Method and system for measuring semiconductor structures using multipath statistical optimization

Abstract

This specification describes a system and method for measuring the physical properties of a sample by an iterative solution of an optimization function that includes both current and previous measurement information. In one embodiment, a maximum posterior probability (MAP) estimation method is used to integrate the prior measurement information with the current measurement information in the optimization function. In some examples, the prior measurement information related to the measurement of a semiconductor structure is available from multiple exogenous sources. In further embodiments, the prior measurement information includes current measurements of the semiconductor structure under measurement as part of a multi-pass measurement. Prior statistics are determined based on an initial set of values ​​for the parameters of interest. These prior statistics are included in a subsequent MAP analysis of the same measurement dataset used in the first measurement pass. In another embodiment, the prior statistics are tracked to determine their impact on the current measurement.

Description

[Technical Field]

[0001] The embodiments described relate to measurement systems and measurement methods, and more particularly to improved methods and systems for measuring semiconductor structures. [Background technology]

[0002] Semiconductor devices, such as logic devices and memory devices, are typically manufactured by a series of processing steps applied to a sample. Various mechanisms and multiple structural levels of semiconductor devices are formed by these processing steps. For example, lithography is one semiconductor manufacturing process, among many, that involves generating patterns on a semiconductor wafer. Further examples of semiconductor manufacturing processes, though not limited to, include chemical mechanical polishing, etching, deposition, and ion implantation. Multiple semiconductor devices can be manufactured on a single semiconductor wafer and then separated into individual semiconductor devices.

[0003] Measurement processes are used at various steps in semiconductor manufacturing to detect defects on wafers and improve yield. Optical and X-ray-based measurement techniques offer the potential for high throughput without the risk of sample destruction. Many measurement-based techniques, including the implementation of scantometry, reflectometry, and ellipsometry, as well as related analytical algorithms, are commonly used to characterize the critical dimensions, film thickness, composition, overlay, and other parameters of nanoscale structures.

[0004] Many metrology techniques are indirect methods of measuring the physical properties of a specimen under measurement. In most cases, the raw measurement signal cannot be used to directly determine the physical properties of the specimen. Instead, a measurement model is used to estimate the value of one or more parameters of interest based on the raw measurement signal. For example, ellipsometry is an indirect method of measuring the physical properties of a specimen under measurement. Generally, a physics-based measurement model or a machine learning-based measurement model is required to determine the physical properties of the specimen based on the raw measurement signal (e.g., α_meas and β_meas).

[0005] In some examples, a physics-based measurement model is created that attempts to predict the raw measurement signal (e.g., α_meas and β_meas) based on assumed values of one or more model parameters. As shown in equations (1) and (2), the measurement model includes parameters related to the metrology tool itself, such as system parameters (P_system), and parameters related to the specimen under measurement. When determining the parameters of interest, some specimen parameters are treated as fixed values (P spec-fixed ), and other specimen parameters of interest are floated (P spec-float ), i.e., solved based on the raw measurement signal. α model =f(P system ,P spec-fixed ,P spec-float ) (1) β model =g(P system ,P spec-fixed ,P spec-float ) (2)

[0006] System parameters are those used to characterize the measurement tool (e.g., ellipsometer 101). Exemplary system parameters include the angle of incidence (AOI), analyzer angle (A0), polarizer angle (P0), irradiation wavelength, numerical aperture (NA), and compensator or waveplate (if present). Sample parameters are those used to characterize the sample (e.g., material and geometric parameters characterizing the structure under measurement). For thin film samples, exemplary sample parameters include the refractive index, dielectric function tensor, nominal layer thickness of all layers, and layer order. For CD samples, exemplary sample parameters include geometric parameter values ​​associated with different layers and refractive indexes associated with different layers. For measurement purposes, many of the system parameters and sample parameters are treated as known fixed-value parameters. However, the values ​​of one or more of the sample parameters are treated as unknown, floating-point parameters of interest.

[0007] In some examples, the values ​​of floating parameters of interest are resolved by an iterative process (e.g., regression) to obtain the best fit between theoretical predictions and experimental data. The model output values ​​and experimentally measured values ​​(e.g., α) are then resolved. meas and β meas The value of the unknown floating parameter of interest is varied until a set of sample parameter values ​​is determined that sufficiently matches the model output value (e.g., α). model and β model These are calculated and iteratively compared with the raw measurement data. In some other examples, floating parameters are resolved by searching a library of pre-calculated solutions to find the closest match.

[0008] Scattering-based measurements often involve indirect methods for measuring the physical properties of a sample under measurement. In these examples, an inverse problem is solved to infer the values ​​of parameters of interest describing a structure based on scattered radiation from a target irradiated by electromagnetic radiation. Scattering information can include reflectance, transmittance, polarization state, etc. Often, the target contains a periodic structure parameterized by a limited number of parameters of interest.

[0009] Inverse problems in measurement are typically solved by presenting them as optimization problems. In many cases, the optimization function optimizes the accuracy of a parametric estimate, given a hypothetical description of measurement noise, by maximizing the likelihood function P(m|x), i.e., the probability of measurement m given a value for parameter x. If properly formulated, this solution can achieve the Kramer-Rao information limit and guarantee the highest accuracy of the estimated parameter set.

[0010] The limitation of maximum likelihood estimation (MLE) is that parameter estimates do not incorporate any exogenous information about the structure under measurement. The information available at the time of solving the optimization problem comes from the current measurement, i.e., the assumed distribution of the measurement signal collected from the current measurement and the noise associated with the current measurement. As the measurement model becomes more complex and includes higher-dimensional parameter vectors, the information content becomes insufficient to resolve the values ​​of the parameters of interest, and the optimization method begins to break down. [Prior art documents] [Patent Documents]

[0011] [Patent Document 1] U.S. Patent Application Publication No. 2017 / 0069080 [Patent Document 2] U.S. Patent No. 9939250 [Patent Document 3] U.S. Patent No. 10345721 [Overview of the project] [Problems that the invention aims to solve]

[0012] Future measurement applications present challenges to measurement due to increasingly smaller resolution requirements, multi-parameter correlations, increasingly complex geometric structures, and the growing use of opaque materials. Therefore, methods and systems to improve the estimation of parameters of interest associated with model-based measurements are desired. [Means for solving the problem]

[0013] This specification describes a system and method for measuring the physical properties of a sample by an iterative solution of an optimization function that incorporates both current and prior measurement information. Prior measurement information incorporates additional measurement information, such as physical process constraints or wafer-based models, into the parameter estimation of the structure under measurement. This additional measurement information enables a more stable solution and higher-dimensional parameterization of the structure under measurement. This improves the robustness of the measurement and allows for more accurate measurement of complex semiconductor structures.

[0014] In one embodiment, a maximum posterior probability (MAP) estimation method is used to integrate prior measurement information with current measurement information in an optimization function used to drive recursive model-based measurements of one or more parameters of interest. The extended optimization function includes a prior distribution and a maximum likelihood estimation (MLE) function for determining the posterior probability, which is optimized during the model-based measurements.

