System and method for controlling measurement of various sample parameters

Abstract

A system and method for controlling measurement of various sample parameters is provided. The system includes a control unit configured as a computer system including data input and output utility, a memory, and a data processor, and configured to communicate with a measurement data provider to receive measurement data indicative of a measurement of a sample. The data processor is configured to perform model-based processing on the measurement data using at least one predetermined model, and for each of one or more measurements of one or more parameters of interest of the sample, determine an estimated upper limit of error values for the individual measurements, and generate output data indicative of the estimated upper limit.

Description

[0001] This application is a divisional application of the Chinese patent application with application number 202180047252.8. Technical Field

[0002] The present invention is in the field of model-based sample inspection / measurement and relates to systems and methods for controlling the measurement of various sample parameters. Background Art

[0003] The present invention is particularly suitable for measuring various characteristics of patterned structures (e.g. semiconductor structures), which is useful for controlling the manufacturing process of such structures and controlling the operating parameters of the measurement system. Semiconductor structures such as integrated circuits have become more complex in terms of the size and shape of the pattern parameters. Therefore, there is an increasing need to provide accurate measurements of such parameters, which also enables the measurement to be applied to structures performed on a production line, i.e. automatic inspection / measurement of patterned structures (metrology, defect detection, process control, etc.).

[0004] As semiconductor structure dimensions shrink, highly sensitive metrology tools and data analysis are required to monitor the properties of semiconductor structures. Metrology tools typically utilize optical critical dimension (OCD) measurement techniques (also known as scatterometry), which are effective for measuring parameters of patterned (periodic) structures such as layer thickness, critical dimension (CD), line spacing, line width, wall depth, wall profile, etc. The measurement of structural parameters is typically a model-based measurement performed using a fitting procedure, and the structural parameters are extracted from the model under the best fit conditions relative to the measured data.

[0005] Various model-based measurement techniques are described, for example, in the following patent publications: US 20130124141; US ​​9,904,993; US 10,295,329; all assigned to the assignee of the present application. Summary of the invention

[0006] What is needed is a novel method to control / validate the measurement of various parameters of a sample / structure via error estimation in the measurement (eg, OCD metrology measurement).

[0007] Under applicable quality standards, the acceptability of a particular sample and / or a particular sample manufacturing process may depend on metrics (quality assurance related indicators) defined according to the specific standards, and if a sample has unacceptable metrics, it may be rejected and / or one or more parameters of its manufacturing process may be changed (optimized). Typically, the measurement data analysis is of a model-based type utilizing machine learning techniques.

[0008] The shrinking dimensions and growing complexity of today’s semiconductor manufacturing processes are pushing metrology for such processes to their limits and making it difficult to keep metrology tools within the specifications required by tight process constraints. Uncertainties in metrology results such as accuracy, process robustness, precision, matching, etc. are difficult to achieve with existing methods. In addition, other metrics such as throughput (TPT), WIW sampling rate limits are facing challenging requirements dictated by process control. Finally, the difficulty of designing quality advantages that are closely related to metrology accuracy is another emerging challenge faced by the community over the past decade. Such advantages are reasonably related to the accuracy of the inference model; easy to compute; and, ideally, unsupervised (meaning that their availability does not depend on the availability of external references to the inference model). In addition, these advantages are easy to calibrate at training time (when the reference is available) and the calibration is stable.

[0009] The present invention provides novel techniques for controlling / validating the measurement of sample parameters using model-based analysis of measured data, and for evaluating / determining measurement errors. In this regard, it should be emphasized that the techniques of the present invention provide error range estimates for each individual measurement of a sample parameter, rather than the usual error estimates that are independent of the characteristics (signals) of the individual measurements. The error estimates provided by the techniques of the present invention depend on the characteristics of the samples measured individually. More specifically, the present invention provides estimates of the error bounds for each measurement individually, i.e., estimates of the error bounds for each parameter of one or more parameters of interest in the measured sample, rather than the usual errors of the measured data provided by measurement tools / systems based on cost function-based methods.

