Method, associated apparatus and computer program for determining a set of metrology points on a substrate

Abstract

A method of determining a set of metrology point locations, the set comprising a subset of potential metrology point locations on a substrate; wherein the method comprises: using prior knowledge to determine a relationship between noise distributions associated with a plurality of the potential metrology point locations; and determining the set using the determined relationship and a model associated with the substrate.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to EP application 19164831.0 filed on March 25, 2019 and EP application 19170764.5 filed on April 24, 2019, the entire contents of which are incorporated herein by reference. Technical Field

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

[0005] Regardless of the type of device employed, the precise placement of patterns on a substrate is a major challenge for reducing the size of circuit components and other products that can be produced by photolithography. In particular, the challenge of accurately measuring features on an already laid substrate is a critical step in being able to overlay successive layers of features accurately enough to produce working devices with a high yield. Typically, in today's submicron semiconductor devices, the so-called overlay should be achieved within tens of nanometers, and can be as low as a few nanometers in the most critical layers.

[0006] Therefore, modern lithography apparatuses involve extensive measurement or "mapping" operations prior to the step of actually exposing or otherwise patterning the substrate at target locations. These operations are time consuming, limiting the throughput of the lithography apparatus and thus increasing the unit cost of the semiconductor or other product.

[0007] As pattern features become smaller and overlay performance requirements become more demanding, so-called advanced alignment models have been and continue to be developed to more accurately model and correct for the nonlinear distortions of the "wafer grid." These advanced models depend on measuring an increasing number of targets on the substrate. Ultimately, however, only a limited number of available targets can be measured without unduly limiting the throughput of the overall lithography process.

[0008] These problems have been addressed by a sampling scheme optimization method that selects a subset of the total number of potential targets (or metrology point locations) on the substrate for use in alignment.

[0009] However, in such approaches there is an implicit assumption that the magnitude of the measurement variations is equal and uncorrelated across the substrate or within the field / image area. This is not true in real systems. For example, the scanner behavior will be correlated within the slit, and the variations may vary across the substrate (e.g. increase at the edges). This results in a sampling scheme that is suboptimal. Summary of the invention

[0010] Therefore, it is desirable to improve the reliability of the alignment model or other metrology process without reducing throughput by taking into account known aspects of the variations and correlations between the variations. This may allow the effects of changes in the variations and / or correlations in the variations to be taken into account in the sampling scheme, thereby reducing their impact on the alignment.

[0011] In one aspect, the present invention provides a method of determining a set of metrology point locations, the set comprising a subset of potential metrology point locations on a substrate; wherein the method comprises: using prior knowledge to determine a relationship between noise distributions associated with a plurality of the potential metrology point locations; and determining the set using the determined relationship and a model associated with the substrate.

[0012] In another aspect, the present invention provides a method of determining a model for fitting measurements, the model comprising a plurality of predetermined basis functions and coefficients associated with each of those basis functions, the method comprising the steps of:

[0013] A relationship between noise distributions associated with a plurality of measurement locations is determined using prior knowledge; and coefficients are determined at the measurement locations using the determined relationship and the calculated values ​​of each basis function.

[0014] In a further aspect, the present invention provides a computer program comprising computer-readable instructions which, when executed on a suitable computer device, cause the computer device to perform the method of the above aspects; a computer program product comprising such a computer program; and a device having a processor which is particularly suitable for performing the steps of the method of the above aspects.

[0015]

[0013] 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

[0016] Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which corresponding reference numerals indicate corresponding parts, and in which:

[0017] Figure 1 depicts a lithographic apparatus according to an embodiment of the invention;

[0018] Figure 2 Schematically illustrates the known practice of Figure 1 the stage of the measurement and exposure process in the device; and

[0019] Figure 3 The diagram illustrates computer system hardware for implementing the processes disclosed herein. DETAILED DESCRIPTION

[0020] Figure 1 A lithographic apparatus LA according to an embodiment of the invention is schematically depicted.

[0021] The device includes:

[0022] - an illumination system (illuminator) IL configured to condition a radiation beam B (eg UV radiation or EUV radiation).

[0023] a support structure (e.g. mask table) MT constructed 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. wafer table) WTa or WTb configured to hold a substrate (e.g. a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate according to certain parameters; and

[0025] - a projection system (eg a refractive projection lens system) PS configured to project the pattern imparted to the radiation beam B by the patterning device MA onto a target portion C of the substrate W (eg comprising one or more dies).