[0015] In preferred embodiments, the optimization used to estimate the values ​​of one or more parameters of interest is performed via a negative (nagated) log-likelihood function. In these embodiments, the optimization function is the sum of the likelihood function and the prior distribution.

[0016] In some examples, pre-measurement information related to the measurement of a semiconductor structure is available from multiple exogenous sources. The pre-statistics include one or more statistical measures that characterize the pre-measurement information. These pre-statistics are included in the MAP analysis of measurement data collected from multiple measurement targets on a wafer or a set of wafers.

[0017] In a further aspect, pre-measurement information associated with a current model-based measurement of a semiconductor structure includes a current measurement of the semiconductor structure itself as part of a multiple-pass measurement of the semiconductor structure of interest.

[0018] In a first measurement pass, for multiple measurement targets on a wafer or a set of wafers, an initial set of initial values of an initial set of parameters of interest is determined. Pre-statistics are determined based on the initial set of initial values of the initial set of parameters of interest. These pre-statistics are included in a subsequent MAP analysis of the same measurement data set used in the first measurement pass.

[0019] In some embodiments, the statistical measures that characterize the pre-measurement information include the mean and variance of an assumed distribution of the pre-values of the parameters of interest. In some embodiments, the distribution is assumed to be a Gaussian distribution.

[0020] In a further embodiment, an additional regularization term is added to the optimization function, and each additional term is based on a different statistical measure that quantifies the pre-measurement information. In some of these embodiments, the statistical measures are statistically independent. In some other embodiments, the statistical measures are statistically dependent.

[0021] In some embodiments, the prior distribution is not accurately described by a Gaussian distribution. In some of these embodiments, the scale of the parameter is a curvature norm calculated as a weighted sum of polynomials or a discrete approximation. In a further aspect, the statistic of the scale of the parameter characterized by the curvature norm is approximated by a bull's-eye distribution.

[0022] Furthermore, the dimensionality of the bullseye distribution is chosen such that both the mean and standard deviation of the ensemble of pre-measured data closely match the bullseye distribution.

[0023] In some embodiments, the noise of the measurement system is characterized by a Poisson distribution rather than a Gaussian distribution.

[0024] In another embodiment, the ensemble statistics associated with each statistical measure are determined for each measurement target based on pre-measurement information across wafers or sets of wafers.

[0025] In some embodiments, a spatially constrained model is determined for each measurement target that characterizes ensemble statistics across a wafer or set of wafers. In these embodiments, the statistics associated with each measurement target depend on the wafer position.

[0026] In some other embodiments, a single aggregated statistic is determined for each measurement target, characterizing the ensemble statistic across a wafer or set of wafers. In these embodiments, the statistic associated with each measurement target is independent of the wafer position.

[0027] In some embodiments, a weighted average of the statistics of measurement targets in the vicinity of a particular measurement target is determined, characterizing the ensemble statistics across a wafer or set of wafers for each measurement target. In some examples, the weights are functionally related to the distance from the measurement target under measurement.

[0028] In another embodiment, prior statistics are tracked to determine the impact of one or more parameters of interest on the current measurement. In some examples, the statistical tracking measure is updated across wafers using Markov chains and post-correction. In some examples, an interacting multiple model (IMM) or other pseudo-Bayesian method is used to track the manufacturing process across wafers.

[0029] In a further embodiment, prior wafer statistics used as part of a multi-pass measurement are updated based on values ​​of a statistical tracking scale. In one example, if the statistical tracking scale indicates a higher probability of process drift, more recent prior statistics or statistics that are more spatially close are weighted more highly, and vice versa.

[0030] The above is a summary and therefore inevitably includes simplifications, generalizations, and omissions of details. Those skilled in the art will understand that the summary is illustrative and not limiting in any way. Other embodiments, features of the invention, advantages of the device, and / or processes described herein will become apparent in the non-limiting detailed description provided herein. [Brief explanation of the drawing]

[0031] [Figure 1] A figure shows one embodiment of a semiconductor measurement system 100 for estimating the values ​​of one or more parameters of interest characterizing a structure under measurement, according to the exemplary methods presented herein. [Figure 2] This figure shows an exemplary multi-path measurement engine 160 in one embodiment. [Figure 3] A diagram shows another embodiment of the semiconductor measurement system 300 for estimating the values ​​of one or more parameters of interest characterizing a structure under measurement, according to the exemplary methods presented herein. [Figure 4] A flowchart of Method 200 for estimating the values ​​of one or more parameters of interest characterizing a structure under measurement, according to the exemplary methods presented herein, is shown. [Modes for carrying out the invention]

[0032] Next, background examples and several embodiments of the present invention will be referred to in detail. These examples are shown in the accompanying drawings.

[0033] This specification describes a method and system for measuring the physical properties of a sample under measurement by an iterative solution of an optimization function that incorporates both current and prior measurement information. Prior measurement information is included as part of the optimization function, rather than relying solely on current measurement information, to estimate the values ​​of parameters of interest associated with the structure under measurement. Prior measurement information incorporates additional measurement information, such as physical process constraints or wafer-based models, for parameter estimation of the structure under measurement. This additional measurement information enables a more stable solution and higher-dimensional parameterization of the structure under measurement. This improves the robustness of the measurement and allows for more accurate measurement of complex semiconductor structures, such as memory structures, characterized by higher-dimensional parameterization.

[0034] In one embodiment, a statistical measure based on prior measurement information is included as part of an optimization function associated with the current measurement of one or more semiconductor structures.

[0035] Maximum posterior probability (MAP) estimation techniques are used to integrate prior measurement information with current measurement information in optimization functions used to drive recursive model-based measurements of one or more parameters of interest. The MAP estimation technique uses an extended optimization function that includes a prior distribution P(x), which statistically quantifies prior measurement information, e.g., prior knowledge, associated with one or more sets of parameters of interest x. The MAP estimator integrates a maximum likelihood estimation (MLE) function P(m|x) with the prior distribution P(x) based on Bayes' theorem, as shown in equation (3), where P(x|m) is the probability of each value of the set of parameters x given a measurement m. P(x│m)=P(m│x)P(x) (3)

[0036] As shown in equation (3), the likelihood function P(m|x) is multiplied by the prior distribution P(x) to obtain the posterior probability P(x|m), which is optimized during model-based measurement. In a preferred embodiment, the optimization used to estimate the values ​​of one or more parameters of interest is performed via a negative log-likelihood function. In these embodiments, since the logarithm of the product is the sum, the optimization function is the sum of the likelihood function P(m|x) and the prior distribution P(x). Thus, the prior distribution P(x) is an additional term in the optimization function that regularizes the optimization by constraining the distribution of the set of parameters x being measured.

[0037] In some cases, the pre-measurement information related to the current measurement of a semiconductor structure can be obtained from multiple extrinsic sources, including, but not limited to, historical reference data, physical-based model simulations (e.g., etching or lithography simulations), measurements performed using different measurement techniques, reference measurements from different wafers performed by reliable measurement systems (e.g., SEM, TEM, AFM, etc.), modelless measurements, and user knowledge.

