U.S. patent application number 11/670507 was filed with the patent office on 2007-11-15 for simultaneous inorganic, organic and byproduct analysis in electrochemical deposition solutions.
This patent application is currently assigned to ADVANCED TECHNOLOGY MATERIALS, INC.. Invention is credited to Jianwen Han, Mackenzie King, Steven M. Lurcott, Glenn M. Tom.
Application Number | 20070261963 11/670507 |
Document ID | / |
Family ID | 38684088 |
Filed Date | 2007-11-15 |
United States Patent
Application |
20070261963 |
Kind Code |
A1 |
Han; Jianwen ; et
al. |
November 15, 2007 |
SIMULTANEOUS INORGANIC, ORGANIC AND BYPRODUCT ANALYSIS IN
ELECTROCHEMICAL DEPOSITION SOLUTIONS
Abstract
Real-time analysis of electrochemical deposition (ECD) metal
plating solutions is described, for the purpose of reducing plating
defects and achieving high quality metal deposition. Improved
plating protocols are utilized for increasing potential signal
strength and reducing the time required for each measurement cycle.
New methods and algorithms for simultaneously determining
concentrations of organic additives, inorganic additives, and/or
byproducts in a sample ECD solution are described. In one aspect, a
method is provided for simultaneously determining concentrations of
all organic additives, inorganic additives, and/or byproducts
within a single experimental run by using a single analytical cell,
while interactions between such additives are properly accounted
for.
Inventors: |
Han; Jianwen; (Danbury,
CT) ; King; Mackenzie; (Southbury, CT) ; Tom;
Glenn M.; (Bloomington, MN) ; Lurcott; Steven M.;
(Sherman, CT) |
Correspondence
Address: |
INTELLECTUAL PROPERTY / TECHNOLOGY LAW
PO BOX 14329
RESEARCH TRIANGLE PARK
NC
27709
US
|
Assignee: |
ADVANCED TECHNOLOGY MATERIALS,
INC.
7 Commerce Drive
Danbury
CT
06810-4169
|
Family ID: |
38684088 |
Appl. No.: |
11/670507 |
Filed: |
February 2, 2007 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
60764614 |
Feb 2, 2006 |
|
|
|
Current U.S.
Class: |
205/81 |
Current CPC
Class: |
C25D 21/14 20130101;
G01N 27/42 20130101 |
Class at
Publication: |
205/081 |
International
Class: |
C25D 21/00 20060101
C25D021/00 |
Claims
1. 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 non-compositional 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 non-compositional 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).
2. The method of claim 1, wherein said one or more
non-compositional variables are identified by conducting analysis
of variance tests on all non-compositional variables having
potential impact on electropotential responses of electrochemical
deposition solutions and selecting those variables having non-zero
coefficients at confidence levels that are not less than 95%.
3. The method of claim 1, wherein said one or more
non-compositional variables are selected from the group consisting
of (1) nucleation potential, (2) nucleation time, (3)
electroplating current, (4) electroplating time, (5) scan rate of
the cyclic voltammetry during pre-plating cleaning process, and (6)
size of the measuring electrode used for conducting the
electrochemical metal deposition.
4. The method of claim 1, wherein said multiple regression model
includes terms that account for interactions (1) between said
non-compositional variables, (2) between the organic additive
concentrations, (3) between the inorganic additives, (4) between
the byproduct(s) and/or (5) between one or more non-compositional
variables and one or more organic additive, inorganic additive,
and/or byproduct concentrations.
5. The method of claim 1, wherein in step (e), said N experimental
runs are conducted in N different electrochemical analytical cells,
wherein each cell performs electropotential measurements on the
sample electrochemical deposition solution according to a unique,
predetermined plating protocol.
6. The method of claim 5, wherein each plating protocol differs
from the other two by at least one factor selected from the group
consisting of (1) nucleation potential, (2) nucleation time, (3)
electroplating current, (4) electroplating time, (5) scan rate of
the cyclic voltammetry during pre-plating cleaning process, and (6)
size of the measuring electrode used for conducting the
electrochemical metal deposition.
7. The method of claim 1, wherein N is in a range from about 3 to
about 10.
8. The method of claim 1, wherein N is 7.
9. The method of claim 1, wherein the byproduct comprises copper
(I) thiolate.
