Method and system for monitoring metrology tool fleet productivity

Abstract

Described herein are methods and systems for assessing the productivity of individual semiconductor metrology tools based on both individual tool productivity metrics and tool fleet productivity metrics. Productivity metrics associated with each individual tool are combined with productivity metrics associated with a fleet of tools to identify problematic tools quickly and with fewer false positives. Tool productivity results are obtained more quickly, particularly in situations where productivity depends on infrequent events. One or more accuracy metrics are estimated to indicate the confidence in the ranking of individual tools in the fleet of metrology tools. Additionally, probabilities of future failure events associated with individual tools in the fleet of metrology tools are predicted based on the difference between a predicted probability distribution of failure events and an actual observed distribution of failure events.

Description

[Technical Field]

[0001] The described embodiments relate to metrology systems and methods, and more particularly to methods and systems for improving measurement accuracy of semiconductor structures. [Background technology]

[0002] Semiconductor devices, such as logic and memory devices, are typically fabricated by a series of processing steps applied to a specimen. The various features and structural levels of a semiconductor device are formed by these processing steps. For example, lithography, among other processes, is one semiconductor manufacturing process that involves creating patterns on a semiconductor wafer. Other examples of semiconductor manufacturing processes include, but are not limited to, chemical-mechanical polishing, etching, deposition, and ion implantation. Multiple semiconductor devices may be formed on a single semiconductor wafer and then separated into individual semiconductor devices.

[0003] Metrology processes are used at various steps in the semiconductor manufacturing process to detect wafer defects and improve yield. Optical and X-ray metrology techniques allow for high throughput without the risk of sample destruction. Techniques based on many metrology modalities, including scatterometry, reflectometry, and ellipsometry implementations and associated analysis algorithms, are commonly used to characterize critical dimensions, film thickness, composition, overlay, and other parameters of nanoscale structures.

[0004] The performance, integration density, and reliability of semiconductor devices have continuously improved over time due to improved processing resolution and increasingly complex device structures. Improved processing resolution allows for a reduction in the minimum critical size of the structures being processed. Processing resolution is primarily dependent on the wavelength of the light source used in the manufacturing process. The latest extreme ultraviolet lithography (EUV) light sources produce wavelengths of 13.5 nanometers, enabling the fabrication of structural features below 32 nanometers. Additionally, more complex device structures, such as FinFET and vertical NAND structures, have been developed, improving overall performance, energy costs, integration density, and reliability.

[0005] As devices (e.g., logic and memory devices) move to ever smaller nanometer scales, their characterization becomes increasingly difficult. This is due to devices incorporating complex three-dimensional shapes and materials with diverse physical properties. In general, metrology systems are being called upon to measure devices with greater precision at more processing steps.

[0006] In addition to accurate device characterization, it is also important to maintain measurement consistency across measurement applications and metrology system tools serving the same measurement purpose. Poor measurement consistency in a production environment can result in a loss of consistency between processed semiconductor wafers, reducing yield to unacceptable levels. Consistent measurement results across multiple applications and systems (i.e., tool-to-tool consistency) ensures that measurements of the same wafer using the same application will produce identical results.

[0007] To achieve profitability in semiconductor manufacturing, the productivity of semiconductor manufacturing facilities is a must. Productivity is directly related to the productivity of individual tools. For example, a single low-performance tool can become a bottleneck that reduces the productivity of the entire production line. Thus, it is essential to closely monitor the productivity of each tool and address performance issues associated with each tool in a timely manner.

[0008] Traditionally, the productivity of each tool is monitored independently of other tools in the tool fleet. Typically, individual tool productivity metrics are expressed statistically, e.g., as a mean, standard deviation, etc. Furthermore, decisions regarding the need for intervention are made based on the value of the individual tool productivity metrics. In one example, a tool reset rate, e.g., the number of tool resets per month, is calculated independently for each tool in the tool fleet. The tool reset rate characterizes the productivity of the individual tool. The tool reset rate of each individual tool is compared to a baseline to improve the performance of low-performing tools. [Prior art documents] [Patent documents]

[0009] [Patent Document 1] U.S. Patent Application Publication No. 2019 / 0012351 [Patent Document 2] U.S. Patent Application Publication No. 2021 / 0375651 [Patent Document 3] International Publication No. 2021 / 130486 Summary of the Invention [Problem to be solved by the invention]

[0010] Evaluation of productivity based on individual tool productivity metrics is hindered by a lack of robustness. Typically, relatively few reset events occur on production tools operating in a manufacturing facility. A single reset event can cause the value of an individual tool productivity metric to deviate from an acceptable baseline range. In other words, the signal from an individual productivity metric is drowned out by noise because the events that drive the signal value are extremely rare.

[0011] One attempt to solve this problem is to simply evaluate individual tool productivity metrics over a longer period of time to improve the robustness of the calculations. For example, tool reset rate may be calculated as the average tool reset rate over several weeks or months. Unfortunately, this approach has several significant limitations. First, extending the period over which individual tool productivity is evaluated can delay the discovery of underperforming tools, reducing the overall productivity of the manufacturing facility for a long period of time. Second, extending the period over which individual tool productivity is evaluated can lead to inaccuracies because the baseline range of tolerances may shift over the extended period.

[0012] As metrology systems evolve to measure devices at more processing steps with greater precision, assessing tool fleet productivity becomes increasingly complex and less effective. Improved methods and tools are needed to reduce the time and costs associated with maintaining high productivity across a metrology tool fleet. [Means for solving the problem]

[0013] A method and system for assessing the productivity of individual semiconductor metrology tools based on both individual tool productivity metrics and tool fleet productivity metrics are described below. The accuracy, speed, and robustness of the productivity assessment for each individual tool are improved by including productivity metrics for both individual equipment and tool fleets. The productivity metrics associated with each individual tool are combined with productivity metrics associated with tool fleets to quickly identify problematic tools and reduce false positives. Tool productivity results are obtained more quickly, especially in situations where productivity depends on infrequent events.

[0014] The tool fleet productivity rating engine characterizes the productivity of each measurement device in a metrology tool fleet and ranks the metrology systems in order of productivity, which ranking can then be used by users to guide decision-making regarding tool repair and maintenance.