[0038] In these examples, prior statistics are determined based on prior measurement information from one or more exogenous sources. The prior statistics include one or more statistical measures characterizing a set of prior values ​​associated with each of the initial sets of parameters of interest. These prior statistics are included in the MAP analysis of measurement data collected from multiple measurement targets on a wafer or set of wafers. MAP-based optimization is used to estimate the values ​​of one or more parameters of interest via a negative log-likelihood function and a shifted log-likelihood function. The optimization function is the sum of the likelihood function and the prior statistics. Therefore, the prior statistics are included as regularization terms in the MAP-based optimization.

[0039] However, determining prior statistics for MAP estimation based solely on exogenous sources may limit the robustness and accuracy of the measurement. For example, when the manufacturing process drifts, exogenous measurements may not accurately reflect the shape or state of the structure being measured.

[0040] In a further embodiment, the multi-pass measurement of a semiconductor structure model includes updating the optimization function for model-based measurement of the semiconductor structure based on the values ​​of one or more parameters of interest that characterize the semiconductor structure, determined by a pre-measurement pass. Each pass of the multi-pass measurement involves regression on the same set of measurement signals, but the optimization function is updated. In these embodiments, the values ​​of one or more parameters of interest that characterize the semiconductor structure, determined by the pre-measurement pass, are used as pre-measurement information in the updated optimization function used to estimate the values ​​of the parameters of interest in subsequent measurement passes. In this way, the prior statistics used in MAP estimation are updated based on the current measurement signals, thus more accurately reflecting the shape or state of the structure under measurement.

[0041] In some embodiments, an initial set of values ​​for an initial set of parameters of interest is determined for multiple measurement targets on a wafer or set of wafers in a first measurement pass. In some embodiments, the initial set of parameters of interest is the same as the set of parameters of interest measured in the final measurement pass. In some other embodiments, the initial set of parameters of interest is a subset of the set of parameters of interest measured in the final measurement pass. In some embodiments, the initial set of values ​​for the initial set of parameters of interest is determined by a conventional MLE analysis used to solve the inverse problem.

[0042] Prior statistics are determined based on an initial set of values ​​for an initial set of parameters of interest. These prior statistics are included in subsequent MAP analyses of the same measurement dataset used in the first measurement pass. In a preferred embodiment, MAP-based optimization used to estimate the values ​​of one or more parameters of interest is performed via a negative log-likelihood function and a shifted log-likelihood function. The optimization function is the sum of the likelihood function and the prior statistics. Thus, the prior statistics are included as regularization terms in subsequent measurement passes. In subsequent measurement passes, subsequent sets of values ​​for subsequent sets of parameters of interest are determined for multiple measurement targets measured in the first pass. In some embodiments, the subsequent sets of parameters of interest are the same as the sets of parameters of interest measured in the final measurement pass.

[0043] In a preferred embodiment, two measurement passes are used to estimate the final set of values ​​for the final set of parameters of interest. However, generally, any number of measurement passes can be envisioned within the scope of this patent document. In each measurement pass, a prior statistic for the subsequent measurement pass is updated based on a statistical measure determined from the set of estimates for the set of parameters of interest determined in the previous measurement pass. In some embodiments, the prior statistic is based solely on the set of estimates for the set of parameters of interest determined from the previous measurement pass. However, in some other embodiments, the prior statistic is based on a combination of statistics derived from the prior measurement pass and an exogenous metric, as described above. In some of these embodiments, the combination of prior statistics is implemented as a weighted sum of prior statistic terms in the current optimization function.

[0044] Each sequential measurement pass can have a different number of parameters. In some embodiments, it may be preferable to perform MLE optimization using lower-dimensional parameterization. This is acceptable because it does not require regularization of all parameters in the subsequent MAP optimization. Furthermore, since MAP optimization is regularized, it can produce acceptable results even for higher-dimensional parameterization or measurement situations where the parameterization of the structure under measurement does not take into account certain physical properties, such as aperiodicity.

[0045] Figure 1 shows a system 100 for measuring the properties of a specimen and estimating the values ​​of one or more parameters of interest associated with each measurement, according to the exemplary methods presented herein. Figure 1 shows one embodiment of a transmission small-angle X-ray scattering (T-SAXS) measurement tool 100 used to perform T-SAXS measurements on an inspection area 102 of a specimen 101 irradiated by an irradiation beam spot.

[0046] In the illustrated embodiment, the measurement tool 100 includes an X-ray irradiation source 110 configured to generate X-ray radiation suitable for T-SAXS measurement. Generally, any suitable high-brightness X-ray irradiation source capable of generating high-brightness X-rays at a flux level sufficient to enable high-throughput inline measurement may be intended to supply X-ray irradiation for T-SAXS measurement. In some embodiments, the X-ray source includes an adjustable monochromator that allows the X-ray source to deliver X-ray radiation at different selectable wavelengths.

[0047] In some embodiments, one or more X-ray sources emitting at photon energies greater than 15 keV are used to ensure that the X-ray sources supply light of wavelengths that allow sufficient penetration of the entire device and wafer substrate. In non-limiting examples, any of the following may be used as the X-ray irradiation source 110: a particle accelerator, a liquid anode source, a rotating anode source, a fixed solid anode source, a microfocus source, a microfocus rotating anode source, a plasma-based source, and an inverse Compton source. In one example, an inverse Compton source, available from Lyncan Technologies, Inc. in Palo Alto, California, USA, may be considered. The inverse Compton source has the additional advantage of being able to generate X-rays across a range of photon energies, thereby allowing the X-ray source to deliver X-ray emission at different selectable wavelengths.

[0048] An exemplary X-ray source includes an electron beam source configured to strike a solid or liquid target to stimulate X-ray emission. A method and system for generating high-intensity liquid metal X-ray irradiation is described in U.S. Patent No. 7,929,667, issued to KLA-Tencor Corp. on 19 April 2011, which is incorporated herein by reference in whole.

[0049] The X-ray source 110 generates X-ray radiation over a source region having a finite lateral dimension (i.e., a non-zero dimension perpendicular to the beam axis). The focusing optical element 111 focuses the radiation from the source toward a measurement target located on the specimen 101. The finite lateral source dimension results in a finite spot size 102 on the target defined by the rays 117 emanating from the edges of the source. In some embodiments, the focusing optical element 111 includes an elliptical focusing optical element.

[0050] A beam divergence control slit 112 is positioned in the beampath between the focusing optical element 111 and the beam shaping slit mechanism 120. The beam divergence control slit 112 limits the divergence of the irradiation provided to the specimen under measurement. In some embodiments, an additional intermediate slit 113 is positioned in the beampath between the beam divergence control slit 112 and the beam shaping slit mechanism 120. The intermediate slit 113 provides additional beam shaping. The beam shaping slit mechanism 120 is positioned in the beampath immediately preceding the specimen 101. The slit of the beam shaping slit mechanism 120 is positioned near the specimen 101 to minimize the enlargement of the incident beam spot size due to beam divergence defined by the finite radiation source size. In one example, with an X-ray source size of 10 micrometers and a distance of 25 millimeters between the beam shaping slit and the specimen 101, the enlargement of the beam spot size due to shadow caused by the finite radiation source size is approximately 1 micrometer. In other examples, beam divergence is controlled by a beam shaping slit positioned less than 100 millimeters from sample 101.

