Exposure process and apparatus

Abstract

A method of determining a reparation dose for a substrate exposed by a lithographic apparatus, the method including: determining a dose profile of an exposure, the dose profile including an accumulated amount of radiation energy within a moving illumination slit delivered to the substrate in a time period measured at a plurality of discrete time points; determining a target dose for the time period; and determining a reparation dose based on a difference between the delivered dose and the target dose for each discrete time point simultaneously.

Description

EXPOSURE PROCESS AND APPARATUSCROSS-REFERENCE TO RELATED APPLICATION

[0001] The Application claims priority of US provisional application number 63 / 679,605 which was filed on 5 August, 2024 and which is incorporated herein its entirety by reference.FIELD

[0002] The present description 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 ART

[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 at 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] Such a lithographic apparatus works in conjunction with a projection optics system that has a narrow imaging slot. Rather than expose the entire wafer at one time, individual fields are scanned onto the wafer one at a time. Moving the wafer and patterning device (e.g., mask) simultaneously such that the imaging slot is moved across the field during the scan does this. The wafer stage is then asynchronously stepped between field exposures to allow multiple copies of the patterning device pattern to be exposed over the wafer surface. In this manner, the quality of the image projected onto the wafer is maximized.

[0006] Conventional lithographic systems and methods form images on a semiconductor wafer. The system typically has a lithographic chamber that is designed to contain an apparatus that performs the process of image formation on the semiconductor wafer. The chamber can be designed to have different grades of vacuum depending on the wavelength of radiation being used. A patterning device is positioned inside the chamber. A beam of radiation is passed from an illumination source (located outside the system) through an optical system, onto an image outline on the patterning device, and a second optical system before interacting with a semiconductor wafer. The patterning device may be transmissive or reflective depending on the wavelength of radiation used; EUV systems for exampleuse a reflective patterning device within a vacuum chamber to prevent absorption of the EUV radiation.SUMMARY

[0007] During a lithographic substrate patterning process it may be desirable to expose an area of a substrate to radiation multiple times, e.g., in the case of an underexposure of radiation during a first pass of radiation. The process of performing multiple exposures e.g., owing to an underexposure of radiation, may in some cases be known as die repair, and a radiation dose substance to an initial dose may be known as reparation dose. Current state-of-the-art die repair methods may need to be adapted to keep up with advancing lithographic technologies (e.g., EUV technologies) that may not be compatible with current die repair methods. Thus, it may be desirable to have improved methods of die repair, die repair control, determining a reparation dose and the like.

[0008] In an aspect, there is provided a method of determining a reparation dose for a substrate exposed by a lithographic apparatus, the method comprising: determining a dose profile of an exposure, the dose profile comprising an accumulated amount of radiation energy within a moving illumination slit delivered to the substrate in a time period measured at a plurality of discrete time points; determining a target dose for the time period; and determining a reparation dose based on a difference between the delivered dose and the target dose for each discrete time point simultaneously.BRIEF DESCRIPTION OF THE DRAWINGS

[0009] 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 2 depicts a purely exemplary plot of dose error DE vs time T in accordance with some embodiments;Figure 3 depicts a purely exemplary plot of energy E vs time T for an energy delivery process in accordance with some embodiments; andFigure 4 depicts a purely exemplary plot of energy E vs time T in accordance with some embodiments.DETAILED DESCRIPTION

[0010] 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 or reticle), a projection system PS and a substrate table WT configured to support asubstrate W.

[0011] 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 faceted field 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.

[0012] 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. Forthat 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).

[0013] 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.

[0014] 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.

[0015] 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 deexcitation and recombination of electrons with ions of the plasma.

[0016] 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 mirrorstructure 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.

[0017] 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.

[0018] 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.

[0019] 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.

[0020] The radiation source SO of the lithographic apparatus is operated with a so-called dose margin that controllably sets the level of energy of the radiation (e.g. EUV) generated, averaged over a particular length of time (also referred to as controlled energy or power), below the source’s maximum output power (also referred to as open-loop energy). A non-zero dose margin enables compensation for temporally short drops in radiation (e.g., EUV) energy, e.g., by adjusting the duration of one or more pulses, or by adjusting the energy of, e.g., one or more laser pulses fired on one or more of next fuel droplets.