[0015] A productivity dataset includes data indicative of individual tool performance characteristics collected from many individual tools in a semiconductor metrology tool fleet. By way of non-limiting example, performance characteristics indicative of tool productivity include tool downtime, tool downtime, tool reset rate, time between unscheduled resets, etc. Productivity metrics are used to numerically characterize individual tool and tool fleet productivity. In general, the value of one or more individual tool productivity metrics characterizing the performance of each individual tool in a metrology tool fleet is determined independently of the value of one or more tool fleet productivity metrics characterizing the performance of the metrology tool fleet.

[0016] An individual tool-based productivity index value associated with each individual tool is determined from the productivity data corresponding to each individual tool in the productivity dataset. Similarly, a group-based productivity index value is determined from the productivity data corresponding to groups of individual tools in the productivity dataset.

[0017] In some examples, the individual tool productivity index and the tool group productivity index are determined based on simple statistical measures, such as the mean and standard deviation of the distribution of performance data, the median of the distribution of performance data, the harmonic mean of the distribution of performance data, the slope of a linear regression performed on the distribution of performance data, etc.

[0018] In some other examples, the individual tool productivity index and the group of tools productivity index are determined based on fitting the performance data to an analytical function, such as a Gaussian function, a Poisson function, etc. In some of these examples, the productivity index values ​​that characterize the performance of an individual tool or a group of tools are parameters of an analytical model.

[0019] In some other examples, the individual tool productivity index and the group of tools productivity index are determined based on a model built based on trained machine learning (ML).

[0020] In one aspect, one or more combined productivity index values ​​associated with each individual tool of the measurement tool group are determined based on one or more individual tool productivity index values ​​and one or more tool group productivity index values ​​associated with each individual tool.

[0021] In some examples, the tool group productivity index and the individual tool-based productivity index are combined by selecting a relevant subset of both the tool group and individual tool-based indices. In some of these examples, the combined productivity index is determined by comparing the value of the individual tool productivity index with the value of the corresponding tool group productivity index. In one example, the difference between the average tool reset rates associated with each individual tool is compared to the average tool reset rates associated with all individual tools in the tool group. Each difference is the combined productivity index value associated with the corresponding individual tool.

[0022] In other examples, the combined productivity index is determined based on the statistical distance between the distribution of productivity index values ​​based on the individual tool and the distribution of productivity index values ​​based on the group of tools, with the statistical difference being used to quantify the degree to which the individual tool differs from the group of tools.

[0023] In a further aspect, the individual tools of the measurement tool group are ranked based on one or more combined productivity index values. If an individual tool performs poorly, the individual tools are selected for intervention, i.e., maintenance, repair, or both, in a ranked order determined by the one or more combined productivity index values. Furthermore, the ranking of the individual tools may be based on one or more combined productivity indexes and one or more individual productivity indexes.

[0024] In some examples, the individual tools are ranked based on at least one combined productivity index. In other examples, the individual tools are ranked based on at least one combined productivity index and an individual productivity index.

[0025] In yet another embodiment, one or more accuracy index values ​​are estimated, the accuracy index indicating the confidence in the ranking of an individual tool within a set of metrology tools.

[0026] In yet another aspect, the probability of a future failure event associated with at least one individual tool of the measurement tool group is predicted based on the difference between a predicted probability distribution of the failure event and an observed actual distribution of the failure event.

[0027] The foregoing is a summary and thus necessarily contains simplifications, generalizations, and omissions of detail. Consequently, those skilled in the art will appreciate that the summary is illustrative only and is not intended to be limiting in any way. Other aspects, inventive features, and advantages of the devices and / or processes described herein will become apparent in the non-limiting detailed description set forth herein. [Brief explanation of the drawings]

[0028] [Figure 1] FIG. 1 is an exploded view illustrating one embodiment of an optical metrology tool for measuring properties of a specimen in accordance with exemplary methods presented herein. [Figure 2] FIG. 1 is a configuration diagram of a tool group productivity evaluation engine in one embodiment. [Figure 3] 10 is a bar graph showing the average tool reset rate associated with each individual tool in a group of measurement tools. [Figure 4] 10 is a bar graph showing the standard deviation of tool reset rates associated with each individual tool in a group of measurement tools. [Figure 5] 1 is a histogram plotting tool reset rates associated with a group of tools. [Figure 6] 10 is a bar graph showing the KL divergence associated with each individual tool in a group of tools measuring tool reset rates. [Figure 7] This is a bar graph showing the KL divergence as shown in Figure 6, where the bars associated with individual tools whose mean tool reset rate is below the tool group average are shown as transparent, and the bars associated with individual tools whose mean tool reset rate is above the tool group average are shown as shaded. [Figure 8] 10 is a list of accuracy index values ​​associated with the KL divergence calculations associated with each tool in the tool set. [Figure 9] 2 is a flow diagram of a method 200 for assessing productivity of a fleet of tools in a semiconductor metrology system in accordance with at least one novel aspect. DETAILED DESCRIPTION OF THE INVENTION

[0029] Reference will now be made in detail to examples of background art and certain embodiments of the present invention, examples of which are illustrated in the accompanying drawings.

[0030] A method and system for assessing the productivity of individual semiconductor metrology tools based on both individual tool productivity metrics and tool fleet productivity metrics is described below. The inclusion of both individual tool productivity metrics and tool fleet productivity metrics improves the accuracy, speed, and robustness of the productivity assessment for each individual tool. The productivity metrics associated with each individual tool are combined with productivity metrics associated with tool fleets to quickly identify problematic tools while reducing false positives / positives. Tool productivity results are obtained more quickly, especially in situations where productivity is dependent on infrequent events.

[0031] Figure 1 illustrates an exemplary metrology system 100 for performing measurements of structural features of semiconductor devices in accordance with the exemplary methods described herein. As shown in Figure 1, metrology system 100 is configured as a broadband spectroscopic ellipsometer configured to perform measurements of structures within a measurement region 116 of a sample 120 positioned on a sample positioning system 140. However, in general, metrology system 100 may be configured as any semiconductor metrology tool or inspection tool, including, but not limited to, optical semiconductor metrology tools, x-ray semiconductor metrology tools, electron beam semiconductor metrology tools, etc.

