Method for generating and optimizing sample scheme

Abstract

A method for sample scheme (624) generation has the steps of: acquiring (606) measurement data (608) associated with a set of positions; analyzing (610) the measurement data to determine statistically distinct groups of positions; and configuring (614) a sample scheme generation algorithm (622) based on the statistically distinct groups. A method includes: obtaining constraints (618) and / or a plurality of key performance metrics (620) associated with a sample scheme across one or more substrates; and using the constraints (618) and / or the plurality of key performance metrics (620) in a sample scheme generation algorithm that includes a multi-objective genetic algorithm (622). The location may define one or more regions spanning a plurality of fields across one or more substrates, and the step of analyzing (610) the measurement data may include stacking across the spanned plurality of fields using different respective sub-samples.

Description

[0001] This application is a divisional application of the Chinese patent application with international application number PCT / EP2019 / 084776, international application date December 12, 2019, national application number 201980084631.7, and invention name “Method for Sample Solution Generation and Optimization”. Technical Field

[0002] The present invention relates to sample plan generation and optimization, and related computer programs, lithography and inspection devices. Background Art

[0003] A lithographic apparatus is a machine that applies a desired pattern to a substrate, usually to a target portion of the substrate. A lithographic apparatus can be used, for example, for the manufacture of an integrated circuit (IC). In this example, a patterning device, alternatively referred to as a mask or reticle, can be used to generate a circuit pattern to be formed on a single layer of an IC. The pattern can be transferred to a target portion (e.g., including a portion, one, or multiple dies) on a substrate (e.g., a silicon wafer). The transfer of the pattern is usually via imaging onto a radiation-sensitive material (resist) layer disposed on the substrate. Typically, a single substrate will contain a network of adjacent target portions of continuous patterning. Known lithographic apparatuses include so-called steppers and so-called scanners, in which each target portion is irradiated by exposing the entire pattern to the target portion at once, and in which each target portion is irradiated by scanning the pattern by a radiation beam in a given direction ("scanning" direction), while synchronously scanning the substrate in parallel or antiparallel to the direction. It is also possible to transfer a pattern from a patterning device to a substrate by imprinting the pattern onto the substrate.

[0004] Regardless of the type of device used, the precise placement of patterns on a substrate is a major challenge for reducing the size of circuit components and other products that can be produced by lithography. In particular, the challenge of accurately measuring features on an already laid substrate is a key step in being able to overlay successive layers of features accurately enough to produce working devices with a high yield. Typically, the so-called overlay should be achieved within tens of nanometers in today's submicron semiconductor devices, and can reach a few nanometers in the most critical layers.

[0005] Calibration and qualification of the performance of a lithographic apparatus (e.g., a scanner) is performed by several tests involving exposure and measurement of marks on a wafer. This measurement of marks is called mark readout. A set of marks read out in a sample plan is called a mark readout layout.

[0006] The exposure occurs under specific test conditions. A specific mask is patterned with marks associated with the test. The exposure using the mask is performed under specific exposure settings, such as illumination, dose, chuck sequence, number of layers, etc. Once the wafer is exposed and developed, a mark readout is performed, such as printed alignment, focus, or overlay marks are measured. The mark readout can be performed by a scanner or other equipment, such as an inspection device (e.g., an angle-resolved scatterometer).

[0007] The readout values ​​are typically used for calibration and / or qualification of a lithographic apparatus (scanner). In both cases, the test returns key performance indicators (KPIs), which are values ​​that indicate how well the test was performed. Typically, each test returns several KPIs.

[0008] These tests are performed when the scanner is manufactured (e.g., in a scanner manufacturing factory during a setup sequence), during recovery (e.g., at a semiconductor manufacturer when parts of a scanner are exchanged), and during production to test the scanner for drift.

[0009] In conventional approaches, all marks exposed in the test are read out from the test wafer, so there is a full mark readout layout. Known approaches aimed at reducing mark readout are limited in their performance because they reduce the accuracy of the calculated KPIs. Summary of the invention

[0010] It would be desirable to have a universal (ie, applicable to all tests of readout tags) method that could reduce the number of readout tags without compromising test performance and allow for shorter setup, recovery, and drift calibration / verification times.

[0011] According to a first aspect of the present invention, there is provided a method comprising:

[0012] - obtaining measurement data associated with a set of locations;

[0013] - analyzing the measurement data to determine statistically distinct groups of locations; and

[0014] -Generate algorithms based on sample scenario configurations for statistically distinct groups.

[0015] According to a second aspect of the present invention, there is provided a method comprising:

[0016] - obtaining constraints and / or a plurality of key performance indicators associated with sample scenarios across one or more substrates; and

[0017] - Using the constraints and / or multiple key performance indicators in a sample solution generation algorithm including a multi-objective genetic algorithm.

[0018] According to a third aspect of the present invention, there is provided a method comprising:

[0019] - acquiring measurement data associated with a set of locations across one or more substrates;

[0020] - Analyze the measurement data; and

[0021] - Optimize the sample plan based on this analysis,

[0022] wherein the location defines one or more regions spanning a plurality of fields across one or more substrates, the plurality of fields having different corresponding sub-samplings in a sampling scheme; and

[0023] Therein, the step of analyzing the measurement data comprises stacking the measurement data across the spanned plurality of fields using different respective sub-sampling thereof.

[0024] According to a fourth aspect of the present invention, in particular, there is provided a lithography apparatus suitable for performing the steps of the method of the first aspect.

[0025] According to a fifth aspect of the present invention, specifically, there is provided an inspection device suitable for executing the steps of the method of the first aspect.

[0026] According to a sixth aspect of the present invention, there is provided a computer program comprising computer readable instructions which, when executed on a suitable computer device, cause the computer device to perform the method of the first aspect.

[0027] According to a seventh aspect of the present invention there is provided a computer program product comprising the computer program of the sixth aspect.

[0028] According to an eighth aspect of the present invention, in particular, there is provided a lithography apparatus suitable for performing the steps of the method of the second aspect.

[0029] According to a ninth aspect of the present invention, there is provided an inspection apparatus specifically adapted to perform the steps of the method of the second aspect.

[0030] According to a tenth aspect of the present invention, there is provided a computer program comprising computer readable instructions which, when executed on a suitable computer device, cause the computer device to execute the method of the second aspect.

[0031] According to an eleventh aspect of the present invention, there is provided a computer program product comprising the computer program of the tenth aspect.

[0032] According to a twelfth aspect of the present invention, specifically, a lithography apparatus suitable for performing the steps of the method of the third aspect is provided.

[0033] According to a thirteenth aspect of the present invention, specifically, there is provided an inspection device suitable for executing the steps of the method of the third aspect.

[0034] According to a fourteenth aspect of the present invention, there is provided a computer program comprising computer readable instructions which, when run on a suitable computer device, cause the computer device to execute the method of the third aspect.

[0035] According to a fifteenth aspect of the present invention there is provided a computer program product comprising the computer program of the fourteenth aspect. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which corresponding reference characters indicate corresponding parts, and in which:

[0037] Figure 1 A lithographic apparatus is schematically depicted;

[0038] Figure 2 Schematically depicts Figure 1 The stages of the measurement and exposure process in the device;

[0039] Figure 3 It is a flow chart from sample plan generation to calibration or qualification of lithography equipment;

[0040] Figure 4 The fit of the Gaussian distributions of the measurements of five different marker groups across the field is described;

[0041] Figure 5 The fit of the Gaussian distribution of measurements for five different marking groups across the wafer is described;

[0042] Figure 6 is a flow chart relating to a method of sample solution generation according to an embodiment;

[0043] Figure 7 is a flow chart of a method involving a multi-objective genetic algorithm according to an embodiment;

[0044] Figure 8 is a flow chart relating to a method of sample solution optimization according to an embodiment;

[0045] Fig. 9 It is related to the combination according to the embodiment Figure 7 and Figure 8 Flow chart of the multi-objective genetic algorithm method of the method;

[0046] Fig.10 depicts two different field mark readout layouts resulting from implementations;

[0047] Fig.11 is the Pareto front of a field having the same simplified tag readout layout compared to the full tag readout layout; and

[0048] Fig.12 depicts a simplified wafer mark readout layout resulting from an implementation; Fig.13 A control unit for a lithography apparatus according to an embodiment. DETAILED DESCRIPTION

[0049] Figure 1 A lithographic apparatus LA is schematically depicted in which embodiments may be implemented. The apparatus comprises:

[0050] i. The illumination system (illuminator) IL is configured to condition a radiation beam B (eg, UV radiation or EUV radiation).

[0051] ii. a support structure (eg, mask table) MT configured to support a patterning device (eg, mask) MA and connected to a first positioner PM configured to accurately position the patterning device according to specific parameters;

[0052] iii. a substrate table (e.g., wafer table) WTa or WTb configured to hold a substrate (e.g., a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate according to specific parameters; and

[0053] iv. a projection system (eg, a refractive projection lens system) PS configured to project the pattern imparted to the radiation beam B by the patterning device MA onto a target portion C of the substrate W (eg, comprising one or more dies).

