Method and apparatus for controlling an industrial process using product grouping
In a lithographic process in which a series of substrates are processed in different contexts, object data (such as performance data representing overlay measured on a set of substrates that have been processed previously) is received. Context data represents one or more parameters of the lithographic process that vary between substrates within the set. By principal component analysis or other statistical analysis of the performance data, the set of substrates are partitioned into two or more subsets. The first partitioning of the substrates and the context data are used to identify one or more relevant context parameters, being parameters of the lithographic process that are observed to correlate most strongly with the first partitioning. The lithographic apparatus is controlled for new substrates by reference to the identified relevant context parameters. Embodiments with feedback control and feedforward control are described.
1. A method of controlling an industrial process, the method comprising:
receiving object data representing one or more parameters measured in relation to a set of product units that have been subjected to chemical, physical, electrical or mechanical processing of the industrial process;
receiving context data representing a plurality of context parameters that are parameters of the industrial process that vary between product units within the set;
defining, by statistical analysis of the object data, a first partitioning that assigns membership of the product units of the set between two or more subsets, the product units in each subset sharing one or more characteristics observed in the object data;
identifying, at least in part based on the first partitioning of the product units and the context data, a set of one or more relevant context parameters among the context parameters; and
controlling the industrial process for new product units at least partially by reference to the identified set of relevant context parameters among context parameters of the new product units,
wherein the number of identified relevant context parameters used to control the industrial process for the new product units is less than the number of context parameters identified in the received context data, so that some product units subjected to different variations of the industrial process are grouped together for the control of the industrial process for the new product units.
2. The method as claimed in claim 1 , wherein identifying the set of one or more relevant context parameters comprises:
(1) using the first partitioning of the product units and the context data to identify a most relevant context parameter being a parameter of the industrial process that is observed to correlate most strongly with the first partitioning;
(2) using the most relevant context parameter to define a revised partitioning by re-assigning product units to a different subset if necessary to enforce a partitioning with respect to the most relevant context parameter;
(3) repeating step (1) using the revised partitioning to identify a next most relevant context parameter; and
(4) repeating step (2) using the next most relevant context parameter to further revise the first partitioning,
wherein steps (3) and (4) are performed one or more times to identify a desired set of relevant context parameters.
3. The method as claimed in claim 2 , wherein in defining the first partitioning each product unit is assigned to a subset having a highest probability according to the statistical analysis, and in step (2) product units are re-assigned by placing them in a subset having a next highest probability according to the statistical analysis.
4. The method as claimed in claim 1 , wherein the received object data for each product unit defines a vector representing that product unit in a multi-dimensional space, and wherein in defining the first partitioning the statistical analysis comprises a multivariate analysis to decompose the set of the vectors representing the product units in the multidimensional space into one or more component vectors, each of the component vectors representing one of the shared characteristics.
5. The method as claimed in claim 1 , wherein the first partitioning is performed so as to minimize distance between members of each subset within a multidimensional space identified by the statistical analysis.
6. The method as claimed in claim 1 , wherein the received object data for each product unit is derived from one or more parameters measured on the product unit at points spatially distributed across the product unit.
7. The method as claimed in claim 1 , wherein the object data includes performance data representing one or more performance parameters measured on the set of product units after they have been subject to the industrial process.
8. The method as claimed in claim 7 , wherein in controlling the industrial process for the new product units the performance parameters of subsets of previously processed product units are used to generate feedback corrections for new product units, the subsets of the previously processed products being defined by reference to the identified relevant context parameters.
9. The method as claimed in claim 7 , wherein the performance parameters include one or more selected from: overlay, critical dimension, side wall angle, wafer quality, and/or focus.
10. The method as claimed in claim 7 , wherein the received object data comprises parameters of a process model calculated using the measured performance parameters.
11. The method as claimed in claim 1 , wherein in controlling the industrial process for the new product units feedforward corrections are generated and applied in processing of the new product units to modify a feedforward control by reference to the identified relevant context parameters among context parameters of the new product units.
