CROSSREFERENCE TO RELATED APPLICATION

[0001]
The benefit of priority of U.S. provisional patent application 60/764,614 filed Feb. 2, 2006 in the names of Jianwen Han, et al. for “SIMULTANEOUS INORGANIC, ORGANIC AND BYPRODUCT ANALYSIS IN ELECTROCHEMICAL DEPOSITION SOLUTIONS,” is hereby claimed under the provisions of 35 USC 119. The disclosure of such U.S. provisional patent application is hereby incorporated herein by reference in its entirety, for all purposes.
FIELD OF THE INVENTION

[0002]
This invention relates generally to methods and apparatuses for monitoring organic and inorganic additives as well as byproduct concentrations in electrochemical copper plating baths, preferably using a single analysis system.
BACKGROUND OF THE INVENTION

[0003]
In the practice of copper interconnect technology in semiconductor manufacturing, electrochemical deposition (ECD) is widely employed for forming copper interconnect structures on microelectronic substrates. The Damascene process, for example, uses physical vapor deposition to deposit a seed layer of copper on a barrier layer, followed by electrochemical deposition of copper.

[0004]
In the ECD operation, organic additives as well as inorganic additives are employed in the plating solution in which the metal deposition is carried out. The ECD process is sensitive to concentration changes of organic, inorganic and, as disclosed herein, byproduct components. Since concentrations of bath components can vary considerably as they are consumed and/or produced during the life of the bath, it therefore is desirable to conduct realtime monitoring and replenishment of all major bath components to ensure optimal process efficiency and yield of the semiconductor product incorporating the electrodeposited copper.

[0005]
Presently, inorganic and organic additives of the copper ECD baths are analyzed using separate analysis systems, none of which are capable of quantifying byproducts. For example, inorganic components of the copper ECD bath, including copper, sulfuric acid and chloride, conventionally are measured by potentiometric analysis. Organic additives such as suppressors, accelerators, and levelers are added to the ECD bath to control uniformity of the film thickness across the wafer surface. The concentration of the organic additives can be measured by pulsed cyclic galvanostatic analysis (PCGA), which mimics the plating conditions occurring on the wafer surface. In the practice of the PCGA method, copper is electroplated onto a working or testing electrode, by supplying a sufficient current (or potential), while monitoring the corresponding potential (or current). The electrical potential (or current) measured during such electroplating step correlates with the organic additive concentrations in the sample electroplating bath, and therefore can be used for determining concentrations of organic additives. For further details regarding the PCGA processes, please see U.S. Pat. No. 6,280,602 issued Aug. 28, 2001 to Peter M. Robertson for “Method and Apparatus for Determination of Additives in Metal Plating Baths,” the disclosure of which hereby is incorporated herein by reference for all purposes.

[0006]
There are several implications associated with said separate analyses including, but not limited to:

 (1) more sample must be used for two or three separate analyses;
 (2) multiple analyzers equates to a larger expense upfront, larger maintenance costs and a larger overall footprint;
 (3) if byproduct(s) cannot be detected then “bleed and feed” schemes cannot be optimized nor can defects on wafers be predicted as a function of foreign bath material.

[0010]
Accordingly, there is a continuing need to improve the PCGA analysis of organic additives in ECD baths and to provide more stable analytical signals and reduce noise and measurement errors.

[0011]
There is also a need to expand the improved PCGA process so that inorganic and byproduct species present in the ECD baths may be analyzed and quantified using the same analysis system.

[0012]
There is a further need to modify the conventional PCGA procedures to achieve shorter calibration and measurement cycles, reduce the analysis time, and simplify the hardware and software required for performing the PCGA analysis.

[0013]
There is still a further need to account for interactions between the different types of ECD additives and their byproducts and their impact on the PCGA analysis results.

[0014]
Other objects and advantages will be more fully apparent from the ensuring disclosure and appended claims.
SUMMARY OF THE INVENTION

[0015]
The present invention relates generally to realtime analysis of ECD metal plating solutions, for the purpose of reducing plating defects and achieving high quality metal deposition, and systems for performing such analysis.

[0016]
One aspect of the present invention relates to methods of analyzing copper ECD bath compositions comprising measuring ECD bath byproducts and, optionally, measuring organic additives and/or inorganic additives in said bath compositions, wherein said measuring is preferably performed using a single analysis system and/or a single bath sample. Most preferably, a single sample of the bath composition is measured using a single analysis system.

[0017]
Another aspect of the present invention relates to methods of analyzing copper ECD bath compositions comprising measuring ECD bath byproducts, organic additives and inorganic additives. One preferred embodiment relates to methods comprising performing said measuring using a single analysis system and/or a single sample. Most preferably, a single sample of the bath composition is measured using a single analysis system.

[0018]
Another aspect of the invention relates to a method for electrochemically determining the concentration of one or more target components in a sample electrochemical deposition solution, comprising the steps of:

 (a) contacting a working electrode and a counter electrode with the sample electrochemical deposition solution;
 (b) applying a potential pulse between the working and counter electrodes for a sufficient period of time to induce metal nucleation on an surface of the working electrode;
 (c) subsequently, applying a constant plating current between the working and counter electrodes sufficient for effectuating electrochemical deposition of metal onto the surface of the working electrode from the sample electrochemical deposition solution;
 (d) monitoring potential response of the sample electrochemical deposition solution under the constant plating current; and
 (e) determining concentration of one or more target components in such sample electrochemical deposition solution, based on the potential response of the sample electrochemical deposition solution measured under the constant plating current.

[0024]
Preferably, such sample electrochemical deposition solution is a copper electroplating solution that comprises copper sulfate, sulfuric acid, chloride, and one or more organic additives such as suppressors, accelerators, and levelers, while the target components for concentration analysis are the one or more organic additives, one or more inorganic additives, and/or byproducts of said additives. Preferably, the measuring is performed using a single analysis system and/or a single sample. Most preferably, a single sample of the bath composition is measured using a single analysis system.

[0025]
Another aspect of the present invention relates to a method for conducting electrochemical analysis of a sample electrochemical deposition solution, said method comprising the steps of providing a measurement chamber having a measuring electrode, a counter electrode, and a reference electrode therein, and performing in such measurement chamber one or more measurement cycles by using said sample electrochemical deposition solution. Each of such measurement cycles comprises the sequential steps of:

 (a) electrostripping the measuring electrode to remove metal residue formed thereon during a previous measurement cycle;
 (b) applying a cyclic electropotential between the measuring and counter electrodes to remove organic residue formed on the measuring electrode during a previous measurement cycle;
 (c) filling the measurement chamber with fresh sample electrochemical deposition solution and allowing the measuring electrode and counter electrode to reach an equilibrium state in the sample solution;
 (d) electrochemically depositing metal onto the measuring electrode by applying a constant electrical current between the measuring electrode and counter electrode through the sample electrochemical deposition solution, while concurrently monitoring potential response of the sample solution; and
 (e) applying an electropotential between the measuring electrode and counter electrode to remove at least a part of the metal deposit formed on the measuring electrode.

[0031]
Preferably, the sample electrochemical deposition solution is a copper electroplating solution that comprises copper sulfate, sulfuric acid, chloride, and one or more organic additives such as suppressors, accelerators, and levelers. Preferably, the analysis measures the concentration of the one or more organic additives, one or more inorganic additives, and/or byproducts of said additives. More preferably, the measuring is performed using a single analysis system and/or using a single sample, most preferably simultaneously using a single analysis system and/or using a single sample.