[0054] The illumination system may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic or other types of optical components, or any combination thereof, for directing, shaping or controlling radiation.

[0055] The support structure supports the patterning device, i.e. bears the weight of the patterning device. It holds the patterning device in a manner that depends on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions (e.g., whether the patterning device is maintained in a vacuum environment). The support structure can use mechanical, vacuum, electrostatic or other clamping techniques to hold the patterning device. The support structure can be, for example, a frame or a stage, which can be fixed or moved as needed. The support structure can ensure that the patterning device is in a desired position, for example, relative to a projection system. Any use of the term "reticle" or "mask" herein may be considered synonymous with the more general term "patterning device".

[0056] The term "patterning device" as used herein should be broadly interpreted as referring to any device that can be used to impart a radiation beam with a pattern in its cross-section, for example to produce a pattern in a target portion of a substrate. It should be noted that the pattern imparted to the radiation beam may not exactly correspond to the desired pattern in the target portion of the substrate, for example if the pattern includes phase-shifting features or so-called assist features. Typically, the pattern imparted to the radiation beam will correspond to a specific functional layer in a device created in the target portion (e.g. an integrated circuit).

[0057] Patterning devices can be transmissive or reflective. Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in lithography and include mask types such as binary, alternating phase shift, and attenuated phase shift, as well as various hybrid mask types. An example of a programmable mirror array employs a matrix arrangement of small mirrors, each of which can be individually tilted to reflect an incident radiation beam in different directions. The tilted mirrors provide a pattern in the radiation beam that is reflected by the matrix of mirrors.

[0058] The term "projection system" as used herein should be broadly interpreted as including any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic and electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation used, or for other factors such as the use of immersion liquid or the use of a vacuum. Any use of the term "projection lens" herein may be considered a synonym for the more general term "projection system".

[0059] As shown herein, the device is of the transmissive type (eg, using a transmissive mask). Alternatively, the device may be of the reflective type (eg, using a programmable mirror array of the type described above, or using a reflective mask).

[0060] The lithographic apparatus may be of a type having two (dual stage) or more substrate tables (and / or two or more mask tables). In such a "multi-stage" machine, the additional tables may be used in parallel, or preparatory steps may be performed on one or more tables while exposure is carried out using one or more other tables. The invention disclosed herein may be used in a stand-alone manner, but in particular it may provide additional functionality in a pre-exposure measurement stage of a single or multi-stage apparatus.

[0061] The lithographic apparatus may also be of a type in which at least a portion of the substrate may be covered by a liquid having a relatively high refractive index, such as water, so as to fill the space between the projection system and the substrate. Immersion liquid may also be applied to other spaces in the lithographic apparatus, such as between the mask and the projection system. Immersion techniques are well known in the art and are used to increase the numerical aperture of the projection system. The term "immersion" as used herein does not mean that structures such as the substrate must be immersed in the liquid, but only means that the liquid is located between the projection system and the substrate during exposure.

[0062] Reference Figure 1 , the illuminator IL receives a radiation beam from a radiation source SO. The source and the lithographic apparatus may be separate entities, for example when the source is an excimer laser. In this case, the source is not considered to form part of the lithographic apparatus, and the radiation beam is transmitted from the source SO to the illuminator IL with the aid of a beam delivery system BD comprising, for example, suitable directing mirrors and / or a beam expander. In other cases, the source may be an integral part of the lithographic apparatus, for example when the source is a mercury lamp. The light source SO and the illuminator IL, together with the beam delivery system BD if necessary, may be referred to as a radiation system.

[0063] The illuminator IL may include an adjuster AD for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer and / or inner radial extent (commonly referred to as -outer and -inner, respectively) of the intensity distribution in a pupil plane of the illuminator can be adjusted. Furthermore, the illuminator IL may include various other components, such as an integrator IN and a condenser CO. The illuminator can be used to adjust the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0064] The radiation beam B is incident on a patterning device (e.g., mask MA) held on a support structure (e.g., mask table MT) and is patterned by the patterning device. After passing through the mask MA, the radiation beam B passes through a projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of a second positioner PW and a position sensor IF (e.g., an interferometric device, a linear encoder, or a capacitive sensor), the substrate table WTa / WTb can be precisely moved, for example, in order to position a different target portion C in the path of the radiation beam B. Similarly, a first positioner PM and a further position sensor (which is located in the substrate) are provided. Figure 1The first positioner PM (not explicitly shown in the figure) can be used to accurately position the mask MA relative to the path of the radiation beam B, for example, after mechanical retrieval from a mask library, or during scanning. Typically, movement of the mask table MT can be achieved with the help of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning) forming part of the first positioner PM. Similarly, movement of the substrate table WTa / WTb can be achieved using a long-stroke module and a short-stroke module forming part of the second positioner PW. In the case of a stepper (as opposed to a scanner), the mask table MT may be connected to the short-stroke actuator only, or may be fixed. The mask MA and the substrate W can be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks as shown occupy dedicated target portions, they can be located in the space between target portions (these are called scribe alignment marks). Similarly, where more than one die is provided on the mask MA, the mask alignment marks can be located between the dies.

[0065] The depicted device can be used in at least one of the following modes:

[0066] 1. In step mode, the mask table MT and substrate table WTa / WTb are held substantially stationary while an entire pattern imparted to the radiation beam is projected at once onto a target portion C (i.e. a single static exposure). The substrate table WTa / WTb is then moved in the X and / or Y direction so that a different target portion C can be exposed. In step mode, the maximum size of the exposure field is limited to the size of the target portion C imaged in a single static exposure.

[0067] 2. In scan mode, the mask table MT and the substrate table WTa / WTb are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e. a single dynamic exposure). The speed and direction of the substrate table WTa / WTb relative to the mask table MT may be determined by the (de)magnification and image reversal characteristics of the projection system PS. In scan mode, the maximum size of the exposure field limits the width of the target portion (in the non-scanning direction) in a single dynamic exposure, while the length of the scanning movement determines the height of the target portion (in the scanning direction).

[0068] 3. In another mode, the mask table MT remains substantially stationary, holds the programmable patterning device, and moves or scans the substrate table WTa / WTb as a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, a pulsed radiation source is typically employed, and the programmable patterning device is updated as required after each movement of the substrate table WTa / WTb, or between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography utilising a programmable patterning device, such as a programmable mirror array of the type described above.

[0069] Combinations and / or variations of the above-described modes of use or entirely different modes of use may also be employed.

[0070] The lithography apparatus LA in this example is a so-called dual-stage type, having two substrate tables WTa and WTb and two stations - an exposure station and a measurement station - between which the substrate table can be exchanged. While one substrate on one substrate table is being exposed at the exposure station EXP, another substrate can be loaded onto another substrate table at the measurement station MEA, so that various preparation steps can be performed. The preparation steps may include mapping the substrate surface using a level sensor LS, and measuring the position of alignment marks on the substrate using an alignment sensor AS. This enables the throughput of the apparatus to be greatly increased. If the position sensor IF cannot measure the position of the substrate table at the measurement station and the exposure station, a second position sensor may be provided so that the position of the substrate table can be tracked at both stations. The present invention can be applied to an apparatus having only one substrate table or more than two substrate tables.

[0071] The device also includes a lithography device control unit LACU, which controls all movements and measurements of various actuators and sensors. LACU also includes signal processing and data processing capabilities to achieve the desired calculations related to the operation of the device. In practice, the control unit LACU will be implemented as a system of many subunits, each subunit processing real-time data acquisition, processing and control of subsystems or components within the device. For example, one processing subsystem can be dedicated to the servo control of the substrate positioner PW. A separate unit can even handle coarse and fine actuators, or different axes. Another unit can be dedicated to the readout of a position sensor. The overall control of the device can be controlled by a central processing unit, which communicates with these subsystem processing units, operators and other devices involved in the lithography manufacturing process.

[0072] Figure 2 Shown in Figure 1 The known steps of exposing a target portion (e.g., a die) on a substrate W in a dual-stage device of the present invention. On the left hand side within the dashed box are the steps performed at the measurement station MEA, while the right hand side shows the steps performed at the exposure station EXP. From time to time, one of the substrate tables WTa, WTb will be located at the exposure station, while the other is located at the measurement station, as described above. For the purpose of this description, it is assumed that the substrate W has already been loaded into the exposure station. At step 200, a new substrate W' is loaded into the device by a mechanism not shown. The two substrates are processed in parallel to increase the throughput of the lithography device. Initially reference is made to the newly loaded substrate W', which may be a previously unprocessed substrate, prepared with a new photoresist for exposure for the first time in the device. However, in general, the lithography process described will be only one step in a series of exposure and processing steps, so that the substrate W' has passed through the device and / or other lithography devices several times, and subsequent processes may also be performed.

[0073] The preceding and / or succeeding processing may be performed in other lithographic apparatuses, as described above, and may even be performed in different types of lithographic apparatuses. For example, some layers in the device manufacturing process that are very demanding on parameters such as resolution and overlay may be performed in more advanced lithographic tools than other layers that are less demanding. Thus, some layers may be exposed in an immersion lithography tool, while other layers are exposed in a "dry" tool. Some layers may be exposed in a tool operating at a DUV wavelength, while other layers are exposed using EUV wavelength radiation.