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

[0027] The support structure supports the patterning device, i.e. bears the weight of the patterning device. It holds the patterning device in a manner that depends on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions (e.g., whether the patterning device is held in a vacuum environment). The support structure can use mechanical, vacuum, electrostatic or other clamping techniques to hold the patterning device. The support structure can, for example, be a frame or a stage that can be fixed or moved as needed. The support structure can ensure that the patterning device is in a desired position, for example, relative to a projection system. Any use of the term "reticle" or "mask" herein can be considered synonymous with the more general term "patterning 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 radiation beam with a pattern in its cross-section so as to create a pattern in a 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 such as an integrated circuit created in the target portion.

[0029] Patterning devices may be transmissive or reflective. Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in lithography and include mask types such as binary, alternating phase shift, and attenuated phase shift, as well as various hybrid mask types. One example of a programmable mirror array employs a matrix arrangement of small mirrors, each of which can be individually tilted to reflect an incident radiation beam in different directions. The tilted mirrors impart a pattern in the radiation beam that is reflected by the matrix of mirrors.

[0030] The term "projection system" as used herein should be broadly interpreted as covering any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic and electrostatic optical systems or any combination thereof, which projection system is suitable for the exposure radiation used or other factors, such as the use of immersion liquid or the use of vacuum. Any use of the term "projection lens" herein may be considered synonymous with the more general term "projection system".

[0031] As depicted here, the device is of the transmissive type (eg, employing a transmissive mask). Alternatively, the device may be of the reflective type (eg, employing a programmable mirror array of the type referred to above, or employing 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 stand-alone manner, but in particular it may provide additional functionality in a pre-exposure measurement stage of a single or multi-stage apparatus.

[0033] The lithographic apparatus may also be of a type in which at least a portion of the substrate may be covered by a liquid having a relatively high refractive index (e.g., water) to fill the space between the projection system and the substrate. Immersion liquid may also be applied to other spaces in the lithographic apparatus, for example, between the mask and the projection system. Immersion techniques are well known in the art and are used to increase the numerical aperture of the projection system. The term "immersion" as used herein does not mean that structures such as the substrate must be submerged in the liquid, but only means that the liquid is located between the projection system and the substrate during exposure.

[0034] refer to Figure 1 , 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 this case, the source is not considered to form a part of the lithographic apparatus, and the radiation beam is transferred from the source SO to the illuminator IL with the aid of a beam delivery system BD including, for example, suitable guide mirrors and / or a beam expander. In other cases, for example, when the source is a mercury lamp, the source may be an integrated part of the lithographic apparatus. If desired, the source SO and the illuminator IL and the beam delivery system BD 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 and / or inner radial extent of the intensity distribution in a pupil plane of the illuminator (commonly referred to as σ-outer and σ-inner, respectively) may be adjusted. Furthermore, the illuminator IL may include various other components, such as an integrator IN and a condenser CO. The illuminator may be used to adjust 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 a projection system PS which focuses the beam onto a target portion C of the substrate W. With the aid of a second positioner PW and a position sensor IF (e.g., an interferometric device, a linear encoder or a capacitive sensor), the substrate table WTa / WTb can be accurately moved, for example, in order to position a different target portion C in the path of the radiation beam B. Similarly, the first positioner PM and the further position sensor (in Figure 1 The first positioner PM may be a first positioner having a plurality of dies (not explicitly depicted in the figure) which may be used to accurately position the mask MA relative to the path of the radiation beam B - for example after mechanical retrieval from a mask library or during a scanning process. Typically, 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. The mask MA and the substrate W may be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks as shown occupy dedicated target portions, they may be located in the spaces between target portions (these are referred to as scribe 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 depicted 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 while an entire pattern imparted to the radiation beam is projected at one time onto a target portion C (i.e. a single static exposure). 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 area limits the size of the target portion C that is imaged in a single static exposure.

[0039] 2. In scan mode, the mask table MT and the substrate table WTa / WTb are scanned synchronously while a pattern imparted to the radiation beam is projected onto a target portion C (i.e. a single dynamic exposure). The speed and direction of the substrate table WTa / WTb relative to the mask table MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS. In scan mode, the maximum size of the exposure area limits the width of the target portion in a single dynamic exposure (in the non-scanning direction), while the length of the scanning movement determines the height of the target portion (in the scanning direction).

