Remaining useful lifetime estimation using multivariate signals

Abstract

Disclosed is a computer implemented method of predicting a remaining useful lifetime of an apparatus or component thereof comprising: receiving high dimensional data corresponding to an operating parameter of the apparatus or component thereof; transforming the high dimensional data into health indicator data, comprising low dimensional data indicative of a health status of the apparatus or component thereof; determining temporal relations within the health indicator data to obtain health indicator trajectory data; receiving historical maintenance data of the apparatus or component thereof; determining a failure probability of the apparatus or component thereof based at least in part on the historical maintenance data and the health indicator trajectory data, and; predicting the remaining useful lifetime of the apparatus or component thereof based at least in part on the failure probability.

Description

REMAINING USEFUL LIFETIME ESTIMATION USING MULTIVARIATE SIGNALSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of EP application 23191644.6 which was filed on 16 August 2023 and which is incorporated herein in its entirety by reference.FIELD

[0002] The present invention relates to methods and apparatus usable, for example, in the manufacture of devices by lithographic techniques, and to methods of manufacturing devices using lithographic techniques.BACKGROUND

[0003] A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. including part of a die, one die, or several dies) on a substrate (e.g., a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. These target portions are commonly referred to as “fields”.

[0004] In the manufacture of complex devices, typically many lithographic patterning steps are performed, thereby forming functional features in successive layers on the substrate. A critical aspect of performance of the lithographic apparatus is therefore the ability to place the applied pattern correctly and accurately in relation to features laid down (by the same apparatus or a different lithographic apparatus) in previous layers. For this purpose, the substrate is provided with one or more sets of alignment marks. Each mark is a structure whose position can be measured at a later time using a position sensor, typically an optical position sensor. The lithographic apparatus includes one or more alignment sensors by which positions of marks on a substrate can be measured accurately. Different types of marks and different types of alignment sensors are known from different manufacturers and different products of the same manufacturer.

[0005] In other applications, metrology sensors are used for measuring exposed structures on a substrate (either in resist and / or after etch). A fast and non-invasive form of specialized inspection tool is a scatterometer in which a beam of radiation is directed onto a target on the surface of the substrate and properties of the scattered or reflected beam are measured. Examples of known scatterometers include angle -resolved scatterometers of the type described in US2006033921A1 and US2010201963A1. In addition to measurement of feature shapes by reconstruction, diffraction basedoverlay can be measured using such apparatus, as described in published patent application US2006066855A1. Diffraction-based overlay metrology using dark-field imaging of the diffraction orders enables overlay measurements on smaller targets. Examples of dark field imaging metrology can be found in international patent applications WO 2009 / 078708 and WO 2009 / 106279 which documents are hereby incorporated by reference in their entirety. Further developments of the technique have been described in published patent publications US20110027704A, US20110043791 A, US2011102753A1, US20120044470A, US20120123581A, US20130258310A, US20130271740A andWO2013178422A1. These targets can be smaller than the illumination spot and may be surrounded by product structures on a wafer. Multiple gratings can be measured in one image, using a composite grating target. The contents of all these applications are also incorporated herein by reference.

[0006] It is desirable to evaluate, monitor and predict the health condition of lithography apparatus to ensure that lithography process steps are performed according to predetermined specifications. In some cases, data-driven predictive maintenance models may be used to this end. These models are typically used to detect specific process characteristics and do not provide an indication of a remaining useful lifetime (RUL) of components.SUMMARY

[0007] The invention in a first aspect provides a computer implemented method of predicting a remaining useful lifetime, RUL, of an apparatus or component thereof comprising: receiving high dimensional data corresponding to an operating parameter of the apparatus or component thereof; transforming the high dimensional data into health indicator data, comprising low dimensional data indicative of a health status of the apparatus or component thereof; determining temporal relations within the health indicator data to obtain health indicator trajectory data; receiving historical maintenance data of the apparatus or component thereof; determining a failure probability of the apparatus or component thereof based at least in part on the historical maintenance data and the health indicator trajectory data, and; predicting the remaining useful lifetime of the apparatus or component thereof based at least in part on the failure probability.