[0051] In some embodiments, the beam shaping slit mechanism 120 includes a plurality of independently operated beam shaping slits. In one embodiment, the beam shaping slit mechanism 120 includes four independently operated beam shaping slits. These four beam shaping slits effectively block a portion of the incident beam 115, generating an irradiation beam 116 having a box-shaped irradiation cross-section.

[0052] Generally, X-ray optical elements shape and direct X-ray radiation toward the specimen 101. In some examples, the X-ray optical elements include an X-ray monochromator to monochromatize the X-ray beam incident on the specimen 101. In some examples, the X-ray optical elements use multilayer X-ray optical elements to collimate or focus the X-ray beam onto the measurement area 102 of the specimen 101 with a divergence of less than 1 milliradian. In these examples, the multilayer X-ray optical elements also function as beam monochromators. In some embodiments, the X-ray optical elements include one or more X-ray collimating mirrors, X-ray apertures, X-ray beam stops, X-ray refractive optical elements, diffractive optical elements such as zone plates, Montell optical elements, specular reflecting X-ray optical elements such as depression-angled incidence ellipsoidal mirrors, polycapillary optical elements such as hollow capillary X-ray waveguides, multilayer optical elements or systems, or any combination thereof. Further details are provided in U.S. Patent Application Publication No. 2015 / 0110249, which is incorporated herein by reference in its entirety.

[0053] The X-ray detector 119 collects scattered X-ray radiation 114 from the sample 101 and generates an output signal 135 that indicates the characteristics of the sample 101, which are highly sensitive to incident X-ray radiation, according to the T-SAXS measurement modality. In some embodiments, while the scattered X-rays 114 are collected by the X-ray detector 119, the sample positioning system 125 determines the position and orientation of the sample 101 to generate angularly resolved, scattered X-rays.

[0054] In some embodiments, the T-SAXS system has a high dynamic range (e.g., 10 5 It includes one or more photon counting detectors having a value greater than . In some embodiments, a single photon counting detector detects the location and number of detected photons.

[0055] In some embodiments, the T-SAXS system is used to determine the characteristics of a specimen (e.g., structural parameter values) based on one or more diffraction orders of scattered light. As shown in Figure 1, the measurement tool 100 includes a computing system 130 that acquires a signal 135 generated by a detector 119 and is used to determine the characteristics of the specimen based at least partially on the acquired signal.

[0056] In some cases, T-SAXS-based measurements involve determining the dimensions of a sample using the measured data by inversely solving a predetermined measurement model. The measurement model includes a small number (approximately 10) of adjustable parameters representing the shape and optical properties of the sample as well as the optical properties of the measurement system. The inverse method may include, but is not limited to, model-based regression, tomography, machine learning, or any combination thereof. In this way, the target profile parameters are estimated by solving for the parameterized measurement model values ​​that minimize the error between the measured scattered X-ray intensity and the modeled result.

[0057] In one embodiment, the computing system 130 is configured as a multi-pass measurement engine, which determines the values ​​of one or more parameters of interest that characterize a measured structure based on measurement data and prior measurement information collected by a measurement system, such as a measurement system 100.

[0058] Figure 2 illustrates a multi-path measurement engine 160 in one embodiment. As shown in Figure 2, the multi-path measurement engine 160 includes an MLE-based measurement module 161 and a MAP-based measurement module 163.

[0059] As shown in Figure 2, for example, measurement data 135 collected from one or more structures under measurement by the measurement system 100 shown in Figure 1 is communicated to an MLE-based measurement module 161. Based on the measurement data 135, the MLE-based measurement module 161 determines an initial set of initial values ​​for an initial set of parameters of interest that characterize the measured structure. The MLE-based measurement module 161 optimizes the likelihood function using regression on the measurement model. The initial values ​​162 of the initial set of parameters of interest are communicated to a MAP-based measurement module 163.

[0060] As shown in Figure 2, measurement data 135 collected from one or more structures under measurement, initial values ​​162 for an initial set of parameters of interest, and optionally prior statistics 165 generated from exogenous sources are received by the MAP-based measurement module 163. Statistical measures characterizing each of the initial value sets for the initial set of parameters of interest, and optional prior statistics 165 from exogenous sources, are included as part of the optimization function driving the MAP-based analysis. Prior statistics for exogenous sources often encompass two uncertainty factors: statistical spread in the measurement ensemble and inherent measurement errors in the external measurements. Generally, both uncertainty factors are combined into a single prior statistical model. The MAP-based measurement module 163 uses regression on the measurement model to optimize a likelihood function, as well as an objective function that includes additional terms containing the statistical measures characterizing each of the initial value sets for the initial set of parameters of interest and the optional prior statistics 165. In some embodiments, estimates 164 of one or more parameters of interest are stored in memory, for example, memory 132, as final estimates 140 of the parameters of interest.

[0061] In some other embodiments, the estimates 164 are evaluated to determine whether measurement requirements 167, such as desired measurement uncertainty, are met. If they are met, the estimates of the parameters of interest are stored in memory, for example, memory 132. If they are not met, the estimates of the parameters of interest are returned to the MAP-based measurement module 163, and subsequent iterations of the MAP-based analysis are performed. In the subsequent iterations, the objective function includes additional terms containing a likelihood function and statistical measures that characterize each of the estimates of the parameters of interest determined in the previous iterations. This iteration continues until the desired measurement requirements are met. The final estimates 140 of one or more parameters of interest are stored in memory, for example, memory 132.

[0062] Generally, prior measurement information is characterized by one or more statistical measures, i.e., prior statistics, which are performed in a MAP-based optimization function.

[0063] The pre-measurement information includes actual measurement data, simulated measurement data, hypothetical measurement data, or any combination thereof. In some embodiments, the pre-measurement information includes simulated measurement data from simulations of measurements of one or more measurement targets that are structurally different from the structure under measurement.

[0064] In some embodiments, pre-measurement information includes actual measurement data from measurements of a specific target using a specific measurement tool. Typically, the measurement data includes actual measurements of the target on a nominal wafer. In some embodiments, the measurement data is collected from multiple wafers. In some embodiments, the measurement data is collected from a Design of Experiment (DOE) wafer. In some embodiments, the measurement data is collected by multiple measurement systems.

[0065] In some embodiments, the pre-measurement information includes assumed values ​​for one or more parameters of interest. In one example, the values ​​of one or more parameters of interest are assumed to be within an expected range. A statistical measure is imposed on one or more parameters based on the assumed range, without using an ensemble of simulated or measured data. In one example, a parameter x is expected to vary within a range [AB]. Gaussian regularization is assumed, and the mean m and standard deviation S are calculated to match the first two moments for an assumed uniform distribution, as shown by equations (4) and (5).