[0021] In case too many consecutive pulses deliver too low an energy to the substrate’s exposed target area, the eventual dose delivered to the target area may be too low.

[0022] In practice, the output of a pulsed radiation source SO will vary with time. If the energy of an individual pulse is higher or lower than a nominal or desired output energy for each pulse then this will contribute to a dose error. The fewer pulses received by a target area, the greater the effect of such an individual pulse energy error will be on the total dose.

[0023] If the dose margin is made smaller and, therefore, if the radiation source SO is operating closer to maximum power, then the time to expose a single substrate W can be decreased if the scan speed is increased. However, operating the source SO with closer to maximum power also increases the chance of having to re-expose certain target areas of the substrate W in a second pass. The reason for this is that there is not always enough energy available in the limited number of subsequent pulses incident on the target area in order to compensate for a drop in energy delivered by preceding pulsesto that target area.

[0024] On some lithographic apparatuses (for example, but not exclusively, EUV lithographic apparatuses), a die re-exposing strategy may be used to remedy dose errors which are detected during exposure of a substrate. This may comprise evaluating the dose received by each field during each exposure (a received dose value per field) in an initial exposure sequence or exposure pass. If one or more fields are evaluated to have received a dose below a threshold dose (e.g., purely for example, a dose error greater than 1% below a requested dose or target dose), then those one or more fields are re-exposed in a second pass. The cumulative (i.e., combined) dose of the two passes for the one or more re-exposed fields should be within a threshold margin of the requested dose, e.g., within + / - 1% of the requested dose.

[0025] The dose evaluation may be performed by convolving, for every exposure, the measured radiation (e.g., EUV) pulse series with the illumination slit profile. This gives a dose error along the scan direction. A control algorithm can be used to assess if the dose error is within the allowed dose error threshold everywhere (i.e., ok, no re-expose necessary) or if there is an under-dose somewhere which will trigger the need for a re-exposure. More specifically, the dose evaluation may comprise the following steps:1) An energy sensor of the lithographic apparatus measures energy of all radiation (e.g., EUV) pulses during an exposure.2) The dose error is calculated by convolution of the energy data with the exposure slit.3) The energies measured during the original exposure are converted to a high resolution ‘requested relative energy profile’ for the re-exposure and sends it to an energy controller for the radiation.4) The energy controller follows the requested energy profile during re-expose, e.g., as requested by lithographic apparatus.5) The dose delivered in the re-exposure is calculated.6) The dose error of the sum of the dose of the original exposure and the dose in the re-exposure is calculated.Step 2) may be performed by a suitable exposure algorithm or exposure controller, for example, which may be part of the lithographic apparatus. Steps 3) to 6) may be performed by a suitable re- exposure algorithm or re-expose controller, for example, which may be part of the lithographic apparatus.

[0026] Typical methods for determining a reparation dose may comprise calculating a reparation dose using a proportional-integral (PI) calculation method which may optimize a reparation dose locally for a dose error region. Such a method may not account for a neighboring area on a substrate (i.e., a region neighboring the dose error region) which may subsequently lead to overexposure in neighboring areas.

[0027] A state-of-the-art method for determining a reparation dose may comprise using an algorithm to loop through a dose error (i.e., a difference between a target dose and a delivered dose)and calculate a repair dose (e.g., for a die on a substrate). Such a method is disclosed in PCT Patent Application Publication No. WO2023 / 110257 which is incorporated herein in its entirety by reference. State-of-the-art scanner systems may have an increased scan speed and / or narrower slit dimensions compared to other scanner systems. Using typical methods for determining and / or delivering a reparation dose using state-of-the-art scanners may lead to the aforementioned overexposure in areas neighboring a dose error region during die repair. Applying repair energy at a particular point in time (which may be referred to as a reparation point) gives a “slit shaped” dose around that reparation point. Thus, the full slit size should be taken into account when an evaluation is made whether a repair to the substrate W should be made or not (i.e. whether there should be a second exposure at this point). A narrower slit will lead to higher energy at the periphery of the slit thus affecting neighboring regions. Furthermore, a faster scan speed will lead to delivered energy variation (i.e., the difference between an ideal and delivered dose) per location being averaged with less time (i.e., fewer energy pulses) causing a higher error.

