Calibration of parametric measurement models based on in-line wafer measurement data

Abstract

Methods and systems for calibrating analog measurement signals generated by a parametric measurement model are described herein. Regression of the real measurement signal is performed using the parametric model. A residual fit error between the real measurement signal and an analog measurement signal produced by the parametric model characterizes an error of the parametric model for each set of estimated values of one or more floating parameters. An analog measurement signal is generated by the parametric model at a specified value of the floating parameter. A residual fit error associated with the analog measurement signal generated at the specified value of the floating parameter is derived from the residual fit error calculated by the regression of the real measurement signal. The analog measurement signal is calibrated by adding the residual fit error to an uncalibrated analog measurement signal. The calibrated analog measurement signal improves the accuracy of the measurement and the development of the measurement recipe.

Description

[0001] Cross - Reference to Related Applications

[0002] This patent application claims priority to U.S. Provisional Patent Application Ser. No. 63 / 409,842, filed Sep. 26, 2022, entitled “Methods for Calibrating the Error of Parametric Models in Simulated Synthetic Spectra Using Inline Wafers for Optical-Based Metrology”, under 35 U.S.C. § 119, the entire disclosure of which is hereby incorporated by reference. TECHNICAL FIELD

[0003] The described embodiments relate to systems for wafer metrology, and more particularly, to the characterization and defect detection of semiconductor structures and materials. BACKGROUND ART

[0004] Semiconductor devices, such as logic and memory devices, are typically fabricated by a sequence of processing steps applied to a sample. Various features and multiple structural layers of the semiconductor device are formed by these processing steps. For example, lithography is in particular a semiconductor manufacturing process involving the generation of patterns on a semiconductor wafer. Additional examples of semiconductor manufacturing processes include, but are not limited to, chemical mechanical polishing, etching, deposition, and ion implantation. Multiple semiconductor devices can be fabricated on a single semiconductor wafer and then separated into individual semiconductor devices.

[0005] During various steps in the semiconductor manufacturing process, metrology processes are used to detect defects on the wafer to facilitate higher yields. Metrology techniques offer the possibility of high throughput without the risk of sample destruction. Several optical and x-ray-based techniques, typically using scatterometry, ellipsometry, and reflectometry implementations, as well as associated analysis algorithms, are used to characterize critical dimensions, film thickness, composition, and other parameters of nanoscale structures.

[0006] Many metrology techniques for measuring semiconductor structures with high throughput are model-based. Metrology techniques are indirect methods of measuring the physical properties of a sample under test, i.e., the measured values cannot be used to directly determine the physical properties of the sample. In these cases, the nominal measurement process consists of a measurement model that formulates an estimate of the measured value for a given measurement case. The measurement model characterizes the interaction between the sample and the measurement system. The measurement model includes a parametric model of the structure under measurement parameterized by various geometric and material parameters (e.g., film thickness, critical dimension, etc.) and a model of the measurement system parameterized by various machine parameters (e.g., wavelength, angle of incidence, polarization angle, etc.).

[0007] The parametric model of the structure under measurement includes floating parameters and fixed parameters. The values of the floating parameters change during the measurement process, while the values of the fixed parameters remain at constant nominal values during the measurement process. Generally, the fixed parameters represent the dimensions of structural features that do not vary significantly for a particular measurement application, while the floating parameters represent the dimensions of structural features that vary significantly for a particular measurement application and have a significant effect on the magnitude of the measurement signal (e.g., measured image, spectrum, etc.).

[0008] The parametric model of the structure under measurement is directly employed in the measurement process. In some instances, an electromagnetic simulation engine operates on the parametric model of the structure under measurement to generate synthetic measurement data. In model-based measurement applications, a regression process (e.g., ordinary least squares regression) is employed to identify the sample parameter values that minimize the difference between the synthetic measurement data and the experimental measurement values. For measurement purposes, the system parameters and some of the structural parameters are treated as known fixed parameters and some of the structural parameters are treated as unknown floating parameters. The floating parameters are solved by an iterative process (e.g., regression) that produces the best fit between the synthetic measurement data and the experimental measurement values.

[0009] In addition, the parametric model of the structure under measurement is indirectly employed during the measurement process. Synthetic measurement data generated based on the parametric model of the structure under measurement is widely used to simulate the variation of the measurement signal for different manufacturing process conditions. Subsequently, the determined sensitivities are used to characterize the measurement capabilities and related measurement performance. In this way, the parametric model of the structure under measurement is critical for the development of a specific measurement recipe for measurement applications.

[0010] As devices (e.g., logic and memory devices) scale towards smaller nanoscale dimensions, characterization becomes more difficult. Devices incorporating complex three-dimensional geometries and materials with different physical properties contribute to the characterization difficulties. As devices become more complex and the measurement requirements become more stringent, the parametric models become more complex and error-prone. Thus, parametric modeling error is a significant limitation in the development of measurement recipes and measurement execution for complex measurement applications.

[0011] Parameter model errors include systematic errors and structural characterization errors. Systematic errors include errors in the characterization of the hardware configuration of the measurement system (e.g., angle of incidence, azimuth angle, etc.). To minimize these errors, the system parameters are perturbed until an optimal match between the synthetic measurement data and the actual measurement data is achieved. Structural characterization errors reflect the failure of the parameter model to fully characterize the measured structure. For example, structural variations induced by real process conditions may not be captured by a particular parameter model.

[0012] Traditionally, minimization of structural characterization errors has been achieved in the same manner as systematic errors, i.e., by perturbing a set of fixed structure parameters until an optimal match between the synthetic measurement data and the actual measurement data is achieved. This requires identifying the set of fixed parameters of the parameter model and defining a range of perturbation values for the parameters that represent the actual structural variations induced by real manufacturing process conditions.

[0013] Unfortunately, this method has proven ineffective for increasingly complex parameter models. More specifically, it has become increasingly difficult to identify the set of fixed parameters to be perturbed and also difficult to determine the range of perturbation values for the parameters that will accurately represent the actual process variations. Additionally, the use of synthetic spectra to characterize the measurement capabilities based on measurement libraries, regression, or both is impaired by inaccurate parameter models. More specifically, it is difficult to reproduce the real measurement data using the synthetically generated measurement data without properly calibrating the parameter model errors.

