Calibration of parametric measurement models based on online wafer measurement data

Abstract

This document describes a method and system for calibrating simulated measurement signals generated by a parametric measurement model. Regression to a real measurement signal is performed using the parametric model. The residual fit error between the real measurement signal and the simulated measurement signal generated by the parametric model characterizes the error of the parametric model at each set of estimates of one or more floating parameters. The simulated measurement signal is generated by the parametric model at specified values ​​of the floating parameters. The residual fit error associated with the simulated measurement signal generated at the specified values ​​of the floating parameters is derived from the residual fit error calculated by the regression to the real measurement signal. The simulated measurement signal is calibrated by adding the residual fit error to an uncalibrated simulated measurement signal. The calibrated simulated measurement signal improves measurement accuracy and facilitates measurement formulation development.

Description

[0001] Cross-reference of related applications

[0002] This patent application claims priority 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,” pursuant to 35 U.S. SC § 119, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The described embodiments relate to systems for wafer measurement, and more specifically, to the characterization and defect detection of semiconductor structures and materials. Background Technology

[0004] Semiconductor devices (such as logic and memory devices) are typically manufactured by a series of processing steps applied to a sample. These processing steps form various features and multiple structural levels of the semiconductor device. For example, photolithography is particularly involved in a semiconductor manufacturing process that creates 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 manufactured on a single semiconductor wafer and then divided into individual semiconductor devices.

[0005] Metrology processes are used at various stages of semiconductor manufacturing to detect defects on wafers, thereby facilitating higher throughput. Metrology techniques offer the potential for high throughput without the risk of sample corruption. Several optical and X-ray-based techniques, including scattering, ellipsometric, and reflectance measurement implementations, along with correlation analysis algorithms, are typically used to characterize the critical dimensions, film thickness, composition, and other parameters of nanoscale structures.

[0006] Many metrology techniques applicable to high-processing-capacity semiconductor structure measurements are model-based. Metrology techniques are indirect methods for measuring the physical properties of a sample under test; that is, the measured values ​​cannot be used to directly determine the physical properties of the sample. In these cases, the nominal measurement process consists of developing a measurement model that estimates the measured values ​​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 measured structure parameterized by various geometric and material parameters (e.g., film thickness, critical dimensions, etc.) and a model of the measurement system parameterized by various machine parameters (e.g., wavelength, angle of incidence, angle of polarization, etc.).

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

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

[0009] Furthermore, a parametric model of the measured structure (MST) is indirectly employed during the measurement process. Synthetic measurement data generated based on the MST's parametric model are widely used to simulate variations in the measurement signal under different manufacturing process conditions. Subsequently, determined sensitivity is employed to characterize measurement capabilities and related measurement performance. In this way, the parametric model of the MST is crucial for the development of specific measurement formulations for measurement applications.

[0010] As devices (e.g., logic and memory devices) move towards smaller nanometer-scale dimensions, characterization becomes more challenging. Devices incorporating complex three-dimensional geometries and materials with varying physical properties contribute to these challenges. As devices become more complex and measurement requirements become more stringent, parametric models become more complex and error-prone. Therefore, parametric modeling errors are a significant limitation in measurement formulation development and measurement execution for complex measurement applications.

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

[0012] Traditionally, minimizing structural characterization errors is achieved in the same way as systematic errors, i.e., by perturbing a fixed set of structural parameters until an optimal match is achieved between synthetic and actual measurement data. This requires identifying the set of fixed parameters of the parametric model and defining the range of perturbation values ​​for parameters representing actual structural variations caused by real manufacturing process conditions.

[0013] Unfortunately, this method has proven ineffective for increasingly complex parametric models. More specifically, it becomes increasingly difficult to identify the set of fixed parameters to be perturbed and to determine the range of perturbation values ​​that will accurately represent variations in the actual process. Furthermore, the ability to characterize measurements based on measurement libraries, regression, or both using synthetic spectra is compromised by inaccurate parametric models. More specifically, it is difficult to reproduce true measurement data using synthetically generated measurement data without properly calibrating the parametric model errors.

[0014] Proper calibration of parametric modeling 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 necessitate improved calibration of parametric models to meet the requirements of the semiconductor manufacturing industry. Therefore, methods and systems for improved calibration of parametric models are desired. Summary of the Invention

[0015] This document describes a method and system for calibrating analog measurement signals generated by a parametric measurement model. Real measurement signals are acquired from measurements of different examples of one or more structures fabricated on a semiconductor wafer. In a preferred embodiment, the semiconductor wafer is an online production wafer capturing structural variations caused by an actual manufacturing process. Regression to the real measurement signals is performed using a parametric model for each set of the real measurement signals. Each regression results in a set of estimates of floating parameters and a residual fitting error between the real measurement signals and the analog measurement signals generated by the parametric model under the estimates of the floating parameters. The residual error characterizes the residual difference between the real and analog measurement signals. In this sense, the residual error characterizes the error of the parametric model under each set of estimates 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 floating parameters is derived from the residual fitting error calculated by regression of the true measurement signal. The simulated measurement signal is calibrated by adding the residual fitting error associated with the specified values ​​of 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 floating parameters.

