System and method for compensating plasma pressure on tin droplets using a nonlinear model

Abstract

An illumination source includes a droplet generator, a laser, a detector, and a controller. The droplet generator produces a stream of droplets of target material directed to an interaction region. The laser irradiates the droplets at the interaction region using a beam of pulses. The irradiated droplets generate output illumination of the illumination source. The detector measures an aspect of an interaction between a pulse from the beam and a droplet from the stream. Controller includes circuitry and determines a pulse timing adjustment that is nonlinearly dependent on the measured aspect. The controller also controls a subsequent laser pulse of the beam based on the pulse timing adjustment.

Description

SYSTEM AND METHOD FOR COMPENSATING PLASMA PRESSURE ON TIN DROPLETS USING A NONLINEAR MODELCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to US Application No. 63 / 738,240, filed December 23, 2024, titled SYSTEM AND METHOD FOR COMPENSATING PLASMA PRESSURE ON TIN DROPLETS USING A NONLINEAR MODEL, which is incorporated herein by reference in its entirety.FIELD

[0002] The present disclosure relates to radiation sources, for example, an extreme ultraviolet illumination system for photolithographic processing of wafers.BACKGROUND

[0003] Illumination generated by a radiation source can be used by tools used for semiconductor manufacturing processes. Examples of such exposure apparatuses include a lithographic apparatus, a metrology or inspection apparatus (e.g., a mask inspection apparatus, an actinic mask inspection apparatus, a defect inspection apparatus, a dimension measurement apparatus, or the like), among others.

[0004] 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 can project a pattern from a patterning device (e.g., a mask) onto a layer of radiation-sensitive material (e.g., a photoresist or resist) provided on a substrate. To project a pattern on a substrate, a lithographic apparatus can use electromagnetic radiation. The wavelength of radiation can determine the minimum size of features that are to be formed on the substrate, with smaller wavelengths allowing for smaller features. For example, a lithographic apparatus that uses extreme ultraviolet (EUV) radiation (having a wavelength within the range 4-20 nm, for example 6.7 nm or 13.5 nm) can print smaller features on a substrate as compared to a lithographic apparatus that uses radiation with a wavelength of 193 nm. A drawback of operating at EUV wavelengths is that many optical materials can absorb EUV illumination, thereby attenuating EUV illumination intensity. Reflective optics can help mitigate attenuation. EUV lithography can implement one or more reflective surfaces to guide EUV radiation along an optical path.

[0005] A mask inspection apparatus (e.g., actinic mask inspection apparatus) is an apparatus that can be used to measure dimensions or detecting defects in masks or mask blanks. Mask blanks used in EUV lithography generally have a multilayer structure that functions as a Bragg reflector. Layers of the multilayer structure can be altematingly molybdenum and silicon. The projected pattern in a lithographic process can become deformed if a defect is present in the multilayer structure. Therefore,a mask inspection is an important, and often necessary, step of mass -production lithographic processes to check whether a defect is present in a mask. EUV mask inspection can be used for several purposes and in several different stages of lithographic fabrication.

[0006] Firstly, mask inspection can be used for the detection of phase defects that occur in mask blanks. Such phase defects can occur during the manufacturing of the multilayer stack of the mask blank. If undetected, phase defects are reproduced on all chips that correspond to the part of the mask containing the phase defects. Such phase defects can be correctly detected by using the same or similar actinic EUV wavelength as the lithography tool (e.g., 13.5 nm). Secondly, at a stage associated with quality control of EUV patterned masks, patterned mask inspection masks can be inspected. Mask inspection can be used to measure critical dimensions on the mask blank. In addition to phase defects, absorber pattern defects on the surface can be detected. Thirdly, mask inspection can be used for simulating exposure and determining the deterioration of optical contrast of a defect detected in the actinic inspection. Fourthly, the mask inspection can be used for optical proximity correction (OPC) evaluation or during a mask repair process to improve pattern transfer fidelity. Further, it can be used for inspecting optical contrast after fixing the defect. In addition to the above, mask inspection can also be used to measure small particle / amplitude effects.

[0007] A metrology apparatus is an apparatus that measures critical dimension and inspects various aspects of the wafer during the semiconductor manufacturing process. A metrology apparatus can also measure and characterize physical properties of materials and components. The metrology apparatus is a precision instrument that ensures product quality and process control. In at least one embodiment, the metrology apparatus employs EUV radiation to inspect and measure dimensions of targets on the substrate.

[0008] EUV illumination sources are complex apparatuses with many active components and interactions. Non-compliance of one or more of those active components and interactions can result in reduced EUV power, reduced output stability, and inefficient operation.SUMMARY

[0009] Embodiments of the present disclosure provide a method for compensating for next-droplet interactions in an EUV radiation source using feedforward adjustments.

[0010] In some embodiments, an illumination source can comprise a droplet generator, a laser, a detector, and a controller. The droplet generator can produce a stream of droplets of target material directed to an interaction region. The laser can irradiate the droplets at the interaction region using a beam of pulses. The irradiated droplets can generate output illumination of the illumination source. The detector can measure an aspect of an interaction between a pulse from the beam and a droplet from the stream. The controller can comprise circuitry and determine a pulse timing adjustment that is nonlinearly dependent on the measured aspect. The controller can also control a subsequent laser pulse of the beam based on the pulse timing adjustment.

[0011] In some embodiments, a non-transitory computer-readable medium can stores a set of instructions. The instructions are executable by at least one processor of an extreme ultraviolet (EUV) radiation source to cause the EUV radiation source to perform operations. The operations can comprise obtaining a measured aspect of an interaction between a pulse from a beam of laser pulses and a droplet from a stream of droplets of target material. The EUV radiation source is configured to irradiate the droplets at the interaction region using the beam. The operations can also comprise determining a pulse timing adjustment that is nonlinearly dependent on the measured aspect. The operations can also comprise controlling a subsequent laser pulse of the beam based on the pulse timing adjustment.

