed herein is universal and is not limited to only Cu damascene processes used during semiconductor manufacturing.

Regarding the flowchart of FIG. 2, the concentration matrix of analysis of variance is based on the two-level-J-constituent fractional factorial. The number of constituents, L, corresponds to the number of constituents of the tested plating solution of copper, acid, chloride, an accelerator, a suppressor and a leveler. Two-level factorial designs are very effective for screening. Each of the constituents of the tested plating solution is present at the concentration level corresponding to the constituents low or high concentration limit of the future calibration, denoted as −1 and 1, respectively. The 2-level-6-constituent factorial consists of 2⁶=64 solution combinations. Preparation of a number of samples is impractical. As such, the concentration matrix is reduced eight times by introducing fractional factorial that retains the orthogonality among the L factors. The design of a two-level-6-constituent fractional factorial of 8 concentration combinations is described as 2_III⁶⁻³, where the subscript III denotes the resolution of the design. The superscript −3 indicates that one-eighth (⅛) of the full factorial of 64 rows is taken as (⅛×64=2⁻³×2⁶=2⁶×2⁻³=2⁶⁻³). Out of eight combinations of triples of design for 2_III⁶⁻³: ±4=12, ±5=13, and ±6=23, the triple of all positive signs was chosen, resulting in a concentration matrix depicted in Table 1. Consequently, the generating relations are G=124, G=135, and G=236, while generators 124, 135, and 236 produce a complete defining relations G=124=135=236=456=1256=1346=2345. The length of the shortest word in the defining relation determines the resolution R=III of the design.

TABLE 1

Concentration matrix for scan development calculated

based on fractional factorial design.

Copper
Acid
Chloride
Accelerator
Suppressor
Leveler

constituent
constituent
constituent
constituent
constituent
constituent

Solution #
l = 1
l = 2
l = 3
l = 4
l = 5
l = 6

D1
−1
−1
−1
1
1
1

D2
1
−1
−1
−1
−1
1

D3
−1
1
−1
−1
1
−1

D4
1
1
−1
1
−1
−1

D5
−1
−1
1
1
−1
−1

D6
1
−1
1
−1
1
−1

D7
−1
1
1
−1
−1
1

D8
1
1
1
1
1
1

As factorials provide an approximation only within the experimental range, the selection of low and high concentration limits, uniformly normalized as −1 and 1 respectively, was carefully selected. The target concentration is included in the concentration range. Also, the experimental range for method development is suggested to be greater than the process control range. The method development range determines the range for the subsequent calibration training set matrix. The calibration needs to cover a wider range than the process range in order to provide accurate concentration predictions, not only for the sample of the target composition, but also for the concentrations of the plating tank solution samples approaching the process control limits. Depending on a specific constituent and the process control requirement, such as the process control range, of the specific plating process, the typical experimental range is ±20-50% of the target composition.

The pure fractional factorial does not provide replicate information, such as analytical measurements including, but not limited to the execution of voltammetric scans for sample solution considered a weakness of this rigorous approach (Brereton R G, (2003), Chemometrics: Data Analysis for the Laboratory and Chemical Plant, Wiley Chichester). The omission of repetitions is a compromise made when optimizing the experiment design. However, the Inventors of the method and apparatus described herein, incorporated repetitions, with some constraints, during the waveform development process by exploiting the unique advantages of the RTA3D™ (Technic, Inc., Cranston, RI), and by doing so, the repetitions did not impose an experimental burden. As the selected RTA3D™ did not alter the sample, it was discovered that the same solution could be analyzed several times in a row providing a much-needed indication of the repeatability of the waveform being developed. The duration of the experiment was extended by the repetition by several minutes. As only the waveform of interest was repeated, the electrode pretreatment scans remained the same for a single or multiple diagnostic waveforms, while data collection, such as measurement was automatically generation without involving the operator. The poor repeatability of a waveform disqualified that waveform at the initial stage of development process. In order to assess the reproducibility of the waveform being developed, each waveform was executed three times for each of the 8 solution compositions provided in Table 1. Consequently, the total number of samples tested was I=3×8=24. The total number of factors L=6 corresponded to the number of the constituents in the tested plating solution: copper, acid, chloride, an accelerator, a suppressor and a leveler whose concentrations of the constituents were varied. The concentration matrix is defined as Y^(I,L). For the tested solution in particular the concentration matrix was Y^(24,6).