[0017] In some embodiments, one or more sets of real measurement signals that most closely match the set of analog measurement signals corresponding to 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 error corresponding to the selected set of real measurement signals.

[0018] In some of these embodiments, a k-nearest neighbor search based on the set of real measurement signals selects one or more sets of real measurement signals that most closely match the set of analog measurement signals. The k-nearest neighbor search identifies k distinct sets of real measurement signals that most closely match the set of analog measurement signals considered.

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

[0020] In some other embodiments, a statistical model based on the values ​​of real measured signals estimates the residual error associated with specified values ​​of one or more floating parameters. The statistical model is evaluated over a set of simulated measured signals associated with specified values ​​of one or more floating parameters to determine the residual error associated with those specified values.

[0021] In a further aspect, the set of estimates for one or more floating parameters of the cross-parameter measurement model determines the variation in the value of each of the one or more floating parameters of the parametric measurement model. In this way, real-world measurement estimates based on examples of one or more structures on a live-line wafer are subject to the range of variation in the geometric profile of the measured structure.

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

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

[0024] The foregoing is an overview and therefore necessarily contains simplifications, generalizations, and omissions of details. Therefore, those skilled in the art will understand that the overview is illustrative only and not in any way limiting. 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. Attached Figure Description

[0025] Figure 1 This is a simplified diagram illustrating a measurement system 100 that can be operated according to a calibration method based on analog measurement signals as described herein.

[0026] Figure 2 This is a graph 130 illustrating the values ​​of the measured spectral signal α for several different measurement examples of structures manufactured on wafers in online production.

[0027] Figure 3 This is to explain in relation to Figure 2 The curve 131 shows the value of the simulated spectral signal α after fitting the real measurement signal.

[0028] Figure 4 It is an explanation and Figure 3 The values ​​of the simulated spectral signals depicted in the figure are... Figure 4 The curve of residual error associated with fitting the real measurement signal is shown in Figure 132.

[0029] Figure 5 This is a graph 133 illustrating the value of the simulated spectral signal α associated with a specified value of the floating parameter.

[0030] Figure 6 It is an explanation and in Figure 5 The graph 134 shows the residual error values ​​associated with the specified values ​​of the floating parameters as described in the diagram.

[0031] Figure 7 It is an explanation and Figure 5 The curve 135 shows the values ​​of the calibrated synthesized spectrum associated with the specified values ​​of the floating parameters described in the diagram.

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

[0033] Figure 9 This is a flowchart illustrating a method 200 for calibrating analog measurement signals as described herein. Detailed Implementation

[0034] Examples of the embodiments described herein will now be described in detail with reference to the background examples and some embodiments of the present invention, and examples of the embodiments will be described in the accompanying drawings.

[0035] This document describes a method and system for estimating parametric model errors and calibrating analog measurement signals generated by a parametric 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 online production wafer that captures structural variations caused by an actual manufacturing process. For each set of real measurement signals (i.e., each measurement example), regression of the real measurement signals is performed using a parametric model. The floating parameters of the parametric model are considered as regression parameters. Each regression results in a set of estimates of the floating parameters and a residual fitting error between the real measurement signals and the analog measurement signals generated by the parametric model under the estimates of the floating parameters.

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

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

[0038] Figure 1 This describes a measurement system 100 used to measure the characteristics of a semiconductor wafer according to the exemplary methods presented herein. For example... Figure 1As shown, system 100 can be used to perform spectral ellipsometric measurements of one or more structures 114 of a semiconductor wafer 112 mounted on a wafer positioning system 110. In this respect, system 100 may include a spectral ellipsometer (SE) 101 equipped with an illuminator 102 and a spectrometer 104. The illuminator 102 of system 100 is configured to generate illumination within a selected wavelength range (e.g., 150 to 850 nm, 190 to 850 nm, 240 to 850 nm, etc.) and direct said illumination onto the structures 114 mounted on the surface of the semiconductor wafer 112. The spectrometer 104 is then configured to receive the illumination reflected from the surface of the semiconductor wafer 112. It should be further noted that a polarization state generator 107 is used to polarize the light emitted from the illuminator 102 to generate a polarized illumination beam 106. The radiation reflected by the structures 114 mounted on the wafer 112 travels through a polarization state analyzer 109 and to the spectrometer 104. The polarization state analysis collects the radiation received by the spectrometer 104 in the collected beam 108, thereby allowing spectral analysis of the radiation transmitted by the analyzer via the spectrometer. The measured spectrum 111 is transmitted 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 may 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 may 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 a 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 understood that the various elements described throughout this disclosure can be implemented by a single computer system 116 or alternatively by multiple computer systems 116. Furthermore, different subsystems of system 100 (e.g., spectroscopic ellipsometer 101) may include computer systems suitable for performing at least a portion of the steps described herein. Therefore, the foregoing description should not be construed as limiting the invention but merely illustrative. Additionally, one or more computing systems 116 may be configured to perform any other step of any of the method embodiments described herein. Furthermore, some or all of one or more computing systems 116 may be located remotely from the wafer measurement site. For example, elements of a computing system 116 configured to perform any calibration frame described herein may be located at another facility located remotely from the measurement wafer site.

