Methods, associated equipment, and computer programs for determining sampling plans

Abstract

A method for determining a sampling plan is disclosed. The method includes obtaining a parallel sensor description, identifying a plurality of candidate acquisition configurations based on the parallel sensor description and potential measurement locations, evaluating each of the candidate acquisition configurations with respect to an evaluation metric, and selecting a candidate acquisition configuration based on the evaluation. The measurement locations corresponding to the selected acquisition configuration are added to the sampling plan.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to EP application 20168243.2 filed on April 6, 2020 and EP application 20168876.9 filed on April 9, 2020, which are incorporated herein by reference in their entirety. Technical Field

[0003] The present invention relates to a method of determining a sampling scheme for a measurement, an associated apparatus and a computer program. Background Art

[0004] A lithographic apparatus is a machine that applies a desired pattern to a substrate (usually applied to a target portion of a substrate). A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In this case, a pattern forming device (alternatively referred to as a mask or reticle) can be used to produce a circuit pattern to be formed on a single layer of the IC. This pattern can be transferred to a target portion (e.g., a portion comprising a die, a die, or several dies) on a substrate (e.g., a silicon wafer). The transfer of the pattern is usually performed by imaging onto a layer of radiation-sensitive material (resist) disposed on the substrate. Typically, a single substrate will contain a network of adjacent target portions that are patterned continuously. Known lithographic apparatus include so-called steppers, in which each target position is irradiated by exposing the entire pattern to the target position at one time, and so-called scanners, in which each target position is irradiated by scanning the substrate in a direction parallel or antiparallel to the scanning direction while the radiation beam is scanning the pattern in a given direction ("scanning" direction). The pattern can also be transferred from the pattern forming device to the substrate by printing the pattern onto the substrate.

[0005] Regardless of the type of equipment employed, accurate 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 photolithography. In particular, the challenge of accurately measuring features already laid out on a substrate is a critical step in being able to accurately position features in successive layers in an additive manner, thereby producing working devices at high yields. Typically, in today's submicron semiconductor devices, this so-called overlay should be achieved to within tens of nanometers, and down to a few nanometers in the most critical layers.

[0006] Therefore, modern lithography equipment involves extensive measurement or "mapping" operations before the actual exposure of target locations or the step of otherwise patterning the substrate. These time-consuming operations limit the throughput of lithography equipment and therefore increase the unit cost of semiconductors or other products.

[0007] As pattern features become smaller and overlay performance requirements become more stringent, so-called advanced alignment models have been and continue to be developed to more accurately model and correct for nonlinear distortions of the wafer "grid." These advanced models rely on measuring an increasing number of targets across the wafer. However, ultimately, only a limited number of available targets can be measured without unduly limiting the throughput and / or cost of the overall lithography process. Summary of the Invention

[0008] Therefore, there is a need to increase the informativeness, coverage and / or throughput of metrology processes in a cost-effective manner.

[0009] In one aspect, the present invention provides a method for determining a sampling scheme that describes a proper subset of measurement locations in a set of potential measurement locations on a substrate; the method comprises: obtaining a parallel sensor description that describes an arrangement of a plurality of measurement sensors capable of performing parallel measurement; identifying a plurality of candidate acquisition configurations based on the parallel sensor description and the potential measurement locations, wherein each candidate acquisition configuration describes a specific position of the sensor description relative to the substrate and, therefore, describes one or more corresponding ones of the potential measurement locations; evaluating each of the candidate acquisition configurations according to an evaluation metric; and defining the sampling scheme to include the corresponding measurement locations for each selected acquisition configuration.

[0010] Those skilled in the art will appreciate these and other features and advantages of certain embodiments of the present invention through consideration of the exemplary embodiments discussed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying schematic drawings in which corresponding reference numerals indicate corresponding parts, and in which;

[0012] Figure 1 (a) depicts a lithographic apparatus according to an embodiment of the present invention;

[0013] Figure 1 (b) schematically illustrates a method according to known practice Figure 1 (a) Stages of measurement and exposure process in the device;

[0014] Figure 2 (a) Depicts possible measurement locations on the substrate;

[0015] Figure 2 (b) depicts exemplary selected measurement locations optimized according to the sampling scheme;

[0016] Figure 3 is a flow chart illustrating a sampling scheme optimization method according to an embodiment of the present invention;

[0017] Figure 4 Shown based on Figure 3 The first measurement strategy of the sampling scheme optimization method;

[0018] Figure 5 Shown based on Figure 3 The second measurement strategy of the sampling scheme optimization method;

[0019] Figure 6 (a) and 6(b) show two views of a parallel sensor measurement device that can utilize a sampling scheme optimization method according to an embodiment; and

[0020] Figure 7 Computer system hardware used to implement the processes disclosed herein is shown. DETAILED DESCRIPTION

[0021] Figure 1 (a) schematically shows a lithographic apparatus LA according to an embodiment of the present invention. The apparatus comprises:

[0022] an illumination system (illuminator) IL configured to condition a radiation beam B (e.g., UV radiation or EUV radiation);

[0023] a support structure (e.g., mask table) MT configured to support a patterning device (e.g., mask) MA and connected to a first positioner PM configured to accurately position the patterning device according to certain parameters;

[0024] a substrate table (e.g., a wafer stage) 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

[0025] A projection system (eg, a refractive projection lens system) PS is 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).

[0026] The illumination system may include various types of optical components for directing, shaping, or controlling radiation, such as refractive, reflective, magnetic, electromagnetic, electrostatic, or other types of optical components, or any combination thereof.

[0027] The support structure supports the pattern forming device, i.e. bears the weight of the pattern forming device. The support structure holds the pattern forming device in a manner that depends on the orientation of the pattern forming device, the design of the lithographic apparatus and other conditions (such as, for example, whether the pattern forming device is maintained in a vacuum environment). The support structure can use mechanical, vacuum, electrostatic or other clamping techniques to hold the pattern forming device. The support structure can be a frame or a table, for example, the support structure can be fixed or movable as required. The support structure can ensure that the pattern forming device is in a desired position, for example relative to the projection system. Any use of the term "reticle" or "mask" in this document can be considered to be synonymous with the more general term "pattern forming device".

[0028] The term "patterning device" as used herein should be broadly interpreted as referring to any device that can be used to impart a pattern in the cross-section of the radiation beam so as to create a pattern in the target portion of the 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 being created in the target portion, such as an integrated circuit.

[0029] The patterning device can be transmissive or reflective. Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in photolithography 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 uses 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 impart a pattern in the radiation beam reflected by the mirror matrix.

[0030] 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 to the exposure radiation used, or to other factors such as the use of immersion liquid or the use of a vacuum. Any use of the term "projection lens" herein should be considered synonymous with the more general term "projection system."

[0031] As described herein, the device is of the transmissive type (eg, using a transmissive mask). Alternatively, the device may be of the reflective type (eg, using the programmable mirror array type mentioned above, or using a reflective mask).

[0032] 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 one or more other tables are being used for exposure. The invention disclosed herein may be used in a standalone manner, and more particularly, it may provide additional functionality during the pre-exposure measurement phase of a single apparatus or multiple apparatuses.

[0033] The lithographic apparatus may also be of a type in which at least a portion of the substrate may be overlapped 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 the space between the mask and the projection system. Immersion techniques are well known in the art for increasing the numerical aperture of a projection system. The term "immersion" as used herein does not imply that structures such as the substrate are necessarily immersed in the liquid, but only that the liquid is located between the projection system and the substrate during exposure.

[0034] refer to Figure 1 (a) The illuminator IL receives a radiation beam from a radiation source SO. For example, when the source is an excimer laser, the source and the lithographic apparatus may be separate entities. In such a case, the source is not considered to form part of the lithographic apparatus, and the radiation beam is transferred from the source SO to the illuminator IL by means of a beam delivery system BD comprising, for example, suitable directing mirrors and / or a beam expander. In other cases, for example, when the source is a mercury lamp, the source may be an integral part of the lithographic apparatus. The source SO and illuminator IL, together with the beam delivery system BD (where necessary), may be referred to as a radiation system.

