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

Abstract

A method and system for calibrating simulated measurement signals generated by a parametric measurement model are described herein. A regression on the actual measurement signal is performed using the parametric model. Residual fitting errors between the actual measurement signal and the simulated measurement signal generated by the parametric model characterize the error of the parametric model at each set of estimated values ​​of one or more floating parameters. The simulated measurement signal is generated by the parametric model at specified values ​​of the floating parameters. Residual fitting errors associated with the simulated measurement signal generated at the specified values ​​of the floating parameters are derived from the residual fitting errors calculated by regression on the actual measurement signal. The simulated measurement signal is calibrated by adding the residual fitting errors to the uncalibrated simulated measurement signal. The calibrated simulated measurement signal improves the accuracy of measurements and measurement recipe development.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority under 35 U.S.C. § 119 to U.S. Provisional Patent Application No. 63 / 409,842, filed September 26, 2022, entitled "Methods for Calibrating the Error of Parametric Models in Simulated Synthetic Spectra Using Inline Wafers for Optical-Based Metrology," the subject matter of which is incorporated herein by reference in its entirety.

[0002] The described embodiments relate to systems for wafer metrology, and more particularly to characterization and defect detection of semiconductor structures and materials. [Background technology]

[0003] Semiconductor devices, such as logic and memory devices, are typically fabricated by a series of process steps applied to a specimen. Various features and structural levels of the semiconductor device are formed by these process steps. For example, lithography, among others, is one semiconductor fabrication process that involves creating patterns on a semiconductor wafer. Additional examples of semiconductor fabrication 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.

[0004] Metrology processes are used at various steps in the semiconductor manufacturing process to detect defects on wafers to promote higher yields. Metrology techniques offer the potential for high throughput without the risk of sample destruction. Several optical and X-ray-based techniques, including scatterometry, ellipsometry, and reflectometry implementations, and associated analysis algorithms, are commonly used to characterize the critical dimensions, film thickness, composition, and other parameters of nanoscale structures.

[0005] Many metrology techniques suitable for high-throughput measurement of semiconductor structures are model-based. Metrology techniques are indirect methods of measuring the physical properties of the sample under test, i.e., the measurements cannot be used to directly determine the physical properties of the sample. In such cases, the nominal measurement process consists of formulating a measurement model that estimates the measurement values ​​for a given measurement scenario. The measurement model characterizes the interaction between the sample and the measurement system. The metrology model includes a parametric model of the structure under test, parameterized by various geometric and material parameters (e.g., film thickness, critical dimensions, etc.), and a model of the measurement system, parameterized by various mechanical parameters (e.g., wavelength, angle of incidence, polarization angle, etc.).

[0006] A parametric model of a structure to be measured has floating parameters and fixed parameters. The values ​​of floating parameters vary during the measurement process, while the values ​​of fixed parameters are held at a constant nominal value during the measurement process. Generally, fixed parameters represent dimensions of structural features that do not vary significantly in a particular measurement application, while floating parameters represent dimensions of structural features that vary significantly in a particular measurement application and have a significant impact on the magnitude of a measurement signal, e.g., a measurement image, spectrum, etc.

[0007] A parametric model of the structure being measured is used directly in the measurement process. In some examples, an electromagnetic simulation engine operates on the parametric model of the structure being measured to generate synthetic measurement data. In model-based measurement applications, a regression process (e.g., ordinary least squares regression) is used to identify sample parameter values ​​that minimize the difference between the synthetic measurement data and the experimental measurements. For measurement purposes, the system parameters and some structural parameters are treated as known fixed parameters, and some structural parameters are treated as unknown floating parameters. The floating parameters are derived by an iterative process (e.g., regression) that results in the best fit between the synthetic measurement data and the experimental measurements.

[0008] In addition, the parametric model of the structure to be measured is indirectly used in the measurement process. Synthetic measurement data generated based on the parametric model of the structure to be measured is widely used to simulate the variation of the measurement signal for different fabrication process conditions. The determined sensitivity is then used to characterize the measurement capability and related measurement performance. Thus, the parametric model of the structure to be measured is important for the development of a specific measurement recipe for a measurement application.

[0009] As devices (e.g., logic and memory devices) progress to smaller nanometer-scale dimensions, characterization becomes more challenging. Devices incorporating complex three-dimensional shapes and materials with diverse physical properties contribute to the difficulty of characterization. As devices become more complex and measurement requirements become more stringent, parametric models become more complex and error-prone. Therefore, parametric modeling error becomes a significant constraint in measurement recipe development and measurement execution for complex measurement applications.

[0010] Parametric model errors include systematic errors and structural characterization errors. Systematic errors include errors in the characterization of the hardware configuration of the measurement system, such as the angle of incidence and azimuth. To minimize these errors, system parameters are perturbed until an optimal match is achieved between the synthetic and actual measurement data. Structural characterization errors reflect the inability of a parametric model to adequately characterize the structure being measured. For example, structural variations induced by actual process conditions may not be captured by a particular parametric model.

[0011] Traditionally, minimizing structural characterization errors is achieved in a similar manner to systematic errors, i.e., by perturbing a set of fixed structural parameters until an optimal match is achieved between synthetic and actual measured data. This requires identifying a set of fixed parameters for a parametric model and defining ranges of perturbation values ​​for the parameters that represent the actual structural variations induced by actual fabrication process conditions.

