Calibration of parametric measurement models based on in-line wafer measurement data
Methods and systems for calibrating simulated measurement signals generated by a parametric measurement model are described herein. Regression on real measurement signals is performed using a parametric model. The residual fitting error between the real measurement signals and simulated measurement signals generated by the parametric model characterizes the error of the parametric model at each set of estimated values of the one or more floating parameters. Simulated measurement signals are generated by the parametric model at specified values of the floating parameters. A residual fitting error associated with the simulated measurement signals generated at the specified values of the floating parameters is derived from the residual fitting errors calculated by the regression on the real measurement signals. The simulated measurement signals are calibrated by adding the residual fitting error to the uncalibrated, simulated measurement signals. The calibrated, simulated measurement signals improve the accuracy of measurements and measurement recipe development.
1 . A method comprising:
receiving real measurement signals associated with measurements of each of a plurality of instances of one or more structures fabricated on one or more semiconductor wafers;
determining a set of estimated values of one or more floating parameters of a parametric measurement model associated with each of the measurements of the plurality of instances of the one or more structures, wherein each set of estimated values of the one or more floating parameters minimizes a residual error, each residual error characterizing a difference between the corresponding real measured signals and a corresponding set of simulated measurement signals generated by the parametric measurement model at each of the sets of estimated values of the one or more floating parameters;
determining a set of simulated measurement signals by evaluating the parametric measurement model at a set of specified values of the one or more floating parameters;
estimating a residual error associated with the specified values of the one or more floating parameters based on the residual errors associated with each of the measurements of the plurality of instances of the one or more structures;
calibrating the set of simulated measurement signals by adding the residual error associated with the specified values of the floating parameters to the set of simulated measurement signals;
receiving real measurement signals associated with a measurement of another instance of the one or more structures;
estimating a value of a parameter of interest characterizing the one or more structures based on the real measurement signals associated with the measurement of another instance of the one or more structures and the calibrated set of simulated measurement signals; and
communicating an indication of the estimated value of the parameter of interest to a semiconductor fabrication tool that causes the semiconductor fabrication tool to adjust one or more parameters of a fabrication process of the semiconductor fabrication tool to achieve a desired output from the semiconductor fabrication tool.
2 . The method of claim 1 , wherein the one or more semiconductor wafers are inline, production wafers.
3 . The method of claim 1 , wherein the measurements of each of a plurality of instances of one or more structures fabricated on one or more semiconductor wafers are optically based spectroscopic measurements or image based scatterometry measurements.
4 . The method of claim 1 , further comprising:
determining a variation of values of each of the one or more floating parameters of the parametric measurement model across the sets of estimated values of the one or more floating parameters of the parametric measurement model associated with the measurements of the plurality of instances of the one or more structures.
5 . The method of claim 4 , further comprising:
generating an expanded set of values of each of the one or more floating parameters based on the determined variations, wherein each expanded set of values is larger than the corresponding set of estimated values.
6 . The method of claim 5 , further comprising:
generating an expanded set of simulated measurement signals by evaluating the parametric measurement model at each of the values of the expanded set of values of each of the one or more floating parameters.
7 . The method of claim 1 , wherein the estimating of the residual error associated with the specified values of the one or more floating parameters involves:
selecting one or more sets of real measurement signals that most closely match the set of simulated measurement signals corresponding to the specified values of the one or more floating parameters; and
estimating the residual error associated with the specified values of the one or more floating parameters based on the residual errors corresponding to the one or more selected sets of real measurement signals.
8 . The method of claim 7 , wherein the selecting of the one or more sets of real measurement signals that most closely match the set of simulated measurement signals involves a K-nearest neighbor search of the sets of real measurement signals.
9 . The method of claim 1 , wherein the estimating of the residual error associated with the specified values of the one or more floating parameters involves:
generating a statistical model of the residual errors characterizing the difference between the corresponding real measured signals and the corresponding set of simulated measurement signals as a function of values of the real measurement signals; and
evaluating the statistical model at the set of simulated measurement signals associated with the specified values of the one or more floating parameters to determine the residual error associated with the specified values of the one or more floating parameters.