[0035] The illuminator IL may include an adjuster AD for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer radial extent and / or the inner radial extent (commonly referred to as "σ-outer" and "σ-inner," respectively) of the intensity distribution in a pupil plane of the illuminator can be adjusted. In addition, the illuminator IL may include various other components, such as an integrator IN and a condenser CO. The illuminator can be used to condition the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0036] 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 traversing the mask MA, the radiation beam B passes through the 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 interferometry device, a linear encoder, or a capacitive sensor), the substrate table WTa / WTb can be accurately moved (e.g. in order to position a different target portion C in the path of the radiation beam B). Similarly, the first positioner PM and another position sensor ( Figure 1 The mask table MT is arranged to move along the path of the radiation beam B accurately (for example after mechanical retrieval from a mask library or during scanning) using a plurality of actuators (not explicitly shown in (a)). In general, movement of the mask table MT may be achieved with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning) which form part of the first positioner PM. Similarly, movement of the substrate table WTa / WTb may be achieved using a long-stroke module and a short-stroke module which form 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. Mask alignment marks M1, M2 and substrate alignment marks P1, P2 may be used to align the mask MA with the substrate W. Although the substrate alignment marks (as shown) occupy dedicated target portions, these marks may be located in the space between target portions (called scribe line alignment marks). Similarly, where more than one die is provided on the mask MA, the mask alignment marks may be located between the dies.

[0037] The described device can be used in at least one of the following modes:

[0038] 1. In step mode, the mask table MT and substrate table WTa / WTb are held substantially stationary (i.e., a single static exposure) while the entire pattern imparted to the radiation beam is projected at one time onto a target portion C. The substrate table WTa / WTb is then shifted 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 limits the size of the target portion C that can be imaged in a single static exposure.

[0039] 2. In scan mode, the mask table MT and substrate table WTa / WTb are scanned synchronously while projecting a pattern imparted to the radiation beam 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 can be determined by the (or less) 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 a single dynamic exposure (in the non-scanning direction), while the length of the scanning motion determines the height of the target portion (in the scanning direction).

[0040] 3. In another mode, the mask table MT is held substantially stationary, thereby holding the programmable patterning device, and the substrate table WTa / WTb is moved or scanned, while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, a pulsed radiation source is typically used, 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 may be readily applicable to maskless lithography utilizing a programmable patterning device, such as a programmable mirror array of the type mentioned above.

[0041] Combinations and / or variations on the above-described modes of use, or entirely different modes of use, may also be employed.

[0042] The lithographic apparatus LA in this example is of a so-called dual-stage type having two substrate tables WTa and WTb and two stations (an exposure stage and a measurement stage) 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 the other substrate table at the measurement station MEA, so that various preparatory steps can be performed. The preparatory steps may include mapping the surface of the substrate using a level sensor LS and measuring the position of the alignment mark on the substrate using an alignment sensor AS. This makes it possible to significantly increase the yield of the apparatus. If the position sensor IF cannot measure the position of the substrate table when the substrate table is at the measurement station as well as the exposure station, a second position sensor may be provided to enable the position of the substrate table to be tracked at the two stations. The present invention is applicable to apparatuses having only one substrate table or having more than two substrate tables.

[0043] The device also includes a lithographic equipment control unit LACU, which controls all movements and measurements of the various actuators and sensors described. The LACU also includes signal processing and data processing capabilities to implement the desired calculations associated with the operation of the device. In practice, the control unit LACU will be implemented as a system of many subunits, each of which processes real-time data acquisition, processing, and control of subsystems or components within the device. For example, a processing subsystem can be dedicated to the servo control of a substrate positioner PW. A separate unit can even process coarse and fine actuators or different axes. Another unit can be dedicated to the readout of a position sensor IF. The overall control of the device can be controlled by a central processing unit that communicates with these subsystem processing units, operators, and other devices involved in the lithographic manufacturing process.

[0044] Figure 1 (b) shows the Figure 1(a) are the known steps for exposing a target portion (e.g. a die) on a substrate W in a dual stage apparatus of (a). On the left hand side within the dotted box are the steps performed at the measurement station MEA, while the right hand side shows the steps performed at the exposure station EXP. Sometimes, one of the substrate tables WTa, WTb will be at the exposure station and the other at the measurement station, as described above. For the purposes 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 apparatus by a mechanism not shown. The two substrates are processed in parallel to increase the throughput of the lithographic apparatus. Reference is first made to the newly loaded substrate W', which may be a previously unprocessed substrate, prepared for the first exposure in the apparatus with new photoresist. However, typically the lithographic process described will be only one step in a series of exposure and processing steps, so that the substrate W' has passed through this apparatus and / or other lithographic apparatus several times, and may also have undergone subsequent processes.

[0045] As just mentioned, previous and / or subsequent processes can be performed in other lithography tools, and even in different types of lithography tools. For example, some layers in the device fabrication process that have very high requirements for parameters such as resolution and overlay can be performed in more advanced lithography tools than other layers with lower requirements. Thus, some layers can be exposed in an immersion lithography tool, while others are exposed in a "dry" tool. Some layers can be exposed in a tool operating at a DUV wavelength, while others are exposed using EUV wavelength radiation.

[0046] At 202, alignment measurements using substrate marks P1 and an image sensor (not shown) are used to measure and record the alignment of the substrate relative to substrate tables WTa / WTb. Additionally, several alignment marks across substrate W' are measured to create 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 wafer height to XY position is also measured for accurate focusing of the exposed pattern.

[0047] When loading substrate W', receive recipe data 206, described recipe data 206 defines the exposure to be performed, and also defines the properties of wafer, and the pattern previously formed and to be formed on wafer. Add the measurement of wafer position, wafer grid and height map carried out at 202, 204 to these recipe data, so that a complete set of recipe and measurement data 208 can be delivered to exposure stage. For example, the measurement of alignment data comprises the X and Y position of alignment target formed with fixed or nominal fixed relationship with product pattern (it is the product of photolithography process). These alignment data that are acquired just before exposure are combined and interpolated to provide the parameters of alignment model. These parameters and alignment model will be used to correct the position of the pattern applied in the current photolithography step during exposure operation. Conventional alignment model can comprise four, five or six parameters, and these parameters together define the translation, rotation and scaling of ideal grid in different dimensions. As described further below, advanced models that use more parameters are also known.

[0048] At 210, wafers W' and W are exchanged so that the measured substrate W' becomes the substrate W entering the exposure station EXP. This exchange is performed by interchanging 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 stages have been exchanged, determining the relative position between the projection system PS and substrate table WTb (formerly WTa) is essential for utilizing the measurement information 202, 204 of substrate W (formerly W') in controlling the exposure step. At step 212, reticle alignment is performed using mask alignment marks M1, M2. In steps 214, 216, 218, scanning motions and radiation pulses are applied at successive target positions across substrate W in order to complete the exposure of a plurality of patterns. By using the alignment data and height maps obtained at the measurement station when performing the exposure step, these patterns can be accurately aligned with respect to the desired positions (and in particular, with respect to features previously laid down on the same substrate). Based on the exposed pattern, the exposed substrate (now labeled W") is unloaded from the apparatus at step 220 to undergo etching or other processes.

[0049] The concepts disclosed herein will be primarily described in the context of overlay measurement and / or alignment measurement. However, this should not be considered limited to this context; the concepts herein are applicable to any measurement of a proper subset of multiple potential measurement points using multiple sensor setups. In any such context, optimization of the sampling scheme used to determine the proper subset can be expected to provide benefits. Thus, while an alignment model will now be described for illustrative purposes, the concepts disclosed herein can also be used, for example, in conjunction with an exposure dose correction model and / or a focus correction model. These models are well known to those skilled in the art and will not be described in any detail.

[0050] Advanced Alignment Model

[0051] The current standard alignment model may have six parameters (actually three in each direction X and Y), and in addition, more advanced alignment models exist. On the other hand, for more demanding processes, more refined corrections to the wafer grid are required to achieve the desired overlay performance. Advanced alignment models have been developed for this purpose. In this article, "advanced" alignment models refer to all types of models with higher complexity than the standard six parameters. While standard models may use less than ten parameters, advanced alignment models typically use more than 15 parameters or more than 30 parameters. Examples of advanced models are high-order wafer alignment (HOWA) models, zone alignment (ZA) and radial basis function (RBF) alignment models. HOWA is a public technology based on third-order and higher-order polynomial functions. Zone alignment is described, for example, in "Overlay improvement by zone alignment strategy" by Huang et al., Proc. SPIE 6922, 69221G (2008), which is incorporated herein by reference. Different versions and extensions of these advanced models can be designed. Advanced models generate complex descriptions of the wafer grid that are corrected during exposure to the target layer. RBF and the latest version of HOWA provide a particularly complex description based on dozens of parameters. This means that a large number of measurements are required to obtain a wafer mesh with sufficient detail.