[0012] Unfortunately, this approach has proven ineffective for increasingly complex parametric models. More specifically, it is increasingly difficult to both identify a set of fixed parameters to perturb and determine a range of parameter perturbation values ​​that accurately represent actual process variations. Furthermore, the use of synthetic spectra to characterize measurement capabilities based on measurement libraries, regression, or both is compromised by inaccurate parametric models. More specifically, if parametric model errors are not properly calibrated, it is difficult to reproduce actual measurement data using synthetically generated measurement data. [Prior art documents] [Patent documents]

[0013] [Patent Document 1] U.S. Patent Application Publication No. 2017 / 0023491 Summary of the Invention [Problem to be solved by the invention]

[0014] Proper calibration of parametric model errors has emerged as a challenge in measurement recipe development and execution for complex metrology applications. In both research and development and manufacturing environments, process and yield control require improved calibration of parametric models to meet the requirements of the semiconductor manufacturing industry. Therefore, methods and systems for improving calibration of parametric models are desirable. [Means for solving the problem]

[0015] A method and system for calibrating simulated measurement signals generated by a parametric measurement model are described herein. The measured signals are obtained from measurements of different instances of one or more structures fabricated on a semiconductor wafer. In a preferred embodiment, the semiconductor wafers are in-line mass-produced wafers that capture structural variations induced by the actual fabrication process. A regression on the measured signals is performed using the parametric model for each set of measured signals. Each regression results in a residual fitting error between a set of estimates of the floating parameters and a simulated measurement signal generated by the parametric model at the estimated floating parameters. The residual error characterizes the remaining difference between the measured signals and the simulated measurement signal. In this sense, the residual error characterizes the error of the parametric model at each set of estimates of one or more floating parameters.

[0016] The simulated measurement signal is generated by the parametric model at specified values ​​of the floating parameters. Residual fitting errors associated with the simulated measurement signal generated at the specified values ​​of the floating parameters are derived from residual fitting errors calculated by regression on the actual measurement signal. The simulated measurement signal is calibrated by adding the residual fitting errors 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 actual measurement signal associated with measuring a structure characterized by the specified values ​​of the floating parameters.

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

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

[0019] In general, k can be any positive integer value. In some embodiments, k is equal to 1. In these examples, the simulated signals associated with the specified values ​​of the one or more floating parameters are calibrated by adding the residual error associated with a selected set of measured signals to the simulated signals 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 examples, the simulated signals associated with the specified values ​​of the one or more floating parameters are calibrated by adding the average residual error associated with a selected set of measured signals to the simulated signals associated with the specified values ​​of the one or more floating parameters.

[0020] In some other embodiments, the residual errors associated with the specified values ​​of the one or more floating parameters are estimated based on a statistical model of the values ​​of the measured signals, which is evaluated with a set of simulated measured signals associated with the specified values ​​of the one or more floating parameters to determine the residual errors 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 manner, a range of variation in the geometric profile of the structure(s) being measured is estimated based on actual measurements of instances of the one or more structures on in-line production wafers.

[0022] In further aspects, an expanded set of values ​​for each of the one or more floating parameters is generated based on the determined variation, each expanded set of values ​​being greater than the corresponding set of estimated values. In these embodiments, the variation in the values ​​of the geometric profile parameters estimated based on actual measurements is used to determine the range of structural variation encompassed by the specified values ​​of the floating parameters.

[0023] In another further aspect, the expanded set of simulated measurement signals is generated by evaluating the parametric measurement model at each of the values ​​of the expanded set of values ​​for each of the one or more floating parameters. In some embodiments, calibrated simulated measurement signals are used to generate the expanded measurement library.

[0024] The foregoing is a summary and, as such, contains necessarily simplifications, generalizations, and omissions of detail. Accordingly, those skilled in the art will appreciate that this summary is merely illustrative and is not intended to be in any way limiting. Other aspects, inventive features, and advantages of the devices and / or processes described herein will become apparent in the non-limiting detailed description set forth herein. [Brief explanation of the drawings]

[0025] [Figure 1] 1 is a simplified diagram illustrating a measurement system 100 operable in accordance with the simulated measurement signal calibration method described herein. [Figure 2] 1 is a plot 130 illustrating values ​​of a measured spectral signal α for several different measurement instances of a structure fabricated on an in-line mass production wafer. [Figure 3] 1 is a plot 131 illustrating values ​​of the simulated spectral signal α after fitting to the measured signal shown in FIG. 2. [Figure 4] 5 is a plot 132 illustrating the residual error associated with fitting the values ​​of the simulated spectral signal shown in FIG. 3 to the measured signal shown in FIG. 4. [Figure 5] 1 is a plot 133 illustrating values ​​of the simulated spectral signal α in relation to specified values ​​of the floating parameter. [Figure 6] 6 is a plot 134 illustrating values ​​of residual error associated with specified values ​​of the float parameters illustrated in FIG. 5. [Figure 7] 6 is a plot 135 illustrating values ​​of the calibrated composite spectrum associated with specified values ​​of the floating parameters illustrated in FIG. 5. [Figure 8] 14 is a table 140 illustrating the performance difference between a relatively small library and a relatively large library based on an evaluation of maximum measurement bias using actual measured spectra, uncalibrated simulated measured spectra, and calibrated simulated measured spectra as input spectra. [Figure 9] 2 is a flow chart illustrating a method 200 for calibrating a simulated measurement signal as described herein. DETAILED DESCRIPTION OF THE INVENTION

[0026] Reference will now be made in more detail to illustrative background and certain embodiments of the present invention, examples of which are illustrated in the accompanying drawings.

[0027]

[0003] Described herein are methods and systems for estimating parametric model errors and calibrating simulated measurement signals generated by a parametric model. The measured signals are obtained from measurements of different instances of one or more structures fabricated on a semiconductor wafer. In a preferred embodiment, the semiconductor wafer is an in-line mass-produced wafer that captures structural variations induced by the actual fabrication process. For each set of measured signals, i.e., each measurement instance, a regression is performed on the measured signals using a parametric model. The floating parameters of the parametric model are treated as regression parameters. Each regression results in a residual fitting error between a set of estimated values ​​of the floating parameters and the simulated measurement signals generated by the parametric model at the estimated values ​​of the floating parameters.