[0008] The above and other aspects of the invention will be understood from a consideration of the examples described below.BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings, in which:Figure 1 depicts a lithographic apparatus;Figure 2 illustrates schematically measurement and exposure processes in the apparatus of Figure 1 ; andFigure 3 depicts a remaining useful lifetime (RUL) prediction pipeline in accordance with some embodiments.DETAILED DESCRIPTION

[0010] Before describing embodiments of the invention in detail, it is instructive to present an example environment in which embodiments of the present invention may be implemented.

[0011] Figure 1 schematically depicts a lithographic apparatus LA. The apparatus includes an illumination system (illuminator) IL configured to condition a radiation beam B (e.g., UV radiation or DUV radiation), a patterning device support or support structure (e.g., a mask table) MT constructed to support a patterning device (e.g., a mask) MA and connected to a first positioner PM configured to accurately position the patterning device in accordance with certain parameters; two substrate tables (e.g., a wafer table) WTa and WTb each constructed to hold a substrate (e.g., a resist coated wafer) W and each connected to a second positioner PW configured to accurately position the substrate in accordance with certain parameters; and a projection system (e.g., a refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by patterning device MA onto a target portion C (e.g., including one or more dies) of the substrate W. A reference frame RF connects the various components, and serves as a reference for setting and measuring positions of the patterning device and substrate and of features on them.

[0012] 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.

[0013] The patterning device support MT 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, such as for example whether or not the patterning device is held in a vacuum environment. The patterning device support can use mechanical, vacuum, electrostatic or other clamping techniques to hold the patterning device. The patterning device support MT may be a frame or a table, for example, which may be fixed or movable as required. The patterning device support may ensure that the patterning device is at a desired position, for example with respect to the projection system.

[0014] The term “patterning device” 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 such 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. Generally, the pattern imparted to the radiation beam will correspond to a particular functional layer in a device being created in the target portion, such as an integrated circuit.

[0015] As here depicted, the apparatus is of a transmissive type (e.g., employing a transmissive patterning device). Alternatively, the apparatus may be of a reflective type (e.g., employing aprogrammable mirror array of a type as referred to above, or employing a reflective mask). Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Any use of the terms “reticle” or “mask” herein may be considered synonymous with the more general term “patterning device.” The term “patterning device” can also be interpreted as referring to a device storing in digital form pattern information for use in controlling such a programmable patterning device.

[0016] The term “projection system” used herein should be broadly interpreted as encompassing any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic and electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation being used, or for other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term “projection lens” herein may be considered as synonymous with the more general term “projection system”.

[0017] The lithographic apparatus may also be of a type wherein at least a portion of the substrate may be covered by a liquid having a relatively high refractive index, e.g., water, so as to fill a space between the projection system and the substrate. An 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 for increasing the numerical aperture of projection systems.

[0018] In operation, the illuminator IL receives a radiation beam from a radiation source SO. The source and the lithographic apparatus may be separate entities, for example when the source is an excimer laser. In such cases, the source is not considered to form part of the lithographic apparatus and the radiation beam is passed from the source SO to the illuminator IL with the aid of a beam delivery system BD including, for example, suitable directing mirrors and / or a beam expander. In other cases the source may be an integral part of the lithographic apparatus, for example when the source is a mercury lamp. The source SO and the illuminator IL, together with the beam delivery system BD if required, may be referred to as a radiation system.

[0019] The illuminator IL may for example include an adjuster AD for adjusting the angular intensity distribution of the radiation beam, an integrator IN and a condenser CO. The illuminator may be used to condition the radiation beam, to have a desired uniformity and intensity distribution in its cross section.

[0020] The radiation beam B is incident on the patterning device MA, which is held on the patterning device support MT, and is patterned by the patterning device. Having traversed the patterning device (e.g., 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 the second positioner PW and position sensor IF (e.g., an interferometric device, linear encoder, 2-D encoder or capacitive sensor), the substrate table WTa or WTb can be moved accurately, e.g., so as to position different target portions C in the path of the radiation beam B. Similarly, the first positioner PM and another position sensor (which is not explicitly depicted in Figure 1) can be used to accurately position the patterning device (e.g., mask) MAwith respect to the path of the radiation beam B, e.g., after mechanical retrieval from a mask library, or during a scan.