[0052] Even in embodiments with multiple substrate tables WTa / WTb, the time taken to obtain sufficient measurements for advanced alignment on each wafer will ultimately impact yield. Reducing the time for each measurement will result in a reduction in the accuracy of each measurement, and so it is difficult to avoid impacting yield. In addition, once corrections have been applied in one layer using an advanced alignment model, the same level of detail should be applied in subsequent layers, otherwise the corrections in the first layer will become a source of error in the overlap of subsequent layers. Therefore, the manufacturer is faced with the difficult choice of whether to accept further measurement overhead by using the advanced model in subsequent layers, or to suffer the consequences of overlap by reverting to a simpler alignment model and measuring fewer marks in subsequent layers.

[0053] There is a significant degree of similarity in the problems faced in alignment and model estimation / correction calculations. The commonality is that a certain system pattern is estimated using a limited set of measurements taken at certain locations. The choice of locations to include in the estimation process determines the reliability of the resulting model. This is because not all measurement locations necessarily provide equivalent information to the estimation process.

[0054] Some HVM (high-volume manufacturing) metrology schemes almost always densely sample a few fields on the substrate, while covering the rest of the substrate sparsely (e.g., one measurement point per field). This is already suboptimal for currently used models and starts to become more problematic with higher-order models. This applies to both metrology performed for alignment (e.g., aligning the substrate relative to the projection optics using an alignment sensor before exposure) and post-exposure metrology for process monitoring.

[0055] In such Figure 1 In the lithographic apparatus shown in (a), alignment is performed on each substrate before exposure. Multiple measurement points (e.g., alignment marks) are used to capture the substrate's shape and average out placement noise (e.g., originating from the lithographic apparatus baseline). Additionally, to monitor the process and determine its correction as part of a process control arrangement, a post-exposure metrology tool (e.g., a scatterometer-based tool or an electron beam tool) can be used to measure parameters of interest (e.g., overlay, focus, critical dimension, or any other metric) from multiple measurement points (e.g., measurement targets). In each case, several measurement targets can be placed in each field on the wafer. To limit the cost of metrology, only a subset of these possible measurement locations is actually measured, and this subset is used as input to a control algorithm that determines the appropriate stage position and / or other exposure parameters (e.g., focus, dose, etc.) based on these measurements and calibrates the lithographic exposure system or other processing equipment (on a field, wafer, or batch basis). Current algorithms for aligning focus, dose, or other exposure parameters determine which measurement locations to sample based on uniform coverage of the substrate (uniformity being defined as equal distance between adjacent measurement points).

[0056] To improve this, WO2015 / 110191 (which is incorporated herein by reference) describes a method for determining a measurement scheme or sampling scheme (e.g., describing which measurement positions out of all available measurement positions will be measured), which may be referred to as sampling scheme optimization (SSO). This method comprises evaluating candidate measurement positions; for example, to determine how much the informativeness of the sampling scheme will be improved if the measurement position is selected. This may comprise evaluating all candidate measurement positions and selecting the candidate measurement position that is determined to add the most information to the measurement scheme. More specifically, each selected measurement point may have an associated exclusion zone around it, and the candidate points may only include potential measurement positions that are outside these exclusion zones. This ensures that the entire sampling scheme is sufficiently distributed over the substrate.

[0057] Alternatively, a sampling scheme can be designed that measures the selected objectives in a sequential manner (best thread) optimized for yield. Hybrids of these approaches are also possible; for example, a sampling scheme that maximizes informativeness while also taking yield / thread into account (e.g., by weighting these two considerations in the evaluation or other methods).

[0058] For each measurement, the sensor needs to be positioned relative to the target. Therefore, the wafer needs to be moved relative to the sensor. This can be done by moving the sensor in x and y, or by moving the wafer in x and y, or a combination of these.

[0059] Whereas the above-described method disclosed in WO2015 / 110191 is designed with a single-sensor metrology device, i.e., a metrology device operable to measure a single measurement point at a time, a parallel-sensor metrology device has been envisioned and described hereafter, comprising a plurality (e.g., between 2 and 10, or alternatively equal to 10 or more, such as between 2 and 25) of sensors, to enable parallel / simultaneous measurement of multiple measurement points (i.e., one measurement point per sensor). Such a parallel-sensor metrology device is envisioned for alignment and post-exposure metrology, and the following disclosure is equally applicable to any type of device, or any other metrology device for which a sampled subset of available measurement points is selected.

[0060] Figure 2 (a) Depicts an exemplary arrangement of available targets on a wafer (in this particular example, the number of targets is 1627). The same arrangement of targets can be used for each field, since each field is imaged by the same reticle. From a control perspective, measuring all targets is not cost-effective and is not necessary. Instead, an "optimal" subset can be selected (e.g. using SSO) that provides the most values ​​for the base model used to apply scanner corrections to minimize overlap (on the next wafer), for base models for other exposure parameters, or for alignment models. Note that due to the repetition at a fixed pitch between fields, the target layout can be very structured (e.g., as Figure 2 (as shown in (a)).

[0061] exist Figure 2 In (b), an exemplary sampling scheme output from such an SSO (e.g. as described in WO2015 / 110191) is shown. From the available 1627 targets, only a proper subset of 220 targets is selected for measurement during the metrology step. Based on these 220 measurements, the process optimization or alignment model is updated. The number of targets selected is a trade-off between metrology cost and process improvement (e.g., overlap reduction). Figure 2 (a) Compared with Figure 2The layout shown in (b) is no longer structured; the SSO process effectively randomizes the targets being measured. In a single-sensor metrology system, the number of measurement positions equals the number of targets being measured. This means that for this single-sensor metrology tool, 220 wafer stage positions are required to measure all selected points on the wafer for this sampling scheme.

[0062] For a parallel sensor array (such as comprising, for example, six parallel pre-adjusted sensors), ideally, for each acquisition configuration (e.g., each sensor grid acquisition position, each sensor movement degree, or more generally, each different position of the sensor array relative to the substrate (whether by moving the sensor grid, moving the wafer, or both)), measurements should be performed in parallel at six previously unmeasured positions. In a specific example, the six sensors may be arranged in a 2x3 grid (of course, the sensor array may include any number of sensors in any arrangement). The sensors may be pre-adjusted such that the xy positions of the sensors are adjusted to a fixed grid aligned with the field pitch or a multiple thereof. Thus, when using a six sensor array, only 220 / 6=37 stage positions should be required to measure the 220 measurement points (resulting in an efficiency of 220 / (37×6)=99.1%). However, due to the "randomized" nature of the grid, the number of stage positions required to measure all measurement points of an SSO optimized sampling scheme using such parallel sensors is typically significantly greater. For example, it has been shown that for a particular SSO-optimized sampling scheme, the pre-adjusted 2x3 sensor array described above requires a total of 188 stage positions to measure all 220 points. Only at the beginning of the measurement process might six unmeasured targets be measured in parallel; soon, the number of previously unmeasured targets measured (for the optimized sampling scheme) at each stage position drops to only one or two. For this case, the resulting efficiency is 220 / (188×6)=20%.

[0063] The invention provides for incorporating (design) knowledge of parallel metrology into the SSO algorithm with the goal of optimally utilizing the potential of parallel sensors in the metrology tool. Note that the goal of the sampling scheme optimization remains the same: to collect as much (overlapping) model-relevant data as possible with minimal metrology cost. However, in order to efficiently utilize all parallel sensors, the sampling scheme should be such that the convolution of the sensor array grid is approximated with a small number of sampling grids. In other words, the sampling scheme (and the threads) are optimized such that, after each move, all sensors are at the position of a measurement target (more preferably, a target that has not been measured before), such that, for example, the number of unmeasured targets that can be measured after each move is maximized and / or the number of targets that are measured multiple times is minimized. As a result of the proposed "parallelism-aware SSO", the randomization of the target scheme will be reduced. Throughout the text, the term "parallel metrology" may include metrology steps that measure only one measurement location (e.g., at the edge of the wafer).

[0064] Figure 3 The present invention is a flowchart describing an algorithm for selecting measurement locations for an estimation process given a certain model. Simultaneously, an attempt is made to position the selected measurement locations uniformly so that the two objectives are balanced. The method described herein can involve multiple sensor measurement devices, where the sensors are maintained in a fixed relationship to one another (i.e., in a fixed grid).

[0065] The algorithm takes as input a list 305 of potential metrology locations or metrology target locations. The list 305 of potential metrology locations can originate from various sources. For example, the list 305 can originate from existing measurement data, in which all potential metrology locations have been measured. Alternatively, the list 305 can originate from a list of possible locations on a reticle, including locations where metrology targets can be inserted based on the reticle design. Thus, the list 305 of potential metrology locations can include locations where metrology locations already exist and / or locations where no metrology locations exist, but where there is a possibility of locating a metrology location there.