[0028] The simulated measurement signal is generated by a parametric model at specified values ​​of the floating parameters. The parametric model error embedded in the simulated measurement signal is estimated as a residual fitting error associated with the specified values ​​of the floating parameters. The residual fitting error is derived from the residual fitting error calculated during regression against the actual measurement signal.

[0029] The simulated measurement signal is calibrated by adding the residual fitting error associated with the specified value of the floating parameter to the value of the simulated measurement signal. In this way, the calibrated simulated measurement signal more accurately reproduces the expected value of the actual measurement signal associated with measuring a structure characterized by the specified value of the floating parameter. In some examples, the calibrated simulated measurement signal more accurately reproduces the variation in the measurement signal resulting from measuring an actual wafer. The calibrated simulated measurement signal described herein can improve the performance of model-based measurements, measurement recipe development, or both.

[0030] FIG. 1 illustrates a metrology system 100 for measuring semiconductor wafer properties according to exemplary methods presented herein. As shown in FIG. 1, the system 100 can be used to perform spectroscopic ellipsometry measurements of one or more structures 114 on a semiconductor wafer 112 disposed on a wafer positioning system 110. In this embodiment, the system 100 can include a spectroscopic ellipsometer (SE) 101 equipped with an illuminator 102 and a spectrometer 104. The illuminator 102 of the system 100 is configured to generate illumination in a selected wavelength range (e.g., 150-850 nm, 190-850 nm, 240-850 nm, etc.) and direct it toward the structures 114 disposed on the surface of the semiconductor wafer 112. The spectrometer 104 is then configured to receive illumination reflected from the surface of the semiconductor wafer 112. It is further noted that the light emitted from the illuminator 102 is polarized using a polarization state generator 107 to generate a polarized illumination beam 106. Radiation reflected by structures 114 disposed on wafer 112 passes through polarization state analyzer 109 and is sent to spectrometer 104. Radiation received by spectrometer 104 in collection beam 108 is analyzed with respect to polarization state, enabling the spectrometer to perform spectral analysis of the radiation passing through the analyzer. The measured spectrum 111 is communicated to computing system 116 for analysis of structures 114.

[0031] In a further embodiment, metrology system 100 is a measurement system 100 that may include one or more computing systems 116 used to perform calibration of simulated measurement signals in accordance with the methods described herein. The one or more computing systems 116 may be communicatively coupled to spectrometer 104. In one aspect, one or more computing systems 116 are configured to receive measurement data 111 related to measurements of structures 114 of sample 112. In one example, measurement data 111 includes an indication of a measured spectral response of the sample by target measurement system 100 based on one or more sampling processes from spectrometer 104.

[0032] It should be appreciated that various elements described throughout this disclosure may be performed by a single computer system 116 or, alternatively, by multiple computer systems 116. Additionally, different subsystems of system 100, such as spectroscopic ellipsometer 101, may include computer systems suitable for performing at least some of the steps described herein. Accordingly, the above description should not be construed as limiting on the present invention, but merely as illustrative. Furthermore, one or more computing systems 116 may be configured to perform any other step(s) of any method or embodiment described herein. Additionally, some or all of one or more computing systems 116 may be located remotely from the wafer measurement site. For example, elements of computing system 116 configured to perform any calibration block described herein may be located in a separate facility located remotely from the site where wafers are measured.

[0033] In this regard, there is no requirement that the spectral acquisition and subsequent analysis of the spectral data be performed simultaneously or in close spatial proximity. For example, the spectral data may be stored in memory for later analysis. In another example, the spectral results may be obtained and transmitted to a remotely located computing system for analysis.

[0034] Additionally, computer system 116 may be communicatively connected to spectrometer 104 and illuminator subsystem 102 of ellipsometer 101 in any manner known in the art. For example, one or more computing systems 116 may be connected to the computing system of spectrometer 104 and the computing system of illuminator subsystem 102 of ellipsometer 101. In another example, spectrometer 104 and illuminator 102 may be controlled by a single computer system. In this manner, computer system 116 of system 100 may be connected to a single ellipsometer computer system.

[0035] The computer system 116 of the system 100 may be configured to receive and / or acquire data or information from subsystems of the system (e.g., the spectrometer 104, the illuminator 102, etc.) via a transmission medium, which may include wired and / or wireless portions. In this manner, the transmission medium may act as a data link between the computer system 116 and other subsystems of the system 100. Additionally, the computing system 116 may be configured to receive measurement data via a storage medium (i.e., memory). For example, spectral results obtained using the spectrometer of the ellipsometer 101 may be stored in a permanent or semi-permanent memory device (not shown). In this regard, measurement results may be imported from an external system.

[0036] Additionally, computer system 116 may transmit data to external systems via a transmission medium. Computer system 116 of system 100 may be configured to receive and / or acquire data or information from other systems (e.g., test results from an inspection system or measurement results from a metrology system) via a transmission medium that may include wired and / or wireless portions. In this manner, the transmission medium may act as a data link between computer system 116 and other subsystems of system 100. Additionally, computer system 116 may transmit data to external systems via a transmission medium.

[0037] Computing system 116 may 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. In general, the term "computing system" may be broadly defined to encompass any device having one or more processors that execute instructions from a memory medium.

[0038] Program instructions 120 implementing methods such as those described herein may be transmitted on 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, a random-access memory, a solid-state memory, a magnetic or optical disk, or a magnetic tape.

[0039] 1 may be further configured as described herein. In addition, system 100 may be configured to perform any other block(s) of any method embodiment(s) described herein.

[0040] As shown in FIG. 1 , a broadband radiation beam from the illuminator 102 is linearly polarized in a polarization state generator 107, and the linearly polarized beam is incident on the sample 112. After reflection from the sample 112, the beam propagates toward a polarization state analyzer 109 while changing its polarization state. In some cases, the reflected beam has an elliptically polarized light. The reflected beam propagates through the polarization state analyzer 109 to the spectrometer 104. In the spectrometer 104, components of the beam 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 detectors may be linear arrays of photodiodes, each measuring radiation in a different wavelength range.

