METHOD FOR AUTOMATED DETERMINATION OF AN OPTIMALLY PARAMETERIZED SCATTEROMETRY MODEL

• US 20120022836A1
• Filed: 07/22/2010
• Published: 01/26/2012
• Est. Priority Date: 07/22/2010
• Status: Active Grant

• Current Assignee: KLA-Tencor Corporation
• Original Assignee: KLA-Tencor Corporation, Tokyo Electron Limited
• Inventors: Hench, John J., Dziura, Thaddeus, Ferns, Jason, Komarov, Serguei
• Granted Patent: US 8,666,703 B2
• Time in Patent Office: Days
• US Class Current: 703/2
• CPC Class Codes: G03F 7/70616 Monitoring the printed patterns
• CPC Class Codes: G03F 7/70625 Dimensions, e.g. line width, critical dimension [CD], profile, sidewall angle or edge roughness

Abstract

Provided is an automated determination of an optimized parameterization of a scatterometry model for analysis of a sample diffracting structure having unknown parameters. A preprocessor determines from a plurality of floating model parameters, a reduced set of model parameters which can be reasonably floated in the scatterometry model based on a relative precision for each parameter determined from the Jacobian of measured spectral information with respect to each parameter. The relative precision for each parameter is determined in a manner which accounts for correlation between the parameters for a combination.

Claims

1. A method for identifying a set of scatterometry model parameters that are to be floated during a scatterometry analysis to fit a model to measured spectral information, the method comprising:

receiving the measured spectral information;

receiving a scatterometry model having a plurality of model parameters (N);

computing a Jacobian matrix of the measured spectral information, the Jacobian matrix containing a column for each of the plurality of model parameters;

identifying, based on a precision metric determined from the Jacobian matrix for each model parameter in a plurality of parameter combinations, a set of model parameters for which each parameter of the set of model parameters is to be fixed to a predetermined parameter value in a revised scatterometry model; and

running a regression on the measured spectral information with the revised scatterometry model to generate simulated spectral information.

2. The method as in claim 1, wherein identifying the set of model parameters to be fixed further comprises:

generating a test matrix including a plurality of combinations of parameter columns derived from the Jacobian matrix;

computing a relative precision metric for each of the parameter columns in each combination, wherein the relative precision metric is a function of the precision metric and an expected process variation associated with the parameter;

identifying, based on an extremum of the relative precision metric for each combination, the combination that satisfies a threshold value of the relative precision metric and includes the greatest number of parameter columns; and

fixing model parameters to predetermined values, each of the model parameters excluded from a set corresponding to the parameter columns of the identified combination.

3. The method as in claim 2, wherein computing the relative precision metric for each of the parameter columns in each identified combination further comprises:

determining a spectral noise covariance (S) for all model parameters;

determining, from S, a covariance of a perturbation (C_p) in the parameter space of the test matrix;

determining the relative precision metric by dividing the parameter precision metric, as determined from C_p, by the expected process variation for that parameter; and

wherein the extremum of the relative precision metric is the maximum of the relative precision metric.

4. The method as in claim 2, wherein:

generating the test matrix further comprises;

iteratively assembling the test matrix, wherein for each successive iteration, N combinations of columns having one additional floating parameter than the previous test matrix iteration are copied from the Jacobian matrix and appended to all parameter combinations having the lowest relative precision metric determined from previous iterations; and

wherein identifying the combination that satisfies a threshold value of the relative precision metric and contains the greatest number of parameter columns further comprises;

floating the parameter combination having the lowest relative precision metric when combined with parameters set to float in previous iterations;

terminating the iterative test matrix assembly in response to a maximum relative precision of the floated parameters reaching a threshold; and

identifying as the set of parameters to fix, a set of the model parameters excluded from the combination floated in the last test matrix assembly iteration.

5. The method as in claim 2, wherein generating the test matrix further comprises:

adding to the test matrix all possible combinations of columns from the Jacobian matrix;

iteratively reducing the test matrix, wherein for each successive iteration, combinations of columns having the highest relative precision metric and one fewer floating parameter than the previous test matrix iteration are retained; and

wherein identifying the combination that satisfies a threshold value of the relative precision metric and contains the greatest number of parameter columns further comprises;

floating the parameter combination having the lowest relative precision metric when combined with parameters set to float in previous iterations;

terminating the iterative test matrix assembly in response to a maximum relative precision of the floated parameters reaching a threshold; and

identifying as the set of parameters to fix, a set of the model parameters excluded from the combination floated in the last test matrix assembly iteration.

6. The method as in claim 2, wherein generating the test matrix comprises generating a plurality of test matrices, each of the plurality including all possible combinations of the N parameters.

7. The method as in claim 2, further comprising:

successively floating each parameter in a subset of the set of fixed parameters, the subset containing parameters having the relative precision metric within a threshold range;

running a verifying regression after each additional parameter is floated; and

fixing the additional parameter at a new fixed parameter value in response to an improvement in a residual of the verifying regression, the new fixed parameter value determined from the verifying regression.

8. The method as in claim 7, further comprising:

determining a difference between the predetermined parameter value and the new fixed parameter value;

normalizing the difference to the parameter'"'"'s precision metric; and

re-computing a Jacobian matrix of the measured spectral information using the revised scatterometry model and new fixed parameter value in response to the normalized difference being greater than a threshold.

9. The method as in claim 8, further comprising:

identifying, based on a precision metric determined from the recomputed Jacobian matrix for each model parameter in a plurality of parameter combinations, a set of model parameters for which each parameter of the set of model parameters is to be fixed to a predetermined parameter value in a newly revised scatterometry model; and

running a regression on the measured spectral information with the newly revised scatterometry model to generate newly simulated spectral information.