10. 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.gtoreq.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.gtoreq.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.
11. The method of claim 10, wherein in step (f), the n selected
compositional terms are determined by: (i) establishing three
matrices X, .beta., and Y to represent the m multiple regression
models as Y=.beta.X, wherein X is a n.times.1 compositional matrix
containing the n compositional terms, wherein .beta. is a m.times.n
coefficient matrix containing the coefficients determined in step
(d), and Y is a m.times.1 response matrix containing the
electropotential responses measured in step (e); and (ii)
determining the compositional matrix X as:
X=(.beta.'.beta.).sup.-1.beta.'Y wherein .beta.' is the transpose
of .beta., and wherein (.beta.'.beta.).sup.-1 is the inverse of
.beta.'.beta..
12. The method of claim 10, wherein said compositional terms are
selected by conducting analysis of variance tests on all linear,
quadratic, and cubic terms related to the copper sulfate, sulfuric
acid, chloride ion, suppressor, accelerator, leveler, byproduct(s)
concentrations and interactions therebetween regarding their
potential impact on electropotential responses of electrochemical
deposition solutions, and selecting those terms having non-zero
coefficients at confidence levels that are not less than 95%.
13. The method of claim 10, wherein 3 multiple regression models
corresponding to 3 time points during the electrochemical metal
deposition process are established.
14. The method of claim 13, wherein said three time points are
selected from the group consisting of 0.2 second, 0.25 second, 0.5
second, 1 second, 5 seconds, 10 seconds, and seconds, as measured
from the initiation of the electrochemical metal deposition
process.
15. The method of claim 10, wherein the byproduct comprises copper
(I) thiolate.
16. A method for simultaneously determining concentrations of
inorganic additives, suppressor, accelerator, leveler, and/or
byproduct(s) thereof in a sample electrochemical deposition
solution, comprising the steps of: (a) identifying one or more
non-compositional 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
non-compositional 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 inorganic
additives, suppressor, accelerator, leveler, and/or byproduct(s)
thereof in the sample electrochemical deposition solution; and (g)
calculating said inorganic additives, suppressor, accelerator,
leveler, and/or byproduct concentrations in the sample solution by
solving the N equations provided in step (f).
17. The method of claim 16, wherein the inorganic additives
comprise a copper salt.
18. The method of claim 16, wherein the inorganic additives
comprise copper sulfate.
19. The method of claim 16, wherein the inorganic additives
comprise sulfuric acid.
20. The method of claim 16, wherein the inorganic additives
comprise chloride ion.
Description
CROSS-REFERENCE 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 real-time 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: [0007] (1) more sample must
be used for two or three separate analyses; [0008] (2) multiple
analyzers equates to a larger expense upfront, larger maintenance
costs and a larger overall footprint; [0009] (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 real-time
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: [0019] (a) contacting a working electrode
and a counter electrode with the sample electrochemical deposition
solution; [0020] (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; [0021] (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;
[0022] (d) monitoring potential response of the sample
electrochemical deposition solution under the constant plating
current; and [0023] (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: [0026] (a)
electrostripping the measuring electrode to remove metal residue
formed thereon during a previous measurement cycle; [0027] (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; [0028] (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; [0029] (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 [0030]
(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: [0037] (a)
identifying one or more non-compositional variables that affect
electropotential responses of electrochemical deposition solutions
during electrochemical metal deposition; [0038] (b) establishing a
multiple regression model that expresses the electropotential
responses of electrochemical deposition solutions as a function of
(1) said one or more non-compositional 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; [0039] (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; [0040] (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 [0041] (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; [0042] (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 [0043] (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
non-composition variables that have significant impact on the
electropotential responses of the electrochemical deposition
solutions. Specifically, a preliminary multiple regression model
including terms for all non-compositional 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 non-zero 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) non-composition 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
pre-plating 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 non-compositional 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 non-compositional variables and/or the
additive (and/or byproduct) concentrations.