[0032]
An electrolytic cleaning solution comprising sulfuric acid can be used for electrostripping in step (a). More preferably, a portion of the electrostripping is conducted while such electrolytic cleaning solution is flushed through the measurement chamber, to remove metal residues that have been stripped off the measuring electrode and avoid further contamination of the measurement chamber by such metal residues.

[0033]
Such electrolytic cleaning solution may also be used to flush the measurement chamber when the cyclic electropotential is applied between the measuring and counter electrodes (i.e., cyclic voltammetry or CV scan) in step (b), to remove organic residues that come off the electrode surface during the CV scan.

[0034]
The equilibrium state in step (c) may be reached by disconnecting the measuring electrode from the counter electrode, to form an open circuit. Alternatively, such equilibrium state can be reached by applying a predetermined electropotential that is less than the copper plating potential between the measuring electrode and the counter electrode.

[0035]
The electroplating in step (d) is preferably preceded by a potential pulse of from about −0.1V to about −1V, to facilitate formation of metal nuclei on the electrode surface, and followed by a stripping electropotential of from about 0.1V to about 0.5V, to remove at least a part of the metal plate formed during step (d) and thereby reduce the risk of alloying between such metal plate and metal component of the measuring electrode.

[0036]
Still another aspect of the present invention relates to a method for simultaneously determining concentrations of copper sulfate, sulfuric acid, chloride ion, suppressor, accelerator, leveler, and/or byproduct(s) thereof in a sample electrochemical deposition solution, comprising the steps of:

 (a) identifying one or more noncompositional variables that affect electropotential responses of electrochemical deposition solutions during electrochemical metal deposition;
 (b) establishing a multiple regression model that expresses the electropotential responses of electrochemical deposition solutions as a function of (1) said one or more noncompositional variables, (2) organic additive concentrations in the solutions, (3) inorganic additive concentrations in the solutions, (4) byproduct concentrations in the solutions, and the corresponding coefficients;
 (c) conducting multiple calibration runs, by measuring electropotential responses of multiple calibration solutions having unique, known organic additive, inorganic additive, and/or byproduct concentrations at unique, predetermined values of said one or more variables;
 (d) determining the coefficients that correspond to said one or more variables and the organic additive, inorganic additive, and/or byproduct concentrations in the multiple regression model, based on information obtained from the calibration runs; and
 (e) conducting N experimental runs, by measuring electropotential responses of the sample electrochemical deposition solution at unique, predetermined values of said one or more variables;
 (f) establishing N number of equations based on the established multiple regression model, said equations containing the coefficients determined in step (d), the electropotential responses measured during the N experimental runs in step (e) and the corresponding predetermined values of said one or more variables, and the unknown concentrations of the copper sulfate, sulfuric acid, chloride ion, suppressor, accelerator, leveler, and/or byproduct(s) thereof in the sample electrochemical deposition solution; and
 (g) calculating said copper sulfate, sulfuric acid, chloride ion, suppressor, accelerator, leveler, and/or byproduct concentrations in the sample solution by solving the N equations provided in step (f),
wherein N corresponds to the total number of organic additive, inorganic additive and/or byproduct species simultaneously quantified using such method.

[0044]
Preferably, analysis of variance is used for identifying the noncomposition variables that have significant impact on the electropotential responses of the electrochemical deposition solutions. Specifically, a preliminary multiple regression model including terms for all noncompositional variables that have potential impact on the electropotential responses is constructed, and analysis of variance tests are carried out to (1) estimate the parameters or coefficients associated with such variables and (2) determine the probability or likelihood that such coefficients are equal to zero. Only those variables having nonzero coefficients at confidence levels of not less than 95% (i.e., the probability of such coefficients being zero is not more than 5%) are selected to be included into a multiple regression model for determination of the organic additive, inorganic additive and/or byproduct concentrations.

[0045]
Six (6) noncomposition variables have been identified using such analysis of variance tests for analysis of organic additive, inorganic additive and/or byproduct concentration in copper electroplating solutions, which include (1) nucleation potential (i.e., the potential pulse before current plating); (2) nucleation time, (3) electroplating current, (4) electroplating time, (5) scan rate (i.e., potential change rate) of the cyclic voltammetry during preplating cleaning process, (6) size of the measuring electrode used during the electrochemical analysis, and (7) temperature.

[0046]
A multiple regression model including terms for these selected noncompositional variables and for the organic additive, inorganic additive and/or byproduct concentrations is then established in step (b). An important advantage of the method of the present invention is that it provides terms to account for interactions between the noncompositional variables and/or the additive (and/or byproduct) concentrations.

[0047]
Once all the coefficients for the noncompositional variables and the additive (and/or byproduct) concentrations in such multiple regression model are determined via calibration, the actual sample analysis starts by conducting N experimental runs, each of which has a different sets of predetermined values for the noncompositional variables. As defined herein, “N” corresponds to the total number of species being quantified, wherein the species may include organic additives, inorganic additives, and/or byproducts thereof. The electroplating potentials of the sample electrochemical deposition solution in such N experimental runs are measured and used to establish N number of equations according to the established multiple regression model. Each equation contains known coefficients, known values of the noncompositional variables, and the electroplating potential value as measured. The only N unknown values in such equations are the organic additive, inorganic additive and/or byproduct concentrations, which can be readily determined by solving the N number of equations.

[0048]
The N experimental runs can be conducted sequentially in a single electrochemical analytical cell. Alternatively, they can be carried out simultaneously in N electrochemical analytic cells having N different plating protocols or settings.

[0049]
A further aspect of the present invention relates to a method for simultaneously determining concentrations of copper sulfate, sulfuric acid, chloride ion, suppressor, accelerator, leveler, and/or byproduct(s) thereof in a sample electrochemical deposition solution, by using a single electrochemical analytical cell and a single plating protocol, comprising the steps of:

 (a) selecting n compositional terms that include copper sulfate concentration, sulfuric acid concentration, chloride ion concentration, suppressor concentration, accelerator concentration, leveler concentration, byproduct(s) concentrations, and interactions between two or more of said concentrations, wherein n≧3;
 (b) establishing m multiple regression models that correspond to m time points during the electrochemical metal deposition process, wherein each model expresses electropotential responses of electrochemical deposition solutions as a function of the n selected compositional terms and their corresponding coefficients, wherein m≧3;
 (c) using said electrochemical analytical cell and said plating protocol for measuring electropotential responses of multiple calibration solutions at each of said m time points, wherein said calibration solutions contain copper sulfate, sulfuric acid, chloride ion, suppressor, accelerator, leveler, and/or byproduct(s) at unique, known concentrations;
 (d) determining the coefficients of said n selected compositional terms for each of the m multiple regression models, based on information obtained in step (c);
 (e) using said electrochemical analytical cell and said plating protocol for measuring electropotential responses of the sample electrochemical deposition solution at each of said m time points; and
 (f) determining the n selected compositional terms based on the established multiple regression models, the coefficients determined in step (d), and the electropotential responses measured in step (e); and
 (g) calculating concentrations of copper sulfate, sulfuric acid, chloride ion, suppressor, accelerator, leveler, and/or byproduct(s) in the sample electrochemical deposition solution from the compositional terms so determined.