12. The method as claimed claim 1 , wherein in controlling the industrial process for the new product units, object data of the new product units is used to generate feedforward corrections for the new product units, the manner of generating the feedforward corrections being defined by reference to the identified relevant context parameters among context parameters of the new product units.
13. A control system for an industrial process, the control system comprising:
storage for object data representing one or more parameters measured in relation to a set of product units that have been subjected to chemical, physical, electrical or mechanical processing of the industrial process;
storage for context data representing a plurality of context parameters that are parameters of the industrial process that vary between product units within the set; and
a processor system configured to:
define, by statistical analysis of the object data, a first partitioning that assigns membership of the product units of the set between two or more subsets, the product units in each subset sharing one or more characteristics observed in the object data;
use the first partitioning of the product units and the context data to identify a set of one or more relevant context parameters among the context parameters; and
control the industrial process for new product units at least partially by reference to the identified set of relevant context parameters among context parameters of the new product units;
wherein the number of identified relevant context parameters used to control the industrial process for the new product units is less than the number of context parameters identified in the received context data, so that some product units subjected to different variations of the industrial process are grouped together for the control of the industrial process for the new product units.
14. A non-transitory computer program product comprising machine readable instructions configured to cause a data processing apparatus to at least:
receive object data representing one or more parameters measured in relation to a set of product units that have been subjected to chemical, physical, electrical or mechanical processing of an industrial process;
receive context data representing a plurality of context parameters that are parameters of the industrial process that vary between product units within the set;
define, by statistical analysis of the object data, a first partitioning that assigns membership of the product units of the set between two or more subsets, the product units in each subset sharing one or more characteristics observed in the object data; and
identify, at least in part based on the first partitioning of the product units and the context data, a set of one or more relevant context parameters among the context parameters,
wherein the number of identified relevant context parameters for use in control of the industrial process for new product units is less than the number of context parameters identified in the received context data, so that some product units subjected to different variations of the industrial process are grouped together for the control of the industrial process for the new product units.
15. The computer program product of claim 14 , wherein the instructions are further configured to cause the data processing apparatus to control the industrial process for new product units at least partially by reference to the identified set of relevant context parameters among context parameters of the new product units.
16. The computer program product of claim 14 , wherein the instructions configured to identify the set of one or more relevant context parameters are further configured to at least:
(1) using the first partitioning of the product units and the context data to identify a most relevant context parameter being a parameter of the industrial process that is observed to correlate most strongly with the first partitioning;
(2) using the most relevant context parameter to define a revised partitioning by re-assigning product units to a different subset if necessary to enforce a partitioning with respect to the most relevant context parameter;
(3) repeating step (1) using the revised partitioning to identify a next most relevant context parameter; and
(4) repeating step (2) using the next most relevant context parameter to further revise the first partitioning,
wherein steps (3) and (4) are performed one or more times to identify a desired set of relevant context parameters.
17. The computer program product of claim 14 , wherein the received object data for each product unit defines a vector representing that product unit in a multi-dimensional space, and wherein in definition of the first partitioning the statistical analysis comprises a multivariate analysis to decompose the set of the vectors representing the product units in the multidimensional space into one or more component vectors, each of the component vectors representing one of the shared characteristics.
18. The computer program product of claim 14 , wherein the first partitioning is performed so as to minimize distance between members of each subset within a multidimensional space identified by the statistical analysis.
19. The computer program product of claim 14 , wherein the received object data for each product unit is derived from one or more parameters measured on the product unit at points spatially distributed across the product unit or wherein the object data includes performance data representing one or more performance parameters measured on the set of product units after they have been subject to the industrial process.
20. The computer program product of claim 14 , wherein the instructions are further configured to cause the computer system to generate feedforward corrections for application in processing of the new product units to modify a feedforward control by reference to the identified relevant context parameters among context parameters of the new product units.