[0047] Once all the coefficients for the non-compositional
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
non-compositional 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 non-compositional
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: [0050]
(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.gtoreq.3; [0051] (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.gtoreq.3; [0052] (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; [0053] (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);
[0054] (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 [0055] (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 [0056] (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, .beta., and Y are constructed for
representing the m multiple regression models as Y=.beta.X, wherein
X is a n.times.1 compositional matrix containing the n
compositional terms, wherein .beta. is a m.times.n coefficient
matrix containing the coefficients determined in step (d), and Y is
a m.times.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=(.beta.'.beta.).sup.-1.beta.'Y, wherein .beta.' is the transpose
of .beta., and wherein (.beta.'.beta.).sup.-1 is the inverse of
.beta.'.beta..
[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.
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: [0069] (a) stripping,
in which the copper layer previously deposited is removed; [0070]
(b) cleaning, in which the measuring electrode surface is
thoroughly cleaned electrochemically or chemically using an acid
bath; [0071] (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 [0072] (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 high-precision
control that is desired from the perspective of high-volume
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.sup.2 to about -1000 mA/cm.sup.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.sup.2 for about 100 seconds. TABLE-US-00001
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 #1-8, as measured under a 0.1 second current
pulse of about -200 mA/cm.sup.2, followed by constant current
plating at -100 mA/cm.sup.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 PCGA-based
concentration analysis.
Electrochemical Concentration Analysis Using a Five-Step
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) post-plating stripping, for further reducing the risk of
cross-contamination 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:
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.times.) 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 re-deposition onto the inner surfaces of the measurement
chamber or counter electrode under the stripping potential.
CV Scan Cleaning:
[0087] The presence of surface-active 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
voltammetry-based (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 micro-bubbles on the
electrode surface within such cyclic range, therefore providing a
vigorous surface process that functions to peel away any
non-oxidizable or non-reducible 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
cross-contamination thereby.
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 two-stage
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.
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.sup.2 to about -1000 mA/cm.sup.2, preferably from about -10
mA/cm.sup.2 to about -500 mA/cm.sup.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.
Post-Plating 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 post-plating
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 post-plating 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 post-plating
electrostripping. More preferably, the measurement chamber
containing the measuring electrode and counter electrode is flushed
with such electrolytic cleaning solution, either throughout the
post-plating 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 80-100 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) two-stage
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.sup.2 for about 20 seconds, during which the
potential responses of the sample ECD solution is continuously
monitored; and (5) post-plating 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
6-10 minutes, which significantly increases the measurement
efficiency and enables true real-time ECD bath analysis. Further,
such measurement cycle further reduces the risk of
cross-contamination between different sample solutions analyzed by
the same electrochemical analytical cell and increases the accuracy
of the measurement results.
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.sup.+ 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), 3-18 (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, 167-177 (1992); Healy, J. P., Pletcher,
D., Goodenough, M., J. Electroanalyt. Chem., 338, 179-187 (1992);
Kim, J. J., Kim, S.-K., Kim, Y. S., J. Electroanalyt. Chem., 542,
61-66 (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.sup.-1), suppressor (2 mL L.sup.-1)
and accelerator (6 mL L.sup.-1) was prepared and an electrochemical
concentration analysis using the five-step 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 Amp-hr L.sup.-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.sup.-1 accelerator, 2 mL L.sup.-1
suppressor, 1.5 mL L.sup.-1 leveler and zero copper thiolate
byproduct. After aging for 4 Amp-hr L.sup.-1, with no additional
dose of accelerator, the concentration of accelerator decreased to
7.9 mL L.sup.-1, while the percent byproduct was 25%. In contrast,
a 4 Amp-hr L.sup.-1 aged bath with a dose of 1.5 mL L.sup.-1
accelerator, had a concentration of accelerator of 10.7 mL L.sup.-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.
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
non-compositional parameters associated with the measurement
cycle.