[0066] The first step of the flowchart may include initializing a sampling plan 300. This step includes selecting one or other (small) number of initially selected acquisition configurations (e.g., stage positions relative to the substrate) for the measurement plan. The initially selected sensor grid acquisition positions may be selected based on a wafer alignment model, based on one or more criteria. The initially selected acquisition configurations may be selected to maximize the number of valid metrology positions or targets measured per grid position, and without duplication (i.e., in the case where there is more than one initially selected acquisition configuration, no selected acquisition configuration includes the same metrology position). In the case where multiple initial grid acquisition positions are selected, they may include positions such that the initially selected metrology positions are well distributed across the substrate. For each initially selected acquisition configuration, a corresponding metrology position is added to the sampling plan.

[0067] Optionally, the initialization step 300 may further include defining an exclusion zone around each selected measurement location, corresponding to one or more initially selected acquisition configurations. The exclusion zone defines a region around each selected measurement point such that other measurement points within the exclusion zone are not considered for inclusion in the sampling scheme; i.e., these measurement points are removed from the candidate measurement points (at least for one iteration, after which they may be included again). All measurement points outside the exclusion zone are candidate measurement points in future iterations (i.e., "selectable"). For example, the exclusion zone may be circular and centered at each selected measurement location, i.e., all measurement locations within a certain distance of the selected measurement location may be within the exclusion zone. The size of the exclusion zone may be variable, so that, for example, if there are not enough candidate points, the exclusion zone may be made smaller to increase their number. The size of the exclusion zone may also be a function of position on the substrate, for example, in order to bias target selection towards or away from a particular region (e.g., having a smaller exclusion zone at the edge of the substrate may encourage selection of edge locations, where greater distortion may be expected). This may be achieved by applying a position-dependent scaling factor to the exclusion zone.

[0068] The evaluation step 310 may include evaluating all candidate acquisition configurations. The candidate acquisition configurations may include all acquisition configurations such that all (or more than a certain number) of corresponding measurement locations (i.e., measurement locations measured by the sensor grid when the sensor grid acquires a location) include candidate measurement locations (i.e., measurement locations that have not been selected and are not within an exclusion zone).

[0069] The evaluation step can be based on any suitable evaluation metric. One such evaluation metric can include an efficiency metric, for example based on the efficiency with which the sensor is used for each candidate acquisition configuration. Efficient use of the sensor can be measurements of measurement points that have not yet been measured. For example, the selected candidate acquisition configuration can be the acquisition configuration that maximizes the number of unmeasured measurement locations, and / or any acquisition configuration that is below an efficiency threshold (such as, less than 100% or 80% of the sensors are used to measure unmeasured points) is no longer considered as a candidate acquisition configuration. Optionally, the threshold can be variable, for example to increase the number of available candidate acquisition configurations. Other efficiency metrics include distribution metrics (for example, distribution metrics that aim to maximize the distribution of measurement locations), or informative metrics that aim to add the most information (for example, candidate acquisition configurations that add the largest total amount of information by the corresponding measurement locations). It can be noted that a candidate acquisition configuration that adds five new measurement locations can add more information (according to the informative metric) than another candidate acquisition configuration that adds six new measurement locations.

[0070] Examples of distribution metrics may include distribution metrics that are assigned a specific density of measurement locations. For example, a wafer and / or field may be divided into a plurality of regions, wherein each region defines a specific number of measurement points. When a specific number of measurement points or target density for a region is reached, no more points may be selected within that region. The density may be globally uniform across the wafer, and / or uniform across the field for a stacked scheme (where all fields overlap). Alternatively, different distribution metrics (density of measurement locations) may be defined for different regions; for example, with a higher density in regions where more local variations are expected, such as the edges of the wafer. In another approach, the distribution metric may be based on the distribution of the distances between each measurement location and its nearest neighbor, as well as the distribution of open areas (e.g., the maximum radius of any circle that can be placed between the selected points). These parameters may describe the level of randomness or non-uniformity at the local level. Typically, it may be desirable to have limited randomness to avoid "gaps" in the sampling scheme.

[0071] A hierarchical approach can be taken, where candidate acquisition configurations are first evaluated at a first level according to a first evaluation metric and at a second level according to a second evaluation metric. For example, the evaluation may include evaluating the number of unmeasured metrology points that each candidate acquisition configuration would measure (an efficiency metric), followed by a distribution metric that describes how distributed the sampling scheme would be across the wafer when the metrology locations corresponding to each candidate acquisition configuration are included. The method may include ranking the candidate acquisition configurations first in terms of the number of corresponding unmeasured candidate metrology locations, and then in terms of maximizing the distribution metric to maximize the distribution or coverage of the selected measurement locations across the wafer (e.g., according to the distribution metric).

[0072] Alternatively or in combination (e.g., as a single metric or at any level of a hierarchy with one or more other metrics), the evaluation step 310 can include calculating how much the informativeness of the sampling scheme would be improved (i.e., according to an informativeness metric) if all corresponding measurement positions of each candidate acquisition configuration were added to the adopted scheme. The concept of quantifying informativeness is described in the aforementioned WO 2015 / 110191. In short, a criterion that can be used in the evaluation step 310 can be D-optimality, as described below.

[0073] In this context, informativeness can be coupled to the control scheme, the underlying model, and / or the expected statistical distribution. For example, if the expected value of the control error using scheme A is lower than the expected value of the control error using scheme B, then scheme A is more informative than scheme B. By way of a specific example related to control: if the control model only allows for tilting on the field, then a point at the center has less information than a point at the edge of the field, since a small measurement error will end up as a larger slope error for a point at the center. In another specific example related to variability: if more variability is expected at the center of the wafer, then increasing the sampling density at the center is better, since this will average out more of the noisy points (the center of the wafer is a known hotspot of focus due to the spin coating process of resist and anti-reflective agent (barc)).

[0074] At step 320 , a candidate acquisition configuration is selected based on the evaluation of all candidate acquisition configurations and the corresponding measurement positions added to the sampling scheme.

[0075] For example, the selected candidate acquisition configuration may be the candidate acquisition configuration that (as a first criterion) maximizes the number of unmeasured measurement locations, followed by the candidate acquisition configuration that (as a second criterion) is determined to maximize the distribution of measurement locations and / or add the most information (e.g., the candidate acquisition configuration that adds the largest total amount of information by the corresponding measurement locations).

[0076] At step 330, it can be determined whether the measurement scheme has enough selected (unique) measurement positions. If so, the algorithm ends 340. If the measurement scheme does not have selected (unique) measurement positions, then at step 350, an exclusion zone can be defined around each newly selected measurement position, for example in addition to the exclusion zone defined around each other selected measurement position. Alternatively or additionally, the method can be repeated for a certain number of iterations, which number of iterations corresponds to a certain number of acquisition configurations, wherein the number of measurement positions in the optimized sampling scheme is thus variable (for example as long as a minimum number is met). Alternatively or additionally, the method can be repeated for a certain number of iterations until the sampling scheme meets a threshold value of the informativeness metric and / or the distribution metric.

[0077] At step 360 , it may be determined whether a sufficient number of candidate measurement positions and / or candidate acquisition configurations remain for the algorithm to select, eg, while maintaining a suitable balance between informativeness and uniformity.

[0078] In an embodiment, if it is determined that there are too few candidate acquisition configurations, this can be addressed at step 370 by reducing the exclusion zone. In this case, the exclusion zone can be reduced for all of the selected measurement locations included in the measurement plan, or only for a subset of these selected measurement locations. The decision to reduce only some of the exclusion zones can be based on various criteria. Such criteria can include the size of the exclusion zone or its location. The exclusion zone can be reduced by a predetermined amount or percentage.

[0079] After step 370, the determination step 360 and (if necessary) the narrowing step 370 are iteratively repeated until there are a sufficient number of candidate acquisition configurations and / or candidate measurement positions to complete the measurement plan. When there are enough candidate acquisition configurations, the evaluation step 310 is repeated and another iteration of the algorithm (steps 310 to 370) begins.

[0080] Figure 4 Step 310 is shown. Figure 4 An array of measurement points MP of a portion of a substrate is shown. The black measurement points are already measured measurement points, for example corresponding in this example to a single acquisition configuration of a linear sensor array comprising five sensors capable of measuring five points in parallel. Around each of these measured measurement points, an exclusion zone EZ is defined (here circular, but other shapes are possible), and any measurement point (grey point) within the exclusion zone EZ is removed from the candidate points. It can then be decided to make any candidate acquisition configuration only include candidate measurement points, so that any acquisition configuration that includes one or more (e.g. grey) points within the exclusion zone is not considered. Thus, acquisition configuration AC1 is not a candidate acquisition configuration, while acquisition configuration AC2 is a candidate acquisition configuration. Of course, the rules for defining candidate acquisition configurations can be different by allowing those acquisition configurations that include one or more non-candidate measurement points. The number of non-candidate measurement points can be variable, for example the number of candidate acquisition configurations should be increased if the number is insufficient. This can be done instead of, or in combination with, reducing the exclusion zone.