[0040] 3. In another mode, the mask table MT is held substantially stationary so as to hold 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 employed, and the programmable patterning device is updated as required after each movement of the substrate table WTa / WTb or between successive radiation pulses during a scan. This mode of operation can be readily applied to maskless lithography utilizing a programmable patterning device, such as a programmable mirror array of the type described 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 lithography apparatus LA in this example is a so-called dual-stage type, which has two substrate tables WTa and WTb and two stations - an exposure station and a measurement station - between which the substrate table can be exchanged. While one substrate on one substrate table is being exposed at the exposure station EXP, another substrate can be loaded onto another substrate table at the measurement station MEA, so that various preparation steps can be performed. The preparation steps may include mapping the surface of the substrate using a horizontal sensor LS, and measuring the position of alignment marks on the substrate using an alignment sensor AS. This enables the throughput of the apparatus to be significantly increased. If the position sensor IF cannot measure the position of the substrate table when it is located at the measurement station and the exposure station, a second position sensor can be provided so that the position of the substrate table can be tracked at the two stations. The present invention can be applied to an apparatus with only one substrate table or with more than two substrate tables.

[0043] The device also includes a lithography device control unit LACU, which controls all movements and measurements of the various actuators and sensors described. LACU also includes signal processing and data processing capabilities to achieve 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 subunit processing 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 the substrate positioner PW. A separate unit can even handle coarse and fine actuators, or different axes. Another unit can be dedicated to the reading of the position sensor IF. The overall control of the device can be controlled by a central processing unit, which communicates with these subsystem processing units, operators, and other devices involved in the lithography manufacturing process.

[0044] Figure 2 The diagram shows Figure 1The invention relates to known steps for exposing a target portion (e.g., a die) on a substrate W in a dual-stage apparatus of the present invention. On the left hand side within the dashed box are the steps performed at the measurement station MEA, while the right hand side shows the steps performed at the exposure station EXP. As described above, from time to time, one of the substrate tables WTa, WTb will be located at the exposure station, while the other is located at the measurement station. For the purpose of this description, it is assumed that the substrate W has already been loaded into the exposure station. At step 200, a new substrate W' is loaded into the apparatus by a mechanism not shown. The two substrates are processed in parallel to increase the throughput of the lithography apparatus. Initially, reference is made to the newly loaded substrate W', which may be a previously unprocessed substrate, prepared with a new photoresist for the first exposure in the apparatus. However, in general, the lithography process described will be only one step in a series of exposure and processing steps, so that the substrate W' has passed through the apparatus and / or other lithography apparatus several times, and subsequent processes may also be performed.

[0045] As just mentioned, the preceding and / or succeeding processes may be performed in other lithography apparatuses, and may even be performed in different types of lithography apparatuses. For example, some layers of the device manufacturing process that are very demanding on parameters such as resolution and overlay may be performed in more advanced lithography tools than other layers that are less demanding. Thus, some layers may be exposed in an immersion lithography tool, while others are exposed in a "dry" tool. Some layers may 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 etc. and an image sensor (not shown) are used to measure and record the alignment of the substrate relative to the substrate table WTa / WTb. In addition, several alignment marks across the substrate W' will be measured to establish a "wafer grid" that very accurately maps the distribution of marks across the substrate, including any distortion relative to the nominal rectangular grid. At step 204, a graph of substrate height versus XY position is also measured for use in accurately focusing the pattern being exposed.

[0047] When substrate W' is loaded, menu data 206 is received, which defines the exposure to be performed, as well as the properties of the substrate and the pattern previously made and to be made thereon. The measurement of the substrate position, substrate grid and height map performed at 202, 204 is added to these menu data so that a complete set of menus and measurement data 208 can be transferred to the exposure station. The measurement of alignment data, for example, includes the X and Y positions of the alignment target, which is formed in a fixed or nominally fixed relationship with the product pattern as the product of the lithography process. These alignment data obtained before exposure are combined and interpolated to provide the parameters of the alignment model. These parameters and the alignment model will be used to correct the position of the pattern applied in the current lithography step during the exposure operation. Traditional alignment models can include four, five or six parameters, which together define the translation, rotation and scaling of the "ideal" grid of different dimensions. As further described below, advanced models using more parameters are known.

