Discrete sampling based nonlinear control system
View Patent ↗System, method and computer program product including instructions executed by a processor system for configuring and controlling a facility to perform a manufacturing process and updating a tool controlling the process according to a model employed for mapping calculated coefficients that characterize non-linear variations observed of a product to actual control parameters governing the processes/tools used by the facility during the manufacturing process. In a semiconductor manufacturing process, the method enables real-time control of variation in an exposure step of a patterning process using an exposure tool to minimize a nonlinear variation in one or more pattern attributes by adjusting the exposure tool or the patterning process corresponding to the calculated coefficients. In the method, measurements of product attributes, obtained by finite sampling over a well defined domain (e.g., a region such as a field/wafer in lithographic patterning), are projected onto a predefined reference mesh spanning the domain, using a physically based model comprised of functions constructed to be orthogonal and normalized over a discrete set of reference mesh locations.
1. A method for dynamically controlling variation during an exposure step of a patterning process using an exposure tool comprising:
measuring a set of one or more pattern attributes at a set of discrete locations on a substrate, the substrate having two or more fields and at least one field having two or more of the set of discrete locations;
selecting a first set of basis functions representing a first variation of the set of one or more pattern attributes over a first set of discrete locations within a first field, and selecting a second set of basis functions representing a second variation of the set of one or more pattern attributes over a second set of discrete locations within a second field;
defining a first set of reference locations within a field;
defining a second set of reference locations over the substrate;
constructing a first orthogonal set of functions from the first set of basis functions on the first set of reference locations and constructing a second orthogonal set of functions from the second set of basis function on the second set of reference locations; and
constructing a third orthogonal set of basis functions comprised of the first set of basis functions and the second set of basis functions and the product of each of the first set of basis functions with each of the second set of basis functions;
fitting the third orthogonal set of functions to the measured set of one or more pattern attributes at the set of discrete locations;
determining, as a result of said fitting, a set of coefficients of the third orthogonal set of functions; and
minimizing a variation in the one or more pattern attributes by adjusting the exposure tool or the patterning process according to one or more said determined set of coefficients.
2. The method of claim 1 , further comprising:
monitoring a remainder of the set of coefficients which are not used to minimize variations for a diagnostic purpose.
3. A method for controlling a nonlinear variation in a manufacturing step using a process tool comprising:
measuring one or more attributes of a product being manufactured by said process tool at a set of one or more discrete times or locations spanning one or more finite temporal or spatial domains, the product having two or more fields and at least one field having two or more of the set of discrete locations;
selecting a first set of basis functions representing a first variation in the set of one or more product attributes over a first set of discrete locations within a first field, and selecting a second set of basis functions representing a second variation of the set of one or more pattern attributes over a second set of discrete locations within a second field;
defining a set of reference times or locations distributed on the product being manufactured, said defined locations comprising a first set of reference locations within a field and a second set of reference locations over the product;
constructing a first orthogonal set of functions from the first set of basis functions, said first orthogonal set of functions being constructed from the set of basis functions on the defined first set of reference locations, and constructing a second orthogonal set of functions from the second set of basis function on the second set of reference locations;
constructing a third orthogonal set of basis functions comprised of the first set of basis functions and the second set of basis functions and the product of each of the first set of basis functions with each of the second set of basis functions;
fitting the third orthogonal set of functions to the measured set of one or more product attributes at the set of discrete times or locations;
determining, as a result of said fitting, a set of coefficients of the third orthogonal set of functions; and
minimizing a variation in the one or more product attributes by adjusting the process tool corresponding to one or more of the coefficients.
4. The method of claim 3 , wherein the reference times or locations are distributed uniformly and symmetrically about the center of each domain.
5. The method of claim 3 , wherein the manufacturing step is an exposure step of a patterning process in integrated circuit manufacturing, said process tool is an exposure tool, said product is a semiconductor substrate on which one or more patterns are exposed, said measuring performed at said set of discrete locations on the substrate, and said spatial domain is comprised of one or more exposure fields on the substrate.