[0010] A measurement system typically provides measurement data (e.g., in the form of a signature, such as a spectral signature) in which a collection of multiple signals that are affected by and therefore indicative of a sample parameter is embedded. The present invention provides a technique for processing such measurement data and providing output data that indicates an estimated upper bound on the measurement error of each measurement, individually, for each of one or more parameters of interest. This enables consideration of measurement errors of specific parameters to determine whether measurements provided by a specific measurement tool (measurement scheme and measurement channel) and / or a measured data analysis based on a specific model are sufficient for a specific parameter of a sample; and enables consideration of measurement errors of a parameter relative to measurement errors of one or more other parameters of interest to decide on the best model for data analysis.

[0011] The present invention utilizes the general principles of a machine learning inference process that is applied to a model after it has been trained (by running a specified subset of data into the model). The present invention provides a novel modification to the training and inference testing phases of data analysis that enables the extraction of error bounds for each measurement from the measured data. The model can be a machine learning model or a hybrid model that is a combination of machine learning and physical models.

[0012] Therefore, according to a broad aspect of the present invention, there is provided a system for controlling various measurements of various sample parameters, the system comprising: a control system configured as a computer system, the computer system comprising data input and output utilities, a memory and a data processor, and configured to communicate with a measurement data provider to receive measurement data collected from the sample, wherein the data processor is configured to perform model-based processing on the measurement data using at least one predetermined model, and for each measurement of one or more parameters of interest of the sample, determine an estimated upper limit value of a separate measurement error, and generate output data indicating the estimated upper limit value.

[0013] It should be noted that the term "sample" as used herein should be interpreted broadly to also include a measurement point in a structure (eg, including a plurality of measurement points).

[0014] The measurement data (measurement signal, e.g., spectrum) can be obtained by N f A multidimensional vector representation of components / elements.

[0015] The data processor can be configured to perform the following model-based processing: applying a training phase to at least one predetermined model to obtain a corresponding at least one training model, and using the training model to determine a functional relationship between the measurement data and the upper error limit of the corresponding individual measurement; and performing an inference testing phase by applying the functional relationship to the measurement data to associate the estimated upper error limit of the corresponding individual measurement with one or more parameters of the measured sample.

[0016] In some embodiments, the training phase of the model-based processing includes:

[0017] When at least one predetermined model is trained using the measured data and the training set, a distance metric D in the signal parameter space is determined. F , and obtain the training model;

[0018] Use the predicted model parameters of the trained model to determine the distance metric D in the error parameter space E , for measuring the error of the predictions relative to the training set; and

[0019] Determine the upper limit on the error in individual measurements with the distance metric D E, thereby defining the functional relationship between the measurement data and the upper error limit for each individual measurement.

[0020] It should be understood that, in contrast to the common approach to evaluating regression error, according to which the training results are used to obtain the average error for each parameter from the training (cross-validation) scheme, which value is then set as the general error estimate for the inference phase, the present invention utilizes the distance metric D in a way that a different error estimate can be obtained for each new sample. F .

[0021] The definition of the functional relationship is based on geometric considerations that allow us to use the distance metric D E An upper error limit is inferred for each measurement of each of the one or more parameters being measured.This geometric consideration is based on the assumption of a geometry defined by the distribution of multiple error components of the multi-dimensional error vector.

[0022] For example, the shape of the error function can be viewed as a hyperellipsoid in the error parameter space; and the error is therefore bounded by a rectangle containing this hyperellipsoid.

[0023] The training phase of the model-based process may further include: determining a distance metric D F With distance metric D E , so that it is possible to use the distance metric D determined for the measured data F To directly determine the distance metric D E .

[0024] Distance metric D F and the distance metric D E The determination of the relationship between can include defining a distance metric D F and the distance measure D E A correlation condition is defined between the respective two predetermined functions.

[0025] In some embodiments, the data processor is configured to perform the distance metric D in the error parameter space by performing the following operations: E The determination of:

[0026] Determine a multidimensional error vector, the multidimensional error vector includes N for each sample p N values ​​of the prediction model parameters p error components; and

[0027] Using the multidimensional error vector and the determined distance metric D F To determine the distance metric D in the error parameter space E .

[0028] In some embodiments, the data processor is configured to determine a distance metric D in the error parameter spaceE and the error vector N p The relationship between the upper limits of each individual error component of the error components.

[0029] The inference test phase may include: performing inference on the measured data of the tested sample by the training model by applying the functional relationship between the measured data and the upper error limit to the measured data; and determining the upper error limit for each individual parameter to form N p parameters.