[0041] In one example, the computing system 116 is programmed with software to receive measurement data (e.g., raw measurement data) from each detector and process the received data in an appropriate manner. The measured spectral response of the sample may be determined by analyzing the change in polarization of radiation reflected from the sample in response to incident radiation having a known polarization state by any number of methods known in the art.

[0042] Both the polarization state generator 107 and the polarization state analyzer 109 may be configured to rotate about their optical axes during measurement operations. In some examples, the computing system 116 is programmed to generate control signals for controlling 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 mounted). The computing system 116 may also receive data indicative of 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 indicative of 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 for processing such orientation data in an appropriate manner.

[0043] 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) is a time-varying intensity as shown in equation (1).

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[0044] In general, the spectral response of a sample to a measurement is given by the spectroscopic data S and a subset of system parameter values ​​P, as shown in equations (4) and (5). sys1 is calculated by the measurement system based on a function of

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[0045] A subset P of system parameter values sys1 are system parameters required to determine the spectral response of the sample to measurements performed by the metrology system.

[0046] For the embodiment described with reference to FIG. 1, the subset of system parameters includes the machine parameters in equations (1)-(3). α meas and β meas The value of is determined based on measurements of a particular sample by measurement system 100 and a subset of the system parameter values ​​described in equations (1)-(3).

[0047] In general, ellipsometry is an indirect method for measuring the physical properties of the sample under test. In most cases, measurements (e.g., α meas and β meas) cannot be used to directly determine the physical properties of the sample. The nominal measurement process is a process that generates measurements (e.g., α meas and β meas ), which consists of formulating a parametric measurement model that estimates the mechanical (P machine ) and sample (P specimen ) parameters.

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[0048] The machine parameters are parameters used to characterize the metrology tool (e.g., ellipsometer 101) and may include some or all of the subset of system parameters described with reference to equations (4) and (5). Exemplary machine parameters include angle of incidence (AOI), analyzer angle (AO), polarizer angle (PO), illumination wavelength, numerical aperture (NA), etc.

[0049] 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 order, etc. For measurement purposes, the mechanical parameters are treated as known fixed parameters, and some or all of the sample parameters are treated as unknown floating parameters. The floating parameters are derived by an iterative process (e.g., regression) that results in the best fit between theoretical predictions and experimental data. The unknown sample parameter P specimen is varied, and the model output value (e.g., α model and β model ) is the correlation between the model output and experimental measurements (e.g., α measand β meas ) until a set of sample parameter values ​​is determined that gives a close match between the

[0050] In model-based measurement applications such as spectroscopic ellipsometry, a regression process (e.g., ordinary least squares regression) is used to identify sample parameter values ​​that minimize the difference between the model output values ​​and the experimental measurements for a fixed set of machine parameter values ​​and a fixed set of sample parameters that are not treated as unknown floating parameters.

[0051] In one aspect, a method and system are presented for calibrating a simulated measurement signal generated by a parametric measurement model. In this manner, the calibrated simulated measurement signal more accurately reproduces an expected value of an actual measurement signal associated with measuring a structure characterized by specified values ​​of the floating parameters. In the embodiment shown in FIG. 1, the computing system 116 is further configured to determine a value of at least one specimen parameter associated with the structure being measured based on the calibrated simulated measurement signal.

[0052] In a further aspect, the measured signals generated by a metrology system, e.g., metrology system 100, are received by a computing system, e.g., computing system 116. The measured signals relate to measurements of each of a plurality of instances of one or more structures fabricated on one or more semiconductor wafers. Equation (8) provides a set of n measured signals m i where i is a subscript from 1 to n, where n is any positive integer. Each set of measurement signals corresponds to a measurement instance of one or more structures to be measured.

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[0053] 1, the measurement signals 116 are actual signals, i.e., spectra, collected from different instances of one or more structures 114 fabricated on the wafer 112. The one or more structures include metrology targets, device structures, proxy structures, etc. The different instances of the one or more structures include repeated instances of the same nominal structure being measured. In a preferred embodiment, the actual signals are collected from in-line mass production wafers that represent actual variations in the process used to fabricate the structures being measured.

[0054] Additionally, a set of estimates of one or more floating parameters of the parametric measurement model associated with each of the measurements of the multiple instances of the one or more structures is determined. Each set of estimates is determined by regressing the measured data with the parametric measurement model that simulates the actual measurements. Values ​​of the floating parameters of the parametric measurement model are derived by regression to minimize an error function that governs the regression. The error function characterizes the difference between the measured signal and the simulated measured signal. Equation (9) is a function of the measured signal m shown in Equation (8). i n sets of simulated measurement signals s corresponding to i , where the value of the simulated measurement signal S is determined in the final iteration of the regression at the estimates of one or more floating parameters.

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[0055] At the end of the regression, the residual error characterizes the remaining difference between the measured signal and the simulated measured signal. In this sense, the residual error characterizes the error of the parametric model at each set of estimates of one or more floating parameters. Equation (10) is a function of the measured signal m i n sets of simulated measurement signals r corresponding to i As shown in equation (11), the residual error signal r i Each set of measured signals m i and the corresponding simulated measurement signal s i It is calculated as the difference between

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[0056] For example, the residual error associated with a spectral measurement is the difference between the measured and simulated measurement signals at each wavelength, i.e., the residual error spectrum. In another example, the residual error associated with an image-based measurement, e.g., a scatterometry image, is the difference between the measured and simulated measurement signals at each pixel of the image, i.e., the residual error image.

[0057] Each set of measured signals, corresponding sets of estimated values ​​for one or more float parameters, and corresponding residual errors are stored in memory, such as carrier medium 118. In a preferred embodiment, the sets of measured signals, corresponding float parameter values, and corresponding residual errors span the process variation space associated with the structure being measured, thereby capturing parametric model error information across process space.