[0041] In this respect, it is not required that the spectral acquisition and subsequent analysis of spectral data be performed simultaneously or in spatial proximity. For example, spectral data can be stored in memory for later analysis. In another example, spectral results can be acquired 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 example, spectrometer 104 and illuminator 102 can be controlled by a single computer system. In this way, 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 (e.g., spectrometer 104, illuminator 102, and the like) via a transmission medium that may include wired and / or wireless components. In this way, the transmission medium can be used as a data link between the computer system 116 and other subsystems of system 100. Furthermore, the 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 with ellipsometer 101 can be stored in a permanent or semi-permanent memory device (not shown). In this respect, spectral results can be imported from an external system.

[0044] Furthermore, computer system 116 can transmit data to external systems via a transmission medium. Computer system 116 of system 100 can be configured to receive and / or acquire data or information from other systems (e.g., inspection results from an inspection system or measurement results from a measurement system) via a transmission medium that may include wired and / or wireless components. In this way, the transmission medium can be used as a data link between computer system 116 and other subsystems of system 100. Furthermore, computer system 116 can transmit data to external systems via the transmission medium.

[0045] Computing system 116 may include, but is not limited to, personal computer systems, mainframe computer systems, workstations, cloud-based computing systems, graphics computers, parallel processors, or any other means known in the art. Generally, the term "computing system" can be broadly defined to encompass any means having one or more processors that execute instructions from memory media.

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

[0047] Further configuration is possible as described in this article. Figure 1 The embodiments of system 100 described herein. Additionally, system 100 may be configured to perform any other block of any of the method embodiments described herein.

[0048] like Figure 1 The description states that a beam of broadband radiation from illuminator 102 is linearly polarized in polarization state generator 107, and the linearly polarized beam is then incident on sample 112. After reflection from sample 112, the beam propagates toward polarization state analyzer 109 with a changed polarization state. In some instances, the reflected beam is elliptically polarized. The reflected beam propagates through polarization state analyzer 109 to spectrometer 104. In spectrometer 104, beam components with 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 measured data (e.g., raw measurement data) from each detector and is programmed with software to process the received data in an appropriate manner. The measured spectral response of the sample can be determined by analyzing the change in polarization of 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 and the polarization state analyzer 109 can be configured to rotate about its optical axis during measurement operations. 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 from an analyzer position sensor associated with the polarization state analyzer 109 indicating the angular orientation of the polarization state analyzer 109. Similarly, the computing system 116 may also receive data from a polarizer position sensor associated with the polarization state generator 107 indicating the angular orientation of the polarization state generator 107. The computing system 116 may be software-programmed to process this orientation data in an appropriate manner.

[0051] In one embodiment, the polarization state generator 107 is a linear polarizer 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 a time-varying intensity as described by equation (1).

[0052] I(t)=I0[1+αcos(2ωt-P0)+βsin(2ωt-P0)] (1)

[0053] Where I0 is a constant depending on the intensity of the radiation emitted by illuminator 102, ω is the angular velocity of polarization state generator 107, and P0 is the ratio of the optical axis of polarization state generator 107 to the incident plane at the initial time (t = 0) (e.g., ...). Figure 1 The angle between the planes, and α and β are values ​​as defined by equations (2) and (3).

[0054] α=[tan 2 Ψ-tan 2 (A-A0)] / [tan 2 Ψ+tan 2 (A-A0)] (2)

[0055] and

[0056] β=[2(tanΨ)(cosΔ)(tan(A-A0))] / [tan 2 Ψ+tan 2 (A-A0)] (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 its electric field in... Figure 1 The polarized radiation component in the plane, where "s" indicates that its electric field is perpendicular to the plane. Figure 1 The component of the polarized radiation in the plane. A is the nominal analyzer angle (e.g., a measured value of the orientation angle supplied, for example, from the analyzer position sensor mentioned above associated with the polarization state analyzer 109). A0 is the actual orientation angle of the polarization state analyzer 109 offset from the reading “A” (e.g., A0 may be non-zero due to machine misalignment).

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

[0059] α meas =m(P sys1 ,S) (4)

[0060] β meas =n(P sys1 ,S) (5)

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

[0062] For reference Figure 1 In the described embodiment, a subset of the system parameters comprises the machine parameters of equations (1) to (3). α meas and β meas The value is determined based on the measurement of a specific sample by the metrology system 100 and a subset of the system parameter values, as described by equations (1) to (3).

