Apparatus and method for controlling droplet generator performance

Abstract

An apparatus and method of controlling the formation of droplets for generating EUV radiation. A droplet source includes a fluid exiting a nozzle and a subsystem having an electrically actuable element that creates a disturbance in the fluid. The droplet source produces a stream that breaks into droplets that in turn coalesce into larger droplets as the droplets progress toward an irradiation region. The electrically actuable element is driven by a control signal having a sinusoidal component and a square wave component. Various parameters, such as a phase difference between the sinusoidal component and the square wave component, are measured and controlled to minimize the formation of uncoalesced satellite droplets in the stream.

Description

[0001] Cross-references to related applications

[0002] This application claims priority to U.S. Application No. 62 / 810,768, filed February 26, 2019; U.S. Application No. 62 / 928,429, filed October 31, 2019; and U.S. Application No. 62 / 959,275, filed January 10, 2020, all of which are incorporated herein by reference in their entirety. Technical Field

[0003] This application relates to extreme ultraviolet (“EUV”) light sources and methods of operating them. These light sources provide EUV light by generating plasma from a source or target material. In one application, EUV light can be collected and used in photolithography processes to produce semiconductor integrated circuits. Background Technology

[0004] Patterned EUV beams can be used to expose resist-coated substrates, such as silicon wafers, to create extremely small features within the substrate. EUV light (sometimes also called soft X-rays) is generally defined as electromagnetic radiation with wavelengths ranging from about 5 nm to about 100 nm. A specific wavelength used for photolithography appears around 13.5 nm.

[0005] Methods for generating EUV light include, but are not limited to, converting a source material into a plasma state having chemical elements that emit spectral lines in the EUV range. These elements may include, but are not limited to, xenon, lithium, and tin.

[0006] In one such method, commonly known as laser-generated plasma (“LPP”), the desired plasma is generated by irradiating a source material (e.g., in the form of droplets, streams, or lines) with a laser beam. In another method, commonly known as discharge-generated plasma (“DPP”), the desired plasma is generated by placing a source material with a suitable emission line between a pair of electrodes and inducing a discharge between the electrodes.

[0007] One technique for generating droplets involves melting a target material, such as tin, sometimes referred to as a source material, and then forcing the molten source material under high pressure through an orifice of relatively small diameter, such as from about 0.1 μm to about 30 μm in diameter, to generate a laminar fluid jet with velocities ranging from about 30 m / s to about 200 m / s. In most cases, naturally occurring instabilities, such as thermal noise or eddy shedding in the flow exiting the orifice, will cause the flow to break into droplets. These droplets have different velocities and combine with each other during flight to coalesce into larger droplets.

[0008] In the EUV generation process considered here, the decomposition / coalescing process needs to be controlled. For example, to synchronize droplets with the optical pulses of an LPP-driven laser, a repetitive perturbation with an amplitude exceeding the random noise amplitude can be applied to the continuous laminar fluid jet emanating from the orifice. By applying the perturbation at the same frequency (or higher harmonics) as the repetition rate of the pulsed laser, the droplets are synchronized with the laser pulse. For example, the perturbation can be applied to the flow by coupling an electrically actuated element (such as a piezoelectric material) to the flow and driving the electrically actuated element with a periodic waveform. In one embodiment, the diameter of the electrically actuated element will contract and expand (on the nanometer scale). This dimensional change is mechanically coupled to a capillary, which undergoes a corresponding diameter contraction and expansion. This volumetric displacement induces acoustic and elastic waves in the capillary terminating at the orifice. The target material in the orifice is then periodically accelerated by the acoustic waves, ultimately resulting in large-spacing droplets appearing at the driving laser frequency in a frequency range far below the natural Rayleigh splitting frequency of the fluid microjets. The natural splitting frequency of the fluid jet is in the range of approximately 3 to approximately 15 MHz, while the driving laser operation is expected to be in the range of approximately 50 to approximately 160 kHz. This means that in order to obtain the desired final droplet, many small droplets must merge into a periodic droplet stream consisting of droplets much larger than the orifice diameter.

[0009] As used herein, the term "electroactable element" and its derivatives refer to a material or structure that undergoes a change in size when subjected to a voltage, an electric field, a magnetic field, or a combination thereof, including but not limited to piezoelectric, electrostrictive, and magnetostrictive materials. Apparatus and methods for controlling droplet flow using electroactable elements are disclosed, for example, in U.S. Patent Application Publication No. 2009 / 0014668A1, entitled "Laser Produced Plasma EUV Light Source Using a Droplet Stream Produced using a Modulated Disturbance Wave," published January 15, 2009, and U.S. Patent No. 8,513,629, entitled "Droplet Generator with Actuator Induced Nozzle Cleaning," published August 20, 2013, both of which are incorporated herein by reference in their entirety.

[0010] Therefore, the task of the droplet generator is to place correctly sized droplets at the prime focus of the collecting mirror used to collect EUV radiation, where they will serve as the target material for generating EUV radiation. The droplets must arrive at the prime focus within specific spatial and temporal stability criteria (i.e., repeatable at both position and time within acceptable margins). They must also arrive at a given frequency and velocity. Furthermore, the droplets must be fully coalesced, meaning they must be monodisperse (uniform in size) and arrive at a given driving frequency.

[0011] For example, the droplet flow should be free of "satellite" droplets—smaller droplets of the target material that fail to coalesce into the main droplet. Meeting these criteria is complex because, for small orifices and high pressures, it may be necessary to use electrically actuated elements to drive the coalescence of many microdroplets. The operating window is typically very small, making the system sensitive to performance variations, such as performance changes over time. For example, when the performance of the droplet generator changes, it may produce droplets that have not fully coalesced by the time they reach the main focus. Eventually, the performance of the droplet generator will deteriorate to the point where it must be taken offline for maintenance or replaced.

[0012] One method for controlling coalescence is to apply a mixing waveform to the molten target material exiting the nozzle. The mixing waveform is a periodic piezoelectric excitation waveform that can be used to control and optimize the coalescence process in various droplet generators on various systems operating at various power levels (such as 250 W). See, for example, International Patent Application No. PCT / EP2019 / 050100 entitled “Apparatus for and Method of Controlling Coalescence of DropletStream”, filed January 3, 2019, which is incorporated herein by reference in its entirety.

[0013] It is necessary to be able to control the formation and coalescence of droplets in a way that allows for optimization of these processes. Summary of the Invention

[0014] To provide a basic understanding of the embodiments, a simplified overview of one or more embodiments is presented below. This overview is not a comprehensive summary of all contemplated embodiments and is not intended to identify key or essential elements of all embodiments, nor is it intended to define the scope of any or all embodiments. Its sole purpose is to present some concepts of one or more embodiments in a simplified form as a prelude to the more detailed description that follows.

[0015] According to one aspect of the embodiments, an apparatus is disclosed comprising: a target material dispenser having a nozzle and adapted to provide a flow of target material, the flow of target material splitting into first droplets after exiting the nozzle; an electrically actuated element mechanically coupled to the target material dispenser and arranged to induce a velocity disturbance in the flow based on an applied waveform, the velocity disturbance causing the first droplets to eventually coalesce into second droplets larger than the first droplets in one or more stages within a coalescence distance from the nozzle; and a waveform generator electrically coupled to the electrically actuated element and adapted to generate the applied waveform having a sine wave component and a square wave component, the sine wave component having an amplitude, and the square wave component having a phase difference from the sine wave component, the amplitude and phase difference being selected to minimize the coalescence distance while avoiding abrupt changes in the coalescence distance. The electrically actuated element may be a piezoelectric element.

[0016] According to another aspect of the embodiments, an apparatus is disclosed comprising: a target material dispenser having a nozzle and adapted to provide a flow of target material, the flow of target material splitting into first droplets after exiting the nozzle; an electrically actuated element mechanically coupled to the target material dispenser and arranged to induce a velocity disturbance in the flow based on an applied waveform, the velocity disturbance causing the first droplets to eventually coalesce into second droplets larger than the first droplets in one or more stages within a coalescence distance from the nozzle, the second droplets being spaced apart such that the second droplets pass through a fixed point at an intersecting interval; an intersecting interval detector arranged to determine the intersecting interval of the second droplets and generate an intersecting interval signal; and a waveform generator electrically coupled to the electrically actuated element and adapted to generate the applied waveform, and adapted to generate the applied waveform at least in part based on the intersecting interval signal.