[0028] Dose quantization is the minimum dose that can be delivered to a substrate by a single energy pulse (e.g., an EUV shot). It is a function of the slit profde and minimum energy (Emin) the source can produce. The higher the dose quantization, the more challenging die repair will be since each shot contributes to more dose, i.e., a higher risk of over-exposure with a single shot. State-of-the- art scanners may comprise a relatively higher pulse energy thus limiting further where and when a reparation dose may be provided to a substrate region.

[0029] Accordingly, there is a desire for improved methods of determining a reparation dose and / or applying a reparation dose that may be compatible with state-of-the-art scanners.

[0030] Known methods for determining a reparation dose may comprise determining a repair profde locally (i.e., at a single point in a slit), which may lead to over-dosing on areas of a substrate that have already been exposed to radiation. That is, known methods may not take into account past dose errors during a reparation dose calculation.

[0031] With reference to Figure 2, in a first aspect there is provided a method for determining a reparation dose comprising determining a dose profile of an exposure, wherein the dose profile comprises an accumulated amount of radiation energy within a moving illumination slit delivered (e.g., to a substrate) in a time period measured at a plurality of discrete time points. The method may further comprise determining an ideal, predicted and / or target dose 260 for the time period and determining a reparation dose based on a difference between the delivered dose 240 and the ideal, predicted and / or target dose 260 for each discrete time point simultaneously.

[0032] The method may further comprise determining a reparation dose profile based on a difference between the delivered dose and the ideal, predicted and / or target dose that provides a lowest possible dose error, wherein the reparation dose is determined from the reparation dose profile.

[0033] In some examples, determining a reparation dose profile based on a difference between the delivered dose 240 and the ideal, predicted and / or target dose 260 for each discrete time pointsimultaneously may comprise using a regression algorithm, or more specifically a minimization regression algorithm.

[0034] For example, a suitable regression algorithm may comprise a linear least squares (LLS) algorithm. An LLS algorithm is a type of linear regression algorithm that may find a solution by minimizing some error. In the case of determining a reparation dose, the LLS algorithm may minimize a dose error between the delivered dose and the ideal, predicted and / or target dose for each discrete time point simultaneously. That is, a reparation dose may be determined by minimizing the sum of the squares of a difference between a requested dose and a measured dose of an exposed area (i.e., rather than a single point) on a substrate. Thus, the proposed method may be considered a global optimization of the dose error (i.e., the reparation dose is determined based on an over or underexposed area rather than a single point or dose). In this way, the determination of a reparation dose may take into account factors such as slit width. This is in contrast to known methods that may calculate a repair profile locally (i.e., at a single point) which may result in a higher computed error (e.g., resulting in overdose). The LLS algorithm may compute a repair profile by minimizing the rootmean-square deviation with respect to the dose error in the energy profile using an iterative approach. Of course, LLS is only an example of a suitable regression algorithm, and any suitable minimization algorithm which minimizes a dose error between the amount of energy delivered and the ideal, predicted and / or target energy for each discrete time point simultaneously may be used.

[0035] With reference to Figure 2, the presently proposed method may comprise determining a dose profile by comparing a dose error with a dose error mask 210a 210b, the dose error mask comprising a minimum dose error mask threshold 230 and a maximum dose error mask threshold 220. An incorrectly accumulated energy controller (EC) integrator value (e.g., from receiving a dose error repair profile that is not large enough to trigger the firing of a pulse) may cause failure to repair a proximate large dose error. Thus, in some examples, a dose mask may be determined (e.g., between maximum dose error mask threshold 220 and minimum dose error mask threshold 230), wherein only dose errors exceeding these thresholds 220, 230 are taken into account in the determination of the reparation dose (e.g., the minimization of Equation (1) below). Dose error DE may be expressed as a percentage with respect to an ideal, predicted and / or target dose. As shown in Figure 2, an area corresponding to where a dose error % (DE%) (i.e., a percentage difference between a delivered dose 240 and ideal, predicted and / or target dose 260) has fallen below the mask threshold 230 is taken into account in the dose profile. Also shown in Figure 2 is the dose profile after repair 250.