Regarding FIG. 2, the preliminary screening 7 step (the first step of the iterative process of waveform parameter optimization) comprises the selection of an initial set of multi-frequency voltammetric waveforms. Each of the N multi-frequency voltammetric waveforms produce a current response predominantly determined by the varying concentration of any of the L=6 constituents of the plating solution. The N multi-frequency voltammetric waveforms are negligibly dependent on the varying concentrations of other constituents in the tested plating solution. As a single multi-frequency waveform may exhibit the diagnostic characteristics for more than one of L=6 constituents, the number N of preliminary screening waveforms may be lower than L.

Having selected an initial set of N multi-frequency voltammetric waveforms, the voltammetric experiments are carried out in step 8 of FIG. 2 for the eight solutions of the compositions listed in the Table 1, each of the composition solutions were analyzed in triplicate.

Factor Analysis/Anova

The data collection step 8 is followed by the constituent analysis step 9. The constituent analysis is performed individually for each of the N waveforms 18 of multi-frequency AC voltammetric data.

In the following detailed description of method discussed herein, the waveform index n=1, . . . , N is intentionally omitted for brevity.

The numerical voltammetric data corresponding to the investigated waveform (one of N) was arranged in a form of a three-way array X^(I,J,K)where J and K denote number of index points of the voltammogram and the number of fundamental frequencies of AC sinusoidal potential perturbations superimposed on the DC ramp. The preliminary assessment of the analytical usefulness of voltammetric data is based on determination of a correlation between the AC current response for each j^thindex point of the voltammogram and the k^thsinusoidal perturbation frequency for each of the l^thconstituents. The squared correlation coefficient is calculated using the I elements of the column vector of three-way array of voltammetric data x_jk^(I)⊂X^(I,J,K)and the I elements of the column vector of the concentration represented by y_l^(I)⊂Y^(I,L). The i, j, k, l variables are the indexes of I, J, K, and L, respectively. The squared correlation coefficient is described by the following formula:

R
jkl

2

=

[

∑

i
=
1

I

⁢

x
ijk

⁢

y
il

-

∑

i
=
1

I

⁢

x
ijk

⁢

∑

i
=
1

I

⁢

y
il

/
I

]

2

[

∑

i
=
1

I

⁢

x
ijk

2

-

(

∑

i
=
1

I

⁢

x
ijk

)

2

/
I

]

[

∑

i
=
1

I

⁢

y
il

2

-

(

∑

i
=
1

I

⁢

y
il

)

2

/
I

]

(
1
)

where x_ijk∈x_jk^(I)and y_il∈y_l^(I). The squared correlation coefficient values are arranged in a three-way array with the number of rows, columns and slabs being J, K, and L, respectively: R_jkl²∈R^2(J,K,L).

Apart from bivariate determination of the squared correlation coefficient of the three-way array, another key parameter used to assess the analytical utility of the investigated multi-frequency AC voltammetric waveform, is the relative F-ratio. The relative F-ratio is calculated by the analysis of the variance for each of the j^thof J index points of the voltammogram, wherein each of the k^thof K sinusoidal perturbation frequencies and each of the l^thof L constituents of the electroplating solution.

The F-ratio calculation starts with determination of the grand average of the AC voltammetric current response for each index point of the voltammogram and each observed perturbation frequency based on the following expression:

x_jk=Σ_i=1^Ix_ijk/I (2)

where x_jk∈X^(J,K).