[0017] According to another aspect of the embodiments, a method is disclosed, the method comprising the steps of: providing a flow of target material using a target material dispenser, the target material dispenser including electrically actuated elements arranged to induce velocity disturbances in the flow based on a droplet control signal; determining whether the flow includes satellite droplets, and generating a satellite detection signal indicating whether the flow includes satellite droplets; generating a waveform based at least in part on the satellite detection signal; and providing the waveform to the target material dispenser. The method may further include the steps of: determining a cross-interval of the flow, and generating a cross-interval signal, wherein the step of generating the waveform includes generating the waveform based at least in part on the cross-interval signal.

[0018] According to another aspect of the embodiments, a method for determining the transfer function of a nozzle of a target material dispenser is disclosed, the method comprising the steps of: dispensing a flow of EUV target material from the target material dispenser; applying a waveform to an electrically actuated element, the electrically actuated element being arranged to induce a velocity disturbance in the flow in response to a control signal; determining a minimum value of the amplitude of a sinusoidal component of the waveform of the flow excluding the satellite; determining the dependence of the coalescing length on the phase difference between the sinusoidal and square wave components of the control signal, and determining the phase difference of the discontinuous jump boundary where the dependence occurs; determining the slope of the dependence of the jump boundary phase on the minimum value; determining a drag coefficient based on the slope; and determining a transfer function at the frequency of the sinusoidal component based on the minimum value and the drag coefficient.

[0019] According to another aspect of the embodiments, a method for optimizing the coalescence behavior of a flow of EUV target material from a target material dispenser is disclosed. The target material dispenser includes electrically actuated elements arranged to induce velocity disturbances in the flow in response to an applied control signal. The method includes the steps of: determining a minimum amplitude of a sinusoidal component of the control signal excluding the satellite in the flow; determining the dependence of the coalescence length on the phase difference between the sinusoidal and square wave components of the control signal, and determining the discontinuous jump boundary phase difference where the dependence occurs; determining the slope of the dependence of the jump boundary phase on the minimum; determining a drag coefficient based on the slope; determining a designed phase delay based on the drag coefficient; and determining an optimal phase difference as the difference between the jump boundary phase difference and the designed phase delay.

[0020] According to another aspect of the embodiments, a method for controlling the coalescence behavior of a flow of EUV target material from a target material dispenser is disclosed. The target material dispenser includes electrically actuated elements arranged to induce velocity disturbances in the flow in response to an applied control signal having sinusoidal and square wave components. The method includes the step of determining the width L of the maximum range of adjacent values ​​of the phase difference between the sinusoidal and square wave components of the flow, excluding satellite components. n ; Determine the width L2 of the maximum range of adjacent values ​​of the phase difference between the sinusoidal and square wave components of the satellite; Determine the value S m As having a width L n Statistical measurement of the variation in flow cross-interval within a certain range; determining the value YZstability as a vector [ry m rz m ] statistical measurement, of which ry m It is a statistical measure of the stability of the flow in the y-direction, rz m It is a statistical measure of the stability of the flow in the z-direction; and it determines the cost function.

[0021]

[0022] Where W1, W2, W3, and W4 are positive real numbers; and the parameters of the sine wave component and the square wave component are adjusted to minimize the cost function.

[0023] According to another aspect of the embodiments, a method is disclosed comprising the steps of: providing a flow of target material using a target material dispenser having a nozzle, the flow splitting into first droplets after exiting the nozzle; using an electrically actuated element mechanically coupled to the target material dispenser to induce a velocity disturbance in the flow based on an applied waveform, the velocity disturbance causing the first droplets to eventually coalesce into second droplets larger than the first droplets in one or more stages within a coalescence distance from the nozzle; and using a waveform generator electrically coupled to the electrically actuated element to generate the applied waveform having a sine wave component and a square wave component, the sine wave component having an amplitude, and the square wave component having a phase difference from the sine wave component, the amplitude and phase difference being selected to minimize the coalescence distance while avoiding abrupt changes in the coalescence distance.

[0024] According to another aspect of the embodiments, a method for operating a target material dispenser in an EUV source is disclosed, the method comprising the steps of: generating a waveform having a sinusoidal component and a square wave component, the sinusoidal component having an amplitude and the square wave component having a phase difference from the sinusoidal component; applying the waveform to an electrically actuated element of the target material dispenser having a nozzle to provide a flow of target material, the flow of target material splitting into first droplets after exiting the nozzle and then coalescing into second droplets larger than the first droplets in one or more stages within a coalescing distance from the nozzle; scanning multiple phase differences for multiple amplitudes to identify jump boundary combinations of amplitude and phase differences where abrupt changes in coalescing distance occur, generating a jump boundary curve; and using the combination of amplitude and phase differences, at least in part, based on the jump boundary curve, during operation of the EUV source.

[0025] According to another aspect of the embodiments, a method is disclosed, the method comprising: releasing a flow of initial droplets of a first size from a droplet generator under the control of an electrical signal, the flow of initial droplets undergoing at least one coalescence after traveling a coalescence length to become a flow of final droplets of a second size greater than the first size, the electrical signal having a first periodic component and a second periodic component differing from the first periodic component by a phase difference; operating the droplet generator if the phase difference is at a value in which the flow of final droplets does not include any satellite droplets smaller than the second size; and changing the value of the phase difference phase until satellite droplets appear in the flow of final droplets to detect a jump boundary of the functional dependence of the coalescence length on the value of the phase difference. When the phase difference is at a value where the final droplet flow does not include any satellite droplets smaller than the second size, operating the droplet generator may include: operating the droplet generator and changing the value of the phase difference phase when the phase difference is at a value expected to be lower than the value at which satellite droplets appear in the final droplet flow, to detect a jump boundary of the functional dependence of the coalescing length on the value of the phase difference, which may include: increasing the value of the phase difference phase until satellite droplets appear in the final droplet flow, to detect a jump boundary of the functional dependence of the coalescing length on the value of the phase difference. The first periodic component may have a first frequency, and the second periodic component may have a second frequency, the second frequency being an integer multiple of the first frequency, including a multiple of one. One of the first periodic component and the second periodic component may be sinusoidal, while the other of the first periodic component and the second periodic component may be a square wave.

[0026] According to another aspect of the embodiments, a method for controlling the coalescence behavior of a flow of EUV target material from a target material dispenser is disclosed. The target material dispenser includes electrically actuated elements arranged to induce velocity disturbances in the flow in response to an applied control signal having sinusoidal and square wave components. The method includes the steps of: determining a first number of adjacent values ​​of the phase difference between the sinusoidal and square wave components of the satellite that are not included in the flow; determining a second number of adjacent values ​​of the phase difference between the sinusoidal and square wave components of the satellite that are indeed included in the flow; and determining that the coalescence behavior of the EUV target material flow is acceptable if the first number and the second number are equal to one.

[0027] Further embodiments, features, and advantages of the present invention, as well as the structure and operation of various embodiments, are described in detail below with reference to the accompanying drawings. Attached Figure Description

[0028] The accompanying drawings, which are incorporated herein and form a part of the specification, illustrate methods and systems of embodiments of the invention by way of example and not limitation. Together with the detailed description, the drawings further serve to explain the principles to those skilled in the art and to enable those skilled in the art to make and use the methods and systems presented herein. In the drawings, the same reference numerals denote the same or functionally similar elements.

[0029] Figure 1 This is a simplified schematic diagram of an EUV light source coupled to an exposure device.

[0030] Figure 2 This is a schematic diagram of the droplet generation subsystem used for EUV light sources.

[0031] Figure 3 A technique for coupling one or more electrically actuated elements to a fluid to generate a disturbance in the flow exiting an orifice is shown;

[0032] Figure 4 This is a diagram showing the coalescing state in a droplet flow.

[0033] Figure 5A and 5B The components of a composite hybrid waveform, such as that used according to one aspect of an embodiment, are shown.

[0034] Figure 6 This is a satellite formation diagram as a function of phase difference, according to one aspect of an embodiment.