[0081] Figure 5 A specific example of evaluation based on efficiency metrics is shown. Figure 5A row of measurement points MP adjacent to the wafer edge WE is shown. Three potential acquisition configurations AC1, AC2, and AC3 for the sensor array SA are shown (each corresponding to the same row as the measurement points MP, but each shifted by one column). An efficiency metric can minimize the number of sampling positions for which not all sensors can measure measurement points on the wafer. Specifically, sampling positions where all measurement points overlap and those that include more measurement points (and preferably, more unmeasured measurement points) should be avoided and therefore removed from candidate acquisition configurations. Therefore, acquisition configurations AC1 and AC2 are not considered candidate acquisition configurations because they overlap and include fewer points than acquisition configuration AC3.

[0082] The proposed method may also include optimizing the threading of the sensor array (ie, the order of the selected acquisition configurations) for throughput.

[0083] It can be shown that, in this example, the parallel-aware SSO measurement method results in a sampling scheme that includes measurement positions that can be measured using only 56 acquisition configurations or stage positions. Thus, the resulting efficiency is 319 / (56×6)=95%. Compared to the previous example, fewer stage positions measure more points (a factor of 319 / 56=5.7x).

[0084] In an alternative embodiment, the pitch of the parallel sensor array can be chosen to be equal to the field grid or a (e.g., small) multiple of the grid. For the case where the in-field position of the target is on a regular grid, it is proposed that the pitch of the sensor grid can also be chosen to include the in-field pitch. For example, the pitch P of the sensor array grid in a first direction (parallel to the substrate plane, e.g., the x-direction) is x，SA Can be defined as:

[0085] P x，SA =N1P x，field +N2P x，intrafield

[0086] Among them, P x，field is the field pitch in the first direction, and P x，intrafield is the intra-field pitch in the first direction. N1 can be any small integer, for example, less than 10; N2 can also be any small integer less than 10, for example, more specifically 0 or 1. Similarly, the pitch P of the sensor array grid in the second direction (perpendicular to the first direction and parallel to the substrate plane, for example, the y direction) is y，SA Can be defined as:

[0087] P y，sa =N3P y，field +N4P y，intra f ield Among them, P y,fieldis the field pitch in the second direction, and P y,intrafield is the intra-field pitch in the second direction. N3 can be any small integer, for example, less than 10; N4 can also be any small integer less than 10, for example, more specifically, 0 or 1.

[0088] In other embodiments, the proposed SSO algorithm can be used to determine the optimal value of one or more of the following: N1, N2, N3, N4; a small number will have the advantage of a more compact sensor array that is less prone to misalignment, while a large number will cover more cross-wafer information in a parallel configuration. This approach can include optimizing only one or two of N1 and N3 (e.g., N2 and N4 are zero) to optimize the sensor spacing to only the field pitch (in one or two directions), or further include optimizing within-field targets by optimizing N2 and / or N4.

[0089] In another alternative embodiment, it is proposed to optimize the target layout of the wafer to enable and maximize the value of the parallel sensing SSO concept. For example, subsets of targets can be grouped according to the pre-adjusted sensor array (for example, in 2×3 groups in the specific example described herein).

[0090] As mentioned above, the criterion that can be used in the evaluation step 310 can be D-optimality. In a D-optimal design, the determinant of the information matrix is ​​maximized (and therefore, the determinant of the variance-covariance matrix is ​​minimized). Assuming a linear model, i.e., a model whose parameters are linear, the following equation can be written:

[0091]

[0092] The measurements are denoted by m, the parameters by p, the residuals by ξ, and the so-called design matrix by C. This design matrix forms the core of the model and consists of basis functions evaluated at the chosen measurement locations where the corresponding measurements are made. Using, for example, a one-dimensional polynomial model of order x (from zero to four), the basis functions would simply be: 1, x, x 2 、x 3 and x 4 . Thus, if a measurement is available for position x=3, without taking normalization into account, the corresponding row in C will be: [1 39 27 81].

[0093] The modeling process can then proceed as follows:

[0094] 1. Measurement can be performed at the selected measurement point;

[0095] 2. Choose an appropriate model form (i.e., a set of basis functions) to obtain relevant information about the underlying data;

[0096] 3. Perform minimization, which may take the form of least squares modeling, to produce parameter values ​​that minimize the distance in some mathematical norm between the model and the measured data.

[0097] Keeping the same notation as above, the optimization problem to be solved in least squares estimation is as follows:

[0098]

[0099] It can be solved as follows:

[0100]

[0101] C T C is the information matrix, and its inverse matrix [C T C] -1 is the variance-covariance matrix. Both the information matrix and the variance-covariance matrix indicate how much information the measurement layout (i.e., the experiments) provides for the chosen model; that is, how well the layout will differentiate the parameters (note that the actual measurements are not used for this). Therefore, minimizing the determinant of the variance-covariance matrix or maximizing the determinant of the information matrix will produce the same result.

[0102] It is important to reiterate that while the above description has been made in terms of overlay and alignment, it is not limited thereto. The methods disclosed herein can be used for metrology of any type of feature that can be measured / modeled (e.g., critical dimension, focus, sidewall angle, etc.). The more expensive the metrology, the greater the added value of a smart sampling scheme with reduced dimensions.

[0103] Although Figure 3 The method of describes adding points until there are a sufficient number of measurement positions and / or acquisition configurations, but this is only one way to perform such a sampling scheme optimization. An alternative method can start with an initial oversampling scheme that includes more sampling positions than desired. In an evaluation step, candidate positions for removal from the scheme can be identified and the candidate positions that are evaluated as most redundant (and / or identified as redundant based on a threshold of the evaluation metric) can be removed to select the remaining candidate positions. Another alternative method can start with a desired number of sampling positions having a random or any other non-optimized distribution and then repeatedly reallocate one or more sampling positions to optimize the evaluation metric (e.g., to increase informativeness, distribution and / or efficiency).

[0104] Figure 66(a) and 6(b) show schematic plan and side view representations, respectively, of a metrology tool arrangement 600 comprising an array of detection optics that can perform metrology on multiple targets in parallel and that can implement the methods described herein. This arrangement is described in more detail in WO 2018 / 238363 (particularly with respect to Figures 9a, 9b, and 10 of that document), which is incorporated herein by reference.

[0105] Each of the detection optical systems may comprise a detection optical sensor 610 and at least one lens for capturing a portion of the illumination radiation scattered by the structure and transmitting the captured radiation towards the detection optical sensor 610. Thus, the detection optical system may form part of a metrology tool for determining a parameter of interest of a structure manufactured on a substrate, the metrology tool further comprising an illumination optical system for illuminating the structure with illumination radiation. Figure 6 Each array element 604 shown can include a detection sensor without an illumination optical system. For the purposes of the following description, each optical detection system will be referred to as an element of the array, or array element 604. Each array element 604 can include an optical detector sensor 610. The optical detector sensor has a sensor axis 606 that extends orthogonally between the detection optical sensor 610 and the plane of the substrate 602.

[0106] The substrate 602 includes a plurality of dies 608, such as Figure 6 (a). Each of the array elements 604 can be positioned relative to a separate die 608 and acquire metrology data from the die 608. Thus, each of the plurality of dies 608 can include a single element array 604. The array elements 604 can be located at a common horizontal position relative to each die 608 so that each sensor 610 can measure metrology marks that are common to each die and have corresponding positions on the die in parallel.

[0107] The array can include a tiled or tessellated arrangement of optical detection systems. Each optical detection system can be arranged in a footprint area having a predetermined shape, wherein the footprint areas are adjacent to each other to provide an array. Each footprint area can be identical and can be polygonal, for example, each footprint area can be triangular, square, or hexagonal. In one example, the array can be arranged in a tessellated arrangement with a hexagonal footprint area to provide a honeycomb array. Thus, the array elements can be arranged in a honeycomb array. The array of optical detection systems is shown as a two-dimensional array having m rows and n columns. The rows m can extend along a first direction (e.g., the x-direction of the substrate), and the columns can extend along a second direction (e.g., the y-direction). Either or both of the directions of the rows and columns can be tilted relative to the x- or y-direction. Typically, the number of rows and columns will each be greater than 2. However, there can be as many rows or columns as desired for a particular field arrangement or measurement footprint on the wafer. The array can also be of any desired shape and is not limited to a square or rectangular configuration. The number of array elements 604 can vary to suit different applications. For example, the size of the array can be up to 15 in the x-direction and up to 100 in the y-direction. In some instances, a single array element 604 can be provided for each of the respective die 608 so as to cover the entire wafer. In other applications, a discrete number of array elements 604 can be provided that is less than the number of die 608. Each member of the array element can be aligned with a different field of the substrate.