[0012] In some embodiments, a lithographic apparatus can comprise a projection system and an illumination source. The illumination source can comprise a droplet generator, a laser, a detector, and a controller. The projection system can project an image of a pattern a patterning device onto a substrate. The illumination source can illuminate the patterning device. The droplet generator can produce a stream of droplets of target material directed to an interaction region. The laser can irradiate the droplets at the interaction region using a beam of pulses. The irradiated droplets can generate output illumination of the illumination source. The detector can measure an aspect of an interaction between a pulse from the beam and a droplet from the stream. The controller can comprise circuitry and determine a pulse timing adjustment that is nonlinearly dependent on the measured aspect. The controller can also control a subsequent laser pulse of the beam based on the pulse timing adjustment.BRIEF DESCRIPTION OF FIGURES

[0013] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings, in which:

[0014] FIG. 1 shows an example lithographic system comprising a lithographic apparatus and a radiation source, consistent with embodiments of the present disclosure.

[0015] FIG. 2 shows an example system for (actinic) mask inspection, consistent with embodiments of the present disclosure. .

[0016] FIG. 3 shows a portion of an example radiation source, consistent with embodiments of the present disclosure.

[0017] FIG. 4 shows a process flow of an example method for compensating for next-droplet interactions, consistent with embodiments of the present disclosure.

[0018] FIG. 5 shows a graph of example measurement data and model behavior under the influence of next-droplet interactions, consistent with embodiments of the present disclosure.

[0019] FIG. 6 shows an example method for compensating for next-droplet interactions, consistent with embodiments of the present disclosure, consistent with embodiments of the present disclosure.

[0020] FIG. 7 shows a process flow of an example method for training model for next-droplet interactions, consistent with embodiments of the present disclosure.DETAILED DESCRIPTION

[0021] Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the drawings. The following description refers to the accompanying drawings in which the same numbers in different drawings represent the same or similar elements unless otherwise represented. The implementations set forth in the following description of exemplary embodiments do not represent an exhaustive set of implementations. Instead, they are merely examples of apparatuses, systems, and methods consistent with aspects related to subject matter that may be recited in the appended claims. For example, although some embodiments are described in the context of EUV-based lithographic apparatuses, the present disclosure is not so limited. Unless infeasible, embodiments described herein can be implemented in any type of lithographic apparatus.

[0022] Electronic devices are constructed of circuits formed on a substrate. The substrate is typically of a semiconductor material (e.g., silicon) and is often referred to as a wafer by persons of skill in the art. Many circuits may be formed together on the same piece of silicon and are called integrated circuits or ICs. With advancements in technology, the size of these circuits has decreased dramatically so that many more of them can fit on the substrate. For example, an IC chip in a smart phone can be as small as a fingernail and yet may include over 2 billion transistors, the size of each transistor being less than 1 / 1, 000th the width of a human hair.

[0023] Making these ICs with extremely small structures or components is a complex, timeconsuming, and expensive process, often involving hundreds of individual steps. Errors in even one step have the potential to result in defects in the finished IC, rendering it useless. Thus, one goal of the manufacturing process is to avoid such defects to maximize the number of functional ICs made in the process, that is, to improve the overall yield of the process.

[0024] Speed, or throughput, has been a traditionally important metric alongside yield. Throughput is a measurable quantity that characterizes the manufacture speed of a fab (e.g., number of IC units produced per unit time). Throughput has become even more important in view of recent global chip shortages. As there are multiple steps in the fabrication of a chip device (e.g., multiple steps for multiple layers), each step can have a characteristic throughput. For example, a throughput value can be assigned to how quickly a lithographic system can conduct an illumination optimization process. Innovations in the design or functions of source optimizers can increase throughput or resolve problems in another aspect while mitigating adverse impact to throughput. One or more properties of a radiation source (e.g., intensity or dose of an EUV source) can directly influence throughput. For example, a higher dose can provide more photons per second (faster exposure), which can reduce exposure time, thereby increasing throughput, and vice versa.

[0025] Yield is a metric that characterizes failure rate in device fabrication, which relates to cost and efficiency. Yield can be defined as a ratio of all the wafers that are produced by a fab to the number of wafers that were introduced to the fab. Or yield can be the number of working chips that successfully result from the device fabrication process performed on a wafer to the number of potential chips thatcan be fabricated from that wafer in the ideal case of zero failure. As some wafers or chips fail during fabrication, the overall yield is less than 100%. For example, to obtain a 75% yield for a 50-step process (where a step can be indicative of the number of layers formed on a wafer), each individual step should typically have a yield greater than 99.4%. In contrast, if each of the individual steps has a yield of 95%, the compounding errors at each step result in an overall process yield as low as 7-8%. Every wafer or chip lost during fabrication is a sunk cost and lost time for the fab. One or more properties of a radiation source (e.g., stability of an EUV source), can directly influence yield. For example, a radiation source with an unstable intensity can exhibit undesirable variability during an exposure, which in turn can affect the accuracy of a subsequent post-exposure develop process, thereby reducing yield.

[0026] To achieve high-yielding lithographic prints of device structures, small wavelength illumination (e.g., EUV wavelength) can be used to print structures that are smaller compared to lithography systems that use larger wavelengths (the smaller the wavelength, the smaller the features that can be fabricated). In a plasma-based EUV source, a plasma can be created by delivering a high-power laser pulse to a target material (e.g., a droplet of tin) to evaporate and ionize the target material. The resulting highly energized plasma can radiate in the EUV -wavelength range. The process to create the plasma is highly controlled so as to prevent instability in the generated EUV radiation. Even a small amount of non-compliance (e.g., tin droplet is off-center with respect to the laser pulse) can severely disrupt the throughput and yield of a fab. Various embodiments described herein provide devices and functions to address physical phenomena that can impede optimal operation of a radiation source (e.g., a plasma pressure that slows a tin droplet on its way to a target location). Some embodiments implement a correction process that accounts for plasma pressure on incoming tin droplets such. The correction process can adjust a timing of the high-power laser to accurately match the arrival of the tin droplet at a target location.

[0027] Objects and advantages of the disclosure can be realized by the elements and combinations as set forth in embodiments described herein. However, embodiments of the present disclosure are not necessarily required to achieve such exemplary objects or advantages. Some embodiments can achieve a different feature or enhancement without necessarily achieving any expressly stated object or advantage.