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[0066] In some embodiments, the statistical measure includes prior values ​​of the parameter of interest, such as prior assumed values, prior simulated values, or the mean and variance in the assumed distribution of prior measurements of the parameter of interest.

[0067] In some embodiments, both the likelihood function P(m|x) and the prior distribution P(x) are assumed to be Gaussian and are parameterized by the mean and variance, as shown by equations (7a) and (7b), where x is the parameter vector, s(x) is the function that generates the signal from the parameterization, and S is the variance of the signal, i.e., E[ss T] and m s m is the average of the signal, x is the mean of the parameters, and T is the variance of the parameters, i.e., E[xx] T ]

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[0068] The objective function C'(p), shown by equation (8), is realized by taking the logarithms of the functions P(m|x) and P(x), reversing the signs to obtain local minima, and removing the constant term so that the local minima is at zero.

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[0069] In a further embodiment, additional regularization terms are added to the optimization function, each additional term based on a different statistical measure that quantifies the prior measurement information.

[0070] In some of these embodiments, the statistical scales fi are statistically independent. In these embodiments, the joint probability associated with a set of statistical scales can be calculated by simply multiplying the probabilities associated with each independent event. Furthermore, the log-likelihood associated with the joint probability associated with a set of statistical scales is calculated as the sum of the probabilities associated with each independent event. In one example, the cost function C''(p) includes two independent statistical scales f1(x) and f2(x) that characterize prior measurement information. C''(p) is given by equation (9), where m1 is the mean of the index f1(x) and V1 is its variance. The form of equation (9) assumes a Gaussian distribution associated with the statistical scales f1 and f2.

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[0071] The cost function shown by equation (9) includes additional regularization terms associated with two additional independent statistical measures f1 and f2. However, in general, the cost function may include additional regularization terms associated with any number of independent prior measurement information statistical measures.

[0072] In some other embodiments, the statistical scale fi is statistically dependent. In these embodiments, the joint probability associated with the set of statistical scales includes an additional term to address the covariance between the scales.

[0073] Generally, the cost function can include additional regularization terms associated with any number of statistical measures of prior measurement information, without requiring the measures to be statistically independent of or dependent on known correlations. In these examples, the cost function includes additional regularization terms associated with any number of statistical measures of prior measurement information, without considering statistical relationships between the statistical measures, in order to simplify optimization and reduce computational effort.

[0074] In some embodiments, the statistical measure characterizing the prior measurement information includes the mean and variance of an assumed distribution of normed values ​​over a set of prior values ​​for several parameters of interest. The normed values ​​are strictly positive and arise from an integral norm of any form. The distribution of the underlying parameters of interest is assumed to be a Gaussian distribution. In general, the class that transforms a multidimensional Gaussian distribution into a reduced statistic on a radius derived from its mean is called a "bulls-eye distribution". Thus, the distribution of normed values ​​is assumed to be a bulls-eye distribution with a probability density function given by equation (10). The bulls-eye function has dimension n and is defined by the scale r.

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[0075] In some of these embodiments, the normed measure r is the integral of the curvature over the profile x, and is given by equation (11).

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[0076] In some embodiments, this integral is calculated exactly when the function y(x) is described as a weighted sum of polynomials, or as a discrete approximation, such as when y is known at discrete points. The cost function term C''' associated with the normed value is given by equation (12).

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[0077] The probability density function of the Bullseye distribution is parameterized by a single parameter σ, which is scaled as the mean, while the variance is handled by changing the dimensionality n. In this way, the Bullseye distribution is fitted to the mean and variance of the ensemble data by selecting n and σ to fit the ensemble data. To fit the Bullseye distribution to the ensemble data, the moment generation function shown by equation (13) is used, where μ is the mean of the ensemble data and V is the variance of the ensemble data.

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[0078] In some examples, the values ​​of σ and n are adjusted using a two-dimensional search algorithm to match the mean and variance of the normed data.

[0079] In another aspect, each statistical scale f i The ensemble statistics associated with (x) are determined for each measurement target based on pre-measurement information collected at different locations across the wafer or set of wafers.

[0080] In some embodiments, a single aggregated statistic is determined for each measurement target, characterizing the ensemble statistic across a wafer or set of wafers. In these embodiments, the statistic associated with each measurement target is independent of the wafer position. In these embodiments, the mean ν of the ensemble of reference data d containing N data points is calculated as shown in equation (14).

number

[0081] In some embodiments, a spatially parameterized model is determined to characterize ensemble statistics associated with pre-measurement information collected at different locations across a wafer or set of wafers for each measurement target. The pre-statistics used for MAP-based optimization are then calculated from this spatially parameterized model. In these embodiments, the statistics associated with each measurement target depend on the wafer location.

[0082] In some embodiments, a spatially parameterized model with respect to the mean ν(ρ,θ) is fitted to the reference data d using least-squares fitting, where ρ and θ are polar coordinates specifying the position on the wafer surface. The variance is obtained by subtracting the mean from the reference data and squaring the result, as shown by equation (15).

number

[0083] For normed data, variance is applied to examples where the mean is fitted to a spatially varying curve. In these examples, the variance is calculated after the mean model has been fitted. Here,

number

number

[0084] In some embodiments, the number of dimensions n of the Bullseye distribution is adjusted to match the mean and variance from a fit as shown by equation (16). The functional form of the mean is scaled by the square root of the number of dimensions to obtain the Bullseye parameter σ, as shown by equation (17).

number

[0085] In some embodiments, a weighted average of statistics for measurement targets in the vicinity of a particular measurement target is determined, characterizing the ensemble statistics across a wafer or set of wafers for each measurement target. In some examples, the weights are functionally related to the distance from the measurement target under measurement, such as through a mathematical process like kriging. In these embodiments, the statistics associated with each measurement target are wafer position-dependent, height-dependent, or both.

[0086] In some embodiments, the noise of the measurement system is characterized more precisely by a Poisson distribution rather than a Gaussian distribution. In these embodiments, the likelihood function P(m|x) is characterized by a Poisson distribution shown by equation (18).

number

[0087] By taking the negative logarithm of the function described by equation (18), reversing the sign, and setting an offset such that the minimum value is zero, we obtain the cost function C_poisson shown by equation (19).

number

[0088] In another embodiment, prior statistics are tracked to determine the impact of one or more parameters of interest on the current measurement. In some embodiments, a statistical tracking scale is determined that characterizes the probability of rapid process drift. The statistical tracking scale has a low probability when the manufacturing process is being tracked normally, and a high probability when the manufacturing process undergoes an unexpected deviation. In this way, the statistical tracking scale tracks the prior and post-statistics of the wafer over time.