[0035] Figure 7 It is a graph of satellite formation behavior as a function of the cross interval and the ratio of the length of the area with satellites to the length of the area without satellites, according to one aspect of the embodiment.

[0036] Figure 8 This is a graph showing the dependence of coalescing length on phase difference according to one aspect of an embodiment.

[0037] Figure 9 It is a graph of coalescing length as a function of sinusoidal amplitude and square phase, according to one aspect of the embodiment.

[0038] Figure 10 The graph shows the effect of the magnitude of the resistance according to one aspect of the embodiment on the relationship between (1) the product of the nozzle transfer function and the sinusoidal amplitude and (2) the square phase.

[0039] Figure 11 It is a graph showing the effect of time elapsed on the relationship between (1) the product of the nozzle transfer function and the sinusoidal amplitude and (2) the square phase, according to one aspect of the embodiment.

[0040] Figure 12This is a diagram illustrating the configuration of a satellite-free operating region as a function of the positive phase and the amplitude of the blocking sine wave, according to one aspect of an embodiment.

[0041] Figure 13 This is a graph showing the relationship between the jump boundary slope and the drag coefficient according to one aspect of an embodiment.

[0042] Figure 14 This is a graph showing the relationship between the drag coefficient and the nozzle transfer function and the blocking sine amplitude according to one aspect of the embodiment.

[0043] Figure 15 This is a flowchart illustrating a process for inferring the presence or absence of satellite droplets using jump boundary data according to one aspect of an embodiment.

[0044] Figure 16 This is a diagram illustrating certain conventions in a coordinate system used to describe EUV radiation generation, according to one aspect of an embodiment.

[0045] Figure 17 This is a diagram illustrating the relationship between droplet positions according to one aspect of an embodiment.

[0046] Figure 18 This is a graph illustrating the relationship between the square phase and the droplet position related to the nozzle transfer function according to one aspect of an embodiment.

[0047] Figure 19 This is a flowchart illustrating a process for determining the transfer function of a droplet generator according to one aspect of an embodiment.

[0048] Figure 20 This is a diagram illustrating the relationship between droplet positions according to one aspect of an embodiment.

[0049] Figure 21 This is a diagram illustrating the relationship between droplet positions according to one aspect of an embodiment.

[0050] Other features and advantages of the invention, as well as the structure and operation of various embodiments thereof, are described in detail below with reference to the accompanying drawings. Note that the invention is not limited to the specific embodiments described herein. Such embodiments are presented herein for illustrative purposes only. Other embodiments will be readily apparent to those skilled in the art based on the teachings contained herein. Detailed Implementation

[0051] Various embodiments will now be described with reference to the accompanying drawings, wherein the same reference numerals are used throughout to refer to the same elements. In the following description, numerous specific details are set forth for purposes of explanation to facilitate a thorough understanding of one or more embodiments. However, it will be apparent in some or all instances that any of the embodiments described below can be practiced without employing the specific design details described below. In other instances, well-known structures and devices are shown in block diagram form to facilitate the description of one or more embodiments. To provide a basic understanding of the embodiments, a simplified overview of one or more embodiments is presented below. This overview is not a broad overview of all contemplated embodiments and is not intended to identify key or essential elements of all embodiments, nor is it intended to define the scope of any or all embodiments.

[0052] However, it is beneficial to present an example environment in which embodiments of the invention can be implemented before describing these embodiments in more detail. In the following description and claims, the terms “upward,” “downward,” “top,” “bottom,” “vertical,” “horizontal,” etc., may be used. These terms are intended to indicate only relative orientation, and not any orientation relative to gravity.

[0053] Original Reference Figure 1 A schematic diagram of an exemplary EUV radiation source (e.g., EUV radiation source 10 for laser-generated plasma) according to one aspect of an embodiment of the present invention is shown. As shown, the EUV radiation source 10 may include a pulsed or continuous laser source 22, which may be, for example, a pulsed gas discharge CO2 laser source that generates a radiation beam 12 with a wavelength typically below 20 μm (e.g., about 10.6 μm or about 0.5 μm or less). The pulsed gas discharge CO2 laser source may have DC or RF excitation operating at high power and high pulse repetition rate.

[0054] The EUV radiation source 10 also includes a target delivery system 24 for delivering source material in the form of droplets or a continuous liquid stream. In this example, the source material is a liquid, but it can also be a solid or a gas. The source material can be made of tin or tin compounds, but other materials can also be used. In the depicted system, the source material delivery system 24 introduces droplets 14 of source material into the interior of the vacuum chamber 26 to an irradiation region 28, in which the source material can be irradiated to generate plasma. It should be noted that, as used herein, an irradiation region is an area where irradiation of the source material can occur, and is an irradiation region even when no actual irradiation occurs. The EUV source may also include a beam focusing and steering system 32, which will be incorporated below. Figure 2 To explain in more detail.

[0055] In the illustrated system, the components are arranged such that the droplet 14 travels substantially horizontally. The direction from the laser source 22 toward the irradiated region 28 (i.e., the nominal propagation direction of the beam 12) can be considered the Z-axis. The path taken by the droplet 14 from the source material delivery system 24 to the irradiated region 28 can be considered the X-axis. Figure 1 The view is therefore perpendicular to the XZ plane. Furthermore, although a system in which the droplet 14 travels substantially horizontally is depicted, those skilled in the art will understand that other arrangements in which the droplet travels vertically or relative to gravity at an angle between 90 degrees (horizontal) and 0 degrees (vertical) (inclusive).

[0056] EUV radiation source 10 may also include an EUV source controller system 60, which may further include a laser emission control system 65 and a beam steering system 32. EUV radiation source 10 may also include detectors, such as a droplet position detection system, which may include one or more droplet imagers 70 that generate an output indicating the absolute or relative position of the droplet (e.g., relative to the irradiated area 28) and provide this output to the target position detection feedback system 62.

[0057] The droplet position detection feedback system 62 can use the output of the droplet imager 70 to calculate the droplet position and trajectory, thereby calculating the droplet position error. The droplet position error can be calculated drop-by-drop, averaged, or otherwise. The droplet position error can then be provided as input to the light source controller 60. In response, the light source controller 60 can generate control signals, such as laser position, direction, or timing correction signals, and provide these control signals to the laser beam steering system 32. The laser beam steering system 32 can use the control signals to change the position and / or power of the laser beam focal spot within the chamber 26. The laser beam steering system 32 can also use the control signals to change the geometry of the interaction between the beam 12 and the droplet 14. For example, the beam 12 can be decentered or impacted with the droplet 14 at an angle of incidence different from a direct head-on collision.

[0058] like Figure 1As shown, the source material delivery system 24 may include a source material delivery control system 90. The source material delivery control system 90 may be operable in response to a signal (e.g., the aforementioned droplet position error or a quantity derived from the droplet position error provided by the system controller 60) to adjust the path of the source material through the irradiation zone 28. This can be achieved, for example, by repositioning the point at which the droplet 14 is released by the source material delivery mechanism 92. The droplet release point can be repositioned, for example, by tilting the target delivery mechanism 92 or by moving the target delivery mechanism 92. The source material delivery mechanism 92 extends into the chamber 26 and is preferably supplied with source material from the outside and connected to a gas source to place the source material in the source material delivery mechanism 92 under pressure.

[0059] continue Figure 1 The radiation source 10 may also include one or more optical elements. In the following discussion, collector 30 is used as an example of such an optical element, but the discussion also applies to other optical elements. Collector 30 may be a vertically incident reflector, for example, implemented as an MLM, with an additional thin barrier layer, such as B4C, ZrC, Si3N4, or C, deposited at each interface to effectively prevent thermally induced interlayer diffusion. Other substrate materials, such as aluminum (Al) or silicon (Si), may also be used. Collector 30 may be in the form of an elongated ellipse with a central aperture to allow laser radiation 12 to pass through and reach the irradiated area 28. Collector 30 may be an elliptical shape, for example, with a first focal point located at the irradiated area 28 and a second focal point located at a so-called midpoint 40 (also referred to as intermediate focal point 40), where EUV radiation can be output from EUV radiation source 10 and input to, for example, an integrated circuit lithography scanner or stepper 50, which, for example, uses radiation to process silicon wafer workpiece 52 using a mask or mask 54 in a known manner. The mask 54 can be transmissive or reflective. For EUV applications, the mask 54 is typically reflective. The silicon wafer workpiece 52 is then further processed in a known manner to obtain an integrated circuit device.