[0057]
Matrix inversion can be used for quickly and directly determining the n selected composition terms in step (f). Specifically, three matrixes X, β, and Y are constructed for representing the m multiple regression models as Y=βX, wherein X is a n×1 compositional matrix containing the n compositional terms, wherein β is a m×n coefficient matrix containing the coefficients determined in step (d), and Y is a m×1 response matrix containing the electropotential responses measured in step (e). The compositional matrix X containing the n compositional terms can be directed determined as X=(β′β)^{−1}β′Y, wherein β′ is the transpose of β, and wherein (β′β)^{−1 }is the inverse of β′β.

[0058]
The time points used for establishing the multiple regression models can be selected from any time instances during the electroplating process. For example, they can be selected from 0.2 second, 0.25 second, 0.5 second, 1 second, 5 seconds, 10 seconds, and 20 seconds.

[0059]
Other aspects, features and embodiments of the invention will be more fully apparent from the ensuing disclosure and appended claims.
BRIEF DESCRIPTION OF THE DRAWINGS

[0060]
FIG. 1A is a graph of multiple electropotential response curves measured over time for a set of electrochemical deposition solutions containing organic additives at different concentrations, wherein the measurements were conducted with a potential pulse followed by current plating.

[0061]
FIG. 1B is a graph of comparative electropotential response curves measured for the same set of electrochemical deposition solutions as in FIG. 1A, wherein the measurements were conducted with a current pulse followed by current plating.

[0062]
FIGS. 2A and 2B are illustrative potential waveforms during exemplary measurement cycles, according to two alternative embodiments of the present invention.

[0063]
FIG. 3 is a plating transient measured for an electrochemical deposition solution having 10% and 50% copper thiolate formation.

[0064]
FIG. 4 is a plating transient for an aging electrochemical deposition solution.

[0065]
FIG. 5 is a plating transient for an aged electrochemical deposition solution in a bleed and feed environment.
DETAILED DESCRIPTION AND PREFERRED EMBODIMENTS THEREOF

[0066]
The present invention proposes various new electrochemical analytical cell designs and new methodologies for conducting concentration analysis of electrochemical deposition (ECD) solutions, which are described in detail as follows. U.S. patent application Ser. No. 10/836,546 for “Methods and Apparatuses for Monitoring Organic Additives in Electrochemical Deposition Solutions” filed on Apr. 30, 2004 in the name of Jianwen Han et al. is hereby incorporated by reference in its entirety.

[0067]
While the invention is described hereinafter in various embodiments employing copper ECD baths utilizing copper sulfate, sulfuric acid and chloride inorganic components, it will be recognized that the utility of the invention is not thus limited, but rather extends to and encompasses the use of other salt, acid and anion inorganic components in ECD baths for copper deposition.

[0000]
Electrochemical Deposition with an Initial Potential Pulse Followed by Constant Current

[0068]
As described by U.S. Pat. Nos. 6,280,602; 6,459,011; 6,592,737; and 6,709,568, a conventional PCGA measurement cycle that is useful for concentration analysis of ECD solutions typically comprises the following four steps:

 (a) stripping, in which the copper layer previously deposited is removed;
 (b) cleaning, in which the measuring electrode surface is thoroughly cleaned electrochemically or chemically using an acid bath;
 (c) equilibration (optional), in which the measuring electrode and the reference electrode are exposed to the sample ECD solution and allowed reach an equilibrium state; and
 (d) plating, in which copper is electrochemically deposited onto the measuring electrode under an initial current pulse followed by a constant current, while the plating potential between the measuring and counter electrodes is monitored and recorded.

[0073]
One problem associated with such conventional PCGA method is that the plating potential signal is not stable during the plating step. As a result, the determinations of organic additive concentrations are not sufficiently accurate for the highprecision control that is desired from the perspective of highvolume manufacturing operations for the next generation of semiconductors, in which reliable metrology is critically important.

[0074]
The present invention therefore provides a new PCGA method, based on the discovery that use of a potential pulse, in place of a current pulse, followed by constant current plating during the plating step, yields a plating potential signal of significantly enhanced stability and accuracy. Such enhancement of stability and accuracy in turn yields improved measured results for organic additive, inorganic additive and/or byproduct concentrations in operation of ECD baths.

[0075]
Specifically, the potential pulse is applied for a sufficient period of time to induce metal nucleation on the electrode surface, and preferably for duration of from about 1 microsecond to about 2.5 seconds. For electrochemical deposition of copper from a sample ECD solution comprising copper sulfate, sulfuric acid, chloride, and one or more organic additives, such potential pulse preferably has a magnitude of from about −0.1V to about −1V, more preferably from about −0.1V to about −0.9V. Magnitude of such potential pulse can be readily modified by a person ordinarily skilled in the art to adapt for electrochemical deposition of other metals or metal alloys using other ECD solutions.

[0076]
For copper ECD, the constant current following such potential pulse is preferably within a range of from about −1 mA/cm^{2 }to about −1000 mA/cm^{2}, which can be readily modified by a person ordinarily skilled in the art for adaptation to other types of ECD reactions using other ECD solutions.

[0077]
FIG. 1A shows the potential response curves of eight (8) different copper ECD solutions containing the suppressor, accelerator, and leveler at different, known concentrations (specified by Table I hereinafter), as measured under a 0.1 second potential pulse of about −0.7 V, followed by constant current plating at −100 mA/cm
^{2 }for about 100 seconds.
 TABLE I 
 
 
 Additive Concentration (ml/L) 
 Solution  Solution  Solution  Solution  Solution  Solution  Solution  Solution 
 #1  #2  #3  #4  #5  #6  #7  #8 
 
Accelerator  3  3  3  3  9  9  9  9 
Leveler  1.25  1.25  3.75  3.75  1.25  1.25  3.75  3.75 
Suppressor  1  3  1  3  1  3  1  3 


[0078]
In comparison, FIG. 1B shows the potential response curves of the same solutions #18, as measured under a 0.1 second current pulse of about −200 mA/cm^{2}, followed by constant current plating at −100 mA/cm^{2 }for about 100 seconds.

[0079]
It is evident that the potential response curves in FIG. 1A contain little fluctuations over time and almost no overlapping between the curves, while the potential response curves in FIG. 1B show significant fluctuations over time and overlapping therebetween.

[0080]
Therefore, use of a potential pulse before constant current plating in the plating process of the present invention provides plating potential signals of significantly enhanced stability and accuracy, in comparison with the conventional plating process that uses a current pulse before the constant current plating, and it constitutes an important advancement in the field of PCGAbased concentration analysis.

[0000]
Electrochemical Concentration Analysis Using a FiveStep Measurement Cycle

[0081]
A conventional measurement cycle useful for concentration analysis of copper ECD solutions typically comprises four steps, which include (1) stripping, (2) cleaning, (3) equilibrium, and (4) plating, as described in U.S. Pat. Nos. 6,280,602; 6,459,011; 6,592,737; and 6,709,568.

[0082]
The present invention provides a new measurement cycle that comprises five steps, including (1) initial stripping, (2) cyclic voltammetry (CV) scan cleaning, (3) equilibrium, (4) plating, and (5) postplating stripping, for further reducing the risk of crosscontamination between sample ECD solutions that are analyzed by sequentially by the same electrochemical analytical cell and further shortening the run time required for one measurement cycle.