[0014] Proper calibration of parameter model errors is becoming a challenge in the development and execution of measurement recipes for complex measurement applications. Process and yield control in both research and development and manufacturing environments require improved calibration of parameter models to meet the requirements of the semiconductor manufacturing industry. Accordingly, there is a need for methods and systems for improved calibration of parameter models. SUMMARY OF THE INVENTION

[0015] Methods and systems are described herein for calibrating simulated measurement signals generated by a parameter measurement model. Real measurement signals are obtained from measurements of different examples of one or more structures fabricated on a semiconductor wafer. In a preferred embodiment, the semiconductor wafer is an in-line production wafer that captures the structural variations induced by the real manufacturing process. A regression of the real measurement signals is performed using the parameter model for each set of real measurement signals. Each regression results in a set of estimated values of floating parameters and a residual fit error between the real measurement signals and the simulated measurement signals generated by the parameter model at the estimated values of the floating parameters. The residual error characterizes the remaining difference between the real measurement signals and the simulated measurement signals. In this sense, the residual error characterizes the error of the parameter model at each set of estimated values of one or more floating parameters.

[0016] The simulated measurement signal is generated by a parametric model at specified values of floating parameters. The residual fitting error associated with the simulated measurement signal generated at the specified values of the floating parameters is derived from the residual fitting error calculated by regression on the true measurement signal. The simulated measurement signal is calibrated by adding the residual fitting error associated with the specified values of the floating parameters to the value of the simulated measurement signal. In this way, the calibrated simulated measurement signal more accurately reproduces the expected value of the true measurement signal associated with the measurement of the structure characterized by the specified values of the floating parameters.

[0017] In some embodiments, one or more sets of true measurement signals that most closely match the set of simulated measurement signals corresponding to the specified values of one or more floating parameters are selected, and the residual error associated with the specified values of the one or more floating parameters is estimated based on the residual errors corresponding to the one or more selected sets of true measurement signals.

[0018] In some of these embodiments, one or more sets of true measurement signals that most closely match the set of simulated measurement signals are selected based on a k-nearest neighbor search of the set of true measurement signals. The k-nearest neighbor search identifies k different sets of true measurement signals that most closely match the set of simulated measurement signals under consideration.

[0019] Generally, k can be any positive integer value. In some embodiments, k equals 1. In these instances, the simulated signal associated with the specified values of the one or more floating parameters is calibrated by adding the residual error associated with the selected set of true measurement signals to the simulated signal associated with the specified values of the one or more floating parameters. In some other embodiments, k is a positive integer value greater than 1. In these instances, the simulated signal associated with the specified values of the one or more floating parameters is calibrated by adding the average residual error associated with the selected set of true measurement signals to the simulated signal associated with the specified values of the one or more floating parameters.

[0020] In some other embodiments, the residual error associated with the specified values of the one or more floating parameters is estimated based on a statistical model of the values of the true measurement signals. The statistical model is evaluated under 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.

[0021] In a further aspect, the variation in the value of each of the one or more floating parameters of the parametric measurement model is determined across a set of estimated values of the one or more floating parameters of the parametric measurement model. In this way, the range of variation in the geometric profile of the measured structure is estimated based on the true measurements of examples of one or more structures on an in-line production wafer.

[0022] In a further aspect, an extended set of values for each of one or more floating parameters is generated based on the determined variations. Each extended set of values is greater than the corresponding set of estimated values. In these embodiments, variations in the values of geometric profile parameters estimated based on true measurements are employed to determine the range of structural variations spanned by the specified values of the floating parameters.

[0023] In another further aspect, an extended set of simulated measurement signals is generated by evaluating a parameter measurement model at each of the values in the extended set of values for each of one or more floating parameters. In some embodiments, the calibrated simulated measurement signals are employed to generate an extended measurement library.

[0024] The foregoing is a summary and thus necessarily contains simplifications, generalizations, and omissions of detail. Accordingly, those skilled in the art will appreciate that the summary is illustrative only and is not limiting in any way. Other aspects, inventive features, and advantages of the apparatus and / or processes described herein will become apparent from the non-limiting detailed description set forth herein. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is a simplified diagram illustrating a metrology system 100 that can operate in accordance with a method for calibration of simulated measurement signals as described herein.

[0026] Figure 2 is a graph 130 showing values of a measured spectral signal α for several different measurement examples of a structure fabricated on an in-line production wafer.

[0027] Figure 3 is illustrative of after fitting to the true measurement signal depicted in Figure 2 is a graph 131 showing values of a simulated spectral signal α.

[0028] Figure 4 is illustrative of Figure 3 is a graph 132 showing residual errors associated with the fitting of the values of the simulated spectral signal depicted in Figure 4 to the true measurement signal depicted in

[0029] Figure 5 is a graph 133 showing values of a simulated spectral signal α associated with specified values of a floating parameter.

[0030] Figure 6 is illustrative of Figure 5 is a graph 134 showing values of residual errors associated with specified values of a floating parameter as illustrated in

[0031] Figure 7 is illustrative of Figure 5 is a graph 135 showing values of a calibrated composite spectrum associated with specified values of a floating parameter as illustrated in

[0032] Figure 8 Table 140 illustrates the performance difference between a relatively small library and a relatively large library in terms of the evaluation of the maximum measurement deviation based on the use of actual measured spectra, uncalibrated simulated measurement spectra, and calibrated simulated measurement spectra as input spectra.

[0033] Figure 9 Figure 200 is a flowchart illustrating a method for calibrating a simulated measurement signal as described herein. DETAILED DESCRIPTION

[0034] Reference will now be made in detail to the background examples and some embodiments of the present invention, examples of which are illustrated in the accompanying drawings.

[0035] Methods and systems are described herein for estimating parametric model error and calibrating simulated measurement signals generated by a parametric model. True measurement signals are obtained from measurements of different examples of one or more structures fabricated on a semiconductor wafer. In a preferred embodiment, the semiconductor wafer is an in-line production wafer that captures the structural variations induced by the actual manufacturing process. For each set of true measurement signals (i.e., each measurement example), a regression of the true measurement signals is performed using a parametric model. The floating parameters of the parametric model are treated as regression parameters. Each regression results in a set of estimated values of the floating parameters and a residual fitting error between the true measurement signal and the simulated measurement signal generated by the parametric model at the estimated values of the floating parameters.

[0036] The simulated measurement signal is generated by the parametric model at a specified value of the floating parameters. The parametric model error embedded in the simulated measurement signal is estimated as the residual fitting error associated with the specified value of the floating parameters. The residual fitting error is derived from the residual fitting error calculated during the regression of the true measurement signals.

[0037] The simulated measurement signal is calibrated by adding the residual fitting error associated with the specified value of the floating parameters to the value of the simulated measurement signal. In this way, the calibrated simulated measurement signal more accurately reproduces the expected value of the true measurement signal associated with the measurement of a structure characterized by the specified value of the floating parameters. In some instances, the calibrated simulated measurement signal more accurately reproduces the variations in the measurement signal resulting from measurements of actual wafers. The calibrated simulated measurement signal as described herein can improve the performance of model-based measurements, measurement recipe development, or both.