[0060] Figure 2 The droplet generation system is shown in more detail. A source material delivery system 90 delivers droplets to an irradiation site / primary focus 48 within chamber 26. A waveform generator 230 provides a driving waveform to electrically actuated elements in the droplet generator 90, the driving waveform inducing velocity disturbances in the droplet flow. The waveform generator 230 operates under the control of a controller 250, based at least in part on data from a data processing module 252. The data processing module receives data from one or more detectors. In the example shown, the detectors include a camera 254 and a photodiode 256. The droplets are irradiated by one or more lasers 258. In this typical arrangement, the detectors detect / image the droplets at points in the flow where aggregation is expected to occur.

[0061] Figure 3 A simplified representation of the components of a droplet source 92 is shown schematically. As illustrated, the droplet source 92 may include a container 94 that holds a fluid 96 (e.g., molten tin) under pressure. The container 94 may also be formed with a nozzle 98, allowing the pressurized fluid 96 to flow out of the container 94 in a continuous flow that subsequently breaks into multiple droplets. A waveform generated by a waveform generator 230 is used to drive an electrically actuated element 150 to generate droplets for EUV output. The electrically actuated element 150 creates disturbances in the fluid that generate droplets with different initial velocities, causing at least some adjacent droplet pairs to coalesce before reaching the irradiated area. The ratio of initial droplets to coalesced droplets can be any number, for example, in the range of about 10 to about 500.

[0062] The entire droplet coalescence process can be considered as a series of multiple coalescence steps or states that evolve with varying distances from the nozzle. This is in Figure 4 As shown in the diagram. For example, in the first state I, when the target material first leaves the orifice or nozzle, the target material is in the form of a laminar fluid jet with velocity perturbations. In the second state II, the fluid jet breaks into a series of droplets with different velocities. In the third state III, measured by time of flight or by distance from the nozzle, the droplets coalesce into medium-sized droplets, called sub-coalescing droplets, with different velocities relative to each other. In the fourth state IV, the sub-coalescing droplets coalesce into droplets with the desired final size. The number of sub-coalescing steps can vary. The distance from the nozzle to the point where the droplet reaches its final coalescing state is the coalescence distance or length L. Ideally, the coalescence distance of the droplets should be as short as possible. When droplets coalesce into larger droplets, they are less sensitive to source conditions such as hydrogen flow and ion bombardment.

[0063] Therefore, when controlled using an excitation signal, the coalescence process can thus be understood as having: an initial partial coalescence or sub-coalescing state that generates medium-sized droplets (higher frequency (typically 500 kHz) droplets) with a spacing of about 2 μs; and a main coalescence in which the sub-coalescing droplets merge into a main droplet with a spacing of about 20 μs (50 kHz), although other spacings are generated in other embodiments.

[0064] Therefore, controlling the splitting / coalescing process involves controlling the droplets so that they are fully coalesced before reaching the irradiation area and have a frequency corresponding to the pulse rate of the laser used to irradiate the coalesced droplets. A mixed waveform can be provided to an electrically actuated element to control the coalescence process of Rayleigh splitting droplets into fully coalesced droplets with a frequency corresponding to the laser pulse rate. Essentially, the mixed waveform can consist of a combination of a first low-frequency periodic waveform and a second high-frequency periodic waveform. For example, the mixed waveform can consist of a low-frequency sine wave and a higher-frequency square wave or block wave. However, it should be understood that a higher-frequency periodic waveform is not necessarily a square wave, and the teachings in this paper relating to implementations using square waves can be considered context-permissible, which also applies to implementations where the second high-frequency periodic signal is not a square wave. Therefore, the mixed waveform signal can be composed of... Figure 5A The low-frequency sine wave shown (such as 50kHz) and Figure 5B The diagram shows a high-frequency block wave (e.g., 500 kHz). The scales of the time and amplitude axes in the diagram are arbitrary. Such a mixed waveform can be characterized by reference to five adjustable parameters, including a) sinusoidal amplitude, b) square phase (i.e., the phase difference between the sine wave and the square wave), c) square amplitude, d) square uptime (duty ratio), and d) square frequency. The main coalescing process depends primarily on the sinusoidal amplitude and square phase, and can further depend on the other three adjustable parameters mentioned above.

[0065] As previously mentioned, if complete coalescence is not achieved, the droplet stream will consist of smaller droplets, referred to as satellite droplets or microsatellites. The presence of satellite droplets can be detected by any combination of methods, such as using a droplet detection module (DDM), cross-spacing, a droplet forming camera (DFC), or even by monitoring changes in the EUV signal. Systems and methods for monitoring droplet streams are disclosed, for example, in U.S. Patent No. 9,241,395, entitled “System and Method for Controlling Droplet Timing in an LPP EUV Light Source,” published January 19, 2016, which is incorporated herein by reference in its entirety. However, using monitoring equipment at a relatively great distance from the stream makes it difficult to directly observe satellites or measure coalescence distances. It would be useful to have methods to infer conditions such as the presence of satellites or coalescence length from more directly determinable parameters.

[0066] Sub-coalescing is a crucial part of the coalescing process using mixed waveform excitation signals because if the sub-coalescing length increases, the main and sub-coalescing processes will interfere with each other, which increases the coalescing length. The increased coalescing length increases the likelihood of satellites being affected by plasma pressure from the irradiated area.

[0067] Furthermore, poor sub-agglomeration will increase the velocity jitter of the sub-agglomerated droplets (at a frequency of up to 500 kHz), which may cause low-frequency satellites (the presence of satellites in the portion adjacent to the main droplet) or poor droplet timing. Satellites and poor timing can affect dose stability and collector lifetime in EUV systems.

[0068] Therefore, it is advantageous to first characterize the sub-coalescing process and use this characterization as at least a partial basis for controlling the time-varying signal that generates pressure changes in the droplet generator nozzle. This determination can be performed iteratively, for example, to improve droplet coalescence (e.g., reduce the occurrence rate of satellite droplets). In the case of using this determination to improve the hybrid waveform, the process can be called Hybrid Waveform Optimization (HWO).

[0069] As mentioned above, one of the main challenges in optimizing the parameters of the hybrid waveform excitation signal is determining the characteristics of the sub-aggregation process using low-frequency droplet measurement equipment typically available on EUV systems. In various systems, there may be settings for image-based low-frequency satellite detection at the irradiated area (e.g., the collector's main focus). The sampling frequency (rate) of this signal can be less than 20 Hz, which is significantly less than the main droplet frequency, which can be 50 kHz. There may also be settings for determining the cross-interval (i.e., the timing between two droplets). The frequency (rate) of this signal can be the same as the main droplet frequency (e.g., 50 kHz). There may also be settings for image-based position measurements of the droplets in the y and z directions: the frequency (rate) of this signal can be 1 kHz, which is less than the main droplet frequency.

[0070] Generally, the signals from these measurements and detections only contain information about the main droplet, and the measurement equipment may not be able to directly measure sub-coalescing performance. According to one aspect of the embodiments, a system and method for quantifying sub-coalescing performance using the aforementioned measurements are disclosed herein. This enables the detection of the presence of low-frequency satellites after tuning to mixed waveform excitation signals that may not be directly observable by typical measurement equipment. It can also optimize sub-coalescing performance using measurements provided by conventional measurement equipment. It can also characterize “health metrics” to characterize the performance of the droplet generator nozzle in generating stable sub-coalescing droplets. It can also optimize sub-coalescing to improve the robustness of the tuning solution.

[0071] According to one aspect of the embodiments, HWO can be used to optimize parameters, such as combinations of the five parameters described above for the mixed waveform excitation signal. For example, in various implementations of optimization, two of these parameters (square amplitude and square uptime) can be used to control the sub-coalescing process.

[0072] In particular, phase scan data can be used to quantify sub-coalescing performance. As used herein, a phase scan refers to the process of scanning the positive phase parameters and determining a set of conditions for a specific value of the scanned phase. One of the conditions is the presence of a satellite at that positive phase value. This is determined by a Boolean "yes or no" value that can be used to set the flag. Another condition among the detected conditions can be a timing extension between two droplets, which is called the cross interval. For example, a statistical measurement of this extension can be determined, such as three sigma, i.e., the interval within three standard deviations of the mean. This can be called the three sigma cross interval and is determined by s i The other detectable condition is represented by the three sigma of the droplet's position in the y and z directions. In each setup, the three sigma values ​​of the droplet position in the y and z directions are determined and assigned by ry. i and rz i express.