[0030] The system may further include an error analyzer utility configured to analyze the measurement error of each of the one or more parameters of interest and generate corresponding alarm data upon identifying that the measurement error is above a specific value. For example, the specific value may be defined by a predetermined accuracy threshold and / or may be determined based on a relationship between measurement errors determined for at least two different parameters of the sample.

[0031] The measurement data provider may be a storage device, which may or may not be part of the measurement system. In some embodiments, the control system is configured to communicate data with an external measurement system / storage device, or may alternatively be integrated with a measurement system configured to perform measurements on a sample and generate (and store) measurement data. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to better understand the subject matter disclosed herein and to illustrate how it can be implemented in practice, embodiments will now be described, by way of non-limiting examples only, with reference to the accompanying drawings, in which:

[0033] Figure 1 is a block diagram of a control system for controlling sample measurement of the present invention;

[0034] Figure 2 is a block diagram illustrating the configuration and operation of a data processor utility program of the control system of the present invention;

[0035] Figure 3A and Figure 3B An example is given of an analysis of OCD measurements of a wafer based on the use of a distribution of distance metrics in the parameter space of the measurement signal, where: Figure 3A shows the performance of the wafer average of the metric for a group of wafers, and Figure 3B The OCD spectra of most corresponding wafers are shown;

[0036] Figure 4 The D defined according to the present invention is illustrated as an example. E and D F The correlation between

[0037] Figure 5A and Figure 5B A graphical illustration of how to determine an upper bound BND for the error in a single i-th parameter i ;

[0038] FIG. 6A to FIG. 6D It shows that the Figure 5A The correlations shown in the figure calculate the D of the four parameters respectively. F and D E the results; and

[0039] Fig. 7A and Figure 7B The implementation of the training and inference testing phases according to the present invention is illustrated by way of a flowchart. DETAILED DESCRIPTION

[0040] refer to Figure 1 , by way of a block diagram, shows a system 10 for managing (controlling / validating) the measurement of various sample parameters. The system 10 comprises a control system 12 configured for data communication with a measurement data provider 14.

[0041] Such a measurement data provider 14 includes a storage device 16 that stores measurement data obtained by one or more measurement tools 18 in one or more measurement sessions performed on a sample. The measurement tool 18 may be part of the measurement data provider 14. The measurement data provider 14 may be an external system in data communication with the control system 12, or may be part of / integrated with the control system. Therefore, in some embodiments, the system 10 is an integrated system including the measurement system (measurement data provider) 14 and the control system 12.

[0042] The control system 12 is configured as a computer system, which includes, among other things, a data input utility 12A, a data output utility 12B, a memory 12C, and a data processor 12D. The data processor 12D is configured to perform model-based processing on the measurement data MD received from the measurement data provider 14 and determine parameter-related error data. The measurement data MD represents a measurement signal (e.g., a signature) whose components are affected by various parameters of a sample measured under given measurement conditions (measurement channels).

[0043] According to the present invention, the data processor 12D is configured and operable to process the measurement data MD using a predetermined model-based processing based on at least one predetermined model and, for each measurement (and therefore for each of one or more parameters of the sample), determine a separate parameter-related estimate for the measurement error of the corresponding parameter.

[0044] Therefore, the error data related to the parameters provided by the processor (e.g., the measurement status of each i-th parameter of interest) may include one or more estimated limits on the error value (maximum value or upper error limit) of each measurement in one or more individual measurements of the one or more parameters of the sample; or alternatively or additionally, such status data may include data indicating whether such error meets the measurement requirements of the parameter. In other words, the processor determines the measurement status of each i-th parameter of interest based on the corresponding estimated maximum measurement error (upper limit of measurement error).

[0045] More specifically, the data processor 12D is configured to perform model-based processing (e.g., machine learning type processing) and includes a first processor 20, which is configured to perform a model training phase relative to an original (selected / predetermined) model M (e.g., stored in the memory 12C) and obtain training model data TM, and use the training model data TM to define an error determination function that describes the relationship between the measurement data and the distribution of maximum error values ​​of multiple measurements / parameters that respectively affect the measurement data.

