Improvements to lithographic methods and apparatus

Abstract

A method for determining an impact of a variation of a first pupil from a target pupil (for example a dipole) in a first direction within a two-dimensional field is disclosed. The method comprises carrying out the following for a plurality of positions within the field. First, reference and signal measurements are made of a quantity indicative of a position / orientation of an aerial image using a reference pupil and the first pupil. Second, a first error is determined as a difference between the reference measurement and the signal measurement. Third, the first error is corrected for a difference that is attributable to the difference between the reference pupil and the target pupil so as to form a second error. The second error quantifies the difference attributable to the variation of the first pupil from the target pupil across the field.

Description

IMPROVEMENTS TO LITHOGRAPHIC METHODS AND APPARATUS CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority of EP application 24151342.3 which was filed on January 11, 2024 and which is incorporated herein in its entirety by reference. FIELD

[0002] The present invention relates to a method for determining an impact of a variation of an illumination pupil from a target pupil in a first direction within a two-dimensional field on the imaging performance of an imaging system. The imaging system may be a lithographic apparatus and the first direction may correspond to a scanning direction of the lithographic apparatus. The present invention also relates to a method for determining a correction for an imaging system based on the determined impact. The present invention also relates to a lithographic method that uses the correction. The present invention also relates to corresponding apparatus operable to carry out one or more of these methods. The present invention may have particular application to extreme ultraviolet (EUV) lithography. BACKGROUND

[0003] A lithographic apparatus is a machine constructed to apply a desired pattern onto a substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus may, for example, project a pattern from a patterning device (e.g., a mask) onto a layer of radiation-sensitive material (resist) provided on a substrate.

[0004] To project a pattern on a substrate a lithographic apparatus may use electromagnetic radiation. The wavelength of this radiation determines the minimum size of features which can be formed on the substrate. A lithographic apparatus, which uses extreme ultraviolet (EUV) radiation, having a wavelength within the range 4-20 nm, for example 6.7 nm or 13.5 nm, may be used to form smaller features on a substrate than a lithographic apparatus which uses, for example, radiation with a wavelength of 193 nm.

[0005] It is desirable to optimize the imaging performance of a lithographic apparatus. In some known lithographic systems, the projection optics of the lithographic apparatus (also referred to as the lens) may be calibrated, for example to minimize optical aberrations. The calibration may involve a measurement of lens aberrations and then the use of an algorithm, for example a so-called lens model, to determine a configuration of the projection optics which minimizes the aberrations. Such known calibration methods typically quantify lens aberrations as a finite number of Zernike coefficients.

[0006] It may be desirable to provide new, alternative apparatus and / or methods for improving imaging performance within a lithographic apparatus that at least partially addresses one or more problems associated with prior art arrangements whether identified herein or otherwise.SUMMARY

[0007] According to a first aspect of the present disclosure there is provided a method for determining an impact of a variation of a first pupil from a target pupil in a first direction within a two- dimensional field having first and second directions on imaging performance of an imaging system, the method comprising: for at least one position in the second direction within the field, carrying out the following: for a plurality of positions in the first direction in the field, at least one of the plurality of positions in the first direction being disposed in a portion of the field in which the variation of the first pupil from the target pupil is minimal: making a reference measurement of a quantity indicative of a position and / or orientation of an aerial image using a reference pupil; making a signal measurement of a quantity indicative of a position and / or orientation of an aerial image using the first pupil; determining a first error as a difference between the reference measurement and the signal measurement; and determining a second error as the difference between the first error for that position in the first direction and the first error for the at least one of the plurality of positions in the first direction in which the variation of the first pupil from the target pupil is minimal.

[0008] The field may comprise a portion of a field plane that is illuminated with radiation by the imaging system. The field may be elongate comprising a shorter dimension (which may correspond to the first direction) and a longer dimension (which may correspond to the second direction).

[0009] It will be appreciated that as used herein a pupil is intended to mean a spatial intensity distribution of radiation in a pupil plane. It will be further appreciated that the pupil plane is a Fourier transform plane of a field plane. It will be further appreciated that the pupil (or the spatial intensity distribution of radiation in the pupil plane) characterizes the angular intensity distribution of radiation in the field plane.

[0010] The method according to the first aspect may have particular application in a lithographic apparatus. That is, the imaging system may comprise a lithographic apparatus. For example, the lithographic apparatus may comprise a scanning lithographic apparatus. For such embodiments, the first direction may correspond to a scanning direction of the lithographic apparatus and the second direction may correspond to a non-scanning direction of the lithographic apparatus.

[0011] Various different pupils may be used for different purposes within a lithographic apparatus. For example, one type of pupil that may be used for calibration of the imaging system has a generally uniform angular intensity distribution across substantially the entire numerical aperture of the imaging system (e.g. projection optics of the lithographic apparatus). Such a pupil may be referred to as a full conventional pupil. With such a pupil, each point on an object (for example a reticle) is illuminated by a solid cone of radiation.

[0012] However, for imaging (during a lithographic exposure process), typically a different pupil will be used. For example, pupils with less intensity in a central portion of the pupil may improve the contrast of the image (as the image is typically diffraction-limited, at the very limit of the resolution ofthe imaging system). Examples of such pupils include an annular pupil, a dipole pupil and a quadrupole pupil.

[0013] In known lithographic systems, the projection optics (also referred to as the lens) may be calibrated, for example to minimize optical aberrations. Typically, such calibration steps are performed using a pupil (for example a full conventional pupil) that may differ significantly from the pupil(s) used during lithographic exposure (where the pupil may be optimized for a particular lithographic process). The calibration may involve a measurement of lens aberrations and then the use of a lens model to determine a configuration of the projection optics which minimizes the aberrations. Such known calibration methods use the lens aberrations (e.g. as a finite number of Zernike coefficients) but do not directly quantify an impact on imaging performance (for example an impact on contrast of an aerial image or overlay). In addition, such known calibration strategies do not take into account that most lithographic exposures use pupils which differ significantly from a full conventional pupil.

[0014] If the imaging optics have been calibrated using a full conventional pupil then one would expect an aerial image subsequently formed using a full conventional pupil at all positions within the field (at wafer level) to be in a nominal, or desired, position. The inventors have realized that there are, in general, two effects that influence the imaging performance when another pupil (that differs from a full conventional pupil) is used a lithographic apparatus instead.

[0015] First, there will be a shift in a position of the aerial image at wafer level due to the change in the pupil.

[0016] Second, with some known lithographic methods there is generally a variation in the pupil across the field (also referred to as an illumination region). In particular, there is typically a correlation between pupil and position in the reticle-level field in a scanning direction of the lithographic apparatus. This correlation results in undesirable overlay errors and loss of contrast. Furthermore, the correlation is, in general, dependent on the pupil. This second effect may be referred to as a “dynamic pupil through scan”.

[0017] The method according to the first aspect is advantageous since, by using a reference pupil, it allows for these two effects to be separated. In particular, the first error for the at least one of the plurality of positions in the first direction in which the variation of the first pupil from the target pupil is minimal effectively accounts for the shift in a position of the aerial image at wafer level due to the change in the pupil (from the reference pupil to the first pupil). Since the second error is the difference between the first error for each position in the first direction and the first error for the at least one of the plurality of positions in the first direction in which the variation of the first pupil from the target pupil is minimal, the effect of the change of pupil has effectively been removed from the second error. Therefore, the second error effectively quantifies the effect of the “dynamic pupil through scan” on imaging performance. Advantageously, this may allow for the dynamic pupil though scan to be corrected for, for example using a lens model.

[0018] The at least one of the plurality of positions in the first direction that is disposed in a portion of the field in which the variation of the first pupil from the target pupil is minimal may be disposed in a central portion of the field in the first direction.

[0019] In some lithographic systems, the intensity profile of the radiation beam in the scanning direction has a generally trapezoidal shape. That is, the profile shape in the scanning direction may comprise a central portion that is generally uniform or flat and two peripheral portions. The intensity of the radiation in the peripheral portions may vary as a function of distance from the central portion from the value of the central portion to zero. However, in some such known systems, there can be a variation in the pupil over the field (illumination region) in a scanning direction of the lithographic apparatus. In particular, one peripheral portion of the field receives radiation predominantly from a first angular range; the central portion receives radiation from substantially the whole angular range; the other peripheral portion of the field receives radiation predominantly from a second, complementary angular range. For such embodiments, the position in the first direction that is disposed in a portion of the field in which the variation of the first pupil from the target pupil is minimal may be disposed in the central portion of the field in the first direction. For example, it may be disposed on a center-line of the field in the first direction.