[0036] In some examples, by determining an area that may be considered for computation by comparison with a dose error mask threshold (e.g., minimum dose error mask threshold 230 and maximum dose error mask threshold 220), there may be provided a reduced computational load. That is, the area considered for computation may be relatively smaller compared to known methods, thus reducing the computation power required to determine a reparation dose. In addition, introducing minimum dose error will also prevent adding unnecessary one or more repair energy pulses that causeoverdose.

[0037] In some examples, an LLS algorithm that determines a dose repair profile with a minimum dose error among possible dose repair profiles x may take the mathematical form:wherein Etarget is an ideal, predicted and / or target dose.

[0038] A source energy controller (EC) may supply energy in bursts of energy pulses (e.g. 10 energy pulses in a burst wherein the bursts have a different (or no) repetition rate than the train of pulses) within a given time frame. Each burst of energy pulses may have a target dose to reach by the end of the time frame. In an RF energy regulated EC mode, an energy controller may calculate the RF power required to ensure that the integrated energy across the burst reaches the target dose by the last pulse in the burst. In a hit / miss EC mode, which is typically used for low doses, an energy controller may control an energy source to deliver pulsed energy (i.e., “hit” fuel droplets) at the lowest possible energy value (i.e., Emin) until the dose target has been reached, then to stop delivering pulses of energy (i.e., “miss” fuel droplets) for the remainder of the burst time period.

[0039] In some examples, the proposed method may further comprise adapting a characteristic of a source EC. For example, a source EC may be configured to stay in a hit / miss mode e.g., as opposed to an RF energy regulated mode. This may in some cases increase a repair success rate. In some examples, a smoothing operation such as a Tikhonov regularization technique may be applied to smooth a repair profile (i.e., applying a Tikhonov regularization or other suitable regularization term to the minimization merit function, e.g., Equation (1)). The Tikhonov regularization technique comprises adding a regularization, or penalty, term to the merit function (e.g., Equation (1)) that acts to smooth out a transition between data points providing a homogeneous distribution of points. This may reduce large (e.g., outlier) variations in a requested energy profile, reducing disturbances in an energy source and enabling the EC to stay in a hit / miss mode.

[0040] The calculation of a reparation dose may be performed e.g., at a scanner host or other platform with suitable processing resources rather than e.g., a dedicated dose control board. Accordingly, rather than sequentially resolving a dose error, then performing die reparation, aspects of the present disclosure may enable parallel processing of e.g., determining a reparation dose and / or reparation dose profile, dose evaluation, dose delivery, scan negotiation and / or queuing of an exposure, thus improving throughput.

[0041] The energy distribution of a dose (e.g., onto a substrate) may be dependent on the physical constraints of a slit. That is, a narrower slit may have a more focused, narrower distribution of radiation onto a target area of a substrate than a wider slit for a given dose. In some examples not shown, it may be possible to modify an amount of radiation through a slit in order to adjust a dose(e.g., a reparation dose). Such modification of radiation may be provided by illuminator optics comprised in illumination system IL. For example, illumination system IL may comprise a microelectromechanical (MEMS) illuminator comprising mirror facets, such as described in PCT Patent Application Publication No. WO2021032483, which is incorporated herein by reference in its entirety. The MEMS illuminator may be configured to transmit radiation from a source to the slit. In some examples, e.g., by limiting transmission of radiation to a subset or mirror facets comprised in the MEMS illuminator, it may be possible to adjust a radiation parameter (e.g., radiation intensity and / or illumination path) transmitted to the slit in order to modify radiation pulse energy. In other examples, the MEMS illuminator may be configured to modify an angular distribution of radiation transmitted to the slit to change the intensity of the radiation.

[0042] In some examples, it may be determined that it is not possible to calculate a reparation dose, e.g., that it may not be possible to maintain a dose error within a margin provided through provision of a reparation dose, e.g., the LLS or other minimization algorithm cannot find a solution within the constraints given. In such an example, it may be possible to modify an angular distribution of radiation through the slit based on maintaining a dose error margin threshold.