[0074] exist Figure 2 In the embodiment of the present invention, at 202, alignment measurements using substrate marks P1 etc. and an image sensor (not shown) are used to measure and record the alignment of the substrate relative to the substrate table WTa / WTb. In addition, several alignment marks across the substrate W' will be measured to establish a "wafer grid" that very accurately maps the distribution of marks across the substrate, including any distortion relative to the nominal rectangular grid. At step 204, a mapping of substrate height relative to XY position is also measured for accurate focusing of the exposure pattern.

[0075] When the substrate W' is loaded, recipe data 206 is received, which defines the exposure to be performed, as well as the characteristics of the substrate and the patterns previously made and to be made thereon. The measurements of the substrate position, substrate grid and height map made at 202, 204 are added to these recipe data so that a complete set of recipe and measurement data 208 can be transferred to the exposure station. The measurement of alignment data includes, for example, the X and Y positions of the alignment targets, which are formed in a fixed or nominally fixed relationship with the product pattern as a product of the lithography process. These alignment data obtained before exposure are combined and interpolated to provide parameters of the alignment model. These parameters and the alignment model will be used during the exposure operation to correct the position of the pattern applied in the current lithography step. Traditional alignment models can include four, five or six parameters, which together define the translation, rotation and scaling of the "ideal" grid of different dimensions. As described further below, advanced models using more parameters are known.

[0076] At 210, substrates W' and W are interchanged so that the substrate W' being measured becomes the substrate W entering the exposure station EXP. This exchange is performed by exchanging supports WTa and WTb within the apparatus so that substrates W, W' remain accurately clamped and positioned on these supports to maintain the relative alignment between the substrate table and the substrate itself. Therefore, once the worktables have been exchanged, determining the relative position between the projection system PS and the substrate table WTb (formerly WTa) is all that is necessary to utilize the measurement information 202, 204 of the substrate W (formerly W') in the control of the exposure step. At step 212, mask alignment is performed using the mask alignment marks M1, M2. In steps 214, 216, 218, scanning movements and radiation pulses are applied at consecutive target positions across the substrate W in order to complete the exposure of a plurality of patterns. By using the alignment data and height maps acquired at the measurement station during the execution of the exposure step, these patterns are accurately aligned relative to the desired positions, in particular relative to features previously placed on the same substrate. At step 220, the exposed substrate, now labeled W", is unloaded from the apparatus for etching or other processes according to the exposed pattern.

[0077] Figure 3 It is a flow chart from sample plan generation to calibration or qualification of lithography equipment.

[0078] A sample plan generation step 302 generates a sample plan, in this case a mark readout layout 304. To calibrate or qualify a lithographic apparatus, a wafer or a series of wafers are exposed and developed 306. The mark readout layout 304 is used to measure marks on the wafer at a mark readout step 308. The measurements yield readout values ​​310, which are used for calibration or qualification 312 to yield calculated key performance indicators (KPIs) 314.

[0079] In an embodiment, the sample solution generation step 302 can be processed as a multi-objective optimization problem, which is solved by a meta-heuristic optimization algorithm. One goal is the number of tags to be read (needs to be reduced), and the other goal is the KPI reduction (should be as small as possible, that is, also reduced).

[0080] A metaheuristic is a high-level procedure or heuristic designed to find, generate, or select a heuristic (partial search algorithm) that provides a sufficiently good solution to an optimization problem, especially in the presence of incomplete or imperfect information or limited computing power.

[0081] Evolutionary algorithm (EA) is a general population-based meta-heuristic optimization algorithm.

[0082] A genetic algorithm (GA) is a type of evolutionary algorithm. In a GA, a population of candidate solutions to an optimization problem (called individuals, organisms, or phenotypes) evolve towards better solutions. Each candidate solution has a set of properties (its chromosome or genotype), represented by coordinates in the solution domain, which can be mutated and changed. Solutions can be represented in binary as strings of 0s and 1s, but other encodings are possible.

[0083] Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. SA is a meta-heuristic algorithm that approximates the global optimum in a large search space or solution domain.

[0084] Tabu search is another metaheuristic search method that uses local search methods for mathematical optimization.

[0085] Genetic algorithms maintain a pool of solutions instead of just one. New candidate solutions are generated not only by "mutation" (as in SA) but also by "recombination" of two solutions in the pool. Probabilistic criteria, similar to those used in SA, are used to select candidates for duplication, mutation, or combination (by crossover), and to discard redundant solutions from the pool.

[0086] In mathematical optimization, a cost function or loss function is a function that maps the value of an event or one or more variables to a real number that intuitively represents some "cost" associated with the event. An optimization problem seeks to minimize the cost function. The objective function can be the cost function or its negative function (sometimes called a merit function, reward function, profit function, utility function, fitness function, etc.), in which case the objective function is to be maximized.

[0087] Constraints are conditions that the solution to an optimization problem must satisfy.

[0088] Embodiments involve performing statistical analysis on test data (e.g., Figure 6 ) at step 610 in order to understand the source of the change.

[0089] Given the readout data from previous tests for all markers (e.g. Figure 6 In step 606 of the test wafer, the marks in the test wafer can be grouped in different ways. For example, the marks can be grouped according to the following: marks in the up-scan (or down-scan) field, marks in different quadrants (or any other wafer partitions relevant to the test), marks in different wafers, marks in different field columns / rows / positions... and combinations of these groupings. For each of these groupings, the distribution of the marks in each group (or a fit to a given distribution, such as a Gaussian distribution) can be plotted to determine statistically different groupings. Examples of statistical differences are:

[0090] Markers in a group have different means of their associated readout values;

[0091] Tags in a group have different std (standard deviation) of their associated read values; and

[0092] None of the groups showed statistical differences in their associated readout values.

[0093] For example, it may be determined that marks in different columns have different meanings, or that marks at the edge of the wafer have a higher variance than marks in the rest of the wafer. Figure 4 and Figure 5 These examples are described.

[0094] Figure 4 The fit of a Gaussian distribution of measurements for five different groups of marks in a field is illustrated. Each group is a different column in the exposure field. The probability density in arbitrary units (vertical axis) is plotted 402 against the mark readout value in arbitrary units (horizontal axis). Different columns have different patterns, as shown by the horizontal offset of the five curves, one for each column group.

[0095] Figure 5 The fit of a Gaussian distribution of measurements of five different groups of marks on a wafer is shown. Each group is a different region on the wafer. The probability density in arbitrary units (vertical axis) is plotted 502, 504 against the mark readout value in arbitrary units (horizontal axis). The marks at the edge of the wafer have a higher variance than marks in the rest of the wafer, as shown by the wider distribution of curve 504 corresponding to the wafer edge group, compared to the narrower distribution of the remaining four curves 502 for regions away from the edge of the wafer. Therefore, there are different standard deviations depending on the position of the mark on the wafer.

[0096] Figure 6 is a flow chart of a method for generating a sample solution according to an embodiment. The method has the following steps:

[0097] 602: With respect to selection of locations across one or more substrates, predefined groups 604 are defined.

[0098] The positions in a group can together define one or more regions within a field that is repeated on one or more substrates. In this case, each field has the same simplified tag readout layout, and the operation (crossover / mutation) is at the intra-field level.

[0099] Additionally or alternatively, a group may be defined as one or more regions across a field, the field being across a wafer, across a wafer batch, or across multiple wafer batches. The locations in a group may together define one or more regions across multiple fields, the fields being across one or more substrates, the multiple fields having different corresponding sub-sampling in a sample plan generated by a sample plan generation algorithm. Fig.12Different subsampling across a basis is shown.

[0100] 606: Acquire measurement data associated with a set of locations across one or more substrates 608. In this example, all exposed marks are read out so that as much information as possible can be used for optimized sample plan generation.

[0101] 610 : Analyzing the measurement data 608 to determine statistically distinct groups 612 of locations. The groups in this example are predefined groups 604 .

[0102] In the case where the positions in the group together define one or more regions spanning multiple fields across one or more substrates (the multiple fields having different corresponding sub-samplings), then the step 610 of analyzing the measurement data includes stacking the measurement data across the multiple fields spanned using their different corresponding sub-samplings to determine statistically different groups of positions. In this case, the different fields have different simplified layouts, and the operation (crossover / variation) is at the field-to-field / wafer-to-wafer / batch level. This can be described as using stacked field / wafer / batch reconstruction.

[0103] As shown in the flowchart connector 1A, for reference Figure 7 In the described method, the constraints obtained in step 702 may be based on the results 612 of the analysis step 610 .

[0104] 614: Configure operators of the sample solution generation algorithm based on the statistically different groups. This step outputs one or more genetic operator configurations 616. The sample solution generation algorithm in this example is a genetic algorithm, and the step of configuring operators includes configuring a crossover operator to exchange sampling information between the determined statistically different groups. The step of configuring operators may also include configuring a mutation operator to mutate the sampling information in the selected determined statistically different groups. The genetic operator configuration 616 may be used in other embodiments, as shown in flowchart connection 1B.