[0089] In some examples, statistical tracking measures are updated across wafers using Markov chains and post-correction. In some examples, interactional multiple models (IMMs) or other pseudo-Bayesian methods are used to track the manufacturing process across wafers. In some examples, statistics may be determined across the entire wafer. In some other examples, statistics may be determined within multiple different regions of the wafer. In these examples, a wafer-wide probability map is determined that shows the probability of rapid process drift associated with each of the different regions of the wafer.

[0090] In a further embodiment, prior wafer statistics used as part of a multi-pass measurement are updated based on values ​​of a statistical tracking scale. In one example, if the statistical tracking scale indicates a higher probability of process drift, more recent prior statistics or statistics that are more spatially close are weighted more highly, and vice versa.

[0091] Additional information regarding the Interacting Multiple Model is found in "Interacting multiple model methods in target tracking: a survey" by E. Mazor et al., IEEE Transactions on Aerospace and Electronic Systems, Volume 34, Issue 1 (January 1998), and its contents are incorporated herein by reference throughout this specification.

[0092] As a non-limiting example, Figure 3 shows a system 300 for measuring the properties of a specimen according to the exemplary method described herein. As shown in Figure 3, the system 300 can be used to perform a spectroscopic ellipsometry measurement of a structure 301. In this embodiment, the system 300 may include a spectroscopic ellipsometer comprising an irradiator 302 and a spectrometer 304. The irradiator 302 of the system 300 is configured to generate and direct an irradiation of a selected wavelength range (e.g., 100 to 2500 nm) onto a structure disposed on the specimen surface on which the structure 301 is manufactured. The spectrometer 304 is configured to receive the irradiation reflected from the structure 301. It should be further noted that the light emitted from the irradiator 302 is polarized using a polarization state generator 307 to generate a polarized irradiation beam 306. The radiation reflected by the structure 301 passes through a polarization state analyzer 309 to reach the spectrometer 304. The radiation received by the spectrometer 304 in the collected beam 308 is analyzed in terms of its polarization state, enabling spectral analysis of the radiation that has passed through the analyzer by the spectrometer. These spectra 311 are passed to the computing system 330 for the analysis of structures such as those described herein.

[0093] As shown in Figure 3, System 300 includes a single measurement technique (i.e., SE). However, generally, System 300 can include any number of different measurement techniques. As a non-limiting example, System 300 can be configured as a spectroscopic ellipsometer (including Müller matrix ellipsometry), spectroreflectometer, spectroscattermeter, overlay scattermeter, angle-resolved beamprofile reflectometer, polarization-resolved beamprofile reflectometer, beamprofile reflectometer, beamprofile ellipsometer, ellipsometer of any single or multiple wavelengths, or any combination thereof. Furthermore, generally, measurement data collected by different measurement techniques and analyzed according to the methods described herein can be collected from multiple tools, a single tool integrating multiple techniques, or a combination thereof.

[0094] In further embodiments, the system 300 may include one or more computing systems 330 used to estimate the values ​​of one or more parameters of interest 340 that characterize a structure measured according to the method described herein. One or more computing systems 330 may be communicatively coupled to the spectrometer 304. In one embodiment, one or more computing systems 330 are configured to receive measurement data 311 associated with the measurement of a structure under measurement (e.g., structure 301).

[0095] In some embodiments, the measurement model is used to estimate the values ​​of geometrically important parameters (e.g., critical dimension, overlay, etc.), dispersion important parameters (e.g., refractive index, etc.), process important parameters (e.g., lithography focus, dose, etc.), electrical important properties (e.g., band gap, etc.), or any combination thereof.

[0096] In a further embodiment, the value of the parameter of interest is determined on one measuring tool or across multiple measuring tools for measurements of production wafers, monitor wafers, or both.

[0097] Generally, measurement data may be collected from any suitable semiconductor measurement system. Suitable systems include, but are not limited to, spectroscopic ellipsometers, spectrophotometers, soft X-ray based measurement systems, small-angle X-ray scattering measurement systems, imaging systems, hyperspectral imaging systems, and the like.

[0098] In some embodiments, the structure under measurement described herein may be an actual device structure or a dedicated measurement target.

[0099] Generally, measurement data may be collected from one or more targets by multiple different measurement systems. In one example, measurement data from a first target may be collected by a spectroscopic ellipsometer, measurement data from the same or different targets may be collected by a small-angle X-ray scattering (SAXS) system, and measurement data from the same or different targets may be collected by an imaging-based measurement system.

[0100] In yet another further embodiment, 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, the values ​​of measurement parameters determined based on the measurement method described herein can be communicated to the etching tool to adjust the etching time to achieve a desired etching depth. Similarly, etching parameters (e.g., etching time, diffusivity, etc.) or deposition parameters (e.g., time, concentration, etc.) can be included in the measurement model to provide active feedback to the etching tool or deposition tool, respectively. In some examples, modifications to process parameters determined based on measured device parameter values ​​can be communicated to the process tools. In one embodiment, the computing system 130 determines the values ​​of one or more parameters of interest. Furthermore, the computing system 130 communicates a control command to the process controller based on the determined values ​​of one or more parameters of interest. The control command causes the process controller to change the state of the process (e.g., stop the etching process, change the diffusivity, etc.). In one example, the control command causes the process controller to adjust the focus of the lithography system, the exposure of the lithography system, or both. In another example, a control command causes the process controller to change the etching rate to improve the measured wafer uniformity of the CD parameter.

[0101] In some cases, the measurement model is implemented as an element of the SpectraShape® optical critical dimension measurement system, available from KLA-Tencor Corporation in Milpitas, California, USA. In this way, the model is created and ready for use immediately after the spectrum is collected by the system.

[0102] In some other examples, the measurement model is performed offline by a computing system running AcuShape® software, for example, available from KLA-Tencor Corporation in Milpitas, California, USA. The resulting trained model may be incorporated as an element of the AcuShape® library, accessible by the measurement system performing the measurements.

[0103] Figure 4 shows a method 200 for estimating the value of one or more quality indicators representing performance characteristics of semiconductor measurements in at least one novel embodiment. Method 200 is suitable for implementation by a measurement system such as the measurement system 100 shown in Figure 1 of the present invention. In one embodiment, it is recognized that the data processing block of Method 200 can be executed by a pre-programmed algorithm executed by one or more processors of the computing system 130, or by any other general-purpose computing system. It is recognized that in this specification, certain structural embodiments of the measurement system 100 should be construed as illustrative only and not as limiting.

[0104] In block 201, irradiation radiation is provided and directed to a measurement site on the surface of the semiconductor wafer.

[0105] In block 202, in response to the irradiation radiation, radiation collected from one or more structures disposed on the semiconductor wafer at the measurement site is detected.

[0106] In block 203, a quantity of measurement data is generated that characterizes the radiation detected from the measurement site.

[0107] In block 204, the values ​​of one or more parameters of interest that characterize one or more structures are estimated based on the measurement data and pre-measurement information. The estimation of the values ​​of one or more parameters of interest involves an iterative solution of an optimization function that includes terms associated with the measurement data and terms associated with the pre-measurement information.