[0073] This data can then be used to optimize sub-aggregation performance. First, check for the presence or absence of satellites, identifying the region where adjacent positive phase settings typically produce satellites; adjacent means the region is not blocked by values ​​that do not produce satellites. Note that this region can be determined using satellite detection with DFC. The results are shown in... Figure 6 In a representative embodiment, Figure 6 It is a graph of the three-sigma cross spacing as a function of the positive phase. Figure 6 In this context, the positive phase values ​​that do not produce satellites are represented by pure dots. The positive phase values ​​that produce satellites are represented by dots with circles. Regions where satellites appear (the range of adjacent phase values) can be called satellite islands (SI). Regions without satellites can be similarly called satellite-free islands (SFI). The width L1 of the positive phase of the widest satellite-free island is determined using a technique used to analyze this data. The width of the satellite-free island in the case of perfect sub-aggregation is represented as L. n In other words, L n It is the theoretical value of the island width assuming the coalescence process begins with uniformly distributed sub-coalescing droplets.

[0074] Note that L n It is a function of the product TF (nozzle transfer function at 50kHz), the sinusoidal amplitude (amplitude of the sinusoidal component), and the droplet drag coefficient. If the measured island width matches L... n If so, then there are uniformly distributed sub-aggregated droplets.

[0075] Next, determine the width of the widest satellite island. This width is denoted by L². In the case of perfect sub-aggregation, this quantity will be equal to 2π - L. n .

[0076] In the next step, statistical measures are determined, such as the p-norm of the cross-interval data in the satellite-free area, and denoted as S. m .

[0077] Next, the statistical measure of the p-norm of three sigma, such as y-stability, is determined as ry_m, and the statistical measure of the p-norm of three sigma, such as z-stability, is determined as rz_m. Then, YZStability is determined as the vector [ry_m]. m rz m The weighted p-norm of ].

[0078] Based on the above determinations, the quantifier for sub-aggregates can be defined as the value that minimizes the cost function, for example, as follows:

[0079]

[0080] Among them, W1, W2, W3, and W4 are some positive real numbers.

[0081] The aforementioned metrics can provide a useful estimate of the likelihood of a satellite presence caused by plasma. In other words, the sub-coalescing parameter can be set to the minimum of the aforementioned cost function. By setting the sub-coalescing parameter to the minimum of the aforementioned cost function, the presence of a satellite can be minimized, thereby optimizing the sub-coalescing performance.

[0082] As another measure of sub-convergence performance, if multiple satellite-less regions are found, the sub-convergence performance may be considered unacceptable. In other words, for the sub-convergence performance to be acceptable, the dependence of the three-sigma cross spacing as a function of the positive phase should have one satellite-less region and one satellite region.

[0083] As mentioned earlier, satellites can occur when sub-coalescing performance malfunctions. Sub-coalescing is related to the high-frequency component of the nozzle transfer function. Therefore, the metrics associated with the aforementioned sub-coalescing provide feedback on this component of the nozzle transfer function.

[0084] The aforementioned techniques / metrics also provide an objective function for the HWO optimization process. It also provides metrics to quantify the performance of the droplet generator in the sub-aggregation process.

[0085] The techniques described in this paper can also reduce the likelihood of satellites being generated by plasma, increase the lifetime (robustness) of tuning solutions determined by HWO, and provide performance metrics based on sub-gathering performance to support exchange decisions, i.e., decisions for disabling and replacing DG.

[0086] For the overall effect of phase scanning, the above metrics (more specifically, L1 and S) can be calculated. mFurthermore, it can be determined which phase scans produce plasma-induced satellites. Phase scans with and without plasma-induced satellites can be classified based on a linear combination of these two metrics. Figure 7 In the diagram, phase scans of satellites induced by plasma are represented by asterisks, while phase scans of satellites without plasma induced by plasma are represented by hollow circles. Therefore, the probability of plasma-induced satellites can be predicted based on the phase scan data. This data can be acquired in the absence of plasma while tuning the droplet generator.

[0087] Based on coalescence simulations and bench tests in a vacuum, the coalescence length decreases approximately linearly with increasing sinusoidal amplitude. The minimum coalescence length is located at the center of a satellite-free region constructed by altering the positive phase.

[0088] The term "blocking sinusoidal amplitude" is used to refer to the minimum sinusoidal amplitude that can be generated without a satellite setting. It is a function of the drag coefficient. It can be used to correct the transfer function to account for drag. Typically, the transfer function is determined based on the assumption that drag has a negligible effect on the droplets in the EUV container. In reality, the hydrogen flow in the container causes non-negligible drag on the droplets. Essentially, the drag is determined, and thus the blocking sinusoidal amplitude is determined. This results in a corrected transfer function. The calculation of this transfer function may require correction based on the drag coefficient.

[0089] Furthermore, it has been determined that the drag caused by hydrogen flow near the droplets and stable container pressure can significantly impact the coalescence process. Special attention needs to be paid to the drag acting on the coalescing droplets during the optimization of the mixing waveform parameters. Without considering the presence of drag, the estimation of the transfer function based on the blocking sinusoidal amplitude in the HWO process may be inaccurate. Moreover, in the presence of drag, the center of the satelliteless region (in the positive phase space) is not the minimum coalescence length.

[0090] Regarding drag, the droplets in the considered state can be regarded as spheres, each with a diameter d. Also in the considered state, the Reynolds number is relatively small, therefore the drag F of a gas flowing through the sphere at a constant velocity is relatively small. D It can be approximated as follows:

[0091]

[0092] Where μ is the gas viscosity, and d p It is the particle diameter, C(Kn) is determined by 2λ / d p The given slip correction factor for the Knudsen number, V p U is the particle velocity, U is the local velocity of the fluid, and C is the particle velocity. D (Re p Rep / 24 is the non-Stokesian correction for fluid inertial effects. See Daniel J. Rader and Anthony S. Geller, “3-Transport and Deposition of Aerosol Particles” (Editor(s): Raji V Kohli, KLMittal, Developments in Surface Contamination and Cleaning, William Andrew Publishing, 2008, Pages 189-266).

[0093] One effect of considering resistance is that the location of the minimum coalescing length becomes partly dependent on the container pressure. The coalescing length is a discontinuous function of the parameters of the excitation signal; the minimum (near discontinuity) of the coalescing length is not a robust operating point relative to variations in the nozzle transfer function.

[0094] As described above, the HWO process can optimize five parameters of the aforementioned mixed waveform excitation signal. In various implementations of this process, two of these parameters (sine amplitude and square phase) can be used to control the main coalescence process, and the remaining parameters can be used to control the sub-coalescing. Compared to optimization assuming negligible resistance, the optimization procedure considering resistance offers the possibility of improved performance. This is especially true when the container pressure is not negligible and a hydrogen flow is present.

[0095] Furthermore, as mentioned above, the coalescence length is the minimum distance from the nozzle where all microdroplets are coalesced (e.g., 50 kHz droplets). If the coalescence length is less than the distance between the nozzle and the main focus of the EUV collector, a satellite-free setup is obtained. The ideal operating point should have a small coalescence length to provide robustness against hydrogen flows and shock waves originating from the plasma.

[0096] In the presence of resistance, the functional dependence of coalescing length on the positive phase is discontinuous. This discontinuity occurs at a boundary within the satellite-free region and is referred to as... Figure 8 The jump boundary is shown. In a simplified version of the HWO process, the operating positive phase can simply be set to the center of the satellite-free region, which is not the minimum coalescing length in the presence of drag. However, the HWO process has the advantage of determining an operating positive phase value that is robust to nozzle performance variations and can provide a smaller coalescing length. Note that in various implementations, this process can be performed using only the satellite detector target formation metrology (TFM) and the DFC at the main focus / irradiation region.