[0063] Generally, ellipsometric measurement is an indirect method for measuring the physical properties of a sample under test. In most cases, the measured value (e.g., α) is used to determine the physical properties of the sample. meas and β meas This cannot be used to directly determine the physical properties of a sample. The nominal measurement process involves estimating the measured value (e.g., α) for a given measurement case. meas and β meas The measurement model consists of parameterized parameters. The measurement model characterizes the interaction between the sample and the measurement system. The measurement model includes parameterizations of the structure (e.g., film thickness, critical dimensions, etc.) and the machine (e.g., wavelength, incident angle, polarization angle, etc.). As explained in equations (6) and (7), the measurement model includes machine-related parameters (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 a measuring instrument (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 containing 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 treated as known fixed parameters, and some or all of the sample parameters are treated as unknown floating parameters. The floating parameters are solved by an iterative process (e.g., regression) that produces a best fit between theoretical predictions and experimental data. The unknown sample parameter P is changed. specimen And calculate the model output value (e.g., α). model and β model Until the model output value is determined to be different from the experimental measurement value (e.g., α), meas and β meas A set of closely matched sample parameter values ​​between ).

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

[0069] In one aspect, a method and system for calibrating analog measurement signals generated by a parametric measurement model are presented. In this way, the calibrated analog measurement signals more accurately reproduce the expected values ​​of real measurement signals associated with measurements of a structure characterized by specified values ​​of floating parameters. Figure 1 In 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 a calibrated analog measurement signal.

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

[0071] M = {m1, m2, ..., m} n} (8)

[0072] exist Figure 1In the embodiments depicted, the measurement signal 116 is a real measurement signal, i.e., a spectrum, collected from different examples of one or more structures 114 fabricated on wafer 112. The one or more structures include metrological targets, device structures, proxy structures, etc. Different examples of one or more structures include repeating examples of the same nominal structure being measured. In a preferred embodiment, the real measurement signal is collected from an online production wafer representing actual variations in the process used to manufacture the measured structure.

[0073] Furthermore, a set of estimates of one or more floating parameters of a parametric measurement model associated with each of the measurements of one or more examples of one or more structures is determined. Each set of estimates is determined by regression of the actual measurement data using a parametric measurement model simulating the actual measurement. The values ​​of the floating parameters of the parametric measurement model are solved by regression to minimize the error function governing the regression. The error function characterizes the difference between the actual measurement signal and the simulated measurement signal. Equation (9) describes a set of n simulated measurement signals S containing the simulated measurement signals si corresponding to the actual measurement signal mi described in Equation (8). The value of the simulated measurement signal S is determined at the final iteration of the regression using the estimates of one or more floating parameters.

[0074] S = {s1, s2, ..., s} n} (9)

[0075] At the termination of the regression, the residual error characterizes the residual difference between the real and simulated measurement signals. In this sense, the residual error characterizes the error of the parametric model under each set of estimates of one or more floating parameters. Equation (10) describes the residual error signal R comprising n sets of simulated measurement signals ri corresponding to the real measurement signal mi described in Equation (8). As explained by Equation (11), each set of residual error signals ri is calculated as the real measurement signal m i With the corresponding analog measurement signal s i The difference between them.

[0076] R = {r1, r2, ..., 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 actual measurement signal and the analog measurement signal at each wavelength (i.e., the residual error spectrum). In another example, the residual error associated with image-based measurements (e.g., scattering measurement images) is the difference between the actual measurement signal and the analog measurement signal at each pixel of the image (i.e., the residual error image).

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

[0080] In a further aspect, the set of analog measurement signals is determined by evaluating the parametric measurement model under different sets of specified values ​​of one or more floating parameters. The set of analog measurement signals is evaluated without calibration and therefore includes the inherent error of the parametric measurement model. Equation (12) describes the analog measurement signal T comprising m sets of analog measurement signals.

[0081] T = {t1, t2, ..., t} m} (12)

[0082] In many instances, the specified value of the floating parameter differs from the estimated value of the floating parameter determined during the regression of the measured signal. However, in general, the specified value can be the same as or different from the estimated value of the floating parameter determined during the regression of the measured signal.

[0083] Furthermore, in many instances, the number of sets of specified values ​​is much larger than the number of sets of actual measurement signals; that is, m is greater than n. In many instances, the set of specified values ​​is synthesized by the user of the metrology system to span the expected range of the geometric contours of one or more measured structures at a resolution higher than the available set of actual measurement signals. For example, the number of available sets of actual measurement signals may be hundreds, while the number of sets of specified values ​​may be thousands or tens of thousands.

[0084] In a further aspect, residual errors associated with specified values ​​of one or more floating parameters are determined based on residual errors associated with each of the measurements of multiple examples of one or more structures. Furthermore, each set of analog measurement signals is calibrated by adding the residual errors associated with the specified values ​​of the floating parameters to the set of analog measurement signals. The errors associated with each set of analog measurement signals (i.e., the inherent errors of the parameter measurement model evaluated under each set of floating parameter values) are corrected based on residual errors derived from actual measurements of the online production wafer. In this way, the calibrated synthetic spectrum more accurately reproduces the variations of the actual measurement signals.