[0028] As used herein, unless specifically stated otherwise, the term “or” encompasses all possible combinations, except where infeasible. For example, if it is stated that a component can comprise A or B, then, unless specifically stated otherwise or infeasible, the component can comprise A, or B, or A and B. As a second example, if it is stated that a component can comprise A, B, or C, then, unless specifically stated otherwise or infeasible, the component can comprise A, or B, or C, or A and B, or A and C, or B and C, or A and B and C.

[0029] Relative dimensions of components in drawings may be exaggerated for clarity. Within the following description of drawings, the same or like reference numbers refer to the same or likecomponents or entities, and only the differences with respect to the individual embodiments are described.

[0030] The term “patterning device” may be considered synonymous with similar terms of art, such as “reticle” or “mask.” The term “patterning device” used herein should be broadly interpreted as referring to any device that can be used to impart a pattern on a cross section of a radiation beam. The radiation beam then can recreate the pattern in a target portion of a substrate.

[0031] The term “projection system” used herein should be broadly interpreted as encompassing any type of projection system, including refractive, reflective, catadioptric, magnetic, electromagnetic, or electrostatic optical systems, or any combination thereof, as appropriate for the exposure radiation being used, or for other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term “projection lens” herein may be considered as synonymous with the more general term “projection system.”

[0032] Illumination can be understood to be a form of radiation. Hence, the terms “radiation” and “illumination” can be used interchangeably.

[0033] FIG. 1 shows an example lithographic system 100 comprising a radiation source SO and a lithographic apparatus LA, consistent with embodiments of the present disclosure. The radiation source SO can generate an EUV radiation beam B and to supply the EUV radiation beam B to the lithographic apparatus LA. The lithographic apparatus LA can comprise an illumination system IL, a support structure MT, a projection system PS, and a substrate table WT. Support structure MT can support a patterning device MA (e.g., a mask). Substrate table WT can support a substrate W.

[0034] Illumination system IL can condition EUV radiation beam B before EUV radiation beam B is incident upon the patterning device MA. Illumination system IL can comprise a faceted field mirror device 10 and a faceted pupil mirror device 11. 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. Illumination system IL can comprise other mirrors or devices in addition to, or instead of, faceted field mirror device 10 and faceted pupil mirror device 11.

[0035] After being conditioned, EUV radiation beam B can interact with 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 patterned EUV radiation beam B’ onto substrate W. Projection system PS can comprise a plurality of mirrors (e.g., mirrors 13 and 14) that project patterned EUV radiation beam B’ onto substrate W held by substrate table WT. Projection system PS can apply a reduction factor to patterned EUV radiation beam B’, thus forming an image with features that are smaller than corresponding features on patterning device MA. For example, a reduction factor of 4 or 8 can be applied. Although projection system PS is illustrated as having two mirrors 13 and 14 in FIG. 1, projection system PS can include a different number of mirrors (e.g., six or eight mirrors).

[0036] Substrate W can include previously formed patterns. Where this is the case, lithographic apparatus LA can align the image formed by patterned EUV radiation beam B’ with the pattern that was previously formed on substrate W.

[0037] In some embodiments, a relative vacuum at a pressure below atmospheric pressure is provided in radiation source SO, in illumination system IL, or in projection system PS. The rarified gas can allow one or more features. For example, a small amount of gas (e.g. hydrogen) allows for better management of tin-based contamination in tin-based EUV sources.

[0038] Lithographic apparatus LA and radiation source SO described herein can be used for performing patterning process for a circuit layout. A circuit layout patterning method can comprise receiving a substrate with a photoresist layer. The method can also comprise directing EUV radiation from a radiation source to the photoresist layer to form a patterned photoresist layer. The method can also comprise developing and etching the patterned photoresist layer to form the circuit layout.

[0039] Radiation source SO can be a laser produced plasma (LPP) source. A laser system 1 (e.g., one or more CO2 lasers, one or more solid-state lasers, or one or more other types of lasers, or combinations thereof) can be arranged to deposit energy via a laser beam 2 into a target material (sometimes referred to as a fuel). Droplet generator 3 can provide the target material in the form of liquid droplets. The target material can be tin (Sn). Although tin is referred to in the following description, any material having an emission spectrum suitable for forming radiation beam B can be used. The target material may, for example, be in liquid form, and may, for example, be a metal or alloy. Droplet generator 3 can comprise a nozzle configured to direct droplets of the target material along a trajectory towards a plasma formation region 4 (laser is focused here, hence it is sometimes referred to as primary focus (PF)). Laser beam 2 can be incident upon the droplets at plasma formation region 4. The deposition of laser energy into the target material can create a plasma 7 at plasma formation region 4. Radiation (e.g., EUV radiation) can be emitted from plasma 7 during deexcitation and recombination of electrons with ions of plasma 7.

[0040] The EUV radiation from plasma 7 can be collected and focused by a collector 5. Collector 5 comprises, for example, a near-normal incidence radiation collector (sometimes referred to more generally as a normal-incidence radiation collector). Collector 5 can comprise a multilayer mirror structure arranged to reflect EUV radiation (e.g., EUV radiation having a desired wavelength such as 13.5 nm). Collector 5 can have an ellipsoidal configuration having two focal points. A first one of the focal points can be at the plasma formation region 4. A second one of the focal points can be at an intermediate focus 6. Such an ellipsoidal geometry can enable light radiated from the formation region 4 to be collected and directed to the location of the intermediate focus 6.

[0041] Laser system 1 can be spatially separated from radiation source SO. Where this is the case, laser beam 2 can 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 or a beam expander,or other optics. Laser system 1, radiation source SO, and the beam delivery system can together be considered to be a radiation system.

[0042] Radiation that is reflected by collector 5 can form EUV radiation beam B. EUV radiation beam B can be focused at intermediate focus 6 to form an image at intermediate focus 6 of plasma 7 at plasma formation region 4. The image at intermediate focus 6 can act as a virtual radiation source for illumination system IL. The radiation source SO can be arranged such that intermediate focus 6 is located at or near to an opening 8 in an enclosing structure 9 of radiation source SO.