[0020] Making a measurement of the quantity indicative of a position and / or orientation of an aerial image may comprise: patterning the radiation using a mark disposed in an object plane; and measuring a position of an image of the mark in the image plane.

[0021] In some embodiments, measuring a position of an image of the mark in the image plane may comprise measuring at least part of the image of the mark using a photosensitive sensor.

[0022] For example, a sensor array (i.e. a camera) may be used to measure at least part of the image of the mark. Alternatively, in other embodiments, a single (or a small number of) photosensitive elements (e.g. photodiodes) may be used.

[0023] Measuring a position of an image of the mark in the image plane may comprise moving the photosensitive sensor relative to the aerial image while monitoring an intensity of radiation detected by the photosensitive sensor.

[0024] For example, the photosensitive sensor may be stepped or scanned (for example in three spatial directions) relative to the aerial image while monitoring an intensity of radiation detected by the photosensitive sensor. The measured position may be a position which maximizes the intensity of radiation detected by the photosensitive sensor.

[0025] In some embodiments, measuring a position of an image of the mark in the image plane may comprise: projecting the image of the mark onto a substrate comprising a layer of photoresist; developing the photoresist to form a patterned photoresist; and measuring the position of the pattern on the patterned photoresist.

[0026] The reference pupil may be a full conventional pupil.

[0027] The method may further comprise a preliminary step of calibrating the imaging system using the reference pupil.

[0028] For example, the step of calibrating the imaging system using the reference pupil may be carried out before other steps of the method. The step of calibrating the imaging system may involve a measurement of lens aberrations and then the use of a lens model to determine a configuration of the projection optics which minimizes the aberrations.

[0029] According to a second aspect of the present disclosure there is provided a method for determining a correction for an imaging system, the method comprising: determining values of one or more parameters of the imaging system that reduce the impact on the imaging performance as determined by the method of the first aspect of the present disclosure.

[0030] That is, the method according to the second aspect may involve determining one or more parameters that generally reduce the second errors across the field. In other words, the second measured errors are transformed into parameters for which there is correction potential within the imaging system. It will be appreciated that the parameters may comprise one or more parameters (position, orientation or shape) of optical elements (e.g. mirrors) within the imaging system and / or the position and / or orientation of a reticle stage and a wafer stage. A lens model may be used to optimize the adjustments to move the optical elements and stages.

[0031] The method according to the second aspect of the present disclosure may further comprise carrying out the method of the first aspect of the present disclosure.

[0032] The method according to the second aspect of the present disclosure may further comprise reading an output of the method of the first aspect of the present disclosure from a storage medium.

[0033] It will be appreciated that determining one or more parameters of the imaging system that reduce the impact on the imaging performance as determined by the method of the first aspect of the present disclosure may use any suitable optimization merit function. For example, in some embodiments, the merit function (which should be minimized) may comprise a sum of the squares of the plurality of determined second errors across the field.

[0034] Determining one or more parameters of the imaging system that reduce the impact on the imaging performance as determined by the method of the first aspect of the present disclosure may comprise determining a set of values of the one or more parameters of the imaging system that minimizes a sum of the squares of the plurality of determined second errors across the field.

[0035] Advantageously, this may result in the optimal configuration of the imaging system.

[0036] Alternatively, in some embodiments, the merit function (which should be minimized) may comprise a weighted sum of the plurality of determined second errors across the field.

[0037] It is possible for the sum of the squares of the plurality of determined second errors across the field to be minimized whilst the individual value of one of the determined second errors is unacceptably large.

[0038] Determining one or more parameters of the imaging system that reduce the impact on the imaging performance as determined by the method of the first aspect of the present disclosure may comprise determining a set of values of the one or more parameters of the imaging system such that all of the plurality of determined second errors are below a threshold value.

[0039] It will be appreciated that determining one or more parameters of the imaging system that reduce the impact on the imaging performance as determined by the method of the first aspect of the present disclosure may comprise any optimization method (for example to minimize a merit function) as desired or required. Examples of such optimization methods may include, for example, any of the following: genetic optimization algorithms; Newton’s method in optimization (also known as the Newton-Raphson method); simulated annealing; a least squares method; and / or a quadratic programming active set method.

[0040] According to a third aspect of the present disclosure there is provided a lithographic method comprising: illuminating a patterning device; using an imaging system, collecting patterned radiation scattered from the patterning device and projecting the patterned radiation onto a substrate so as to form an image of the patterning device on the substrate; wherein the imaging system is configured using values of one or more parameters of the imaging system determined using the method of the second aspect of the present disclosure.

[0041] According to a fourth aspect of the present disclosure there is provided a computer comprising: one or more processors; and storage media, the storage media having instructions to cause the one or more processors to carrying out the method of any one of the first and second aspects of the present disclosure.

[0042] The one or more processors may be configured to store on the storage media: a plurality of second errors determined by the method of the first aspect of the present disclosure; and / or values of one or more parameters of an imaging system determined by the method of the second aspect of the present disclosure.

[0043] According to a fifth aspect of the present disclosure there is provided a computer-readable medium having instructions for carrying out the method of any one of the first and second aspects of the present disclosure.

[0044] The computer-readable medium may be a non-transitory computer-readable medium.

[0045] According to a sixth aspect of the present disclosure there is provided a lithographic apparatus or a lithographic system comprising a controller operable to: perform the method according to any one of the first, second or third aspects of the present disclosure; and / or carry out the instructions of the computer-readable medium of the fifth aspect of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings, in which:- Figure 1 depicts a lithographic system comprising a lithographic apparatus and a radiation source; - Figure 2A schematically shows a generally circular portion of the field facet mirror device of the lithographic system shown in Figure 1, showing a central obscuration portion and two portions which receive radiation; - Figure 2B shows an example shape of a field facet for a faceted field mirror device in a known EUV lithographic apparatus of the form shown in Figure 1; - Figure 3A shows an example of an intensity profile of a radiation beam in a scanning direction that has a generally trapezoidal shape; - Figure 3B shows two variants of the example intensity profile shown in Figure 3A; a first variant of the example intensity profile has larger, shallower peripheral portions whereas a second variant of the example intensity profile has smaller, steeper peripheral portions; - Figure 4 shows: an example slit profile; the pupil at three different positions in the scanning direction through the slit profile; and an illustration of the aerial image formed by the projection system at these three different positions (bottom) in the scanning direction through the slit profile; - Figure 5 schematically shows the steps of a method for determining an impact of a variation of an illumination pupil from a target pupil within a two-dimensional field on imaging performance of an imaging system (for example the projection system of the lithographic apparatus shown in Figure 1) according to an embodiment of the present disclosure; - Figure 6 schematically illustrates how a field of an imaging system may be sampled when carrying out the method shown in Figure 5; - Figure 7 schematically shows a method for determining a correction for an imaging system (for example the projection system of the lithographic apparatus shown in Figure 1), which reduces an impact on the imaging performance as determined by the method shown in Figure 5; and - Figure 8 shows a lithographic method which uses an imaging system that is configured using values of one or more parameters determined using the method shown in Figure 7. DETAILED DESCRIPTION

[0047] Figure 1 shows a lithographic system comprising a radiation source SO and a lithographic apparatus LA. The radiation source SO is configured to generate an EUV radiation beam B and to supply the EUV radiation beam B to the lithographic apparatus LA. The lithographic apparatus LA comprises an illumination system IL, a support structure MT configured to support a patterning device MA (e.g., a mask), a projection system PS and a substrate table WT configured to support a substrate W.

[0048] The illumination system IL is configured to condition the EUV radiation beam B before the EUV radiation beam B is incident upon the patterning device MA. Thereto, the illumination system IL may include a facetted field mirror device 10 and a facetted pupil mirror device 11. The facetedfield mirror device 10 and faceted pupil mirror device 11 together provide the EUV radiation beam B with a desired cross-sectional shape and a desired intensity distribution. The illumination system IL may include other mirrors or devices in addition to, or instead of, the faceted field mirror device 10 and faceted pupil mirror device 11.