[0032] The metrology system 100 includes an illumination source 110 that generates a beam of illumination light 117 incident on the wafer 120. In some embodiments, the illumination source 110 is a broadband illumination source that emits illumination light in the ultraviolet, visible, and infrared spectrums. In one embodiment, the illumination source 110 is a laser-sustained plasma (LSP) light source (also known as a laser-driven plasma light source). The pump laser of an LSP light source can be continuous wave or pulsed. Laser-driven plasma sources can generate significantly more photons than xenon lamps across a wavelength range of 150 nanometers to 2000 nanometers. The illumination source 110 can be a single light source or a combination of multiple broadband or discrete wavelength light sources. The light generated by the illumination source 110 includes a continuous spectrum or a portion of a continuous spectrum from ultraviolet to infrared (e.g., vacuum ultraviolet to mid-infrared). Typically, the illumination source 110 can include a supercontinuous laser source, an infrared helium-neon laser source, an arc lamp, or other suitable light source.

[0033] In a further aspect, the amount of illumination is broadband illumination including a wavelength range spanning at least 500 nanometers. In one example, the broadband illumination includes wavelengths below 250 nanometers and above 750 nanometers. Generally, broadband illumination includes wavelengths between 120 nanometers and 3,000 nanometers. In some embodiments, broadband illumination including wavelengths above 3,000 nanometers may be utilized.

[0034] As shown in FIG. 1 , metrology system 100 includes an illumination subsystem configured to direct illumination light 117 to one or more structures formed on wafer 120. The illumination subsystem is shown to include a light source 110, one or more optical filters 111, a polarizing element 112, a field stop 113, an aperture stop 114, and illumination optics 115. One or more optical filters 111 are used to control the light level, spectral output, or both from the illumination subsystem. In some examples, one or more multi-zone filters are utilized as optical filters 111. Polarizing element 112 generates a desired polarization state exiting the illumination subsystem. In some embodiments, the polarizing element is a polarizer, a compensator, or both, and may include any suitable commercially available polarizing element. The polarizing element may be fixed, rotatable to different fixed positions, or continuously rotatable. While the illumination subsystem shown in FIG. 1 includes one polarizing element, the illumination subsystem may include multiple polarizing elements. Field stop 113 controls the field of view (FOV) of the illumination subsystem and may include any suitable commercially available field stop. Aperture stop 114 controls the numerical aperture (NA) of the illumination subsystem and may include any suitable commercially available aperture stop. Light from illumination source 110 passes through illumination optics 115 and is focused onto one or more structures (not shown in FIG. 1 ) on wafer 120. The illumination subsystem may include optical filters 111, polarizing elements 112, field stop 113, aperture stop 114, and illumination optics 115 of any type and configuration known in the art of spectroscopic ellipsometry, reflectometry, and scatterometry.

[0035] 1, as a beam of illumination light 117 propagates from illumination source 110 to wafer 120, it passes through optical filter 111, polarizing element 112, field stop 113, aperture stop 114, and illumination optics 115. Beam 117 illuminates a portion of wafer 120 that covers measurement spot 116.

[0036] Measurement system 100 also includes a collection optics subsystem configured to collect light generated by the interaction of one or more structures with incident illumination beam 117. The collected beam of light 127 is focused from measurement spot 116 by collection optics 122. Collected light 127 passes through collection aperture stop 123, polarizing element 124, and field stop 125 of the collection optics subsystem.

[0037] The collection optics 122 includes any suitable optical element for collecting light from one or more structures formed on the wafer 120. The collection aperture stop 123 controls the NA of the collection optics subsystem. The polarizing element 124 analyzes the desired polarization state. The polarizing element 124 may be a polarizer or compensator. The polarizing element 124 may be fixed, rotatable to different fixed positions, or continuously rotatable. While the collection subsystem shown in FIG. 1 includes a single polarizing element, the collection subsystem may include multiple polarizing elements. The collection field stop 125 controls the field of view of the collection subsystem. The collection subsystem collects light from the wafer 120 and directs it through the collection optics 122 and the polarizing element 124 to be focused onto the collection field stop 125. In some embodiments, the collection field stop 125 serves as a spectrometer slit of a spectrometer in the detection subsystem. However, the collection point 125 may be located at or near the spectrometer slit of a spectrometer in the detection subsystem.

[0038] The collection subsystem may include collection optics 122, aperture stop 123, polarizing element 124, and field stop 125 of any type and configuration known in the art of spectroscopic ellipsometry, reflectometry, and scatterometry.

[0039] In the embodiment shown in FIG. 1 , the collection optics subsystem directs light to a spectrometer 126. The spectrometer 126 generates an output in response to light collected from one or more structures illuminated by the illumination subsystem. In one example, the detector(s) of the spectrometer 126 are charge-coupled devices (CCDs) sensitive to ultraviolet and visible light (e.g., light with wavelengths between 190 nanometers and 860 nanometers). In another example, one or more detectors of the spectrometer 126 are photodetector arrays (PDAs) sensitive to infrared light (e.g., light with wavelengths between 950 nanometers and 2500 nanometers). However, other detector technologies (e.g., position-sensitive detectors (PSDs), infrared detectors, photovoltaic detectors, etc.) are generally contemplated. Each detector converts the incident light into an electrical signal indicative of the spectral intensity of the incident light. Generally, the spectrometer 126 generates an output signal 128 indicative of the spectral response of the structure being measured to the illuminating light.

[0040] The wafer stage 140 adjusts the position of the wafer 120 relative to the ellipsometer. In some embodiments, the wafer stage 140 moves the wafer 120 in the XY plane by combining two orthogonal translational motions (e.g., motion in the X and Y directions) to adjust the position of the wafer 120 relative to the ellipsometer. In some embodiments, the wafer stage 140 is configured to control the orientation of the wafer 120 relative to the illumination provided by the optical ellipsometer with six degrees of freedom. In one embodiment, the wafer stage 140 is configured to control the azimuthal angle AZ of the wafer 120 relative to the illumination provided by the optical ellipsometer by rotation about the z-axis. In general, the specimen positioning system 140 may include any suitable combination of mechanical elements to achieve the desired linear and angular positioning performance, including, but not limited to, a goniometer stage, a hexapod stage, a square stage, and a linear stage. The computing system 130 is communicatively coupled to the wafer stage 140 and transmits motion command signals 141 to the wafer stage 140. In response, the wafer stage 140 follows the motion control commands to adjust the position of the wafer 120 relative to the ellipsometer.

[0041] Metrology system 100 also includes a computing system 130 that is utilized to acquire signals 128 generated by detector 126 and determine characteristics of the structure of interest based at least in part on the acquired signals. As shown in Figure 1, computing system 130 is configured to receive signals 128 indicative of a measured spectral response of the structure of interest and estimate values ​​129 of one or more parameters of interest, such as CD, overlap, wafer tilt, etc., based on the measured spectral response.