[0058] In a further aspect, the set of simulated measurement signals is determined by evaluating the parametric measurement model at different sets of specified values ​​for one or more floating parameters. The set of simulated measurement signals is evaluated without calibration and therefore contains errors inherent in the parametric measurement model. Equation (12) shows the simulated measurement signal T, which includes m sets of simulated measurement signals.

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[0059] In many instances, the specified value of the floating parameter will be different from the estimate of the floating parameter determined during regression on the measured signal, but in general the specified value may be the same as or different from the estimate of the floating parameter determined during regression on the measured signal.

[0060] Furthermore, in many instances, the number of sets of prescribed values ​​is much greater than the number of sets of measured signals, i.e., m is greater than n. In many instances, the sets of prescribed values ​​are synthetically generated by a user of the metrology system to cover the expected range of geometric profiles of one or more structures to be measured with a higher resolution than the sets of available measured signals. For example, the sets of available measured signals may number in the hundreds, while the sets of prescribed values ​​may number in the thousands or tens of thousands.

[0061] In a further aspect, residual errors associated with specified values ​​of one or more floating parameters are determined based on the residual errors associated with each of measurements of multiple instances of one or more structures. Furthermore, each set of simulated measurement signals is calibrated by adding the residual errors associated with the specified values ​​of the floating parameters to the set of simulated measurement signals. The errors associated with each set of simulated measurement signals, i.e., the errors inherent in the parametric measurement model evaluated at each set of values ​​of the floating parameters, are corrected based on the residual errors derived from actual measurements of in-line mass production wafers. In this way, the calibrated composite spectrum more accurately reproduces the variations in the actual measurement signals.

[0062] The error associated with each set of specified values ​​for one or more floating parameters is given by equation (13).

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[0063] Each set of calibrated simulated measurement signals c k is the uncalibrated simulated measurement signal t as shown in equation (14). k and the corresponding error e k where k is a subscript from 1 to m, and m is any positive integer.

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[0064] The resulting set of calibrated simulated measurement signals C is given by equation (15).

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[0065] In some embodiments, a set of one or more measured signals that most closely matches the set of simulated measured signals corresponding to the specified values ​​of the one or more floating parameters is selected, and a residual error associated with the specified values ​​of the one or more floating parameters is estimated based on the residual error corresponding to the one or more selected sets of measured signals.

[0066] In some of these embodiments, the set of one or more actual measured signals that most closely matches the set of simulated measured signals is selected based on a K-nearest neighbor search of the set M of actual measured signals. The K-nearest neighbor search of M identifies k different sets of actual measured signals that most closely match the set of simulated measured signals under consideration. In general, k can be any positive integer value. In some embodiments, k is equal to 1. In these examples, the residual errors associated with the selected set of actual measured signals are treated as residual errors associated with specified values ​​of one or more floating parameters. In these examples, the simulated signals associated with specified values ​​of the one or more floating parameters are calibrated by adding the residual errors associated with the selected set of actual measured signals to the simulated signals 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 examples, the residual errors associated with the selected set of actual measured signals are averaged, and the average residual error is treated as the residual error associated with the specified values ​​of the one or more floating parameters. In these examples, the simulated signals associated with the specified values ​​of the one or more floating parameters are calibrated by adding the mean residual error associated with a selected set of measured signals to the simulated signals associated with the specified values ​​of the one or more floating parameters.

[0067] In some other embodiments, the residual errors associated with the specified values ​​of the one or more floating parameters are estimated based on a statistical model. In these embodiments, a statistical model of the residual errors is generated that characterizes the differences between each set of actual measured signals and a corresponding set of simulated measured signals. The statistical model is a function of the values ​​of the actual measured signals.

[0068] In one example, a Gaussian model of the residual error associated with the measured signal is generated. The Gaussian model specifies values ​​of the residual error over a range of values ​​of the measured signal. For example, in the case of a spectral measurement, the Gaussian model specifies values ​​of the residual error over a range of values ​​of the spectral signal, e.g., α, at each wavelength. Equation (16) shows the Gaussian model in one example, where N is the Gaussian distribution of the values ​​of the residual error associated with the spectral signal α at wavelength λ, μ is the mean value of the Gaussian distribution N, and σ is the standard deviation of the Gaussian distribution N.

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[0069] In image-based measurements, the Gaussian model specifies the value of the residual error over the range of measured intensity values ​​for each pixel.

[0070] The statistical model is evaluated with a set of simulated measurement signals associated with specified values ​​of the one or more floating parameters to determine residual errors associated with the specified values ​​of the one or more floating parameters.

[0071] 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 manner, a range of variation in the geometric profile of the structure(s) being measured is estimated based on actual measurements of instances of the one or more structures on in-line production wafers.

[0072] In further aspects, an expanded set of values ​​for each of the one or more floating parameters is generated based on the determined variation, each expanded set of values ​​being greater than the corresponding set of estimated values. In these embodiments, the variation in the values ​​of the geometric profile parameters estimated based on actual measurements is used to determine the range of structural variation encompassed by the specified values ​​of the floating parameters.

[0073] In another further aspect, the set of expanded simulated measurement signals is generated by evaluating the parametric measurement model at each of the values ​​of the expanded set of values ​​for each of the one or more floating parameters.

[0074] 2 is a plot 130 illustrating values ​​of the measured spectral signal α for several different measurement instances, the measured spectral signal being an actual measurement signal of a structure fabricated on an in-line mass production wafer.

[0075] FIG. 3 is a plot 131 illustrating the value of the simulated spectral signal α after fitting to the measured signal shown in FIG.

[0076] FIG. 4 is a plot 132 illustrating the residual error, i.e., the difference between the values ​​of the simulated spectrum signal and the measured signal, associated with fitting the values ​​of the simulated spectrum signal shown in FIG. 3 to the measured signal shown in FIG. 4.