[0116] First, various non-compositional 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 non-compositional variables are measured to
establish a sample data set for analysis of variance tests, in
which the estimated coefficient (i.e., parameter) of each
non-compositional variable and the probability that such
coefficient may equal zero are determined. The non-compositional
variables having non-zero 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 non-compositional 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 de-aeration, 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 above-described non-compositional
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 non-compositional 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=.beta..sub.0+.beta..sub.1.times.A+.beta..sub.2.times.B+.beta..sub.3.tim-
es.C+.beta..sub.4.times.D+.beta..sub.5.times.E+.beta..sub.6.times.Acc+.bet-
a..sub.7.times.Lev+.beta..sub.8.times.Supp+.beta..sub.9.times.Cop+.beta..s-
ub.10.times.Sul+.beta..sub.11.times.Chl+.beta..sub.12.times.Byp+.beta..sub-
.13.times.A.sup.2+.beta..sub.14.times.AC+.beta..sub.15.times.AE+.beta..sub-
.16.times.A.times.Acc+.beta..sub.17.times.B.sup.2+.beta..sub.18.times.BD+.-
beta..sub.19.times.C.sup.2+.beta..sub.20.times.CE+.beta..sub.21.times.C.ti-
mes.Lev+.beta..sub.22.times.D.sup.2+.beta..sub.23.times.E.sup.2.beta..sub.-
24.times.AE.times.Lev+.beta..sub.25.times.AE.times.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.sup.2); D is the CV scan
duration (second); E is the size of the measuring electrode
(.mu.m); 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 two-way
interactions between the non-compositional variables ABCDE;
A.times.Acc and C.times.Lev represent two-way interactions between
a non-compositional variable and an additive concentration;
AE.times.Lev and AE.times.Sup represent three way interactions
between two non-compositional variables and an additive
concentration; A.sup.2, B.sup.2, C.sup.2, D.sup.2, and E.sup.2 are
the quadratic terms of the non-compositional variables ABCDE;
.beta..sub.0 is the intercept; and .beta..sub.1-.beta..sub.25 are
the coefficients for all the terms of the multiple regression
model. Other two-way and three-way 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., .beta., may be
necessary.
[0121] The intercept .beta..sub.0 and the coefficients
.beta..sub.1-.beta..sub.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
non-compositional 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
non-compositional 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.sub.N=.beta..sub.0+.beta..sub.1.times.A.sub.N+.beta..sub.2.ti-
mes.B.sub.N+.beta..sub.3.times.C.sub.N+.beta..sub.4.times.D.sub.N+.beta..s-
ub.5.times.E.sub.N+.beta..sub.6.times.Acc+.beta..sub.7.times.Lev+.beta..su-
b.8.times.Sup+.beta..sub.9.times.Cop+.beta..sub.10.times.Sul+.beta..sub.11-
.times.Chl+.beta..sub.12.times.Byp+.beta..sub.13.times.A.sub.N.sup.2+.beta-
..sub.14.times.A.sub.NC.sub.N+.beta..sub.15.times.A.sub.NE.sub.N+.beta..su-
b.16.times.A.sub.N.times.Acc+.beta..sub.17.times.B.sub.N.sup.2+.beta..sub.-
18.times.B.sub.ND.sub.N+.beta..sub.19.times.C.sub.N.sup.2+.beta..sub.20.ti-
mes.C.sub.NE.sub.N+.beta..sub.21.times.C.sub.N.times.Lev+.beta..sub.22.tim-
es.D.sub.N.sup.2+.beta..sub.23.times.E.sub.N.sup.2+.beta..sub.24.times.A.s-
ub.NE.sub.N.times.Lev+.beta..sub.25.times.A.sub.NE.sub.N.times.Sup
wherein Y.sub.N corresponds to the electroplating potentials of the
sample ECD solution as measured during the N experimental runs,
wherein A.sub.N-E.sub.N are the respective predetermined values of
the non-compositional 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
non-compositional variables ABCDE.
[0126] The number and type of non-compositional 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
non-compositional 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.
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 non-compositional 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 non-zero 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: TABLE-US-00002 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.sub.1, t.sub.2, . . . t.sub.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.gtoreq.3.