[0048] At 210, substrates W' and W are exchanged so that the substrate W' being measured becomes the substrate W entering the exposure station EXP. This exchange is performed by exchanging supports WTa and WTb within the device 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 exchange stations have been exchanged, determining the relative position between the projection system PS and the substrate table WTb (formerly WTa) is all that is necessary to utilize the measurement information 202, 204 of the substrate W (formerly W') in the control of the exposure step. At step 212, line alignment is performed using mask alignment marks M1, M2. In steps 214, 216, 218, scanning movements and radiation pulses are applied at consecutive target positions across the substrate W so as to complete the exposure of multiple patterns. By using the alignment data and height maps acquired at the measurement station in the performance of the exposure step, these patterns are accurately aligned relative to the desired positions - in particular relative to the features previously placed on the same substrate. At step 220, the exposed substrate (now labeled W") is unloaded from the apparatus for etching or other processes according to the exposed pattern.

[0049] Current standard alignment models may include six parameters (actually three in each X direction and three in each Y direction). This may be sufficient for some applications, but for more demanding processes, more detailed corrections to the wafer grid may be required to achieve the desired overlay performance. Advanced alignment models have been developed for this purpose. In this article, the term "advanced alignment model" is used to refer to models with higher complexity than the standard six parameters. While simpler 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 alignment models based on radial basis functions (RBF). HOWA is a public technique 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. (Conference SPIE 6922, 69221G (2008)). Different versions and extensions of these advanced models can be designed. Advanced models generate complex wafer grid descriptions that are corrected during exposure of 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 measurement volume is required to obtain a wafer grid with sufficient detail.

[0050] Even in embodiments with multiple substrate tables WTa / WTb, the time spent obtaining enough measurements for advanced alignment on each substrate will ultimately impact throughput. Reducing the time per measurement will tend to reduce the accuracy of each measurement, making it difficult to avoid an impact on throughput. Furthermore, 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 overlay of subsequent layers. Manufacturers are therefore faced with a difficult choice between accepting further measurement overhead by using an advanced model in subsequent layers, or suffering the adverse consequences of overlay by reverting to a simpler alignment model and measuring fewer marks in subsequent layers.

[0051] There is a great degree of similarity in the problems faced in alignment and model estimation / correction calculations. The commonality is to estimate a systematic pattern using a finite set of measurements made at certain locations. The choice of the locations of the measurements included in the estimation process determines the reliability of the resulting model. This is because not all measurement locations are necessarily equally informative for the estimation process.

[0052] Current customer high volume manufacturing (HVM) metrology schemes typically sample four to eight fields densely across a substrate, while covering the rest of the substrate in a sparse manner (e.g., one metrology point per field). This is already suboptimal for currently used models, and starts to become more problematic for higher order models.

[0053] In such Figure 1 In the lithographic apparatus shown in , alignment is performed on each substrate prior to exposure. A plurality of metrology points (e.g., alignment marks) are used to capture the shape of the substrate and average out placement noise (e.g., originating from the lithographic apparatus baseline). Typically, a subset of metrology point locations are selected for sampling from a plurality of possible metrology point locations on the substrate, the subset of metrology point locations comprising far fewer locations than the number of possible metrology point locations. Current algorithms for alignment determine which metrology point locations to select for sampling based on covering the substrate in a uniform manner, with uniformity being defined as equal or approximately equal distances between adjacent metrology points.

[0054] There are various methods for determining the location of the metrology points on the substrate that are selected for the sampling process. One such method is proposed in US 9,811,006 B2, where a measurement plan optimization algorithm is used to evaluate and select a range of potential metrology points.

[0055] The criterion for evaluating whether the meter point locations should be selected for inclusion in the sampling process 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). An example is provided below for illustration.

[0056] Assuming a linear model, i.e. a model whose parameters are linear, the following equation can be written:

[0057]

[0058] 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 selected metrological locations where the corresponding measurements were made. For example, using a one-dimensional polynomial model with x-orders from 0 to 4, 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 considering normalization, the corresponding row in C will be: [1 3 9 27 81].