[0046] The data processor 12D further comprises a second processor 22 configured to apply an inference test phase process (so-called "run time") to the measurement data (new measurement data) using the error determination function and determine the measurement state of each parameter of interest. The result of the inference test phase process is an estimated upper bound of the error value BND, which is assigned to each i-th measurement / parameter respectively according to one or more parameters of interest of the measured sample.

[0047] The selected model M may be of any known suitable type, such as a machine learning model, or any hybrid model that is a combination of a machine learning model and a physical model.

[0048] As also shown in the figure, the control system 12 may include an error analyzer 23 configured to analyze the measurement error bound BND of each i-th parameter of interest. i (eg based on a predefined criterion), and upon identifying that the measurement error limit is above a certain value, generates a corresponding control signal CS to the alarm generator 25 i For example, the specific value may be defined by a predetermined accuracy threshold and / or may be determined based on a relationship between measurement errors determined for at least two different parameters of the sample.

[0049] The model-based processing of the present invention provides a method for predicting the p Component p i (i = 1,2, ...,N p ) to represent the set of multiple parameters of the sample (or the measurement point in the sample), and these components are the output of the training model TM, which is obtained by training the model on the training set D train These parameters may be, for example, geometric (dimensional) and / or material parameters describing the profile (2D or 3D) of the patterned structure for a particular processing step (such as width, CD's, height, sidewall angles, fillets, etc.). (For example, parameters of a FIN in a FEOL advanced semiconductor manufacturing process).

[0050] The measured data MD obtained as input data for the training model TM consists of N f Component (f j , j = 1,2, ...,Nf) vector Represents and can describe multiple types of measurements (e.g., metrology signals) in multiple types of measurement channels. For example, such measurement channels can include reflectance measurements and / or ellipsometry measurements. The measured signals can represent values ​​of optical reflectance at a set of light wavelengths and different illumination angles and polarizations for a spectroscopic reflectometer, angular scatterometer, or spectroscopic ellipsometer.

[0051] The output parameters of the model are predicted by , and the true value (GT) of these parameters is given by For simplicity, Represents the error in the model prediction :

[0052]

[0053] parameter The true value of can be the result of non-optical metrology such as CDSEM or cross-sectional TEM, or in some cases it can also be the result of optical metrology using a large number of optical channels and physical / geometric models that are very accurate when many optical channels are used.

[0054] Referring to FIG. 10 for illustrating the configuration and operation of the data processor 12D Figure 2 As shown, the first processor 20 performing the model training phase includes a distance metric determination utility 24 , a calibration utility 26 , and an error function determination utility 28 ; and the second processor 22 includes a parameter error generator 30 and a measurement state generator 32 .

[0055] The distance metric determination utility 24 is configured to use the selected model M and the predetermined training set D train To process the measurement data MD (measurement signal) to determine the distance measure D in the signal space with respect to the model training set F, and determine the distance metric D of the measurement error in the error space with respect to the model training set E The calibration utility 26 is configured to determine the distance metric D F and D E The error function determination utility 28 is configured to utilize geometric considerations to infer the distance metric D E and the error BND of each individual i-th measurement / parameter of one or more parameters of the measured sample i The relationship between the upper limit of BND i (D E ).

[0056] The inference test processor 22 includes a parameter error generator 30 which uses the function BND i (D E ) to determine a parameter-specific (measurement-specific) maximum error in the actual measurement data, i.e., to assign a maximum value of a possible measurement error to each parameter of interest of the measured sample (e.g., a parameter of a specific measurement point in the measured structure). The processor 22 may further include a measurement status generator 32, which analyzes the maximum error relative to the requirement for the parameter and generates corresponding data (e.g., an alarm).

[0057] An example of the operation of the model training processor will now be described in more detail.

[0058] More specifically, the distance metric D in the signal space F The determination includes the qualification and calculation of any new and potentially anomalous measurements (set of signals) and training set D train This could be, for example, And in the training set D train Dataset Center Therefore, for the new set of signals This distance metric D F It can be determined as follows:

[0059]

[0060] Or as a weighted distance metric ,

[0061]

[0062] where w is a weighting factor that can depend on the characteristics of the signal space at training time, such as The variance of , since it is encoded in the noise spectrum, can be measured by computing its probability density, as well as any of its moments Γ pTensor, as shown below:

[0063]

[0064] Where <, > train set is the average value of the entire training set.