[0133] For example, three multiple regression models that
correspond to three time points (t.sub.1, t.sub.2, and t.sub.3) can
be established, as follows:
Y.sub.1=.beta..sub.A.sup.1.times.A+.beta..sub.B.sup.1.times.B+.-
beta..sub.C.sup.1.times.C+.beta..sub.D.sup.1.times.D+.beta..sub.E.sup.1.ti-
mes.E+.beta..sub.F.sup.1.times.F+.beta..sub.G.sup.1.times.G+.beta..sub.AB.-
sup.1.times.AB+.beta..sub.AC.sup.1.times.AC+.beta..sub.ABC.sup.1.times.ABC-
+.beta..sub.AA.sup.1.times.AA+.beta..sub.BB.sup.1.times.BB+.beta..sub.CC.s-
up.1.times.CC+.beta..sub.DD.sup.1.times.DD+.beta..sub.EE.sup.1.times.EE+.b-
eta..sub.FF.sup.1.times.FF+.beta..sub.GG.sup.1.times.GG
Y.sub.2=.beta..sub.A.sup.2.times.A+.beta..sub.B.sup.2.times.B+.beta..sub.-
C.sup.2.times.C+.beta..sub.D.sup.2.times.D+.beta..sub.E.sup.2.times.E+.bet-
a..sub.F.sup.2.times.F+.beta..sub.G.sup.2.times.G+.beta..sub.AB.sup.2.time-
s.AB+.beta..sub.AC.sup.2.times.AC+.beta..sub.ABC.sup.2.times.ABC+.beta..su-
b.AA.sup.2.times.AA+.beta..sub.BB.sup.2.times.BB+.beta..sub.CC.sup.2.times-
.CC+.beta..sub.DD.sup.2.times.DD+.beta..sub.EE.sup.2.times.EE+.beta..sub.F-
F.sup.2.times.FF+.beta..sub.GG.sup.2.times.GG
Y.sub.3=.beta..sub.A.sup.3.times.A+.beta..sub.B.sup.3.times.B+.beta..sub.-
C.sup.3.times.C+.beta..sub.D.sup.3.times.D+.beta..sub.E.sup.3.times.E+.bet-
a..sub.F.sup.3.times.F+.beta..sub.G.sup.3.times.G+.beta..sub.AB.sup.3.time-
s.AB+.beta..sub.AC.sup.3.times.AC+.beta..sub.ABC.sup.3.times.ABC+.beta..su-
b.AA.sup.3.times.AA+.beta..sub.BB.sup.3.times.BB+.beta..sub.CC.sup.3.times-
.CC+.beta..sub.DD.sup.3.times.DD+.beta..sub.EE.sup.3.times.EE+.beta..sub.F-
F.sup.3.times.FF+.beta..sub.GG.sup.3.times.GG wherein Y.sub.1,
Y.sub.2, and Y.sub.3 are the electroplating potentials measured at
respective time points t.sub.1, t.sub.2, and t.sub.3;
.beta..sub.A.sup.1-.beta..sub.GG.sup.1 are the coefficients for the
selected compositional terms A-GG at time point t.sub.1;
.beta..sub.A.sup.2-.beta..sub.GG.sup.2 are the coefficients for the
selected compositional terms A-GG at time point t.sub.2;
.beta..sub.A.sup.3-.beta..sub.GG.sup.3 are the coefficients for the
selected compositional terms A-GG at time point t.sub.3.
[0134] The values of the coefficients
.beta..sub.A.sup.1-.beta..sub.GG.sup.1,
.beta..sub.A.sup.2-.beta..sub.GG.sup.2, and
.beta..sub.A.sup.3-.beta..sub.GG.sup.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.sub.1, t.sub.2, and
t.sub.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.sub.1, t.sub.2, and t.sub.3 are sequentially measured during the
experimental run and recorded as Y.sub.1, Y.sub.2, and Y.sub.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, .beta., and Y are constructed as
follows: X = ( A B C D E F G AB A .times. .times. C ABC AA BB CC DD
EE FF GG ) ##EQU1## B = ( .beta. A 1 .beta. B 1 .beta. C 1 .beta. D
1 .beta. E 1 .beta. F 1 .beta. G 1 .beta. AB 1 .beta. A .times.
.times. C 1 .beta. ABC 1 .beta. AA 1 .beta. BB 1 .beta. CC 1 .beta.
DD 1 .beta. EE 1 .beta. FF 1 .beta. GG 1 .beta. A 2 .beta. B 2
.beta. C 2 .beta. D 2 .beta. E 2 .beta. F 2 .beta. G 2 .beta. AB 2
.beta. A .times. .times. C 2 .beta. ABC 2 .beta. AA 2 .beta. BB 2
.beta. CC 2 .beta. DD 2 .beta. EE 2 .beta. FF 2 .beta. GG 2 .beta.
A 3 .beta. B 3 .beta. C 3 .beta. D 3 .beta. E 3 .beta. F 3 .beta. G
3 .beta. AB 3 .beta. A .times. .times. C 3 .beta. ABC 3 .beta. AA 3
.beta. BB 3 .beta. CC 3 .beta. DD 3 .beta. EE 3 .beta. FF 3 .beta.