[0042] 2 illustrates one embodiment of a tool fleet productivity rating engine 150 that characterizes the productivity of each metrology tool in a metrology tool fleet and ranks the metrology systems in order of productivity. The rankings can then be used by a user to guide tool repair and maintenance decisions. In some embodiments, computing system 130 is configured as tool fleet productivity rating engine 150 as described herein. However, in general, any suitable computing system communicatively coupled to a metrology tool fleet may be configured as tool fleet productivity rating engine 150 as described herein.

[0043] As shown in FIG. 2, an exemplary tool fleet productivity assessment engine 150 includes a trained quality control encoder module 152, a tool fleet-based productivity index module 151, an individual tool-based productivity index module 152, and a combined productivity index module 153, and optionally a tool productivity ranking module 154.

[0044] 2 , a productivity dataset 155 is received by the tool fleet productivity assessment engine 150. The productivity dataset 155 includes data indicative of individual tool performance characteristics collected from multiple individual tools in a semiconductor metrology tool fleet. In some examples, the productivity dataset 155 may be transmitted from a metrology tool, e.g., the metrology tool 100, a network-accessible computing system configured to store productivity data collected from one or more metrology systems, a network-accessible data storage system configured to store productivity data collected from one or more metrology systems, or any combination thereof. As non-limiting examples, performance characteristics indicative of tool productivity include tool downtime, tool downtime, tool reset rate, time between unscheduled resets, etc.

[0045] 1 is an individual tool in a fleet of semiconductor metrology tools utilized in a semiconductor manufacturing facility. In general, however, a fleet of metrology tools may include any number of the same or different metrology tools utilized in a semiconductor manufacturing facility.

[0046] Productivity indices are used to numerically characterize the productivity of individual tools and tool families. Generally, the value of one or more individual tool productivity indices characterizing the performance of each individual tool in a metrology tool family is determined independently of the value of one or more tool family productivity indices characterizing the performance of the metrology tool family.

[0047] 2, the productivity dataset 155 is communicated to an individual tool-based productivity index module 152. The individual tool-based productivity index module 152 determines one or more individual tool productivity indexes 158 associated with each individual tool from the productivity data corresponding to each individual tool in the productivity dataset 155.

[0048] Similarly, the productivity dataset 155 is communicated to a tool group-based productivity index module 151. The tool group-based productivity index module 151 determines one or more tool group productivity indexes 157 associated with the individual tools from the productivity data in the productivity dataset 155 corresponding to the individual tools of the individual tools.

[0049] In some examples, the individual tool productivity index and the tool group productivity index are determined based on simple statistical indexes, such as the mean and standard deviation of the distribution of performance data, the median of the distribution of performance data, the harmonic mean of the distribution of performance data, the slope of a linear regression performed on the distribution of performance data, etc.

[0050] FIG. 3 shows a chart 170 depicting the average tool reset rate associated with each individual tool in a group of 23 measurement tools. Each individual tool is assigned a tool identification number plotted on the X-axis. The average number of resets per unit time is plotted on the Y-axis. FIG. 4 shows a chart 175 depicting the standard deviation of the distribution of tool reset rates associated with each individual tool in a group of 23 measurement tools.

[0051] The mean values ​​shown in FIG. 3 and standard deviations shown in FIG. 4 are the two statistically based individual tool productivity indices 158 used to characterize the productivity of each of the 23 tools in the metrology tool set.

[0052] In some other examples, the individual tool productivity index and the group of tools productivity index are determined based on fitting the performance data to analytical functions, such as, for example, Gaussian functions, Poisson functions, etc. In some of these examples, the productivity indexes that characterize the performance of individual tools or groups of tools are parameters of the analytical model.

[0053] FIG. 5 illustrates a histogram 180 plotting tool reset rates associated with a group of 23 tools. As shown in FIG. 5, the x-axis is subdivided into 11 distinct event bins. Each event bin represents the number of resets per unit of time for each tool. The number of events corresponding to each event bin is plotted along the y-axis. For example, in a data set describing the number of resets over time for a group of 23 tools, there were over 350 events with zero resets per unit of time, e.g., two weeks, for each individual tool in the group of 23 tools. Similarly, there were over 100 events with one reset per unit of time, e.g., two weeks, for each individual tool in the group of 23 tools.

[0054] The distribution of reset events per unit time for the 23-tool tool group is described by an analytical function 171. As shown in FIG. 5, a Gamma-Poisson function 171 is fitted to the tool reset rate dataset to accurately describe the tool group productivity. In this example, the tool group productivity index 157 characterizing the tool reset rate for the 23-tool tool group are fitting parameters that characterize the Gamma-Poisson function 171 fitted to the tool reset rate distribution plotted in FIG. 5. While a Gamma-Poisson function may be used to describe the distribution of events across the tool group, in general, any suitable mathematical function may be used, such as an exponential distribution. In another example, the tool group productivity index 157 characterizing tool group performance, such as reset events per unit time, is the expectation and variance associated with a Gaussian fit to the productivity dataset 155.

[0055] In some other examples, the individual tool productivity index and the group of tools productivity index are determined based on a trained machine learning (ML)-based model. The ML-based model is trained based on actual performance data, simulated performance data, or both. In some of these examples, the productivity index values ​​characterizing the performance of an individual tool or group of tools are parameters of the ML-based model. In some examples, input performance data is analyzed based on the trained ML model to arrive at the individual tool productivity index and the group of tools productivity index values. In one example, principal component analysis is used to convert the input performance data into productivity index values ​​using the trained ML model.

[0056] In one aspect, one or more combined productivity index values ​​associated with each of the individual tools of the measurement tool group are determined based on the one or more individual tool productivity indexes associated with each individual tool and the one or more tool group productivity index values.

[0057] 2, the value of the tool group productivity index 157 and the value of the individual tool productivity index 158 are communicated to the combined productivity index module 153. The combined productivity index module 153 determines the value of one or more combined productivity indexes 159 based on the value of the tool group productivity index 157 and the value of the individual tool productivity index 158.