[0077] FIG. 5 is a plot 133 illustrating values ​​of the simulated spectral signal α in relation to specified values ​​of the floating parameter.

[0078] FIG. 6 is a plot 134 illustrating the values ​​of the residual error associated with the specified values ​​of the float parameters illustrated in FIG.

[0079] FIG. 7 is a plot 135 illustrating values ​​of a calibrated synthetic spectrum associated with specified values ​​of the floating parameters illustrated in FIG. 5. The calibrated synthetic spectrum is generated as the sum of the uncalibrated simulated spectrum signal illustrated in FIG. 5 and the residual error illustrated in FIG. 6. As shown in FIG. 6, the residual error across the wavelength range and all signal channels varies within ±0.1. These nontrivial errors are accounted for in the calibrated synthetic spectrum shown in FIG. 7.

[0080] In some embodiments, calibrated simulated measurement signals are used 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, generating a measurement library of sufficient coverage and density based on actual measurement data is often impractical. To overcome this limitation, it is common to synthetically generate measurement library data. Unfortunately, any errors present in the synthetic measurement data will be reflected in the resulting measurement library. Therefore, it is important to ensure the accuracy of the synthetic measurement data used to generate the measurement library.

[0081] In one example, two different measurement libraries are evaluated to determine the quality of the measurement library, where the first library is relatively small and the second library is relatively large, and the second library is generated by extending the parameter range of the first library.

[0082] The library-based measurement is performed by searching the library for the closest match between the input spectrum and a spectrum stored in the library. The value of the parameter of interest associated with the stored spectrum that has the closest match with the input spectrum is the measured value of the parameter of interest. Measurement bias is assessed 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.

[0083] 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 difference between the values ​​of the parameter of interest estimated by both the original library and the extended library. If the maximum measurement bias is large, the extended library provides a significant performance advantage over the original library. If the maximum measurement bias is small, the extended library does not provide a significant performance advantage.

[0084] FIG. 8 is a table 140 illustrating the performance difference between a relatively small library and a relatively large library based on an evaluation of the maximum measurement bias using actual measured spectra, uncalibrated simulated measured spectra, and calibrated simulated measured spectra as input spectra.

[0085] As shown in Figure 8, the maximum bias for the parameters of interest associated with the evaluation of the original and expanded libraries is 10 when evaluated based on the measured spectra, 0.0008 when evaluated based on the uncalibrated simulated spectra, and 2.3 when evaluated based on the calibrated simulated spectra. These results indicate that there is a significant performance difference between the two libraries when evaluated using the measured spectra, and that this significant performance difference is also captured when the libraries are evaluated using the calibrated simulated spectra. However, this performance difference is not captured when evaluating the libraries based on uncalibrated simulated data. Therefore, the calibrated simulated spectra described herein can be utilized to effectively evaluate the performance of measured libraries in ways that uncalibrated simulated spectra cannot.

[0086] Figure 8 also shows the fit of the expanded library using the actual measured spectrum, the uncalibrated simulated measured spectrum, and the calibrated simulated measured spectrum as input spectra. In this example, the fit is CHI 2The fit is quantified as a χ value. The fit is evaluated based on the residual between the input spectrum and the library spectrum that has the closest fit to the input spectrum. The residual is evaluated for a large number of samples, i.e., 100 different input spectra. The average CHI 2 The CHI values ​​associated with each sample 2 The average CHI is calculated by averaging the values. 2 The values ​​were 45 when evaluated based on the measured spectra, 30 when evaluated based on the uncalibrated simulated spectra, and 47 when evaluated based on the calibrated simulated spectra. These results indicate that the performance of the expanded library, as characterized by goodness of fit, is judged to be similar when evaluated using measured and calibrated simulated spectra. However, when evaluated using uncalibrated simulated spectra, performance is judged to be better; i.e., a lower goodness of fit value indicates a better fit. This means that evaluation of a measurement library using uncalibrated simulated spectra may demonstrate higher performance than would be achieved if the library were used to perform measurements on actual measurement data. Furthermore, evaluation of a measurement library using measured and calibrated simulated spectra demonstrates comparable performance, consistent with the expected performance of the measurement library when used to perform measurements on actual measurement data. Again, the calibrated simulated spectra described herein can be utilized to effectively evaluate the performance of a measurement library in ways that uncalibrated simulated spectra cannot.

[0087] Although the calibration of simulated measurement data is described herein with reference to spectral measurement data generated by a spectroscopic ellipsometry system, i.e., metrology system 100, in general, the calibration techniques described herein may be applied to any semiconductor metrology data used as part of a model-based measurement. Exemplary systems include, but are not limited to, optical-based spectroscopic measurement systems, such as ellipsometry, reflectometry, and angle-resolved reflectometry systems, and image-based scatterometry measurement systems, such as X-ray-based scatterometry measurement systems.

[0088] In general, the calibrated simulated measurement signals may be used to measure structural and material properties associated with different semiconductor fabrication processes (e.g., material composition, dimensional properties of structures and films, etc.) More specifically, the calibrated simulated measurement signals may be used as part of regression against actual measurement data, library-based regression against actual measurement data, metrology library synthesis and evaluation, measurement recipe development, etc.

[0089] 9 illustrates a method 200 suitable for implementation by the metrology system 100 of the present invention. It is recognized that, in one aspect, the data processing blocks of method 200 may be performed via pre-programmed algorithms executed by one or more processors of computing system 116. While the following description is presented in the context of metrology system 100, it is recognized that the specific structural aspects of metrology system 100 herein do not represent limitations and should be construed as illustrative only.

[0090] In block 201, measured signals are received by a computing system. The measured signals relate to measurements of each of a plurality of instances of one or more structures fabricated on one or more semiconductor wafers.

[0091] In block 202, a set of estimates of one or more floating parameters of the parametric measurement model is determined. The set of estimates is associated with each of the measurements of the multiple instances of the one or more structures. Each set of estimates of the one or more floating parameters minimizes a residual error. Each residual error characterizes the difference between a corresponding actual measurement signal and a corresponding set of simulated measurement signals generated by the parametric measurement model at each of the sets of estimates of the one or more floating parameters.

