阅读说明：本技术 控制液滴生成器性能的设备和方法 (Apparatus and method for controlling drop generator performance ) 是由 P·贝亚吉 B·罗林格 于 2020-02-06 设计创作，主要内容包括：一种控制用于生成EUV辐射的液滴的形成的设备和方法。液滴源包括离开喷嘴的流体和具有在流体中产生扰动的可电致动元件的子系统。液滴源产生流,该流分裂成液滴,当液滴朝向辐照区域前进时,液滴转而聚结成更大的液滴。可电致动元件由具有正弦波分量和方波分量的控制信号驱动。测量和控制各种参数,诸如正弦波分量与方波分量之间的相位差,以使流中未聚结的卫星液滴的形成最小化。(An apparatus and method for controlling the formation of droplets for generating EUV radiation. The droplet source includes a fluid exiting a nozzle and a subsystem having an electrically actuatable element that creates a disturbance in the fluid. The droplet source produces a stream that breaks up into droplets that in turn coalesce into larger droplets as they progress toward the irradiation region. The electrically actuable element is driven by a control signal having a sinusoidal wave component and a square wave component. Various parameters, such as the phase difference between the sinusoidal and square wave components, are measured and controlled to minimize the formation of uncoalesced satellite droplets in the stream.)

1. An apparatus, comprising:

a target material dispenser having a nozzle and adapted to provide a stream of target material that breaks into first droplets after exiting the nozzle;

an electrically actuatable element mechanically coupled to the target material distributor and arranged to cause a velocity perturbation in the stream based on the applied waveform, the velocity perturbation causing the first drop to eventually coalesce into a second drop larger than the first drop in one or more stages within a coalescing distance from the nozzle; and

a waveform generator electrically coupled to the electrically actuatable element and adapted to generate the applied waveform, the 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, the amplitude and the phase difference selected to minimize the coalescence distance while avoiding abrupt changes in the coalescence distance.

2. The apparatus of claim 1, wherein the electrically actuatable element is a piezoelectric element.

3. An apparatus, comprising:

a target material dispenser having a nozzle and adapted to provide a stream of target material that breaks into first droplets after exiting the nozzle;

an electrically actuatable element mechanically coupled to the target material dispenser and arranged to cause a velocity perturbation in the stream based on the applied waveform, the velocity perturbation causing the first drop to eventually coalesce into a second drop larger than the first drop in one or more stages within a coalescing distance from the nozzle, the second drop being spaced such that the second drop passes a fixed point at a crossover spacing;

a cross-interval detector arranged to determine the cross-interval of the second droplet and to generate a cross-interval signal; and

a waveform generator electrically coupled to the electrically actuatable element and adapted to generate the applied waveform and to generate the applied waveform based at least in part on the crossing interval signal.

4. A method, comprising:

providing a stream of target material using a target material dispenser comprising an electrically actuatable element arranged to cause a velocity disturbance in the stream based on a droplet control signal;

determining whether the stream includes satellite droplets and generating a satellite detection signal indicative of whether the stream 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.

5. The method of claim 4, further comprising: determining a cross-interval of the stream, and generating a cross-interval signal, and wherein generating a waveform comprises generating the waveform based at least in part on the cross-interval signal.

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

dispensing a stream of EUV target material from the target material dispenser;

applying a waveform to an electrically actuable element arranged to cause a velocity disturbance in the flow in response to a control signal;

determining a minimum of the amplitude of the sine wave component of the waveform for which the stream does not include satellites;

determining a dependency of a coalescence length on a phase difference between a sine wave component and a square wave component of the control signal, and determining a discontinuous jump boundary phase difference at which the dependency occurs;

determining a slope of a dependency of the jump boundary phase on the minimum;

determining a drag coefficient based on the slope; and

determining a transfer function at a frequency of the sinusoidal component based on the minimum value and the drag coefficient.

7. A method, comprising:

providing a stream of target material using a target material dispenser having a nozzle, the stream of target material breaking into first droplets after exiting the nozzle;

using an electrically actuatable element mechanically coupled to the target material dispenser to induce a velocity perturbation in the stream based on the applied waveform that causes a first drop to eventually coalesce into a second drop larger than the first drop in one or more stages within a coalescing distance from the nozzle; and

generating the applied waveform using a waveform generator electrically coupled to the electrically actuatable element, the 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, the amplitude and the phase difference selected to minimize the coalescing distance while avoiding abrupt changes in the coalescing distance.

8. A method, comprising:

releasing a stream of initial droplets of a first size from a droplet generator under the control of an electrical signal, the stream of initial droplets undergoing at least one coalescence to become a stream of final droplets of a second size larger than the first size after traveling a coalescence length, the electrical signal having a first periodic component and a second periodic component that is out of phase with the first periodic component;

operating the drop generator if the phase difference is at a value where the stream of final drops does not include any satellite drops smaller than the second size; and

changing the value of the phase difference to a value at which satellite droplets appear in the stream of final droplets to detect a jump boundary of the functional dependence of the coalescence length on the value of the phase difference.