[0105] Multi-objective genetic algorithms (MOGA) are an extension of genetic algorithms (GA). They are a class of algorithms that are able to optimize multi-objective optimization problems (convex or non-convex, constrained or unconstrained, ...). GAs are single-objective optimization algorithms. These algorithms consider "individuals": possible solutions to the problem that one wants to solve. In this example, the individuals are simplified marker readout layouts. The individuals are evaluated according to a fitness function. In this example, the fitness function will return the calculated key performance indicators for a given simplified marker readout layout.

[0106] In this example, where the sample solution generation algorithm 622 comprises a multi-objective genetic algorithm, the method further comprises obtaining a plurality of key performance indicators associated with the sample solution across one or more substrates 620. In the sample solution generation algorithm, the key performance indicators are used in a fitness function. The fitness function comprises a comparison between the key performance indicators calculated for the measurement data of the set of positions and the key performance indicators calculated for a single simplified marker readout layout.

[0107] For match overlay between machines (during scanner calibration or qualification), a goodness of fit function can be used to return only KPIs relevant to machine performance (e.g., average + 3std, 99.7th percentile of x and y for chuck 1 and chuck 2 for average wafer and wafer-to-wafer variation). A larger set of KPIs required for diagnostics (e.g., intra-field, inter-field, or slot fingerprint parameters) can also be used.

[0108] The fitness function returns the difference in KPI values ​​between the full readout layout and the generated simplified tag readout layout. The fitness function can return more complex metrics related to how the simplified layout performs on a set of machines compared to the full layout.

[0109] GA uses a group of individuals (called a "population") that changes in an iterative process. Given a population of generation X, a population of generation X+1 is obtained to perform genetic operations on the individuals of generation X. These operations can be divided into three groups:

[0110] Selection: Some individuals of generation X are not considered. The remaining individuals are used as input to the following two operations. Examples of selection are tournament selection and roulette.

[0111] Crossover (recombination): Create a new individual using two (or more) selected individuals. For example, if the analysis step 610 indicates that there is a difference between the alignment or overlay standard deviation of the mark to the edge of the wafer relative to the marks in the rest of the wafer, the crossover operation can be configured accordingly. Thus, given two individuals I1 and I2, a new individual is created by crossover using the edge mark present in I1 and the remaining mark present in I2.

[0112] Mutation: A selected individual is used to create a new individual. For example, if the analysis step 610 shows that the standard deviation of the marks present in the lower quadrant of the wafer is significantly higher than the standard deviation of the marks present in the upper quadrant of the wafer, then mutation can be implemented accordingly. For example, the mutation operation can be configured to increase the number of marks read in the lower quadrant of the wafer.

[0113] These genetic operations can have constant parameters, or parameters that vary from generation to generation.

[0114] In MOGA, other operators (in addition to those described with respect to step 622) may be implemented to provide a simplified layout of marker readouts. For example, field reconstruction may be implemented: given a set of fields, each of the fields is subsampled such that not all markers are read out for any field in the set (i.e., no intra-field mapping can be created), but the combination of markers read out in the fields allows the field to be recreated.

[0115] Based on the results 612 of the analysis step 610, constraints 618 may be added to the solution created by MOGA. The constraints 618 are associated with sample solutions across one or more substrates. The constraints 618 are used as input to a sample solution generation algorithm 622. The constraints may be based on the analysis 610. For example, if the analysis step 610 shows that there are significant differences 612 between the tags present in different field columns, then MOGA may be forced to create a solution (i.e., a simplified tag readout layout) such that no field columns disappear in the simplified tag readout layout. This means that missing tags in a column is allowed, but deleting all tags in a column is not allowed.

[0116] Because the fitness function returns more than one KPI, MOGA can return a solution that satisfies all of these KPIs. Then, MOGA of the sample solution generation step 622 will return a simplified field marker readout layout 624. Therefore, the sample solution generation algorithm is used to generate an optimized sample solution 624.

[0117] Figure 7 is a flow chart of a method involving MOGA according to an embodiment. The method has the following steps:

[0118] 702 : Obtain constraints 718 associated with sample scenarios across one or more substrates. As shown in flowchart connector 1A, these constraints may be based on the results 612 of the analysis step 610 .

[0119] 704: Obtain a plurality of key performance indicators 720 associated with sample solutions across one or more bases. KPI 720 can be used to reference Figure 6 In the described embodiment, as shown in the flowchart connector 2A.

[0120] 722: Use constraints 718 and / or multiple key performance indicators 720 in a sample solution generation algorithm including a multi-objective genetic algorithm. The genetic operator configuration 716 can be based on Figure 6 Step 614 is configured as shown in flowchart connector 1B.

[0121] The sample plan generation algorithm is used to generate an optimized sample plan (simplified marker read layout) 724. The optimized marker read layout allows faster testing without compromising the test KPI. This results in reduced setup, recovery and drift calibration / verification time.

[0122] Figure 8 is a flow chart of a method for sample solution optimization according to an embodiment. The method has the following steps:

[0123] 806: Acquire measurement data associated with a set of locations across one or more substrates 808. The locations define one or more regions across multiple fields, the fields across the one or more substrates, the multiple fields having different corresponding sub-sampling in a sampling scheme.

[0124] 810: Analyzing the measurement data by stacking the measurement data across a plurality of fields spanned by using their different corresponding sub-sampling spans.

[0125] 822: Optimize the sample solution based on the analysis of step 810.

[0126] The sample plan generation algorithm is used to generate an optimized sample plan (simplified marker readout layout) 824. When the sample plan generation algorithm is MOGA, different fields have different simplified layouts, and the operation (crossover / mutation) is at the field-to-field / wafer-to-wafer / batch level. This can be described as using stacked field / wafer / batch reconstruction. The optimized marker readout layout allows faster testing without compromising the test KPI. This results in reduced setup, recovery, and drift calibration / verification time.

[0127] Fig. 9 It is a combination according to an embodiment Figure 7 and Figure 8 Flowchart of the MOGA method.

[0128] refer to Fig. 9 , this method has the same Figure 7 and Figure 8 Same steps, Figure 7 and Figure 8 Labeled with the same reference numerals:

[0129] 806: Acquire measurement data associated with a set of locations across one or more substrates 808. The locations define one or more regions across multiple fields, the fields across the one or more substrates, the multiple fields having different corresponding sub-sampling in a sampling scheme.

[0130] 810: Analyzing the measurement data by stacking the measurement data across a plurality of fields spanned by using their different corresponding sub-sampling spans.

[0131] 702 : Obtain constraints 718 associated with sample scenarios across one or more bases. These constraints are based on the results of the analysis step 810 .

[0132] 704: Obtain a plurality of key performance indicators 720 associated with sample scenarios across one or more substrates.

[0133] 922: Optimize the sample plan based on the analysis. This step 922 may use the constraints 718 and / or the multiple key performance indicators 720 in the MOGA. The constraints may be based on the analysis 810. For example, if the analysis step 810 shows that there are significant differences between the marks present in different field columns, the genetic algorithm may be forced to create a solution (i.e., a simplified mark readout layout) such that no field column disappears in the simplified mark readout layout. This means that missing marks in a column are allowed, but not all marks in a column are allowed to be deleted. This step 922 may involve configuring the crossover operator of the sample plan generation algorithm to exchange sampling information between fields. This step may involve configuring the mutation operator of the sample plan generation algorithm to mutate the sampling information in the selected field. When the sample plan generation algorithm is a genetic algorithm, different fields have different simplified layouts, and the operations (crossover / mutation) are at the field-to-field / wafer-to-wafer / batch level. This can be described as using stacked field / wafer / batch reconstruction. The operator configuration 916 is based on the analysis step 810.

[0134] The sample plan optimization step 922 is used to generate a simplified marker read layout 924.

[0135] Fig.10 Two different field mark readout layouts resulting from implementations are depicted. Fig.10 The field mark layout in is returned by the MOGA implemented to match the overlay mark sampling of different scanners. Each mark is represented by a cross-hatched rectangle. The leftmost field 1002 has 10 marks. The rightmost field 1004 has 16 marks.

[0136] Fig.11 is the Pareto front of a field with the same simplified tag readout layout compared to the full tag readout layout. MOGA returns a lot of data, the most important of which is the simplified layout. But with the remaining data, it is possible to plot the Pareto front (and other plots). The purpose of the Pareto front is to see how different objectives relate to each other. This information can be used, for example, to better understand the problem or to improve MOGA. These plots show how different KPIs relate to each other in the optimization problem under consideration. Reference Fig.11 , the Pareto front is shown for an example with the same marker readout layout for all fields. The horizontal axis is the number of markers read out per field (N). The vertical axis is the delta mean (M) and standard deviation (SD) (in nm) between the fully sampled marker readout layout and the simplified (optimized) marker readout layout. A graph (dashed line) of these means 1102 and standard deviations 1104 shows that performance is significantly enhanced if 24 or more markers are read out per field compared to fewer markers per field.