[0083]
Each steps of such new measurement cycle are described in detail in the ensuring sections:

[0000]
Electrostripping:

[0084]
The new measurement cycle of the present invention starts with electrostripping of the measuring electrode, which is carried out by applying a positive potential (i.e., stripping potential) between the measuring electrode and the counter electrode that is sufficient for electrochemically removing the metal residue formed on the measuring electrode during a previous measurement cycle.

[0085]
When such measurement cycle is used for measuring sample ECD solutions that comprise copper sulfate, sulfuric acid, chloride, and optionally one or more organic additives, the stripping potential is preferably within a range of from about 0.5V to about 1V, and more preferably from about 0.6V to about 0.8V. The duration of the electrostripping is preferably from about 40 seconds to about 200 seconds and more preferably from about 60 seconds to about 120 seconds. Electrostripping at a stripping potential of less than 08V and for duration of at least twice of the plating duration (i.e., 2×) is particularly suitable for producing reliable and stable measurement results.

[0086]
An electrolytic cleaning solution containing sulfuric acid is preferably used for conducting the electrostripping of the measuring electrode, by immersing both the measuring and the counter electrodes in such cleaning solution. More preferably, the measurement chamber containing the measuring electrode and counter electrode is flushed with such electrolytic cleaning solution during the electrostripping. The flushing may be carried out through the entire time of the electrostripping, or for only a predetermined period of time (e.g., 10 seconds or 20 seconds). In such manner, at least a portion of the metal residue stripped off the measuring electrode is carried out of the measurement chamber by the electrolytic cleaning solution, thereby reducing the metal concentration in the measurement chamber and reducing the risk of metal redeposition onto the inner surfaces of the measurement chamber or counter electrode under the stripping potential.

[0000]
CV Scan Cleaning:

[0087]
The presence of surfaceactive organic materials, such as the suppressor, accelerator, and leveler in the sample ECD solution leads to formation of an organic surface residual layer on the surface of the measuring electrode, resulting in electrode passivation or a change in the electrode surface state, and causing significant measurement errors after such measuring electrode is used for an extended period of time. Maintenance of a clean, reproducible electrode surface therefore is of critical importance in making meaningful electroanalytical measurements.

[0088]
The present invention therefore provides a cyclic voltammetrybased (CV scan) cleaning step for removing the organic surface residue from the measuring electrode, as well as the residue copper plated on the surface of the measuring electrode. CV scan is particularly effective for in situ cleaning and depassivating the electrode, with significantly shortened system down time and reduced damages to the electrode surface.

[0089]
Specifically, a cyclic electropotential is applied between the measuring electrode and the counter electrode, while both electrodes are immersed in either a sample ECD solution or an electrolytic cleaning solution as described hereinabove. Effective cleaning can be achieved by a cyclic electropotential that oscillates between about −4V to about +4 v, more preferably from about −1V to about +1V, and most preferably from about −0.7V to about 0.25V. Within such cycling range, the cyclic electropotential oxidizes and/or reduces the organic surface residue and the residue copper absorbed on the measuring electrode, therefore depassivating the measuring electrode. Further, such cyclic electropotential also generates multiple hydrogen and oxygen microbubbles on the electrode surface within such cyclic range, therefore providing a vigorous surface process that functions to peel away any nonoxidizable or nonreducible solid or liquid residues on the electrode surface. CV scan results can also be used as an indicator of the cleanness of the surface of the measuring electrode. In the cathodic potential scan range, four absorption/desorption hydrogen peaks should be shown clearly if the measuring electrode surface is sufficiently clean.

[0090]
The scan rate (i.e., potential change rate) of the CV scan is preferably within the range of from about 0.1V/second to about 0.5V/second and more preferably from about 0.2V/second to about 0.4V/second.

[0091]
The CV scan duration is preferably at least 10 cycles, and more preferably at least 15 cycles, and most preferably at least 20 cycles.

[0092]
When the measurement cycle is used for measuring sample ECD solutions that comprise copper sulfate, sulfuric acid, chloride, and optionally one or more organic additives, an electrolytic cleaning solution containing sulfuric acid as described hereinabove is preferably used for conducting the CV scan cleaning step. More preferably, the measurement chamber containing the measuring electrode and counter electrode is flushed with such electrolytic cleaning solution during the CV scan cleaning, so as to carry the organic surface residue out of the measurement chamber and reduce crosscontamination thereby.

[0000]
Equilibrium:

[0093]
After the stripping and cleaning steps and before the actual plating, the measurement chamber is filled with a fresh sample ECD solution to be analyzed, and the measuring and counter electrodes are both immersed in such fresh sample ECD solution for a sufficient period of time until a steady state or an equilibrium state is reached.

[0094]
Such equilibrium state can be reached either by disconnecting the measuring electrode from the counter electrode to form an open circuit with no electrical current passing therethrough, or by maintaining a closed circuit while applying between the measuring and counter electrodes a predetermined electropotential that is less than the plating potential required. In a specific embodiment of the present application, a twostage equilibrium is achieved by applying a potential of from about −1V to about −0.1V during a first stage, and a potential of from about 0.1V to about 1V during a second stage, wherein the duration of the first stage is at least twice longer than the second stage. Preferably, during such first stage of the equilibrium, the sample ECD solution is continuously flushed through the measurement chamber.

[0000]
Plating:

[0095]
Metal electroplating in the present invention is preferable carried out at constant plating current, while the potential response of the sample ECD solution is concurrently monitored as an analytical signal for determining the organic additive, inorganic additive and/or byproduct concentrations in such sample solution.

[0096]
Constant plating current within a range of from about −1 mA/cm^{2 }to about −1000 mA/cm^{2}, preferably from about −10 mA/cm^{2 }to about −500 mA/cm^{2}, is sufficient for electrochemical metal deposition, and the plating duration is preferably from about 10 seconds to about 60 seconds, more preferably from 10 seconds to about 30 seconds, and most preferably from about 15 seconds to about 25 seconds.

[0097]
Preferably but not necessarily, the constant current plating is preceded by a potential pulse of from about −0.1V to about −1V, which lasts only from about 1 microsecond to about 2.5 seconds. Such potential pulse is particularly useful for optimizing metal nucleation on the electrode surface and stabilizing the potential signals during the subsequent current plating stage.

[0000]
PostPlating Stripping:

[0098]
The metal deposition layer formed on the measuring electrode during the plating step, if not timely removed, may alloy with the metal component of the measuring electrode, thereby deleteriously changing the surface state of the measuring electrode in an irreversible manner and causing significant measurement errors for future measurements.

[0099]
Since the time interval between two adjacent measurement cycles may vary significantly, it is important to ensure timely removal of such metal deposition layer and avoid formation of alloy between such metal deposition layer and the metal component of the measuring electrode.

[0100]
The present invention therefore provides postplating electrostripping immediately after the plating step, to remove at least a portion of the metal deposition layer before the commencement of the next measurement cycle. Therefore, prolonged time intervals between measurement cycles will no longer cause surface state changes of the measuring electrode or reduce the measurement accuracy.

[0101]
Such postplating electrostripping can be carried out by applying a positive potential (i.e., the stripping potential) of from about 0.1V to about 0.3V between the measuring electrode and the counter electrode for from about 20 seconds to about 60 seconds.