[0043] Lithographic apparatus LA can also comprise a control system 15, detector 16, and detector 17. Control system 15 can comprise one or more processors and circuitry to control various functions of lithographic apparatus LA (e.g., feedback signals, droplet generation of droplet generator 3, laser pulse generation of laser system 1, or the like). Detector 16 can be disposed past intermediate focus 6 (downstream) for monitoring one or more properties of radiation beam B (e.g., monitor brightness, wavelength, pulse characteristics, or the like). Detector 17 can be disposed to have line of sight to plasma formation region 4 (e.g., proximal to a lip of collector 5). Detector 17 can be used for monitoring one or more properties of the plasma generated at plasma formation region 4 (e.g., monitor plasma volume, plasma shape, radiation brightness, radiation wavelength, pulse characteristics, or the like). Detectors 16 or 17 can comprise one or more a suitable photon-sensitive devices according to the properties being monitored (e.g., an image capture device such as a camera, a single-pixel sensor such as a photodiode, or the like).

[0044] EIG. 2 shows an example mask inspection system 200, consistent with embodiments of the present disclosure. Mask inspection system 200 can be used to identify or inspect defects in a mask to be used in a lithographic apparatus (e.g., lithographic apparatus LA of EIG. 1). Mask inspection system 200 can comprise a radiation source 202, an illumination system 204, and a detection system 206. A mask 208 (e.g., patterning MA of FIG. 1) is placed on a mask stage 210. Mask 208 can be illuminated by illumination system 204, which can guide radiation from radiation source 202 via reflection. Detection system 206 can guide radiation scattered from the illuminated mask 208 via reflection. The radiation from illuminated mask 208 can be received at a detector 212 (e.g., an image capture device). Defects of mask 208 can be determined based on radiation detected by detector 212.

[0045] FIG. 3 shows a portion of an example radiation source 300, consistent with embodiments of the present disclosure. In some embodiments, radiation source 300 comprises a laser system 302, a droplet generator 304, a collector 306, a detector 308, and a control system 310. Laser system 302 can generate a laser beam 312 (e.g., a pulsed laser beam). The laser beam can be directed toward a plasma formation region 314 (e.g., PF). Laser 312 can energize a droplet of a target comprising material (e.g., target material such as tin, xenon, or the like) to generate a plasma 316 that emits photons (e.g., at EUV wavelength(s)) which are focused or otherwise collected into a beam of radiation 318. Radiation source 300 can represent a more detailed view of radiation source SO (FIG. 1). For example, laser system 302, droplet generator 304, collector 306, detector 308, control system 310, laser beam 312,plasma formation region 314, plasma 316, and radiation beam 318 can correspond to laser system 1, droplet generator 3, collector 5, detector 17, control system 15, laser beam 2, plasma formation region 4, plasma 7, and EUV radiation beam B, respectively (FIG. 1).

[0046] Droplet generator 304 (e.g., a target material droplet dispenser) can comprise a nozzle 320. Nozzle 320 can dispense and direct droplets of target material toward plasma formation region 314 to intersect with laser beam 312. Nozzle 320 can be configured to dispense droplets at a given velocity v (indicated with an arrow). FIG. 3 can represent a “snapshot” in time, in which a droplet 322 is the “current” droplet being ionized at plasma formation region 314 while a next droplet 324 is the trailing droplet that follows droplet 322.

[0047] In some embodiments, a next-droplet interaction (NDI) is a phenomenon that occurs when next droplet 324 experiences an interaction with plasma 316. For example, plasma 316 can generate a pressure that pushes against the motion of next droplet 324, resulting in a deviation of the velocity of next droplet 324. Plasma 416 can generate a pressure on the next droplet via direct ion momentum transfer or surface evaporation by radiation. The change in velocity of the next droplet 324 can delay the arrival of the next droplet at that the plasma formation region 314. Such a delay can disrupt efficient generation of radiation beam 318. The disruption can occur due to mistiming of pulses of laser beam 312 with respect to delayed droplets. If next droplet 324 lags due to the plasma pressure, then the desired intersection of next droplet 324 and a pulse of laser beam 312 can be disrupted (illustrated as delayed next-droplet position 326), causing instability and poor performance of intensity of radiation beam 318 (e.g., lower power, flicker, inefficient power conversion, or the like). In some embodiments, the pulse of laser beam 312 can be a group of three pulses (e.g., a pre-pulse, a rarefaction pulse, and a main-pulse that ignites the EUV -generating plasma). The term “next-droplet interaction” can also be referred to via terms such as “momentum transfer,” “momentum transfer event,” or the like, as a reference to the momentum transferred to next droplet 324 from plasma 316. Other terms can also be used, such as “plasma pressure,” “plasma repulsion,” “plasma force,” “droplet slowdown by plasma,” “droplet deformation by plasma,” or the like.

[0048] In an example arrangement to address next-droplet interactions, detector 308 can be used to monitor plasma formation region 314 for the purpose of correcting the timing of pulses of laser beam 312 (e.g., using a feedback loop). However, such an arrangement may be insufficient to provide immediate correction (e.g., on next pulse). It may take several pulse cycles for radiation system 300 to compensate for performance issues arising from next-droplet interactions.

[0049] Another example method to reduce next-droplet interactions can be to increase the distance d between droplet 322 and next droplet 324. The distance d can be increased a number of ways, each with potential tradeoffs or limitations. For example, reducing a frequency of generated droplets can increase d with a tradeoff in average EUV power (e.g., fewer droplets per second reduces EUV intensity per unit time). Another way to increase d without reducing EUV power is to increase thevelocity v for each droplet. However, adjustments to droplet velocities can have severe constraints (e.g., nozzle limitations, fluid dynamics, turbulence, droplet deformation, or the like).

[0050] Hence, some embodiments described herein provide devices and functions for immediate correction of next-droplet interactions.

[0051] FIG. 4 shows a process flow 400 of an example method for compensating for next-droplet interactions, consistent with embodiments of the present disclosure. In some embodiments, the method is executed using devices and functions described in reference to FIGS. 1-4 (e.g., control system 15 or 310 (FIGS. 1 and 4)).

[0052] Process flow 400 can comprise a feedforward loop 402 that compensates for undesirable nextdroplet interactions. Feedforward loop 402 can comprise a momentum transfer model 404 that takes into account a nonlinear dependence of the plasma force exerted upon next droplet 324 with respect to a property of plasma 316 (FIG. 3) (e.g., EUV intensity, energy, or the like). Before proceeding further with the description of process flow 400, it is instructive to first appreciate the nonlinear dependence that is worked into the momentum transfer model 404, as shown in FIG. 5.