[0065] For example, the Euclidean distance weighted by the second moment of the training set is as follows:

[0066]

[0067] In general, the weighting factor w is a function of any combination of K moment tensors The set of moments can be represented by {Γ}, and the more general distance metric can be written as follows:

[0068]

[0069] The choice of parameters q and weights w are hyperparameters of the metric. Additional hyperparameters can include any regularization properties designed to eliminate the effects of D F sensitivity to different types of noise and make it more robust. This will be described further below.

[0070] Used to determine the distance metric D in the signal space F Another possible example is to calculate a new measurement and any measurement The pairwise weighted distance between train Then, we can use the weight These distances are further weighted, with the weights Can rely on metadata (such as the time span between dates of pairs of members):

[0071]

[0072] or as summarized below:

[0073]

[0074] It should be noted that when defining the distance metric D F After it has been trained in the training set, it can be applied at inference time and used as a statistical analysis of the results to make decisions. F A threshold is set for each measurement value to determine whether the sample is abnormal and generate a corresponding alarm. At the same time, D of a group of samples (such as a single wafer or batch) can be F Analyze the distribution of to make decisions based on its mean, variance, etc.

[0075] The distance D in the signal spaceF Setting rules and thresholds for their statistical properties can be done at any of the above levels, as well as generalizations thereof (such as a group of wafers belonging to a given process DOE or at a given time interval frame). Some methods for setting these thresholds are further described below.

[0076] Figure 3A The metric of Equation 7 is shown How the wafer average (wafer mean) of performs for a group of wafers. Here, the measurement data includes OCD measurements at normal illumination angles and two polarization channels. Wafer W1 is a normal distribution wafer, and wafer W2 is an outlier wafer.

[0077] Figure 3B Shows Figure 3A of Normal (measurement data MD1) and Figure 3A of OCD spectra of most wafers that “jump” to outliers (measurement data MD2).

[0078] It should be noted that the distance metric D defined and calculated in the signal space is F The processing can be considered as a function D F The "training" of The value of this attribute is calculated as shown in Formula 4 above.

[0079] Back to Figure 2 The distance metric determination utility 24 is further configured to determine a distance metric D of the measured error in the error space with respect to the model training set. E To this end, a similar approach can be used to determine the distance metric D F , but with the error parameter space modified. More specifically, the same equations and methods above can be used with the following substitutions:

[0080]

[0081] For each sample, considering the vector YesN f -dimensional, and the vector YesN p -Wei, = (e1 e2, ...eN p ), where N p is the number of prediction parameters:

[0082]

[0083] Therefore, the distance metric determination utility 24 implements a training scheme (which may be any known suitable scheme at this stage) to obtain N for each sample (e.g., consisting of measurement points in the structure) p -dimensional error vector , and calculate the distance metric D for each sample F (Use Equation 5 or Equation 7 above).

[0084] Then we can use the distance metric D F To obtain the distance metric D for each sample E (Equation 9 above).

[0085] It should be noted that if the distance metric D E According to the well-defined relationship (function) and distance metric D F related, we can determine and use D E With D F This means that for each new measurement, using this relationship / function, the distance metric D of the “measurement” can be F Directly calculate the distance metric D E . This could be a linear function, for example.

[0086] To this end, the calibration utility 26 performs a distance metric D E To the distance metric D F calibration.

[0087] Preferably, D F Set the threshold. Here is an example of setting such a threshold:

[0088] Functional dependencies A(x; h) and B(x; g), where h and g represent the set of hyperparameters that define A and B. Basic choices of functions A and B (such as logarithms or polynomials) can also be considered hyperparameters.

[0089] Using validation and cross validation methods, the tuple (h, g) is optimized and (h0, g0) is calculated. In the training set A (x = D E ; h = h0) and B (x = D F ; g = g0). Using these validation and cross-validation methods, A(x=D E ; h = h0) and B (x = D F ; g=g0) will calibrate A to B.

[0090] For example, using quadratic correlation, the result is the following model / relationship:

[0091] A=α+β·B+γ·B 2

[0092] It predicts A based on B. Higher capacity models such as kernel regression, neural networks, tree regression, etc. can also be considered.