[0043] A typical EC that may determine when to provide an energy pulse may comprise a proportional-integral (PI) controller designed around a nominal use case wherein an energy target is constant during normal exposure conditions. In contrast, a die repair use case may comprise requests arriving infrequently (i.e., for relatively small reparation doses). A PI controller may operate by using a closed-loop feedback control mechanism that adjusts based on a difference between a setpoint (e.g., a predicted, target and / or ideal energy) and a variable (e.g., a delivered energy). The integral part of the PI controller may accumulate based on an energy history of an exposure, i.e., an accumulation based on an error between a target energy and delivered energy. In a normal use case, a PI controller may determine not to provide an energy pulse based on the accumulated energy history, which may in some cases leave an under-dose unrepaired. Thus, it may be desirable to have improved methods of energy control that are better suited to the die repair use case.

[0044] In a further aspect of the present disclosure, there may be provided a method of controlling the delivery of an energy dose (e.g., as delivered by an EC). The method may comprise resetting an integrator (e.g., of a PI controller) after a predetermined time. In some examples, the predetermined time may be Tslit / 2, wherein Tslit is the time taken for a point on a substrate to travel completely across the width of a slit (i.e., the exposure slit defined by a lithographic apparatus). In this way, any history comprised in an accumulated integrator value that is irrelevant to delivering energy for current or future requests (e.g., for a reparation dose) may be removed from the integrator value.

[0045] In other words, for any single energy pulse to contribute to an energy request, the pulse will have been delivered within + / -Tslit / 2 from the time of the energy request. Therefore, the energy pulses which contribute to an energy request may be limited to those which were delivered within a time period defined by + / -Tslit / 2 from the time of the energy request. Thus, the integrator mayremember any positive error only for Tslit / 2 since the most recent request. Further, to ensure the EC takes into account an error contributed by the energy delivered, it may also take into account the negative error for only Tslit / 2 since it last delivered an energy pulse. This may allow the EC to determine to provide an energy pulse even if the EC has determined that too much energy has been delivered in the recent past, and / or account for over-delivered energy only for the appropriate amount of time in the future.

[0046] Figure 3 depicts a purely exemplary plot of energy E vs time T for an energy delivery process. Depicted are purely exemplary plots of requested energy 320 (gray line), delivered energy 310 (black line) and integrator value (double -compound black line) 340. A first non-zero energy request 320a is met by delivering three pulses 310a, a second non-zero energy request 320b is met by delivering single pulse 310b and a third non-zero energy request 320c is met by delivering single pulse 310c. As can be seen from the plot, the integrator value is first reset at first reset point 330a, which is at time Tslit / 2 after the immediately preceding pulse 310b. This allows for an EC to determine to provide an energy pulse 310c; if the integrator value was not reset at 330a, the pulse 320c would not have been provided, thus leading to an under-dose. The integrator is again reset at second reset point 320b at time Tslit / 2 after pulse 310c. Note that there is no reset between the final pulse of pulses 310a and pulse 310b, as the time between these pulses is less than Tslit / 2.

[0047] In some examples, the integrator value resetting may be performed only during a repair process.

[0048] In an embodiment, there may be provided a method of controlling the delivery of an energy dose, the method comprising applying a negative bias to the integrator. Based on Emin being the energy of one energy pulse (i.e., the minimum energy that an energy source may deliver in a single energy pulse), to ensure that a difference between an integrated energy and an integrated delivered energy is not more than half the energy of one pulse, a negative bias may be applied to the integrator. In some examples, the negative bias may be Emin / 2. In this way, the EC may avoid providing an energy pulse until a sufficient amount of energy request has been accumulated, thus reducing a risk of overdosing.