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

[0086] E = {e1, e2, ..., e} m} (13)

[0087] Calculate the calibrated analog measurement signal c k Each set is used as an uncalibrated analog measurement signal t k With corresponding error e k The sum of, as illustrated by equation (14), where k is an index from 1 to m, where m is any positive integer.

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

[0089] The set of calibrated analog measurement signals C is described by equation (15).

[0090] C = {c1, c2, ..., c} m} (15)

[0091] In some embodiments, one or more sets of real measurement signals that most closely match the set of analog measurement signals corresponding to 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 error corresponding to the selected set of real measurement signals.

[0092] In some of these embodiments, a K-nearest neighbor search based on the set of true measurement signals M selects one or more sets of true measurement signals that most closely match the set of analog measurement signals. The K-nearest neighbor search of M identifies k distinct sets of true measurement signals that most closely match the set of considered analog measurement signals. 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 true measurement signals is considered as the residual error associated with specified values ​​of one or more floating parameters. In these instances, the analog signal associated with the specified values ​​of one or more floating parameters is calibrated by adding the residual error associated with the selected set of true measurement signals to the analog signal associated with the specified values ​​of one or more floating parameters. In some other embodiments, k is a positive integer value greater than 1. In these instances, the residual error associated with the selected set of true measurement signals is averaged, and the average residual error is considered as the residual error associated with the specified values ​​of one or more floating parameters. In these examples, the analog signal associated with the specified value of one or more floating parameters is calibrated by adding the average residual error associated with a selected set of real measurement signals to the analog signal associated with the specified value of one or more floating parameters.

[0093] In some other embodiments, residual errors associated with specified values ​​of one or more floating parameters are estimated based on statistical models. In these embodiments, statistical models are generated to express the residual errors between each set of characteristic real measurement signals and the corresponding set of analog measurement signals. The statistical model is a function of the values ​​of the real measurement signals.

[0094] In one instance, a Gaussian model is generated for the residual error associated with the actual measured signal. The Gaussian model specifies the value of the residual error across the range of values ​​of the actual measured signal. For example, for a spectral measurement, the Gaussian model specifies the value of the residual error for each wavelength across the range of values ​​of the spectral signal (e.g., α). Equation (16) illustrates the Gaussian model in one instance, where N is a Gaussian distribution of the values ​​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 value of the residual error for each pixel across the range of measured intensity values.

[0097] Evaluate a statistical model over a set of analog measurement signals associated with specified values ​​of one or more floating parameters to determine the residual error associated with the specified values ​​of one or more floating parameters.

[0098] In a further aspect, the set of estimates for one or more floating parameters of the cross-parameter measurement model determines the variation in the value of each of the one or more floating parameters of the parametric measurement model. In this way, real-world measurement estimates based on examples of one or more structures on a live-line wafer are subject to the range of variation in the geometric profile of the measured structure.

[0099] In a further aspect, an expanded set of values ​​for each of one or more floating parameters is generated based on the determined variation. Each expanded set of values ​​is greater than the corresponding set of estimated values. In these embodiments, the variation in the values ​​of geometric profile parameters estimated based on actual 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 analog measurement signals is generated by evaluating a parameter measurement model under each of the extended set of values ​​of one or more floating parameters.

[0101] Figure 2 This is Graph 130, illustrating the values ​​of the measured spectral signal α for several different measurement examples. The measured spectral signal is the actual measurement signal of the structure manufactured on a wafer in online production.

[0102] Figure 3 This is to explain in relation to Figure 2 The curve 131 shows the value of the simulated spectral signal α after fitting the real measurement signal.

[0103] Figure 4 It is an explanation and Figure 3 The values ​​of the simulated spectral signals depicted in the figure are... Figure 4 The curve 132 depicts the residual error associated with the fitting of the real measurement signal (i.e., the difference between the values ​​of the simulated spectral signal and the real measurement signal).

[0104] Figure 5 This 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 It is an explanation and in Figure 5 The graph 134 shows the residual error values ​​associated with the specified values ​​of the floating parameters as described in the diagram.

[0106] Figure 7 It is an explanation and Figure 5 The curve 135 shows the values ​​of the calibrated synthesized spectrum associated with the specified values ​​of the floating parameters described in the diagram. The calibrated synthesized spectrum is generated as... Figure 5 The uncalibrated analog spectral signal described in the text is related to... Figure 6 The sum of residual errors described in the text. For example... Figure 6 The data describes residual errors varying within a range of + / -0.1 across the wavelength range and all signal channels. Figure 7 These nontrivial errors are taken into account in the calibrated synthetic spectra depicted in the figure.