[0108] In a further embodiment, the system 100 includes one or more computing systems 130 used to perform measurements of semiconductor structures according to the method described herein. One or more computing systems 130 may be communicably connected to one or more spectrometers, active optical elements, process controllers, irradiation sources, etc. In one embodiment, one or more computing systems are configured to receive measurement data associated with the measurement of one or more structures disposed on a wafer.

[0109] It should be recognized that one or more steps described throughout this disclosure may be performed by a single computer system 130 or, alternatively, by multiple computer systems 130. Furthermore, different subsystems of system 100 may include computer systems suitable for performing at least some of the steps described herein. Accordingly, the foregoing description should not be construed as a limitation on the invention, but merely as an example.

[0110] Furthermore, the computer system 130 can be communicatively coupled to the detector in any manner known in the art. For example, one or more computing systems 130 may be coupled to a computing system associated with the detector. In another example, the detector may be directly controlled by a single computer system coupled to the computer system 130.

[0111] The computer system 130 of system 100 can be configured to receive and / or acquire data or information from subsystems of the system (e.g., detectors) via a transmission medium which may include wired and / or wireless portions. In this way, the transmission medium can function as a data link between the computer system 130 and other subsystems of system 100.

[0112] The computer system 130 of system 100 can be configured to receive and / or acquire data or information (e.g., measurement results, modeling inputs, modeling results, reference measurement results, etc.) from other systems via a transmission medium which may include a wired portion and / or a wireless portion. In this way, the transmission medium can function as a data link between the computer system 130 and other systems (e.g., a memory-equipped system 100, external memory, or other external systems). For example, the computing system 130 can be configured to receive measurement data from a storage medium (i.e., memory 132 or external memory) via the data link. For example, measurement results acquired using the detector described herein can be stored in a persistent or semi-persistent memory device (e.g., memory 132 or external memory). In this regard, measurement results can be imported from onboard memory or an external memory system. Furthermore, the computer system 130 can send data to other systems via the transmission medium. For example, measurement models or estimated parameter values ​​determined by the computer system 130 may be communicated and stored in external memory. In this regard, measurement results may be exported to another system.

[0113] The computing system 130 may include, but is not limited to, a personal computer system, a cloud-based computing system, a mainframe computer system, a workstation, an image computer, a parallel processor, or any other device known in the art. Generally, the term “computing system” can be broadly defined to encompass any device having one or more processors that execute instructions from a memory medium.

[0114] Program instructions 134 that implement methods such as those described herein can be transmitted via a transmission medium such as a wired, cable, or wireless transmission link. For example, as shown in Figure 1, program instructions 134 stored in memory 132 are transmitted to the processor 131 via bus 133. Program instructions 134 are stored in a computer-readable medium (e.g., memory 132). Exemplary computer-readable mediums include read-only memory, random-access memory, magnetic or optical disks, or magnetic tapes.

[0115] As used herein, the term “critical dimension” includes any critical dimension of a structure (e.g., bottom critical dimension, mid-section critical dimension, top critical dimension, side wall angle, grid height, etc.), critical dimensions between any two or more structures (e.g., distance between two structures), and displacements between two or more structures (e.g., overlay displacement between overlaid grid structures, etc.). Structures may include three-dimensional structures, patterned structures, overlay structures, etc.

[0116] As used herein, the terms “critical dimension application” or “critical dimension measurement application” include any critical dimension measurement.

[0117] As used herein, the term “measurement system” includes any system used at least partially to characterize a specimen in any aspect, including measurement applications such as critical dimension measurement, overlay measurement, focus / exposure measurement, and composition measurement. However, such technical terms do not limit the scope of the term “measurement system” as used herein. In addition, system 100 may be configured for the measurement of patterned wafers and / or unpatterned wafers. The measurement system may consist of an LED inspection tool, an edge inspection tool, a back inspection tool, a macro inspection tool, or a multimode inspection tool (including data from one or more platforms simultaneously), and any other measurement or inspection tool that benefits from the calibration of system parameters based on critical dimension data.

[0118] Various embodiments of semiconductor measurement systems are described herein, which may be used to measure specimens within any semiconductor processing tool (e.g., inspection system or lithography system). The term “specimen” is used herein to refer to a wafer, reticle or any other sample which may be processed (e.g., printed or inspected for defects) by means known in the art.

[0119] As used herein, the term “wafer” typically refers to a substrate formed from a semiconductor or non-semiconductor material. Examples include, but are not limited to, single-crystal silicon, gallium arsenide, and indium phosphide. Such substrates may be those commonly found and / or processed within semiconductor manufacturing facilities. In some cases, a wafer may consist only of a substrate (i.e., a bare wafer). Alternatively, a wafer may consist of one or more layers of different materials formed on the substrate. One or more layers formed on the wafer may be “patterned” or “unpatterned.” For example, a wafer may consist of multiple dies having repeating pattern features.

[0120] A “reticle” may be a reticle at any stage of the reticle manufacturing process, or a finished reticle that may or may not be released for use within a semiconductor manufacturing facility. A reticle or “mask” is typically defined as a substantially transparent substrate on which substantially opaque regions are formed and which are composed of a certain pattern. The substrate may include, for example, a glass material such as amorphous SiO2. The pattern on the reticle may be transferred to the resist by being placed on a resist-coated wafer during the exposure step of a lithography process.

[0121] One or more layers formed on a wafer may be patterned or unpatterned. For example, a wafer may contain multiple dies, each having repeating pattern features. The formation and processing of such layers of material may result in a finished element. Many different types of elements may be formed on a wafer, and the term wafer as used herein is intended to include wafers on which any type of element known in the art is fabricated.

[0122] In one or more exemplary embodiments, the described functions may be implemented in hardware, software, firmware, or any combination thereof. Where the functions are implemented in software, the functions may be stored on a computer-readable medium or transmitted as one or more instructions or codes on a computer-readable medium. Computer-readable medium includes both computer storage media and communication media, and these include any media that facilitate the transfer of computer programs from one location to another. Storage media may be any available media accessible by a general-purpose or dedicated computer. Such computer-readable media may comprise, but are 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 media that can be used to transmit or store desired program code means in the form of instructions or data structures, and can be accessed by a general-purpose or dedicated computer or a general-purpose or dedicated processor. Any connection is also appropriately referred to as computer-readable medium. For example, if software is transmitted from a website, server, or another remote source using coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave, then coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of media. As used herein, disk and disc include compact discs (CDs), laser discs, optical discs, digital multipurpose discs (DVDs), floppy disks, and Blu-ray discs, in which case disks typically copy data magnetically, while discs optically copy data by laser. The above combinations should also be included in the scope of computer-readable media.

[0123] Although certain embodiments have been described above for illustrative purposes, the teachings in this patent document have general applicability and are not limited to the specific embodiments described above. Accordingly, various modifications, adaptations, and combinations of various features of the embodiments described may be implemented without departing from the scope of the invention as set forth in the claims.