[0137] In the first approach, the positions in the group can together define one or more regions within a field, and the field repeated across one or more substrates gives an indication of how the reduced number of readout markers affects the KPI under consideration. For example, a performance drop of no more than + / -5% (which we call "degradation") is acceptable. This means that for each KPI, the value returned by the simplified layout is at most +5% or -5% compared to the KPI returned by the full layout.

[0138] As described above, in the second method, in addition to or in lieu of the first method, a group can be defined as one or more regions across a field, the field being across a wafer, across a wafer batch, or across multiple wafer batches. The locations in the group can together define one or more regions across multiple fields, the fields being across one or more substrates, with the multiple fields having different corresponding sub-samplings in the sampling scheme generated by the sample scheme generation algorithm. In this case, the sample scheme generation or optimization can return a simplified layout with the same performance as the first method, but with fewer markers read out. For example, if the test under consideration has 70 fields, a simplified layout with 10 markers per field (i.e., with a total of 700 marker reads) and + / -5% degradation is generated, then the second method can return another layout with + / -5% degradation, which has a total of less than 700 marker reads.

[0139] In MOGA, other operators (in addition to those described with respect to step 622) may be implemented to provide a simplified layout of marker readouts. For example, field reconstruction may be implemented: given a set of fields, each of the fields is subsampled such that not all markers are read out for any field in the set (i.e., no intra-field mapping can be created), but the combination of markers read out in the fields allows the field to be recreated.

[0140] Fig.12 Depicted by reference Figure 6 and Figure 7 A simplified wafer mark readout layout produced by the described embodiment. Wafer map 1202 is divided into fields 1204. Within wafer map 1202, the mark layout is shown with small dots representing mark readout. This is an optimized mark readout layout that allows faster testing without compromising test KPIs. This results in reduced setup, recovery, and drift calibration / verification times.

[0141] Embodiments are applicable to all tests that read out markers from exposed wafers. The method described above returns a simplified set of marker readouts so that the KPIs returned by each test have no degradation (i.e., they are equal to the values ​​returned when all markers are read out) or little degradation. This in turn reduces setup and recovery time.

[0142] The measurements referred to in this document may correspond to the acquisition of the value of any parameter having a spatial distribution (fingerprint) across a plane associated with or defined by one or more substrates. For example, the measured value may refer to the value of the overlay error, critical dimension, focus, edge placement error measured by inspecting product features and / or target features on processed substrates. Alternatively, the measured value may refer to the value of the dose, focus, (mask) mark position or aberration level of the projection system PS, which is measured by a sensor at multiple positions on the optical plane of the projection system PS. Typically, the optical plane is the image plane of the projection system PS (where the substrate is typically positioned when exposed by the lithographic apparatus). In most cases, the measurement is performed in a field included in the optical plane of the lithographic apparatus, which is an extension of the optical plane illuminated by the lithographic apparatus (during the exposure operation). Therefore, the embodiments herein are not limited to measurements, readouts and measurement data obtained by inspecting structures on a substrate, but any measurement and / or measurement results obtained by any sensing system on the optical plane of the lithographic apparatus and / or substrate are within the scope of the present invention.

[0143] In the case of cross-field measurements in the optical plane, the sensor is typically a dose, aberration or image sensor. The image sensor is typically a sensor configured to measure the relative position of marks on the mask with respect to the substrate table WT. In the case where the sensor is integrated in the substrate table, measurements across the field can be performed by moving the substrate table to a position where the sensor measures the parameter of interest at the desired position in the field.

[0144] However, measuring the parameter of interest at many locations may be too time consuming and is not necessary to obtain a sufficiently accurate behavior of the parameter of interest in the field.

[0145] Given a previous test from all locations (e.g. simulate to Figure 6 The sensor readout data obtained in step 606 of the above process, the locations where the sensor has measured the parameter of interest can be grouped in different ways. For example, the locations in the field can be grouped according to their positions in different field columns / rows / positions. For the selected groupings, the distribution of the locations in each group can be plotted (or a fit to a given distribution, such as a Gaussian distribution) to determine statistically different groups. Examples of statistical differences are:

[0146] The locations in a group have different means of their associated sensor readouts;

[0147] The locations in a group have different std (standard deviation) of their associated sensor readings; and

[0148] None of the groups showed statistical differences in their associated readout values.

[0149] For example, it may be determined that sensor readouts at locations in different columns across the field have different means, or that locations at the edge of the field have a higher variance than locations in the rest of the field.

[0150] Similarly, in cases where the measurements are related to in-field sensor-based measurements rather than inspection of target structures, the sample plan generation algorithm can be configured using the same approach as previously described, in which case the sample plan generation algorithm is configured to define the locations in the field where the sensor should measure parameters of interest (aberrations, dose, marker positions, focus, etc.).

[0151] In an embodiment, a method is provided, comprising: obtaining measurement data associated with a plurality of measurements performed across one or more fields; analyzing the measurement data to determine statistically distinct locations within the one or more fields; and configuring operators of a sample solution generation algorithm based on the statistically distinct locations.

[0152] Optionally, the location defines one or more regions spanning multiple fields, the multiple fields having different corresponding sub-samplings in a sample scheme generated by a sample scheme generation algorithm; and the step of analyzing the measurement data includes stacking the measurement data across the multiple fields spanned using their different corresponding sub-samplings to determine statistically different locations.

[0153] Optionally, the sample solution generation algorithm includes a genetic algorithm.

[0154] Optionally, the step of configuring the operator comprises configuring a crossover operator to exchange sampling information between the determined statistically different locations.

[0155] Optionally, the step of configuring the operator includes configuring the mutation operator to mutate the sampling information in selected, determined statistically different locations.

[0156] Optionally, the sample solution generation algorithm includes a multi-objective genetic algorithm, and the method further includes:

[0157] - obtaining constraints associated with sample scenarios across fields; and

[0158] -Use constraints as input to a sample solution generation algorithm.

[0159] Optionally, the sample solution generation algorithm comprises a multi-objective genetic algorithm, and the method further comprises: acquiring a plurality of key performance indicators associated with the sample solutions across the field; and using the key performance indicators in a fitness function in the sample solution generation algorithm.

[0160] Optionally, the fitness function comprises a comparison between key performance indicators calculated for the measurement data of the set of locations and key performance indicators calculated for the simplified sample scenario individuals.

[0161] In the above described embodiments, the simplified layout for calibration and qualification of scanner performance is fixed once determined. The readout is therefore static: measurements continue even though they no longer add any significant information. The readout strategy is predefined and cannot be changed.

[0162] As a specific example, a machine match overlay test (qualification or verification test of overlay) may include exposing and measuring six wafers under identical conditions: three exposed on a first chuck (e.g., of a dual stage system) and three exposed on a second chuck. In the above embodiment, very identical mark readouts may be applied to all six wafers, even if all wafers exposed on the same chuck have very similar measured mark values ​​in the infield.

[0163] Methods are presented in which a flexible sampling scheme or measurement scheme can be implemented. Such a flexible sampling scheme can include, for example, measuring all marks on a first wafer exposed on a first chuck. Then, for a second wafer exposed on the first chuck, the measurement of the marks can start centrally (e.g., the marks in the inner field), with each measurement immediately checked to determine the degree of variation of the measured value from the corresponding mark on the first wafer. If the variation is small enough (within specification) for at least one or the first few marks (e.g., for at least a predetermined minimum number of marks), it can be decided to skip the measurement of some marks (e.g., other unmeasured marks in the inner field) and directly start sampling fields that are expected to have more variation (e.g., at or near the edges). Depending on the level of variation in these edge fields, dense sampling can be selected for fields expected to have a large degree of variation, or less dense sampling can be selected for fields expected to have a small degree of variation.

[0164] More generally, such methods may include a "previous measurement-based" approach. For any test, verification, or calibration that measures more than one wafer, all marks on a first set of wafers (e.g., including one or more wafers) may be measured. The acceptable bounds for measurement error are known. For a second set of wafers (e.g., wafers after the first set of wafers), flexible sampling is performed. This may include measuring only a few marks (a first subset) on the first wafer in the second set of wafers. If the difference between the measured values ​​of these marks and the measured values ​​of the corresponding marks in the first set of wafers (when the first set of wafers includes more than one wafer, the corresponding mark values ​​may be averaged or otherwise combined) is within the measurement error bounds, the measurement of the current wafer may end, and the measurement of the next wafer of the second set of wafers may begin immediately. However, if the measured values ​​on the second wafer are outside the bounds, more marks on the current wafer are measured. In such an embodiment, the first marks measured may be those that are expected to have the greatest variation between wafers.

[0165] Alternatively, determining that the first value is within specification may trigger the end of measurement of a particular region of the wafer (e.g., a first region or a central region) and the start of measurement of another region of the same wafer (e.g., a second region or an edge region, also referred to as a peripheral region); in such an embodiment, the first marks measured may be those that are expected to have minimal or at least less variation between wafers. The same flexible sampling scheme approach may then be taken for this second region, such that some or all marks in the region are measured depending on the variation of the measured values ​​of the first few marks relative to the corresponding marks in the first group and the allowed measurement error. Measurements may then be made with the next region (if more than two) or the next wafer.