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

[0108] In one instance, two different measurement libraries are evaluated to determine the quality of the 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] Library-based measurements are performed by searching the library for the closest match between the input spectrum and the stored spectrum. The value of the parameter of interest associated with the stored spectrum that has the closest match to the input spectrum is the measured value of the parameter of interest. Measurement bias is evaluated by performing library-based measurements from the same input spectrum using two libraries and assessing the difference between the estimated values ​​of the parameter of interest.

[0110] In one instance, the relative quality of the library 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 and extended libraries. If the maximum measurement bias is large, the extended library provides a significant performance advantage compared to the original library. If the maximum measurement bias is small, the extended library does not provide a significant performance advantage.

[0111] Figure 8 Table 140 illustrates the performance differences between a relatively small library and a relatively large library, based on the assessment of the maximum measurement deviation using actual measured spectra, uncalibrated simulated measured spectra, and calibrated simulated measured spectra as input spectra.

[0112] like Figure 8 The study describes that the maximum deviation of the parameters of interest associated with the evaluation of the original and extended libraries is 10 when evaluated based on real measured spectra, 0.0008 when evaluated based on uncalibrated simulated spectra, and 2.3 when evaluated based on calibrated simulated spectra. These results demonstrate a significant performance difference between the two libraries when evaluated using real measured spectra, and this significant performance difference is captured when evaluating the library using calibrated simulated spectra. However, this performance difference is not captured when evaluating the library based on uncalibrated simulated data. Therefore, calibrated simulated spectra, as described herein, can be used to effectively evaluate the performance of measurement libraries in ways that uncalibrated simulated spectra cannot.

[0113] Figure 8 The goodness-of-fit of an expanded library of input spectra using actual measured spectra, uncalibrated simulated measured spectra, and calibrated simulated measured spectra is also explained. In this example, the goodness-of-fit is quantified as CHI. 2 The goodness of fit is evaluated based on the residual difference between the input spectrum and the library spectrum that best fits the input spectrum. The residual is evaluated for many samples (i.e., 100 different input spectra). The CHI value associated with each sample is averaged. 2 The average value of CHI is calculated. 2 Value. For example... Figure 8 The text explains that averaging CHI... 2The value is 45 when evaluated based on real measured spectra, 30 when evaluated based on uncalibrated simulated spectra, and 47 when evaluated based on calibrated simulated spectra. These results indicate that the performance of the extended library, characterized by goodness-of-fit, is judged to be similar when evaluated using real measured spectra and calibrated simulated spectra. However, when evaluated using uncalibrated simulated spectra, the performance is judged to be better; that is, a lower goodness-of-fit value indicates a better fit. This suggests that evaluating the measurement library using uncalibrated simulated spectra can indicate higher performance than would be achieved when using the library to perform measurements on actual measurement data. Furthermore, evaluating the measurement library using real measured spectra and calibrated simulated spectra indicates similar performance levels, consistent with the expected performance of the measurement library when used to perform measurements on actual measurement data. Also, as described herein, calibrated simulated spectra can be used to effectively evaluate the performance of the measurement library in ways that uncalibrated simulated spectra cannot.

[0114] Although the calibration of analog measurement data is described herein with reference to spectral measurement data generated by a spectral ellipsometry measurement system (i.e., metrology system 100), in general, the calibration techniques described herein can be applied to any semiconductor metrology data used as a part of model-based measurements. Exemplary systems include, but are not limited to, optical-based spectral measurement systems (e.g., ellipsometry, reflectance measurement, and angle-resolved reflectance measurement systems), image-based scattering measurement systems (e.g., X-ray-based scattering measurement 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 and dimensional properties of structures and films). More specifically, calibrated analog measurement signals can be used for regression of actual measurement data, library-based regression of actual measurement data, measurement library synthesis and evaluation, measurement formulation development, and other related purposes.

[0116] Figure 9 A method 200 suitable for implementation by the measurement system 100 of the present invention is described. In one aspect, it should be understood that the data processing portion of method 200 may be implemented via a pre-programmed algorithm executed by one or more processors of the computing system 116. Although the following description is presented in the background of the measurement system 100, it should be understood herein that specific structural aspects of the measurement system 100 are not intended to be limiting and should be interpreted only as illustrative.

[0117] In box 201, a computing system receives a real measurement signal. The real measurement signal is associated with a measurement of each of several examples of one or more structures fabricated on one or more semiconductor wafers.

[0118] In box 202, a set of estimates for one or more floating parameters of the parametric measurement model is determined. The set of estimates is associated with each of the measurements of multiple examples of one or more structures. Each set of estimates for the one or more floating parameters minimizes a residual error. Each residual error is characterized by the difference between the true measurement signal and the corresponding set of simulated measurement signals generated by the parametric measurement model under each of the sets of estimates for the one or more floating parameters.

[0119] In box 203, the set of analog measurement signals is determined by evaluating the parametric measurement model under a set of specified values ​​of one or more floating parameters.

[0120] In box 204, the 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 one or more examples of one or more structures.

[0121] In box 205, the set of analog measurement signals is calibrated by adding the residual error associated with the specified value of the floating parameter to the set of analog measurement signals.