[0049] After being thus conditioned, the EUV radiation beam B interacts with the patterning device MA. As a result of this interaction, a patterned EUV radiation beam B’ is generated. The projection system PS is configured to project the patterned EUV radiation beam B’ onto the substrate W. For that purpose, the projection system PS may comprise a plurality of mirrors 13, 14 which are configured to project the patterned EUV radiation beam B’ onto the substrate W held by the substrate table WT. The projection system PS may apply a reduction factor to the patterned EUV radiation beam B’, thus forming an image with features that are smaller than corresponding features on the patterning device MA. For example, a reduction factor of 4 or 8 may be applied. Although the projection system PS is illustrated as having only two mirrors 13, 14 in Figure 1, the projection system PS may include a different number of mirrors (e.g. six or eight mirrors).

[0050] The substrate W may include previously formed patterns. Where this is the case, the lithographic apparatus LA aligns the image, formed by the patterned EUV radiation beam B’, with a pattern previously formed on the substrate W.

[0051] A relative vacuum, i.e. a small amount of gas (e.g. hydrogen) at a pressure well below atmospheric pressure, may be provided in the radiation source SO, in the illumination system IL, and / or in the projection system PS.

[0052] The radiation source SO shown in Figure 1 is, for example, of a type which may be referred to as a laser produced plasma (LPP) source. A laser system 1, which may, for example, include a CO2 laser, is arranged to deposit energy via a laser beam 2 into a fuel, such as tin (Sn) which is provided from, e.g., a fuel emitter 3. Although tin is referred to in the following description, any suitable fuel may be used. The fuel may, for example, be in liquid form, and may, for example, be a metal or alloy. The fuel emitter 3 may comprise a nozzle configured to direct tin, e.g. in the form of droplets, along a trajectory towards a plasma formation region 4. The laser beam 2 is incident upon the tin at the plasma formation region 4. The deposition of laser energy into the tin creates a tin plasma 7 at the plasma formation region 4. Radiation, including EUV radiation, is emitted from the plasma 7 during de- excitation and recombination of electrons with ions of the plasma.

[0053] The EUV radiation from the plasma is collected and focused by a collector 5. Collector 5 comprises, for example, a near-normal incidence radiation collector 5 (sometimes referred to more generally as a normal-incidence radiation collector). The collector 5 may have a multilayer mirror structure which is arranged to reflect EUV radiation (e.g., EUV radiation having a desired wavelength such as 13.5 nm). The collector 5 may have an ellipsoidal configuration, having two focal points. A first one of the focal points may be at the plasma formation region 4, and a second one of the focal points may be at an intermediate focus 6, as discussed below.

[0054] The laser system 1 may be spatially separated from the radiation source SO. Where this is the case, the laser beam 2 may be passed from the laser system 1 to the radiation source SO with the aid of a beam delivery system (not shown) comprising, for example, suitable directing mirrors and / or a beam expander, and / or other optics. The laser system 1, the radiation source SO and the beam delivery system may together be considered to be a radiation system.

[0055] Radiation that is reflected by the collector 5 forms the EUV radiation beam B. The EUV radiation beam B is focused at intermediate focus 6 to form an image at the intermediate focus 6 of the plasma present at the plasma formation region 4. The image at the intermediate focus 6 acts as a virtual radiation source for the illumination system IL. The radiation source SO is arranged such that the intermediate focus 6 is located at or near to an opening 8 in an enclosing structure 9 of the radiation source SO.

[0056] Although Figure 1 depicts the radiation source SO as a laser produced plasma (LPP) source, any suitable source such as a discharge produced plasma (DPP) source or a free electron laser (FEL) may be used to generate EUV radiation.

[0057] The faceted field mirror device 10 and the faceted pupil mirror device 11 are arranged to provide a desired angular distribution of the radiation beam B, at the patterning device MA, as well as a desired uniformity of radiation intensity at the patterning device MA. The illumination system IL may be arranged to provide Kohler illumination of an illumination region IR (that the patterning device MA may be moved through during exposure of a substrate W) such that the plasma at the plasma formation region 4 is out of focus (and therefore does not influence properties of the radiation beam) at the patterning device MA and in the conjugate plane of the substrate W. As used herein, the illumination region IR may also be referred to as the illumination slit or the slit.

[0058] The illumination region IR is in a field plane in which the reticle MA is disposed during a lithographic exposure. Therefore, the illumination region IR may be referred as a reticle-level or object- level illumination region IR. It will be appreciated that projection system PS forms an image IR’ of the illumination region IR in the plane of the substrate W. The image IR’ of the illumination region IR in the plane of the substrate W may be referred to as a wafer-level or image-level illumination region IR’. As used herein, the wafer-level illumination region IR’ may also be referred to as the slit.

[0059] In lithography, the illumination of the patterning device MA is very important. In particular, it is desirable to control the angular distribution of the radiation at the illumination region IR where the patterning device MA is exposed to radiation. This angular distribution of the radiation is conveniently described in terms of the spatial distribution of the radiation in an illumination pupil plane, which describes how a cone of light that is incident on each point on the patterning device MA is filled. In an ideal conventional illumination mode, the radiation uniformly fills a circular region of the illumination pupil plane centred on the optical axis such that each point on the patterning device is illuminated by a solid cone of light. Note that, in practice, such an ideal conventional illumination mode (with a truly uniform pupil fill across the illumination pupil plane) may not be achievable using the illuminationsystem IL. However, a close approximation of such a conventional illumination mode may be achieved (for example by using diffusive optics at reticle level, for example on the support structure MT). It will be appreciated that as used herein a conventional illumination mode should be understood to cover both the ideal conventional illumination mode and close approximations thereof. In dipole illumination mode, the radiation fills two regions of the illumination pupil plane that are spaced apart from, and on opposite sides to, the optical axis. Many other illumination modes are known. In principle, an optimum illumination mode can be defined to image a given pattern under given conditions. Therefore, it may be desirable to provide flexibility in the illumination mode that can be achieved by the lithographic apparatus LA. That is, it may be desirable for the illumination system IL to be configurable in any one of a plurality of configurations, each one of the plurality of configurations projecting the radiation beam B onto the reticle MA with a different illumination mode.

[0060] The uniformity of the illumination is also very important. The uniformity of illumination affects the uniformity of dose to which the target portion of the substrate W is exposed, which affects critical dimension uniformity (CDU), an important measure of the uniformity of the dimension of features formed on the substrate W. For example, it may be desirable to maintain a desired spatial intensity distribution of radiation across the illumination region IR. As used herein the spatial intensity distribution of radiation across the illumination region IR may be referred to as the slit profile.

[0061] The collector 5 is generally of the form of a concave mirror, which is arranged to collect the radiation which is emitted from the plasma formation region 4 into a solid angle subtended by the collector 5. This radiation is reflected and focused at the intermediate focus 6. As a result, within the housing, the radiation beam B is generally of the form of a converging cone of radiation, which converges at the intermediate focus 6, an outer edge of this cone being indicated in Figure 1 by two lines. Downstream of the intermediate focus 6, the radiation beam B is generally of the form of a diverging cone of radiation, which is incident on the generally circular field facet mirror device 10. However, the radiation source SO may comprise an obscuration that will block a portion of this radiation cone such that there will be some portion of the diverging cone of radiation that will not receive radiation from the collector 5. For example, the radiation source SO may comprise a shield (not shown) which may be arranged to prevent the laser beam 2 from propagating through the opening 8 and into the lithographic apparatus LA (where it may damage optical components). This shield may be supported by the enclosing structure via a support (not shown). Together, the shield and the support form an obscuration of the radiation source SO. Therefore, as indicated schematically in Figure 2A a generally circular portion 20 of the field facet mirror device 10 may comprise a central portion 22, which coincides with the obscuration of the radiation source SO and does not receive any radiation, and two portions 24, 26 which do receive radiation. It will be appreciated that this is schematic and that the obscuration may have any shape or configuration.