[0166] Subsequent wafers in the second set may be measured using the same sampling scheme designed for the first wafer in the second set, or a flexible approach may be taken for each wafer in the second set using the same approach for each wafer such that the sampling scheme is flexible between wafers.

[0167] In another embodiment, a method for determining a flexible sampling scheme or measurement scheme based on a dynamic model is proposed. Once again, such a method can be applicable to any test, verification or calibration that measures more than one wafer. Alternatively or additionally, such a method can be used for any test that tracks a parameter of interest (such as overlay): for example, such a strategy can be used to examine a WEC (wafer error correction) diagram. This embodiment may use a "dynamic model" of what is to be measured. The term "dynamic model" in this article can be understood to mean a function that outputs a regression or fitting model based on a relatively sparse measurement data set (measurement data for only a few positions), and the regression or fitting model extrapolates and / or interpolates values ​​for wafer positions (unmeasured positions) for which no corresponding measurement data is available. For example, a dynamic model can fit a given field-to-field shape based on a few sparse measurements.

[0168] Such a method may include a first step of measuring several marks from a first wafer (or a first group of wafers) and fitting a dynamic model with them to obtain a fitted model for the wafer. The next step includes measuring further marks and comparing each measured value or a corrected value of the fit of the entire wafer taking into account the new measured value with the value predicted by the fitted model. If enough measured values ​​are within a given tolerance range, the measurement can be stopped. It should be understood that the measurement can be performed until the confidence level exceeds a certain standard. This way of working is similar to Bayesian reasoning techniques and active learning. In these techniques, new data acquisition aims to minimize the uncertainty of the model. Therefore, the method may include dynamically updating the confidence (uncertainty measure) associated with the unmeasured positions on the wafer being measured based on the wafers that have been measured; and the dynamically available measurement results of the wafer currently being measured.

[0169] The decision of which marker should be the next marker to be measured can be made based on a Gaussian process; for example, the next marker to be measured can be:

[0170] i. The marker with the highest uncertainty in the fitted model;

[0171] ii. This marker has the greatest chance of containing the min / max peak of the model.

[0172] In an embodiment, the dynamic model may evolve over time to accommodate drift. For example, assuming the initial dynamic model is of the form: f = c1X 2 +c2Y 2 (where X and Y are the wafer coordinates of the markers). Once the model is fitted, it returns a model that is fitted between fields. The first measurement on the wafer enables the determination of c1 and c2 and thus the extrapolation of values ​​for non-measured locations of the wafer. However, if the values ​​predicted by the fitted model differ significantly from the measured values ​​(by a threshold or percentage), the dynamic model may change the actual model, for example, updating the model f' = c1X 2 +c2Y 2 +c3X. If this updated model f' fits the measured data better than f, then this model can be selected as the initial dynamic model for subsequent wafers.

[0173] The evolution (change over time) of a model may be based on:

[0174] Prior knowledge: For example, if it is known that the degradation of a wafer stage adds terms to the wafer stage model, then the model terms can be added at the same time as the wafer stage degradation;

[0175] Software: Genetic programming software can select the best model consisting of a finite set of given functions.

[0176] If, after measuring all markers, the confidence level of the measurement for the current wafer (compared to the fitted model) does not exceed a certain threshold, the function defining the dynamic model can be changed. This allows the model to adapt to drift.

[0177] Another method for flexible sampling may include searching for a given point. This method may include searching for a specific shape on the wafer (e.g., based on prior knowledge and known behavioral patterns), which may vary in orientation, displacement, etc. Once the shape is found, the location of its maximum value may be determined and / or characterized with a minimum number of measurements. This may be accomplished by sampling the wafer the minimum number of times required to match a given shape with its orientation, displacement, etc., and then sampling the wafer at the area within the matching shape where the maximum value is expected to be found.

[0178] The latter approach may also be applicable to the qualification of scanner components (e.g., instead of wafer measurement). For example, when an immersion hood is produced, it must be tested to check whether all holes (i.e., holes for supplying water, removing water, and blowing out CO2) are open and do not contain contaminants that affect the flow through these holes. This can be performed using a device that measures the flow output from these holes when pressure is applied. In the prior art, the measurement scheme may follow a fixed (e.g., 6×6) grid for all holes, so that each hole is sampled at 36 points. If the holes are properly open and unobstructed, the 6×6 flow measurements should be defined as a Gaussian shape. Therefore, the Gaussian shape can be a specific shape with a peak at the center that is searched for in this embodiment; applying this flexible measurement scheme to the test can reduce the number of measurements for each hole from 36 to a minimum of 5 (e.g., describing a Gaussian shape), thereby reducing the test time.

[0179] The steps of the above method can be Figure 1 The lithography apparatus control unit LACU shown may be automated in an inspection apparatus such as an angle-resolved scatterometer. The unit LACU may include computer components such as Fig.13 As shown. In an embodiment of the assembly according to the invention, the computer assembly may be a dedicated computer in the form of a control unit or, alternatively, may be a central computer controlling the lithographic projection apparatus. The computer assembly may be arranged for loading a computer program product comprising computer executable code. When downloading the computer program product, this may enable the computer assembly to control the above-described use of the lithographic apparatus having an embodiment of the level and alignment sensors AS, LS.

[0180] The memory 1329 connected to the processor 1327 may include a plurality of memory components, such as a hard disk 1361, a read-only memory (ROM) 1362, an electrically erasable programmable read-only memory (EEPROM) 1363, or a random access memory (RAM) 1364. Not all of the aforementioned memory components need to be present. Furthermore, it is not necessary for the aforementioned memory components to be physically adjacent to the processor 1327 or to each other. They may be located far away.

[0181] The processor 1327 may also be connected to some kind of user interface, such as a keyboard 1365 or a mouse 1366. A touch screen, trackball, voice converter or other interface known to those skilled in the art may also be used.

[0182] The processor 1327 may be connected to a read-out unit 1367, which is arranged to read data, for example in the form of computer executable code, from a data carrier, such as a solid-state drive 1368 or a CDROM 1369, and in some cases store the data on a data carrier, such as a solid-state drive 1368 or a CDROM 1369. DVDs or other data carriers known to those skilled in the art may also be used.

[0183] The processor 1327 may also be connected to a printer 1370 for printing out data on paper, and to a display 1371, such as a monitor or LCD (Liquid Crystal Display) or any other type of display known to those skilled in the art.

[0184] The processor 1327 may be connected to a communication network 1372, such as a public switched telephone network (PSTN), a local area network (LAN), a wide area network (WAN), etc., via a transmitter / receiver 1373 responsible for input / output (I / O). The processor 1327 may be arranged to communicate with other communication systems via the communication network 1372. In an embodiment of the present invention, an external computer (not shown), such as an operator's personal computer, may log in to the processor 1327 via the communication network 1372.

[0185] Processor 1327 can be implemented as a stand-alone system or multiple processing units operating in parallel, where each processing unit is arranged to perform a subtask of a larger program. The processing unit can also be divided into one or more main processing units with several sub-processing units. Some processing units of processor 1327 can even be located at a distance away from other processing units and communicate via communication network 1372. The connection between modules can be wired or wireless.

[0186] The computer system may be any signal processing system with analog and / or digital and / or software technology arranged to perform the functions discussed herein.

[0187] The term substrate as used herein may refer to a wafer or a patterning device, such as a mask. In photolithography, a mask has a pattern that is imaged onto a target substrate, such as a wafer.

[0188] Further embodiments of the invention are disclosed in the following list of numbered items:

[0189] 1. A method comprising:

[0190] - acquiring measurement data associated with a set of locations across one or more substrates;

[0191] - analyzing the measurement data to determine statistically distinct groups of locations; and

[0192] - Operators of sample solution generation algorithms based on statistically different groups of configurations or sample solution generation algorithms based on statistically different groups of configurations.

[0193] 2. A method according to claim 1, wherein the positions in the group together define one or more regions within a field, and the field is repeated across one or more substrates.

[0194] 3. A method according to claim 1, wherein:

[0195] - the positions in the group together define one or more regions spanning a plurality of fields, the fields spanning one or more substrates, the plurality of fields having different corresponding subsamplings in a sample plan generated by a sample plan generation algorithm; and

[0196] The step of analyzing the measurement data comprises stacking the measurement data across the plurality of fields spanned using different respective sub-samplings thereof to determine statistically distinct groups of locations.

[0197] 4. A method according to any of the preceding items, wherein the sample solution generation algorithm comprises a genetic algorithm.

[0198] 5. A method according to item 4, wherein the step of configuring the operator includes configuring a crossover operator to exchange sampling information between the determined statistically different groups.

[0199] 6. A method according to item 4, wherein the step of configuring the operator includes configuring a mutation operator to mutate the sampling information in the selected determined statistically different groups.