[0038] Figure 1 Illustrated is a metrology system 100 for measuring the characteristics of a semiconductor wafer according to the exemplary methods presented herein. As Figure 1As shown, system 100 can be used to perform spectroscopic ellipsometry of one or more structures 114 of a semiconductor wafer 112 placed on a wafer positioning system 110. In this regard, system 100 can include a spectroscopic ellipsometer (SE) 101 equipped with an illuminator 102 and a spectrometer 104. The illuminator 102 of system 100 is configured to generate illumination in a selected wavelength range (e.g., 150 to 850 nm, 190 to 850 nm, 240 to 850 nm, etc.) and direct the illumination to the structure 114 placed on the surface of the semiconductor wafer 112. Subsequently, the spectrometer 104 is configured to receive the illumination reflected from the surface of the semiconductor wafer 112. Further note that a polarization state generator 107 is used to polarize the light exiting the illuminator 102 to generate a polarized illumination beam 106. The radiation reflected by the structure 114 placed on the wafer 112 travels through the polarization state analyzer 109 and to the spectrometer 104. With respect to polarization state analysis, the radiation received by the spectrometer 104 in the collection beam 108 is collected, thereby allowing spectroscopic analysis of the radiation transmitted by the analyzer by the spectrometer. The measured spectrum 111 is communicated to the computing system 116 for analysis of the structure 114.

[0039] In a further embodiment, the metrology system 100 is a measurement system 100 that can include one or more computing systems 116 for performing calibration of analog measurement signals according to the methods described herein. The one or more computing systems 116 can be communicatively coupled to the spectrometer 104. In one aspect, the one or more computing systems 116 are configured to receive measurement data 111 associated with the measurement of the structure 114 of the sample 112. In one example, the measurement data 111 includes an indication of the spectral response of the sample measured by the target measurement system 100 based on one or more sampling processes from the spectrometer 104.

[0040] It should be recognized that the various elements described throughout this disclosure can be implemented by a single computer system 116 or alternatively by multiple computer systems 116. Moreover, different subsystems of system 100 (e.g., the spectroscopic ellipsometer 101) can include computer systems suitable for implementing at least part of the steps described herein. Thus, the foregoing description should not be construed as a limitation on the invention but only as an illustration. In addition, the one or more computing systems 116 can be configured to perform any other steps of any of the method embodiments described herein. Moreover, some or all of the one or more computing systems 116 can be located remote from the site of wafer measurement. For example, elements of the computing system 116 configured to perform any of the calibration blocks described herein can be located at another facility located remote from the site of the measurement wafer.

[0041] In this regard, it is not required that spectral acquisition of spectral data and subsequent analysis be performed simultaneously or in spatially close proximity. For example, spectral data can be stored in a memory for subsequent analysis. In another example, spectral results can be obtained and transmitted to a computing system located at a remote location for analysis.

[0042] Additionally, computer system 116 can be communicatively coupled to the illuminator subsystem 102 of spectrometer 104 and ellipsometer 101 in any manner known in the art. For example, one or more computing systems 116 can be coupled to the computing systems of spectrometer 104 and illuminator subsystem 102 of ellipsometer 101. In another instance, spectrometer 104 and illuminator 102 can be controlled by a single computer system. In this way, the computer system 116 of system 100 can be coupled to a single ellipsometer computer system.

[0043] The computer system 116 of system 100 can be configured to receive and / or acquire data or information from subsystems of the system (such as spectrometer 104, illuminator 102, and the like) via a transmission medium that can include wired and / or wireless portions. In this way, the transmission medium can serve as a data link between the computer system 116 and other subsystems of system 100. Additionally, computing system 116 can be configured to receive measurement data via a storage medium (i.e., memory). For example, spectral results obtained using the spectrometer of ellipsometer 101 can be stored in a permanent or semi-permanent memory device (not shown). In this regard, spectral results can be imported from an external system.

[0044] Furthermore, computer system 116 can send data to an external system via the transmission medium. The computer system 116 of system 100 can be configured to receive and / or acquire data or information from other systems (such as inspection results from an inspection system or metrology results from a metrology system) via a transmission medium that can include wired and / or wireless portions. In this way, the transmission medium can serve as a data link between the computer system 116 and other subsystems of system 100. Furthermore, computer system 116 can send data to an external system via the transmission medium.

[0045] Computing system 116 can include, but is not limited to, a personal computer system, a mainframe computer system, a workstation, a cloud-based computing system, an image computer, a parallel processor, or any other device known in the art. Generally speaking, the term "computing system" can be broadly defined to cover any device having one or more processors that execute instructions from a memory medium.

[0046] Program instructions 120 for implementing a method such as the methods described herein may be transmitted via or stored on a carrier medium 118. The carrier medium may be a transmission medium, such as a wire, cable, or wireless transmission link. The carrier medium may also include a computer-readable medium, such as a read-only memory, random access memory, solid-state memory, magnetic disk, or optical disk, or magnetic tape.

[0047] may be further configured as described herein Figure 1 an embodiment of the system 100 as illustrated in. Additionally, the system 100 may be configured to perform any other block of any of the method embodiments described herein.

[0048] As Figure 1 As illustrated in, a beam of broadband radiation from the illuminator 102 is linearly polarized in the polarization state generator 107, and the linearly polarized beam is then incident on the sample 112. After reflection from the sample 112, the beam propagates towards the polarization state analyzer 109 with a changed polarization state. In some instances, the reflected beam has elliptical polarization. The reflected beam propagates through the polarization state analyzer 109 into the spectrometer 104. In the spectrometer 104, beam components having different wavelengths are refracted (e.g., in a prism spectrometer) or diffracted (e.g., in a grating spectrometer) in different directions to different detectors. The detector may be a linear array of photodiodes, where each photodiode measures radiation in a different wavelength range.

[0049] In one example, the computing system 116 receives the measured data (e.g., raw measurement data) from each detector and is programmed with software to process the data it receives in an appropriate manner. The measured spectral response of the sample may be determined by analyzing the change in polarization of the radiation reflected from the sample in response to incident radiation having a known polarization state in any number of ways known in the art.

[0050] Either the polarization state generator 107 or the polarization state analyzer 109 may be configured to rotate about its optical axis during a measurement operation. In some instances, the computing system 116 is programmed to generate control signals to control the angular orientation of the polarization state generator 107 and / or the polarization state analyzer 109 or other elements of the system 100 (e.g., the wafer positioning system 110 on which the sample 112 is placed). The computing system 116 may also receive data indicating the angular orientation of the polarization state analyzer 109 from an analyzer position sensor associated with the polarization state analyzer 109. Similarly, the computing system 116 may also receive data indicating the angular orientation of the polarization state generator 107 from a polarizer position sensor associated with the polarization state generator 107. The computing system 116 may be programmed with software to process this orientation data in an appropriate manner.