[0062] The total amount of radiation energy delivered by the lithographic apparatus LA to a particular target area on the surface of the substrate W is referred to as the dose. The desired dose to bedelivered to target areas on a substrate W (for example a dose that achieves a change or curing of a photoresist on the surface of the substrate W) may differ depending on the sensitivity of the photoresist. For example, in the case of a highly sensitive photoresist, a relatively small dose (e.g.20 mJ / cm2) may be desired in order to image the pattern onto the substrate W. However, in the case of a less sensitive photoresist, a larger dose (e.g.70 mJ / cm2) may be desired.

[0063] The radiation, e.g. EUV radiation, may be delivered in pulses, for example at a frequency in the order of 50 kHz. In the case of a pulsed radiation beam, the total dose delivered to the substrate is the sum of the individual doses delivered in each pulse.

[0064] If a target area on a substrate W receives a dose which differs from the desired dose, this is referred to as a dose error. In particular, the dose error is the difference between the actual dose received by a target area and the desired dose. A dose error may be ‘positive’ (i.e. in the event that a target area receives a larger dose than the desired dose) or ‘negative’ (i.e. in the event that a target area receives a smaller dose than the desired dose). Any dose error will result in some printing errors as some parts of the resist will receive an insufficient dose and some parts will receive an excess dose. A negative dose error may be corrected by providing an additional dose in order to compensate the previous shortfall. However, it may not be possible to correct a positive dose error since an excessive dose (e.g. leading to overexposure) has already been given, the change in the photoresist generally being irreversible. This may result in irreparable damage to the substrate W.

[0065] It may be desirable, therefore, to operate the lithographic system such that none of the target areas receive an excessive dose. It will be appreciated that a certain level of positive dose error may be considered to be acceptable in accordance with manufacturing tolerances. For example, a positive dose error of up to 1%, in particular up to 0.5% may be considered to be acceptable, depending on requirements. An excessive dose as referred to herein means a dose which falls outside of the acceptable tolerance level.

[0066] In practice, the output power of a pulsed radiation source SO will vary with time (under either open-loop or closed-loop control). If the power of an individual pulse is higher or lower than a nominal or desired output power for each pulse then this will contribute to a dose error for any parts of the substrate W that receive that pulse. The fewer pulses received by each part of the substrate W, the greater the effect of such an individual pulse power error will be on the total dose. In some cases, the available open-loop power may be instantaneously lower than the requested operating power, resulting in too low a dose being delivered at that moment. In order to reduce the likelihood of too small a dose being delivered (also referred to as a negative dose error), the nominal operating power may be set such that it is lower than the maximum output power. This may allow for the negative dose error to be at least partially corrected by increasing the power of one or more subsequent pulses.

[0067] However, if the nominal operating power is set too low, the throughput of the system may be negatively affected. It will be appreciated, therefore, that in order to improve the throughput of the lithographic apparatus it may be desirable to increase the nominal output power of the radiation sourceSO. Therefore, there is a tension between limiting the effect of negative dose errors on the overall total dose and the throughput of the lithographic apparatus.

[0068] Even when controlling the radiation source using a closed loop control, there is a chance that at least one target area of the substrate W receives an actual dose of radiation which is less than the desired dose. This can be compensated for by a second, subsequent exposure pass. In other words, if the system fails to deliver a desired dose to a target area on the substrate W at a given instant during a first time period, that target area may be re-exposed at a later step in order to deliver the missing dose. Such re-exposures may be referred to as die repair.

[0069] The dose margin represents a difference between a maximum available output power of the radiation source SO and a nominal operating power of the radiation source SO and may be determined in dependence on a setpoint value.

[0070] It will be appreciated that the maximum available output power (open-loop power) and / or an operating power (closed-loop power) of the radiation source SO may be not constant but rather may be subject to some variations (for example, for a pulsed radiation source SO there may be pulse-to- pulse variations). It will therefore be understood that the dose margin may represent a difference between the average or nominal maximum available output power of the radiation source SO and an average or nominal operating power of the radiation source SO (rather than being based on instantaneous powers).

[0071] For example, if a dose margin of 10% is used, the output power may be reduced by 10% relative to the average open-loop power in order to give the nominal operating power (which is therefore 90% of the average open-loop power). This allows better controllability of the amount of radiation delivered to the substrate W, in particular since, on a pulse-by-pulse basis, in general a requested operating power may be increased or decreased (relative to nominal operating power) according to requirements. It will, of course, be appreciated that if the radiation source SO were operated at maximum available output power as nominal operating power, in general, there would be no scope to request an increased operating power relative to the nominal operating power in any circumstance (and therefore no facility to compensate for negative dose errors).

[0072] A known faceted field mirror device 10 used in an EUV lithographic apparatus of the type shown in Figure 1 is now described with reference to Figures 2A and 2B.

[0073] In known EUV lithographic apparatus, the faceted field mirror device 10 comprises a plurality of field facets. In particular, in such known EUV lithographic apparatus, the portions 24, 26 of the faceted field mirror device 10 that receive radiation from the radiation source SO are provided with a plurality of field facets. For example, the portions 24, 26 of the faceted field mirror device 10 that receive radiation from the radiation source SO may be provided with of the order of 100 field facets (for example 300 field facets). In a plane of the faceted field mirror device 10 each field facet may have a curved shape 28, as shown in Figure 2B. In general, in the plane of the faceted field mirror device 10 each field facet may have an elongate shape having a longer dimension in an x-direction and a shorterdimension in a y-direction. Each field facet comprises a mirror that may be arranged to image the intermediate focus 6 onto the faceted pupil mirror device 11. To achieve this, the field facets may, for example, be concave.

[0074] The faceted pupil mirror device 11 comprises a plurality of pupil facets. The faceted pupil mirror device 11 is arranged to project an image of each field facet of the faceted field mirror device 10 onto an illumination region IR (also referred to as the slit or illumination slit) at the patterning device MA. The illumination system IL is configured so that each field facet is imaged on the illumination region IR in an overlapping manner. The overlap of the images of the field facets at least partially evens out irregularities in the radiation beam B provided by the radiation source SO.

[0075] The illumination region IR may be curved or straight. In general, in a scanning lithographic apparatus LA, the illumination region IR is elongate having a longer dimension and a shorter dimension. The shorter dimension may coincide with a scanning direction of the support structure MT and the longer dimension may coincide with a non-scanning direction. The illumination region IR may be curved or straight. The illumination region IR is indicated in Figure 1, which shows the patterning device in cross section. The longer dimension (in the x-direction) of the illumination region IR is perpendicular to the plane of Figure 1 and the shorter dimension (in the y-direction) of the illumination region IR lies in the plane of Figure 1.

[0076] In some known lithographic apparatus and methods, a substrate W (for example a resist- coated silicon wafer) is exposed to patterned radiation B’ during a scanning exposure process. A radiation beam B illuminates an illumination region IR (also known as “illumination slit” or just “slit”) while a patterning device MA (for example a reticle) is scanned through the illumination region in a scanning direction. Typically the radiation comprises pulsed radiation. Radiation scattered from the patterning device MA is collected by imaging optics PS and projected onto a substrate W so as to form an image of the patterning device MA in a plane of the substrate W. The substrate W is also scanned so that the image is stationary with respect to the substrate W.

[0077] The pulsed radiation source SO will, in general, have instabilities (pulse to pulse energy variations) and occasionally will have energy drop outs (one or more pulses with energy significantly less than a target or nominal pulse energy). As explained above, the radiation B may be operated at a lower power than a maximum achievable power and a controller of the radiation source SO may be operable to compensate for drops in source energy using this reserved power capability (referred to as a “dose margin”).

[0078] It is important for each part of the substrate W that receives radiation to receive substantially the same dose of radiation (for example to maintain critical dimension uniformity CDU). However, since the radiation beam B is pulsed, in general, not all parts of the substrate W will receive exactly the same number of pulses. Typically, the intensity profile of the radiation beam B in the scanning direction has a generally trapezoidal shape. An example of such an intensity profile 30 is shown in Figure 3A. This shape can help with accurate dose control. Furthermore, the trapezoidalshape defines the robustness of the lithographic apparatus LA dose performance to radiation source SO instabilities and energy drop outs, as now discussed. An intensity profile of the radiation beam B in the scanning direction with a shallower slope is more robust to source energy drop out and can improve the correctability of the die repair.