[0200] 7. The method according to any one of items 4 to 6, wherein the sample solution generation algorithm comprises a multi-objective genetic algorithm, and the method further comprises:

[0201] - obtaining constraints associated with sample scenarios across one or more bases; and

[0202] -Use constraints as input to a sample solution generation algorithm.

[0203] 8. The method according to any one of clauses 4 to 7, wherein the sample solution generation algorithm comprises a multi-objective genetic algorithm, and the method further comprises:

[0204] - obtaining a plurality of key performance indicators associated with sample scenarios across one or more substrates; and

[0205] -Use key performance indicators in the fitness function in the sample solution generation algorithm.

[0206] 9. A method according to clause 8, wherein the fitness function comprises a comparison between key performance indicators calculated for the measurement data of the set of locations and key performance indicators calculated for the simplified sample scenario individuals.

[0207] 10. A method comprising:

[0208] - obtaining constraints and / or a plurality of key performance indicators associated with sample scenarios across one or more substrates; and

[0209] -Using constraints and / or multiple key performance indicators in sample solution generation algorithms including multi-objective genetic algorithms.

[0210] 11. The method according to item 10, further comprising:

[0211] - acquiring measurement data associated with a set of locations across one or more substrates;

[0212] - Analyze the measurement data; and

[0213] - optimizing a sample plan based on analysis, wherein a location defines one or more regions spanning multiple fields across one or more substrates, the multiple fields having different corresponding subsamplings in the sample plan;

[0214] wherein the constraints are based on analysis; and

[0215] Therein, the step of analyzing the measurement data comprises stacking the measurement data across the plurality of fields spanned using their different respective sub-sampling spans.

[0216] 12. A method according to item 11, wherein the step of optimizing the sample plan includes configuring a crossover operator of the sample plan generation algorithm to exchange sampling information between fields.

[0217] 13. The method according to item 11, wherein the step of optimizing the sample plan includes configuring a mutation operator of a sample plan generation algorithm to mutate the sampling information in the selected field.

[0218] 14. A method comprising:

[0219] - acquiring measurement data associated with a set of locations across one or more substrates;

[0220] - Analyze the measurement data; and

[0221] - Optimize sample solutions based on analysis,

[0222] wherein the location defines one or more regions across a plurality of fields, the fields spanning one or more substrates, the plurality of fields having different corresponding subsamplings in the sample scheme; and

[0223] Therein, the step of analyzing the measurement data comprises stacking the measurement data across the plurality of fields spanned using their different respective sub-sampling spans.

[0224] 15. A lithographic apparatus, in particular adapted to perform the steps of the method of any one of items 1 to 9, or items 10 to 13 or item 14.

[0225] 16. An inspection device, in particular, adapted to perform the steps of the method of any one of items 1 to 9, or items 10 to 13 or item 14.

[0226] 17. A computer program comprising computer readable instructions which, when executed on a suitable computer device, cause the computer device to perform the method of any one of items 1 to 9, or items 10 to 13 or item 14.

[0227] 18. A computer program product comprising the computer program of item 17.

[0228] 19. A method comprising:

[0229] - Acquire measurement data associated with a set of positions; spans typically included in the optical plane

[0230] One or more fields within;

[0231] - analyzing the measurement data to determine statistically distinct groups of locations; and

[0232] - Operators of the algorithm for generating sample scenarios based on statistically different groups of configurations.

[0233] 20. A method according to clause 19, wherein the positions in the group together define one or more areas within the field.

[0234] 21. The method of claim 19, wherein:

[0235] - the locations in the group together define one or more regions spanning a plurality of fields, the plurality of fields having different corresponding subsamplings in a sample plan generated by the sampling plan generation algorithm; and

[0236] The step of analyzing the measurement data comprises stacking the measurement data across the plurality of fields spanned using different respective sub-samplings thereof to determine statistically distinct groups of locations.

[0237] 22. A method according to any one of items 19 to 21, wherein the sample solution generation algorithm includes a genetic algorithm.

[0238] 23. A method according to item 22, wherein the step of configuring the operator includes configuring a crossover operator to exchange sampling information between the determined statistically different groups.

[0239] 24. A method according to item 22, wherein the step of configuring the operator includes configuring a mutation operator to mutate the sampling information in the selected determined statistically different groups.

[0240] 25. A method according to any one of items 22 to 24, wherein the sample solution generation algorithm comprises a multi-objective genetic algorithm, and the method further comprises: - obtaining constraints associated with the sample solutions across the field; and

[0241] -Use constraints as input to a sample solution generation algorithm.

[0242] 26. A method according to any one of items 22 to 25, wherein the sample solution generation algorithm comprises a multi-objective genetic algorithm, and the method further comprises: - obtaining a plurality of key performance indicators associated with the sample solutions across the field; and

[0243] -Use key performance indicators in the fitness function in the sample solution generation algorithm.

[0244] 27. A method according to clause 26, wherein the fitness function comprises a comparison between key performance indicators calculated for the measurement data of the set of locations and key performance indicators calculated for the simplified sample scenario individuals.

[0245] 28. A method according to any one of items 19 to 27, wherein the measurement data comprises the value of a parameter measured across the field by a sensor in the optical plane.

[0246] 29. A method according to claim 28, wherein the parameter is: one of: aberration level, dose, focus level and detection position of the mark.

[0247] 30. A method of determining a flexible measurement scheme, the flexible measurement scheme defining a flexible subset of measurement locations associated with one or more objects or regions of objects, the method comprising:

[0248] - acquiring measurement data relating to measurements at one or more of said measurement locations;

[0249] - acquiring feature data relating to features of one or more objects or regions of objects; and

[0250] --Determine flexible measurement scheme based on characteristic data and measurement data.

[0251] 31. A method according to item 30, wherein the measurement data provides information for describing a variation of a parameter described by the measurement data according to a criterion.

[0252] 32. A method according to item 30 or 31, wherein the measurement data comprises a first set of measurements and a subsequent set of measurements, wherein the characteristic data is associated with the first set of measurements and associated tolerance margins, the first set of measurements being associated with a first appropriate subset of one or more objects or regions of the objects; and the method comprises: comparing one or more subsequent measurement values ​​included in the subsequent set of measurements with corresponding first measurement values ​​included in the first set of measurements; and

[0253] A flexible measurement scheme is determined based on whether a difference between one or more subsequent measurement values ​​and a corresponding first measurement value is within the tolerance margin.

[0254] 33. The method according to item 32, wherein determining the flexible measurement scheme comprises acquiring the subsequent measurement values ​​by sequentially measuring unmeasured measurement positions among the measurement positions on the currently measured object or the region thereof; and

[0255] Based on whether the difference value is within the tolerance margin, it is determined whether the number of measurements performed on the object or region thereof currently being measured is sufficient.

[0256] 34. The method according to item 33, when there are more objects or regions thereof to be measured, starting to measure subsequent objects or regions thereof.

[0257] 35. A method according to any one of items 32 to 34, wherein one or more objects include at least a first region and a second region, such that the difference in the first region is expected to vary less than the difference in the second region.

[0258] 36. A method according to clause 35, wherein the step of determining a flexible measurement scheme is performed separately for the first and second regions of the object.

[0259] 37. A method according to item 35 or 36, wherein the first area includes a central area of ​​one or more objects, and the second area includes a peripheral area of ​​one or more objects.

[0260] 38. A method according to any one of items 32 to 37, wherein the flexible measurement scheme determined for a first subsequent object is performed on each of the other subsequent objects.

[0261] 39. A method according to any one of clauses 32 to 37, wherein the step of determining a flexible measurement scheme is performed separately for each of the subsequent objects.

[0262] 40. A method according to clause 30, wherein the feature data comprises a model describing parameters of one or more objects or regions of objects associated with the measurement data, and the measurement data comprises a first set of measurements and a subsequent set of measurements; the method comprising:

[0263] Fit the model to the first set of measurements to obtain a fitted model;

[0264] Assess model performance of the fitted model using subsequent group measurements; and

[0265] A flexible measurement scheme is determined based on an evaluation of the performance of the fitted model.

[0266] 41. A method according to clause 40, wherein the first set of measurements relates to a first object of the one or more objects or a first area of ​​the areas of an object.

[0267] 42. A method according to item 40 or 41, wherein said evaluating model performance comprises the following sequential steps:

[0268] obtaining subsequent measurement values ​​associated with unmeasured measurement locations in a subsequent set of measurements;

[0269] The subsequent measurements are compared to corresponding individual predicted measurements predicted using the fitted model.

[0270] 43. A method according to item 42, wherein the sequential steps are performed until the evaluation step determines that a certain number of subsequent measurements are within the tolerance margin.

[0271] 44. A method according to clause 40 or 41, wherein the method comprises determining a value describing the goodness of fit of the fitted model, and said assessing model performance comprises the following sequential steps:

[0272] Obtaining subsequent measurements by measuring unmeasured measurement locations in a subsequent set of measurements;

[0273] Repeat the fitting step;

[0274] Determine revised values ​​that describe goodness of fit; and

[0275] Evaluate whether the goodness of fit has improved.