[0053] FIG. 5 shows a graph 500 of example measurement data and model behavior under the influence of next-droplet interactions, consistent with embodiments of the present disclosure. In some embodiments, the vertical axis of graph 500 represents, in arbitrary units, a momentum transfer caused by EUV plasma pressure (e.g., next-droplet interaction). The momentum transfer is an example of a metric that is indicative of a change in velocity (Av) or slowdown of next droplet 324 that results from the EUV plasma pressure generated by plasma 316 (FIG. 3).

[0054] It can be hypothesized that a more intense plasma (e.g., a brighter EUV output) causes a proportional increase of momentum transferred to a droplet (linear increase). It is to be appreciated that a measure of plasma intensity is one example of numerous aspects that can be used to quantify an interaction between a pulse of laser beam 312 and droplet 322 (FIG. 3). Other examples can include laser pulse energy, laser pulse fluence, EUV pulse intensity, EUV pulse energy or brightness, or the like.

[0055] Furthermore, it can also be hypothesized that the magnitude of momentum transfer obeys the inverse square law. In other words, the magnitude of momentum transfer can fall off in proportion to the inverse square of the distance d (FIG. 3) (linear decrease). The two proportionalities can be combined as a single combined parameter (e.g., EUV energy divided by z / A2) and it would be reasonable to expect that the momentum transfer is linear with respect to the combined parameter. The horizontal axis of graph 500 represents this combined parameter, in arbitrary units.

[0056] However, instead of the hypothesized linear behavior, the measurement data in graph 500 shows nonlinearity. Graph 500 includes measurement data 502. Graph 500 also includes a plot representative of a nonlinear model 504 (based on the observed nonlinear behavior of measurement data 502), as well as another plot representative of a linear model 506 (based on a linear fit of measurement data 502). The momentum transfer of a given model informs the change in velocity (Av)of a droplet, which can be used to set the corrective time adjustment for a next pulse of laser beam 312 (FIG. 3) (e.g., time adjustment At is related to other parameters via At = Av I d). A more accurate model can result in a more accurate corrective time delay for a next pulse of laser beam 312 such that next droplet 324 can optimally intercept the next laser pulse at plasma formation region 314, thereby mitigating the situation illustrated by delayed next-droplet position 326 (FIG. 3). A technical significance of nonlinear model 504 is the ability to generate more accurate time adjustments for pulses of laser beam 312 (FIG. 3) as compared to using linear model 506. Hence, use of nonlinear model 504 can result in more efficient and stable EUV output. Calibrations can also be improved by using nonlinear model 504. For example, under an assumption of linearity (no offset), a calibration that includes a zero point (no plasma) may not be correct, whereas a calibration using nonlinear model 504 can avoid such an error. Furthermore, operating a linear model controller near the non-linearity can induce instability, which can be exacerbated depending on interaction with other system behaviors (e.g., modulation of the drive laser energy can increase the instability).

[0057] In some embodiments, parameters such as droplet separation distance d and aspect(s) of the interaction between a pulse of laser beam 312 and droplet 322 (FIG. 3) are set or predetermined (e.g., known quantities based on system settings). If a parameter is subject to drift or uncertainty, then a measurement can be performed to ascertain the value of the uncertain quantity. For example, fluctuations of the aspect(s) of the interaction between a pulse of laser beam 312 and droplet 322 can be quantified in real time (e.g., per shot / pulse) via detector 308 (FIG. 3). Such information can be used when implementing timing corrections in real time. Detector 408 can measure the relative position between droplet and laser beams at plasma event.

[0058] Referring back to FIG. 4, momentum transfer model 404 can comprise a momentum transfer model formalism 406 that comprises a plurality of input variables (e.g., adjustable or fixed parameters). As a set of input variables 408, momentum transfer model formalism 406 can accept quantities related to source configuration 408. Source configuration 408 can include droplet size, droplet spacing (d in FIG. 3), droplet speed (v in FIG. 3), and base laser timings. Base laser timings can refer to a baseline timing of laser pulses in the absence of next-droplet interactions and effects. As another set of input variables 410, momentum transfer model formalism 406 can accept nonlinear model parameters, which are labeled as a,y, or the like. Such parameters can include coefficients, offsets, or the like, that correspond to the nonlinear model 504. For example, if nonlinear model 504 (FIG. 5) is based on a polynomial best fit (e.g., quadratic), then momentum transfer model 404 can include coefficients and offsets that correspond to the polynomial that represents nonlinear model 504.

[0059] Momentum transfer model 404 can be referred to as a physical model that is based on droplet physics. Droplets have a diameter / cross-section and are under the influence of inverse square effects with respect to distance from plasma 314 (FIG. 3), as well as other physical effects. Momentum transfer model formalism 406, set of input variables 408 (e.g., drag cross section oc droplet diameter),and set of input variables 410 (nonlinear plasma pressure) are rooted in physics and can therefore accurately predict droplet behavior more accurately than a linear model implementation.

[0060] Momentum transfer model formalism 406 can receive yet another input parameter 412: a measured aspect of the interaction between a pulse of laser beam 312 and droplet 322 (FIG. 3). The measured aspect of the interaction can be the measured EUV energy of the most recent shot (pulse), the measured laser energy of the most recent pulse of laser beam 312, or the like. Another example of the measured aspect of the interaction is a measured amount of energy proportional to the laser energy reflected off of the droplet (the reflection can be projected onto a camera or quad-cell detector or other sensor to measure the relative position of the droplet relative to the beam, referenced to the camera’s coordinate system). The aspect of the interaction between a pulse of laser beam 312 and droplet 322 can be measured via detector 308 (FIG. 3). Based on these inputs, a suitable momentum transfer value can be determined based on nonlinear model 504 (FIG. 5). The determined value serves as a prediction (feedforward) for the momentum transferred to next droplet 324 (FIG. 3). Momentum transfer model 404 can output a laser timing compensation 414. At laser adjustment 416, laser timing compensation 414 can be a correction term that gets applied to the base laser timing for the next droplet event. In various implementations, momentum transfer model 404 can be implemented in the form of calculations (e.g., combinations of linear, constant-offset, polynomial, exponential, trigonometric, or other mathematical functions) in combination with various parameters such as input variables 408 and 410. In other implementations, momentum transfer model 404 can be implemented in the form of look-up tables or interpolation tables that store relationships such as the behavior indicated in FIG. 5. Alternatively, momentum transfer model 404 can be implemented in the form of calculations in combination with look-up tables.