[0021] The lithographic apparatus may comprise an aberration sensor for the verification of an aberration fingerprint of the projection system PS. In an embodiment such an aberration fingerprint, i.e. aberrations per field point of the projection system PS, may be determined using a such wavefront aberration sensor. A wavefront aberration sensor of a known type, for instance such as described in US2002 / 0001088 may be used. Such a wavefront aberration sensor may be based on the principle of shearing interferometry and comprises a source module and a sensor module. The source module may comprise a patterned layer of chromium that is placed in the object plane (i.e. where during production the pattern of the patterning means is) of the projection system PS and has additional optics provided above the chromium layer. The combination provides a wavefront of radiation to the entire pupil of the projection system PS. The sensor module may comprise a patterned layer of chromium that is placed in the image plane of the projection system (i.e. where during production the substrate W is) and a camera that is placed some distance behind said layer of chromium. The patterned layer of chromium on the sensor module diffracts radiation into several diffraction orders that interfere with each other giving rise to an interferogram. The interferogram is measured by the camera. The aberrations in the projection lens can be determined by software based upon the measured interferogram. The wavefront aberration sensor may be configured to transfer information with respect to the aberration fingerprint towards the control unit.

[0022] Patterning device (e.g., mask) MA and substrate W may be aligned using mask alignment marks Ml, M2 and substrate alignment marks Pl, P2. Although the substrate alignment marks as illustrated occupy dedicated target portions, they may be located in spaces between target portions (these are known as scribe-lane alignment marks). Similarly, in situations in which more than one die is provided on the patterning device (e.g., mask) MA, the mask alignment marks may be located between the dies. Small alignment marks may also be included within dies, in amongst the device features, in which case it is desirable that the markers be as small as possible and not require any different imaging or process conditions than adjacent features. The alignment system, which detects the alignment markers is described further below.

[0023] The depicted apparatus could be used in a variety of modes. In a scan mode, the patterning device support (e.g., mask table) MT and the substrate table WT 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 WT relative to the patterning device support (e.g., mask table) MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS. In scan mode, the maximum size of the exposure field limits the width (in the non-scanning direction) of the target portion in a single dynamic exposure, whereas the length of the scanning motion determines the height (in the scanning direction) of the target portion. Other types of lithographic apparatus and modes of operation are possible, as is well-known in the art. For example,a step mode is known. In so-called “maskless” lithography, a programmable patterning device is held stationary but with a changing pattern, and the substrate table WT is moved or scanned.

[0024] Combinations and / or variations on the above described modes of use or entirely different modes of use may also be employed.

[0025] Lithographic apparatus LA is of a so-called dual stage type which has two substrate tables WTa, WTb and two stations - an exposure station EXP and a measurement station MEA - between which the substrate tables can be exchanged. While one substrate on one substrate table is being exposed at the exposure station, another substrate can be loaded onto the other substrate table at the measurement station and various preparatory steps carried out. This enables a substantial increase in the throughput of the apparatus. The preparatory steps may include mapping the surface height contours of the substrate using a level sensor LS and measuring the position of alignment markers on the substrate using an alignment sensor AS. If the position sensor IF is not capable of measuring the position of the substrate table while it is at the measurement station as well as at the exposure station, a second position sensor may be provided to enable the positions of the substrate table to be tracked at both stations, relative to reference frame RF. Other arrangements are known and usable instead of the dual-stage arrangement shown. For example, other lithographic apparatuses are known in which a substrate table and a measurement table are provided. These are docked together when performing preparatory measurements, and then undocked while the substrate table undergoes exposure.