[0276] 45. A method according to item 44, wherein the consecutive steps are performed until the evaluation step determines that the goodness of fit is within a tolerance margin.

[0277] 46. ​​A method according to any one of items 42 to 45, wherein the evaluating model performance includes determining an uncertainty metric describing the level of uncertainty associated with an unmeasured position; and performing the sequential steps on the subsequent measurement values ​​until the uncertainty metric satisfies an uncertainty criterion.

[0278] 47. A method according to claim 46, comprising: determining the next unmeasured measurement position for measurement in the first sequential step by selecting the unmeasured measurement position determined to have the highest uncertainty in the fitted model; or the unmeasured measurement position having the greatest chance of containing the minimum / maximum value in the fitted model.

[0279] 48. A method according to any one of items 40 to 47, comprising:

[0280] When the model performance of the model is below a threshold, adjusting the model;

[0281] Evaluate model performance of the tuned model;

[0282] The model performance of the adjusted model is compared with the model performance of the model; if the model performance of the adjusted model is better than the model performance of the model, the model is updated by the adjusted model.

[0283] 49. A method according to clause 48, wherein the updating of the model is based on one or both of the following:

[0284] Knowledge of known and / or expected behavior; and

[0285] Genetic programming software that can be operated to select the best model consisting of a finite set of given functions.

[0286] 50. A method according to clause 30, wherein the characteristic data comprises a desired pattern or shape; and the method comprises:

[0287] acquiring measurement data relating to measurements at one or more of the measurement locations of one or more objects;

[0288] Determine where the maximum or minimum of a pattern or shape is located; and

[0289] Another measurement data related to the measurement at the location is acquired.

[0290] 51. A method according to any one of items 30 to 50, wherein the object or region of the object each comprises a substrate for patterning in a photolithography process.

[0291] 52. A method according to clause 50, wherein the object or the region of the object each comprises an aperture of an immersion hood for a lithographic apparatus.

[0292] 53. A lithographic apparatus particularly adapted to perform the steps of the method of any one of items 19 to 52.

[0293] 54. An inspection device, particularly suitable for performing the steps of the method described in any one of items 19 to 52.

[0294] 55. A computer program comprising computer readable instructions which, when executed on a suitable computer device, cause the computer device to perform the method of any one of items 19 to 52.

[0295] 56. A computer program product comprising the computer program of item 55.

[0296] 57. A method according to item 50, wherein the object or the region of the object each comprises a component of a lithographic apparatus.

[0297] Although specific reference may be made herein to the use of lithographic apparatus in IC manufacturing, it should be understood that the lithographic apparatus described herein may have other applications, such as processing of substrates in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat panel displays, liquid crystal displays (LCDs), thin film magnetic heads, etc. Those skilled in the art will understand that in the context of these alternative applications, any use of the terms "wafer" or "field" / "die" herein may be considered synonymous with the more general terms "substrate" or "target portion", respectively. Before or after exposure, the substrates described herein may be processed in, for example, a track (a tool that typically applies a resist layer to a substrate and develops the exposed resist), a metrology tool, and / or an inspection tool. Where applicable, the disclosure herein may be applied to such and other substrate processing tools. In addition, a substrate may be processed more than once, for example to create a multi-layer IC, so that the term substrate used herein may also refer to a substrate that already contains multiple processed layers.

[0298] Although specific reference has been made above to the use of embodiments of the invention in the context of optical lithography, it will be appreciated that the invention may be used in other applications, such as imprint lithography, and that the invention is not limited to optical lithography where the context permits. In imprint lithography, the topography in the patterning device defines the pattern produced on the substrate. The topography of the patterning device may be pressed into a resist layer provided to the substrate, upon which the resist is cured by applying electromagnetic radiation, heat, pressure, or a combination thereof. The patterning device is removed from the resist, leaving a pattern therein after the resist has cured.

[0299] As used herein, the terms "radiation" and "beam" include all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having a wavelength of or about 365, 248, 193, 157, or 126 nanometers) and extreme ultraviolet (EUV) radiation (e.g., having a wavelength in the range of 5-20 nanometers), as well as particle beams, such as ion beams or electron beams.

[0300] The term "lens," where the context allows, may refer to any one or combination of various types of optical components, including refractive, reflective, magnetic, electromagnetic, and electrostatic optical components.

[0301] Although specific embodiments of the present invention have been described above, it will be appreciated that the present invention may be practiced in a manner other than that described. For example, the present invention may take the form of a computer program comprising one or more machine-readable instruction sequences describing the methods described above, or a data storage medium (e.g., a semiconductor memory, a magnetic disk, or an optical disk) having such a computer program stored therein.

[0302] The above description is intended to be illustrative, not restrictive. Therefore, it will be apparent to those skilled in the art that the present invention may be modified as described without departing from the scope of the appended claims. In addition, it should be understood that the structural features or method steps shown or described in any one embodiment herein may also be used in other embodiments.

Claims

1. A method for determining a flexible measurement scheme, the flexible measurement scheme defining a flexible subset of measurement locations associated with one or more objects or regions of objects, the method comprising: acquiring measurement data related to measurements at one or more of said measurement locations; Acquiring feature data related to features of the one or more objects or regions of the objects; as well as The flexible measurement scheme is determined based on the characteristic data and the measurement data.

2. A method according to claim 1, the measurement data comprising a first set of measurements and a subsequent set of measurements, wherein the characteristic data is associated with the first set of measurements and associated tolerance margins, the first set of measurements being associated with a first appropriate subset of the one or more objects or regions of the objects; and the method comprising: comparing one or more subsequent measurement values ​​included in the subsequent set of measurements to respective corresponding first measurement values ​​included in the first set of measurements; and The flexible measurement scheme is determined based on whether a difference between the one or more subsequent measurement values ​​and each corresponding first measurement value is within the tolerance margin.

3. The method according to claim 2, wherein determining the flexible measurement scheme comprises acquiring the subsequent measurement values ​​by sequentially measuring unmeasured measurement positions among the measurement positions on the currently measured object or a region thereof; and Based on whether the difference value is within the tolerance margin, it is determined whether the number of measurements performed on the object or the region thereof currently being measured is sufficient. 4 . The method according to claim 3 , when there are more objects or regions thereof to be measured, starting to measure subsequent objects or regions thereof. 5 . The method according to claim 2 , wherein the one or more objects include at least a first region and a second region, such that the difference in the first region is expected to vary less than the difference in the second region. 6 . The method according to claim 2 , wherein the flexible measurement scheme determined for a first one of the subsequent objects is performed on each of the other subsequent objects, or is performed separately for each of the subsequent objects.

7. The method of claim 1, wherein the feature data comprises a model describing parameters of the one or more objects or regions of the objects associated with the measurement data, and the measurement data comprises a first set of measurements and a subsequent set of measurements; the method comprising: fitting the model to the first set of measurements to obtain a fitted model; evaluating model performance of the fitted model using the subsequent set of measurements; as well as The flexible measurement scheme is determined based on an evaluation of the performance of the fitted model.

8. The method of claim 7, wherein said evaluating model performance comprises the following sequential steps: obtaining subsequent measurement values ​​associated with unmeasured measurement positions in the subsequent set of measurements; The subsequent measurements are compared to corresponding respective predicted measurement values ​​predicted using the fitted model.

9. The method of claim 7, wherein the method comprises determining a value describing the goodness of fit of the fitted model, and said evaluating the model performance comprises the following sequential steps: obtaining subsequent measurement values ​​by measuring unmeasured measurement positions in the subsequent set of measurements; Repeat the fitting step; determining a revised value describing the goodness of fit; as well as Evaluate whether the goodness of fit has improved.

10. The method of claim 8, wherein said evaluating said model performance comprises determining an uncertainty metric describing a level of uncertainty associated with an unmeasured position; and performing said sequential steps on said subsequent measurements until said uncertainty metric satisfies an uncertainty criterion; and The next unmeasured measurement position for measurement in the first sequential step is determined by selecting the unmeasured measurement position determined to have the highest uncertainty in the fitted model; or the unmeasured measurement position having the greatest chance of including a minimum / maximum value in the fitted model.

11. The method according to claim 7, comprising: When the model performance of the model is below a threshold, adjusting the model; Evaluate model performance of the tuned model; comparing a model performance of the adjusted model to a model performance of the model; If the model performance of the adjusted model is better than the model performance of the model, updating the model by the adjusted model, The model is updated based on one or both of the following: Knowledge of known and / or expected behavior; and Genetic programming software that can be operated to select the best model consisting of a finite set of given functions.

12. The method of claim 1, wherein the characteristic data comprises a desired pattern or shape; and the method comprises: acquiring measurement data related to measurements at one or more of the measurement locations of the one or more objects; determining where a maximum or minimum of the pattern or shape is located; as well as Further measurement data related to the measurement at the location is acquired.

13. A computer program comprising computer readable instructions which, when executed on a suitable computer device, cause the computer device to perform the method according to any one of claims 1 to 12.

14. A computer program product comprising the computer program according to claim 13.

15. An inspection device configured to perform the method according to any one of claims 1 to 12.

Images