6. The method of claim 5 , wherein said product attributes include a pattern placement error or overlay error.
7. A system for controlling nonlinear variation in a manufacturing step using a process tool comprising:
a measuring device for dynamically measuring one or more attributes of a product being manufactured at a set of one or more discrete times or locations spanning one or more finite temporal or spatial domains, the product having two or more fields and at least one field having two or more of the set of discrete locations;
a memory device;
a processing device operatively coupled to the memory device and configured to perform a method comprising:
selecting a first set of basis functions representing a first variation in the set of one or more product attributes over a first set of discrete locations within a first field, and selecting a second set of basis functions representing a second variation of the set of one or more pattern attributes over a second set of discrete locations within a second field;
defining a set of reference times or locations distributed on the product being manufactured, said defined locations comprising a first set of reference locations within a field and a second set of reference locations over the product;
constructing a first orthogonal set of the set of functions from the first set of basis functions on the defined first set of reference locations, and constructing a second orthogonal set of functions from the second set of basis function on the second set of reference locations;
constructing a third orthogonal set of basis functions comprised of the first set of basis functions and the second set of basis functions and the product of each of the first set of basis functions with each of the second set of basis functions;
fitting the third orthogonal set of functions to the measured set of one or more product attributes at the set of discrete times or locations;
determining, as a result of said fitting, a set of coefficients of the third orthogonal set of functions; and
minimizing a variation in the one or more product attributes by adjusting the process tool corresponding to one or more of the coefficients.
8. The system of claim 7 , wherein the manufacturing step is an exposure step of a patterning process in integrated circuit manufacturing, said process tool is an exposure tool, said product is a semiconductor substrate on which one or more patterns are exposed, said dynamically measuring performed at a set of discrete locations on the substrate, and said spatial domain is comprised of one or more exposure fields on the substrate.
9. The method of claim 8 , wherein said product attributes include a pattern placement error or overlay error.
10. The system of claim 8 , wherein the substrate has two or more fields and at least one field has two or more of the set of discrete locations, and said second set of reference locations are defined over the substrate, said process tool adjusting comprising adjusting the exposure tool or the patterning process corresponding to one or more coefficients of the set of coefficients of the third orthogonal set of functions.
11. A computer program product for controlling a nonlinear variation in a manufacturing step using a process tool, the computer program device comprising a storage medium readable by a processing circuit and storing instructions run by the processing circuit for performing a method, the method comprising:
initiating a measurement, by a measurement device, of one or more attributes of a product being manufactured by said process tool at a set of one or more discrete times or locations spanning one or more finite temporal or spatial domains, the product having two or more fields and at least one field having two or more of the set of discrete locations;
selecting a first set of basis functions representing a first variation in the set of one or more product attributes over a first set of discrete locations within a first field, and selecting a second set of basis functions representing a second variation of the set of one or more pattern attributes over a second set of discrete locations within a second field;
defining a set of reference times or locations distributed on the product being manufactured, said defined locations comprising a first set of reference locations within a field and a second set of reference locations over the product;
constructing a first orthogonal set of functions from the first set of basis functions on the defined first set of reference locations, and constructing a second orthogonal set of functions from the second set of basis function on the second set of reference locations;
constructing a third orthogonal set of basis functions comprised of the first set of basis functions and the second set of basis functions and the product of each of the first set of basis functions with each of the second set of basis functions;
fitting the third orthogonal set of functions to the measured set of one or more product attributes at the set of discrete times or locations;
determining, as a result of said fitting, a set of coefficients of the third orthogonal set of functions; and
minimizing a variation in the one or more product attributes by adjusting the process tool corresponding to one or more of the coefficients.
12. The computer program product of claim 11 , wherein the manufacturing step is an exposure step of a patterning process in integrated circuit manufacturing, said process tool is an exposure tool, said product is a semiconductor substrate on which one or more patterns are exposed, said measurement performed at a set of discrete locations on the substrate, and said spatial domain is comprised of one or more exposure fields on the substrate.
13. The computer program product of claim 12 , wherein the substrate has two or more fields and at least one field has two or more of the set of discrete locations, and said second set of reference locations are defined over the substrate, said process tool adjusting comprising adjusting the exposure tool or the patterning process corresponding to one or more coefficients of the set of coefficients of the third orthogonal set of functions.