[0102]
An electrolytic cleaning solution containing sulfuric acid is preferably used for conducting the postplating electrostripping. More preferably, the measurement chamber containing the measuring electrode and counter electrode is flushed with such electrolytic cleaning solution, either throughout the postplating electrostripping step or for at least a sufficient period of time (e.g., 20 to 40 seconds).

[0103]
FIGS. 2A and 2B shows the potential waveforms for a two measurement cycle, according to two slightly different embodiments of the present invention.

[0104]
Specifically, FIG. 2A shows a measurement cycle that comprises (1) an initial electrostripping carried out in a sulfuric acid cleaning solution at a stripping potential of about 0.7V for about 80100 seconds, during which the sulfuric acid cleaning solution flushes the measurement chamber for about 10 seconds; (2) CV scan cleaning carried out in a sulfuric acid cleaning solution at a cyclic potential that oscillates between −0.7V to about 0.25V for about 20 cycles (i.e., n=20) with a scan rate of about 0.3V/second, throughout which the sulfuric acid cleaning solution continuously flushes the measurement chamber; (3) twostage equilibrium carried out in a fresh sample ECD solution with a close circuit between the measuring and counter electrodes, wherein a first potential of about −0.7V is applied for about 80 seconds with the sample ECD solution continuously flushing through the measurement chamber during a first stage, and a second potential of about 0.82V is applied for about 5 seconds in the sample ECD solution; (4) electroplating carried out in the sample ECD solution, by applying an initial potential pulse of about −0.17V for about 0.141 seconds and a subsequent constant plating current of about −940 mA/cm^{2 }for about 20 seconds, during which the potential responses of the sample ECD solution is continuously monitored; and (5) postplating electrostripping carried out in a sulfuric acid cleaning solution at a stripping potential of about 0.3V for about 40 seconds, throughout which the sulfuric acid continuously flushes the measurement chamber.

[0105]
FIG. 2B shows a measurement cycle similar to that illustrated in FIG. 4A, except that the equilibrium is reached in an open circuit without sample flushing.

[0106]
The entire runtime required for the measurement cycle of the present invention is not more than 20 minutes, and typically around 610 minutes, which significantly increases the measurement efficiency and enables true realtime ECD bath analysis. Further, such measurement cycle further reduces the risk of crosscontamination between different sample solutions analyzed by the same electrochemical analytical cell and increases the accuracy of the measurement results.

[0000]
Detection of Copper Thiolate Byproduct in Copper ECD Bath

[0107]
The present invention provides a method for analyzing copper ECD bath byproducts, such as copper thiolate, using the same analysis system used to quantify organic and inorganic additives. Accordingly, another aspect of the inventions relates to methods of analyzing copper ECD bath compositions comprising measuring ECD bath byproducts in addition to organic additives and inorganic additives, and systems for performing such analysis. One preferred embodiment of the invention uses a single analysis system and/or a single sample. Most preferably, a single sample of the bath composition is measured using a single analysis system.

[0108]
Recently, it has been concluded that copper (I) thiolate species are formed through the redox reaction of Cu^{+} with the accelerator additive bis(sodiumsulfopropyl) disulfide (SPS) (Vereecken, P. M., Binstead, R. A., Deligianni, H., Andricacos, P. C., IBM J. Res. & Dev., 49(1), 318 (2005)). It is well recognized in the ECD art that the byproduct copper thiolate may play a role in accelerating copper deposition during damascene plating (Healy, J. P., Pletcher, D., Goodenough, M., J. Electroanalyt. Chem., 338, 167177 (1992); Healy, J. P., Pletcher, D., Goodenough, M., J. Electroanalyt. Chem., 338, 179187 (1992); Kim, J. J., Kim, S.K., Kim, Y. S., J. Electroanalyt. Chem., 542, 6166 (2003).

[0109]
Given its role as an accelerator in the copper ECD bath, the copper thiolate byproduct is preferably monitored with the intent of controlling the overall concentration of said byproduct. For example, using a bleed and feed environment, when the concentration of copper thiolate becomes too great, some of the bulk ECD bath may be bled off and fresh chemistries introduced.

[0110]
We have unexpectedly discovered that copper thiolate may be monitored and quantified using the same analysis system used to quantify organic and inorganic additives.

[0111]
A copper ECD bath including copper sulfate, sulfuric acid, chloride ion, leveler (1.5 mL L^{−1}), suppressor (2 mL L^{−1}) and accelerator (6 mL L^{−1}) was prepared and an electrochemical concentration analysis using the fivestep measurement cycle described herein was performed at constant current. A Defect Analysis Reduction Tool (DART) plating transient was obtained, which provides information on the electrode interface as well as a reflection of what species are present in the bulk solution. The DART plating transient shown in FIG. 3 shows that when just 10% of the SPS accelerator converted into byproduct, and the change in potential of the ECD bath was quantifiable Clearly, the breakdown product copper thiolate is very easy to distinguish in a fresh ECD bath.

[0112]
Thereafter, aged baths were monitored to determine the effect of the copper thiolate byproduct on the DART plating transient. Referring to FIG. 4, it can be seen that aged ECD baths continued to accelerate through 4, 8 and 12 Amphr L^{−1}. Importantly, the shape of the transients in FIGS. 3 and 4 essentially mimic one another, which supports that notion that copper thiolate or similar species are the primary byproduct over time.

[0113]
FIG. 5 represents the measurement of copper thiolate byproduct in a bleed and feed environment, using both fresh chemistries as well as aged chemistries. The target ECD bath solution included 9 mL L^{−1 }accelerator, 2 mL L^{−1 }suppressor, 1.5 mL L^{−1 }leveler and zero copper thiolate byproduct. After aging for 4 Amphr L^{−1}, with no additional dose of accelerator, the concentration of accelerator decreased to 7.9 mL L^{−1}, while the percent byproduct was 25%. In contrast, a 4 Amphr L^{−1 }aged bath with a dose of 1.5 mL L^{−1 }accelerator, had a concentration of accelerator of 10.7 mL L^{−1 }and a percent byproduct of 12.6%. Importantly, it is possible to quantify the acceleration differences associated with aging (and hence copper thiolate production) and the addition of fresh accelerator chemistries.

[0114]
In conclusion, the present inventors have shown that the copper thiolate byproduct may be monitored and quantified using the same analysis system used to quantify organic and inorganic additives. Furthermore, the existence of the byproduct species may be monitored in aged ECD baths.

[0000]
Concentration Analysis Based on a Single Multiple Regression Model

[0115]
The present invention provides a method for simultaneously determining the concentrations of multiple organic additives, e.g., suppressor, accelerator, and leveler, multiple inorganic additives, e.g., copper sulfate, sulfuric acid, chloride ion, and/or byproducts (e.g., copper thiolate) thereof, in a sample ECD solution, based on a single multiple regression model that defines the electroplating potential of the sample solution as a function of multiple variables that represent both the compositional parameters, such as the additive concentrations, as well as noncompositional parameters associated with the measurement cycle.

[0116]
First, various noncompositional variables that may have potential impacts on the electroplating potential of the sample ECD solution are tested for their respective significance with respect to the electroplating potential. Specifically, electroplating potentials of one or more sample ECD solutions under varying values of the potential noncompositional variables are measured to establish a sample data set for analysis of variance tests, in which the estimated coefficient (i.e., parameter) of each noncompositional variable and the probability that such coefficient may equal zero are determined. The noncompositional variables having nonzero coefficients at confidence levels above a predetermined threshold (for example, not less than 95%, which means that the probability that the coefficients of such variables are not zero is equal to or more than 95%) are selected.