[0097] In summary, for fixed values ​​of sine amplitude, positive normal operating time, positive amplitude, and positive frequency, the coalescing length is a discontinuous function of the positive phase. That is, the graph of the coalescing length as a function of the positive phase will exhibit discontinuities for certain values ​​of the positive phase. Just before the discontinuity, the coalescing length will be at or near its minimum value, and at the point of discontinuity, the coalescing length will be at or near its maximum value. This point of discontinuity is referred to in this paper as the jump boundary.

[0098] Another approach to this phenomenon is to consider the square phase, which leads to discontinuities as a function of the amplitude of the sinusoidal component. This is in Figure 9 As shown in [the image]. Figure 9 In the diagram, the x-axis represents the increasing sine amplitude, and the y-axis represents the increasing square phase. The gray shading, from dark to light, represents variations in coalescing length, with darker shades indicating shorter lengths and lighter shades indicating longer lengths. The boundary between the region of maximum coalescing length (brightest) and the region of minimum coalescing length (darkest) defines a curve, illustrating the dependence of the jump boundary as a function of the sine amplitude on the location of the coalescing boundary.

[0099] Figure 9 The jump boundary curve provides a tool for determining the location of the jump boundary for various values ​​of the sine amplitude based on measurements of only one location on the jump boundary curve. In other words, once the shape of a portion of the curve is determined, the shape of other portions of the curve can be determined by extrapolation. The curve can be calibrated for different resistance conditions by using a lookup table showing the y-displacement of the curve under different resistance conditions.

[0100] The jump boundary curve depends on the normal operating time and amplitude of the positive side, and can also vary over time (phase drift). However, in general, the shape of the curve defined by this dependence will remain essentially unchanged with changes in time or resistance, and the effect of these changes will be phase drift, shifting these curves along the y-axis. This is in Figure 10 and Figure 11 As shown in the image. Figure 10 Three jump boundary curves are shown: the curve labeled "large F0" indicates a curve with relatively greater resistance; the curve labeled "small F0" indicates a curve with relatively less resistance; and the unlabeled intermediate curve is used for medium-sized resistance. It can be seen that the curves are essentially the same shape and simply shift perpendicular to each other. The offset is an indicator of the magnitude of the resistance. However, Figure 11 This suggests that the shift in the curve may also be at least partly attributable to the passage of time.

[0101] The resistance function and transfer function can also be determined based on the slope of the curves showing the dependence of the blocking sine amplitude and the limiting jump boundary on the sine amplitude. Figure 12First, the blocking sinusoidal amplitude is determined by recursively scanning the phase with different sinusoidal amplitudes. From this, a curve defining the dependence of the jump boundary on the sinusoidal amplitude is established. Therefore, the jump boundary curve can also be used to determine the drag coefficient (…). Figure 13 The transfer function can be calculated based on the blocking sine amplitude and the drag coefficient. Figure 14 Note that the jump boundary can be determined even with an uncertain cross interval, because the transfer function is essentially a horizontal scale of the curve representing the jump boundary's dependence on the sine amplitude.

[0102] Once the jump boundary is determined, operating conditions can be selected to minimize the coalescing length in a way that prevents it from approaching the jump boundary. It is desirable to obtain a smaller coalescing length using this process than with other techniques, as it provides a margin relative to flow and plasma perturbations. The method described above also minimizes the possibility of generating satellites due to plasma generation.

[0103] The above provides a method for estimating the nozzle transfer function, since the transfer function is only scaled on the horizontal axis. It is also a method for optimizing parameters of mixed waveform excitation signals. Furthermore, it provides a novel method for determining container pressure and drag coefficients within a vessel.

[0104] Statistical measurements of the change in cross spacing (such as the three-sigma value of the cross spacing) will increase near the jump boundary. This is an alternative method for finding the location of the jump boundary based on the cross spacing without using satellite detector measurements.

[0105] As mentioned above, even though satellite detection measurements are far from the nozzle and these conditions cannot be directly observed, quantifying these parameters allows for characterization of satellite formation, skip boundaries, and coalescence length.

[0106] According to one aspect, such as Figure 15 The flowchart shown illustrates that flow conditions, such as coalescing length or satellite conditions (present or absent), can be inferred from jump boundary data. In the first step S10, a sinusoidal amplitude value is selected. In step S20, the positive phase is scanned for the current sinusoidal amplitude, and the jump boundary is determined to be a combination of sinusoidal amplitude and positive phase with a sudden increase in coalescing length, i.e., exhibiting discontinuity. In step S30, it is determined whether a positive phase scan has been performed for all desired sinusoidal amplitude values. If yes, then in step S40, the jump boundary data is used during operation to infer flow conditions under a given combination of sinusoidal amplitude and positive phase (satellite conditions are used as an example in the figure). If not, then in step S35, the sinusoidal amplitude is changed and the process returns to step S10.

[0107] As previously described, when using a mixed waveform to form droplets, the initial droplets—that is, the droplets initially formed based on the splitting of the flow leaving the nozzle of the droplet generator—coalesce into higher frequency (typically 500 kHz) droplets (referred to herein as sub-coalescing droplets). These sub-coalescing droplets then coalesce again into fully coalesced main frequency (typically 50 kHz) droplets. Ideally, during operation, neither these droplets nor the sub-coalescing droplets should reach the irradiated site. When they do, any of these higher frequency sub-coalescing droplets that reach the main focus are referred to herein as sub-coalescing satellite droplets. Any droplets that reach the main focus will be referred to as droplet satellites. Other techniques for optimizing the parameters of the mixed waveform excitation signal utilize information about the position and size of the droplets and satellites.

[0108] As mentioned above, generally speaking, for a reference coordinate system, such as Figure 16 As shown in the conceptual diagram of the EUV system, Z is the direction along which the laser beam 12 propagates, and it is also the direction from the collector 30 to the irradiated site or main focus 28 and the EUV intermediate focus. X is in the droplet propagation plane. Y is orthogonal to the XZ plane. To make it a right-handed coordinate system, the trajectory of the droplet flow 14 is considered to be in the -X direction. The origin is considered to be the irradiated site 28. The presence of satellite droplets in the flow at the irradiated site 28 can be detected by any one method or a combination of methods, for example, by observing the flow at the irradiated site using DDM or DFC.

[0109] like Figure 17 As shown, each fully coalesced droplet 400 has a sinusoidal amplitude range of sub-coalescing satellite droplets 410 in its vicinity, as indicated by the arrows, shifted in the -X direction of flow propagation, also referred to herein as the flow direction. The distance between the droplet and the satellite in the X direction (labeled "A" in the figure) is called STDD (satellite-to-droplet distance). STDD is a linear function of the positive phase, as shown in the figure. Figure 18 As shown. In Figure 18 In the diagram, line 450 shows the simulation of STDD with positive phase, where the sine amplitude is at the first value; line 460 shows the simulation of STDD with positive phase, where the sine amplitude is at the second value; and line 470 shows the simulation of STDD with positive phase, where the sine amplitude is at the third value. The slope of these lines is a measurement of the transfer function multiplied by the sine amplitude, and therefore can be used to determine the nozzle transfer function.

[0110] The analytical expression for the relationship between the quantized STDD and the positive phase (denoted by φ) is determined as follows:

[0111]

[0112] Where TF is the transfer function, LDFC is the flow-direction distance between the end of the droplet generator nozzle and the position where the camera used to observe the flow captures the flow image, and U0 is the velocity of the main coalescing droplet.

[0113] The nozzle transfer function is a crucial indicator of the droplet generator's operational status because it indicates the amount of voltage required to apply a given relative velocity to the droplets. This relative velocity determines how quickly the droplets coalesce. The transfer function can guide replacement decisions; for example, if the droplet generator cannot generate sufficient relative velocity at its maximum input voltage to achieve complete coalescence at an acceptable distance before reaching the irradiated area, then the droplet generator should be replaced.

[0114] According to one aspect, such as Figure 9 The flowchart illustrates the process as follows: In step S50, a sine amplitude value is selected. In step S60, the functional dependence of STDD on the positive phase is determined at the selected sine amplitude. In step S70, the transfer function is determined based on the slope of the functional dependence determined in step S60. In step S80, the droplet generator (DG in the figure) is operated according to the determined transfer function, including but not limited to possible assessments of repairing or replacing the droplet generator based on the transfer function.