[0122] In box 206, a calibrated set of analog measurement signals is stored in memory (e.g., carrier media 118).

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

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

[0125] In another aspect, the measurement results described herein can be used to provide active feedback to process tools (e.g., lithography tools, etching tools, deposition tools, etc.). For example, values ​​of measured parameters determined based on the measurement methods described herein can be communicated to the lithography tool to adjust the lithography system to achieve the desired output. Similarly, 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 or deposition tool, respectively. In some instances, corrections to process parameters determined based on the measured device parameter values ​​and the trained measurement model can be communicated to the lithography tool, etching tool, or deposition tool.

[0126] Metrological systems configured to measure the geometry and material properties of dielectric and metallic films and structures can employ the methods described herein. By way of non-limiting examples, these measurements include film properties and dimensions, CD, stacking, and composition measurements. These metrological 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 metrological systems can employ several measurement techniques, including but not limited to all implementations of ellipsometers (including broadband spectroscopy or single-wavelength, single or multiple angle or angular resolution, using fixed or rotating polarizers and compensators), all implementations of reflectometers (including spectroscopy or single-wavelength, single or multiple angle or angular resolution), differential measurements (e.g., interferometers), and X-ray-based metrology.

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

[0128] This document describes various embodiments of semiconductor processing systems (e.g., metrology systems or lithography systems) that can be used to process samples. The term "sample" is used herein to refer to a wafer, a photomask, or any other sample that can be processed by methods known in the art (e.g., printing or inspecting for defects).

[0129] As used herein, the term "wafer" generally refers to a substrate formed of semiconductor or non-semiconductor materials. 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 comprise one or more different layers of material formed on the substrate.

[0130] One or more layers may be formed on a 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 may be formed.

[0131] One or more layers formed on a wafer may be “patterned” or “unpatterned.” For example, a wafer may comprise multiple dies with repeatable pattern features. The formation and processing of these material layers can ultimately result in a completed device. Many different types of devices can 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] A typical semiconductor process involves batch processing of wafers. As used herein, a “batch” is a group of wafers processed together (e.g., a group of 25 wafers). Each wafer in a batch comprises numerous exposure fields from photolithography tools (e.g., steppers, scanners, etc.). Multiple dies may exist 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 dies, each with repeatable patterned features. The formation and processing of these material layers ultimately result in a completed device. Many different types of devices can 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 "reducing mask" can be a reducing mask at any stage of the reducing mask manufacturing process, or a completed reducing mask that may or may not be released for use in a semiconductor manufacturing facility. A reducing mask, or "mask," is generally defined as a substantially transparent substrate having substantially opaque areas formed thereon and arranged in a pattern. The substrate may comprise, for example, a glass material, such as quartz. The reducing mask can be placed over a photoresist-covered wafer during the exposure step of the photolithography process, such that the pattern on the reducing mask 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 as one or more instructions or program code on or transmitted via a computer-readable medium. Computer-readable media includes both computer storage media and communication media (including any media that facilitates the transfer of a computer program from one location to another). Storage media may be any available media accessible by a general-purpose or special-purpose computer. By way of example and without limitation, such computer-readable media may include RAM, ROM, EEPROM, CD-ROM or other optical disc storage, disk storage or other magnetic storage devices, or any other media that can be used to carry or store desired program code elements 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. Furthermore, any connection is appropriately referred to as computer-readable media. 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 technology (such as infrared, radio, and microwave), then 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, disks and optical discs include optical discs (CDs), laser discs, optical discs, digital versatile discs (DVDs), floppy disks, and Blu-ray discs, wherein disks typically magnetically reproduce data while optical discs optically reproduce data using 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 guiding purposes, the teachings of this patent document are generally applicable and not limited to the specific embodiments described above. Therefore, various modifications, adaptations, and combinations of the features of the described embodiments can be practiced without departing from the scope of the invention as set forth in the claims.

Claims

1. A method comprising: Receive a real measurement signal associated with the measurement of each of a plurality of examples of one or more structures manufactured 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, each residual error characterizing the difference between a 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. The set of analog measurement signals is determined by evaluating the parameter measurement model under a set of specified values ​​of the one or more floating parameters; The residual error is estimated based on the residual error associated with each of the measurements of the plurality of examples of the one or more structures and the specified value of the one or more floating parameters. The set of analog measurement signals is calibrated by adding the residual error associated with the specified value of the floating parameter to the set of analog measurement signals; and The calibrated set of analog measurement signals is stored in memory.

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

3. The method of claim 1, wherein the measurement of each of the plurality of examples of one or more structures fabricated on one or more semiconductor wafers is based on optical spectral measurement or image-based scattering measurement.

4. The method of claim 1, further comprising: The set of estimated values ​​of one or more floating parameters of the parameter measurement model associated with the measurements of the one or more examples of the one or more structures determines the variation in the value of each of the one or more floating parameters of the parameter measurement model.