[0108] As indicated by arrows 612a, 612b, 612c, the array can be adjustable so that array elements 604 (or portions thereof) can be moved relative to each other or substrate 602. As shown, adjacent array elements 604 are separated by a first distance. The first distance between adjacent array elements can correspond to the pitch of a die or measurement target. The first distance can be the same for each adjacent pair of array elements 604. As indicated by arrow 612a, each array element 604 can be moved so that the spacing between adjacent array elements can be changed from the first distance to a second distance. Movement of the array elements 604 can be accomplished in the x and / or y directions.

[0109] The spacing may be a fixed pitch based on the pitch of the die 608 or measurement targets distributed across the substrate 602. Thus, the spacing of the array elements 604 may be standard and one of a plurality of predetermined discrete pitch settings corresponding to standard features (such as the pitch of the die). For example, the pitch may be 26 mm in the x-direction and 33 mm in the y-direction to correspond to conventional die sizes. Other pitches may include 26 mm and 16.5 mm. The metrology tool 600 may incorporate or have access to a list or library of one or more spacings that are commonly or frequently used. The predetermined spacing may form part of a manufacturing recipe or be included as part of a setup process for a particular process.

[0110] To obtain good measurement data, the sensor axis 606 is preferably aligned so that it is perpendicular to the plane of the substrate 602 surface. The substrate surface of the processed wafer 602 can show local tilt variations on the order of hundreds of microradians. To handle these local tilt variations, the array elements can be tiltable 612b so as to change the angle between the sensor axis 606 and the substrate 602 surface. Tilt can be limited to two orthogonal directions (e.g., the x and y directions), where tilting the sensor in the x direction will cause the sensor axis to move along the x direction, and tilting the sensor in the y direction will cause the sensor axis to move along the y direction. The combination of two tilt directions can allow for adaptation to any substrate tilt. Since the surface level variations can be local, each array element can be moved independently of the other array elements 604. Generally, when tilting about the x-axis, movement in the y direction will occur (and vice versa).

[0111] To determine the tilt of array element 604, a tilt sensor may be incorporated into each array element. The tilt sensor may be an optical sensor as known in the art and may advantageously be incorporated into optical sensor 610. Thus, each array element 604 may include a combined overlay and tilt sensor.

[0112] When using a metrology tool to obtain overlay measurement data, it is advantageous to be able to correct for measurement errors caused by sensor asymmetry. Such errors can be referred to as tool guide shift (TIS). In order to address TIS (or other similar problems), the array elements 604 can each be rotatable about the sensing axis 606. Thus, each array element 604 can be rotated from a first rotational position to a second rotational position, wherein the first position and the second position are antiparallel to the extent that they need to account for tool guide shift. Thus, the sensor can be rotated by approximately 180 degrees. This rotation will typically be about the insertion axis 606, however, when processing the acquired measurement data, the position difference between the first rotational position and the second rotational position relative to the surface of the substrate can be taken into account. That is, the shift in the xy position of the sensing axis 606 due to rotation can be accommodated by modifying the overlay data with alignment data obtained from the corresponding first rotational position and the second rotational position.

[0113] The movement of the array elements 604 can be achieved using suitable actuators known in the art. For example, the actuators can be piezoelectric motors. Thus, each array element 604 can include one or more actuators for each of the described ranges of motion.

[0114] The measurement tool can incorporate a position controller 614 that is configured to control the movement of the array elements 604. Thus, the position controller 614 will communicate with each actuator to provide the necessary control signals. The position controller 614 can also be arranged to receive position data from the actuators, the array elements 604, or some other source that can provide an indication of the position of the array elements relative to the substrate 602. The position controller 614 can be distributed among the element array or be provided as a central unit that is arranged to control all array elements individually. The central unit can be located in the measurement tool 600 or remotely located from the measurement tool 600. The position controller 614 can form part of a larger control system. In use, the position controller 614 can receive or determine the desired spacing between adjacent array elements before moving each array element 604 to the correct position. Once the array elements 604 have been positioned, position verification and any adjustments are performed, measurement data can be obtained as described above.

[0115] Array elements 604 may be individually controllable. Array elements 604 may have one or more of the aforementioned ranges of motion. Thus, there may be instances where array elements 604 are arranged to tilt in the xy direction but not move. This is useful in situations where the spacing of the array elements can be fixed in the xy direction.

[0116] Array elements 604 may be similar or identical. For example, all array elements may be configured to operate within the same operating wavelength range. Even if array elements 604 are similar or identical, this does not preclude each array element from receiving illumination radiation of a different wavelength within the array element's full operating wavelength range. For example, different array elements may receive light of different wavelengths within the operating wavelength range of 200 nm to 2000 nm. However, all array elements 604 need not be similar or identical to one another. There may be at least one array element 604 that is different from the other array elements 604. Array elements 604 may also be subdivided into groups of array elements 604, with the array elements within each group of array elements 604 being similar or identical, but they may differ between groups of array elements 604. For example, the first row or column of the array may include array elements of a first type, the second row or column of the array may include array elements of a second type, and so on. Note that an array element comprises a combination of an illumination optical system and a detection optical system. If the array elements are different, their respective illumination optical systems and / or their respective detection optical systems may differ from one another.

[0117] The array of array elements 604 can be arranged at fixed positions in a metrology tool, while the metrology tool is configured to move the substrate 602 using, for example, a movable substrate stage. The array of array elements 604 can also be movable in the metrology tool. For example, the array of array elements 604 can be movable so that a group of array elements 604 is located at a certain position, such as a center position of the substrate stage and the substrate 602. Thus, the group of array elements 604 located at the center can be used to perform measurements on the entire substrate 602 based on the movement of the substrate 602 relative to the array of array elements 604.

[0118] Implementation Method

[0119] The steps of the above method are Figure 1 The lithographic apparatus control unit LACU shown in (a) may be automated. The unit LACU may include Figure 7 The computer assembly shown. The computer assembly can be a dedicated computer in the form of a control unit in an embodiment of an assembly according to the present invention, or alternatively, a central computer that controls a lithographic projection apparatus. The computer assembly can be arranged to load a computer program product comprising computer executable code. This can enable the computer assembly to control the lithographic apparatus and the above-described use of embodiments of the leveling and alignment sensors AS and LS when the computer program product is downloaded.

[0120] The memory 729 connected to the processor 727 may include multiple memory components, such as a hard disk 761, a read-only memory (ROM) 762, an electrically erasable programmable read-only memory (EEPROM) 763, and / or a random access memory (RAM) 764. Not all of the above memory components need to be present. In addition, the above memory components do not need to be physically close to the processor 727 or close to each other. They can be located in a remote location.

[0121] The processor 727 may also be connected to some kind of user interface, such as a keyboard 765 or a mouse 766. A touch screen, trackball, voice converter, or other interface known to those skilled in the art may also be used.

[0122] The processor 727 may be connected to a reading unit 767, which is arranged to read data (e.g., in the form of computer executable code) from a data carrier such as a floppy disk 768 or a CDROM 769, and in some cases store the data on the data carrier. DVD data carriers or other data carriers known to those skilled in the art may also be used.

[0123] The processor 727 may also be connected to a printer 770 to print out output data on paper, and to a display 771, such as a monitor or an LCD (Liquid Crystal Display) or any other type of display known to those skilled in the art.

[0124] The processor 727 may be connected to a communication network 772, such as a public switched telephone network (PSTN), a local area network (LAN), a wide area network (WAN), etc., by means of a transmitter / receiver 773 responsible for input / output (I / O). The processor 727 may be arranged to communicate with other communication systems via the communication network 772. In an embodiment of the present invention, an external computer (not shown) (e.g., an operator's personal computer) may be connected to the processor 727 via the communication network 772.

[0125] The processor 727 can be implemented as a standalone system or multiple processing units operating in parallel, wherein 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 multiple sub-processing units. Some processing units of the processor 727 can even be located away from other processing units and connected via the communication network 772. The connection between modules can be carried out by wire or wireless.

[0126] The computer system may be any signal processing system having analog and / or digital and / or software technology arranged to perform the functions discussed herein.