9. The method of claim 8, wherein

In a case where the phase difference is at a value where the stream of final droplets does not include any satellite droplets smaller than the second size, operating the droplet generator comprises: operating the drop generator if the phase difference is at a value that is expected to be lower than the value at which satellite drops appear in the stream of final drops, and

varying the value of the phase difference phase until a satellite drop appears in the stream of final drops to detect a jump boundary of the functional dependence of coalescence length on the value of the phase difference comprises: increasing the value of the phase difference phase until a satellite droplet appears in the stream of final droplets to detect a jump boundary of the functional dependence of the coalescence length on the value of the phase difference.

10. The method of claim 8, wherein the first periodic component has a first frequency and the second periodic component has a second frequency that is an integer multiple of the first frequency, the integer multiple comprising one.

11. The method of claim 8, wherein one of the first and second periodic components is sinusoidal and the other of the first and second periodic components is a square wave.

12. A method, comprising:

providing a stream of droplets of fully coalesced target material using a target material dispenser comprising an electrically actuatable element arranged to cause a velocity disturbance in the stream based on a droplet control signal;

determining whether the stream further includes sub-coalesced satellites and generating a sub-coalesced drop detection signal indicative of whether the stream includes sub-coalesced satellites;

generating a waveform based at least in part on the sub-coalesced drop detection signal; and

providing the waveform to the electrically actuatable element in the target material dispenser.

13. The method of claim 1, wherein determining whether the stream includes sub-coalesced satellites comprises: it is determined whether the size of any satellite droplets corresponds to the known size of a sub-coalesced droplet.

14. The method of claim 1, wherein determining whether the stream includes sub-coalesced satellites comprises: the magnitude of the displacement of the flow direction of any satellite from a fully coalesced drop is determined.

15. A method, comprising:

providing a stream of coalesced droplets of target material using a target material dispenser comprising an electrically actuatable element arranged to cause a velocity disturbance in the stream based on a droplet control signal, the control signal having a sinusoidal component;

determining a minimum of the magnitude of the amplitude of the sinusoidal component of the stream in which satellite droplets are present;

determining a sub-coalescence length based on the minimum value; and

controlling operation of the target material distributor based on the determined sub-coalescence length.

Technical Field

The present application relates to extreme ultraviolet ("EUV") light sources and methods of operating the same. These light sources provide EUV light by generating a plasma from a source or target material. In one application, EUV light may be collected and used in a lithographic process to produce semiconductor integrated circuits.

Background

The patterned EUV beam may be used to expose a resist-coated substrate, such as a silicon wafer, to produce very small features in the substrate. EUV light (also sometimes referred to as soft X-rays) is generally defined as electromagnetic radiation having a wavelength in the range of about 5nm to about 100 nm. One particular wavelength for lithography occurs around 13.5 nm.

Methods for generating EUV light include, but are not necessarily limited to, converting a source material into a plasma state having a chemical element that emits a line in the EUV range. These elements may include, but are not limited to, xenon, lithium, and tin.

In one such method, commonly referred to as laser produced plasma ("LPP"), the desired plasma may be produced by irradiating a source material (e.g., in the form of a droplet, stream, or line) with a laser beam. In another method, commonly referred to as discharge generated plasma ("DPP"), the desired plasma may be generated by placing a source material having an appropriate emission line between a pair of electrodes and causing a discharge to occur between the electrodes.

One technique for generating droplets involves melting a target material, such as tin, sometimes referred to as a source material, and then forcing the melted source material at high pressure through a relatively small diameter orifice, such as an orifice having a diameter of about 0.1 μm to about 30 μm, to produce a laminar fluid jet having a velocity in the range of about 30m/s to about 200 m/s. In most cases, naturally occurring instabilities, such as thermal noise or vortex shedding in the stream exiting the orifice will cause the stream to break up into droplets. These droplets have different velocities and combine with each other in flight to coalesce into larger droplets.

In the EUV generation process considered here, it is necessary to control the decomposition/coalescence process. For example, to synchronize the droplets with the LPP drive laser light pulses, a continuous laminar fluid jet emanating from the orifice may be subjected to repeated perturbations with an amplitude that exceeds the amplitude of the random noise. The droplets are synchronized with the laser pulses by applying a disturbance at the same frequency (or higher harmonics thereof) as the repetition rate of the pulsed laser. For example, a disturbance may be applied to the flow by coupling an electrically actuatable element (such as a piezoelectric material) to the flow and driving the electrically actuatable element in a periodic waveform. In one embodiment, the diameter of the electrically actuatable element will contract and expand (on the order of nanometers). This dimensional change mechanically couples with the capillary tube, which undergoes corresponding diameter contraction and expansion. This volume displacement causes acoustic and elastic waves in the capillary that ends at the orifice. The target material in the orifice is then periodically accelerated by the acoustic wave, eventually resulting in the presence of widely spaced droplets at the drive laser frequency in a frequency range well below the natural Rayleigh splitting frequency of the fluid microjet. The natural splitting frequency of the fluid jet is in the range between about 3 to about 15MHz, while the drive laser operation is expected to be in the range between about 50 and about 160 kHz. This means that in order to obtain the desired final droplets, many small droplets must merge into a periodic stream of droplets consisting of droplets much larger than the diameter of the orifice.