[0115] Several methods exist for detecting sub-coalescing satellite droplets. Another method is to use an imager such as DFC to determine whether the size of all satellite droplets corresponds to the known size of the sub-coalescing droplets. Here and elsewhere, "corresponds" means that the size of the satellite is closer to the size of the sub-coalescing droplets than the size of a fully coalesced droplet or microdroplet. s equals the droplet at a higher frequency.

[0116] Another method for detecting sub-coalescing satellite droplets is based on the coordinates of the satellite's position in the lateral (Z) direction, which is an indirect measurement of the droplet size. The hydrogen flow in the chamber separates fully coalesced droplets from smaller droplets in the lateral direction. Therefore, for a given flow condition within the chamber, the sub-coalescing satellite droplets are translated a specific distance B from the main fully coalesced droplets in the Z direction, such as... Figure 20 As shown.

[0117] Information on the position and size of the droplets and satellites can also be used to measure the sub-coalescing length, i.e., the distance from the nozzle exit to the location where the microdroplets have coalesced into sub-coalescing droplets. A technical challenge in hybrid waveform tuning is that increasing the sinusoidal amplitude causes interference between the main coalescence and sub-coalescing. As the main coalescence length decreases, the sub-coalescing process is affected by the strong velocity generated by the low-frequency (sinusoidal) portion of the signal. In other words, when the voltage of the low-frequency portion of the signal increases, microdroplet satellites, such as… Figure 21As shown, the sub-coalescing length can be determined by measuring the minimum sinusoidal amplitude value of the generated droplet satellites. Therefore, the sub-coalescing length can be used as an objective function in the optimization process of sub-coalescing parameters (square uptime, square amplitude). This process also provides an upper limit on the sinusoidal amplitude value that can be used to optimize the sinusoidal amplitude. This can be used as a parameter to evaluate the operational state of the droplet generator.

[0118] The invention has been described above using functional building blocks that illustrate the implementation of specific functions and their relationships. For ease of description, the boundaries of these functional building blocks have been arbitrarily defined herein. Alternative boundaries can be defined as long as the specified functions and their relationships are properly performed.

[0119] The foregoing description of specific embodiments will so fully reveal the general nature of the invention that others can readily modify and / or adapt these specific embodiments to various applications by applying knowledge within the art without departing from the general concept of the invention, without excessive experimentation. Therefore, based on the teachings and guidance presented herein, such adaptations and modifications are intended to fall within the meaning and scope of equivalents of the disclosed embodiments. It should be understood that the wording or terminology herein is for descriptive rather than limiting purposes, and that the terminology or terminology of this specification will be interpreted by those skilled in the art based on the teachings and guidance. The breadth and scope of the invention should not be limited by any of the exemplary embodiments described above, but should be defined only by the appended claims and their equivalents.

[0120] Other aspects of the invention are set forth in the following numbered clauses.

[0121] 1. An apparatus comprising:

[0122] A target material dispenser having a nozzle and adapted to provide a flow of target material, the flow breaking into first droplets after leaving the nozzle;

[0123] An electrically actuated element, mechanically coupled to a target material dispenser and arranged to induce velocity disturbances in the flow based on an applied waveform, the velocity disturbances causing a first droplet to eventually coalesce into a second droplet larger than the first droplet in one or more stages within a coalescence distance from the nozzle; and

[0124] A waveform generator is electrically coupled to an electrically actuated element and is adapted to generate an applied waveform having a sine wave component and a square wave component, the sine wave component having an amplitude, and the square wave component having a phase difference with the sine wave component, the amplitude and phase difference being selected to minimize the coalescing distance while avoiding abrupt changes in the coalescing distance.

[0125] 2. The device pursuant to Clause 1, wherein the electrically actuated element is a piezoelectric element.

[0126] 3. An apparatus comprising:

[0127] A target material dispenser having a nozzle and adapted to provide a flow of target material, the flow of target material breaking into first droplets after leaving the nozzle;

[0128] An electro-actuable element is mechanically coupled to a target material dispenser and is arranged to induce velocity disturbances in the flow based on an applied waveform. The velocity disturbances cause the first droplet to eventually coalesce into a second droplet larger than the first droplet in one or more stages within a coalescence distance from the nozzle. The second droplets are spaced apart such that the second droplets pass through a fixed point at an intersecting interval.

[0129] A cross-space detector is configured to determine the cross-space of the second droplet and generate a cross-space signal; and

[0130] A waveform generator, electrically coupled to an electrically actuated element, is adapted to generate an applied waveform, and is adapted to generate the applied waveform at least in part based on a cross-interval signal.

[0131] 4. A method comprising:

[0132] A target material dispenser is used to provide a flow of target material. The target material dispenser includes electrically actuated elements that are arranged to induce velocity disturbances in the flow based on droplet control signals.

[0133] Determine whether the flow includes satellite droplets and generate a satellite detection signal indicating whether the flow includes satellite droplets;

[0134] The waveform is generated based at least in part on satellite detection signals; and

[0135] The waveform is provided to the target material dispenser.

[0136] 5. The method according to Clause 4 further includes: determining the cross interval of the stream, and generating a cross interval signal, wherein the step of generating a waveform includes generating the waveform based at least in part on the cross interval signal.

[0137] 6. A method for determining the transfer function of a nozzle of a target material dispenser, the method comprising:

[0138] Distribute the flow of EUV target material from the target material dispenser;

[0139] A waveform is applied to an electrically actuated element, which is arranged to induce a velocity disturbance in the flow in response to a control signal;

[0140] Determine the minimum amplitude of the sinusoidal component of the waveform of the stream, excluding the satellite;

[0141] Determine the dependence of coalescing length on the phase difference between the sinusoidal and square wave components of the control signal, and determine the discontinuous jump boundary phase difference where the dependence occurs.

[0142] Determine the slope of the jump boundary phase's dependence on the minimum value;

[0143] The drag coefficient is determined based on the slope; and

[0144] Based on the minimum value and the drag coefficient, the transfer function at the frequency of the sinusoidal component is determined.

[0145] 7. A method for optimizing the coalescence behavior of a flow of EUV target material from a target material dispenser, the target material dispenser including an electrically actuated element arranged to induce a velocity disturbance in the flow in response to an applied control signal, the method comprising:

[0146] Determine the minimum amplitude of the sinusoidal component of the control signal from the satellite that does not include the stream;

[0147] Determine the dependence of coalescing length on the phase difference between the sinusoidal and square wave components of the control signal, and determine the discontinuous jump boundary phase difference where the dependence occurs.

[0148] Determine the slope of the jump boundary phase's dependence on the minimum value;

[0149] Determine the drag coefficient based on the slope;

[0150] Based on the drag coefficient, determine the phase delay of the design; and

[0151] The optimal phase difference is determined as the difference between the jump boundary phase difference and the designed phase delay.

[0152] 8. A method for controlling the coalescence behavior of a flow of EUV target material from a target material dispenser, the target material dispenser including an electrically actuated element arranged to induce a velocity disturbance in the flow in response to an applied control signal having a sinusoidal component and a square wave component, the method comprising:

[0153] Determine the width Ln of the maximum range of adjacent values ​​of the phase difference between the sinusoidal and square wave components of the stream, excluding the satellite.

[0154] Determine the width L2 of the maximum range of adjacent values ​​of the phase difference between the sinusoidal and square wave components of the satellite in the flow;

[0155] The value Sm is determined as a statistical measure of the variation in flow cross-interval within a range with width Ln;

[0156] The value YZstability is defined as a statistical measure of the vector [rym, rzm], where rym is the statistical measure of the stability of the flow in the y-direction, and rzm is the statistical measure of the stability of the flow in the z-direction; and

[0157] Determine the cost function

[0158]

[0159] Where W1, W2, W3, and W4 are positive real numbers; and

[0160] Adjust the parameters of the sinusoidal and square wave components to minimize the cost function.

[0161] 9. A method comprising:

[0162] A target material dispenser with a nozzle is used to provide a flow of target material, which breaks into first droplets after leaving the nozzle.

[0163] Using an electrically actuated element mechanically coupled to a target material dispenser, a velocity disturbance is induced in the flow based on an applied waveform. This velocity disturbance causes a first droplet to eventually coalesce into a second droplet larger than the first droplet in one or more stages within a coalescence distance from the nozzle.