[0059] The modeling process can then continue as follows:

[0060] 1. Measurements at selected metering point locations are made available;

[0061] 2. Choose an appropriate model form (i.e., a set of basis functions) to capture the relevant information behind the data;

[0062] 3. Perform minimization to produce parameter values ​​that minimize some mathematical norm of the distance between the model and the measured data. This minimization can take the form of least squares modeling.

[0063] Keeping the same notation as above, the optimization problem solved in the least squares estimation is as follows:

[0064]

[0065] This can be solved as follows:

[0066]

[0067] C T C is the information matrix, and its inverse [C T C] -1 is the variance-covariance matrix. Both the information matrix and the variance-covariance matrix indicate how informative the measurement scheme (i.e., the experiment) is about the chosen model; that is, how well the measurement scheme will allow the parameters to be distinguished (it should be noted 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.

[0068] The goal of the D-optimality method is to minimize the amount of uncertainty associated with the coefficients of the model that the user wants to apply to fit the measurement results. Therefore, the sampling scheme optimization method using D-optimality provides the best sampling scheme for a specific predefined model. However, this assumes that the measurement point locations are uncorrelated with each other.

[0069] When the known meter point locations are statistically uncorrelated and / or the variance of the noise is non-uniform, the covariance matrix expressing the cross-correlations is not the identity matrix and is therefore not a conventional design matrix that needs to be considered when choosing a sampling scheme.

[0070] Therefore, the sampling scheme optimization method of the embodiment of the present invention does not consider the information matrix C T C (or variance-covariance matrix [C T C] -1 ), but seeks to minimize the determinant of the matrix M defined as follows:

[0071] M=(C T .∑ -1 .C) -1

[0072] where Σ is the covariance matrix, which combines knowledge of the variation behavior and the correlations. The covariance matrix is ​​constructed using knowledge of the variation behavior, which can be obtained from one or more of a range of sources such as dense on-product measurements or scanner measurement data.

[0073] Using such knowledge improves sampling scheme optimization by allowing more weight (ie, additional target density) to be placed in areas showing stronger variations, such as substrate edges. It can also improve sampling scheme optimization by taking into account repetitive features, such as correlated scanner behavior within slits.

[0074] A covariance matrix taking into account correlations, such as used in the above-described embodiments, may be constructed in a variety of ways depending on the knowledge of the available correlations.

[0075] One way to construct the covariance matrix is ​​to use the maximum likelihood estimator of the covariance matrix ∑. Let X∈M n×p is a matrix with measurement data, where the first index runs on all measurements of a single substrate, the total number of measurements is n, and the second index p runs on all measured substrates. Now we can get To estimate ∑.

[0076] Unfortunately, to get a good estimate this would require p>>n, which is generally not feasible at the consumer level.

[0077] Therefore, it is preferred to incorporate domain knowledge into the construction of the covariance matrix. Again, this can be done in several ways.

[0078] According to an embodiment of the present invention, one method is to perform a cascaded subspace method as set forth below.

[0079] The mean field for each substrate is first calculated, and this mean field is mapped to the entire layout, giving X avgf From this, the maximum likelihood covariance estimator can be calculated for the mean field using the method described above: S avgf ∈M nxn This describes average field effects such as reticle alignment errors.

[0080] On the residual, that is, XX avgf (with all substrates of the mean field removed), we can now project onto the typical set of interfield models, HOWA3, giving, for example, X inter ∈M nxp and its maximum likelihood covariance estimator: S inter This describes inter-field effects such as substrate alignment errors.

[0081] On the further residual, that is, X res :=XXavgf -X inter , then it is possible to "stack the fields", i.e. reshape the matrix so that each column represents an exposure field, where q is the number of markers per field, giving an estimate S stacked ∈M q×q We can now create S F2F ∈M n×n As S stacked The block diagonal matrix of the matrix. This describes field-to-field effects, such as stage positioning errors when moving a lens from one field to another.

[0082] Total estimate S = S avgf +S stacked +S F2F A good estimate should be given where the number of substrates p>>q and more limited p>>r, where r is the number of inter-field parameters used.

[0083] The above model uses domain knowledge to reduce the effective degrees of freedom from which S can be estimated. The domain knowledge used is the assumption that the average field effect, the inter-field effect, and the field-to-field effect cover most of the known contributors to overlay, and that each has a different root cause so that the cross-covariance between each of these subspaces is small. Either or both of the steps in the above model can be performed to obtain a useful estimate of S, relying on further knowledge about whether these effects are present in the data.