[0026] Figure 2 illustrates the steps to expose target portions (e.g. dies) on a substrate W in the dual stage apparatus of Figure 1. On the left hand side within a dotted box are steps performed at a measurement station MEA, while the right hand side shows steps performed at the exposure station EXP. From time to time, one of the substrate tables WTa, WTb will be at the exposure station, while the other is at the measurement station, as described above. For the purposes of this description, it is assumed that a substrate W has already been loaded into the exposure station. At step 200, a new substrate W’ is loaded to the apparatus by a mechanism not shown. These two substrates are processed in parallel in order to increase the throughput of the lithographic apparatus.

[0027] Referring initially to the newly-loaded substrate W’, this may be a previously unprocessed substrate, prepared with a new photo resist for first time exposure in the apparatus. In general, however, the lithography process described will be merely one step in a series of exposure and processing steps, so that substrate W’ has been through this apparatus and / or other lithography apparatuses, several times already, and may have subsequent processes to undergo as well. Particularly for the problem of improving overlay performance, the task is to ensure that new patterns are applied in exactly the correct position on a substrate that has already been subjected to one or more cycles of patterning and processing. These processing steps progressively introduce distortions in the substrate that must be measured and corrected for, to achieve satisfactory overlay performance.

[0028] The previous and / or subsequent patterning step may be performed in other lithography apparatuses, as just mentioned, and may even be performed in different types of lithography apparatus.For example, some layers in the device manufacturing process which are very demanding in parameters such as resolution and overlay may be performed in a more advanced lithography tool than other layers that are less demanding. Therefore some layers may be exposed in an immersion type lithography tool, while others are exposed in a ‘dry’ tool. Some layers may be exposed in a tool working at DUV wavelengths, while others are exposed using EUV wavelength radiation.

[0029] At 202, alignment measurements using the substrate marks Pl etc. and image sensors (not shown) are used to measure and record alignment of the substrate relative to substrate table WTa / WTb. In addition, several alignment marks across the substrate W’ will be measured using alignment sensor AS. These measurements are used in one embodiment to establish a “wafer grid”, which maps very accurately the distribution of marks across the substrate, including any distortion relative to a nominal rectangular grid.

[0030] At step 204, a map of wafer height (Z) against X-Y position is measured also using the level sensor LS. Conventionally, the height map is used only to achieve accurate focusing of the exposed pattern. It may be used for other purposes in addition.

[0031] When substrate W’ was loaded, recipe data 206 were received, defining the exposures to be performed, and also properties of the wafer and the patterns previously made and to be made upon it. To these recipe data are added the measurements of wafer position, wafer grid and height map that were made at 202, 204, so that a complete set of recipe and measurement data 208 can be passed to the exposure station EXP. The measurements of alignment data for example comprise X and Y positions of alignment targets formed in a fixed or nominally fixed relationship to the product patterns that are the product of the lithographic process. These alignment data, taken just before exposure, are used to generate an alignment model with parameters that fit the alignment model to the data. These parameters and the alignment model will be used during the exposure operation to correct positions of patterns applied in the current lithographic step. The model in use interpolates positional deviations between the measured positions. A conventional alignment model might comprise four, five or six parameters, together defining translation, rotation and scaling of the ‘ideal’ grid, in different dimensions. Advanced models are known that use more parameters.

[0032] At 210, wafers W’ and W are swapped, so that the measured substrate W’ becomes the substrate W entering the exposure station EXP. In the example apparatus of Figure 1 , this swapping is performed by exchanging the supports WTa and WTb within the apparatus, so that the substrates W, W’ remain accurately clamped and positioned on those supports, to preserve relative alignment between the substrate tables and substrates themselves. Accordingly, once the tables have been swapped, determining the relative position between projection system PS and substrate table WTb (formerly WTa) is all that is necessary to make use of the measurement information 202, 204 for the substrate W (formerly W’) in control of the exposure steps. At step 212, reticle alignment is performed using the mask alignment marks Ml, M2. In steps 214, 216, 218, scanning motions and radiation pulses areapplied at successive target locations across the substrate W, in order to complete the exposure of a number of patterns.

[0033] By using the alignment data and height map obtained at the measuring station in the performance of the exposure steps, these patterns are accurately aligned with respect to the desired locations, and, in particular, with respect to features previously laid down on the same substrate. The exposed substrate, now labeled W” is unloaded from the apparatus at step 220, to undergo etching or other processes, in accordance with the exposed pattern.

