Method and apparatus for multidomain data analysis

• US 20040172202A1
• Filed: 03/02/2004
• Published: 09/02/2004
• Est. Priority Date: 04/04/2000
• Status: Active Grant

• Current Assignee: John J. Sidorowich
• Original Assignee: John J. Sidorowich
• Inventors: Sidorowich, John J.
• Granted Patent: US 7,050,179 B2
• Time in Patent Office: Days
• US Class Current: 702/40
• CPC Class Codes: G01N 21/8422 Investigating thin films, e.g. matrix isolation method
• CPC Class Codes: G01N 21/9501 Semiconductor wafers manufacturing processes per se of semiconductor devices implementing a measuring step H01L22/10
• CPC Class Codes: G06F 18/2111 by using evolutionary computational techniques, e.g. genetic algorithms
• CPC Class Codes: G06N 3/126 Evolutionary algorithms, e.g. genetic algorithms or genetic programming

Abstract

An optical measuring device generates a plurality of measured optical data from inspection of a thin film stack. The measured optical data group naturally into several domains. In turn the thin film parameters associated with the data fall into two categories: local and global. Local “genes” represent parameters that are associated with only one domain, while global genes represent parameters that are associated with multiple domains. A processor evolves models for the data associated with each domain, which models are compared to the measured data, and a “best fit” solution is provided as the result. Each model of theoretical data is represented by an underlying “genotype” which is an ordered set of the genes. For each domain a “population” of genotypes is evolved through the use of a genetic algorithm. The global genes are allowed to “migrate” among multiple domains during the evolution process. Each genotype has a fitness associated therewith based on how much the theoretical data predicted by the genotype differs from the measured data. During the evolution process, individual genotypes are selected based on fitness, then a genetic operation is performed on the selected genotypes to produce new genotypes. Multiple generations of genotypes are evolved until an acceptable solution is obtained or other termination criterion is satisfied.

Claims

1. A multidomain method for evaluating parameters of a semiconductor wafer or wafer set comprising:

identifying a group of semiconductor wafer parameters-to be evaluated;

mapping the semiconductor wafer parameters into at least one genotype, said genotype comprising a collection of genes, each gene corresponding to a selected one of the group of semiconductor wafer parameters to be evaluated;

defining more than one domain as a collection of genotypes, each domain with its own population of genotypes;

deriving a set of theoretical data for each genotype;

inspecting the semiconductor wafer or wafer set using a beam of radiation and generating therefrom sets of measured data;

comparing a set of measured data to a corresponding set of derived theoretical data for each genotype in each domain in order to determine a level of fitness for each genotype;

migrating genotypes among the domains by selecting at least one genotype from a current domain population and adding it to the population of a different domain;

evolving a next population for each domain by selecting at least one genotype from the current population based on the fitness level of the genotype and performing a genetic operation on the at least one genotype, thereby creating at least one new genotype and adding the at least one new genotype to the next population; and

repeating the comparing, migrating, and evolving steps so that for each domain the fittest genotype becomes increasingly more fit.

2. A method as recited in claim 1 wherein the likelihood of selecting a genotype for a genetic operation from a domain population is proportional to the degree to which the derived theoretical data associated with that genotype matches the measured data.

3. A method as recited in claim 1 wherein the likelihood of selecting a genotype for migration from a domain population depends upon the degree to which the derived theoretical data associated with that genotype matches the measured data.

4. A method as recited in claim 1, wherein the level of fitness of a genotype is determined by calculating the fitness as a function of the difference between the theoretical data and the measured data.

5. A method as recited in claim 1, wherein the performing step includes reproducing an identical copy of the at least one genotype.

6. A method as recited in claim 1, wherein the performing step includes selecting a gene from the at least one genotype and mutating the gene.

7. A method as recited in claim 1, wherein the performing step includes selecting corresponding genes in a pair of genotypes and exchanging the genes.

8. A method as recited in claim 6, wherein the step of selecting a gene includes randomly selecting the gene.

9. A method as recited in claim 7, wherein the step of selecting corresponding genes includes randomly selecting the genes.