[0164] A waveform generator electrically coupled to an electrically actuated element is used to generate the applied waveform, which has a sine wave component and a square wave component. The sine wave component has an amplitude, and the square wave component has a phase difference with the sine wave component. The amplitude and phase difference are selected to minimize the coalescing distance while avoiding sudden changes in the coalescing distance.

[0165] 10. A method for operating a target material dispenser in an EUV source, the method comprising:

[0166] Generate a waveform with sinusoidal and square wave components, where the sinusoidal component has amplitude and the square wave component has a phase difference with the sinusoidal component;

[0167] A waveform is applied to an electrically actuated element that is mechanically coupled to a target material dispenser with a nozzle to provide a flow of target material. The flow of target material breaks into first droplets after leaving the nozzle and then coalesces into second droplets larger than the first droplets in one or more stages at a coalescence distance from the nozzle.

[0168] For multiple amplitudes, multiple phase differences are scanned to identify jump boundary combinations of amplitude and phase differences where sudden changes in coalescing distance occur, generating jump boundary curves; and

[0169] During the operation of the EUV source, a combination of amplitude and phase difference is used, at least in part, based on the jump boundary curve.

[0170] 11. A method comprising:

[0171] Under the control of an electrical signal, a flow of initial droplets of a first size is released from the droplet generator. The flow of initial droplets undergoes at least one coalescence after traveling a coalescence length to become a flow of final droplets of a second size larger than the first size. The electrical signal has a first periodic component and a second periodic component that differs from the first periodic component by a phase difference.

[0172] Operate the droplet generator when the phase difference is such that the final droplet flow does not include any satellite droplets smaller than the second size; and

[0173] The phase difference value is varied to the value at which the satellite droplet appears in the final droplet flow to detect jump boundaries in the functional dependence of the coalescence length on the phase difference value.

[0174] 12. The method according to Clause 11, wherein

[0175] When the phase difference is at a value where the final droplet stream does not include any satellite droplets smaller than the second size, operating the droplet generator includes: operating the droplet generator when the phase difference is at a value expected to be lower than the value at which satellite droplets appear in the final droplet stream, and

[0176] The step-by-step method of changing the phase difference value until the satellite droplet appears in the final droplet flow to detect the jump boundary of the functional dependence of the coalescence length on the phase difference value includes: increasing the phase difference value until the satellite droplet appears in the final droplet flow to detect the jump boundary of the functional dependence of the coalescence length on the phase difference value.

[0177] 13. The method according to Clause 11, wherein the first periodic component has a first frequency and the second periodic component has a second frequency, the second frequency being an integer multiple of the first frequency, the integer multiple including one.

[0178] 14. The method according to Clause 11, wherein one of the first periodic component and the second periodic component is sinusoidal, and the other of the first periodic component and the second periodic component is a square wave.

[0179] 15. A method for controlling the coalescence behavior of a flow of EUV target material from a target material dispenser, the target material dispenser including an electrically actuated element arranged to induce a velocity disturbance component in the flow in response to an applied control signal having a sinusoidal component and a square wave component, the method comprising:

[0180] Determine a first number of adjacent values ​​of the phase difference between the sinusoidal and square wave components of the stream, excluding the satellite.

[0181] Determine the second number of values ​​that the flow actually includes the range of adjacent values ​​of the phase difference between the sinusoidal and square wave components of the satellite; and

[0182] If the first number and the second number are equal to one, then the coalescence behavior of the EUV target material flow is deemed acceptable.

[0183] 16. A method comprising:

[0184] Using a target material dispenser, a flow of droplets of fully coalesced target material is provided. The target material dispenser includes electrically actuated elements arranged to induce velocity disturbances in the flow based on droplet control signals.

[0185] Determine whether the stream also includes sub-agglomerated satellite droplets, and generate a sub-agglomerated droplet detection signal indicating whether the stream includes sub-agglomerated satellite droplets;

[0186] The waveform is generated based at least in part on the detection signal of the sub-agglomerated droplets; and

[0187] The waveform is provided to the electrically actuated element in the target material dispenser.

[0188] 17. The method according to Clause 1, wherein determining whether a stream comprises satellite droplets of sub-aggregation comprises: determining whether the size of any satellite droplet corresponds to a known size of a sub-aggregate droplet.

[0189] 18. The method according to Clause 1, wherein determining whether a flow includes satellite droplets that are coalescing sub-droplets comprises: determining the magnitude of the flow-direction displacement of any satellite droplets from a fully coalesced droplet.

[0190] 19. A method comprising:

[0191] A target material dispenser is used to provide a flow of coalesced droplets of target material. The target material dispenser includes electrically actuated elements arranged to induce velocity disturbances in the flow based on a droplet control signal having a sinusoidal component.

[0192] Determine the minimum magnitude of the sinusoidal component of the satellite droplet appearing in the flow;

[0193] Determine the sub-aggregate length based on the minimum value; and

[0194] The operation of the target material dispenser is controlled based on the determined sub-agglomeration length.

[0195] 20. A method comprising:

[0196] Using a target material dispenser, a flow of coalesced droplets of target material is provided. The target material dispenser includes a nozzle and an electrically actuated element, which is arranged to induce velocity disturbances in the flow leaving the nozzle based on a droplet control signal to generate a flow that splits into microdroplets. The control signal has a sinusoidal component and a square wave component that differs from the sinusoidal component by a phase difference.

[0197] Determine the dependence of the magnitude of the directional displacement of any satellite droplet from the coalescing droplet on the magnitude of the phase difference;

[0198] Based on this dependency, the transfer function between the control signal and the velocity disturbance at the nozzle exit is determined; and

[0199] The operation of the target material dispenser is controlled based on the determined transfer function.

Claims

1. An apparatus comprising: A target material dispenser having a nozzle and adapted to provide a flow of target material, the flow breaking into first droplets after exiting the nozzle; An electro-actuable element, mechanically coupled to the target material dispenser and arranged to induce a velocity disturbance in the flow based on an applied waveform, the velocity disturbance causing the first droplet to eventually coalesce into a second droplet larger than the first droplet in one or more stages within a coalescing distance from the nozzle, and the coalescing distance being the distance from the nozzle to the point where the first droplet eventually coalesces into the second droplet in its final coalescing state; as well as A waveform generator, electrically coupled to the electrically actuated element and adapted to generate the applied waveform having a sine wave component and a square wave component, the sine wave component having an amplitude, and the square wave component having a phase difference with the sine wave component, the amplitude and the phase difference being selected to control the amplitude of the coalescing distance while avoiding abrupt changes in the amplitude of the coalescing distance.

2. The device according to claim 1, wherein the electrically actuated element is a piezoelectric element.

3. The device according to claim 1, wherein the sine wave component has a first frequency and the square wave component has a second frequency, the second frequency being an integer multiple of the first frequency, the integer multiple including one.

4. The device of claim 1, wherein the amplitude and the phase difference are selected to minimize the amplitude of the coalescing distance while avoiding abrupt changes in the amplitude of the coalescing distance.

5. A method comprising: A target material dispenser with a nozzle is used to provide a flow of target material, which breaks into first droplets after leaving the nozzle; Using an electrically actuated element mechanically coupled to the target material dispenser, a velocity disturbance is induced in the flow based on an applied waveform. This velocity disturbance causes the first droplet to eventually coalesce into a second droplet larger than the first droplet in one or more stages within a coalescing distance from the nozzle, whereby the coalescing distance is the distance from the nozzle to the point where the first droplet eventually coalesces into the second droplet in its final coalescing state. as well as The applied waveform is generated using a waveform generator electrically coupled to the electrically actuated element. The waveform has a sine wave component and a square wave component, the sine wave component having an amplitude, and the square wave component having a phase difference with the sine wave component. The amplitude and the phase difference are selected to control the amplitude of the coalescing distance while avoiding sudden changes in the amplitude of the coalescing distance.

6. The method of claim 5, wherein the sine wave component has a first frequency and the square wave component has a second frequency, the second frequency being an integer multiple of the first frequency, the integer multiple including one.

7. The method of claim 5, wherein the amplitude and the phase difference are selected to minimize the amplitude of the coalescing distance while avoiding a sudden change in the amplitude of the coalescing distance.

Images