[0092] In block 203, a set of simulated measurement signals is determined by evaluating the parametric measurement model at a set of specified values ​​for one or more floating parameters.

[0093] At block 204, a residual error associated with a specified value of one or more floating parameters is estimated based on the residual error associated with each of the measurements of the multiple instances of the one or more structures.

[0094] In block 205, the 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.

[0095] In block 206, the set of calibrated simulated measurement signals is stored in a memory, for example, the carrier medium 118.

[0096] As previously described herein, there is no requirement that the acquisition and subsequent analysis of measurement data described herein be performed simultaneously or in close spatial proximity. For example, the measurement data may be stored in a memory for later analysis. In another example, the measurement data may be obtained and transmitted to a remotely located computing system for analysis.

[0097] In some cases, the representation of the measured spectral response may be expressed as α, which is derived from the measured data by methods known in the art, such as those previously described herein with reference to equations (1)-(3). meas and β measIn other examples, other representations of the measured spectral response may be considered (e.g., tan Ψ and Δ, etc.). The foregoing spectral response representations are provided as non-limiting examples. Other representations or combinations of representations may also be considered. It is important to note that the spectral representation is based on the spectral response of the sample, and not a specific index (e.g., film thickness, refractive index, dielectric constant, etc.) that may be derived from the spectral response of the sample.

[0098] In yet another aspect, the measurements described herein can be used to provide active feedback to a process tool (e.g., a lithography tool, an etch tool, a deposition tool, etc.). For example, values ​​of measurement parameters determined based on the measurement methods described herein may be communicated to a lithography tool to adjust the lithography system to achieve a desired output. In a similar manner, etching parameters (e.g., etch time, diffusivity, etc.) or deposition parameters (e.g., time, concentration, etc.) may be included in a metrology model to provide active feedback to an etch tool or a deposition tool, respectively. In some examples, corrections to process parameters determined based on measured device parameter values ​​and a learned metrology model may be communicated to a lithography tool, an etch tool, or a deposition tool.

[0099] Metrology systems configured to measure the shape and material properties of dielectric and metal films and structures can employ the methods described herein. Such measurements include, by way of non-limiting example, film property and dimension, CD, overlay, and composition measurements. Such metrology systems may include any number of illumination sources, including, but not limited to, lamps, lasers, laser-driven sources, X-ray sources, and EUV sources. Such metrology systems may employ a number of measurement techniques, including, but not limited to, all implementations of ellipsometers (including broadband spectroscopic or single wavelength, single-angle or multi-angle, or angle-resolved, with fixed or rotating polarizers and compensators), all implementations of reflectometers (including spectroscopic or single wavelength, single-angle or multi-angle, or angle-resolved), differential measurements such as interferometers, and X-ray-based metrology.

[0100] The term "metrology system," as used herein, includes any system used at least in part to characterize a specimen in any manner. Exemplary terms used in the art include a "defect inspection" system or an "inspection" system. However, such terminology does not limit the scope of the term "metrology system" as used herein. Additionally, metrology systems 100 and 400 may be configured for inspection of patterned 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 (including simultaneous data from one or more platforms), and any other metrology or inspection tool that benefits from calibration of system parameters based on differences in error spectra between a reference and a target metrology tool.

[0101] Various embodiments are described herein with respect to a semiconductor processing system (e.g., a metrology system or a lithography system) that may be used to process a specimen. The term "specimen" is used herein to refer to a wafer, a reticle, or any other sample that may be processed (e.g., printed or inspected for defects) by means known in the art.

[0102] As used herein, the term "wafer" generally refers to a substrate formed of a semiconductor or non-semiconductor material. Examples include, but are not limited to, monocrystalline silicon, gallium arsenide, and indium phosphide. Such substrates may be commonly found and / or processed in semiconductor fabrication facilities. In some cases, a wafer may include only a substrate (i.e., a bare wafer). Alternatively, a wafer may include one or more layers of different materials formed on a substrate.

[0103] One or more layers may be formed on the wafer. For example, such layers may include, but are not limited to, resist, dielectric material, conductive material, and semiconductive material. Many different types of such layers are known in the art, and the term wafer as used herein is intended to encompass wafers on which all types of such layers may be formed.

[0104] One or more layers formed on a wafer may be "patterned" or "unpatterned." For example, a wafer may include multiple dies with repeatable pattern features. The formation and processing of such layers of material 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 upon which any type of device known in the art may be fabricated.

[0105] A typical semiconductor process involves wafer processing by lot. As used herein, a "lot" refers to a group of wafers (e.g., a group of 25 wafers) that are processed together. Each wafer in a lot includes multiple exposure fields from a lithography process tool (e.g., a stepper, scanner, etc.). Within each field, there may be multiple dies. A die is a functional unit that ultimately becomes a single chip. One or more layers formed on a wafer may be patterned or unpatterned. For example, a wafer may include multiple dies, each with repeatable patterned features. The formation and processing of such layers of material 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 a wafer on which any type of device known in the art may be fabricated.

[0106] A "reticle" may be a reticle at any stage in the reticle fabrication process or a finished reticle that may or may not have been released for use in a semiconductor fabrication facility. A reticle or "mask" is generally defined as a substantially transparent substrate having substantially opaque areas formed thereon and configured in a pattern. The substrate may comprise a glass material such as quartz. A reticle may be placed over a resist-coated wafer during an exposure step of a lithography process so that the pattern on the reticle can be transferred to the resist.