[0117]
By testing various noncompositional variables, nucleation potential, nucleation time, electroplating current, electroplating time, with or without CV scan cleaning, scan rate of the CV scan, types of cleaning solution used, size of the measuring electrode used, sample solution deaeration, and equilibrium time have been found to have impact on the electroplating potential. Particularly, the nucleation potential, the nucleation time, the electroplating current, the electroplating time, the CV scan duration, and the size of the measuring electrode influence have significant impact on the plating potential.

[0118]
A multiple regression model can therefore be established to express the electropotential responses of ECD solutions as a function of one or more abovedescribed noncompositional variables, the organic additives concentrations, the inorganic additives concentrations, the byproduct(s) concentration(s) and their corresponding coefficients.

[0119]
Preferably, one or more terms representing the interactions between the organic additive, inorganic additive and/or byproduct concentrations and the noncompositional variables are included in such multiple regression model. Quadratic terms and/or cubic terms can also be included.

[0120]
For illustration purposes while without limiting the broad scope of the present application, an exemplary multiple regression model is established as follows:
Y=β _{0}+β_{1} ×A+β _{2} ×B+β _{3} ×C+β _{4} ×D+β _{5} ×E+β _{6} ×Acc+β _{7} ×Lev+β _{8} ×Supp+β _{9} ×Cop+β _{10} ×Sul+β _{11} ×Chl+β _{12} ×Byp+β _{13} ×A ^{2}+β_{14} ×AC+β _{15} ×AE+β _{16} ×A×Acc+β _{17} ×B ^{2}+β_{18} ×BD+β _{19} ×C ^{2}+β_{20} ×CE+β _{21} ×C×Lev+β _{22} ×D ^{2}+β_{23} ×E ^{2}β_{24} ×AE×Lev+β _{25} ×AE×Sup
wherein Y is the electroplating potential measured for a sample ECD solution; A is the nucleation potential (V); B is the nucleation time (second); C is the electroplating current (mA/cm^{2}); D is the CV scan duration (second); E is the size of the measuring electrode (μm); Acc is the concentration of the accelerator in the ECD solution; Lev is the concentration of the leveler; Sup is the concentration of the suppressor; Cop is the concentration of the copper sulfate in the ECD solution; Sul is the concentration of the sulfuric acid in the ECD solution; Chl is the concentration of the chloride ion in the ECD solution; Byp is the concentration of the byproduct in the ECD solution; AC, AE, BD, and CE represent twoway interactions between the noncompositional variables ABCDE; A×Acc and C×Lev represent twoway interactions between a noncompositional variable and an additive concentration; AE×Lev and AE×Sup represent three way interactions between two noncompositional variables and an additive concentration; A^{2}, B^{2}, C^{2}, D^{2}, and E^{2 }are the quadratic terms of the noncompositional variables ABCDE; β_{0 }is the intercept; and β_{1}β_{25 }are the coefficients for all the terms of the multiple regression model. Other twoway and threeway interactions (with coefficients), as readily determined by one skilled in the art, may be incorporated into the exemplary regression model. In addition, more or less additives and/or byproducts may be incorporated into the model. Thus, more or less coefficients, i.e., β, may be necessary.

[0121]
The intercept β_{0 }and the coefficients β_{1}β_{25 }of the above multiple regression model can be readily determined by running multiple calibration measurements, each of which measures the electroplating potential of a calibration solution containing copper sulfate, sulfuric acid, chloride ion, the suppressor, the accelerator, the leveler, and/or the byproduct(s) at known concentrations at predetermined measurement settings, i.e., with predetermined values of the noncompositional variables A, B, C, D, and E.

[0122]
Subsequently, N experimental runs are designed for measuring the sample ECD solution containing the organic additives, inorganic additives and/or byproduct(s) at unknown concentrations. Each experimental run is characterized by a unique, predetermined measurement setting, i.e., with predetermined values of the noncompositional variables A, B, C, D, and E. As defined herein, “N” corresponds to the total number of species being quantified, wherein the species may include organic additives, inorganic additives, and/or byproducts thereof. For example, as incorporated into the multiple regression model hereinabove, seven species may be quantified simultaneously, including copper sulfate, sulfuric acid, chloride ion, leveler, accelerator, suppressor, and copper thiolate (byproduct). It should be appreciated that more or less species are simultaneously quantifiable.

[0123]
The electroplating potentials of the sample ECD solution are then measured for these N experimental runs, to establish N equations, as follows:
Y _{N}=β_{0}+β_{1} ×A _{N}+β_{2} ×B _{N}+β_{3} ×C _{N}+β_{4} ×D _{N}+β_{5} ×E _{N}+β_{6} ×Acc+β _{7} ×Lev+β _{8} ×Sup+β _{9} ×Cop+β _{10} ×Sul+β _{11} ×Chl+β _{12} ×Byp+β _{13} ×A _{N} ^{2}+β_{14} ×A _{N} C _{N}+β_{15} ×A _{N} E _{N}+β_{16} ×A _{N} ×Acc+β _{17} ×B _{N} ^{2}+β_{18} ×B _{N} D _{N}+β_{19} ×C _{N} ^{2}+β_{20} ×C _{N} E _{N}+β_{21} ×C _{N} ×Lev+β _{22} ×D _{N} ^{2}+β_{23} ×E _{N} ^{2}+β_{24} ×A _{N} E _{N} ×Lev+β _{25} ×A _{N} E _{N} ×Sup
wherein Y_{N }corresponds to the electroplating potentials of the sample ECD solution as measured during the N experimental runs, wherein A_{N}E_{N }are the respective predetermined values of the noncompositional variables ABCDE during the N experimental runs.

[0124]
Therefore, N equations contain only N unknown values. Such unknown concentration values can thus be readily determined by solving N equations.

[0125]
The N experimental runs can be carried out sequentially in the same electrochemical analytical cell. Alternatively, they can be carried out simultaneously in N electrochemical analytical cells, each of which operates according to a unique, predetermined measurement protocol with predetermined values for the noncompositional variables ABCDE.

[0126]
The number and type of noncompositional variables to be included into the multiple regression model can be readily modified by a person ordinarily skilled in the art. The essence of this invention is to use N experimental runs to provide N equations with only N unknown values corresponding to the additive and/or byproduct concentrations, which are readily solvable for concentration determination. Therefore, as few as one noncompositional variable and as many as infinite number of variables can be included into the model. When more variables are included, the model is more sophisticated and provides more accurate analytical results.

[0000]
Concentration Analysis Using a Single Experimental Run

[0127]
The present invention provide another method for simultaneously determining concentrations of organic additive (e.g., accelerator, leveler, and suppressor), inorganic additive (e.g., copper sulfate, sulfuric acid, chloride ion) and/or byproduct(s) (e.g., copper thiolate) in a sample ECD solution within a single experimental run, wherein time is used as a variable for constructing three or more multiple regression models, and wherein interactions between the additives and/or byproduct(s) are accounted for.

[0128]
This method, unlike the method described in the previous section, does not rely on usage of any noncompositional variables associated with the experimental settings. Instead, it considers only compositional terms associated with the additive and/or byproduct(s) concentrations and the interactions therebetween.