[0093] For example, Figure 4 It shows that B=D E and A=D F The correlation between , both are defined by Equation 6 above. Figure 4 The “shape” illustrated in corresponds to the calculation of D using Equation 6 E and D F The data in the figure represent the data for about 300 wafers and for N p =10 and N f = 980. The Pearson correlation coefficient obtained is 0.94.

[0094] The way to set the threshold depends on the definition of B. For example, in the simplest case, where N p =1, and A= For each measurement we have:

[0095] e=±A

[0096] In this case, the accuracy specification Δ can be used as a threshold for |e| = A, thereby flagging each measurement or group of measurements with an error larger than the specification.

[0097] In some other cases, where, for example, N p =2, and A= The equation describing the relationship between the two errors and e2 is as follows:

[0098]

[0099] Then, for a given value of A, you can do:

[0100] e 1(2) The prior information of e is used to obtain the 2(1) For example, if p1 is a parameter with an external reference, but p2 is not, then that reference data can be used to determine if e2 is within specification, otherwise flagging the associated measurement.

[0101] In the absence of such a priori information, and in the case where Equation 6 and Equation 8 represent closed shapes (such as Equation 10), it is possible to calculate the shape of the closed shape for each parameter i = 1, 2, ..., N p The error determination bound BND in i (A). For example, in the two-dimensional case of Equation 10, Figure 5A Shows N p=2, and A= Although the error in the parameter can vary over a finite range and there is a finite uncertainty associated with both, they are both bounded by ±A. Therefore, the bound on A is:

[0102]

[0103] BND1,2 (can now be obtained from D by the correlation between B and A and Equation 10 F Calculated in real time) Any measurement that is greater than the corresponding customer specification of accuracy in p1 or p2 can be flagged.

[0104] The generalization of the above is straightforward: the calibration of A to B done at training time can be used to estimate B from A. Then, once A is measured and the value A=a is determined, and when A( ) = a is a closed function. p -dimensional shape, we can find N that restricts this shape p -dimensional hypercube, and its edges can be used to define the bounds of each parameter. Figure 5B This is illustrated by an example.

[0105] As mentioned above, the geometric considerations used here are based on the assumption of a geometric shape defined by the distribution of multiple error components of a multidimensional error vector. For example, the error function can be viewed as a hyperellipsoid in the error parameter space; the error is therefore defined by a rectangle containing such a hyperellipsoid.

[0106] Considering Equation 3a above, in 2D projection with q=2, we have:

[0107]

[0108] It defines an ellipse in the error space, where the error e2 (for parameter N2) can be expressed in terms of the error e1 for parameter N1.

[0109] Therefore, plotting e2 as a function of e1 will result in an ellipse as shown. The ellipse is bounded by a rectangle that defines the upper limit of each parameter error. In the figure, the vertical edges of the rectangle define the limit BND2 on the error component e2, and the horizontal edges define the limit BND1 on the error component e1.

[0110] In higher dimensions (N p >2), D E In N p A hyperellipsoid is defined in the dimensional space, and the boundary of the hypercube (the boundary of the hyperellipsoid) defines the upper limit of each error component.

[0111] As an example, FIG. 6A to FIG. 6DShows the Figure 5A The results for four parameters P1, P2, P3, P4 out of ten parameters of the correlation A and B using Equation 6, respectively, are shown in FIG. The data represented in these figures are for grain-level prediction of the error, where the discrete points correspond to the error magnitude |e| for the above specified error from the above parameters, and the bounds are represented by monotonically increasing points); the Y-axis shows the error and the X-axis the value of B. These figures show that the bound is valid: on the one hand, most of the points are below it, and on the other hand, it is not a loose bound.

[0112] Therefore, return to Figure 2 The error determination utility 26 is configured to utilize the above-mentioned geometric considerations to determine the distance metric D E The error BND is determined separately for each i-th parameter of one or more parameters of the measured sample i upper limit.

[0113] Referring to FIG. 10 which more specifically illustrates an example of the operation of the processors 20 and 22 of the data processor 12D. Fig. 7A and Figure 7B .