[0049] In some lithography systems, an energy source and / or a dose controller may operate at a frequency e.g., of 50kHz, i.e. capable of delivering 50000 energy pulses per second. Determined energy profiles may comprise a set of discreet data points each corresponding to an energy-time pair of e.g., 1000 data points for a 100ms exposure, which in this example would correspond to 5000 energy pulses. Thus, in some cases profile handling such as up-sampling and / or down-sampling of an energy profile (e.g., for a reparation dose) may be required, e.g., to improve data transferring time between an energy source and a scanner. Typical profile handling may use e.g., linear interpolation to up-sample an energy profile received from a scanner back to a fuel droplet rate of the lithography system. In the case of repair energy profiles having e.g., accentuated peaks, linear interpolation may lead to an increased interpolation error. In order to address this issue, there may be provided a methodof up-sampling an energy profile (e.g., a repair energy profile) comprising determining an area-based interpolation of the energy profile. An area-based interpolation method may conserve an energy requested in an interval of the energy profile, thus reducing an interpolation error.

[0050] With reference to Figure 4, in a non-limiting example, determining an area-based interpolation of the energy profile may comprise calculating an integrated area under the energy profile (i.e., energy E with respect to time T).

[0051] Still referencing Figure 4, determining an area based interpolation of an energy profile may comprise determining a first area between a time (t ) of a previous energy pulse (E(t )) and a point in the energy profile with time stamp tScn (i.e„ a time during a scan), determining a second area between time tsCnand a time tN+i of a current energy pulse (E(tN+i)), wherein the energy for an interpolated energy pulse EpUise is determined as the total area averaged over the time period between the previous energy pulse and the current energy pulse (i.e., tN+i - t ) (Eq. 2).Epulse = ((E(tN)+E(tscn)) / 2*(tscn ' tN)+(E(tscn) + E(t +1) ) / 2*(tN+l-tscn) ) / (tN+l - t ) (2)

[0052] If there is no point in the energy profile between a time of a previous energy pulse (e.g., E(t )) and a time of a current energy pulse (e.g., E(tN+i)), the energy for the interpolated energy pulse may be determined as the mean of the energy of the previous pulse and the current pulse.

[0053] In the example shown in Figure 4, there is no point between a previous pulse at time (tN+i) and a current pulse at time (tN+2), thus the energy for the interpolated energy pulse in this example may be calculated according to:Epulse = ( E(tN+l) + E(tN+2) ) / 2 (3)

[0054] In some examples, it may not be possible to maintain energy within a given specification (e.g., within a 1% DE threshold). For example, an algorithm (e.g., the LLS algorithm) may not find a solution to minimize a dose error within a given threshold. In such examples, it may be possible to adjust a specification such as dose error margin such that the specification may be met (e.g., adjusting a 1% DE threshold to a 1.5% DE threshold for re-exposure). This may provide a temporary solution in cases where, e.g., an LLS algorithm is not able to minimize an error within a specified threshold.

[0055] In some examples, the dose error margin, rather than being a fixed value (i.e., 0.5% increase on re-exposure), may be dose dependent. For example, die repair failure may be more likely to occur at lower doses. Thus, an increased dose error margin at higher doses may not be necessary and may negatively affect throughput. Thus, it is desirable to be able to adjust a specification such as dose error target threshold based on a dose of a first, or initial exposure. For example, the dose error target threshold may be adjusted only when the energy of an initial exposure is below an energy threshold.

[0056] In some examples, it may be possible to decrease an amount of quantization in pulse energy. For example, it may be possible to use an alternative actuator (e.g. pre-pulse energy, pedestal energy, laser timing and / or the like) during die repair to enable an energy controller to access lower values of on-droplet pulse energy (i.e., lower than the current Emin).

[0057] In some examples, rather than determining a dose repair profile, it may be possible to configure an energy controller to set an RF command and a hit / miss command to values which would be expected to produce the optimal dose error, thus providing for an “inline” dose controller enabling die repair within a single function.

[0058] In a further example, it may be possible to determine a reparation dose based on a minimum energy producing capability of a source. For example, it may be possible to employ a mixed integer linear programming methodology (also known as intlinprog) by providing an algorithm (e.g., the LLS algorithm) with a minimum radiation (e.g., EUV) producing capability of a source as an input. Such a methodology may comprise providing an array of 0s and Is corresponding to, e.g., missing and hit fuel droplets. Such a methodology may comprise using a nearest neighbor interpolation of a repair profile (e.g., in contrast to linear interpolation).

[0059] 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, liquidcrystal displays (LCDs), thin-film magnetic heads, etc.