[0061] In some embodiments, a feedback loop for fine tuning model parameters can be implemented in conjunction with feedforward loop 402. The feedback loop can comprise error analysis 418 and model parameter fine tuning 420. It is noted that a feedforward adjustment relies on a prediction. Feedforward methods are very sensitive to the accuracy of the underlying predictor (in this case, the nonlinear model). Error analysis 418 provides an assessment of the error associated with the most recent prediction made by momentum transfer model 404. For example, error analysis 418 can rely on measurement information (e.g., measured relative position of droplet using a sensor or camera as described above). Based on the determined error, model parameter fine tuning 420 can be used to finely adjust the input variables 410 (the nonlinear model parameters). The speed of the fine tuning (“learning rate”) can be set or adjusted as desired. The feedback loop can be repeated at each shot or cycle (e.g., at each plasma ignition). The learning rate can set the approximate number of cycles it takes for the fine tuning to stabilize or converge.

[0062] Using the feedforward loop embodiments described above may provide accurate pulse timing corrections prior to a next droplet (in other words, on a per shot basis). The prediction power ofnonlinear model 504 promotes efficient and maximum production of EUV output from radiation sources SO or 310 (FIGS. 1 and 4).

[0063] FIG. 6 shows example operations of a method 600 for compensating for next-droplet interactions, consistent with embodiments of the present disclosure. In some embodiments, the method is executed using devices and functions described in reference to FIGS. 1-6 (e.g., control system 15 or 310 (FIGS. 1 and 4)). Method 600 can be a simplified analog to process flow 400 (FIG.4).

[0064] At operation 602, a stream of droplets of target material can be generated and directed to an interaction region (e.g., droplets 322 and 324 directed to plasma formation region 4 or 314 (FIGS. 1 and 4)).

[0065] At operation 604, the droplets can be irradiated at the interaction region using a beam of pulses (e.g., laser beam 2 or 312 in pulsed mode can intersect droplets 322 and 324 at plasma formation region 4 or 314 (FIGS. 1 and 4)).

[0066] At operation 606, an aspect of an interaction between a pulse from the beam and a droplet from the stream can be measured (e.g., detector 17 or 308 can be used for measuring the interaction between a pulse of laser beam 312 and droplet 322 (FIGS. 1 and 4)).

[0067] At operation 608, a pulse timing adjustment (a correction term) that is nonlinearly dependent on the measured aspect can be determined (e.g., control systems 15 or 310 can generate a laser timing compensation 414 using nonlinear model 504 (FIGS. 1 and 4-6)).

[0068] At operation 610, a subsequent laser pulse can be controlled based on the pulse timing adjustment (e.g., control systems 15 or 310 can perform laser adjustment 416 (FIGS. 1, 4, and 5)).

[0069] In addition to the operations shown in FIG. 6, embodiments directed to method 600 can comprise other operations directed to devices and functions described in reference to FIGS. 1-6.

[0070] Description of the timing correction in reference to FIGS. 5-7 were provided in the context of a predetermined model (e.g., nonlinear model 504 is known ahead of time). In instances where a model has not been determined with sufficient detail, a model can be trained using embodiments described below.

[0071] FIG. 7 shows a process flow 700 of an example method fortraining model for next-droplet interactions, consistent with embodiments of the present disclosure. In some embodiments, the method is executed using devices and functions described in reference to FIGS. 1-7 (e.g., control system 15 or 310 (FIGS. 1 and 4)). Process flow 700 can reuse one or more of the assets described in reference to process flow 400 (FIG. 4). Hence, unless otherwise stated, some elements shown in FIG.7 can be the same or substantially similar to corresponding elements of FIG. 4. For brevity, description of common elements in FIGS. 5 and 8 are to be inferred from the above description of FIG. 2. For corresponding elements, the leading (left-most) digit(s) can denote the figure in which the elements first appear while the trailing (right-most) digit(s) can identify the element. Examples of corresponding elements can include a feedforward loop 702, a momentum transfer model 704, amomentum transfer model formalism 706, a set of input variables 708, another set of input variables 710, a laser timing compensation 714, laser adjustment 716, error analysis 718, and model parameter fine tuning 720.

[0072] Because physical model parameters are derived from the energy partition of the EUV plasma, it is expected that model parameters (e.g., set of input variables 710) are transferrable and invariant from one radiation source to another, with no adjustments or only small adjustments needed from one source device to another (e.g., model parameters can be invariant if droplet size is changed).

[0073] Hence, the training of method 700 replaces input parameter 412 (FIG. 4) with a scan 712’ of an interaction between a pulse of laser beam 312 and droplet 322 (FIG. 3) (e.g., the measured EUV energy of the most recent shot (pulse), the measured laser energy of the most recent pulse of laser beam 312, or the like). For example, scan 712’ can involve a set of measurements made with a variety of values for the input parameter (such as laser pulse energy or generated EUV energy) to gather data on the observed response of a system. These measurements may be collected over time during regular operation or they may be gathered during a dedicated analysis or calibration period for a system, such as with an stepwise organized scan of a range of energy values for pulses of laser beam 312 (FIG. 3). The scan can create different plasma pressure forces to train momentum transfer model 704. Using scan 712’, the entire accessible NDI parameter space can be mapped. Hence, the nonlinear momentum transfer behavior depicted in FIG. 5 can be characterized.

[0074] At the initial stages of the training, there can be undetermined input variables in momentum transfer model formalism 706. Hence, baseline model parameters 722 can be loaded to initialize momentum transfer model formalism 706. It follows that the model parameters (e.g., set of input variables 710) can be fine-tuned from the pre-defined baseline values. Even if droplet size is changed, model parameters can remain robust. Baseline model parameters 722 can still be used as the starting point for model parameter fine tuning.