10 . A metrology system comprising:
an illumination source configured to generate an amount of illumination light directed to one or more structures fabricated on a semiconductor wafer;
a detector configured to detect an amount of light from the one or more structures in response to the amount of illumination light and generate real measurement signals indicative of the detected light; and
one or more computer systems configured to:
receive real measurement signals associated with measurements of each of a plurality of instances of the one or more structures fabricated on one or more semiconductor wafers;
determine a set of estimated values of one or more floating parameters of a parametric measurement model associated with each of the measurements of the plurality of instances of the one or more structures, wherein each set of estimated values of the one or more floating parameters minimizes a residual error, each residual error characterizing a difference between the corresponding real measured signals and a corresponding set of simulated measurement signals generated by the parametric measurement model at each of the sets of estimated values of the one or more floating parameters;
determine a set of simulated measurement signals by evaluating the parametric measurement model at a set of specified values of the one or more floating parameters;
estimate a residual error associated with the specified values of the one or more floating parameters based on the residual errors associated with each of the measurements of the plurality of instances of the one or more structures;
calibrate the set of simulated measurement signals by adding the residual error associated with the specified values of the floating parameters to the set of simulated measurement signals;
receive real measurement signals associated with a measurement of another instance of the one or more structures;
estimate a value of a parameter of interest characterizing the one or more structures based on the real measurement signals associated with the measurement of another instance of the one or more structures and the calibrated set of simulated measurement signals; and
communicate an indication of the estimated value of the parameter of interest to a semiconductor fabrication tool that causes the semiconductor fabrication tool to adjust one or more parameters of a fabrication process of the semiconductor fabrication tool to achieve a desired output from the semiconductor fabrication tool.
11 . The metrology system of claim 10 , wherein the one or more semiconductor wafers are inline, production wafers.
12 . The metrology system of claim 10 , wherein the measurements of each of a plurality of instances of one or more structures fabricated on one or more semiconductor wafers are optically based spectroscopic measurements or image based scatterometry measurements.
13 . The metrology system of claim 10 , the one or more computing systems further configured to:
determine a variation of values of each of the one or more floating parameters of the parametric measurement model across the sets of estimated values of the one or more floating parameters of the parametric measurement model associated with the measurements of the plurality of instances of the one or more structures.
14 . The metrology system of claim 13 , the one or more computing systems further configured to:
generate an expanded set of values of each of the one or more floating parameters based on the determined variations, wherein each expanded set of values is larger than the corresponding set of estimated values.
15 . The metrology system of claim 14 , the one or more computing systems further configured to:
generate an expanded set of simulated measurement signals by evaluating the parametric measurement model at each of the values of the expanded set of values of each of the one or more floating parameters.
16 . The metrology system of claim 10 , wherein the estimating of the residual error associated with the specified values of the one or more floating parameters involves:
selecting one or more sets of real measurement signals that most closely match the set of simulated measurement signals corresponding to the specified values of the one or more floating parameters; and
estimating the residual error associated with the specified values of the one or more floating parameters based on the residual errors corresponding to the one or more selected sets of real measurement signals.
17 . The metrology system of claim 16 , wherein the selecting of the one or more sets of real measurement signals that most closely match the set of simulated measurement signals involves a K-nearest neighbor search of the sets of real measurement signals.
18 . The metrology system of claim 10 , wherein the estimating of the residual error associated with the specified values of the one or more floating parameters involves:
generating a statistical model of the residual errors characterizing the difference between the corresponding real measured signals and the corresponding set of simulated measurement signals as a function of values of the real measurement signals; and
evaluating the statistical model at the set of simulated measurement signals associated with the specified values of the one or more floating parameters to determine the residual error associated with the specified values of the one or more floating parameters.
19 . A metrology system comprising:
an illumination source configured to generate an amount of illumination light directed to one or more structures fabricated on a semiconductor wafer;
a detector configured to detect an amount of light from the one or more structures in response to the amount of illumination light and generate real measurement signals indicative of the detected light; and
a non-transitory, computer-readable medium storing instructions that, when executed by one or more processors, causes the one or more processors to:
receive real measurement signals associated with measurements of each of a plurality of instances of the one or more structures fabricated on one or more semiconductor wafers;
determine a set of estimated values of one or more floating parameters of a parametric measurement model associated with each of the measurements of the plurality of instances of the one or more structures, wherein each set of estimated values of the one or more floating parameters minimizes a residual error, each residual error characterizing a difference between the corresponding real measured signals and a corresponding set of simulated measurement signals generated by the parametric measurement model at each of the sets of estimated values of the one or more floating parameters;
determine a set of simulated measurement signals by evaluating the parametric measurement model at a set of specified values of the one or more floating parameters;
estimate a residual error associated with the specified values of the one or more floating parameters based on the residual errors associated with each of the measurements of the plurality of instances of the one or more structures;
calibrate the set of simulated measurement signals by adding the residual error associated with the specified values of the floating parameters to the set of simulated measurement signals;
receive real measurement signals associated with a measurement of another instance of the one or more structures;
estimating a value of a parameter of interest characterizing the one or more structures based on the real measurement signals associated with the measurement of another instance of the one or more structures and the calibrated set of simulated measurement signals; and
communicate an indication of the estimated value of the parameter of interest to a semiconductor fabrication tool that causes the semiconductor fabrication tool to adjust one or more parameters of a fabrication process of the semiconductor fabrication tool to achieve a desired output from the semiconductor fabrication tool.
20 . The metrology system of claim 19 , wherein the one or more semiconductor wafers are inline, production wafers, and wherein the measurements of each of a plurality of instances of one or more structures fabricated on one or more semiconductor wafers are optically based spectroscopic measurements or image based scatterometry measurements.