System and method of curve fitting

A system comprising:

• a tool for processing a substrate;
• a central processor unit (CPU);
• memory coupled to said CPU, wherein said memory is operable to store program instructions, and wherein the CPU is operable to execute said program instructions;
• an input device for receiving a plurality of data points, wherein said plurality of data points are representative of measurements of structures formed on said substrate at different settings of said tool;
• wherein said program instructions are executable by said CPU to perform:
• a) fitting a first curve to a first set of data points selected from said plurality of data points;
• b) including other data points from said plurality of data points that are not included in said first set of data points individually with said first set of data points in an iterative manner until an ending criteria is met to form another set of data points in response to another curve fit to said another set of data points upon each iteration that satisfies a first pre-determined condition;
• c) outputting to an output device a curve fitted immediately prior to said ending criteria being met as a best fit curve for said plurality of data points, wherein said output device is coupled to said tool;
• d) determining from said best fit curve a value of a setting for said tool, wherein said value satisfies a third pre-determined condition;
• and
• e) outputting said determined value to said tool;
• and
• means for adjusting said setting for said tool to said determined value.

A method of determining a best focus condition for a photolithographic tool, the method comprising:

• a) providing a substrate including a photoresist layer patterned with a plurality of images formed at different settings of said photolithographic tool;
• b) measuring said plurality of images to obtain a plurality of image size data points, wherein said plurality of image size data points are representative of measurements of said images corresponding respectively to said different settings of said photolithographic tool;
• c) fitting a first curve to a first set of data points selected from said plurality of image size data points;
• d) including other data points from said plurality of image size data points that are not included in said first set of data points individually with said first set of data points in an iterative manner until an ending criteria is met to form another set of data points in response to another curve fit to said another set of data points upon each iteration that satisfies a first pre-determined condition;
• e) accepting a curve fitted immediately prior to said ending criteria being met as a best fit curve for said plurality of image size data points;
• f) determining a best focus condition from said best fit curve, wherein said best focus condition comprises a focus value which satisfies a third pre-determined condition;
• g) inputting said determined focus value to said photolithographic tool;
• and
• h) adjusting a focus of said photolithographic tool to said determined focus value.

A method comprising:

• a) providing a substrate including a plurality of structures formed thereupon, said plurality of structures formed at different settings of a process tool;
• b) measuring said plurality of structures to obtain a plurality of data points, wherein said plurality of data points are representative of measurements of said structures corresponding respectively to said different settings of said process tool;
• c) fitting a first curve to a first set of data points selected from said plurality of data points;
• d) including other data points from said plurality of data points that are not included in said first set of data points individually with said first set of data points in an iterative manner until an ending criteria is met to form another set of data points in response to another curve fit to said another set of data points upon each iteration that satisfies a first pre-determined condition;
• e) accepting a curve fitted immediately prior to said ending criteria being met as a best fit curve for said plurality of data points;
• f) determining an operating condition for said process tool from said best fit curve, wherein said operating condition comprises a value for a setting of said process tool obtained from said best fit curve which satisfies a third pre-determined condition;
• g) inputting said determined value to said process tool;
• and
• h) adjusting said setting of said process tool to said determined value.