10. A method as recited in claim 1, wherein the step of inspecting includes measuring one wafer at multiple points with data generated from each point being used to define a set of measured data.

11. A method as recited in claim 1, wherein the step of inspecting includes measuring multiple wafers.

33. A method as recited in claim 1 or claim 12 or claim 17 or claim 27 wherein the step of deriving a set of theoretical data for each genotype includes the use of a nonlinear least squares optimization algorithm for selected genotypes.

12. A multidomain method for evaluating parameters of a semiconductor wafer or wafer set, comprising:

identifying a group of semiconductor wafer parameters to be evaluated;

mapping the semiconductor wafer parameters into at least one genotype, said genotype comprising a collection of genes, each gene corresponding to a selected one of the group of semiconductor wafer parameters to be evaluated;

defining more than one domain as a collection of genotypes, each domain with its own population of genotypes;

deriving a set of theoretical data for each genotype;

inspecting the semiconductor wafer or wafer set using a beam of radiation and generating therefrom sets of measured data;

comparing a set of measured data to a corresponding set of derived theoretical data for each genotype in each domain in order to determine a level of fitness for each genotype;

migrating genotypes among the domains by selecting at least one genotype from a current domain population and adding it to the population of a different domain;

evolving a new population of genotypes for each domain by selecting at least one genotype from the current domain population based on the fitness of the genotype and performing a genetic operation on the at least one genotype to form at least one new genotype, said genetic operation being selected from one of the following;

reproducing an identical copy of the at least one genotype;

selecting a gene from the at least one genotype and mutating the gene;

or selecting corresponding genes in a pair of genotypes and exchanging the genes, and adding the at least one new genotype to a next population; and

repeating the comparing, migrating, and evolving steps so that for each domain the fittest genotype becomes increasingly more fit.

13. A method as recited in claim 12, wherein the step of selecting at least one genotype for evolution includes selecting at least one genotype in proportion to its fitness.

14. A method as recited in claim 12 wherein the likelihood of selecting a genotype for migration from a domain population depends upon the degree to which the derived theoretical data associated with that genotype matches the measured data.

15. A method as recited in claim 12, wherein the step of selecting a gene includes randomly selecting the gene.

16. A method as recited in claim 12, wherein the step of selecting corresponding genes includes randomly selecting the genes.

17. A multidomain method for evaluating parameters of a semiconductor wafer or wafer set comprising:

identifying a group of semiconductor wafer parameters to be evaluated;

mapping the semiconductor wafer parameters into at least one genotype, said genotype comprising a collection of genes, each gene corresponding to a selected one of the group of semiconductor wafer parameters to be evaluated;

dividing the genes into at least two different gene classes, at least one of said gene classes being subject to a migration operation;

defining more than one domain as a collection of genotypes, each domain with its own population of genotypes;

deriving a set of theoretical data for each genotype;

inspecting the semiconductor wafer or wafer set using a beam of radiation and generating therefrom sets of measured data;

comparing a set of measured data to a corresponding set of derived theoretical data for each genotype in each domain in order to determine a level of fitness for each genotype;

applying a migration operation to at least one genotype from a current domain population, said migration operation including a mechanism for moving genes in at least one of said gene classes to the genotype population of a different domain;

evolving a next population for each domain by selecting at least one genotype from the current population based on the fitness level of the genotype and performing a genetic operation on the at least one genotype, thereby creating at least one new genotype and adding the at least one new genotype to the next population; and

repeating the comparing, migration operation, and evolving steps so that for each domain the fittest genotype becomes increasingly more fit.

18. A method as recited in claim 17 wherein the likelihood of selecting a genotype for a genetic operation from a domain population is proportional to the degree to which the derived theoretical data associated with that genotype matches the measured data.

19. A method as recited in claim 17 wherein the likelihood of selecting a genotype for migration from a domain population depends upon the degree to which the derived theoretical data associated with that genotype matches the measured data.

20. A method as recited in claim 17, wherein the level of fitness of a genotype is determined by calculating the fitness as a function of the difference between the theoretical data and the measured data.

21. A method as recited in claim 17, wherein the performing step includes reproducing an identical copy of the at least one genotype.