[0084] In general, this approach can be generalized to domain knowledge giving us a mapping The concept of is significantly shorter than n 2 Using this mapping And therefore S can be found using maximum likelihood estimation.

[0085] An alternative approach is to use some prior statistical knowledge about the distribution of S. This does not completely restrict S to some subspace, but rather gradually suppresses unlikely results in the estimate. An example of such an approach is the graphical lasso, which reduces the 1-norm of S; this is not basis-independent, so domain knowledge is required to find a suitable basis.

[0086] Alternatively, the covariance matrix may be determined without reliance on any client measurements, for example based purely on a priori knowledge of the noise contribution in the machine.

[0087] In addition to being used in the sampling scheme optimization embodiments described above, the covariance matrix (whether determined by one of the methods described above or otherwise) may also be used in a fitting process for estimating overlay error as described in the embodiments below.

[0088] The covariance matrix has been determined and is then applied to the design matrix. To estimate the parameters based on the design matrix C without taking into account the covariance, maximum likelihood estimation is used: in: is a vector containing the values ​​of the parameters to be determined, and It is the overlay result for the substrate.

[0089] To include the covariance matrix, The maximum likelihood estimator of can be calculated as:

[0090] It should be appreciated that while the above description is presented in the context of overlay and alignment, it is not limited thereto. The methods disclosed herein can be used in 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 reduced-size smart metrology solution.

[0091] Further embodiments of the invention are disclosed in the following list of numbered clauses:

[0092] 1. A method of determining a set of metrology point locations, the set comprising a subset of potential metrology point locations on a substrate; wherein the method comprises:

[0093] determining a relationship between noise distributions associated with a plurality of said potential metering point locations using prior knowledge; and

[0094] The set is determined using the determined relationship and a model associated with the substrate.

[0095] 2. The method of clause 1, wherein the relationship describes the covariance between each of the plurality of potential meter point locations.

[0096] 3. A method according to clause 1 or 2, wherein the relationship comprises a relative magnitude of a variance associated with the noise distribution.

[0097] 4. A method according to clause 2, wherein the relationship has the shape of a covariance matrix, and the method further comprises, for each of the potential meter point locations, minimizing the determinant of a matrix formed by: a design matrix describing the model with potential meter point locations; and a covariance matrix.

[0098] 5. A method according to any of the preceding clauses, wherein the metrology point positions contained in the set are the metrology point positions that contribute a maximum level of information about the substrate for a predetermined size of the set.

[0099] 6. A method according to any of the preceding clauses, further comprising the step of performing a metrology operation on the substrate using measurements obtained exclusively from metrology points located at the set of metrology point locations.

[0100] 7. A method according to any of clauses 1 to 5, further comprising the step of performing alignment operations on the substrate during a lithography process using measurements obtained exclusively from metrology points located at the set of metrology point locations.

[0101] 8. The method of clause 7, further comprising the step of performing a patterning operation on the substrate after performing the aligning operation.

[0102] 9. A method according to any of clauses 1 to 5, further comprising the step of modelling distortions in the lithographic process using measurements obtained exclusively from metrology points located at the set of metrology point locations.

[0103] 10. A method of determining a model for fitting measurements, the model comprising a plurality of predetermined basis functions and coefficients associated with each of those basis functions, the method comprising the steps of:

[0104] determining a relationship between noise distributions associated with a plurality of measurement locations using prior knowledge; and

[0105] The coefficients are determined at the measurement location using the determined relationship and the calculated values ​​of each basis function.

[0106] 11. The method of clause 10, wherein the relationship describes the covariance between each of the plurality of measurement locations.

[0107] 12. A method according to clause 10 or 11, wherein the relationship comprises a relative magnitude of a variance associated with the noise distribution.

[0108] 13. A method according to any one of clauses 10 to 12, wherein the step of determining the coefficients uses a least squares method.

[0109] 14. A method according to any of clauses 10 to 12, wherein the step of determining the coefficients comprises calculating a maximum likelihood estimator of a vector comprising the coefficients.

[0110] 15. A method according to any preceding clause, wherein the prior knowledge comprises previous measurements of noise data associated with the metering point location.