[0079] The example profile shape 30 in the scanning direction shown in Figure 3A has a generally trapezoidal shape. That is, the profile shape 30 in the scanning direction comprises a central portion 32 that is generally uniform or flat and two peripheral portions 34a, 34b. The intensity of the radiation in the peripheral portions 34a, 34b varies as a function of distance from the central portion 32 from the value of the central portion 32 to zero. A gradient, and / or extent, of the peripheral portions 34a, 34b may characterize how robust the lithographic apparatus LA is to energy variations and energy drop outs of the radiation source SO. Two variants of the example intensity profile 30a, 30b are shown in Figure 3B; a first variant of the example intensity profile 30a has larger, shallower peripheral portions 34a, 34b whereas a second variant of the example intensity profile 30b has smaller, steeper peripheral portions 34a, 34b. Larger, shallower peripheral portions 34a, 34b are more robust to energy variations and energy drop outs of the radiation source SO whereas smaller, steeper peripheral portions 34a, 34b are less robust to energy variations and energy drop outs of the radiation source SO.

[0080] In one known EUV lithographic system, a laser-produced plasma (LPP) radiation source SO illuminates a first optical component 10 with EUV radiation. The first optical component 10 comprises a plurality of facet mirrors, each being generally concave and having a shape that is similar to that of the illumination region IR. The radiation from all of the facet mirrors is directed to the illumination region IR via a second optical component 11 such that an image of each facet mirror is formed, the plurality of images generally overlapping so as to achieve a desired intensity distribution (e.g. the trapezoidal profile). In a central portion 32 of the illumination region IR (in the scanning direction), substantially all of the field facet images overlap and intensity is at maximum. In the peripheral portions 34a, 34b of the illumination region IR (in the scanning direction), edges of the field facet images are staggered so as to achieve an intensity fall-off and realize the trapezoidal intensity profile 30.

[0081] It has been proposed to use a faceted field mirror device 10 having a large number of individually directable or movable reflective optical elements so as to provide better control over the illumination modes of the lithographic apparatus LA. It has been further proposed to use a faceted pupil mirror device 11 having a large number of individually directable or movable reflective optical elements so as to provide better control over the illumination modes of the lithographic apparatus LA.

[0082] Each of the independently movable reflective optical elements may comprise a micro- electromechanical system (MEMS). Therefore, the faceted field mirror device 10 and / or the faceted pupil mirror device 11 may be considered to comprise a MEMS micro-mirror array.

[0083] Each of the reflective optical elements may, for example, be a multilayer mirror. Each of the reflective optical elements may be configured such that its orientation can be controlled about oneor two axes so that a direction to which it directs radiation can be controlled. For example, each of the reflective optical elements may have one or more actuators by which the reflective optical element can be rotated about an axis or two orthogonal axes. Thereby, each of the reflective optical elements can be controlled to direct radiation in a specific direction.

[0084] The faceted field mirror device 10 may comprise of the order of 100,000 independently movable reflective optical elements. These reflective optical elements may substantially cover the portions 24, 26 of the faceted field mirror device 10 that receive radiation from the radiation source SO (see Figure 2A and accompanying discussion).

[0085] In some known lithographic apparatus, such a faceted field mirror device 10 comprising a MEMS micro-mirror array is used as follows. The two-dimensional array of independently movable reflective optical elements provided on the faceted field mirror device 10 may be considered to comprise a plurality of groups of reflective optical elements. Each group of reflective optical elements may comprise a plurality of adjacent independently movable reflective optical elements on the faceted field mirror device 10. Each of the plurality of groups of reflective optical elements may be referred to as a cluster of reflective optical elements.

[0086] Each group of reflective optical elements may be configured generally to replace one of the field facets discussed above. For example, each group may cover a region of the faceted field mirror device 10 that generally corresponds to the shape of a field facet of the known faceted field mirror device 10 discussed above (for example a region having a shape generally the same as the shape 28 shown in Figure 2B). It will be appreciated that each of the reflective optical elements may be generally square or rectangular in shape and therefore if the group is arranged as a generally curved elongate region of the faceted field mirror device 10 (similar to the shape 28 shown in Figure 2B), the shape may have jagged or pixelated edges along the curved sides of the shape. Furthermore, the orientations of the reflective optical elements within each group may be configured so as to provide an equivalent optical power or concave shape to a field facet of an existing faceted field mirror device 10.

[0087] Each of the plurality of groups may be referred to as a field facet mirror or a virtual field facet mirror. There may be of the order of 100, for example 300, groups of independently movable reflective optical elements. Each group may comprise of the order of 1000 independently movable reflective optical elements. For example, in one embodiment each group may comprise 10 rows of independently movable reflective optical elements, each row having 100 independently movable reflective optical elements.

[0088] The plurality of adjacent independently movable reflective optical elements in each group substantially cover a continuous region of the faceted field mirror device 10. It will be appreciated that this may mean that any gaps between adjacent reflective optical elements may be minimal.

[0089] A shape of a continuous region of the first optical component covered by the plurality of adjacent independently movable reflective optical elements in a group of independently movable reflective optical elements may be referred to as a shape of that group of independently movablereflective optical elements. The shape of each of the groups of independently movable reflective optical elements may generally correspond to a shape of the illumination region IR (in a similar manner to the shape of each of the field facets described above generally corresponding to a shape of the illumination region IR).

[0090] Each of the plurality of groups of independently movable reflective optical elements may have substantially the same size and shape. In some embodiments, the shape of each of the plurality of groups may be curved. In some embodiments, each of the plurality of groups may be generally rectangular in shape.

[0091] This known illumination system can achieve a trapezoidal slit profile in the scanning direction (y), however, there is typically a variation in the pupil over the illumination region IR in a scanning direction of the lithographic apparatus LA. In particular, one peripheral portion 34a of the slit receives radiation predominantly from a first angular range; the central portion 32 receives radiation from substantially the whole angular range; the other peripheral portion 34b of the slit receives radiation predominantly from a second, complementary angular range.

[0092] This is illustrated in Figure 4. Figure 4 shows an example slit profile 40 in the scanning direction (y) which is generally of the form of the example intensity profiles 30, 30a, 30b shown in Figures 3A and 3B in that it has a generally flat central portion although the two peripheral portions are not linear. Figure 4 also shows the pupil 42a, 42b, 42c at 3 different positions in the scanning direction through the profile 40 when a target illumination mode comprises two dipoles separated in a y-direction (a direction in the pupil plane that corresponds to the scanning direction in the plane of the reticle MA). The pupils 42a, 42c are from a peripheral portion of the profile 40 and pupil 42b is from a central portion of the profile 40. It can be clearly seen from pupils 42a, 42c that the peripheral portions of the illumination region IR each receives radiation predominantly from two different, complementary angular ranges. This is not telecentric illumination, i.e. a net direction of the total radiation received by these parts of the wafer-level illumination region is not perpendicular to a plane of the substrate W. It can also be seen from Figure 4, from pupil 42b, that the central portion of the illumination region IR receives radiation from substantially the whole pupil plane (i.e. dipole illumination). This is telecentric illumination, i.e. a net direction of the total radiation received by these parts of the wafer-level illumination region is generally perpendicular to a plane of the substrate W. It will be appreciated that, in general, each point in the target region receives radiation from a range of angles and may therefore be considered to receive a plurality of contributions, each contribution defined by a different element of solid angle and having a constant direction vector. The net direction of the total radiation received by a point in the target region of the substrate may be defined as a vector sum of the direction vectors of each contribution to that point, the sum being weighted by the energy received by each such contribution.

[0093] Figure 4 also shows an illustration of the aerial image formed by the projection system at the three different positions in the scanning direction through the profile 40 that correspond to the threedifferent pupils 42a, 42b, 42c. A first one of the three different positions corresponds to a position in a first peripheral portion of the profile 40; a second one of the three different positions corresponds to a position in a central portion of the profile 40; and a third one of the three different positions corresponds to a position in a second peripheral portion of the profile 40.

[0094] It can be seen that at the second position the illumination is generally dipole illumination and this is telecentric. As a result, any defocus of the aerial image should not contribute to overlay errors. It can also be seen that at the first and third positions the illumination is almost monopole illumination and this is non-telecentric such that the aerial image is rotated. As a result, any defocus of the aerial image will, in general, contribute to an overlay error in the scanning direction of the lithographic apparatus.