[0034] The skilled person will know that the above description is a simplified overview of a number of very detailed steps involved in one example of a real manufacturing situation. For example rather than measuring alignment in a single pass, often there will be separate phases of coarse and fine measurement, using the same or different marks. The coarse and / or fine alignment measurement steps can be performed before or after the height measurement, or interleaved.

[0035] Currently, data-driven predictive maintenance models may be used to evaluate, monitor and predict the health condition of a component of a scanner. Such methods may capture a simplified representation of component health indicators (His) and use thresholds for such HI values to determine the state of a component. There are also existing machine learning models which can predict remaining useful lifetime (RUL) of a component.

[0036] In some cases, a traffic light based predictive maintenance model may be used to map raw component data onto a discrete lower dimensional space (e.g., “red”, “orange” or “green” being indicative of component health, for example: being healthy, partial degraded and degraded respectively). This approach is explanatory rather than predictive and does not take into account multivariate temporal dependencies in the raw component data that may signal component degradation and ultimately end of useful lifetime.

[0037] Owing to the high dimensionality of raw signal data from lithography apparatus, known methods of predictive maintenance may comprise capturing a simplified representation of component health and applying subjective thresholds to determine the health state of components (e.g. healthy, partially degraded, degraded). These methods may have limited predictive capability and reliability issues because of the subjective nature of the threshold determination, with no unifying objective pattern or threshold agreed upon by operators. Thus, RUL cannot be predicted far into the future.

[0038] Predictive maintenance widely uses data driven methods to build predictive models to monitor the health condition of components. In many cases, there is no straightforward mapping of raw component data onto health condition metrics, even though the degree of representation of component health that forms the output of this modelling phase serves as the input for any subsequent model phases. Complex relationships between input variables that may have a temporal effect in determining the health trajectory of a component may not be captured by known methods (e.g. principal / independent component analysis (PCA / ICA), factory analysis or other conventional solutions). The complexity of lithographic apparatus having multiple physical degradation processes with measurements performedin multiple settings (e.g. wavelength, depth), down to component level degradation, is sufficiently high that the problem of deriving health indicators from raw data is not addressed by conventional machine learning techniques.

[0039] It is highly desirable for operators to have an indicator (e.g. a visual indicator) of component health and trend of future behavior to support and inform decision making. Such an indicator should be both understandable but not too simplistic such that it results in low accuracy in RUL prediction. Neither the traffic light model which is easily understandable but too simplistic, nor the existing machine learning RUL models which have better prediction accuracy but require analysis to understand, satisfy both these requirements. Moreover, in many situations there are multiple types of reliability data, such as run-to-failure (R2F) data, lifetime data or health indicator thresholds. Although existing RUL models may use machine learning and neural networks to learn complex relations within component data, the existing methods typically focus on one specific type of reliability data and produce output (e.g. RUL, failure probability), without giving insight into the intermediate triggers that lead to the output.

[0040] Accordingly, it is desirable to have a predictive maintenance pipeline that can make use of multiple types of reliability data (e.g. R2F, lifetime data, or known thresholds), allows extraction of health indicators from the reliability data, and can accurately project the future behavior of the health indicators. In some aspects, the methods proposed herein aim to determine a relationship between intermediate values and failure probability / RUL by an arbitrary complex relation, which may in turn allow, for example, a decision tree to infer more complex rules than simple thresholds.

[0041] Figure 3 shows a schematic diagram of a predictive maintenance system for predicting a remaining useful lifetime (RUL) of an apparatus or component thereof in accordance with some embodiments of the present disclosure.