[0075] A non-transitory computer-readable medium may be provided that stores instructions for a processor of a controller (e.g., control system 15 or 310 in FIGS. 1 and 4) for compensating for nextdroplet interactions according to the process flows and method of FIGS. 5, 7, and 8 above, consistent with embodiments in the present disclosure. For example, the instructions stored in the non-transitory computer-readable medium may be executed by the circuitry of the controller for performing process flows 400 or 700 or method 600 in part or entirely. Common forms of non-transitory media include, for example, a floppy disk, a flexible disk, hard disk, solid-state drive, magnetic tape, or any other magnetic data storage medium, a Compact Disc Read-Only Memory (CD-ROM), any other optical data storage medium, any physical medium with patterns of holes, a Random Access Memory (RAM), a Programmable Read-Only Memory (PROM), a Field Programmable Gate Array (FPGA), and Erasable Programmable Read-Only Memory (EPROM), a FLASH-EPROM or any other flash memory, Non-Volatile Random Access Memory (NVRAM), a cache, a register, any other memory chip or cartridge, and networked versions of the same.

[0076] Some embodiments may further be described using the following clauses:1. An illumination source comprising:a droplet generator configured to produce a stream of droplets of target material directed to an interaction region;a laser configured to irradiate the droplets at the interaction region using a beam of pulses, wherein the irradiated droplets are configured to generate output illumination of the illumination source;a detector configured to measure an aspect of an interaction between a pulse from the beam and a droplet from the stream; anda controller comprising circuitry and configured to:determine a pulse timing adjustment that is nonlinearly dependent on the measured aspect; andcontrol a subsequent laser pulse of the beam based on the pulse timing adjustment.2. The illumination source of clause 1, wherein the controller is further configured to:determine a metric that is indicative of a speed of droplets in the stream; anddetermine the pulse timing adjustment based on the metric.3. The illumination source of clause 2, wherein:the measured aspect is representative of an extreme ultraviolet (EUV) energy produced by the interaction or an energy of the pulse from the beam; andthe controller is further configured to determine the metric based on a nonlinear analysis of:a ratio of a first quantity indicative of the EUV energy to a second quantity indicative of a square of a spacing of droplets of the stream; ora ratio of a third quantity indicative of the energy of the pulse to the second quantity.4. The illumination source of clauses 2 or 3, wherein the metric is based on a physical model of the interaction.5. The illumination source of clause 4, wherein the physical model comprises adjustable parameters.6. The illumination source of clause 5, wherein the controller is further configured to adapt the physical model by adjusting one or more of the adjustable parameters.7. The illumination source of any one of clauses 4 to 6, wherein the controller is further configured to determine the metric based on a configuration of the laser and a nonlinear characteristic of the physical model.8. The illumination source of any one of clauses 2 to 7, wherein:the illumination source is configured to operate the laser to scan a range of energy values for the pulses; andthe controller is further configured to train a physical model used for determining the metric.9. A non-transitory computer-readable medium that stores a set of instructions that is executable by at least one processor of an extreme ultraviolet (EUV) radiation source to cause the EUV radiation source to perform operations, the operations comprising:obtaining a measured aspect of an interaction between a pulse from a beam of laser pulses and a droplet from a stream of droplets of target material, wherein the EUV radiation source is configured to irradiate the droplets at the interaction region using the beam;determining a pulse timing adjustment that is nonlinearly dependent on the measured aspect; andcontrolling a subsequent laser pulse of the beam based on the pulse timing adjustment.10. The non-transitory computer-readable medium of clause 9, where in the operations further comprise:determining a metric that is indicative of a speed of droplets in the stream; and determining the pulse timing adjustment based on the metric.11. The non-transitory computer-readable medium of clause 10, wherein:the measured aspect is representative of an EUV energy produced by the interaction or an energy of the pulse from the beam; andthe operations further comprise determining the metric based on a nonlinear analysis of: a ratio of a first quantity indicative of the EUV energy to a second quantity indicative of a square of a spacing of droplets of the stream; ora ratio of a third quantity indicative of the energy of the pulse to the second quantity.12. The non-transitory computer-readable medium of clauses 10 or 11, wherein the metric is based on a physical model of the interaction.13. The non-transitory computer-readable medium of clause 12, wherein the physical model comprises adjustable parameters.14. The non-transitory computer-readable medium of clause 13, wherein the operations further comprise adapting the physical model by adjusting one or more of the adjustable parameters.15. The non-transitory computer-readable medium of any one of clauses 12 to 14, wherein the operations further comprise determining the metric based on a configuration of the laser and a nonlinear characteristic of the physical model.16. The non-transitory computer-readable medium of any one of clauses 10 to 15, wherein:the EUV radiation source is configured to operate the laser to scan a range of energy values for the pulses; andthe operations further comprise training a physical model used for determining the metric. 17. A lithographic apparatus comprising:a projection system configured to project an image of a pattern a patterning device onto a substrate; andan illumination source configured to illuminate the patterning device, the illumination source comprising:a droplet generator configured to produce a stream of droplets of target material directed to an interaction region;a laser configured to irradiate the droplets at the interaction region using a beam of pulses, wherein the irradiated droplets are configured to generate output illumination of the illumination source;a detector configured to measure an aspect of an interaction between a pulse from the beam and a droplet from the stream; anda controller comprising circuitry and configured to:determine a pulse timing adjustment that is nonlinearly dependent on the measured aspect; andcontrol a subsequent laser pulse of the beam based on the pulse timing adjustment.18. The lithographic apparatus of clause 17, wherein the controller is further configured to:determine a metric that is indicative of a speed of droplets in the stream; anddetermine the pulse timing adjustment based on the metric.19. The lithographic apparatus of clause 18, wherein:the measured aspect is representative of an extreme ultraviolet (EUV) energy produced by the interaction or an energy of the pulse from the beam; andthe controller is further configured to determine the metric based on a nonlinear analysis of:a ratio of a first quantity indicative of the EUV energy to a second quantity indicative of a square of a spacing of droplets of the stream; ora ratio of a third quantity indicative of the energy of the pulse to the second quantity.20. The lithographic apparatus of clauses 18 or 19, wherein the metric is based on a physical model of the interaction.21. The lithographic apparatus of clause 20, wherein the physical model comprises adjustable parameters.22. The lithographic apparatus of clause 21, wherein the controller is further configured to adapt the physical model by adjusting one or more of the adjustable parameters.23. The lithographic apparatus of any one of clauses 20 to 22, wherein the controller is further configured to determine the metric based on a configuration of the laser and a nonlinear characteristic of the physical model.24. The lithographic apparatus of any one of clauses 18 to 23, wherein:the illumination source is configured to operate the laser to scan a range of energy values for the pulses; andthe controller is further configured to train a physical model used for determining the metric.