[0114] Fig. 7A A flow chart 100 is shown of the model training phase performed by the processor 20. As shown, the selected model M is trained using the input measurement data MD to determine a distance metric D in the signal parameter space for each sample. F , as described above with reference to Equation 5 (step 102). Using the training model, together with the measured data MD, to be N for each sample p prediction parameter prediction error vector = ( e1, e2, ... eN p ), as described above with reference to Equation 9 (step 104). Based on the prediction error vector (which may also include some reference data or prior knowledge), determine the distance metric D in the error parameter space E (Step 106). Calibration considerations are applied to the distance measure D thus determined F and D E (Step 108) to determine the F Prediction D E Then, using the prediction model based on D F Estimated / predicted D E and geometric considerations to determine the function BND i (A), this function is used to calculate the upper limit BND i The calculation model (calculation method) of (A), as described above, also represents the BND for each individual i-th error component of the error vector relative to the i-th parameter of the sample i (DE ) (step 110), and generates corresponding training phase results 112 (used by the inference phase processor 22 for at least BND i calculation method).

[0115] Figure 7B 120 illustrates an example of inference phase processing. In this phase, the training model implements the above method to perform inference on the measured signal vector of the new sample. , and the prediction error vector N p parameters / components.

[0116] As mentioned above, for the measured signal vector, the distance metric D can be calculated F , and is used to infer the distance metric D using the relationship between these distance metrics during the training phase E . So determined D E The upper bound BND used to calculate the error of each i-th parameter i As a result, the trained model individually attaches / assigns an error estimate to each measurement of each of the one or more measured parameters of the sample.

[0117] Back to FIG. 6A to FIG. 6D , it can be seen that the above technique is able to provide the user with information about each given value B (and therefore about the distance metric D F ) or more information about the error distribution of each given interval of values ​​B. To do this, the probability density function can be calculated and the cumulative distribution function During the inference phase, these functions can be used to estimate the probability that a parameter falls near a boundary line. Fig. 7A and Figure 7B Shown in.

[0118] The above techniques of the present invention can be generalized to wafer-level processing or group-level processing by merging multiple dies in a given wafer or group. This can be performed as follows:

[0119] In a preprocessing step, the average values ​​of the measurement signal and the error vector can be determined over the wafer or group. The distance metric D is then determined as described above. E and the distance metric D F , and determine the wafer or group averages of these distance metrics (both of which are essentially defined at the die level). E To D F The calibration is applied to the grain size D F , from which the grain size D E The results are then used to obtain the grain-level boundaries and averaged to obtain the wafer / group-level anomaly index.g Given a given case of grains, concatenate the grain-level signal vectors of these grains and / or error vector , and the new N g x N f -dimensional signal vector and N g x N p The -dimensional error vector is used as input to the calibration and thresholding procedures described above. The limits of each parameter data can then be averaged across multiple die within a given wafer / group.

[0120] As mentioned above, preferably, the distance metric D is eliminated F The sensitivity to different types of noise can be increased to make the measurement more robust. In reality, the measured signal is always noisy.

[0121]

[0122] in p process The distribution of is related to the manufacturing process, and p measurement The distribution of is related to the measurement procedure itself. To incorporate the effects of measurement noise into the distance measurement, the above limitation can be modified by averaging the two sources of variation in the data. For example, Equation 12 becomes:

[0123]

[0124] where the mean is taken from the joint probability distribution .

[0125] Ideally, the above averages are estimated empirically on a training set, where the measurement of each sample is repeated several times to simulate measurement noise. In practice, measurement noise is rarely estimated in this way due to throughput requirements. Instead, the noise is either estimated theoretically or empirically for several different samples. This makes it difficult to estimate the joint distribution and, therefore, the above averages.

[0126] For simplicity, we can assume as well as are statistically independent. The independence assumption can be relaxed when only partial moments are needed; for example, if only 2 nd Moment into the defined distance, as in Equation 5, assuming and Irrelevant is enough.

[0127] In this case, we can use the normal training set and p measurement to estimate the mean above (usually, only the first few moments are needed).

[0128] The invention thus provides a novel method for controlling / validating the measurement of various sample parameters. The method provides for accompanying / assigning to the parameter measurement values ​​an estimated upper limit of the individual measurement error of said parameter.