[0058] In some examples, the tool group productivity index and the individual tool-based productivity index are combined by selecting relevant subsets of both the tool group and the individual tool-based indexes. In some of these examples, the combined productivity index is determined by comparing the value of the individual tool productivity index with the value of the corresponding tool group productivity index. In one example, the difference between the mean values ​​of the tool reset rates associated with each individual tool is compared to the mean values ​​of the tool reset rates associated with all the individual tools in the tool group. Each difference is the combined productivity index value associated with the corresponding individual tool.

[0059] In some other examples, the combined productivity index is determined based on the statistical distance between the distribution of productivity index values ​​based on an individual tool and the distribution of productivity index values ​​based on a group of tools, and the statistical difference is used to quantify the degree to which the individual tool differs from the group of tools.

[0060] In one example, the statistical distance is determined as the Kullback-Leibler (KL) divergence shown in equation (1), where P(x) is the discrete probability distribution of a single tool reset and Q(x) is the discrete probability distribution of a group of tools reset. KL divergence = Σ x P(x)log(P(x) / Q(x)) (1)

[0061] Figure 6 shows a chart 185 illustrating the KL divergence associated with each individual tool in a tool population of 23 metrology tools for tool reset rate. Each individual tool is assigned a tool identification number plotted on the x-axis. The KL divergence value is plotted on the y-axis. As shown in Figure 6, the individual tools are plotted in order of KL divergence value. Tools with larger values ​​of KL divergence have distributions of tool reset rates that diverge from the tool population distribution of tool reset rates. Conversely, tools with smaller values ​​of KL divergence have distributions of tool reset rates that are closer to the tool population distribution of tool reset rates.

[0062] In a further aspect, the individual tools of the measurement tool group are ranked based on one or more combined productivity index values. If an individual tool performs poorly, the individual tool is selected for intervention, i.e., maintenance, repair, or both, in a ranked order determined by the one or more combined productivity index values. Furthermore, the ranking of the individual tools may be based on one or more combined productivity indexes and one or more individual productivity indexes.

[0063] 2, values ​​of combined productivity index 159, tool group productivity index 157, and individual tool productivity index 158 are communicated to tool productivity ranking module 154. Tool productivity ranking module 154 ranks individual tools in order of urgency for initiating maintenance / repair work based at least in part on one or more combined productivity index values. Tool productivity rankings 160 are communicated to a memory, such as memory 132.

[0064] In some examples, individual tools are ranked based on at least one combined productivity metric. For example, as shown in FIG. 6, individual tools are ranked based on KL divergence values. In one example, individual tools are selected for intervention, i.e., maintenance, repair, or both, based on the KL divergence values. In the example shown in FIG. 6, tool 18 is selected for intervention first, followed by tool 22, then tool 8, etc.

[0065] In some other examples, individual tools are ranked based on at least one combined productivity index and an individual productivity index. For example, KL divergence provides an indication of how well an individual distribution compares to the tool group distribution. However, individual tools with relatively large KL divergence values ​​may perform exceptionally well or exceptionally poorly. To resolve this dilemma, in some examples, the average tool reset rate associated with each individual tool is compared to the average tool reset rates associated with all individual tools in the tool group. Tools with an average tool reset rate below the tool group average are considered acceptable, while tools with an average tool reset rate above the tool group average are considered to require intervention, i.e., maintenance, repair, or both. In some other examples, the standard deviation of the tool reset rate associated with each individual tool is compared to the standard deviation of the tool reset rate associated with the tool group. Tools with a standard deviation of the tool reset rate below the tool group are considered acceptable, while tools with a standard deviation of the tool reset rate above the tool group are considered to require intervention, i.e., maintenance, repair, or both. In some other examples, both the mean and standard deviation of the tool reset rate associated with each individual tool are compared to the mean and standard deviation of the tool reset rate associated with the group of tools, and tools with both a higher mean and standard deviation of the tool reset rate than the group of tools are considered to be in need of intervention, i.e., maintenance, repair, or both.

[0066] FIG. 7 shows a chart 190 representing the KL divergence associated with each individual tool in the group of 23 measurement tools shown in FIG. 6 for tool reset rate. However, bars associated with individual tools whose mean tool reset rate is below the group average are plotted transparent, while bars associated with individual tools whose mean tool reset rate is above the group average are shaded. As shown in FIG. 7, tools 18 and 22 have relatively high KL divergence values, but their mean tool reset rate is below the mean for both tools. Therefore, these tools are performing exceptionally well. Therefore, in the example shown in FIG. 7, tool 8 would be selected for intervention first, followed by tool 3, and then tool 17.

[0067] In general, tools may be ranked based on any number of productivity metrics. In one example, tools are ranked based on tool reset rate and repair time. In this example, it may be advantageous to prioritize tools that can be repaired quickly over less productive tools to improve the overall performance of the tool fleet in a shorter amount of time. In another example, tools are ranked based on tool reset rate and the tool's impact on the overall productivity of the factory. In this example, it may be advantageous to prioritize tools that have a greater impact on overall factory productivity over individually less productive tools to improve the overall performance of the tool fleet.

[0068] In some instances, user input is received by the tool fleet productivity assessment engine to determine which productivity metrics to use in the analysis and the relative importance of the selected productivity metrics. Additionally, user input may be used to determine the combination of individual and tool fleet metrics relevant to tool productivity monitoring. Generally, there are many different tool characteristics that contribute to the overall performance of a metrology tool, and the most relevant productivity metrics will vary depending on the metrology tool's use case. In some instances, minimizing tool downtime may be most important. In other instances, minimizing the rate of unscheduled tool resets may be most important.

[0069] In yet another embodiment, values ​​of one or more accuracy indices are estimated. The accuracy indices indicate the reliability of the ranking of individual tools in the set of measurement tools. In some examples, p-value analysis is used to estimate p-values ​​associated with statistically derived productivity indices. In some examples, goodness-of-fit analysis is used to estimate values ​​of one or more goodness-of-fit parameters, such as residual values, associated with the model-based productivity indices.

[0070] In one example, the uncertainty associated with calculating the mean value of a productivity metric is high when there are not enough data points, for example, when a tool has been idle for an extended period of time. FIG. 8 shows a chart 195 of precision indices associated with the calculation of the mean and standard deviation associated with a productivity metric, such as tool reset rate, associated with each tool in a group of 23 tools. As shown in FIG. 8, the precision indices value 196 associated with tool 21 is relatively small. In this example, precision indices value 196 is a p-value associated with the calculation of the mean and standard deviation associated with tool 21. A relatively small p-value indicates high uncertainty / low confidence in the approximation of the mean and standard deviation using the available data set.

