Methods and systems for regularizing the optimization of application specific semiconductor measurement system parameter settings
Methods and systems for optimizing a semiconductor measurement recipe that is robust to variations of hardware modeling parameters and geometric modeling errors are described herein. Robust measurement recipe optimization minimizes a cost function including one or more regularization terms that constrain the process space, and thus, significantly reduces the computational effort required to optimize a measurement recipe. This reduces overall process time and improves wafer throughput. In some examples, optimization is performed based on measurement data associated with multiple instances of a semiconductor structure; each instance characterized a different value of one or more geometric parameters of interest. In some examples, the search for optimized measurement recipes is limited to the discrete set of measurement system parameter values associated with the available measurement data set. In this manner, the performance of a particular measurement recipe is validated using existing measurement data.
1. A method comprising:
generating measurement data associated with a first plurality of measurements of at least one semiconductor structure having known values of one or more parameters of interest, the first plurality of measurements each having different values of one or more measurement system parameters;
estimating values of the one or more parameters of interest associated with the at least one semiconductor structure based on the measurement data and a measurement model;
determining a sensitivity of a value of each of the one or more parameters of interest to changes of value of each of the one or more measurement system parameters at each of the different values of the one or more measurement system parameters; and
determining an optimized set of values of the one or more measurement system parameters based on an optimization of a regularized cost function including the determined sensitivities.
2. The method of claim 1 , wherein the regularized cost function includes a constraint on measurement time.
3. The method of claim 1 , wherein the measurement data is simulated measurement data, actual measurement data, or both.
4. The method of claim 1 , wherein the measurement data includes a plurality of instances of the at least one semiconductor structure, each of the plurality of instances having a different, known value of the one or more parameters of interest.
5. The method of claim 4 , wherein a value of the regularized cost function associated with a measurement recipe is an average of values of the regularized cost function associated with each of the plurality of instances of the at least one semiconductor structure.
6. The method of claim 1 , further comprising:
determining a value of a measurement performance metric based on the optimized set of values of the one or more measurement system parameters.
7. The method of claim 1 , wherein the one or more measurement system parameters includes azimuth angle, angle of incidence, and exposure time.
8. The method of claim 1 , wherein the optimized set of values of the one or more measurement system parameters is a discrete subset of the different values of one or more measurement system parameters.
9. The method of claim 1 , the regularized cost function includes a characterization of the at least one semiconductor structure.
10. The method of claim 9 , wherein the characterization includes any of a symmetry of the at least one semiconductor structure, an optical density of the at least one semiconductor structure, a height of the at least one semiconductor structure, a structural class of the at least one semiconductor structure, or any combination thereof.
11. The method of claim 1 , wherein the optimization of the regularized cost function involves a search through a library of candidate sets of measurement system parameters.
12. The method of claim 1 , wherein the optimization is a non-linear integer optimization.
13. The method of claim 1 , further comprising:
validating measurement performance based on a regression test on synthetic measurement data or actual measurement data.
14. The method of claim 13 , wherein the validating is based on the measurement data associated with the first plurality of measurements of the at least one semiconductor structure.
15. A system comprising:
a metrology tool including an illumination source and a detector configured to collect a first amount of actual measurement data from measurements of one or more semiconductor structures disposed on a first wafer in accordance with a set of optimized measurement system parameter values; and
a computing system configured to:
generate measurement data associated with a first plurality of measurements of at least one semiconductor structure having known values of one or more parameters of interest, the first plurality of measurements each having different values of one or more measurement system parameters;
estimate values of the one or more parameters of interest associated with the at least one semiconductor structure based on the measurement data and a measurement model;
determine a sensitivity of a value of each of the one or more parameters of interest to changes of value of each of the one or more measurement system parameters at each of the different values of the one or more measurement system parameters; and
determine the set of optimized measurement system parameter values based on an optimization of a regularized cost function including the determined sensitivities.
16. The system of claim 15 , wherein the measurement data includes a plurality of instances of the at least one semiconductor structure, each of the plurality of instances having a different, known value of the one or more parameters of interest.
17. The system of claim 16 , wherein a value of the regularized cost function associated with a measurement recipe is an average of values of the regularized cost function associated with each of the plurality of instances of the at least one semiconductor structure.
18. The system of claim 15 , wherein the set of optimized measurement system parameter values is a discrete subset of the different values of one or more measurement system parameters.
19. The system of claim 18 , wherein the optimization is a non-linear integer optimization.
20. The system of claim 15 , wherein the regularized cost function includes a characterization of the at least one semiconductor structure.
21. The system of claim 20 , wherein the characterization includes any of a symmetry of the at least one semiconductor structure, an optical density of the at least one semiconductor structure, a height of the at least one semiconductor structure, a structural class of the at least one semiconductor structure, or any combination thereof.
22. The system of claim 15 , wherein the optimization of the regularized cost function involves a search through a library of candidate sets of measurement system parameters.
23. A system comprising:
a metrology tool including an illumination source and a detector configured to collect a first amount of actual measurement data from measurements of one or more semiconductor structures disposed on a first wafer in accordance with a set of optimized measurement system parameter values; and
a non-transitory, computer-readable medium including instructions that when executed by one or more processors of a computing system cause the computing system to:
generate measurement data associated with a first plurality of measurements of at least one semiconductor structure having known values of one or more parameters of interest, the first plurality of measurements each having different values of one or more measurement system parameters;
estimate values of the one or more parameters of interest associated with the at least one semiconductor structure based on the measurement data and a measurement model;
determine a sensitivity of a value of each of the one or more parameters of interest to changes of value of each of the one or more measurement system parameters at each of the different values of the one or more measurement system parameters; and
determine the set of optimized measurement system parameter values based on an optimization of a regularized cost function including the determined sensitivities.