Claims

1. It is a system, An irradiation source configured to provide irradiation radiation directed to a measurement site on the surface of a semiconductor wafer, A detector configured to detect radiation collected from one or more structures disposed on the semiconductor wafer at the measurement site in response to the aforementioned irradiation radiation, A computing system, The system generates measurement data that characterizes the radiation detected from the measurement site. A computing system configured to estimate the values ​​of one or more parameters of interest that characterize one or more structures based on the measurement data and pre-measurement information, wherein the estimation of the values ​​of the one or more parameters of interest involves an iterative solution of an optimization function that includes terms associated with the measurement data and terms associated with the pre-measurement information. A system characterized by comprising the following features.

2. The system according to claim 1, wherein the computing system is A system further configured to estimate a prior value of at least one of the one or more parameters of interest that characterize the one or more structures, based on the measurement data, wherein the estimation of the prior value of at least one of the one or more parameters of interest involves an iterative solution of a prior optimization function that includes a term associated with the measurement data, and the prior measurement information includes the prior value of at least one of the one or more parameters of interest.

3. The system according to claim 2, characterized in that the iterative solution method for the optimization function is based on maximum posterior probability (MAP) analysis, and the iterative solution method for the prior optimization function is based on maximum likelihood estimation (MLE) analysis.

4. The system according to claim 3, wherein the optimization function is a negative log-likelihood function, and the term associated with the measurement data is a likelihood function, The system is characterized in that the term associated with the pre-measurement information includes a positive function characterized by a statistical model of the pre-measurement information.

5. The system according to claim 4, wherein the statistical model of the pre-measurement information is parameterized by the wafer position.

6. A system according to claim 4, wherein the statistical model of the pre-measurement information characterizes the statistical spread of the pre-measurement information in the measurement ensemble and the measurement error of the exogenous measurement used to measure the pre-measurement information.

7. The system according to claim 1, wherein the term associated with the measurement data includes a statistical model of the measurement noise, and the statistical model assumes a Gaussian distribution of the measurement noise.

8. The system according to claim 1, wherein the term associated with the pre-measurement information includes a positive function characterized by a statistical model of the pre-measurement information, the statistical model assuming a Gaussian distribution of at least one of the one or more prior values ​​of interest.

9. The system according to claim 1, wherein the term associated with the measurement data includes a statistical model of the measurement noise, and the statistical model assumes a Poisson distribution of the measurement noise.

10. The system according to claim 1, wherein the term associated with the prior measurement information includes a positive function characterized by a statistical model of the prior measurement information, the statistical model assumes a generalized bullseye distribution of the normalized value, and the normalized value is determined from prior values ​​of at least two parameters of interest.

11. The system according to claim 10, wherein the computing system is The system is further configured to determine the value of the number of dimensions of the generalized bullseye distribution such that the statistical model best matches the mean and standard deviation of the ensemble of normed values.

12. The system according to claim 1, characterized in that the pre-measurement information incorporated into the optimization function is derived from one or more extrinsic sources.

13. The system according to claim 1, wherein the computing system is Track the values ​​of one or more statistical measures that characterize the pre-wafer statistics that characterize the pre-measurement information, The pre-measurement information is updated based on the value of one or more of the statistical scales. A system characterized by being further configured in such a way.

14. A system according to claim 1, characterized in that the irradiation source and the detector include an optical measurement system or an X-ray-based measurement system.

15. The system according to claim 1, wherein the pre-measurement information includes assumed values ​​of one or more parameters of interest, and the assumed values ​​are within the predicted range of values ​​of the one or more parameters of interest. The system is characterized in that the assumed values ​​are characterized by an assumed statistical distribution.

16. It is a method, To provide irradiation radiation directed to a measurement site on the surface of a semiconductor wafer, In response to the aforementioned irradiation radiation, the radiation collected from one or more structures disposed on the semiconductor wafer at the measurement site is detected. To generate measurement data characterizing the detected radiation from the measurement site, The method involves estimating the value of one or more parameters of interest that characterize one or more structures based on the measurement data and pre-measurement information, wherein the estimation of the value of one or more parameters of interest involves an iterative solution of an optimization function that includes terms associated with the measurement data and terms associated with the pre-measurement information. A method characterized by including the following.

17. The method according to claim 16, Based on the measurement data, the method involves estimating a prior value of at least one of the one or more parameters of interest that characterize the one or more structures, wherein the estimation of the prior value of at least one of the one or more parameters of interest involves an iterative solution of a prior optimization function that includes terms associated with the measurement data, and the prior measurement information includes the prior value of at least one of the one or more parameters of interest. A method characterized by further comprising the following.

18. The method according to claim 16, wherein the optimization function is a negative log-likelihood function, and the term associated with the measurement data is a likelihood function, The method is characterized in that the term associated with the pre-measurement information includes a positive function characterized by a statistical model of the pre-measurement information.

19. A method according to claim 18, wherein the statistical model is parameterized by the wafer position.

20. A method according to claim 16, wherein the term associated with the measurement data includes a statistical model of the measurement noise, the statistical model assumes a Poisson distribution of the measurement noise.

21. A method according to claim 16, wherein the term associated with the prior measurement information includes a positive function characterized by a statistical model of the prior measurement information, the statistical model assumes a generalized bullseye distribution of the normalized value, and the normalized value is determined from prior values ​​of at least two parameters of interest.

22. The method according to claim 16, Tracking the values ​​of one or more statistical measures that characterize the pre-wafer statistics that characterize the aforementioned pre-measurement information, Updating the pre-measurement information based on the value of one or more statistical scales, A method characterized by further comprising the following.

23. It is a system, An irradiation source configured to provide irradiation radiation directed to a measurement site on the surface of a semiconductor wafer, A detector configured to detect radiation collected from one or more structures disposed on the semiconductor wafer at the measurement site in response to the aforementioned irradiation radiation, A non-temporary computer-readable medium for storing instructions, wherein when an instruction is executed by one or more processors, the instructions are sent to the one or more processors. To generate measurement data characterizing the detected radiation from the measurement site, Based on the measurement data and pre-measurement information, the values ​​of one or more parameters of interest characterizing the one or more structures are estimated, and the estimation of the values ​​of the one or more parameters of interest involves an iterative solution method of an optimization function that includes terms associated with the measurement data and terms associated with the pre-measurement information. To generate first measurement data characterizing the detected radiation from the measurement site, Using a trained quality monitoring model, the values ​​of one or more target measurement quality indicators are determined based on the first measurement data, and each of the one or more target measurement quality indicators represents the measurement quality associated with a different operating element of the measurement system, in a non-temporary computer-readable medium. A system characterized by comprising the following features.

24. The system according to claim 23, wherein the non-temporary computer-readable medium further stores instructions, and when the instructions are executed by the one or more processors, the one or more processors A system characterized in that, based on the measurement data, it estimates at least one prior value of one or more parameters of interest that characterize one or more structures, the estimation of the at least one prior value of one or more parameters of interest involves an iterative solution of a prior optimization function that includes a term associated with the measurement data, and the prior measurement information includes the at least one prior value of one or more parameters of interest.

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