[0051] In one embodiment, the polarization state generator 107 is a linear polarizer that is controlled to rotate at a constant speed, and the polarization state analyzer is a non-rotating linear polarizer ("analyzer"). The signal received at each detector of the spectrometer 104 (i.e., the raw measurement data) will be the time-varying intensity described by Equation (1),

[0052] I(t) = I 0 [1 + α cos(2ωt - P 0 ) + β sin(2ωt - P 0 )] (1)

[0053] where I 0 is a constant that depends on the intensity of the radiation emitted by the illuminator 102, ω is the angular velocity of the polarization state generator 107, P 0 is the angle between the optical axis of the polarization state generator 107 and the plane of incidence at the initial time (t = 0) (e.g., Figure 1 the plane of), and α and β are values defined as described by Equations (2) and (3),

[0054] α = [tan 2 Ψ - tan 2 (A - A 0 )] / [tan 2 Ψ + tan 2 (A - A 0 )] (2)

[0055] and

[0056] β = [2(tan Ψ)(cos Δ)(tan(A - A 0 ))] / [tan 2 Ψ + tan 2 (A - A 0 )] (3)

[0057] where tan(Ψ) is the amplitude of the complex ratio of the p and s reflection coefficients of the sample, and Δ is the phase of the complex ratio of the p and s reflection coefficients of the sample. The "p" component represents the component of the polarized radiation whose electric field is in the Figure 1 plane, and "s" represents the component of the polarized radiation whose electric field is perpendicular to the Figure 1 plane. A is the nominal analyzer angle (e.g., a measured value of the orientation angle supplied from the aforementioned analyzer position sensor associated with the polarization state analyzer 109). A 0 is the offset of the actual orientation angle of the polarization state analyzer 109 from the reading "A" (e.g., due to machine misalignment, A 0 can be non-zero).

[0058] Generally, the spectral response of a sample to a measurement is a function of the metrology system based on spectral data S and a subset P of the system parameter values sys1 calculated as illustrated by equations (4) and (5).

[0059] α meas = m(P sys1 , S) (4)

[0060] β meas = n(P sys1 , S) (5)

[0061] The subset P of the system parameter values sys1 are those system parameters required to determine the spectral response of the sample to the measurements performed by the metrology system.

[0062] For the embodiment described with reference Figure 1 the subset of system parameters includes the machine parameters of equations (1) through (3). The values of α meas and β meas are determined based on the measurements of metrology system 100 on a particular sample and the subset of system parameter values as described by equations (1) through (3).

[0063] Generally, ellipsometry is an indirect method of measuring the physical properties of a sample under test. In most cases, the measured values (e.g., α meas and β meas ) cannot be used to directly determine the physical properties of the sample. The nominal measurement process consists of a parametric measurement model that formulates estimates of the measured values (e.g., α meas and β meas ) for a given measurement case. The measurement model characterizes the interaction of the sample with the measurement system. The measurement model includes parameterizations of the structure (e.g., film thickness, critical dimension, etc.) and the machine (e.g., wavelength, angle of incidence, angle of polarization, etc.). As illustrated in equations (6) and (7), the measurement model includes parameters associated with the machine (P machine ) and parameters associated with the sample (P specimen ).

[0064] α model = f(P machine , P specimen ) (6)

[0065] β model = g(P machine , P specimen (7)

[0066] Machine parameters are parameters used to characterize metrology tools (e.g., ellipsometer 101) and may include some or all of a subset of the system parameters described by reference equations (4) and (5). Exemplary machine parameters include angle of incidence (AOI), analyzer angle (A0), polarizer angle (P0), illumination wavelength, numerical aperture (NA), etc.

[0067] Sample parameters are parameters used to characterize a sample (e.g., sample 112 including structure 114). For thin film samples, exemplary sample parameters include refractive index, dielectric function tensor, nominal layer thickness of all layers, layer sequence, etc. For measurement purposes, machine parameters are considered known fixed parameters and some or all of the sample parameters are considered unknown floating parameters. The floating parameters are solved by an iterative process (e.g., regression) that produces the best fit between the theoretical prediction and the experimental data. Changing the unknown sample parameter P specimen and calculating the model output values (e.g., α model and β model ) until a set of sample parameter values that result in a close match between the model output values and the experimental measurement values (e.g., α meas and β meas ) is determined.

[0068] In model-based measurement applications (e.g., spectroscopic ellipsometry), a regression process (e.g., ordinary least squares regression) is employed to identify sample parameter values that minimize the difference between the model output values and the experimental measurement values for a fixed set of machine parameter values and a fixed set of any sample parameters not considered unknown floating parameters.

[0069] In one aspect, a method and system for calibrating a simulated measurement signal generated by a parameter measurement model are presented. In this way, the calibrated simulated measurement signal more accurately reproduces the expected value of the true measurement signal associated with the measurement of a structure characterized by a specified value of a floating parameter. In Figure 1 the embodiment depicted, the computing system 116 is further configured to determine the value of at least one sample parameter associated with the measured structure based on the calibrated simulated measurement signal.

[0070] In a further aspect, the true measurement signal generated by a metrology system (e.g., metrology system 100) is received by a computing system (e.g., computing system 116). The true measurement signal is associated with the measurement of each of a plurality of examples of one or more structures fabricated on one or more semiconductor wafers. Equation (8) illustrates the true measurement signal M that includes n sets of measurement signals mi, where i is an index from 1 to n, and where n is any positive integer. Each set of measurement signals corresponds to a measurement example of one or more measured structures.

[0071] M = {m 1 ,m2 ,..., m n} (8)

[0072] In the embodiment depicted in Figure 1 , the measurement signal 116 is a true measurement signal collected from different examples of one or more structures 114 fabricated on the wafer 112, i.e., a spectrum. The one or more structures include metrology targets, device structures, surrogate structures, etc. Different examples of the one or more structures include repeated examples of the same measured nominal structure. In a preferred embodiment, the true measurement signal is collected from an in-line production wafer representative of the actual variations in the process used to fabricate the measured structure.

[0073] In addition, a set of estimates of one or more floating parameters of a parametric measurement model associated with each of the measurements of the multiple examples of the one or more structures is determined. Each set of estimates is determined by regression of the true measurement data using the parametric measurement model that simulates the actual measurement. The values of the floating parameters of the parametric measurement model are solved by the regression to minimize an error function that governs the regression. The error function characterizes the difference between the true measurement signal and the simulated measurement signal. Equation (9) illustrates a simulated measurement signal S that includes n sets of simulated measurement signals si corresponding to the true measurement signal mi illustrated in Equation (8). The value of the simulated measurement signal S is determined at the estimates of the one or more floating parameters at the final iteration of the regression.