Claims

1. A system for controlling the measurement of various sample parameters, the system comprising: a control unit configured as a computer device, the computer device comprising a data input and output utility, a memory and a data processor, and configured to communicate with a measurement data provider to receive measurement data indicative of measurements of a sample, wherein the data processor is configured to perform model-based processing on the measurement data using at least one predetermined model, and for each of one or more measurements of one or more parameters of interest of the sample, determine an estimated upper bound for an error value of the individual measurement, and generate output data indicative of the estimated upper bound, wherein The parameters are geometric parameters and / or material parameters describing the profile of the patterned semiconductor structure, and The measurement data describe various types of measurements in various types of measurement channels, Wherein, the data processor is configured to perform the model-based processing including: applying a training phase to at least one predetermined model to obtain a corresponding at least one training model, and using the training model to determine a functional relationship between the measurement data and an upper limit on the error of each measurement of a parameter affecting each corresponding sample of the measurement data; and performing an inference testing phase by applying the functional relationship to the measurement data to individually associate an upper limit on the error value estimated separately with each of the one or more parameters of the measured sample, and Wherein, the training phase of the model-based processing includes: When the at least one predetermined model is trained using the measured data and the training set, a distance metric D in the signal parameter space is determined. F , and obtain the training model; The prediction model parameters of the training model are used to determine the distance metric D in the error parameter space. E , which measures the error of the predictions relative to the model training set; and Determine the upper error limit and the distance metric D of the sample parameter E , thereby defining the functional relationship between the measurement signal and the upper error limit.

2. The system according to claim 1, wherein: The measurement data indicates a measurement signal affected by one or more parameters of the sample, and the data processor is configured to obtain a measurement signal by N f A multidimensional vector of components is used to represent the measurement data.

3. The system according to claim 1, wherein: The at least one predetermined model includes at least one from: a machine learning model and a hybrid model that is a combination of a machine learning model and a physical model.

4. The system according to claim 1, wherein: The training phase of the model-based processing further comprises: determining the distance metric D F With the distance metric D E The relationship between , so that the distance metric D determined for the measurement data can be F To directly determine the distance metric D E .

5. The system according to claim 4, wherein: The determination of the relationship comprises defining the distance metric D F and the distance metric D E The correlation condition between the respective two predetermined functions.

6. The system according to claim 1, wherein: The data processor is configured to perform the distance metric D in the error parameter space by performing the following operations: E The determination of: Determine a multidimensional error vector, the multidimensional error vector comprising N p N values ​​of the prediction model parameters p error components; as well as Using the multidimensional error vector and the distance metric D in the determined signal parameter space F To determine the distance metric D in the error parameter space E .

7. The system according to claim 1, wherein: The data processor is configured to determine the distance metric D in the error parameter space E and the error vector N p The relationship between the upper limits of each individual error component of the error components.

8. The system according to claim 1, wherein: The inference test phase includes: performing inference on the measurement data of the tested sample by the training model by applying the functional relationship between the measurement signal and the upper error limit to the measurement data; and determining the upper error limit for each individual parameter to form N p parameters.

9. The system of claim 1 , further comprising an error analyzer utility configured and operable to analyze measurement errors of each of the one or more parameters of interest and, upon identifying that the measurement errors may be above a particular value, generate corresponding alarm data.

10. A method for controlling the measurement of various sample parameters, the method comprising: providing measurement data indicative of a plurality of measurement signals affected by a parameter of the sample; as well as applying model-based processing to the measurement data using at least one predetermined model and determining, for each of one or more parameters of interest, an estimated upper limit value for an individual measurement of the parameter, and generating output data indicative of the estimated upper limit value, wherein The parameters are geometric parameters and / or material parameters describing the profile of the patterned semiconductor structure, and The measurement data describe various types of measurements in various types of measurement channels, The data processing comprises: applying a training phase to at least one predetermined model to obtain a corresponding at least one training model, and using the training model to determine a functional relationship between the measurement signal and an upper limit on the error of a sample parameter affecting the measurement signal; and performing an inference test phase by applying the functional relationship to the measurement data to individually associate an estimated upper limit on the error value with each of the one or more parameters of the measured sample, and Wherein, the training phase of the model-based processing includes: When the at least one predetermined model is trained using the measured data and the training set, a distance metric D in the signal parameter space is determined. F , and obtain the training model; The prediction model parameters of the training model are used to determine the distance metric D in the error parameter space. E , which measures the error of the predictions relative to the model training set; and Determine the upper limit of the error of the sample parameter and the distance metric D E , thereby defining the functional relationship between the measurement signal and the upper error limit.

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