For each l^thconstituent of the electroplating solution, the three-way array of the voltammetric data X^(I,J,K)

is split into two three-way subarrays of the same dimensions (I/2, J, K). One subarray denoted by the subscript “−1”, corresponds to voltammetric data recorded for a lower concentration level, −1, (Table 1) of the l^thconstituent:

X

-
1

l
,

(

I
2

,
J
,
K

)

.

The other subarray, denoted by a subscript “1”, contains voltammetric data obtained for the upper concentration level, 1, of the l^thconstituent of electroplating solution:

X
1

l
,

(

I
2

,
J
,
K

)

.

Using the data arranged into subarrays based on the concentration of l^thconstituent, the response average is calculated for both the lower and upper concentration levels individually for each j^thindex point of the AC voltammogram and the k^thperturbation frequency utilizing the following formulae:

x
_

-
1

,
jk

l

=

2
×

∑

i
=
1

I
/
2

⁢

x

-
1

,
ijk

l

/
I

⁢

and

(
3
)

x
_

1
,
jk

l

=

2
×

∑

i
=
1

I
/
2

⁢

x

1
,
ijk

l

/
I

⁢

where

(
4
)

x

-
1

,
ijk

l

∈

X

-
1

l
,

(

I
2

,
J
,
K

)

⁢

and
⁢

x

1
,
ijk

l

∈

X
1

l
,

(

I
2

,
J
,
K

)

.

The response averages were used to obtain the standard deviation values that were calculated separately within the subgroups that were divided based on the concentration of the l^thconstituent for each j^thindex point of the AC voltammogram and the k^thsinusoidal perturbation frequency as expressed by following equations:

s

-
1

,
jk

l

=

∑

i
=
1

I
/
2

⁢

(

x

-
1

,
ijk

l

-

x
_

-
1

,
jk

l

)

2

I
/
2

-
1

(
5
)

s

1
,
jk

l

=

∑

i
=
1

I
/
2

⁢

(

x

1
,
ijk

l

-

x
_

1
,
jk

l

)

2

I
/
2

-
1

(
6
)

for the low and high concentration limits of l^thconstituent, respectively. The standard deviation values were used to calculate the standard errors individually within each l^thconstituent concentration based divided subgroup for each j^thindex point of the AC voltammogram and the k^thsinusoidal perturbation frequencies employing the formulae:

SE_−1,jk^l=s_−1,jk^l/√{square root over (I/2)} (7)

SE_1,jk^l=s_1,jk^l/√{square root over (I/2)} (8)

for both the low and high concentration limits of the l^thconstituent, respectively.

The factor effect of low concentration of the l^thconstituent for the j^thindex point of the AC voltammogram and the k^thfrequency was obtained by subtracting from the response average for the low concentration (Equation 3) and the grand average (Equation 2):

FE_−1,jk^l=x_−1,jk^l−x_jk (9)

The factor effect for the high concentration of the l^thconstituent for the j^thindex point of the AC voltammogram and the k^thfrequency was determined by subtracting from the response average for low concentration (Equation 4) and the grand average (Equation 2):

FE_1,jk^l=x_1,jk^l−x_jk (10)

Uniquely for the two-level factorial design and for the same number of samples for the low and the high concentration of the I/2 the factor effect and for the low concentration equals the negative factor effect for high concentration as follows:

FE_−1,jk^l=−FE_1,jk^l (11)

The above relationship stems from the fact that:

x_−1,jk^l+x_1,jk^l=2×x_jk (12)

The Analysis of Variance (ANOVA) sum of the squares of the low and high concentrations of the l^thconstituent are defined by the corresponding constituent effects as expressed by Equations 9 and 10, respectively, to obtain:

SS_−1,jk^l=I/2×(FE_−1,jk^l)² (13)

and

SS_1,jk^l=I/2×(FE_1,jk^l)² (14)

respectively. Because of the relationship described by Equation 11, the sum of the squares for the low and high concentrations are equal to each other for two level factorial design and the equal dimensions of the data subarrays corresponding to the low and high concentrations. Therefore, there is no need to distinguish the sum of squares whether or not the sum corresponds to the low or high concentrations:

SS_jk^l=SS_−1,jk^l+SS_1,jk^l=2×SS_−1,jk^l=2×SS_1,jk^l (15)

The Analysis of Variance (ANOVA) mean square for the two-level factorial design of equal size of subgroups is defined by subtracting the sum of the squares described in Equation 15 by the number of degrees of freedom for the l^thconstituent, df^l:

MS_jk^l=SS_jk^l/df^l (16)

The MS_jk^lis an element of the 3-way array of mean squares MS^(J,K,L).

The ANOVA F-ratio is calculated individually for each of the l^thconstituent of the electroplating bath, each j^thindex point of the AC voltammogram and each of the k^thperturbation frequencies, by dividing the mean square (Equation 16) by the error of variance:

F
jk

l

=

MS
jk

l

σ

e
,
jk

2

(
17
)

An approximate estimate of the error variance, σ_e,jk², is determined by pooling the sum of the squares corresponding to the constituents having the lowest mean square. The pooling is conducted within the ANOVA parameters calculated individually for each j^thindex point of the voltammogram and the k^thperturbation frequency. The sum of the squares corresponding to the bottom half of the constituents (as defined by the lower mean square) corresponding to about half of the degrees of freedom, is used to estimate the error mean square or error variance; the number of constituents, J=6, each having the same number of degrees of freedom df_j. The error variance is estimated as:

σ

e
,
jk

2

=

∑

l
=
1

L
/
2

⁢

SS
jk

l

df

l

(
18
)

Usually, the Analysis of Variance (ANOVA) parameters defined above are reported in a form of the ANOVA table prepared using as the input the univariate response vector x_jk^(I)and a matrix of factors Y^(I,L)(in the example discussed herein, the concentration values). The obtained Mean Square (MS) values of the analysis of variance are used to rank the relative importance of each factor, such as the concentrations of the plating solution constituents, with respect to the observed variation in the response. The variation attributable to the least influential constituents as quantified by MS are consolidated. The method pools variation with the data, e.g., multi-frequency voltammetric data, from many marginal factors without taking more than half the total degrees of freedom. If the F-ratio nears 1.0 for the constituent, then the effect of that constituent is not distinguishable from the background noise. If the effect of the constituent is not distinguishable from the background noise, the concentration of the constituent cannot be measured from the response.

There is no upper limit for the F-ratio value. In the example provided herein, the development of a multi-frequency AC voltammetric waveform that exhibits a current response that is predominantly affected by a single constituent concentration of a plating solution constituent, while being negligibly dependent on other factors caused by varying concentrations of the other bath constituents was the goal. To achieve the intended goal, the F-ratio obtained for the j^thfactor of interest was significantly greater than F-ratio of the remaining J−1 factors. As the Analysis of Variance (ANOVA) is conducted individually for each univariate response vector, x_jk^(I), the method has to be executed J×K (where J×K is the total number of univariate response vectors) times to determine the J×K×L F-ratio values. F-ratio values obtained for J×K univariate response cases need to be normalized in order to make the F-ratio values comparable with each other for the various j^thand k^thindexes as the response data in the example provided herein is in a form of a multiway array X^(I,J,K). For example, the predominant F-ratio for the l^thconstituent for certain values of j^thand kth indexes was 100, while the predominant ratio calculated for the same constituent for other j^thand k^thindexes was 10,000. The two exemplary values of F-ratio are quantitatively incomparable with each other. However, their corresponding variables of multivariate voltammetric data are analytically useful provided said corresponding variables of multivariate voltammetric data are analyzed in response to concentration changes of the j^thconstituent. In order to enable comparative analysis of F-ratios calculated for the multivariate voltammetric data, the scaling of the F-ratio resulted in a parameter called the “relative F-ratio” (RF), defined as:

RF
jk

l

=

F
jk

l

∑

l
=
1

L

⁢

F
jk

l

(
19
)

The values of relative F-ratios are uniformly scaled within the range of [Image Omitted] 0: 1 for any j^thand k^thindexes, with the F-ratio values corresponding to variables of multivariate voltammetric data of high analytical utility to be closer to 1, wherein the F-ratio values corresponding to variables of multivariate voltammetric data of no analytical utility to be closer to 0.

The substitution of F-ratio in Equation 19 with the value obtained by Equation 17, leads to following equation:

RF
jk

l

=

MS
jk

l

/

σ

e
,
jk

2

∑

l
=
1

L

⁢

(

MS
jk

l

/

σ

e
,
jk

2

)

(
20
)

that, after simplification, results in the formula for the relative F-ratio:

RF
jk

l

=

MS
jk

l

∑

l
=
1

L

⁢

MS
jk

l

(
21
)

Based on Equation 21, the relative F-ratio is a relative Mean Square (RMS):

RMS_jk^l=RF_jk^l (22)

Generating a Consolidated Designer Waveform (CDW)

The decisive quantitative parameters for the preliminary waveform assessment determined by the Factor analysis step 9 are relative to the F-ratio (Equation 21) and R²(Equation 1). These two parameters react in unison to indicate the portions of a voltammogram for N waveforms that are useful for further modeling. Any dissonance between the relative F-ratio (Equation 21) and R²(Equation 1) indicates problems with the data, such as the presence of artefacts that may render the data useless. In the acceptance of extracted waveform step 10, analytically useful portions of individual N multi-frequency voltammograms are extracted. The useful portions having a value that is likely to be different from N and greater than or equal to L, are iteratively optimized in the optimizing waveform/extraction of relative portions step 11 starting from the measurements of these selected fragments only taken in the measurement taking step 8 for each of the eight solution composition combinations describe in Table 1. Each solution is analyzed in triplicate. The next step is the Factor analysis step 9 that is executed for the generated multi-frequency voltammetric data for each of the selected fragments of the N initial waveforms individually. The Factor Analysis step 9 is executed by implementing Equations 1 to 21.

Provided that the generated waveforms based on the extracted fragments of the preliminary waveforms exhibit a comparable analytical utility to that of the initial waveforms, as quantified by the relative F-ratio (Equation 21) and R²(Equation 1) complementing each other, these fragments of the preliminary waveforms are consolidated to build a designer waveform 12.

The newly created Consolidated Designer Waveform (CDW) is thereafter iteratively optimized by steps 13-16 starting from performing the measurements 13 for the 8 solution composition combinations of Table 1. Each solution is analyzed in triplicate. The next step is the Factor analysis step 14 performed using the multi-frequency voltammetric data for the CDW following the calculations of Equations 1 to 21. Provided the multi-frequency voltammetric data of the CDW exhibits comparable analytical usefulness as do the individual fragments of multi-frequency voltammetric waveforms taken into consolidation, as quantified by the relative F-ratio (Equation 21) and R²(Equation 1) complement each other, the generated CDW is accepted for building the calibration model.

FIG. 3 illustrates a single period of the multi-frequency sinusoidal applied to a potential perturbation 27 consisting of summed 14 sine curves 26 of different frequencies and amplitudes 28. This complex periodical perturbation was superimposed on the consolidated DC potential ramps 29, 30 that correspond to the analytically useful fragments extracted from the initial waveform used in step 7 of FIG. 2.