[0077] It will be appreciated that the embodiments of the present disclosure are not limited to the exact construction that has been described above and illustrated in the accompanying drawings and that various modifications and changes may be made without departing from the scope thereof.

Claims

CLAIMS1. An illumination source comprising:a droplet generator configured to produce a stream of droplets of target material directed to an interaction region;a laser configured to irradiate the droplets at the interaction region using a beam of pulses, wherein the irradiated droplets are configured to generate output illumination of the illumination source;a detector configured to measure an aspect of an interaction between a pulse from the beam and a droplet from the stream; anda controller comprising circuitry and configured to:determine a pulse timing adjustment that is nonlinearly dependent on the measured aspect; andcontrol a subsequent laser pulse of the beam based on the pulse timing adjustment.

2. The illumination source of claim 1, wherein the controller is further configured to:determine a metric that is indicative of a speed of droplets in the stream; anddetermine the pulse timing adjustment based on the metric.

3. The illumination source of claim 2, wherein:the measured aspect is representative of an extreme ultraviolet (EUV) energy produced by the interaction or an energy of the pulse from the beam; andthe controller is further configured to determine the metric based on a nonlinear analysis of:a ratio of a first quantity indicative of the EUV energy to a second quantity indicative of a square of a spacing of droplets of the stream; ora ratio of a third quantity indicative of the energy of the pulse to the second quantity.

4. The illumination source of claim 2, wherein the metric is based on a physical model of the interaction.

5. The illumination source of claim 4, wherein the physical model comprises adjustable parameters.

6. The illumination source of claim 5, wherein the controller is further configured to adapt the physical model by adjusting one or more of the adjustable parameters.

7. The illumination source of claim 4, wherein the controller is further configured to determine the metric based on a configuration of the laser and a nonlinear characteristic of the physical model.

8. The illumination source of claim 2, wherein:the illumination source is configured to operate the laser to scan a range of energy values for the pulses; andthe controller is further configured to train a physical model used for determining the metric.

9. A non-transitory computer-readable medium that stores a set of instructions that is executable by at least one processor of an extreme ultraviolet (EUV) radiation source to cause the EUV radiation source to perform operations, the operations comprising:obtaining a measured aspect of an interaction between a pulse from a beam of laser pulses and a droplet from a stream of droplets of target material, wherein the EUV radiation source is configured to irradiate the droplets at the interaction region using the beam;determining a pulse timing adjustment that is nonlinearly dependent on the measured aspect; andcontrolling a subsequent laser pulse of the beam based on the pulse timing adjustment.

10. The non-transitory computer-readable medium of claim 9, where in the operations further comprise:determining a metric that is indicative of a speed of droplets in the stream; and determining the pulse timing adjustment based on the metric.

11. The non-transitory computer-readable medium of claim 10, wherein:the measured aspect is representative of an EUV energy produced by the interaction or an energy of the pulse from the beam; andthe operations further comprise determining the metric based on a nonlinear analysis of: a ratio of a first quantity indicative of the EUV energy to a second quantity indicative of a square of a spacing of droplets of the stream; ora ratio of a third quantity indicative of the energy of the pulse to the second quantity.

12. The non-transitory computer-readable medium of claim 10, wherein the metric is based on a physical model of the interaction.

13. The non-transitory computer-readable medium of claim 12, wherein the physical model comprises adjustable parameters.

14. The non-transitory computer-readable medium of claim 13, wherein the operations further comprise adapting the physical model by adjusting one or more of the adjustable parameters.

15. The non-transitory computer-readable medium of claim 12, wherein the operations further comprise determining the metric based on a configuration of the laser and a nonlinear characteristic of the physical model.

16. The non-transitory computer-readable medium of claim 10, wherein:the EUV radiation source is configured to operate the laser to scan a range of energy values for the pulses; andthe operations further comprise training a physical model used for determining the metric.

17. A lithographic apparatus comprising:a projection system configured to project an image of a pattern a patterning device onto a substrate; andan illumination source configured to illuminate the patterning device, the illumination source comprising:a droplet generator configured to produce a stream of droplets of target material directed to an interaction region;a laser configured to irradiate the droplets at the interaction region using a beam of pulses, wherein the irradiated droplets are configured to generate output illumination of the illumination source;a detector configured to measure an aspect of an interaction between a pulse from the beam and a droplet from the stream; anda controller comprising circuitry and configured to:determine a pulse timing adjustment that is nonlinearly dependent on the measured aspect; andcontrol a subsequent laser pulse of the beam based on the pulse timing adjustment.

18. The lithographic apparatus of claim 17, wherein the controller is further configured to:determine a metric that is indicative of a speed of droplets in the stream; anddetermine the pulse timing adjustment based on the metric.

19. The lithographic apparatus of claim 18, wherein:the measured aspect is representative of an extreme ultraviolet (EUV) energy produced by the interaction or an energy of the pulse from the beam; andthe controller is further configured to determine the metric based on a nonlinear analysis of:a ratio of a first quantity indicative of the EUV energy to a second quantity indicative of a square of a spacing of droplets of the stream; ora ratio of a third quantity indicative of the energy of the pulse to the second quantity.

20. The lithographic apparatus of claim 18, wherein the metric is based on a physical model of the interaction.

21. The lithographic apparatus of claim 20, wherein the physical model comprises adjustable parameters.

22. The lithographic apparatus of claim 21, wherein the controller is further configured to adapt the physical model by adjusting one or more of the adjustable parameters.

23. The lithographic apparatus of claim 20, wherein the controller is further configured to determine the metric based on a configuration of the laser and a nonlinear characteristic of the physical model.

24. The lithographic apparatus of claim 18, wherein:the illumination source is configured to operate the laser to scan a range of energy values for the pulses; andthe controller is further configured to train a physical model used for determining the metric.

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