[0071] In yet another aspect, a probability of a future failure event associated with at least one individual tool in the fleet of metrology tools is predicted based on the difference between the predicted probability distribution of the failure event and the actual observed distribution of the failure event. In this manner, a prediction of future tool performance, such as tool downtime, tool reset rate, and time interval between resets, is realized. The performance prediction enables early intervention to further improve productivity. Additionally, one or more accuracy metrics indicative of the confidence in the prediction of future tool performance are calculated as described herein. In this manner, the confidence in the prediction of the future failure event can be taken into account when determining whether to implement early intervention measures.

[0072] In one embodiment, the predicted number of future reset events associated with each tool is determined based on an analytical fit to the actual reset probability distribution. P(N) denotes the predicted probability of N resets. P(N) is calculated using individual tool statistics or tool group statistics. The number of resets that have occurred in the past is known for each tool in the group. The observed frequency of reset events, ObsFreq(N), is determined based on the known reset history. The probability of N future resets is determined by comparing the predicted value, P(N), with the observed value, ObsFreq(N). The probability of N future resets is used as a prediction of the future reset generation frequency for each tool. Additionally, a p-value analysis of the statistically derived productivity index is used to estimate the confidence level of the prediction of the frequency of future reset events. A relatively low p-value indicates high uncertainty / low confidence in the prediction of the frequency of future reset events.

[0073] In alternative embodiments, the metrology tools included in a metrology tool group as described herein may include the same or different types of metrology tools. By way of non-limiting example, individual tools in a metrology tool group may include any of a spectroscopic ellipsometer, a spectroscopic reflectometer, a soft X-ray reflectometer, a small angle X-ray scattering instrument, an imaging system, a hyperspectral imaging system, a scatterometry overlap metrology system, etc. In one example, a tool group of five metrology tools may include three spectroscopic ellipsometry (SE) metrology tools and two SAXS metrology tools.

[0074] Generally, a discrete semiconductor metrology tool is any metrology tool utilized in a semiconductor manufacturing facility, including semiconductor metrology tools, semiconductor inspection tools, etc. A discrete semiconductor metrology tool may be optical-based, x-ray-based, electron-beam-based, or any combination thereof. Furthermore, a group of discrete semiconductor metrology tools may include one or more optical semiconductor metrology tools, one or more x-ray-based semiconductor metrology tools, one or more electron-beam-based semiconductor metrology tools, or any combination thereof.

[0075] As shown in FIG. 1 , system 100 includes a single metrology technique (i.e., SE). However, in general, system 100 may include any number of different metrology techniques. By way of non-limiting example, system 100 may be configured as a reflection small-angle X-ray scattering instrument, a soft X-ray reflectometer, a spectroscopic ellipsometer (including Mueller matrix ellipsometry), a spectroscopic reflectometer, a spectroscopic scatterometer, an overlap scatterometer, an angle-resolved scatterometer, an overlap scatterometer, an angle-resolved beam profile reflectometer, a polarization-resolved beam profile reflectometer, a beam profile reflectometer, a beam profile ellipsometer, any single-wavelength or multi-wavelength ellipsometer, a hyperspectral imaging system, or any combination thereof. Furthermore, in general, the measurement data collected by different metrology techniques and analyzed according to the methods described herein may be collected by multiple tools, by a single tool integrating multiple techniques, or by any combination thereof.

[0076] In further embodiments, the system 100 may include one or more computing systems 130 that are utilized to perform measurements on structures and estimate values ​​of parameters of interest according to the methods described herein. The one or more computing systems 130 may be communicatively coupled to the detector 116. In one aspect, the one or more computing systems 130 are configured to receive measurement data 126 associated with measurements of structures to be measured (e.g., structures disposed on the sample 120).

[0077] In yet another aspect, the measurements described herein can be used to provide active feedback to a processing tool (e.g., a lithography tool, an etch tool, a deposition tool, etc.). For example, values ​​of measured parameters determined based on the measurement methods described herein can be communicated to an etch tool to adjust the etch time to achieve a desired etch depth. In a similar manner, etch parameters (e.g., etch time, diffusivity, etc.) or deposition parameters (e.g., time, concentration, etc.) can be included in a measurement model to provide active feedback to the etch tool or deposition tool, respectively. In some examples, corrections to processing parameters determined based on measured device parameter values ​​can be communicated to the processing tool. In one embodiment, the computing system 130 determines values ​​of one or more parameters of interest. The computing system 130 also communicates control commands to a process controller based on the determined values ​​of the one or more parameters of interest. The control commands cause the process controller to change a state of the process (e.g., stop the etch process, change the diffusivity, etc.). In one example, the control command causes the process controller to adjust the focus of the lithography system, the dose of the lithography system, or both. In another example, the control command causes the process controller to change the etch rate to improve the measured wafer uniformity of the CD parameter.

[0078] In some examples, the metrology model is implemented as an element of a SpectraShape® Optical Critical Dimension Metrology System available from KLA-Tencor Corporation, Milpitas, Calif. In this manner, the model is generated and available immediately after a spectrum is collected by the system.

[0079] In some other instances, the metrology model is implemented offline, for example, by a computing system implementing AcuShape® software available from KLA-Tencor Corporation, Milpitas, Calif. The resulting trained model may be incorporated as an element of an AcuShape® library that is accessible to the metrology system that performs the measurements.

[0080] 9 illustrates a method 200 for assessing productivity of a tool fleet of a semiconductor metrology system in at least one novel aspect. Method 200 is suitable for implementation by a metrology system, such as metrology system 100 shown in FIG. 1 of the present invention. It is understood that, in one aspect, the data processing blocks of method 200 may be performed via pre-programmed algorithms executed by one or more processors of computing system 130, or any other general-purpose computing system. It is understood that the specific structural aspects of metrology system 100 herein are not intended to be limiting and should be construed as illustrative only.

[0081] In block 201, values ​​of one or more individual tool productivity metrics that characterize the performance of each individual tool in a fleet of metrology tools operating in a semiconductor manufacturing facility are estimated.

[0082] In block 202, values ​​of one or more tool fleet productivity metrics that characterize the performance of a metrology tool fleet operating within a semiconductor manufacturing facility are estimated.

[0083] At block 203, one or more combined productivity index values ​​associated with each of the individual tools in the metrology tool family are determined, the determined values ​​being based on one or more individual tool productivity index values ​​and one or more tool family productivity index values ​​associated with each individual tool.