[0042] Still referring to Figure 3, in some embodiments a signal data sequence 301 may be received by the predictive maintenance system. The signal data sequence 301 may comprise raw signal data from a device, that corresponds to an operating parameter of the device. For example, the raw signal data may comprise raw alignment data. In some embodiments, the signal data sequence comprises high dimensional data. In some embodiments, the signal sequence data may be received by dimensionality reduction network or autoencoder (AE) network 303. AE network 303 may be a (e.g., deep) neural network for dimensionality reduction. In some embodiments, the AE network 303 may receive the signal data sequence 301 and output a representation of the signal data sequence 301 onto a reduced dimensional latent space. In addition to dimensionality reduction, AE network 303 may in some embodiments de-noise or detect anomalies in the signal data sequence 301. AE network 303 architecture may comprise an encoder to convert data input to embeddings such as health indicator (HI) embeddings 307 and a decoder to reconstruct input data using the embeddings.

[0043] In some embodiments, a relation modeling network 304 for modeling temporal relations within data may receive data from AE network 303. For example, the relation modeling network may comprise a long short term memory (LSTM) network 304 (e.g., a recurrent neural network). In someembodiments, LSTM network 304 may model temporal relations within the reduced dimensional representations of equipment health or HI embeddings 307, derived from AE network 303, and predict these embeddings into the future. For example, the LSTM network 304 may take a sequence of multivariate embeddings of a certain window size w as an input, and may predict n steps into the future, where w and n may be hyperparameters which can be optimized. In this way, a trajectory of a component’s health may be acquired, e.g. HI trajectory data 308. Thus, in contrast to, for example, a health status representing a single data point, a full future trajectory of data representing component or device health may be determined. LSTM network 304 may be any suitable type of recurrent neural network (RNN) for modelling temporal relations within datasets.

[0044] In this way, by providing intermediate outputs (e.g. HI embeddings 307 and / or HI trajectories 308), dimensionality reduction network (e.g., AE network 303) and relation modeling network (e.g., LSTM network 304) may provide data that is more interpretable (e.g. because of the reduced dimensionality) than current state-of-the-art methods.

[0045] In some embodiments, prognostic failure estimator 305 may comprise a learning model that may be trained to estimate a survival function related to the RUL of a device or component based on data from the LSTM network 304, (e.g. HI trajectories 308), and lifetime data of historical maintenance activity, (e.g. maintenance data 302), of the device or component. The prognostic failure estimator may operate on the basis of two assumptions: that a health metric exists that captures component health (e.g. maintenance data 302), and that a trend is known and can be predicted into the future (e.g. HI trajectories 308). Prognostic failure estimator 305 may comprise any suitable learning model such as a tree based model. The model, or survival function estimator, may estimate failure probability based on health indicator values (e.g. HI trajectories 308). A tree based model may provide a visual output compared to other learning models that may be data heavy. Thus, a tree based model may be interpretable by an operator. A tree based model may not require a specific data type to be trained on and thus may be more suitable for multivariate solutions. In some cases, data (e.g. maintenance data 302) may comprise imbalanced data, owing to, for example, operator bias. Advantageously, tree based models are known to provide a balanced model when presented with imbalanced data. Thus, in some embodiments, prognostic failure estimator 305 preferably comprises a tree based learning model.

[0046] In some embodiments, meta-model 306 may estimate an RUL of a device or a component based on an output (e.g. a failure probability) from the LSTM network. In some cases, the meta-model may find a mapping of predicted health onto failure probability to estimate RUL.

[0047] A suitable maintenance action (e.g., component replacement) may be scheduled and / or performed on the apparatus or component thereof, based on the predicted RUL.

[0048] In some embodiments, meta-model 306 may comprise two distinct phases, for example a first distinct phase (e.g. dimensionality reduction / AE network 303) and a second distinct phase (e.g. trajectory prediction / LSTM network 304), wherein the first distinct phase may be associated with a first loss in the meta-model 306 and the second distinct phase may be associated with a second loss in themeta-model 306. In this way, a weighted meta-loss comprising a weighted sum of the first loss and the second loss may be defined. The weighting of the weighted sum may be configurable as appropriate. Advantageously, this may allow for an output of the meta meta-model 306 to be balanced, for example, between interpretability and predictive accuracy.

[0049] The following describes a working example of dimensionality reduction and trajectory prediction in accordance with aspects of the present disclosure and is not an exhaustive approach.