[0111] 16. A method according to any preceding clause, wherein the prior knowledge comprises assumptions about the interrelationships between a plurality of factors affecting the variations between meter point locations.

[0112] 17. A method according to any of the preceding clauses, wherein when determining a covariance measure, prior knowledge is used to reduce the degrees of freedom from which the covariance measure can be determined.

[0113] 18. A method according to any of the preceding clauses, as applied in or to a lithographic process, wherein the relationship is determined by calculating the mean field for each substrate from which measurement data are obtained.

[0114] 19. A method according to any preceding clause, as applied in or to a lithographic process, wherein the relationship is determined by calculating inter-field effects between fields on the substrate from which the measurement data are obtained.

[0115] 20. A method according to any preceding clause, as applied in or to a lithographic process, wherein the relationship is determined by calculating field to field effects when moving between fields on a substrate from which measurement data is obtained.

[0116] 21. A computer program comprising computer readable instructions which, when executed on suitable computer means, cause the computer means to perform the method of any of the preceding clauses.

[0117] 22. A computer program product comprising the computer program of clause 21.

[0118] 23. An apparatus having a processor, the processor being particularly adapted to perform the steps of the method according to any of clauses 1 to 20.

[0119] 24. The apparatus of clause 23, being specifically configured as a lithographic apparatus operable to perform a lithographic process on a substrate.

[0120] The steps of the above method can be Figure 1 The lithographic apparatus shown in FIG. 1 is automated in a control unit LACU. The unit LACU may include Figure 3 In an embodiment of the accessory according to the invention, the computer accessory may be a dedicated computer in the form of a control unit or, alternatively, a central computer controlling the lithographic projection apparatus. The computer accessory may be arranged for loading a computer program product comprising computer executable code. When downloading the computer program product, this may enable the computer accessory to control the above-described use of the lithographic apparatus with embodiments of the level and alignment sensors AS, LS.

[0121] The memory 1229 connected to the processor 1227 may include a plurality of memory components, such as a hard disk 1261, a read-only memory (ROM) 1262, an electrically erasable programmable read-only memory (EEPROM) 1263, and a random access memory (RAM) 1264. Not all of the aforementioned memory components need to be present. In addition, it is not necessary that the aforementioned memory components are physically adjacent to the processor 1227 or to each other. They may be located far away.

[0122] The processor 1227 may also be connected to some kind of user interface, such as a keyboard 1265 or a mouse 1266. A touch screen, trackball, voice converter, or other interface known to those skilled in the art may also be used.

[0123] The processor 1227 may be connected to a reading unit 1267 which is arranged to read data from, and in some cases store data on, a data carrier such as a floppy disk 1268 or a CDROM 1269, e.g. in the form of computer executable code. A DVD or other data carrier known to the person skilled in the art may also be used.

[0124] The processor 1227 may also be connected to a printer 1270 to print out data on paper and to a display 1271, such as a monitor or LCD (Liquid Crystal Display) or any other type of display known to those skilled in the art.

[0125] The processor 1227 may be connected to a communication network 1272, such as a public switched telephone network (PSTN), a local area network (LAN), a wide area network (WAN), etc., via a transmitter / receiver 1273 responsible for input / output (I / O). The processor 1227 may be arranged to communicate with other communication systems via the communication network 1272. In an embodiment of the present invention, an external computer (not shown), such as an operator's personal computer, may log in to the processor 1227 via the communication network 1272.

[0126] Processor 1227 can be implemented as a stand-alone system or multiple processing units operating in parallel, where each processing unit is arranged to perform a subtask of a larger program. The processing unit can also be divided into one or more main processing units with several sub-processing units. Some processing units of processor 1227 can even be located at a distance away from other processing units and communicate via communication network 1272. The connection between modules can be wired or wireless.

[0127] The computer system may be any signal processing system with analog and / or digital and / or software technology arranged to perform the functions discussed herein.

[0128] Although specific reference may be made herein to the use of lithographic apparatus in IC manufacturing, it should be understood that the lithographic apparatus described herein may have other applications, such as the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat panel displays, liquid crystal displays (LCDs), thin film magnetic heads, etc. Those skilled in the art will appreciate that in the context of such alternative applications, any use of the terms "wafer" or "field" / "die" herein may be considered synonymous with the more general terms "substrate" or "target portion", respectively. Before or after exposure, the substrate referred to herein may be processed in, for example, a track (a tool that typically applies a resist layer to a substrate and develops the exposed resist), a metrology tool, and / or an inspection tool. Where applicable, the disclosure herein may be applied to such and other substrate processing tools. In addition, a substrate may be processed more than once, for example to create a multi-layer IC, so that the term substrate used herein may also refer to a substrate that already contains multiple processing layers.