[0127] Other embodiments are disclosed in the following list of numbered items.

[0128] 1. A method for determining a sampling scheme, the sampling scheme describing a proper subset of measurement locations among a set of potential measurement locations on a substrate; the method comprising:

[0129] obtaining a parallel sensor description describing an arrangement of a plurality of measurement sensors capable of performing parallel measurements;

[0130] identifying a plurality of candidate acquisition configurations based on the parallel sensor description and the potential metrology locations, wherein each candidate acquisition configuration describes a particular location of the sensor description relative to the substrate and, thus, describes a respective one or more metrology locations of the potential metrology locations;

[0131] evaluating at least some of the candidate acquisition configurations with respect to an evaluation metric;

[0132] selecting a candidate acquisition configuration based on the evaluation; and

[0133] The sampling scheme is defined as a scheme comprising a respective measurement position for each selected acquisition configuration.

[0134] 2. The method of clause 1, wherein the evaluation metrics include one or more of:

[0135] an efficiency metric that quantifies an efficiency of a candidate acquisition configuration in terms of using the plurality of measurement sensors;

[0136] an informativeness metric that quantifies the amount of information added to the sampling scheme by corresponding measurement positions of a candidate acquisition configuration; and

[0137] A distribution metric quantifies the coverage of the sampling scheme over the substrate and / or an area or field of the substrate.

[0138] 3. The method of clause 2, wherein the selecting step comprises selecting:

[0139] the most efficient candidate acquisition configuration with respect to the efficiency metric;

[0140] the candidate acquisition configuration whose corresponding measurement position adds the most information to the sampling scheme with respect to the informativeness metric; and / or

[0141] A candidate acquisition configuration whose corresponding measurement positions maximize the coverage of the sampling scheme on the substrate with respect to the distribution metric.

[0142] 4. A method according to clause 2 or 3, wherein the evaluating step comprises evaluating according to two or more of the efficiency metric, the informativeness metric and the distribution metric in a hierarchy.

[0143] 5. A method according to any of clauses 2 to 4, wherein the efficiency metric maximizes the number of unmeasured potential measurement positions corresponding to each candidate acquisition configuration evaluated.

[0144] 6. A method according to any of clauses 2 to 5, wherein the efficiency metric excludes from the candidate acquisition configurations those acquisition configurations for which all corresponding measurement positions overlap with an acquisition configuration comprising more measurement positions.

[0145] 7. A method according to any one of clauses 2 to 6, wherein the informativeness measure is D-optimality.

[0146] 8. A method according to item 7, wherein the sampling scheme involves a modeling scheme, and the method further includes maximizing the determinant of the design matrix describing the modeling scheme with the measurement position corresponding to the candidate acquisition configuration, or minimizing the determinant of the variance-covariance matrix corresponding to the design matrix for each of the measurement positions corresponding to the candidate acquisition configuration.

[0147] 9. A method according to any one of the preceding clauses, wherein the method comprises:

[0148] Repeating the iteration of the evaluation step for the candidate acquisition configurations and, based on the evaluation, adding corresponding measurement positions to the sampling plan or removing corresponding measurement positions from the sampling plan until one or more of the following conditions are met:

[0149] The sampling scheme includes a threshold number of measurement locations;

[0150] The sampling scheme involves a threshold number of acquisition configurations;

[0151] A threshold value of the evaluation metric is satisfied by the sampling scheme.

[0152] 10. A method according to any preceding clause, comprising:

[0153] determining an initial sampling plan comprising a desired number of measurement locations and / or an acquisition configuration having a non-optimized distribution; and

[0154] Based on the evaluation, one or more acquisition configurations are repeatedly redistributed to optimize the sampling scheme with respect to the evaluation metric.

[0155] 11. A method according to any of the preceding clauses, wherein the step of identifying a plurality of candidate acquisition configurations comprises an initialization step of determining a plurality of candidate measurement positions from the potential measurement positions; wherein each of the candidate acquisition configurations is determined to be those candidate acquisition configurations having a threshold minimum number of corresponding candidate measurement positions.

[0156] 12. A method according to any of the preceding clauses, wherein exclusion zones are defined around each measurement position included in the sampling plan, and wherein the candidate measurement positions only comprise potential measurement positions that are located outside these exclusion zones.

[0157] 13. A method according to clause 12, wherein the candidate measurement positions include all the potential measurement positions that are not within an exclusion area.

[0158] 14. A method according to clause 12 or 13, comprising:

[0159] determining that there are sufficient candidate measurement locations for a next iteration of the method; and

[0160] In the event that there are insufficient candidate measurement positions, the areas of some or all of the exclusion zones are reduced.

[0161] 15. A method according to any of clauses 12 to 14, wherein each exclusion zone is substantially circular and is centred on its respective selected measurement location.

[0162] 16. A method according to any of clauses 12 to 15, wherein the area of ​​each exclusion zone varies depending on the position of the corresponding selected metrology location on the substrate.

[0163] 17. The method of clause 16, wherein the area of ​​each exclusion zone tends to increase as its corresponding selected metrology position is closer to the center of the substrate.

[0164] 18. The method of any preceding clause, comprising optimizing the arrangement of the metrology locations on the substrate according to the sensor description.

[0165] 19. A method according to clause 18, wherein the measurement locations are arranged in groups corresponding to the sensor descriptions.

[0166] 20. A method according to any preceding clause, comprising optimizing the arrangement of a plurality of metrology sensors according to at least one substrate grid associated with the substrate.

[0167] 21. The method of clause 20, wherein the at least one substrate grid comprises one or both of an inter-field grid and an intra-field grid.

[0168] 22. The method of clause 21, wherein the optimizing comprises determining the sensor pitch in at least one direction based on one or a sum of integer multiples of a pitch of the inter-field grid and integer multiples of a pitch of the intra-field grid.

[0169] 23. The method of clause 22, further comprising optimizing the integer multiple of one or both of: a pitch of the inter-field grid and a pitch of the intra-field grid.

[0170] 24. A method according to any preceding clause, comprising performing an initialisation step, wherein an initialisation subset of said potential measurement positions is preselected for inclusion in said sampling scheme, said initialisation subset corresponding to one or more acquisition configurations.

[0171] 25. A method according to any preceding clause, comprising optimizing a thread describing an order of consecutive acquisition configurations for measuring measurement positions described by the sampling scheme.

[0172] 26. The method of any preceding clause, comprising the step of performing a metrology operation on the substrate using a metrology tool with the arrangement of a plurality of metrology sensors described by the sensor description according to the sampling scheme.

[0173] 27. The method of clause 26, wherein the metrology operation comprises an alignment operation or a post-exposure monitoring operation for monitoring product functionality, overlay, any product dimension, focus and / or dose monitoring operations, or any combination thereof.

[0174] 28. A computer program comprising computer-readable instructions which, when executed on a suitable processor, cause the processor to perform the method of any one of clauses 1 to 27.

[0175] 29. A computer program product comprising a computer program according to clause 28.

[0176] 30. A measuring device comprising:

[0177] a sensor arrangement comprising an arrangement of a plurality of measurement sensors capable of performing parallel measurements as described in the sensor description;

[0178] processor; and

[0179] Storage means comprising a computer program according to clause 28.

[0180] 31. The metrology device of clause 30, wherein the sensor arrangement is optimized to maximize one or more of an efficiency metric, an informativeness metric, or a distribution metric for a given number of sampling locations.

[0181] 32. The metrology apparatus of clause 30 or 31 , wherein the metrology sensors are spaced apart at integer multiples of a field grid.

[0182] 33. A metrology device according to clause 30, 31 or 32, wherein the number of metrology sensors is less than 10.

[0183] 34. A lithography cell comprising a lithographic apparatus operable to expose a pattern on a substrate; and

[0184] Measuring apparatus according to any of clauses 30 to 33.

[0185] Although specific reference may be made herein to the use of lithographic equipment in IC manufacturing, it should be understood that the lithographic equipment described herein may have other applications, such as manufacturing integrated optical systems, guidance and detection patterns for magnetic domain memories, flat panel displays, liquid crystal displays (LCDs), thin film heads, etc. The skilled person will understand that in the context of these alternative applications, any use of the term "wafer" or "field" / "die" herein may be considered synonymous with the more general term "substrate" or "target portion", respectively. The substrates referred to herein may be processed before or after exposure 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 a detection tool. Where applicable, the disclosure herein may be applied to these and other substrate processing tools. In addition, a substrate may be processed more than once, for example to form a multi-layer IC, so that the term substrate as used herein may also refer to a substrate that already contains multiple processed layers.