[0107] In one or more exemplary embodiments, the functions described may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functions may be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Computer-readable media includes both computer storage media and communication media, including any medium that facilitates transfer of a computer program from one place to another. Storage media may be any available medium that can be accessed by a general-purpose or special-purpose computer. By way of example, such computer-readable media may include, but is not limited to, RAM, ROM, EEPROM, CD-ROM or other optical disk storage devices, magnetic disk storage devices or other magnetic storage devices, or any other medium that can be used to carry or store desired program code means 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. Also, any connection is properly termed a computer-readable medium. For example, if software is transmitted from a website, server, or other remote source using coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave, the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included within the definition of medium. Disk and disc, as used herein, include compact discs (CDs), laser discs, optical discs, digital versatile discs (DVDs), floppy disks, and Blu-ray discs; disks typically reproduce data magnetically, while discs reproduce data optically with a laser. Combinations of the above are also intended to be included within the scope of computer-readable media.

[0108] Although certain specific embodiments are described above for illustrative purposes, the teachings of this patent specification have general applicability and are not limited to the specific embodiments described above. Accordingly, various modifications, adaptations, and combinations of the various features of the described embodiments may be made without departing from the scope of the invention as set forth in the claims.

Claims

1. 1. A method comprising: receiving a measurement signal associated with a measurement of each of a plurality of instances 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 instances of the one or more structures, each set of estimates of the one or more floating parameters minimizing a residual error, each residual error characterizing a difference between the corresponding actual measurement signal and a corresponding set of simulated measurement signals generated by the parametric measurement model at each of the set of estimates 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 value of the one or more floating parameters based on the residual error 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 value of the floating parameter to the set of simulated measurement signals; storing the set of calibrated simulated measurement signals in a memory; A method comprising:

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

3. 10. The method of claim 1, wherein the measurement of each of a plurality of instances of one or more structures fabricated on one or more semiconductor wafers is an optical-based spectroscopic measurement or an image-based scatterometry measurement.

4. determining a variation in value of each of the one or more floating parameters of the parametric measurement model across a set 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. The method of claim 1 further comprising:

5. generating a set of extended values ​​for each of the one or more floating parameters based on the determined variations, each set of extended values ​​being greater than the corresponding set of estimated values. The method of claim 4 further comprising:

6. 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 ​​for each of the one or more floating parameters. The method of claim 5 further comprising:

7. The estimate of the residual error associated with the specified value of the one or more floating parameters is selecting a set of one or more actual measured signals that most closely match the set of simulated measured signals that correspond to the specified values ​​of the one or more floating parameters; estimating the residual errors associated with the specified values ​​of the one or more floating parameters based on the residual errors corresponding to the set of one or more selected measured signals; The method of claim 1, comprising:

8. The method of claim 7 , wherein the selection of the set of one or more actual measured signals that most closely matches the set of simulated measured signals comprises a K-nearest neighbor search of the set of actual measured signals.

9. The estimate of the residual error associated with the specified value of the one or more floating parameters is generating a statistical model of the residual error characterizing the difference between the corresponding actual signal and the corresponding set of simulated measurement signals as a function of the value of the actual signal; evaluating the statistical model with 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; The method of claim 1, comprising:

10. 1. A measurement system comprising: an illumination source configured to generate a quantity of illumination light directed toward 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 a measured signal indicative of the detected light; one or more computer systems, receiving a measurement signal associated with a measurement of each of a plurality of instances of the 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 instances of the one or more structures, each set of estimates of the one or more floating parameters minimizing a residual error, each residual error characterizing a difference between the corresponding actual measurement signal and a corresponding set of simulated measurement signals generated by the parametric measurement model at each of the set of estimates 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 value of the one or more floating parameters based on the residual error 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 value of the floating parameter to the set of simulated measurement signals; one or more computer systems configured to perform A measurement system comprising:

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

12. 11. The metrology system of claim 10, wherein the measurement of each of a plurality of instances of one or more structures fabricated on one or more semiconductor wafers is an optical-based spectroscopic measurement or an image-based scatterometry measurement.

13. the one or more computing systems, determining a variation in value of each of the one or more floating parameters of the parametric measurement model across a set 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; The measurement system of claim 10 further configured to:

14. the one or more computing systems, generating a set of extended values ​​for each of the one or more floating parameters based on the determined variations, each set of extended values ​​being greater than the corresponding set of estimated values. The metrology system of claim 13 , further configured to:

15. the one or more computing systems, 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 ​​for each of the one or more floating parameters; The measurement system of claim 14 further configured to:

16. The estimate of the residual error associated with the specified value of the one or more floating parameters is selecting a set of one or more actual measured signals that most closely match the set of simulated measured signals that correspond to the specified values ​​of the one or more floating parameters; estimating the residual errors associated with the specified values ​​of the one or more floating parameters based on the residual errors corresponding to the set of one or more selected measured signals; The measurement system of claim 10 , comprising:

17. 17. The metrology system of claim 16, wherein the selection of the set of one or more actual measured signals that most closely matches the set of simulated measured signals comprises a K-nearest neighbor search of the set of actual measured signals.

18. The estimate of the residual error associated with the specified value of the one or more floating parameters is generating a statistical model of the residual error characterizing the difference between the corresponding actual signal and the corresponding set of simulated measurement signals as a function of the value of the actual signal; evaluating the statistical model with 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; The measurement system of claim 10 , comprising:

19. 1. A measurement system comprising: an illumination source configured to generate a quantity of illumination light directed toward 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 a measured signal indicative of the detected light; A non-transitory computer-readable medium storing instructions that, when executed by one or more processors, cause the one or more processors to: receiving a measurement signal associated with a measurement of each of a plurality of instances of the 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 instances of the one or more structures, each set of estimates of the one or more floating parameters minimizing a residual error, each residual error characterizing a difference between the corresponding actual measurement signal and a corresponding set of simulated measurement signals generated by the parametric measurement model at each of the set of estimates 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 value of the one or more floating parameters based on the residual error 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 value of the floating parameter to the set of simulated measurement signals; a non-transitory computer-readable medium for causing A measurement system comprising:

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

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