[0060] 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 apparatuses may be generally referred to as lithographic apparatuses or lithographic tools. Such a lithographic apparatus may use vacuum conditions or ambient (nonvacuum) conditions.

[0061] 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, where the context allows, is not limited to optical lithography and may be used in other applications, for example imprint lithography.

[0062] 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.

[0063] 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. Other aspects of the invention are set-out as in the following numbered clauses.1. A method of determining a reparation dose for a substrate exposed by a lithographic apparatus, the method comprising: determining a dose profile of an exposure, the dose profile comprising an accumulated amount of radiation energy within a moving illumination slit delivered to the substrate in a time period measured at a plurality of discrete time points; determining a target dose for the time period; and determining a reparation dose based on a difference between the delivered dose and the target dose for each discrete time point simultaneously.2. The method of clause 1, wherein determining the dose profile comprises comparing the difference between the delivered dose and the target dose to a threshold value.3. The method of clause 1 or clause 2, wherein the dose profile relates to a time period wherein the difference between the delivered dose and the target dose exceeds the threshold value.4. The method of any previous clause, further comprising determining a reparation dose profile based on the difference between the delivered dose and the target dose, wherein the reparation dose is determined based on the reparation dose profile.5. The method of clause 4, wherein the determining a reparation dose profile comprises performing a minimization of an error between the delivered dose and the target dose.6. The method of clause 4 or clause 5, wherein the determining a reparation dose profile comprises using a linear least squares algorithm to minimize an error between the delivered dose and the target dose.7. The method of any of clauses 4 to 6, further comprising performing a smoothing operation on the reparation dose profile.8. The method of clause 7, wherein the smoothing operation comprises applying a Tikhonov regularization during the determination.9. The method of any of clauses 4 to 8, further comprising modifying a radiation parameter ofradiation comprised in the reparation dose based on a failure to minimize the error, wherein the radiation parameter comprises intensity, illumination path or angular distribution.10. The method of clause 9, wherein the modifying a radiation parameter comprises forming radiation in the illumination slit using a MEMS illuminator.11. The method of any of clauses 4 to 10, further comprising: determining an integrated area beneath the reparation dose profde, and determining the reparation dose from the integrated area.12. The method of clause 11, further comprising: determining a first integrated area between a time of a previous energy pulse and a point in the reparation dose profile; determining a second integrated area between the point in the reparation dose profile and a time of a current energy pulse; and determining the energy for an interpolated energy pulse from the total integrated area averaged over the time period between the previous energy pulse and the current energy pulse.13. The method of clause 11 or clause 12, further comprising, when there is no point in the reparation dose profile between the previous energy pulse and the current energy pulse, determining the energy for an interpolated energy pulse for the reparation dose from the mean of the energy of the previous energy pulse and the current energy pulse.14. The method of any of clauses 4 to 13, further comprising calculating the reparation dose profile in parallel with determining the dose profile and queuing an exposure.15. The method of any previous clause, further comprising: determining that a target threshold for dose error is not met by the determined reparation dose; adjusting the threshold target for dose error based on the determination that the target threshold was not met; and re-determining the reparation dose based on an adjusted target threshold.16. The method of clause 15, wherein the adjusting the target threshold for dose error is based on an energy level of an initial exposure.17. The method of clause 15, further comprising adjusting the target threshold when the energy level of the initial exposure is below an energy threshold.18. A method of delivering a reparation dose for a substrate exposed by a lithographic apparatus, the method comprising, accumulating, by an integral term of a proportional integral controller, an error between a target radiation energy and delivered radiation energy; delivering a reparation dose to the substrate based on the integral term meeting a threshold value; and resetting the integral term after a predetermined time.19. The method of clause 18, wherein the predetermined time is Tslit / 2, wherein Tslit is a time taken for a point on the substrate to travel across the width of a slit of the lithographic apparatus.20. The method of any of clauses 18 or 19, further comprising delivering the reparation dose in accordance with the method of any of clauses 1 to 17.21. A method of delivering a reparation dose for a substrate exposed by a lithographic apparatus, the method comprising: accumulating, by an integral term of a proportional integral controller, an error between a target radiation energy and delivered radiation energy; applying a negative bias to the integral term; and delivering a reparation dose to the substrate based on the integral term meeting a threshold value.22. The method of clause 21, wherein the negative bias corresponds to Emin / 2, wherein Emin is a minimum amount of energy that an energy source of the lithographic apparatus may deliver in a single energy pulse.23. A method of delivering a reparation dose to a substrate comprising: determining the reparation dose in accordance with any of clauses 1 to 17; and delivering the reparation dose to the substrate.24. An energy controller for a lithographic apparatus, configured to perform the method of any of clauses 1 to 23.25. A lithographic apparatus comprising a projection system configured to project a radiation beam to project a pattern from a patterning device onto a substrate, wherein the lithographic apparatus is configured to perform the method of any of clauses 1 to 23.