[0129]
The concentrations of copper sulfate, sulfuric acid, chloride ion, accelerator, leveler, suppressor, and/or byproduct(s) are the basic and necessary compositional variables to be included. Additional compositional terms representing interactions between the additives, byproduct(s) or quadratic/cubic terms may also be included. For example, additional compositional terms have potential impacts on the electroplating potential of the sample ECD solution can be tested for their respective significance with respect to the electroplating potential. Specifically, electroplating potentials of one or more sample ECD solutions under varying values of such additional compositional terms are measured to establish a sample data set for analysis of variance tests, in which the estimated coefficient (i.e., parameter) of each additional compositional term and the probability that such coefficient may equal zero are determined. The additional compositional terms having nonzero coefficients at confidence levels above a predetermined threshold (for example, not less than 95%, which means that the probability that the coefficients of such variables are not zero is equal to or more than 95%) can be selected for inclusion.

[0130]
For illustrative purposes, the following compositional terms can be selected, which include:


A  Accelerator concentration 
B  Leveler concentration 
C  Suppressor concentration 
D  Copper sulfate concentration 
E  Sulfuric acid concentration 
F  Chloride ion concentration 
G  Byproduct concentration 
AB  Interaction between accelerator and leveler 
AC  Interaction between accelerator and suppressor 
ABC  Interaction between accelerator, leveler, and suppressor 
AA  Quadratic term for accelerator 
BB  Quadratic term for leveler 
CC  Quadratic term for suppressor 
DD  Quadratic term for copper sulfate 
EE  Quadratic term for sulfuric acid 
FF  Quadratic term for chloride ion 
GG  Quadratic term for byproduct 


[0131]
Other compositional interactions are readily determined by one skilled in the art and may be incorporated into the multiple regression models herein. In addition, more or less additives and/or byproducts may be incorporated into said models.

[0132]
The selected compositional terms can then be used to establish m multiple regression models that corresponds to m time points (t_{1}, t_{2}, . . . t_{m}) during the electrochemical metal deposition process, wherein each model expresses electropotential responses of the ECD solutions as a function of the selected compositional terms and their corresponding coefficients, wherein m≧3.

[0133]
For example, three multiple regression models that correspond to three time points (t_{1}, t_{2}, and t_{3}) can be established, as follows:
Y _{1}=β_{A} ^{1} ×A+β _{B} ^{1} ×B+β _{C} ^{1} ×C+β _{D} ^{1} ×D+β _{E} ^{1} ×E+β _{F} ^{1} ×F+β _{G} ^{1} ×G+β _{AB} ^{1} ×AB+β _{AC} ^{1} ×AC+β _{ABC} ^{1} ×ABC+β _{AA} ^{1} ×AA+β _{BB} ^{1} ×BB+β _{CC} ^{1} ×CC+β _{DD} ^{1} ×DD+β _{EE} ^{1} ×EE+β _{FF} ^{1} ×FF+β _{GG} ^{1} ×GG
Y _{2}=β_{A} ^{2} ×A+β _{B} ^{2} ×B+β _{C} ^{2} ×C+β _{D} ^{2} ×D+β _{E} ^{2} ×E+β _{F} ^{2} ×F+β _{G} ^{2} ×G+β _{AB} ^{2} ×AB+β _{AC} ^{2} ×AC+β _{ABC} ^{2} ×ABC+β _{AA} ^{2} ×AA+β _{BB} ^{2} ×BB+β _{CC} ^{2} ×CC+β _{DD} ^{2} ×DD+β _{EE} ^{2} ×EE+β _{FF} ^{2} ×FF+β _{GG} ^{2} ×GG
Y _{3}=β_{A} ^{3} ×A+β _{B} ^{3} ×B+β _{C} ^{3} ×C+β _{D} ^{3} ×D+β _{E} ^{3} ×E+β _{F} ^{3} ×F+β _{G} ^{3} ×G+β _{AB} ^{3} ×AB+β _{AC} ^{3} ×AC+β _{ABC} ^{3} ×ABC+β _{AA} ^{3} ×AA+β _{BB} ^{3} ×BB+β _{CC} ^{3} ×CC+β _{DD} ^{3} ×DD+β _{EE} ^{3} ×EE+β _{FF} ^{3} ×FF+β _{GG} ^{3} ×GG
wherein Y_{1}, Y_{2}, and Y_{3 }are the electroplating potentials measured at respective time points t_{1}, t_{2}, and t_{3}; β_{A} ^{1}β_{GG} ^{1 }are the coefficients for the selected compositional terms AGG at time point t_{1}; β_{A} ^{2}β_{GG} ^{2 }are the coefficients for the selected compositional terms AGG at time point t_{2}; β_{A} ^{3}β_{GG} ^{3 }are the coefficients for the selected compositional terms AGG at time point t_{3}.

[0134]
The values of the coefficients β_{A} ^{1}β_{GG} ^{1}, β_{A} ^{2}β_{GG} ^{2}, and β_{A} ^{3}β_{GG} ^{3 }can be readily determined by running multiple calibration measurements of various calibration solutions having unique, known organic additive, inorganic additive, and/or byproduct concentrations, and during each calibration measurement, the electroplating potential is measured three times, at each of the time points t_{1}, t_{2}, and t_{3}.

[0135]
Subsequently, a single experimental run is carried out for measurement of the sample ECD solution that contains the additives and/or byproduct(s) at unknown concentrations. Electroplating potentials of such sample ECD solution at the three time points t_{1}, t_{2}, and t_{3 }are sequentially measured during the experimental run and recorded as Y_{1}, Y_{2}, and Y_{3}.

[0136]
Based on the three multiple regression models established hereinabove, the coefficient values determined via calibration measurements, and the electroplating potentials measured during the experimental run, one can readily calculating the organic additive concentrations A, B, and C, the inorganic concentrations D, E, and F, and the byproduct concentration G.