[0050] In the non-limiting example, alignment metrics may be acquired from an alignment tool and passed to an AE network for dimensionality reduction and subsequently an LSTM network for trajectory prediction. In the example, negative skew is observed indicating the presence of a downward trend in the observed component signal. As the sparse regions identified may be indicators of component degradation, a loss function may be used that may adjust a prediction error by the weighted sum of absolute values of the predicted and observed value, which may put more weight on prediction accuracy for lower (i.e. likely degrading) observations. In this way, a symmetric mean absolute percentage error (sMAPE) (Equation 1) may be used for reconstruction loss in training and evaluation for the AE network.

[0051] For the LSTM network, an sMAPE may be used for observed and predicted trajectories as loss function during training, and for evaluation a Frechet distance (FD) (Equation 2) may be used. The FD metric accounts for distance, magnitude, and direction of predicted (P) against observed (Q) trajectories. Computing the FD between two curves may be computationally expensive, thus, sMAPE may preferably be used during training.

[0052] In the present example, the AE network is trained for 100 epochs using an Adam optimizer (a = 0.005) for different numbers of latent dimensions (1,2,4,6,8,10). Reconstructed signals may be compared per-degradation episode against the original observed signal data of that episode.

[0053] The LSTM network may be trained on sliding windows of a random train subset with window size w = 14 and for 150 epochs using an Adam optimizer (a = 0.01). These are purely exemplary values.

[0054] In the present example, both the AE and LSTM networks show improvement over baseline measurements.

[0055] While specific embodiments of the invention have been described above, it will be appreciated that the invention may be practiced otherwise than as described.

[0056] Although specific reference may have 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, for example imprint lithography, and where the context allows, is not limited to optical lithography. In imprint lithography a topography in a patterning device defines the pattern created on a substrate. The topography of the patterning device may be pressed into a layer of resist supplied to the substrate whereupon the resist is cured by applying electromagnetic radiation, heat, pressure or a combination thereof. The patterning device is moved out of the resist leaving a pattern in it after the resist is cured.

[0057] The terms “radiation” and “beam” used herein encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having a wavelength of or about 365, 355, 248, 193, 157 or 126 nm) and extreme ultra-violet (EUV) radiation (e.g., having a wavelength in the range of 1-100 nm), as well as particle beams, such as ion beams or electron beams.

[0058] The term “lens”, where the context allows, may refer to any one or combination of various types of optical components, including refractive, reflective, magnetic, electromagnetic and electrostatic optical components. Reflective components are likely to be used in an apparatus operating in the UV and / or EUV ranges.Other aspects of the invention are set out in the following numbered clauses:1. A computer implemented method of predicting a remaining useful lifetime of an apparatus or component thereof comprising: receiving high dimensional data corresponding to an operating parameter of the apparatus or component thereof; transforming the high dimensional data into health indicator data, comprising low dimensional data indicative of a health status of the apparatus or component thereof; determining temporal relations within the health indicator data to obtain health indicator trajectory data; receiving historical maintenance data of the apparatus or component thereof; determining a failure probability of the apparatus or component thereof based at least in part on the historical maintenance data and the health indicator trajectory data, and; predicting the remaining useful lifetime of the apparatus or component thereof based at least in part on the failure probability.2. The method as set out in clause 1 , wherein the apparatus or component thereof is an exposure apparatus or component thereof.3. The method as set out in clause 2, wherein the high dimensional data comprises raw signal metric data of a component of the exposure apparatus or component thereof.4. The method as set out in clauses 2 or 3, wherein the high dimensional data comprises raw alignment metric data.5. The method as set out in any previous clause, wherein said health indicator trajectory data comprises a future prediction of the low dimensional data.6. The method as set out in any previous clause, wherein the transforming step comprises transforming the data using a dimensionality reduction network.7. The method as set out in clause 6, wherein the dimensionality reduction network comprises an autoencoder network.8. The method as set out in any previous clause, comprising using a recurrent neural network to perform said step of determining temporal relations.9. The method as set out in clause 8, wherein the recurrent neural network is a long short term memory network.10. The method of set out in any previous clause, comprising using a tree based learning model to perform said step of determining a failure probability.11. The method as set out in any previous clause, wherein the historical maintenance data comprises lifetime data of historical maintenance activity and / or run-to-failure history.12. The method as set out in any previous clause, wherein the predicting the remaining useful lifetime comprises mapping the historical maintenance data to the health indicator trajectory data.13. The method as set out in any previous clause, comprising using a meta-model to perform the step of predicting the remaining useful lifetime.14. The method as set out in clause 13, wherein the meta-model comprises: a first distinct phase associated with a first loss in the meta-model; and a second distinct phase associated with a second loss in the meta-model.15. The method as set out in clause 14 comprising: determining a weighted meta-loss based on the first loss and the second loss; and balancing an output of the meta-model based on the weighted meta-loss.16. The method as set out in any previous clause, comprising scheduling and / or performing a maintenance action on said apparatus or component thereof, based on the predicted remaining useful lifetime.17. A computer program comprising program instructions operable to perform the clause of any preceding clause, when run on a suitable apparatus.18. A non-transient computer program carrier comprising the computer program of clause 17.19. A processing arrangement comprising: a non-transient computer program carrier comprising a computer program comprising program instructions operable to perform the method of any of clauses 1 to 16, when run on a suitable apparatus; and a processor operable to run the computer program comprised on said non-transient computer program carrier.20. An exposure apparatus comprising the processing arrangement of clause 19.21. An exposure apparatus as set out in clause 20, said exposure apparatus comprising a lithographic apparatus.22. An exposure apparatus as set out in clause 20, said exposure apparatus comprising a metrology apparatus.