[0186] Although specific reference may have been made above to the use of embodiments of the present invention in the context of optical lithography, it should be understood that the present invention is not limited to optical lithography and, where the context permits, may be used in other applications such as imprint lithography. In imprint lithography, the topography in a patterning device defines the pattern formed on a substrate. The topography of the patterning device can be imprinted into a resist layer provided to the substrate, and the resist on the resist layer is cured by applying electromagnetic radiation, heat, pressure, or a combination thereof. After the resist is cured, the patterning device is removed from the resist, leaving a pattern therein.

[0187] As used herein, the terms "radiation" and "beam" encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having a wavelength of at or about 365 nm, 248 nm, 193 nm, 157 nm, or 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having a wavelength in the range of 5 nm-20 nm); and particle beams (such as ion beams or electron beams).

[0188] The term "lens" may refer, where the context permits, to any one or combination of various types of optical components, including refractive, reflective, magnetic, electromagnetic, and electrostatic optical components.

[0189] Although specific embodiments of the present invention have been described above, it should be understood that the present invention may be implemented in forms other than those described. For example, the present invention may take the form of a computer program comprising one or more sequences of machine-readable instructions that describe the methods disclosed above, or a data storage medium (e.g., a semiconductor memory, a magnetic disk, or an optical disk) having such a computer program stored thereon.

[0190] The above description is intended to be illustrative rather than restrictive. Therefore, those skilled in the art will appreciate that modifications may be made to the described invention without departing from the scope of the following claims. Furthermore, it should be understood that structural features or method steps shown or described herein in any embodiment may also be used in other embodiments.

Claims

1. A method for determining a sampling scheme, the sampling scheme describing a proper subset of measurement locations among a set of potential measurement locations on a substrate; the method comprising: obtaining a parallel sensor description describing an arrangement of a plurality of measurement sensors capable of performing parallel measurements; identifying a plurality of candidate acquisition configurations based on the parallel sensor description and the potential metrology locations, wherein each candidate acquisition configuration describes a particular location of the sensor description relative to the substrate and, thus, describes a corresponding one or more metrology locations of the potential metrology locations; evaluating at least some of the candidate acquisition configurations with respect to an evaluation metric; selecting a candidate acquisition configuration based on the evaluation; and The sampling scheme is defined as a scheme comprising a respective measurement position for each selected acquisition configuration.

2. The method according to claim 1, wherein The evaluation metrics include one or more of the following: an efficiency metric that quantifies an efficiency of a candidate acquisition configuration in terms of using the plurality of measurement sensors; an informativeness metric that quantifies the amount of information added to the sampling scheme by corresponding measurement positions of the candidate acquisition configuration; as well as A distribution metric quantifies the coverage of the sampling scheme over the substrate and / or an area or field of the substrate.

3. The method according to claim 2, wherein: The selecting step includes selecting: the most efficient candidate acquisition configuration with respect to the efficiency metric; With respect to the informativeness metric, the corresponding measurement position is the candidate acquisition configuration that adds the most information to the sampling scheme; and / or A candidate acquisition configuration whose corresponding measurement positions maximize the coverage of the sampling scheme on the substrate with respect to the distribution metric.

4. The method according to claim 2 or 3, wherein: The evaluating step includes evaluating according to two or more of the efficiency metric, the informativeness metric, and the distribution metric in a hierarchy.

5. The method according to claim 2 or 3, wherein The efficiency metric maximizes the number of unmeasured potential measurement locations corresponding to each candidate acquisition configuration being evaluated.

6. The method according to claim 2 or 3, wherein: The efficiency metric excludes from the candidate acquisition configurations those acquisition configurations for which all corresponding measurement positions overlap with an acquisition configuration comprising more measurement positions.

7. The method according to claim 2 or 3, wherein: The informativeness measure is D-optimality.

8. The method according to claim 7, wherein: The sampling scheme relates to a modeling scheme, and the method further includes maximizing, for each measurement position in the measurement positions corresponding to the candidate acquisition configuration, a determinant of a design matrix describing the modeling scheme with the measurement positions corresponding to the candidate acquisition configuration, or minimizing a determinant of a variance-covariance matrix corresponding to the design matrix.

9. The method according to claim 1 or 2, wherein: The method comprises: Repeating the iteration of the evaluation step for the candidate acquisition configurations and, based on the evaluation, adding corresponding measurement positions to the sampling plan or removing corresponding measurement positions from the sampling plan until one or more of the following conditions are met: The sampling scheme includes a threshold number of measurement locations; The sampling scheme involves a threshold number of acquisition configurations; The sampling scheme satisfies a threshold of the evaluation metric.

10. The method according to claim 1 or 2, comprising: determining an initial sampling plan comprising a desired number of measurement locations and / or an acquisition configuration having a non-optimized distribution; and Based on the evaluation, one or more acquisition configurations are repeatedly redistributed to optimize the sampling scheme with respect to the evaluation metric.

11. The method according to claim 1 or 2, wherein: The step of identifying a plurality of candidate acquisition configurations comprises an initialization step of determining a plurality of candidate measurement positions from the potential measurement positions; wherein each of the candidate acquisition configurations is determined to be those having a threshold minimum number of corresponding candidate measurement positions.

12. The method according to claim 11, wherein Exclusion zones are defined around each measurement position included in the sampling plan, and wherein the candidate measurement positions only include potential measurement positions that are outside these exclusion zones.

13. The method according to claim 12, wherein: The candidate measurement positions include all the potential measurement positions that are not within the exclusion area.

14. The method according to claim 12, comprising: determining that there are sufficient candidate measurement locations for a next iteration of the method; and In the event that there are insufficient candidate measurement positions, the areas of some or all of the exclusion zones are reduced.

15. The method according to claim 12, wherein: Each exclusion zone is substantially circular and is centered at its corresponding selected measurement location.

16. The method according to claim 12, wherein: The area of ​​each exclusion zone varies depending on the location of the corresponding selected metrology location on the substrate.

17. The method according to claim 16, wherein The area of ​​each exclusion zone tends to increase as its corresponding selected metrology position is closer to the center of the substrate.

18. The method according to claim 1 or 2, comprising optimizing the arrangement of the metrology locations on the substrate according to the sensor description.

19. The method according to claim 18, wherein The measurement positions are arranged in groups corresponding to the sensor descriptions.

20. The method of claim 1 or 2, comprising optimizing the arrangement of a plurality of metrology sensors according to at least one substrate grid associated with the substrate.

21. The method according to claim 20, wherein The at least one substrate grid includes one or both of an inter-field grid and an intra-field grid.

22. The method according to claim 21, wherein The optimization includes determining the sensor pitch in at least one direction according to one or a sum of the following parameters: an integer multiple of a pitch of the inter-field grid and an integer multiple of a pitch of the intra-field grid.

23. The method of claim 22, further comprising optimizing the integer multiple of one or both of a pitch of the inter-field grid and a pitch of the intra-field grid.

24. The method according to claim 1 or 2, comprising performing an initialization step, wherein: An initialization subset of the potential measurement locations is preselected for inclusion in the sampling scheme, the initialization subset corresponding to one or more acquisition configurations.

25. The method of claim 1 or 2, comprising optimizing a thread describing an order of consecutive acquisition configurations for measuring measurement positions described by the sampling scheme.

26. The method according to claim 1 or 2, comprising the step of performing a metrology operation on the substrate according to the sampling scheme using a metrology tool with the arrangement of a plurality of metrology sensors described by the sensor description.

27. The method according to claim 26, wherein The metrology operations include alignment operations or post-exposure monitoring operations for monitoring product functionality, overlay, any product dimensions, focus and / or dose monitoring operations, or any combination thereof.

28. A computer program comprising computer readable instructions which, when executed on a suitable processor, cause the processor to perform the method according to any one of claims 1 to 27.

29. A computer program product comprising a computer program according to claim 28.

30. A measuring device comprising: a sensor arrangement comprising an arrangement of a plurality of measurement sensors capable of performing parallel measurements as described in the sensor description; processor; as well as Storage means comprising a computer program according to claim 28.

31. The measurement device according to claim 30, wherein The sensor arrangement is optimized to maximize one or more of an efficiency metric, an informativeness metric, or a distribution metric for a given number of sampling locations.

32. The measuring device according to claim 30 or 31, wherein: The metrology sensors are spaced apart at integer multiples of the field grid.

33. The measurement device according to claim 30 or 31, wherein: The number of the measurement sensors is less than 10.

34. A lithography cell comprising a lithographic apparatus operable to expose a pattern on a substrate; and Measuring apparatus according to any one of claims 30 to 33.

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