Computational metrology

1. A method, comprising:

determining a first distribution of a first parameter associated with an error or residual in performing a device manufacturing process, the first distribution comprising measured data or data obtained from a simulation or model;

determining a second distribution of a second parameter associated with an error or residual in performing the device manufacturing process, the second distribution comprising measured data or data obtained from a simulation or model; and

determining, by a hardware computer, a distribution of a parameter of interest associated with the device manufacturing process using a function operating on the first and second distributions.

2. The method of claim 1 , wherein the first parameter, the second parameter and the parameter of interest are the same.

3. The method of claim 1 , wherein the first distribution is specific to the device manufacturing process but not specific to any particular substrate processed using the device manufacturing process.

4. The method of claim 1 , wherein the second distribution is specific to a particular substrate processed using the device manufacturing process but not generic to other substrates processed using the device manufacturing process.

5. The method of claim 1 , wherein the first distribution and/or second distribution comprises one or more selected from: a contribution of a servo error to the respective first and/or second parameter, a contribution of an alignment model residual to the respective first and/or second parameter, a contribution of a projection system aberration or image plane deviation to the respective first and/or second parameter, a contribution of a projection system model residual to the respective first and/or second parameter, and/or a contribution of a substrate surface height to the respective first and/or second parameter.

6. The method of claim 1 , wherein determining the first distribution further comprises obtaining measured data of the first parameter and removing therefrom a contribution of a particular device of the device manufacturing process to the first parameter.

7. The method of claim 6 , wherein the contribution of the particular device comprises one or more selected from: a contribution of a servo error, a contribution of an alignment model residual, a contribution of a projection system aberration or image plane deviation, a contribution of a projection system model residual, and/or a contribution of a substrate surface height.

8. The method of claim 1 , further comprising using the distribution of the parameter of interest to perform any one or more selected from: predict a defect for a substrate, control the device manufacturing process, monitor the device manufacturing process, design an aspect of the device manufacturing process, and/or calibrate a mathematical model.

9. The method of claim 1 , wherein the first parameter, the second parameter and/or the parameter of interest is one or more selected from: overlay, critical dimension, focus, dose, and/or edge position.

10. The method of claim 1 , wherein the function comprises one or more selected from: an arithmetic addition, a convolution and/or a neural network.

11. The method of claim 1 , wherein the first parameter and/or the second parameter is different than the parameter of interest and further comprising converting the first parameter and/or the second parameter to the parameter of interest.

12. The method of claim 1 , wherein the function comprises a correlation operating on the first and second distributions.

13. The method of claim 12 , wherein:

the determined first distribution comprises a first modeled distribution of values, and

the determined second distribution comprises a second modeled distribution of values, and

the parameter of interest is the first parameter, and

the method comprises:

obtaining a first distribution of values of the first parameter;

obtaining a second distribution of values of the second parameter;

modeling the first and second distribution of values to obtain the first modeled and second modeled distribution of values; and

determining the distribution of the parameter of interest based on scaling the second modeled distribution of values using a scaling factor obtained by mapping between a first model coefficient associated with the first modeled distribution of values and a second model coefficient associated with the second modeled distribution of values.

14. The method of claim 13 , comprising:

determining a scale of variation for which a correlation between values of the first distribution and values of the second distribution exceeds a threshold; and

modeling the first and second distribution of values in dependence of the determined scale of variation to obtain the first modeled and second modeled distribution of values.

15. The method of claim 13 , comprising using the scaling factor to exclude a modeled component from the step of determining the distribution of the parameter of interest.

16. A method, comprising:

determining a first distribution of measured alignment data in performing a device manufacturing process;

determining a second distribution of alignment data derived from a processing parameter in the device manufacturing process, the second distribution comprising alignment data derived from measured data of the processing parameter or comprising alignment data derived from data of the processing parameter obtained from a simulation or model; and

determining, by a hardware computer system, a distribution of alignment data associated with the device manufacturing process as a function of the first and second distributions.

17. The method of claim 16 , wherein the processing parameter comprises one or more selected from: a substrate height or unflatness, a process effect, optical element heating, optical aberration, and/or patterning device writing error.

18. The method of claim 16 , further comprising altering a sampling of metrology data based on the distribution of alignment data.

19. A computer program product comprising a non-transitory computer readable medium having instructions therein, the instructions, upon execution by a computer system, configured to cause the computer system to at least:

determine a first distribution of a first parameter associated with an error or residual in performing a device manufacturing process, the first distribution comprising measured data or data obtained from a simulation or model;

determine a second distribution of a second parameter associated with an error or residual in performing the device manufacturing process, the second distribution comprising measured data or data obtained from a simulation or model; and

determine a distribution of a parameter of interest associated with the device manufacturing process using a function operating on the first and second distributions.

20. A computer program product comprising a non-transitory computer readable medium having instructions therein, the instructions, upon execution by a computer system, configured to cause the computer system to at least:

determine a first distribution of measured alignment data in performing a device manufacturing process;

determine a second distribution of alignment data derived from a processing parameter in the device manufacturing process, the second distribution comprising alignment data derived from measured data of the processing parameter or comprising alignment data derived from data of the processing parameter obtained from a simulation or model; and

determine a distribution of alignment data associated with the device manufacturing process as a function of the first and second distributions.