[0059] The breadth and scope of the present invention should not be limited by any of the abovedescribed exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.

Claims

CLAIMS1. A computer implemented method of predicting a remaining useful lifetime of an apparatus or component thereof comprising: receiving high dimensional data corresponding to an operating parameter of the apparatus or component thereof; transforming the high dimensional data into health indicator data, comprising low dimensional data indicative of a health status of the apparatus or component thereof; determining temporal relations within the health indicator data to obtain health indicator trajectory data; receiving historical maintenance data of the apparatus or component thereof; determining a failure probability of the apparatus or component thereof based at least in part on the historical maintenance data and the health indicator trajectory data, and; predicting the remaining useful lifetime of the apparatus or component thereof based at least in part on the failure probability.

2. The method as claimed in claim 1 , wherein the apparatus or component thereof is an exposure apparatus or component thereof.

3. The method as claimed in claim 2, wherein the high dimensional data comprises raw signal metric data of a component of the exposure apparatus or component thereof.

4. The method as claimed in claim 2 or 3, wherein the high dimensional data comprises raw alignment metric data.

5. The method as claimed in any previous claim, wherein said health indicator trajectory data comprises a future prediction of the low dimensional data.

6. The method as claimed in any previous claim, wherein the transforming step comprises transforming the data using a dimensionality reduction network.

7. The method as claimed in claim 6, wherein the dimensionality reduction network comprises an autoencoder network.

8. The method as claimed in any previous claim, wherein the historical maintenance data comprises lifetime data of historical maintenance activity and / or run-to-failure history.

9. The method as claimed in any previous claim, wherein the predicting the remaining useful lifetime comprises mapping the historical maintenance data to the health indicator trajectory data.

10. The method as claimed in any previous claim, comprising scheduling and / or performing a maintenance action on said apparatus or component thereof, based on the predicted remaining useful lifetime.

11. A computer program comprising program instructions operable to perform the method of any preceding claim, when run on a suitable apparatus.

12. A non-transient computer program carrier comprising the computer program of claim 11.

13. A processing arrangement comprising: a non-transient computer program carrier comprising a computer program comprising program instructions operable to perform the method of any of claims 1 to 10, when run on a suitable apparatus; and a processor operable to run the computer program comprised on said non-transient computer program carrier.

14. An exposure apparatus comprising the processing arrangement of claim 13.

15. An exposure apparatus as claimed in claim 14, said exposure apparatus comprising a lithographic apparatus.

16. An exposure apparatus as claimed in claim 14, said exposure apparatus comprising a metrology apparatus.

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