[0074] S = {s 1 , s 2 ,..., s n} (9)

[0075] At the termination of the regression, the residual error characterizes the remaining difference between the true measurement signal and the simulated measurement signal. In this sense, the residual error characterizes the error of the parametric model at each set of estimates of the one or more floating parameters. Equation (10) illustrates a residual error signal R that includes n sets of residual error signals ri corresponding to the true measurement signal mi illustrated in Equation (8). As illustrated by Equation (11), each set of the residual error signal ri is calculated as the difference between the true measurement signal m i and the corresponding simulated measurement signal s i .

[0076] R = {r 1 , r 2 ,…, r n} (10)

[0077] r i = m i ― s i (11)

[0078] For example, the residual error associated with spectral measurements is the difference between the true measurement signal and the simulated measurement signal at each wavelength (i.e., the residual error spectrum). In another example, the residual error associated with image-based measurements (e.g., scatterometry images) is the difference between the true measurement signal and the simulated measurement signal at each pixel of the image (i.e., the residual error image).

[0079] Each set of true measurement signals, the corresponding set of estimated values of one or more floating parameters, and the corresponding residual errors are stored in a memory (e.g., carrier medium 118). In a preferred embodiment, the set of true measurement signals, the corresponding floating parameter values, and the corresponding residual errors span the process variation space associated with the structure being measured, and thus capture parameter model error information across the process space.

[0080] In a further aspect, a set of simulated measurement signals is determined by evaluating a parameter measurement model at different sets of specified values of one or more floating parameters. The set of simulated measurement signals is evaluated without calibration, and thus, contains the errors inherent in the parameter measurement model. Equation (12) illustrates the simulated measurement signal T that includes m sets of simulated measurement signals.

[0081] T = {t 1 ,t 2 ,...,t m} (12)

[0082] In many instances, the specified values of the floating parameters are different from the estimated values of the floating parameters determined during the regression of the measurement signals. However, in general, the specified values can be the same as or different from the estimated values of the floating parameters determined during the regression of the measurement signals.

[0083] In addition, in many instances, the number of sets of specified values is much larger than the number of sets of true measurement signals, i.e., m is greater than n. In many instances, the sets of specified values are synthetically generated by the user of the metrology system to span the expected range of the geometric profile of one or more structures being measured at a resolution higher than that of the available sets of true measurement signals. For example, the number of available sets of true measurement signals can be in the hundreds, while the number of sets of specified values can be in the thousands or tens of thousands.

[0084] In a further aspect, a residual error associated with a specified value of one or more floating parameters is determined based on each of the measurements of a plurality of examples of one or more structures. Additionally, each set of simulated measurement signals is calibrated by adding the residual error associated with the specified value of the floating parameter to the set of simulated measurement signals. Errors associated with each set of simulated measurement signals (i.e., errors inherent in the parameter measurement model evaluated at each set of values of the floating parameter) are corrected based on residual errors derived from true measurements of in-line production wafers. In this way, the calibrated synthetic spectra more accurately reproduce the variations of the true measurement signals.

[0085] The error associated with each set of specified values of one or more floating parameters is illustrated by Equation (13).

[0086] E = {e 1 , e 2 , ..., e m} (13)

[0087] Each set of calibrated simulated measurement signals c k is calculated as the sum of the uncalibrated simulated measurement signals t k and the corresponding error e k , as illustrated by Equation (14), where k is an index from 1 to m, and m is any positive integer.

[0088] c k = t k + e k (14)

[0089] The resulting set of calibrated simulated measurement signals C is illustrated by Equation (15).

[0090] C = {c 1 , c 2 , ..., c m} (15)

[0091] In some embodiments, one or more sets of true measurement signals that most closely match the set of simulated measurement signals corresponding to the specified values of one or more floating parameters are selected, and the residual error associated with the specified values of one or more floating parameters is estimated based on the residual errors corresponding to the one or more selected sets of true measurement signals.

[0092] In some of these embodiments, a K-nearest neighbor search based on a set of real measurement signals M selects one or more sets of real measurement signals that most closely match a set of simulated measurement signals. The K-nearest neighbor search of M identifies k different sets of real measurement signals that most closely match the set of simulated measurement signals under consideration. Generally, k can be any positive integer value. In some embodiments, k equals 1. In these instances, the residual error associated with the selected set of real measurement signals is considered the residual error associated with a specified value of one or more floating parameters. In these instances, the simulated signal associated with the specified value of one or more floating parameters is calibrated by adding the residual error associated with the selected set of real measurement signals to the simulated signal associated with the specified value of one or more floating parameters. In some other embodiments, k is a positive integer value greater than 1. In these instances, the residual errors associated with the selected sets of real measurement signals are averaged, and the average residual error is considered the residual error associated with a specified value of one or more floating parameters. In these instances, the simulated signal associated with the specified value of one or more floating parameters is calibrated by adding the average residual error associated with the selected sets of real measurement signals to the simulated signal associated with the specified value of one or more floating parameters.

[0093] In some other embodiments, the residual error associated with a specified value of one or more floating parameters is estimated based on a statistical model. In these embodiments, a statistical model is generated that characterizes the difference between each set of real measurement signals and the corresponding set of simulated measurement signals. The statistical model is a function of the values of the real measurement signals.

[0094] In one instance, a Gaussian model of the residual error associated with the real measurement signals is generated. The Gaussian model specifies the values of the residual error across a range of values of the real measurement signals. For example, for spectral measurements, the Gaussian model specifies the values of the residual error across a range of values of the spectral signal (e.g., α) for each wavelength. Equation (16) illustrates the Gaussian model in one instance, where N is the Gaussian distribution of the value of the residual error associated with the spectral signal α at wavelength λ, μ is the mean of the Gaussian distribution N, and σ is the standard deviation of the Gaussian distribution N.

[0095] N(μ, σ; λ, α) (16)

[0096] For image-based measurements, the Gaussian model specifies the values of the residual error across a range of values of the measured intensity for each pixel.

[0097] The statistical model is evaluated under the set of simulated measurement signals associated with the specified value of one or more floating parameters to determine the residual error associated with the specified value of one or more floating parameters.

[0098] In a further aspect, a set of estimated values of one or more floating parameters of a cross-parameter measurement model determines the variation in the value of each of the one or more floating parameters of the parameter measurement model. In this way, the range of variation of the geometric profile of the measured structure is estimated based on the true measurements of examples of one or more structures on an in-line production wafer.

[0099] In a further aspect, an extended set of values for each of the one or more floating parameters is generated based on the determined variation. Each extended set of values is greater than the corresponding set of estimated values. In these embodiments, the variation in the value of the geometric profile parameter estimated based on true measurements is used to determine the range of structural variation spanned by a specified value of the floating parameter.