10. The method as in claim 1, wherein the measured spectral information characterizes a grating formed on a semiconductor wafer.

11. A machine-accessible storage medium having instructions stored thereon which cause a data processing system to perform a method for identifying a set of scatterometry model parameters that are to be floated during a scatterometry analysis to fit a model to measured spectral information, the method comprising:

receiving the measured spectral information;

receiving an initial scatterometry model having a plurality (N) of model parameters;

computing a Jacobian matrix of the measured spectral information, the Jacobian matrix containing a column for each of the plurality of model parameters;

identifying, based on a precision metric determined from the Jacobian matrix for each model parameter in a plurality of parameter combinations, a set of model parameters for which each parameter of the set is to be fixed to a predetermined parameter value in a revised scatterometry model; and

running a regression on the measured spectral information with the revised scatterometry model to generate a simulated spectral information.

12. The storage medium as in claim 11, wherein the instructions for identifying the set of model parameters to be fixed further comprises instructions for:

generating a test matrix including a plurality of different combinations of parameter columns copied from the Jacobian matrix;

computing a relative precision metric for each of the parameter columns in each combination, the relative precision metric a function of the precision metric and an expected process variation associated with the parameter;

identifying, based on an extremum of the relative precision metric for each combination, the combination that satisfies a threshold value of the relative precision metric and contains the greatest number of parameter columns; and

fixing to the predetermined value, each of the model parameters not in a set corresponding to the parameter columns of the identified combination.

13. The storage medium as in claim 12, wherein the instructions for computing the relative precision metric for each of the parameter columns in each identified combination further comprise instructions for:

determining a spectral noise covariance (S) for all model parameters;

determining, from S, a covariance of a perturbation (C_p) in the parameter space of the test matrix;

determining the relative precision metric by dividing the parameter precision metric, as determined from C_p, by the expected process variation for that parameter; and

wherein the extremum of the relative precision metric is the maximum of the relative precision metric.

14. The storage medium as in claim 12, wherein the instructions for generating the test matrix further comprise instructions for:

iteratively assembling the test matrix, wherein for each successive iteration, N combinations of columns having one additional floating parameter than the previous test matrix iteration are copied from the Jacobian matrix and appended to all parameter combinations having the lowest relative precision metric determined from previous iterations; and

wherein the instructions for identifying the combination that satisfies a threshold value of the relative precision metric and contains the greatest number of parameter columns further comprise instructions for;

floating the parameter combination having the lowest relative precision metric when combined with parameters set to float in previous iterations;

terminating the iterative test matrix assembly in response to a maximum relative precision of the floated parameters reaching a threshold; and

identifying as the set of parameters to fix, a set of the model parameters excluded from the combination floated in the last test matrix assembly iteration.

15. The storage medium as in claim 12, further comprising instructions stored thereon which cause the data processing system to perform a method further comprising:

successively floating each parameter in a subset of the set of fixed parameters, the subset containing parameters having a relative precision metric within a threshold range the relative precision metric a function of the precision metric and an expected process variation associated with the parameter;

running a verifying regression after each additional parameter is floated; and

fixing the additional parameter at a new fixed parameter value in response to an improvement in a residual of the verifying regression, the new fixed parameter value determined from the verifying regression.

16. The storage medium as in claim 15, further comprising instructions stored thereon which cause the data processing system to perform a method further comprising:

determining a difference between the predetermined parameter value and the new fixed parameter value;

normalizing the difference to the parameter'"'"'s precision metric; and

re-computing a Jacobian matrix of the measured spectral information using the revised scatterometry model and new fixed parameter value in response to the normalized difference being greater than a threshold.

17. An optical metrology system for analysis of a sample diffracting structure having unknown parameters, the system comprising:

a scatterometry model preprocessor configured to;

compute a Jacobian matrix of spectral information measured by the metrology system, the Jacobian matrix containing a column for each of a plurality of initial model parameters;

identify, based on a precision metric determined from the Jacobian matrix for each model parameter in a plurality of parameter combinations, a set of model parameters for which each parameter of the set is to be fixed to a predetermined parameter value in a revised scatterometry model; and

a metrology processor to run a regression on the measured spectral information with the revised scatterometry model and generate simulated spectral information.

18. The optical metrology system as in claim 17, wherein the scatterometry model preprocessor is further configured to:

generate a test matrix including a plurality of combinations of parameter columns from the Jacobian matrix;

compute a relative precision metric for each of the parameter columns in each combination, the relative precision metric a function of the precision metric and an expected process variation associated with the parameter;

identify, based on an extremum of the relative precision metric for each combination, a combination that satisfies a threshold value of the relative precision metric and contains the greatest number of parameter columns; and

fix to the predetermined value, each of the model parameters not in a set corresponding to the parameter columns of the identified combination.

19. The optical metrology system as in claim 18, wherein the scatterometry model preprocessor is further configured to:

successively float each parameter in a subset of the set of fixed parameters, the subset containing parameters having a relative precision metric within a threshold range, the relative precision metric a function of the precision metric and an expected process variation associated with the parameter;

perform a verifying regression after each additional parameter is floated; and

fix the additional parameter at a new fixed parameter value in response to an improvement in a residual of the verifying regression, the new fixed parameter value determined from the verifying regression.

20. The optical metrology system as in claim 17, wherein the scatterometry model preprocessor is further configured to:

determine a difference between the predetermined parameter value and the new fixed parameter value;

normalize the difference to the parameter'"'"'s precision metric; and

re-compute a Jacobian matrix of the measured spectral information using the revised scatterometry model and new fixed parameter value in response to the normalized difference being greater than a threshold.