[0084] At block 204, the individual tools of the metrology tool set are ranked based on one or more combined productivity index values.

[0085] In a further embodiment, the system 100 includes one or more computing systems 130 that are utilized to perform measurements on the semiconductor structures based on the measurement data according to the methods described herein. The one or more computing systems 130 may be communicatively coupled to one or more detectors, active optical elements, process controllers, etc.

[0086] It will be appreciated that one or more steps described throughout this disclosure may be performed by a single computer system 130, or may be performed 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 above description should not be construed as limiting the present invention, but rather as illustrative only.

[0087] Additionally, computer system 130 may be communicatively coupled to other elements of the metrology system in any manner known in the art. For example, one or more computer systems 130 may be coupled to a computer system associated with a detector. In another example, the detector may be directly controlled by a single computer system coupled to computer system 130.

[0088] The computer system 130 of the system 100 may be configured to receive and / or acquire data or information from subsystems (e.g., detectors, etc.) of the system over a transmission medium that may include wired and / or wireless portions. In this manner, the transmission medium may serve as a data link between the computer system 130 and other subsystems of the system 100.

[0089] The computer system 130 of the system 100 may 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 wired and / or wireless portions. In this manner, the transmission medium may serve as a data link between the computer system 130 and other systems (e.g., memory onboard the system 100, external memory, or other external systems). For example, the computer system 130 may 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 obtained using the detectors described herein may be stored in permanent or semi-permanent storage (e.g., memory 132 or external memory). In this regard, measurement results may be imported from onboard memory or an external memory system. Additionally, the computer system 130 may 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 other systems.

[0090] Computing system 130 may include, but is not limited to, a personal computer system, a mainframe computer system, a workstation, a graphics computer, a parallel processor, or any other device known in the art. In general, the term "computing system" may be broadly defined to encompass any device having one or more processors that execute instructions from a memory medium.

[0091] Program instructions 134 for implementing the methods described herein may be transmitted over a transmission medium such as a wire, cable, or wireless transmission link. For example, as shown in Figure 1, program instructions 134 stored in memory 132 are transmitted to processor 131 over bus 133. Program instructions 134 are stored in a computer-readable medium (e.g., memory 132). Exemplary computer-readable media include read-only memory, random-access memory, a magnetic or optical disk, or magnetic tape.

[0092] The term "critical dimension" as used herein includes any critical dimension of a structure (e.g., bottom critical dimension, middle critical dimension, top critical dimension, sidewall angle, grating height, etc.), the critical dimension between any two or more structures (e.g., the distance between two structures), and the displacement between two or more structures (e.g., the overlay displacement between overlapping grating structures, etc.). The structures may include three-dimensional structures, patterned structures, overlapping structures, etc.

[0093] As used herein, the terms "critical dimension application" or "critical dimension measurement application" include any critical dimension measurement.

[0094] The term "metrology system" as used herein includes any system utilized at least in part to characterize a specimen in any manner, including measurement applications such as critical dimension metrology, overlap metrology, focus / dose metrology, and composition metrology. However, such terminology is not intended to limit the scope of the term "metrology system" as used herein. Additionally, system 100 may be configured to measure patterned and / or non-patterned wafers. The metrology system may be configured as an LED inspection tool, an edge inspection tool, a backside inspection tool, a macro inspection tool, or a multi-mode inspection tool (including simultaneous acquisition of data from one or more platforms), as well as any other metrology or inspection tool that can benefit from the techniques described herein.

[0095] Described herein are various embodiments of semiconductor metrology systems that may be used to measure specimens in any semiconductor processing tool (e.g., an inspection system or a lithography system). As used herein, the term "specimen" refers to a wafer, a reticle, or any other sample that may be processed (e.g., printed or inspected for defects) by means known in the art.

[0096] As used herein, the element "wafer" generally refers to a substrate formed of a semiconductor or non-semiconductor material. Some examples include, but are not limited to, monocrystalline silicon, gallium arsenide, indium phosphide, etc. Such substrates are commonly found and / or processed in semiconductor manufacturing facilities. In some cases, a wafer may include only the substrate (i.e., a bare wafer). Alternatively, a wafer may include one or more layers of different materials formed on a substrate. One or more layers formed on a wafer may be "patterned" or "unpatterned." For example, a wafer may include multiple dies having repeatable pattern features.

[0097] A "reticle" may refer to a reticle at any stage in the reticle manufacturing process or to a completed reticle that may or may not be released for use in a semiconductor manufacturing facility. A reticle, or "mask," is generally defined as a substantially transparent substrate with substantially opaque regions formed thereon, configured as a pattern. The substrate may comprise, for example, a glass material such as amorphous SiO2. A reticle may be placed over a resist-covered wafer during the exposure step of a lithography process so that the pattern on the reticle can be transferred to the resist.

[0098] One or more layers formed on a wafer may be patterned or unpatterned. For example, a wafer may include multiple dies, each having a repeatable pattern feature. The formation and processing of these layers of material ultimately results in a completed device. Many different types of devices may be formed on a single wafer, and the term "wafer" as used herein is intended to include a wafer on which any type of device known in the art is fabricated.

[0099] In one or more exemplary embodiments, the functions described may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functions may be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Computer-readable media includes both computer storage media and communication media, including any medium that enables a computer program to be transferred from one place to another. A storage medium may be any available medium that can be accessed by a general-purpose or special-purpose computer. By way of example, and not limitation, such computer-readable media may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code means in the form of instructions or data structures and that can be accessed by a general-purpose or special-purpose computer or a general-purpose or special-purpose processor. Additionally, any connection is properly termed a computer-readable medium. For example, if software is transmitted from a website, server, or other remote source using coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio waves, and microwaves, the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio waves, and microwaves are included within the definition of media. As used herein, disk and disc include compact discs (CDs), laser discs, optical discs, digital versatile discs (DVDs), floppy disks, and Blu-ray discs, where disks typically reproduce data magnetically, while discs reproduce data optically with a laser. Combinations of the above should also be included within the scope of computer-readable media.

[0100] Although certain specific embodiments are described above for purposes of illustration, the teachings of this patent document are generally applicable and are not limited to the particular embodiments described above. Accordingly, various modifications, adaptations, and combinations of the various features of the above-described embodiments can be made without departing from the scope of the invention as set forth in the claims.