[0100] In another further aspect, an extended set of simulated measurement signals is generated by evaluating the parameter measurement model at each of the values in the extended set of values for each of the one or more floating parameters.

[0101] Figure 2 is a graph 130 illustrating the value of the measured spectral signal α for several different measurement examples. The measured spectral signal is the true measurement signal of a structure fabricated on an in-line production wafer.

[0102] Figure 3 is illustrative of the Figure 2 graph 131 of the value of the simulated spectral signal α after fitting to the true measurement signal depicted in

[0103] Figure 4 is illustrative of the Figure 3 residual error (i.e., the difference between the value of the simulated spectral signal and the true measurement signal) associated with the fitting of the value of the simulated spectral signal depicted in Figure 4 to the true measurement signal depicted in

[0104] Figure 5 is a graph 133 illustrating the value of the simulated spectral signal α associated with a specified value of the floating parameter.

[0105] Figure 6 is illustrative of the Figure 5 graph 134 of the value of the residual error associated with the specified value of the floating parameter illustrated in

[0106] Figure 7 is illustrative of the Figure 5 graph 135 of the value of the calibrated synthetic spectrum associated with the specified value of the floating parameter illustrated in Figure 5 The calibrated synthetic spectrum is generated as the sum of the uncalibrated simulated spectral signal illustrated in Figure 6 and the residual error illustrated in Figure 6depicted, the residual error across the wavelength range and all signal channels varies within the range of + / -0.1. These non-trivial errors are taken into account in the calibrated composite spectrum depicted in Figure 7 .

[0107] In some embodiments, calibrated analog measurement signals are employed to generate an extended measurement library. Library-based solutions are a common approach for solving the inverse measurement problems inherent in many semiconductor metrology modalities. However, it is often impractical to generate a measurement library with sufficient span and density based on real measurement data. To overcome this limitation, measurement library data is typically generated synthetically. Unfortunately, errors present in the synthetic measurement data are reflected in the resulting measurement library. Thus, it is important to ensure the accuracy of the synthetic measurement data used to generate the measurement library.

[0108] In one example, two different measurement libraries are evaluated to determine the quality of the measurement library. The first library is relatively small and the second library is relatively large. The second library is generated by expanding the parameter range of the first library.

[0109] A library-based measurement is performed by searching the library for the closest match between the input spectrum and the spectra stored in the library. The value of the parameter of interest associated with the stored spectrum having the closest match to the input spectrum is the measured value of the parameter of interest. The measurement bias is evaluated by performing library-based measurements from the same input spectrum using both libraries and assessing the difference between the estimated values of the parameter of interest.

[0110] In one example, the relative quality of the libraries is evaluated based on the maximum measurement bias. The maximum measurement bias is calculated by taking the maximum of the differences between the values of the parameter of interest estimated by both the original and the extended libraries. If the maximum measurement bias is large, then the extended library provides a significant performance advantage compared to the original library. If the maximum measurement bias is small, then the extended library does not provide a significant performance advantage.

[0111] Figure 8 Table 140 illustrates the performance difference between a relatively small library and a relatively large library in terms of the evaluation of the maximum measurement bias based on the use of actual measurement spectra, uncalibrated analog measurement spectra, and calibrated analog measurement spectra as input spectra.

[0112] As Figure 8As depicted, the maximum deviation of the parameter of interest associated with the evaluation of the original library and the extended library is 10 when evaluated based on the true measured spectrum, 0.0008 when evaluated based on the uncalibrated simulated spectrum, and 2.3 when evaluated based on the calibrated simulated spectrum. These results indicate that there is a significant performance difference between the two libraries when using the true measured spectrum for evaluation, and this significant performance difference is also captured when using the calibrated simulated spectrum to evaluate the library. However, when evaluating the library based on the uncalibrated simulated data, this performance difference is not captured. Therefore, the calibrated simulated spectrum described herein can be used to effectively evaluate the performance of the measurement library in a way that the uncalibrated simulated spectrum cannot.

[0113] Figure 8 Also illustrated is the goodness of fit of the extended library using the actual measured spectrum, the uncalibrated simulated measured spectrum, and the calibrated simulated measured spectrum as the input spectrum. In this example, the goodness of fit is quantified as the CHI 2 value. The goodness of fit is evaluated based on the residual difference between the input spectrum and the library spectrum with the closest fit to the input spectrum. The residuals are evaluated for a number of samples (i.e., 100 different input spectra). The average CHI 2 value is calculated by averaging the CHI 2 values associated with each sample. As Figure 8 illustrated, the average CHI 2 value is 45 when evaluated based on the true measured spectrum, 30 when evaluated based on the uncalibrated simulated spectrum, and 47 when evaluated based on the calibrated simulated spectrum. These results indicate that when using the true measured spectrum and the calibrated simulated spectrum for evaluation, the performance of the extended library characterized by the goodness of fit is judged to be similar. However, when using the uncalibrated simulated spectrum for evaluation, the performance is judged to be better, i.e., a lower value of the goodness of fit indicates a better fit result. This implies that using the uncalibrated simulated spectrum to evaluate the measurement library may indicate a performance higher than that which would be achieved when using the library to perform measurements on actual measured data. Additionally, using the true measured spectrum and the calibrated simulated spectrum to evaluate the measurement library indicates similar performance levels and is consistent with the expected performance of the measurement library when used to perform measurements on actual measured data. Again, the calibrated simulated spectrum described herein can be used to effectively evaluate the performance of the measurement library in a way that the uncalibrated simulated spectrum cannot.

[0114] Although the calibration of simulated measurement data is described herein with reference to the spectral measurement data generated by a spectroscopic ellipsometry system (i.e., metrology system 100), in general, the calibration techniques described herein can be applied to any semiconductor metrology data that is part of a model-based measurement. Exemplary systems include but are not limited to optical-based spectroscopic measurement systems (e.g., ellipsometry, reflectometry, and angle-resolved reflectometry systems), image-based scatterometry systems (e.g., x-ray based scatterometry systems), etc.

[0115] Generally, calibrated analog measurement signals can be used to measure structural and material properties associated with different semiconductor manufacturing processes (e.g., material composition of structures and films, dimensional characteristics, etc.). More specifically, calibrated analog measurement signals can be part of regression on actual measurement data, library-based regression on actual measurement data, measurement library synthesis and evaluation, measurement recipe development, etc.

[0116] Figure 9 Describe a method 200 suitable for implementation by the metrology system 100 of the present invention. In one aspect, it should be recognized that the data processing blocks of the method 200 can be implemented via pre-programmed algorithms executed by one or more processors of the computing system 116. Although the following description is presented in the context of the metrology system 100, it should be recognized herein that the specific structural aspects of the metrology system 100 do not represent limitations and should only be construed as illustrative.