[0095] This partial pupil provided to the peripheral portions of the slit may be referred to as a “dynamic pupil” or a “dynamic pupil through slit”. This correlation results in undesirable overlay errors. Furthermore, the correlation becomes greater (and, therefore, overlay errors become larger) if an extent of the peripheral portions is increased.

[0096] Embodiments of the present disclosure relate to a method for determining an impact of a variation of an illumination pupil from a target pupil in a first direction within a two-dimensional field having first and second directions on imaging performance of an imaging system. For example, the method may be for determining an impact of a dynamic pupil (variation of an illumination pupil in the scanning direction of a lithographic apparatus) on imaging performance of an imaging system.

[0097] A method 100 for determining an impact of a variation of an illumination pupil from a target pupil in a first direction within a two-dimensional field having first and second directions on imaging performance of an imaging system (for example projection system PS) is now described with reference to Figures 5 and 6.

[0098] Figure 5 schematically shows the steps of the new method 100 and Figure 6 schematically illustrates how a field 200 of an imaging system may be sampled.

[0099] The method 100 comprises sampling the two-dimensional field 200 of the imaging system in a plurality of positions. The field 200 may comprise a portion of a field plane that is illuminated with radiation by the imaging system (for example the projection system PS shown in Figure 1). The field 200 may be elongate comprising a shorter dimension (which may correspond to a first direction) and a longer dimension (which may correspond to a second direction). For example, the field 200 may be the wafer-level illumination region IR’ of the lithographic apparatus LA, i.e. a region in the plane of the substrate W which is conjugate to the illumination region IR in the plane of the reticle MA. Therefore, as shown in Figure 6, the field in this embodiment is generally the same shape as the curved shape 28 shown in Figure 2B. [000100] The field 200 is sampled at at least one position in the non-scanning direction (x), which may be referred to as a second direction. In general, ^ positions in the non-scanning direction are sampled. The positions in the non-scanning direction that are sampled may be referred to as ^^, where^ = 1, … ^. For the or each position in the non-scanning position, ^^, the field 200 is sampled at aplurality of different positions in the scanning direction (y), which may be referred to as a first direction. In general, for each position in the non-scanning direction, ^^, ^ positions in the scanning direction aresampled. The positions in the scanning direction that are sampled may be referred to as ^^ , where ^ =1, … ^. In general, unless stated otherwise, in the following the index ^ will refer to a position in thenon-scanning direction and the index ^ will refer to a position in the scanning direction. [000101] At least one of the plurality of positions in the scanning direction ^^should be disposed in a portion of the field 200 in which the variation of the first pupil from the target pupil is minimal. In the following, a position in the scanning direction that is disposed in a portion of the field 200 in which the variation of the first pupil from the target pupil is minimal will be referred to as ^constand, in general, a quantity ^ that is evaluated at this position ^constin the scanning direction will be referred to as ^const. For example, for embodiments wherein the method 100 is being used to determine an impact of the dynamic pupil described above, at least one at of the plurality of positions in the scanning direction should be disposed in the central portion 32 of the intensity profile 30 in the scanning direction, since these positions receive radiation from substantially the whole angular range (i.e. the pupil at these points should correspond to a target pupil). [000102] A non-limiting example of such sampling is shown schematically in Figure 6, which shows 35 field points (each point represented by a cross). With this example sampling, the field IR’ is sampled at seven positions in the non-scanning direction and, for each of these seven positions, the field is sampled at a five different positions in the scanning direction. The seven positions in the non-scanningdirection may be referred to as ^^, where ^ = 1, 2, 3, 4, 5, 6 or 7. The five positions in the scanningdirection may be referred to as ^^ , where ^ = 1, 2, 3, 4 or 5. Note that one of the five different positionsin the scanning direction lies on a centre-line 202 of the field 200 in the scanning direction (y). The position in the scanning direction that lies on the centre-line 202 of the field 200 in the scanningdirection may be referred to as ^^ in the following. For this embodiment, it may be that ^const = ^^.[000103] The method 100 shown schematically in Figure 5 shows the steps of the method that are carried out for each position ^^in the non-scanning direction that is sampled. Therefore, it will be appreciated that for the example sampling shown in Figure 6, these steps are repeated for each of the seven positions ^^in the non-scanning direction. [000104] For the or each position ^^in the non-scanning direction, the method 100 comprises a step 110 of: for each of the plurality of positions ^^in the scanning direction making a reference measurement ^^of a quantity that is indicative of a position and / or orientation of an aerial image (x, y, z) using a reference pupil. [000105] It will be appreciated that as used herein a pupil is intended to mean a spatial intensity distribution of radiation in a pupil plane. It will be further appreciated that the pupil plane is a Fourier transform plane of a field plane. It will be further appreciated that the pupil (or the spatial intensitydistribution of radiation in the pupil plane) characterizes the angular intensity distribution of radiation in the field plane. [000106] The reference pupil may be a full conventional pupil. As discussed above, such a pupil has a generally uniform angular intensity distribution across substantially the entire numerical aperture of the imaging system (e.g. projection optics PS of the lithographic apparatus LA). With such a pupil, each point on an object (for example the plane of the reticle MA) is illuminated by a solid cone of radiation. [000107] For the or each position ^^in the non-scanning direction, the method 100 comprises a step 120 of: for each of the plurality of positions ^^in the scanning direction making a signal measurement ^^of a quantity that is indicative of a position and / or orientation of an aerial image (x, y, z) using the illumination pupil (also referred to as the first pupil). [000108] The illumination pupil may be a pupil that is used for imaging (during a lithographic exposure process). For example, the illumination pupil may be an annular pupil, a dipole pupil or a quadrupole pupil. [000109] For the or each position ^^in the non-scanning direction, the method 100 comprises a step 130 of: for each of the plurality of positions ^ in the scanning direction determ (^) ^ ining a first error ^^as a difference between the reference measurement ^^and the signal measurement ^^. That is, the first error ^(^) ^ is given by: ^(^) ^= ^^ − ^^ . (1)[000110] For the or each position ^^in the non-scanning direction, the method 100 comprises a step 140 of: for each of the plurality of positions ^^in the scanning direction determining a second error ^(^) as the differen (^) ^ ce between the first error ^^for that position ^^in the first direction and the first error ^ (^) constfor the position ^constin the scanning direction in which the variation of the first pupil from the is minimal. That is, the (^)second error ^^is given by: ^(^) ( ^= ^^) ^− ^(^) const ,(2)and for the example sampling shown in Figure 6, the second error ^(^) ^ is given by: ^(^) (^) ( ^= ^^) ^− ^^ .(3)[000111] In known lithographic systems, the projection optics (also referred to as the lens or projection system PS) may be calibrated, for example to minimize optical aberrations. Typically, such calibration steps are performed using a pupil (for example a full conventional pupil) that may differ significantly from the pupil(s) used during lithographic exposure (where the pupil may be optimized for a particular lithographic process). The calibration may involve a measurement of lens aberrations and then the use of a lens model to determine a configuration of the projection optics which minimizes the aberrations. Such known calibration methods use the lens aberrations (e.g. as a finite number of Zernike coefficients) but do not directly quantify an impact on imaging performance (for example an impact on contrast of an aerial image or overlay). In addition, such known calibration strategies do not take into account that most lithographic exposures use pupils which differ significantly from a full conventional pupil. [000112] If the imaging optics (for example the projection system PS) have been calibrated using a full conventional pupil then one would expect an aerial image subsequently formed using a full conventional pupil at all positions within the field (at wafer level) to be in a nominal, or desired, position. The inventors have realized that there are, in general, two effects that influence the imaging performance when another pupil (that differs from a full conventional pupil) is used a lithographic apparatus instead. [000113] First, there will be a shift in a position of the aerial image at wafer level due to the change in the pupil. [000114] Second, as described above with reference to Figure 4, with some known lithographic methods there is generally a variation in the pupil across the field (also referred to as an illumination region). In particular, there is typically a correlation between pupil and position in the reticle-level field in a scanning direction of the lithographic apparatus. This correlation results in undesirable overlay errors and loss of contrast. Furthermore, the correlation is, in general, dependent on the pupil. As stated above, this second effect may be referred to as a “dynamic pupil”. [000115] The method 100 shown in Figure 5 is advantageous since, by using a reference pupil, it allows for these two effects to be separated. In particular, the first error ^ (^) constfor the position ^constin the scanning direction in which the variation of the illumination pupil from the target pupil is minimal effectively accounts for the shift in a position of the aerial image at wafer level due to the change in the pupil (from the reference pupil to the illumination pupil). Since the second error ^(^) ^ is the difference between the first error ^(^) (^) ^ for each position in the first direction and the first error ^constfor the position ^constin the scanning direction in which the variation of the illumination pupil from the target pupil is minimal, the effect of the change of pupil has effectively been removed from the second error E(^). Therefore, the second error ^(^) ^ effectively quantifies the effect of the “dynamic pupil” on imagingperformance. Advantageously, this may allow for the dynamic pupil through scan to be corrected for, for example using a lens model. [000116] An additional benefit of the method 100 shown in Figure 5 is that allows for a combination of adjustments (of the lithographic apparatus LA) to be identified than can subsequently be simultaneously controlled regardless of whether the steps of method 100 have been performed immediately preceding such control. Such a combination of adjustments may be referred to as a “control knob”. Such a control knob could be used on request, even without the measurement steps of the method 100 having been performed immediately before. Additionally or alternatively, such a control knob may be used in the system with different magnitude to deal with, for example, situations where the measurement is not easily performed. Such a control knob may be used to overcorrect for changes due to the dynamic pupil. For example, the method 100 of Figure 5 may be performed in the most unfavourable conditions (defined based on a certain use case) and the corrections determined may also be applied in different scenarios (e.g. with more favourable conditions). [000117] As explained above, the position ^constin the scanning direction that is disposed in a portion of the field in which the variation of the first pupil from the target pupil is minimal may be disposed in a central portion of the field 200 in the scanning direction. For example, this position ^constmay be disposed on the centre-line 202 of the field 200 in the scanning direction. [000118] In some embodiments of the method 100 shown in Figure 5, making a measurement (either measuring ^^at step 110 or measuring ^^at step 120) of a quantity indicative of a position and / or orientation of an aerial image may comprise: patterning the radiation using a mark disposed in an object plane; and measuring a position of an image of the mark in the image plane. [000119] Patterning the radiation using a mark disposed in an object plane may be achieved by positioning a mark at a point in the reticle-level illumination