GG 3 ) ##EQU1.2## Y = ( Y 1 Y 2 Y 3 ) ##EQU1.3##
[0138] The three multiple regression models as described herein
above can be represented by a simple matrix-based model that
defines Y=.beta.X, wherein X is a compositional matrix containing
the selected compositional terms, wherein .beta. 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 .beta. and Y contain known elements
(i.e., .beta..sub.A.sup.1-.beta..sub.CC.sup.1,
.beta..sub.A.sup.2-.beta..sub.CC.sup.2,
.beta..sub.A.sup.3-.beta..sub.CC.sup.3, and Y.sub.1-Y.sub.2), they
can be used to determined the unknown elements (i.e., A, B, C, . .
. GG) contained in matrix X.
[0140] From .beta.X=Y, the following can be obtained:
(.beta.'.beta.)X=Y.beta.'
(.beta.'.beta.).sup.-1(.beta.'.beta.)X=Y.beta.'(.beta.'.beta.).sup.-1
wherein .beta.' is the transpose of .beta., and wherein
(.beta.'.beta.).sup.-1 is the inverse of .beta.'.beta..
[0141] Since (.beta.'.beta.).sup.-1(.beta.'.beta.) 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=Y.beta.'(.beta.'.beta.).sup.-1
[0142] When .beta. is known, its transpose, .beta.', and the
inverse of their product (.beta.'.beta.).sup.-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.gtoreq.3, and
m.gtoreq.3), as follows:
Y.sub.1=.beta..sub.11.times.X.sub.1+.beta..sub.12.times.X.sub.2+.beta..su-
b.13.times.X.sub.3+ . . . .beta..sub.1n.times.X.sub.n
Y.sub.2=.beta..sub.21.times.X.sub.1+.beta..sub.22.times.X.sub.2+.beta..su-
b.23.times.X.sub.3+ . . . +.beta..sub.2n.times.X.sub.n
Y.sub.3=.beta..sub.31.times.X.sub.1+.beta..sub.32.times.X.sub.2+.beta..su-
b.33.times.X.sub.3+ . . . +.beta..sub.3n.times.X.sub.n
Y.sub.m=.beta..sub.m1.times.X.sub.1+.beta..sub.m2.times.X.sub.2+.beta..su-
b.m3.times.X.sub.3+ . . . +.beta..sub.mn.times.X.sub.n wherein
X.sub.1, X.sub.2, X.sub.3, . . . , X.sub.n are the n selected
compositional terms; Y.sub.1, Y.sub.2, Y.sub.3, . . . , Y.sub.m are
the electroplating potentials measured at m time points t.sub.1,
t.sub.2, t.sub.3, . . . , t.sub.m; .beta..sub.11-.beta..sub.1n are
the coefficients for the selected compositional terms
X.sub.1-X.sub.n at time point t.sub.1; .beta..sub.21-.beta..sub.2n
are the coefficients for the selected compositional terms
X.sub.1-X.sub.n at time point t.sub.2; .beta..sub.31-.beta..sub.3n
are the coefficients for the selected compositional terms
X.sub.1-X.sub.n at time point t.sub.3; . . . ; and
.beta..sub.m1-.beta..sub.mn are the coefficients for the selected
compositional terms X.sub.1-X.sub.n at time point t.sub.m.
[0145] The three matrices X, .beta., and Y can then be constructed
as follows: X = ( X 1 X 2 X 3 X n ) ##EQU2## B = ( .beta. 11 .beta.
12 .beta. 13 .beta. 1 .times. n .beta. 21 .beta. 22 .beta. 23
.beta. 2 .times. n .beta. 31 .beta. 32 .beta. 33 .beta. 3 .times. n
.beta. m .times. .times. 1 .beta. m .times. .times. 2 .beta. m
.times. .times. 3 .beta. m .times. .times. n ) ##EQU2.2## Y = ( Y 1
Y 2 Y 3 Y m ) ##EQU2.3##
[0146] As shown, the generalized compositional matrix X is a
n.times.1 matrix containing the n compositional terms; the
generalized coefficient matrix .beta. is a m.times.n matrix; and
the generalized response matrix Y is a m.times.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.
* * * * *