[0117] At block 201, a true measurement signal is received by the computing system. The true measurement signal is associated with the measurement of each of a plurality of examples of one or more structures fabricated on one or more semiconductor wafers.

[0118] At block 202, a set of estimated values of one or more floating parameters of a parameter measurement model is determined. The set of estimated values is associated with each of the measurements of a plurality of examples of one or more structures. Each set of estimated values of the one or more floating parameters minimizes a residual error. Each residual error characterizes the difference between a corresponding true measurement signal and a corresponding set of simulated measurement signals generated by the parameter measurement model under each of the sets of estimated values of the one or more floating parameters.

[0119] At block 203, a set of simulated measurement signals is determined by evaluating the parameter measurement model under a specified set of values of the one or more floating parameters.

[0120] At block 204, a residual error associated with the specified values of the one or more floating parameters is estimated based on the residual errors associated with each of the measurements of a plurality of examples of one or more structures.

[0121] At block 205, the set of simulated measurement signals is calibrated by adding the residual error associated with the specified values of the floating parameters to the set of simulated measurement signals.

[0122] At block 206, the calibrated set of simulated measurement signals is stored in a memory (e.g., the carrier medium 118).

[0123] As discussed above, it is not required that the acquisition of measurement data and subsequent analysis of the measurement data described herein be performed simultaneously or in spatially close proximity. For example, the measurement data may be stored in a memory for subsequent analysis. In another example, the measurement data may be obtained and transmitted to a computing system located at a remote location for analysis.

[0124] In some instances, an indication of the measured spectral response is the α meas and β meas values derived from the measurement data by methods known in the art as discussed above with reference to equations (1) to (3). In other instances, other indications of the measured spectral response (e.g., tan Ψ and Δ, etc.) may be considered. The foregoing spectral response indications are provided by way of non-limiting examples. Other indications or combinations of indications may be considered. It should be noted that the spectral indication is based on the spectral response of the sample, rather than a specific metric (e.g., film thickness, refractive index, dielectric constant, etc.) that can be derived from the spectral response of the sample.

[0125] In yet another aspect, the measurement results described herein can be used to provide active feedback to a process tool (e.g., a lithography tool, an etching tool, a deposition tool, etc.). For example, the value of the measured parameter determined based on the measurement method described herein can be communicated to a lithography tool to adjust the lithography system to achieve the desired output. In a similar manner, etching parameters (e.g., etching time, diffusion rate, etc.) or deposition parameters (e.g., time, concentration, etc.) can be included in the measurement model to provide active feedback to the etching tool or deposition tool, respectively. In some instances, the correction of the process parameter determined based on the measured device parameter value and the trained measurement model can be communicated to the lithography tool, the etching tool, or the deposition tool.

[0126] A metrology system configured to measure the geometry and material properties of dielectric and metal films and structures can employ the methods described herein. By way of non-limiting examples, these measurements include film properties and dimensions, CD, overlay, and composition measurements. These metrology systems can include any number of illumination sources, including but not limited to lamps, lasers, laser-driven sources, x-ray sources, and EUV sources. These metrology systems can employ several measurement techniques, including but not limited to all implementations of ellipsometry (including broadband spectroscopy or single wavelength, single or multi-angle or angle-resolved, using fixed or rotating polarizers and compensators), all implementations of reflectometry (including spectroscopy or single wavelength, single or multi-angle or angle-resolved), differential measurements (e.g., interferometers), and x-ray-based metrology.

[0127] As described herein, in any aspect, the term "metrology system" encompasses any system that is at least partially used to characterize a sample. Exemplary terms used in the art may include "defect inspection" systems or "inspection" systems. However, these technical terms do not limit the scope of the term "metrology system" as described herein. Additionally, metrology systems 100 and 400 may be configured for inspection of patterned wafers and / or unpatterned wafers. The metrology system may be configured as an LED inspection tool, an edge inspection tool, a backside inspection tool, a macro inspection tool, or a multi-mode inspection tool (involving data from one or more platforms simultaneously) and any other metrology or inspection tool that benefits from calibration of system parameters based on the difference in error spectra between a reference and a target metrology tool.

[0128] Various embodiments of semiconductor processing systems (e.g., metrology systems or lithography systems) that can be used to process samples are described herein. The term "sample" is used herein to refer to a wafer, a reticle, or any other sample that can be processed (e.g., printed or inspected for defects) by methods known in the art.

[0129] As used herein, the term "wafer" generally refers to a substrate formed of semiconductor or non-semiconductor material. Examples include (but are not limited to) single crystal silicon, gallium arsenide, and indium phosphide. These substrates are typically found and / or processed in semiconductor manufacturing facilities. In some cases, a wafer may consist only of the substrate (i.e., a bare wafer). Alternatively, a wafer may include one or more different material layers formed on the substrate.

[0130] One or more layers may be formed on the wafer. For example, these layers may include but are not limited to photoresist, dielectric materials, conductive materials, and semiconductive materials. Many different types of these layers are known in the art, and the term wafer as used herein is intended to encompass wafers on which all types of these layers can be formed.

[0131] One or more layers formed on the wafer may be "patterned" or "unpatterned". For example, a wafer may include multiple die having repeatable pattern features. The formation and processing of these material layers may ultimately result in a completed device. Many different types of devices may be formed on a wafer, and the term wafer as used herein is intended to encompass wafers on which any type of device known in the art is manufactured.

[0132] Typical semiconductor processes involve wafers processed in batches. As used herein, "batch" is a group of wafers processed together (e.g., a group of 25 wafers). Each wafer in a batch includes a number of exposure fields from a lithography processing tool (e.g., stepper, scanner, etc.). Multiple die may be present within each field. A die is a functional unit that ultimately becomes a single chip. One or more layers formed on the wafer may be patterned or unpatterned. For example, a wafer may contain multiple die each having repeatable patterned features. The formation and processing of these material layers may ultimately result in a completed device. Many different types of devices may be formed on a wafer, and the term wafer as used herein is intended to encompass wafers on which any type of device known in the art is fabricated.

[0133] A "reticle" may be a reticle at any stage of the reticle manufacturing process or a completed reticle that may be released or may not be released for use in a semiconductor manufacturing facility. A reticle or "mask" is generally defined as a substantially transparent substrate having substantially opaque regions formed thereon and configured in a pattern. The substrate may comprise, for example, a glass material such as quartz. The reticle may be positioned above a photoresist-covered wafer during the exposure step of a lithography process such that the pattern on the reticle can be transferred to the photoresist.