[0137]
A quick and direct method for calculating the additive and/or byproduct(s) concentrations relies on matrix inversion. Specifically, three matrices X, β, and Y are constructed as follows:
$X=\left(\begin{array}{c}A\\ B\\ C\\ D\\ E\\ F\\ G\\ \mathrm{AB}\\ A\text{\hspace{1em}}C\\ \mathrm{ABC}\\ \mathrm{AA}\\ \mathrm{BB}\\ \mathrm{CC}\\ \mathrm{DD}\\ \mathrm{EE}\\ \mathrm{FF}\\ \mathrm{GG}\end{array}\right)$
$B=\left(\begin{array}{ccccccccccccccccc}{\beta}_{A}^{1}& {\beta}_{B}^{1}& {\beta}_{C}^{1}& {\beta}_{D}^{1}& {\beta}_{E}^{1}& {\beta}_{F}^{1}& {\beta}_{G}^{1}& {\beta}_{\mathrm{AB}}^{1}& {\beta}_{A\text{\hspace{1em}}C}^{1}& {\beta}_{\mathrm{ABC}}^{1}& {\beta}_{\mathrm{AA}}^{1}& {\beta}_{\mathrm{BB}}^{1}& {\beta}_{\mathrm{CC}}^{1}& {\beta}_{\mathrm{DD}}^{1}& {\beta}_{\mathrm{EE}}^{1}& {\beta}_{\mathrm{FF}}^{1}& {\beta}_{\mathrm{GG}}^{1}\\ {\beta}_{A}^{2}& {\beta}_{B}^{2}& {\beta}_{C}^{2}& {\beta}_{D}^{2}& {\beta}_{E}^{2}& {\beta}_{F}^{2}& {\beta}_{G}^{2}& {\beta}_{\mathrm{AB}}^{2}& {\beta}_{A\text{\hspace{1em}}C}^{2}& {\beta}_{\mathrm{ABC}}^{2}& {\beta}_{\mathrm{AA}}^{2}& {\beta}_{\mathrm{BB}}^{2}& {\beta}_{\mathrm{CC}}^{2}& {\beta}_{\mathrm{DD}}^{2}& {\beta}_{\mathrm{EE}}^{2}& {\beta}_{\mathrm{FF}}^{2}& {\beta}_{\mathrm{GG}}^{2}\\ {\beta}_{A}^{3}& {\beta}_{B}^{3}& {\beta}_{C}^{3}& {\beta}_{D}^{3}& {\beta}_{E}^{3}& {\beta}_{F}^{3}& {\beta}_{G}^{3}& {\beta}_{\mathrm{AB}}^{3}& {\beta}_{A\text{\hspace{1em}}C}^{3}& {\beta}_{\mathrm{ABC}}^{3}& {\beta}_{\mathrm{AA}}^{3}& {\beta}_{\mathrm{BB}}^{3}& {\beta}_{\mathrm{CC}}^{3}& {\beta}_{\mathrm{DD}}^{3}& {\beta}_{\mathrm{EE}}^{3}& {\beta}_{\mathrm{FF}}^{3}& {\beta}_{\mathrm{GG}}^{3}\end{array}\right)$
$Y=\left(\begin{array}{c}{Y}_{1}\\ {Y}_{2}\\ {Y}_{3}\end{array}\right)$

[0138]
The three multiple regression models as described herein above can be represented by a simple matrixbased model that defines Y=βX, wherein X is a compositional matrix containing the selected compositional terms, wherein β is a coefficient matrix containing the coefficients determined via calibration measurements, and Y is a response matrix containing the electropotential responses measured via experimental run.

[0139]
Since both matrices β and Y contain known elements (i.e., β_{A} ^{1}β_{CC} ^{1}, β_{A} ^{2}β_{CC} ^{2}, β_{A} ^{3}β_{CC} ^{3}, and Y_{1}Y_{2}), they can be used to determined the unknown elements (i.e., A, B, C, . . . GG) contained in matrix X.

[0140]
From βX=Y, the following can be obtained:
(β′β)X=Yβ′
(β′β)^{−1}(β′β)X=Yβ′(β′β)^{−1 }
wherein β′ is the transpose of β, and wherein (β′β)^{−1 }is the inverse of β′β.

[0141]
Since (β′β)^{−1}(β′β) equals the identity matrix I, and since the product of identity matrix I with any matrix A will still be A, we can derive X as:
X=Yβ′(β′β)^{−1 }

[0142]
When β is known, its transpose, β′, and the inverse of their product (β′β)^{−1 }can be readily calculated. Therefore, the concentrations of the organic additives (A, B, and C), inorganic additives (D, E, and F) and/or byproduct(s) (G) can be directly determined as the elements of the matrix X.

[0143]
The above example uses seventeen compositional terms and three multiple regression models for simplicity. In practice, the number of compositional terms can be more or less than seventeen (but not less than three), while more than three multiple regression models can be used.

[0144]
In general, n compositional terms can be selected to establish m multiple regression models (n≧3, and m≧3), as follows:
Y _{1}=β_{11} ×X _{1}+β_{12} ×X _{2}+β_{13} ×X _{3}+ . . . β_{1n} ×X _{n }
Y _{2}=β_{21} ×X _{1}+β_{22} ×X _{2}+β_{23} ×X _{3}+ . . . +β_{2n} ×X _{n }
Y _{3}=β_{31} ×X _{1}+β_{32} ×X _{2}+β_{33} ×X _{3}+ . . . +β_{3n} ×X _{n }
Y _{m}=β_{m1} ×X _{1}+β_{m2} ×X _{2}+β_{m3} ×X _{3}+ . . . +β_{mn} ×X _{n }
wherein X_{1}, X_{2}, X_{3}, . . . , X_{n }are the n selected compositional terms; Y_{1}, Y_{2}, Y_{3}, . . . , Y_{m }are the electroplating potentials measured at m time points t_{1}, t_{2}, t_{3}, . . . , t_{m}; β_{11}β_{1n }are the coefficients for the selected compositional terms X_{1}X_{n }at time point t_{1}; β_{21}β_{2n }are the coefficients for the selected compositional terms X_{1}X_{n }at time point t_{2}; β_{31}β_{3n }are the coefficients for the selected compositional terms X_{1}X_{n }at time point t_{3}; . . . ; and β_{m1}β_{mn }are the coefficients for the selected compositional terms X_{1}X_{n }at time point t_{m}.

[0145]
The three matrices X, β, and Y can then be constructed as follows:
$X=\left(\begin{array}{c}{X}_{1}\\ {X}_{2}\\ {X}_{3}\\ \dots \\ {X}_{n}\end{array}\right)$
$B=\left(\begin{array}{ccccc}{\beta}_{11}& {\beta}_{12}& {\beta}_{13}& \dots & {\beta}_{1n}\\ {\beta}_{21}& {\beta}_{22}& {\beta}_{23}& \dots & {\beta}_{2n}\\ {\beta}_{31}& {\beta}_{32}& {\beta}_{33}& \dots & {\beta}_{3n}\\ \dots & \dots & \dots & \dots & \dots \\ {\beta}_{m\text{\hspace{1em}}1}& {\beta}_{m\text{\hspace{1em}}2}& {\beta}_{m\text{\hspace{1em}}3}& \dots & {\beta}_{m\text{\hspace{1em}}n}\end{array}\right)$
$Y=\left(\begin{array}{c}{Y}_{1}\\ {Y}_{2}\\ {Y}_{3}\\ \dots \\ {Y}_{m}\end{array}\right)$

[0146]
As shown, the generalized compositional matrix X is a n×1 matrix containing the n compositional terms; the generalized coefficient matrix β is a m×n matrix; and the generalized response matrix Y is a m×1 matrix.

[0147]
Various time points during the electrochemical deposition process can be selected for constructing the multiple regression models. For example, for constructing the three multiple regression models as illustrated hereinabove, the time points at 5 seconds, 10 seconds, and 20 seconds can be used, while additional time points at 0.2 second, 0.25 second, 0.5 second, and 1 second can also be used.

[0148]
While the ensuing description of the invention contains reference to illustrative embodiments and features, it will be recognized that the methodology and apparatus of the invention are not thus limited, but rather generally extend to and encompass the determination of analytes in fluid media. For example, although the present description is directed primarily to copper ECD deposition analysis, the invention is readily applicable to other ECD processes, including deposition of silver, gold, iridium, palladium, tantalum, titanium, chromium, cobalt, tungsten, etc., as well as deposition of alloys and deposition of amalgams such as solder. Examples of additional applications of the invention other than ECD plating of semiconductor device structures include analysis of reagents in reaction media for production of therapeutic agents such as pharmaceutical products, and biotechnology applications involving the concentrations of specific analytes in human blood or plasma. It will therefore be appreciated that the invention is of broad application, and that the ECD system and method described hereafter is but one of a myriad of potential uses for which the invention may be employed.