region IR that the method 100 samples (for example at a position corresponding to one of the positions shown in the field 200 in Figure 6). For example, one or more marks may be provided on the support structure MT, for example a portion of the support structure MT that the patterning device MA is not disposed on. For example, these one or more marks may be provided on a plate or a fiducial disposed on the support structure MT. Alternatively, these one or more marks may be provided on a reticle MA disposed on the support structure MT. Positioning a mark at a point in the reticle-level illumination region IR that the method 100 samples may be achieved by positioning the support structure MT appropriately. [000120] In some embodiments, each point in the field may be sampled sequentially. For example, a single mark may be moved to a first point in the reticle level illumination region IR during a measurement (either measuring ^^at step 110 or measuring ^^at step 120) of a quantity indicative of a position and / or orientation of an aerial image. Once complete, the support structure MT may be moved so that the single mark is now disposed at a second point in the reticle level illumination region IR anda measurement is made at that second point. This is repeated until measurements have been made at all of the points of the field that the method 100 is sampling. [000121] Alternatively, in some other embodiments, all of the points in the field may be sampled simultaneously. For example, a plurality of marks may be provided at reticle level and positioned in the reticle level illumination region IR such that each mark is disposed at one of the points in the field to be sampled. The measurement (either measuring ^^at step 110 or measuring ^^at step 120) of a quantity indicative of a position and / or orientation of an aerial image can then be made for all of the field points simultaneously. [000122] Measuring a position of an image of a mark in the image plane may be achieved by positioning a suitable sensor at a point in the wafer-level illumination region IR’ that the method 100 samples (for example at a position corresponding to one of the positions shown in the field 200 in Figure 6). For example, one or more sensors may be provided on the substrate table WT, for example a portion of the substrate table WT that the substrate W is not disposed on. Positioning a sensor at a point in the wafer-level illumination region IR’ that the method 100 samples may be achieved by positioning the substrate table WT appropriately. [000123] In some embodiments, measuring a position of an image of a mark in the image plane may comprise measuring at least part of the image of the mark using a photosensitive sensor. For example, a sensor array (i.e. a camera) may be used to measure at least part of the image of the mark. Alternatively, in other embodiments, a single (or a small number of) photosensitive elements (e.g. photodiodes) may be used. [000124] In some embodiments, measuring a position of an image of the mark in the image plane may comprise moving a photosensitive sensor relative to the aerial image while monitoring an intensity of radiation detected by the photosensitive sensor. For example, the photosensitive sensor may be stepped or scanned (for example in three spatial directions) relative to the aerial image while monitoring an intensity of radiation detected by the photosensitive sensor. The position may be a position which maximizes the intensity of radiation detected by the photosensitive sensor. [000125] In some embodiments, measuring a position of an image of a mark in the image plane comprises: (a) projecting the image of the mark onto a substrate W comprising a layer of photoresist; (b) developing the photoresist to form a patterned photoresist; and (c) measuring the position of the pattern on the patterned photoresist. For such embodiments, the step of projecting the image of the mark onto a substrate W comprising a layer of photoresist may be achieved as a static exposure. Alternatively, it may be achieved as a dynamic (scanning exposure). [000126] As shown as a dotted line in Figure 5, optionally, in some embodiments the method 100 may further comprise a preliminary step 105 of calibrating the imaging system using the reference pupil. [000127] For example, the step 105 of calibrating the imaging system using the reference pupil may be carried out before other steps of the method 100. The step 105 of calibrating the imaging systemmay involve a measurement of lens aberrations and then the use of a lens model to determine a configuration of the projection optics which minimizes the aberrations. [000128] Some embodiments of the present disclosure relate to a method for determining a correction for an imaging system (for example the projection system PS of the lithographic apparatus shown in Figure 1). An example of such a method 300 for determining a correction for an imaging system (for example the projection system PS of the lithographic apparatus shown in Figure 1) is shown schematically in Figure 7. [000129] The method 300 comprises a step 310 of determining values of one or more parameters of the imaging system that reduce the impact on the imaging performance as determined by the method 100 shown in Figure 5. [000130] That is, the method 300 shown in Figure 7 may involve determining one or more parameters that generally reduce the second errors ^(^) (^) ^ across the field. In other words, the second errors ^^are transformed into parameters for which there is correction potential within the imaging system. It will be appreciated that the parameters may comprise one or more parameters (position, orientation or shape) of optical elements (e.g. mirrors) within the imaging system and / or the position and / or orientation of a reticle stage (support structure MT) and a wafer stage (the substrate table WT). A lens model may be used to optimize the adjustments to move the optical elements and stages. [000131] As shown as a dotted line in Figure 7, optionally, in some embodiments the method 300 may further comprise carrying out the method 100 shown in Figure 5. That is, in some embodiments, the method 300 shown in Figure 7 may comprise an initial step 100 of determining an impact of a dynamic pupil on imaging performance of an imaging system using the method 100 shown in Figure 5. [000132] Additionally or alternatively, as shown as a dotted line in Figure 7, optionally the method 300 shown in Figure 7 may further comprising a step 305 of reading an output of the method 100 of Figure 5 from a storage medium. It will be appreciated that the method 100 shown in Figure 5 may have previously been used to determining an impact of a dynamic pupil on imaging performance of an imaging system and then this may have been stored in memory. [000133] In some embodiments, the step 310 of determining one or more parameters of the imaging system that reduce the impact on the imaging performance as determined by the method 100 of Figure 5 may comprise determining values of the one or more parameters of the imaging system that minimizes a sum of the squares of the plurality of determined second errors ^(^) ^ across the field 200. Advantageously, this may result in the optimal configuration of the imaging system. [000134] It is possible for the sum of the squares of the plurality of determined second errors ^(^) ^ across the field to be minimized whilst the individual value of one of the determined second errors is unacceptably large. Therefore, in some embodiments, the step 310 of determining one or more parameters of the imaging system that reduce the impact on the imaging performance as determined by the method 100 of Figure 5 may comprise determining values of the one or more parameters of theimaging system such that all of the plurality of determined second errors ^(^) ^ are below a threshold value. [000135] An additional benefit of the method 300 shown in Figure 7 is that allows for a combination of adjustments (of the lithographic apparatus LA) to be identified than can subsequently be simultaneously controlled regardless of whether the steps of method 100 shown in Figure 5 have been performed immediately preceding such control. Such a combination of adjustments may be referred to as a “control knob”. Such a control knob could be used on request, even without the measurement steps of the method 100 of Figure 5 having been performed immediately before. Additionally or alternatively, such a control knob may be used in the system with different magnitude to deal with, for example, situations where the measurement (i.e. the method 100 of Figure 5) is not easily performed. Such a control knob may be used to overcorrect for changes due to the dynamic pupil. For example, the method 100 of Figure 5 may be performed in the most unfavourable conditions (defined based on a certain use case) and the corrections determined may also be applied in different scenarios (e.g. with more favourable conditions). [000136] Some embodiments of the present disclosure relate to a lithographic method. An example of such a lithographic method 400 is shown schematically in Figure 8. [000137] The lithographic method 400 comprises a step 410 of illuminating a patterning device MA. The lithographic method 400 further comprises a step 420 of using an imaging system (for example the projection system PS) to collect patterned radiation B’ scattered from the patterning device MA. In particular, the imaging system is configured using values of one or more parameters of the imaging system determined using the method 300 shown in Figure 7. The lithographic method 400 further comprises a step 430 of projecting the patterned radiation B’ onto a substrate W so as to form an image of the patterning device MA on the substrate W. [000138] Some embodiments of the present disclosure relate to a computer comprising: one or more processors; and storage media, the storage media having instructions to cause the one or more processors to carrying out the method 100 shown in Figure 5 and / or the method 300 shown in Figure 7 and / or the method 400 shown in Figure 8. [000139] The one or more processors may be configured to store on the storage media: a plurality of second errors ^(^) ^ determined by the method 100 shown in Figure 5; and / or values of one or more parameters of an imaging system determined by the method 300 shown in Figure 7. [000140] Some embodiments of the present disclosure relate to a computer-readable medium having instructions for carrying out the method 100 shown in Figure 5 and / or the method 300 shown in Figure 7 and / or the method 400 shown in Figure 8. [000141] Some embodiments of the present disclosure relate to a lithographic apparatus or a lithographic system comprising a controller operable to: perform the method 100 shown in Figure 5 and / or the method 300 shown in Figure 7 and / or the method 400 shown in Figure 8; and / or carry outthe instructions of the computer-readable medium. The lithographic apparatus or lithographic system may be generally of the form of the lithographic apparatus LA shown in Figure 1 and may comprise any of the feature thereof. [000142] Although specific reference may be made in this text to the use of lithographic apparatus in the manufacture of ICs, it should be understood that the lithographic apparatus described herein may have other applications. Possible other applications include 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. [000143] Although specific reference may be made in this text to embodiments of the invention in the context of a lithographic apparatus, embodiments of the invention may be used in other apparatus. Embodiments of the invention may form part of a mask inspection apparatus, a metrology apparatus, or any apparatus that measures or processes an object such as a wafer (or other substrate) or mask (or other patterning device). These apparatus may be generally referred to as lithographic tools. Such a lithographic tool may use vacuum conditions or ambient (non-vacuum) conditions. [000144] Where the context allows, embodiments of the invention may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the invention may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, a machine-readable medium may include read only memory (ROM); random access memory (RAM); magnetic storage media; optical storage media; flash memory devices; electrical, optical, acoustical or other forms of propagated signals (e.g. carrier waves, infrared signals, digital signals, etc.), and others. Further, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be appreciated that such descriptions are merely for convenience and that such actions in fact result from computing devices, processors, controllers, or other devices executing the firmware, software, routines, instructions, etc. and in doing that may cause actuators or other devices to interact with the physical world. [000145] While specific embodiments of the invention have been described above, it will be appreciated that the invention may be practiced otherwise than as described. The descriptions above are intended to be illustrative, not limiting. Thus it will be apparent to one skilled in the art that modifications may be made to the invention as described without departing from the scope of the claims set out below.