[0129] Although specific reference has been made above to the use of embodiments of the invention in the context of optical lithography, it will be appreciated that the invention may be used in other applications, such as imprint lithography, and is not limited to optical lithography where the context permits. In imprint lithography, the topography in the patterning device defines the pattern produced on the substrate. The topography of the patterning device may be pressed into a resist layer provided to the substrate, and the resist is then cured by applying electromagnetic radiation, heat, pressure, or a combination thereof to the resist layer. The patterning device is removed from the resist, leaving a pattern therein after the resist has cured.

[0130] The terms "radiation" and "beam" as used herein encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having a wavelength of or about 365, 248, 193, 157 or 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having a wavelength in the range of 5-20 nm), as well as particle beams, such as ion beams or electron beams.

[0131] The term "lens," where the context permits, may refer to any one or combination of various types of optical components, including refractive, reflective, magnetic, electromagnetic, and electrostatic optical components.

[0132] Although specific embodiments of the present invention have been described above, it should be appreciated that the present invention may be practiced in ways other than those described. For example, the present invention may take the form of a computer program comprising one or more machine-readable instruction sequences of 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 therein.

[0133] The above description is intended to be illustrative, not restrictive. Therefore, it will be apparent to those skilled in the art that the present invention may be modified as described without departing from the scope of the claims set forth below. In addition, it should be understood that the structural features or method steps shown or described in any one of the embodiments herein may also be used in other embodiments.

Claims

1. A method of determining a set of metrology point locations, the set comprising a subset of potential metrology point locations on a substrate; The method comprises: determining, using prior knowledge, a relationship between noise distributions associated with a plurality of said potential metering point locations; as well as The set is determined using the determined relationship and a model associated with the substrate.

2. The method of claim 1, wherein the relationship describes a covariance between each of the plurality of potential metering point locations.

3. A method according to claim 1 or claim 2, wherein the relationship comprises the relative magnitude of the variance associated with the noise distribution.

4. The method of claim 2, wherein the relationship has the shape of a covariance matrix, and the method further comprises, for each of the potential meter point locations, minimizing a determinant of a matrix formed by: a design matrix describing the model with the potential meter point locations; and the covariance matrix.

5. A method according to any one of the preceding claims, wherein the metrology point positions comprised in the set are those which contribute a maximum level of information about the substrate for a predetermined size of the set.

6. A method according to any one of the preceding claims, further comprising the step of performing a metrology operation on the substrate using measurements obtained exclusively from metrology points located at the set of metrology point locations.

7. A method according to any one of claims 1 to 5, further comprising the step of performing alignment operations on said substrate during a lithography process using measurements obtained exclusively from metrology points located at said set of metrology point locations.

8. The method of claim 7, further comprising the step of performing a patterning operation on the substrate after performing the aligning operation.

9. A method according to any one of claims 1 to 5, further comprising the step of modelling distortions in the lithographic process using measurements obtained exclusively from metrology points located at said set of metrology point locations.

10. A method of determining a model for fitting measurements, the model comprising a plurality of predetermined basis functions and coefficients associated with each of the basis functions, the method comprising the steps of: using existing knowledge to determine a relationship between noise distributions associated with a plurality of measurement locations; as well as The coefficients are determined at the measurement location using the determined relationship and the calculated values ​​of each basis function. The method of claim 10 , wherein the relationship describes a covariance between each of the plurality of measurement locations.

12. A method according to claim 10 or claim 11, wherein the relationship comprises the relative magnitude of the variance associated with the noise distribution.

13. A method according to any one of claims 10 to 12, wherein the step of determining the coefficients uses a least squares method.

14. A method according to any one of claims 10 to 12, wherein the step of determining the coefficients comprises calculating a maximum likelihood estimator of a vector comprising the coefficients.

15. A method according to any preceding claim, wherein the prior knowledge comprises previous measurements of noise data associated with the metering point locations.

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