Claims

1. estimating values ​​of one or more individual tool productivity metrics that characterize the performance of each individual tool of a fleet of metrology tools operating in the semiconductor manufacturing facility; estimating values ​​of one or more tool fleet productivity metrics that characterize the performance of the metrology tools operating at the semiconductor manufacturing facility; determining one or more combined productivity index values ​​associated with each of the individual tools of the metrology tool family, the determined values ​​being based on the one or more individual tool productivity index values ​​and the one or more tool family productivity index values ​​associated with each individual tool; The method includes ranking the individual tools of the group of metrology tools based on the value of the one or more combined productivity metrics.

2. 2. The method of claim 1, wherein determining the value of the one or more combined productivity indexes associated with each of the individual tools of the group of measurement tools comprises determining a statistical distance between a value of an individual tool productivity index associated with an individual tool of the group of measurement tools and a value of a tool group productivity index associated with the group of measurement tools.

3. The method of claim 1 , further comprising selecting individual tools for maintenance based on values ​​of the one or more combined productivity indices associated with the individual tools.

4. determining a difference between a value of the one or more individual tool productivity indexes associated with each individual tool and an average value of the one or more individual tool productivity indexes associated with the individual tools included in the group of measurement tools; The method of claim 1 , further comprising selecting individual tools for maintenance based on the determined difference and the value of the one or more combined productivity indices associated with the individual tools.

5. The method of claim 1 , wherein the performance of each individual tool in the fleet of measurement tools is a tool downtime rate, a tool downtime, a tool reset rate, a time between scheduled resets, a time between unscheduled resets, or any combination thereof.

6. The method of claim 1 , wherein at least one of the one or more individual tool productivity metrics characterizing the performance of each individual tool in the fleet of metrology tools is a statistically based metric.

7. The method of claim 1 , wherein at least one of the one or more individual tool productivity metrics characterizing the performance of each individual tool of the fleet of metrology tools is a parameter of a model constructed based on analytics or machine learning.

8. The method of claim 1 , further comprising estimating a value of an accuracy index indicating a degree of confidence in the ranking of individual tools in the group of metrology tools.

9. 10. The method of claim 1, further comprising predicting a probability of a future failure event associated with at least one tool in the measurement tool fleet based on a difference between a predicted probability distribution of failure events and an observed actual distribution of failure events.

10. 10. The method of claim 1, wherein each individual tool in the group of metrology tools is one of a spectroscopic ellipsometer, a spectroscopic reflectometer, a soft x-ray reflectometer, a small angle x-ray scattering instrument, an imaging system, a hyperspectral imaging system, and a scatterometry overlap measurement system.

11. an irradiation source configured to apply a dose of irradiation to one or more structures disposed on a semiconductor wafer; a detector configured to receive the amount of illumination collected from the one or more structures in response to the amount of illumination and to generate a measurement signal indicative of the collected illumination; estimating values ​​of one or more individual tool productivity metrics that characterize the performance of each tool of a fleet of metrology tools operating in the semiconductor manufacturing facility; estimating values ​​of one or more tool fleet productivity metrics that characterize the performance of the metrology tools operating at the semiconductor manufacturing facility; determining one or more combined productivity index values ​​associated with each of the individual tools of the metrology tool family, the determined values ​​being based on the one or more individual tool productivity index values ​​associated with each individual tool and the one or more tool family productivity index values; and one or more computer systems configured to rank the individual tools of the group of metrology tools based on the one or more combined productivity index values.

12. 12. The system of claim 11, wherein determining the value of the one or more combined productivity indexes associated with each of the individual tools of the group of measurement tools comprises determining a statistical distance between a value of an individual tool productivity index associated with an individual tool of the group of measurement tools and a value of a tool group productivity index associated with the group of measurement tools.

13. the one or more computing systems further comprising: The system of claim 11 , configured to select individual tools for maintenance based on values ​​of the one or more combined productivity indices associated with the individual tools.

14. the one or more computing systems further comprising: The system of claim 11 , configured to estimate a value of an accuracy index indicating a degree of confidence in the ranking of individual tools in the group of metrology tools.

15. the one or more computing systems further comprising:

12. The system of claim 11, configured to predict a probability of a future failure event associated with at least one tool in a fleet of metrology tools based on a difference between the predicted probability distribution of failure events and an observed actual distribution of failure events.

16. an irradiation source configured to apply a dose of irradiation to one or more structures disposed on a semiconductor wafer; a detector configured to receive the amount of illumination collected from the one or more structures in response to the amount of illumination and to generate a measurement signal indicative of the collected illumination; A non-transitory computer-readable medium storing computer-readable instructions that, when executed by one or more processors of a computing system, cause a computing system to: estimating values ​​of one or more individual tool productivity metrics that characterize the performance of each individual tool of a group of metrology tools operating in the semiconductor manufacturing facility; estimating values ​​of one or more tool fleet productivity metrics characterizing the performance of the metrology tools operating at the semiconductor manufacturing facility; determining one or more combined productivity index values ​​associated with each of the individual tools of the metrology tool group, the determined values ​​being based on one or more individual tool productivity index values ​​associated with each individual tool and the one or more tool group productivity index values; a non-transitory computer-readable medium for causing individual tools of the group of metrology tools to be ranked based on the value of the one or more combined productivity metrics;

17. 17. The system of claim 16, wherein determining the value of the one or more combined productivity indexes associated with each of the individual tools of the family of measurement tools comprises determining a statistical distance between a value of an individual tool productivity index associated with an individual tool of the family of measurement tools and a value of a tool family productivity index associated with the family of measurement tools.

18. the non-transitory computer-readable medium further storing computer-readable instructions that, when executed by the one or more processors, cause the computing system to: The system of claim 16 , further comprising selecting individual tools for maintenance based on the one or more combined productivity index values ​​associated with the individual tools.

19. the non-transitory computer-readable medium further storing computer-readable instructions that, when executed by the one or more processors, cause the computing system to: The system of claim 16 , further comprising estimating a value of an accuracy index indicating a degree of confidence in the ranking of individual tools in the group of metrology tools.

20. the non-transitory computer-readable medium further storing computer-readable instructions that, when executed by the one or more processors, cause the computing system to:

17. The system of claim 16, further comprising: predicting a probability of a future failure event associated with at least one tool in the fleet of metrology tools based on a difference between a predicted probability distribution of failure events and an observed actual distribution of failure events.

Images