Claims

CLAIMS 1. A method for determining an impact of a variation of a first pupil from a target pupil in a first direction within a two-dimensional field having first and second directions on imaging performance of an imaging system, the method comprising: for at least one position in the second direction within the field, carrying out the following: for a plurality of positions in the first direction in the field, at least one of the plurality of positions in the first direction being disposed in a portion of the field in which the variation of the first pupil from the target pupil is minimal: making a reference measurement of a quantity indicative of a position and / or orientation of an aerial image using a reference pupil; making a signal measurement of a quantity indicative of a position and / or orientation of an aerial image using the first pupil; determining a first error as a difference between the reference measurement and the signal measurement; and determining a second error as the difference between the first error for that position in the first direction and the first error for the at least one of the plurality of positions in the first direction in which the variation of the first pupil from the target pupil is minimal.

2. The method of claim 1 wherein the at least one of the plurality of positions in the first direction that is disposed in a portion of the field in which the variation of the first pupil from the target pupil is minimal is disposed in a central portion of the field in the first direction.

3. The method of any preceding claim wherein making a measurement of the quantity indicative of a position and / or orientation of an aerial image comprises: patterning the radiation using a mark disposed in an object plane; and measuring a position of an image of the mark in the image plane.

4. The method of claim 3 wherein measuring a position of an image of the mark in the image plane comprises measuring at least part of the image of the mark using a photosensitive sensor.

5. The method of claim 4 wherein measuring a position of an image of the mark in the image plane comprises moving the photosensitive sensor relative to the aerial image while monitoring an intensity of radiation detected by the photosensitive sensor.

6. The method of claim 3 wherein measuring a position of an image of the mark in the image plane comprises:projecting the image of the mark onto a substrate comprising a layer of photoresist; developing the photoresist to form a patterned photoresist; and measuring the position of the pattern on the patterned photoresist.

7. The method of any preceding claim wherein the reference pupil is a full conventional pupil.

8. The method of any preceding claim further comprising a preliminary step of calibrating the imaging system using the reference pupil.

9. A method for determining a correction for an imaging system, the method comprising: determining values of one or more parameters of the imaging system that reduce the impact on the imaging performance as determined by the method of any preceding claim.

10. The method of claim 9 further comprising carrying out the method of any one of claims 1 to 8.

11. The method of claim 9 or claim 10 further comprising reading an output of the method of any one of claims 1 to 8 from a storage medium.

12. The method of any one of claims 9 to 11 wherein determining one or more parameters of the imaging system that reduce the impact on the imaging performance as determined by the method of any one of claims 1 to 8 comprises determining a set of values of the one or more parameters of the imaging system that minimizes a sum of the squares of the plurality of determined second errors across the field.

13. The method of any one of claims 9 to 12 wherein determining one or more parameters of the imaging system that reduce the impact on the imaging performance as determined by the method of any one of claims 1 to 8 comprises determining a set of values of the one or more parameters of the imaging system such that all of the plurality of determined second errors are below a threshold value.

14. A lithographic method comprising: illuminating a patterning device; using an imaging system, collecting patterned radiation scattered from the patterning device and projecting the patterned radiation onto a substrate so as to form an image of the patterning device on the substrate; wherein the imaging system is configured using values of one or more parameters of the imaging system determined using the method of any one of claims 9 to 13.

15. A computer comprising:one or more processors; and storage media, the storage media having instructions to cause the one or more processors to carrying out the method of any one of claims 1 to 13.

16. The computer of claim 15 wherein the one or more processors are configured to store on the storage media: a plurality of second errors determined by the method of any one of claims 1 to 8; and / or values of one or more parameters of an imaging system determined by the method of any one of claims 9 to 13.

17. A computer-readable medium having instructions for carrying out the method of any one of claims 1 to 13.

18. A lithographic apparatus or a lithographic system comprising a controller operable to: perform the method according to any one of claims 1 to 14; and / or carry out the instructions of the computer-readable medium of claim 17.

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