5. The method of claim 4, further comprising: Based on the determined changes, an expanded set of values ​​is generated for each of the one or more floating parameters, wherein each expanded set of values ​​is greater than the corresponding set of estimated values.

6. The method of claim 5, further comprising: An extended set of analog measurement signals is generated by evaluating the parameter 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 of claim 1, wherein estimating the residual error associated with the specified value of the one or more floating parameters involves: Select one or more sets of real measurement signals that most closely match the set of analog measurement signals corresponding to the specified values ​​of the one or more floating parameters; and The residual error is estimated based on the residual error corresponding to the selected set of one or more real measurement signals and associated with the specified value of the one or more floating parameters.

8. The method of claim 7, wherein selecting the set of real measurement signals of the set that most closely matches the simulated measurement signals involves a K-nearest neighbor search of the set of real measurement signals.

9. The method of claim 1, wherein estimating the residual error associated with the specified value of the one or more floating parameters involves: A statistical model is generated to determine the residual error, which is a characteristic of the difference between the corresponding sets of real and analog measurement signals, varying according to the value of the real measurement signal; and The statistical model is evaluated on the set of analog 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 system of weights and measures, comprising: A light source configured to generate a certain amount of illumination light directed to one or more structures fabricated on a semiconductor wafer; A detector configured to detect a certain amount of light from the one or more structures in response to the certain amount of illumination light and to generate a measurement signal indicating the actual measured light; and One or more computer systems configured to: Receive a real measurement signal associated with the measurement of each of the multiple examples of the one or more structures manufactured 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, each residual error characterizing the difference between a 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. The set of analog measurement signals is determined by evaluating the parameter measurement model under a set of specified values ​​of the one or more floating parameters; The residual error estimated based on the residual error associated with each of the measurements of the plurality of examples of the one or more structures is the residual error associated with the specified value of the one or more floating parameters; and The set of analog measurement signals is calibrated by adding the residual error associated with the specified value of the floating parameter to the set of analog measurement signals.

11. The measurement system of claim 10, wherein the one or more semiconductor wafers are produced in-line.

12. The measurement system of claim 10, wherein the measurement of each of the plurality of examples of one or more structures fabricated on one or more semiconductor wafers is based on optical spectral measurement or image-based scattering measurement.

13. The measurement system of claim 10, wherein the one or more computing systems are further configured to: The set of estimated values ​​of one or more floating parameters of the parameter measurement model associated with the measurements of the one or more examples of the one or more structures determines the variation in the value of each of the one or more floating parameters of the parameter measurement model.

14. The measurement system of claim 13, wherein the one or more computing systems are further configured to: Based on the determined changes, an expanded set of values ​​is generated for each of the one or more floating parameters, wherein each expanded set of values ​​is greater than the corresponding set of estimated values.

15. The measurement system of claim 14, wherein the one or more computing systems are further configured to: An extended set of analog measurement signals is generated by evaluating the parameter measurement model under each of the values ​​of the extended set of values ​​of each of the one or more floating parameters.

16. The measurement system of claim 10, wherein the estimation of the residual error associated with the specified value of the one or more floating parameters involves: Select one or more sets of real measurement signals that most closely match the set of analog measurement signals corresponding to the specified values ​​of the one or more floating parameters; and The residual error is estimated based on the residual error corresponding to the selected set of one or more real measurement signals and associated with the specified value of the one or more floating parameters.

17. The measurement system of claim 16, wherein the selection of the set of real measurement signals of the set that most closely matches the simulated measurement signals involves a K-nearest neighbor search of the set of real measurement signals.

18. The measurement system of claim 10, wherein the estimation of the residual error associated with the specified value of the one or more floating parameters involves: A statistical model is generated to determine the residual error, which is a characteristic of the difference between the corresponding sets of real and analog measurement signals, varying according to the value of the real measurement signal; and The statistical model is evaluated on the set of analog 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 system of weights and measures, comprising: A light source configured to generate a certain amount of illumination light directed to one or more structures fabricated on a semiconductor wafer; A detector configured to detect a certain amount of light from the one or more structures in response to the certain amount of illumination light and to generate a true measurement signal indicating 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 a real measurement signal associated with the measurement of each of the multiple examples of the one or more structures manufactured 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, each residual error characterizing the difference between a 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. The set of analog measurement signals is determined by evaluating the parameter measurement model under a set of specified values ​​of the one or more floating parameters; The residual error estimated based on the residual error associated with each of the measurements of the plurality of examples of the one or more structures is the residual error associated with the specified value of the one or more floating parameters; and The set of analog measurement signals is calibrated by adding the residual error associated with the specified value of the floating parameter to the set of analog measurement signals.

20. The measurement system of claim 19, wherein the one or more semiconductor wafers are produced in-line, and wherein the measurement of each of a plurality of examples of the one or more structures manufactured on the one or more semiconductor wafers is based on optical spectral measurement or image-based scattering measurement.

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