Claims

1. CLAIMS1. A method of determining a reparation dose for a substrate exposed by a lithographic apparatus, the method comprising: determining a dose profile of an exposure, the dose profile comprising an accumulated amount of radiation energy within a moving illumination slit delivered to the substrate in a time period measured at a plurality of discrete time points; determining a target dose for the time period; and determining a reparation dose based on a difference between the delivered dose and the target dose for each discrete time point simultaneously.

2. The method of claim 1, wherein determining the dose profile comprises comparing the difference between the delivered dose and the target dose to a threshold value.

3. The method of claim 1 or claim 2, wherein the dose profile relates to a time period wherein the difference between the delivered dose and the target dose exceeds the threshold value.

4. The method of any previous claim, further comprising determining a reparation dose profile based on the difference between the delivered dose and the target dose, wherein the reparation dose is determined based on the reparation dose profile.

5. The method of claim 4, wherein the determining a reparation dose profile comprises performing a minimization of an error between the delivered dose and the target dose by a using linear least squares algorithm.

6. The method of any of claims 4 and 5, further comprising performing a smoothing operation on the reparation dose profile, by applying a Tikhonov regularization during the determination.

7. The method of any of claims 4 to 6, further comprising modifying a radiation parameter of radiation comprised in the reparation dose based on a failure to minimize the error, wherein the radiation parameter comprises intensity, illumination path or angular distribution, and wherein forming radiation in the illumination slit using a MEMS illuminator.

8. The method of any of claims 4 to 7, further comprising: determining an integrated area beneath the reparation dose profile, and determining the reparation dose from the integrated area.

9. The method of claim 8, further comprising: determining a first integrated area between a time of a previous energy pulse and a point in the reparation dose profile; determining a second integrated area between the point in the reparation dose profile and a time of a current energy pulse; determining the energy for an interpolated energy pulse from the total integrated area averaged over the time period between the previous energy pulse and the current energy pulse, and when there is no point in the reparation dose profile between the previous energy pulse and the current energy pulse, determining the energy for an interpolated energy pulse for the reparation dose from the mean of the energy of the previous energy pulse and the current energy pulse.

10. A method of delivering a reparation dose for a substrate exposed by a lithographic apparatus, the method comprising, accumulating, by an integral term of a proportional integral controller, an error between a target radiation energy and delivered radiation energy; delivering a reparation dose to the substrate based on the integral term meeting a threshold value; and resetting the integral term after a predetermined time.

11. The method of any of claim 10, further comprising delivering the reparation dose in accordance with the method of any of claims 1 to 9.

12. A method of delivering a reparation dose for a substrate exposed by a lithographic apparatus, the method comprising: accumulating, by an integral term of a proportional integral controller, an error between a target radiation energy and delivered radiation energy; applying a negative bias to the integral term; and delivering a reparation dose to the substrate based on the integral term meeting a threshold value.

13. A method of delivering a reparation dose to a substrate comprising: determining the reparation dose in accordance with any of claims 1 to 9; and delivering the reparation dose to the substrate.

14. An energy controller for a lithographic apparatus, configured to perform the method of any of claims 1 to 13.

15. A lithographic apparatus comprising a projection system configured to project a radiation beam to project a pattern from a patterning device onto a substrate, wherein the lithographic apparatus is configured to perform the method of any of claims 1 to 13.

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