The data collected during the F-factor analysis (31 of FIG. 5) as quantified by the relative F-ratio (Equation 21) for each of the L=6 constituents of the plating bath, is presented in FIG. 5. The same data is presented in a different projection, as contours 32 evidence high analytical utility ranges, individually for each constituent in FIG. 6. The data presented in FIG. 6 is consolidated into a single contour graph 33 from all six bath constituents as presented in FIG. 7. An analytically useful area occupies a significant portion of the contour graph of FIG. 7. The fundamentally novel rigorous steps 7-17 of FIG. 2 allow for the development of a single designer voltammogram, CDW, capable of measuring simultaneously the concentrations of the six distinct constituent chemical species both qualitatively and quantitatively. As an additional challenge, the distinct chemical species are intended to interact with each other synergistically during the monitored plating process. The concentrations of the plating bath constituents are determined in an unaltered solution sample by an electrochemical method, such as Complex Designer Voltammetry (CDV) utilizing experimental conditions mirroring those of the chosen plating process resulting in high analytical and process control relevance. The application of multi-sinusoidal potential perturbation 23 on DC ramps 29, 30 allows to achieve experimental conditions requirements needed for analyses of all deliberately added bath constituents. The application of multi-sinusoidal potential perturbation 23 on DC ramps 29, 30 allows analyses of all deliberately added bath constituents with a single Consolidated Designer Waveform. The application of multi-sinusoidal potential perturbation 23 on DC ramps 29, 30 allows simultaneous analyses of constituents of fundamentally different properties, such as chemical structure, concentration, electrochemical reactivity with a single Consolidated Designer Waveform. The application of multi-sinusoidal potential perturbation 23 on DC ramps 29, 30 does not compromise the experimental time as compared to the DC ramp. Multi-frequency potential perturbations upgrade a conventional electroanalytical first-order instrument to a second-order instrument without additional experimental time.

Building Calibration Model

Once the CDW is accepted in step 17 of FIG. 2, it is the CDW is used to collect master calibration voltammetric data 18 by analyzing (step 25 of FIG. 2) solutions having concentrations of L=6 bath constituents that are varied linearly at 5 levels according to a 5-level-6-constituent linear orthogonal array (Table 2). Each of the 25 solutions contained in Table 2 were analyzed in a triplicate resulting in a total of 75 samples of the master calibration training set.

TABLE 2

Concentration matrix for master calibration model calculated

based on 5-level-6-constituent linear orthogonal array.