[0134] In one or more exemplary embodiments, the functionality may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functionality may be stored on or transmitted via a computer-readable medium as one or more instructions or program code. Computer-readable media includes both computer storage media and communication media including any medium that facilitates transfer of a computer program from one location to another. The storage media may be any available media that can be accessed by a general purpose or special purpose computer. By way of example, and not limitation, these computer-readable media may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store the desired program code in the form of instructions or data structures and that can be accessed by a general purpose or special purpose computer or a general purpose or special purpose processor. Further, any connection is properly termed a computer-readable medium. For example, if software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technology such as infrared, radio, and microwave, then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technology such as infrared, radio, and microwave is included in the definition of media. As used herein, disk and disc include optical discs (CD), laser discs, optical discs, digital versatile discs (DVD), floppy disks, and Blu-ray discs, where disks typically reproduce data magnetically and discs reproduce data optically with lasers. The above combinations should also be included within the scope of computer-readable media.

[0135] While certain specific embodiments have been described above for purposes of illustration, the teachings of this patent document are of general applicability and are not limited to the specific embodiments described above. Accordingly, various modifications, adaptations, and combinations of the various features of the embodiments may be practiced without departing from the scope of the invention as set forth in the claims.

Claims

1. A method, which comprises: receiving true measurement signals associated with measurements of each of a plurality of examples of one or more structures fabricated on one or more semiconductor wafers; determining a set of estimates of one or more floating parameters of a parametric measurement model associated with each of the measurements of the plurality of examples of the one or more structures, wherein each set of estimates of the one or more floating parameters minimizes a residual error, each residual error characterizing the difference between the corresponding true measurement signal and a corresponding set of simulated measurement signals generated by the parametric measurement model under each of the sets of estimates of the one or more floating parameters; determining a set of simulated measurement signals by evaluating the parametric measurement model under 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 examples 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; and storing the calibrated set of simulated measurement signals in a memory.

2. The method according to claim 1, wherein the one or more semiconductor wafers are in-line production wafers.

3. The method according to claim 1, wherein the measurement of each of the plurality of examples of the one or more structures fabricated on one or more semiconductor wafers is an optical spectroscopic measurement or an image-based scatter measurement.

4. The method according to claim 1, which further comprises: determining a variation in the value of each of the one or more floating parameters of the parametric measurement model across the set of estimates of the one or more floating parameters associated with the measurements of the plurality of examples of the one or more structures.

5. The method according to claim 4, which further comprises: generating an extended set of values of each of the one or more floating parameters based on the determined variation, wherein each extended set of values is greater than the corresponding set of estimated values.

6. The method according to claim 5, which further comprises: generating an extended set of simulated measurement signals by evaluating the parametric measurement model under each of the values of the extended set of values of each of the one or more floating parameters.

7. The method according to claim 1, wherein the estimating the residual error associated with the specified values of the one or more floating parameters involves: selecting one or more sets of true 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 true measurement signals.

8. The method according to claim 7, wherein said selecting the one or more sets of true measurement signals that most closely match the set of simulated measurement signals involves a K-nearest neighbor search of the set of true measurement signals.

9. The method according to claim 1, wherein said estimating the residual error associated with the specified values of the one or more floating parameters involves: generating a statistical model of the residual error that characterizes the difference between the corresponding true measurement signal and the corresponding set of simulated measurement signals and that varies in accordance with the values of the true measurement signals; and evaluating the statistical model under 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, which comprises: a light source configured to generate a quantity of illumination light directed to one or more structures fabricated on a semiconductor wafer; a detector configured to detect a quantity of light from the one or more structures in response to the quantity of illumination light and to generate a true measurement signal indicative of the detected light; and one or more computer systems configured to: receive true measurement signals associated with measurements of each of a plurality of examples 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 parameter measurement model associated with each of the measurements of the plurality of examples 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 the difference between the corresponding true measurement signal and a corresponding set of simulated measurement signals generated by the parameter measurement model under each of the sets of estimated values of the one or more floating parameters; determine a set of simulated measurement signals by evaluating the parameter measurement model under 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 examples of the one or more structures; and 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.

11. The metrology system according to claim 10, wherein the one or more semiconductor wafers are in-line production wafers.

12. The metrology system according to claim 10, wherein the measurement of each of the plurality of examples of the one or more structures fabricated on one or more semiconductor wafers is an optical spectroscopic measurement or an image-based scatter measurement.

13. The metrology system according to claim 10, the one or more computing systems further configured to: The set of estimated values of the one or more floating parameters of the parametric measurement model associated with the measurements across the plurality of examples of the one or more structures determines the variation in the value of each of the one or more floating parameters of the parametric measurement model.

14. The metrology system of claim 13, wherein the one or more computing systems are further configured to: Generate an extended set of values of each of the one or more floating parameters based on the determined variation, wherein each extended set of values is greater than the corresponding set of estimated values.

15. The metrology system of claim 14, wherein the one or more computing systems are further configured to: Generate an extended set of simulated measurement signals by evaluating the parametric measurement model at each of the values of the extended set of values of each of the one or more floating parameters.

16. The metrology system of claim 10, wherein the estimating 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 error corresponding to the one or more selected sets of real measurement signals.

17. The metrology system of claim 16, wherein the selecting 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 set of real measurement signals.

18. The metrology system of claim 10, wherein the estimating the residual error associated with the specified values of the one or more floating parameters involves: Generating a statistical model of the residual error that characterizes the difference between the corresponding real measurement signal and the set of simulated measurement signals as varying according to the value of the real measurement signal; 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, which comprises: A light source configured to generate a quantity of illumination light directed to one or more structures fabricated on a semiconductor wafer; A detector configured to detect a quantity of light from the one or more structures in response to the quantity of illumination light and generate a real measurement signal indicative of the detected light; and A non-transitory computer-readable medium storing instructions that, when executed by one or more processors, cause the one or more processors to: Receive real measurement signals associated with measurements of each of a plurality of examples of the one or more structures fabricated on one or more semiconductor wafers; Determine a set of estimates of one or more floating parameters of a parametric measurement model associated with each of the measurements of the plurality of examples of the one or more structures, wherein each set of estimates of the one or more floating parameters minimizes a residual error that characterizes the difference between the corresponding true measurement signal and a corresponding set of simulated measurement signals generated by the parametric measurement model under each of the sets of estimates of the one or more floating parameters; Determine a set of simulated measurement signals by evaluating the parametric measurement model under 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 error associated with each of the measurements of the plurality of examples of the one or more structures; and 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.

20. The metrology system of claim 19, wherein the one or more semiconductor wafers are in-line production wafers, and wherein the measurement of each of the plurality of examples of the one or more structures fabricated on the one or more semiconductor wafers is based on optical spectroscopic measurement or image-based scatterometry measurement.

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