One-point recalibration method for reducing error in concentration measurements for an electrolytic solution
The present invention relates to a method for mathematically re-calibrating and adjusting an initial concentration analysis model that suffers from electrochemical measurement errors caused by surface state changes in the working/counter/reference electrode after extended usage. Specifically, such recalibration method reimburses long-term drift in the electrochemical measurements based on a single point testing.
1. A method for reducing measurement error in concentration analysis of electrolytic solution, comprising:
(a) establishing an initial model for determining concentration Y of a component of interest in electrolytic solution based on a measurable parameter X that is correlative to Y, wherein correlation between X and Y in said initial model is expressed as Y=ƒ(X);
(b) providing a standard electrolytic solution that contains said component of interest at a known concentration Y s ;
(c) calculating a theoretical parameter value X s for said standard electrolytic solution, wherein X s =ƒ −1 (Y s );
(d) measuring the actual parameter value X o of said standard electrolytic solution;
(e) determining an adjustment factor e, wherein e=X s −X o ;
(f) constructing a revised model that provides Y=ƒ(X+e) for future concentration determination of the component of interest; and
(g) optionally, repeating steps (b)–(f) for model revision on a periodical or threshold basis.
2. The method of claim 1 , wherein said electrolytic solution comprises electrochemical deposition solution containing one or more metal components.
3. The method of claim 2 , wherein said metal components are selected from the group consisting of aluminum, silver, gold, iridium, palladium, tantalum, titanium, chromium, cobalt, tungsten, tin, and lead.
4. The method of claim 1 , wherein said electrolytic solution is free of metal components.
5. The method of claim 1 , wherein said electrolytic solution comprises copper electrochemical deposition solution containing copper sulfate, chloride, and sulfuric acid.
6. The method of claim 5 , wherein said copper electrochemical deposition solution further comprises one or more organic additives selected from the group consisting of suppressors, accelerators, and levelers.
7. The method of claim 5 , wherein the component of interest is sulfuric acid.
8. The method of claim 5 , wherein the component of interest is copper.
9. The method of claim 1 , wherein the measurable parameter X is obtained by immersing first and second electrodes in the electrolytic solution, applying a cyclic electrical potential between said first and second electrodes, and analyzing current response of the electrolytic solution.
10. The method of claim 9 , wherein the current response of the electrolytic solution contains one or more current peaks, and wherein said measurable parameter X is the integrated area of one of said current peaks.
11. The method of claim 1 , wherein the initial model for determining concentration Y of the component of interest in electrolytic solution is established by:
(i) providing multiple calibration electrolytic solutions containing the component of interest at unique, known concentrations;
(ii) measuring the respective parameter X for each of said calibration electrolytic solutions; and
(iii) constructing the initial model, by correlating said unique, known concentrations Y of the component of interest in the calibration solutions with the respective parameters X measured for said calibration solutions to form an empirical correlation function in which Y=ƒ(X).
12. A method for recalibrating a predetermined concentration analysis model, in which concentration Y of a target component in electrolytic solution is determined by a measurable parameter X and a function Y=ƒ(X), said method comprising the steps of:
(a) providing a standard electrolytic solution that contains said target component at a known concentration Y s ;
(b) calculating a theoretical parameter value X s for said standard solution, based on Y s and inverse of the function Y=ƒ(X);
(c) measuring the actual parameter value X o of said standard solution;
(d) determining an adjustment factor e, wherein e=X s −X o ;
(e) constructing a recalibrated concentration analysis model that provides Y=ƒ(X+e).
13. The method of claim 12 , wherein said electrolytic solution comprises electrochemical deposition solution containing one or more metal components.
14. The method of claim 13 , wherein said metal components are selected from the group consisting of aluminum, silver, gold, iridium, palladium, tantalum, titanium, chromium, cobalt, tungsten, tin, and lead.
15. The method of claim 12 , wherein said electrolytic solution is free of metal components.
16. The method of claim 12 , wherein said electrolytic solution comprises copper electrochemical deposition solution containing copper sulfate, chloride, and sulfuric acid.
17. The method of claim 16 , wherein said copper electrochemical deposition solution further comprises one or more organic additives selected from the group consisting of suppressors, accelerators, and levelers.
18. The method of claim 16 , wherein the component of interest is sulfuric acid.
19. The method of claim 16 , wherein the component of interest is copper.
20. The method of claim 12 , wherein the measurable parameter X is obtained by immersing first and second electrodes in the electrolytic solution, applying a cyclic electrical potential between said first and second electrodes, and analyzing current response of the electrolytic solution.
21. The method of claim 20 , wherein the current responses of the electrolytic solution contain one or more current peaks, and wherein said measurable parameter X is the integrated area of one of said current peaks.
22. A method for reducing measurement error in concentration analysis of electrolytic solution, comprising:
(a) establishing an initial model for determining concentration Y of a component of interest in electrolytic solution based on a measurable parameter X that is correlative to Y, wherein correlation between X and Y in said initial model is expressed as Y=ƒ(X);
(b) providing a standard electrolytic solution that contains said component of interest at a known concentration Y s ;
(c) calculating a theoretical parameter value X s for said standard electrolytic solution, wherein X s =ƒ −1 (Y s );
(d) measuring the actual parameter value X o of said standard electrolytic solution;
(e) determining an adjustment factor e, wherein
e
=
X
s
X
0
;
(f) constructing a revised model that provides Y=ƒ(X×e) for future concentration determination of the component of interest; and
(g) optionally, repeating steps (b)–(f) for model revision on a periodical or threshold basis.
23. A method for recalibrating a predetermined concentration analysis model, in which concentration Y of a target component in electrolytic solution is determined by a measurable parameter X and a function Y=ƒ(X), said method comprising the steps of:
(a) providing a standard electrolytic solution that contains said target component at a known concentration Y s ;
(b) calculating a theoretical parameter value X s for said standard solution, based on Y s and inverse of the function Y=ƒ(X);
(c) measuring the actual parameter value X o of said standard solution;
(d) determining an adjustment factor e, wherein
e
=
X
s
X
0
;
(e) constructing a recalibrated concentration analysis model that provides Y=ƒ(X×e).