Copper
Acid
Chloride
Accelerator
Suppressor
Leveler

constituent
constituent
constituent
constituent
constituent
constituent

Solution #
l = 1
l = 2
l = 3
l = 4
l = 5
l = 6

C1
−1
−1
−1
−1
−1
−1

C2
−1
−0.5
−0.5
−0.5
−0.5
−0.5

C3
−1
0
0
0
0
0

C4
−1
0.5
0.5
0.5
0.5
0.5

C5
−1
1
1
1
1
1

C6
−0.5
−1
−0.5
0
0.5
1

C7
−0.5
−0.5
0
0.5
1
−1

C8
−0.5
0
0.5
1
−1
−0.5

C9
−0.5
0.5
1
−1
−0.5
0

C10
−0.5
1
−1
−0.5
0
0.5

C11
0
−1
0
1
−0.5
0.5

C12
0
−0.5
0.5
−1
0
1

C13
0
0
1
−0.5
0.5
−1

C14
0
0.5
−1
0
1
−0.5

C15
0
1
−0.5
0.5
−1
0

C16
0.5
−1
0.5
−0.5
1
0

C17
0.5
−0.5
1
0
−1
0.5

C18
0.5
0
−1
0.5
−0.5
1

C19
0.5
0.5
−0.5
1
0
−1

C20
0.5
1
0
−1
0.5
−0.5

C21
1
−1
1
0.5
0
−0.5

C22
1
−0.5
−1
1
0.5
0

C23
1
0
−0.5
−1
1
0.5

C24
1
0.5
0
−0.5
−1
1

C25
1
1
0.5
0
−0.5
−1

Various chemometric techniques are used for calibration calculations consisting of data compression and relevant information extraction combined with regression coefficient calculation for each of the bath constituents. The selection of a chemometric technique for calibration calculation is conducted individually for each of the six plating bath constituents depending on the dimensionality of the voltammetric data of the highest utility to build the master calibration analytical model. The multivariate voltammetric data for a single sample of the training set is in the form of either a vector, several vectors of different dimensions or a matrix. Provided the multivariate calibration data of a single sample is in the form of a vector, the suitable chemometric techniques used are Principal Component Regression (PCR) and Partial Least Squares (PLS). If each of the 75 samples of the training set are several vectors of varying lengths, then the following chemometric techniques are used for calibration calculation: Consensus Principal Component Regression (CPCR), Hierarchical Principal Component Regression (HPCR), Hierarchical Partial Least Squares (HPLS) or Multi-block Partial Least Squares (MBPLS). If the training set sample is a matrix, then use of the following multi-way chemometric techniques are optimal: Parallel Factor Analysis (PARAFAC) for multi-way array decomposition coupled with Inverse Least Squares (ILS) (PARAFAC/ILS) regression, Direct Trilinear Decomposition (DTLD) coupled with ILS (DTLD/ILS) and Multi-linear Partial Least Squares (N-PLS). Preferably, at least two chemometric techniques are applied comparatively for the same set of multivariate voltammetric data as the similarity of predictive performance among various regression techniques indicates that the developed calibration models are useful. The similarity among the various decomposition and regression approaches provides more information about the robustness of the analytical model, as each of the techniques analyzes data from a different perspective.

The inventors recommend that the voltammetric data used for the calculation of the master calibration analytical models for each of the L=6 constituents of the plating bath solution only should be for one type of CDW. By using only one type of CDW for concentration determination of all deliberately added bath constituents the duration of the complete can be reduced to several minutes.

Once the master calibration is calculated for all of the plating bath constituents based on the CDW data obtained from the primary instruments, the model is then transferred to numerous secondary instruments in the field, such as semiconductor manufacturing plants where the RTA3D™ systems are being employed to control plating processes. The design of the secondary instruments should be similar to the primary instrument as depicted in FIG. 1. When manufacturing the FIG. 1 instruments, it is imperative to ascertain the interchangeability between the instruments allowing a transference of the master calibration method based on the collection of CDW data for a calibration transfer subset consisting of three samples of the most representative composition (Jaworski A et al., (2009), Anal Chim Acta, 656(1-2):42-50). The simple and fast transference of the master calibration to the secondary instruments is of critical importance for the proper servicing and maintenance of the process control equipment so as not to interfere with the continuous production flow. Because of the high stability of the Multi-Task Electrical Probe (MTEP™) readings in real-time, the apparatus depicted in FIG. 1 seldomly requires (once every half a year) standardization of the transferred calibration model. Typically, other process control instruments require frequent repetition of full calibration (as opposed to calibration transfer via training subsets) to be performed either on-site or by taking the instrument off the line and re-calibrating seriously impeding the production flow.

EQUIVALENTS

While specific embodiments of the subject invention have been discussed, the above specification is illustrative and not restrictive. Many variations of the invention will become apparent to those skilled in the art upon review of this specification. The full scope of the invention should be determined by reference to the claims, along with their full scope of equivalents, and the specification, along with such variations.

Unless otherwise indicated, all numbers expressing quantities of ingredients, reaction conditions, and so forth used in the specification and claims are to be understood as being modified in all instances by the term “about”. Accordingly, unless indicated to the contrary, the numerical parameters set forth in this specification and attached claims are approximations that may vary depending upon the desired properties sought to be obtained by the present invention.

The above discussion is meant to be illustrative of the principle and various embodiments of the present invention. Numerous variations and modifications will become apparent to those skilled in the art once the above disclosure is fully appreciated. It is intended that the following claims be interpreted to embrace all such variations and modifications.