22. A method as recited in claim 17, wherein the performing step includes selecting a gene from the at least one genotype and mutating the gene.

23. A method as recited in claim 17, wherein the performing step includes selecting corresponding genes in a pair of genotypes and exchanging the genes.

24. A method as recited in claim 22, wherein the step of selecting a gene includes randomly selecting the gene.

25. A method as recited in claim 23, wherein the step of selecting corresponding genes includes randomly selecting the genes.

26. A method as recited in claim 17, wherein the permissible range of values for genes in at least one of said gene classes that is subject to a migration operation becomes increasingly narrow as the comparing, migration operation, and evolving steps are repeated.

27. A multidomain method for evaluating parameters of a semiconductor wafer or wafer set, comprising:

identifying a group of semiconductor wafer parameters to be evaluated;

mapping the semiconductor wafer parameters into at least one genotype, said genotype comprising a collection of genes, each gene corresponding to a selected one of the group of semiconductor wafer parameters to be evaluated;

dividing the genes into at least two different gene classes, at least one of said gene classes being subject to a migration operation;

defining more than one domain as a collection of genotypes, each domain with its own population of genotypes;

deriving a set of theoretical data for each genotype;

inspecting the semiconductor wafer or wafer set using a beam of radiation and generating therefrom sets of measured data;

comparing a set of measured data to a corresponding set of derived theoretical data for each genotype in each domain in order to determine a level of fitness for each genotype;

applying a migration operation to at least one genotype from a current domain population, said migration operation including a mechanism for moving genes in at least one of said gene classes to the genotype population of a different domain;

evolving a new population of genotypes for each domain by selecting at least one genotype from the current domain population based on the fitness of the genotype and performing a genetic operation on the at least one genotype to form at least one new genotype, said genetic operation being selected from one of the following;

reproducing an identical copy of the at least one genotype;

selecting a gene from the at least one genotype and mutating the gene;

or selecting corresponding genes in a pair of genotypes and exchanging the genes, and adding the at least one new genotype to a next population; and

repeating the comparing, migration operation, and evolving steps so that for each domain the fittest genotype becomes increasingly more fit.

28. A method as recited in claim 27, wherein the step of selecting at least one genotype for evolution includes selecting at least one genotype in proportion to its fitness.

29. A method as recited in claim 27 wherein the likelihood of selecting a genotype for migration from a domain population depends upon the degree to which the derived theoretical data associated with that genotype matches the measured data.

30. A method as recited in claim 27, wherein the step of selecting a gene includes randomly selecting the gene.

31. A method as recited in claim 27, wherein the step of selecting corresponding genes includes randomly selecting the genes.

32. A method as recited in claim 27, wherein the permissible range of values for genes in at least one of said gene classes that is subject to a migration operation becomes increasingly narrow as the comparing, migration operation, and evolving steps are repeated.

34. A multidomain process for evaluating parameters of a semiconductor wafer or wafer set comprising:

identifying a group of semiconductor wafer parameters to be evaluated;

inspecting the semiconductor wafer or wafer set using a beam of radiation and generating therefrom sets of measured data, each set of measured data corresponding to a different measurement;

defining more than one search domain, each search domain corresponding to a set of measured data;

applying an iterative search method to each search domain in order to generate a group of optimized parameter values for each search domain, said iterative search method including the steps of;

generating a set of theoretical parameter values associated with each search domain;

deriving a set of theoretical data for each set of theoretical parameter values;

comparing the sets of theoretical data associated with the set of parameter values associated with each search domain to the set of measured data corresponding to each search domain;

generating a new set of theoretical parameter values of each search domain based on the comparing step in a manner so as to identify increasingly more optimal theoretical parameter values for each search domain; and

wherein said iterative search method further includes the step of migrating a set of theoretical parameter values from one search domain to another search domain.

35. A method as recited in claim 34, wherein the step of inspecting includes measuring one wafer at multiple points.

36. A method as recited in claim 34, wherein the step of inspecting includes measuring multiple wafers.

37. A method as recited in claim 34 wherein said iterative search method is a genetic algorithm.