As used herein, the term "electrically actuatable element" and derivatives thereof refer to materials or structures that undergo a dimensional change when subjected to an electrical voltage, an electrical field, a magnetic field, or a combination thereof, including, but not limited to, piezoelectric materials, electrostrictive materials, and magnetostrictive materials. Apparatus and methods for controlling the flow of droplets Using electrically actuatable elements are disclosed, for example, in U.S. patent application publication No. 2009/0014668a1 entitled "Laser Produced Plasma EUV Light Source Using a drop Stream Produced Modulated discharge Wave" published on 1, 15 of 2009 and U.S. patent No. 8,513,629 entitled "drop Generator with Actuator Induced Nozzle Cleaning" published on 8, 20 of 2013, both of which are incorporated herein by reference in their entirety.

The task of the drop generator is therefore to place correctly sized drops in the main focus of the collecting mirror for collecting EUV radiation, where they will serve as target material for producing EUV radiation. The droplets must arrive at the primary focus within certain spatial and temporal stability criteria (i.e., where position and time are repeatable within acceptable margins). They must also arrive at a given frequency and speed. Furthermore, the droplets must be completely coalesced, which means that the droplets must be monodisperse (uniform in size) and be reached at a given drive frequency.

For example, the drop stream should be free of "satellites," i.e., smaller droplets of the target material that fail to coalesce into a main drop. Meeting these criteria is complicated because for small orifices and large pressures, it may be necessary to use an electrically actuatable element drive form to coalesce many droplets. The operating window is typically very small, making the system sensitive to changes in performance (such as performance changes over time). For example, as the performance of the drop generator changes, it may produce drops that have not completely coalesced by the time the primary focus is reached. Eventually, the performance of the drop generator will deteriorate to the point that the drop generator must be taken offline for maintenance or replacement.

One method of controlling coalescence is to apply a mixing waveform to the molten target material exiting the nozzle. The blended waveform is a periodic piezoelectric excitation waveform that can be used to control and optimize the coalescence process for use in various drop generators on various systems operating at various power levels, such as 250W. See, for example, International patent application No. PCT/EP2019/050100, entitled "Apparatus for and Method of Controlling Coolescence of Draplet Stream", filed on 3.1.2019, which is incorporated herein by reference in its entirety.

It is desirable to be able to control the generation and coalescence of droplets in a manner that allows these processes to be optimized.

Disclosure of Invention

The following presents a simplified summary of one or more embodiments in order to provide a basic understanding of such embodiments. This summary is not an extensive overview of all contemplated embodiments, and is intended to neither identify key or critical elements of all embodiments nor delineate 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 is presented later.

According to one aspect of an embodiment, there is disclosed an apparatus comprising: a target material dispenser having a nozzle and adapted to provide a stream of target material that breaks into first droplets after exiting the nozzle; an electrically actuatable element mechanically coupled to the target material dispenser and arranged to induce a velocity perturbation in the flow based on the applied waveform, the velocity perturbation causing the first drop to eventually coalesce into a second drop larger than the first drop in one or more stages within a coalescence distance from the nozzle; and a waveform generator electrically coupled to the electrically actuatable element and adapted to generate an applied 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, the amplitude and phase difference selected to minimize the coalescence distance while avoiding abrupt changes in the coalescence distance. The electrically actuable element may be a piezoelectric element.

According to another aspect of the embodiments, there is disclosed an apparatus comprising: a target material dispenser having a nozzle and adapted to provide a stream of target material that breaks into first droplets after exiting the nozzle; an electrically actuatable element mechanically coupled to the target material dispenser and arranged to cause a velocity disturbance in the flow based on the applied waveform, the velocity disturbance causing the first drop to eventually coalesce into a second drop larger than the first drop in one or more stages within a coalescence distance from the nozzle, the second drops being spaced apart such that the second drop passes a fixed point at a crossover spacing; a cross-interval detector arranged to determine a cross-interval of the second droplet and to generate a cross-interval signal; and a waveform generator electrically coupled to the electrically actuatable element and adapted to generate an applied waveform and to generate the applied waveform based at least in part on the crossing interval signal.

According to another aspect of the embodiments, a method is disclosed, comprising the steps of: providing a stream of target material using a target material dispenser, the target material dispenser comprising an electrically actuatable element arranged to cause a velocity disturbance in the stream based on a droplet control signal; determining whether the stream includes satellite droplets and generating satellite detection signals indicative of whether the stream 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 comprise the steps of: determining a cross-interval of the flow, and generating a cross-interval signal, and wherein the step of generating a waveform comprises generating the waveform based at least in part on the cross-interval signal.

According to another aspect of the embodiments, a method of determining a transfer function of a nozzle of a target material dispenser is disclosed, the method comprising the steps of: dispensing a stream of EUV target material from a target material dispenser; applying a waveform to an electrically actuable element, the electrically actuable element being arranged to cause a velocity disturbance in the flow in response to a control signal; determining a minimum value of the amplitude of the sine wave component of the waveform for which the stream does not include satellites; determining a dependence of the coalescence length on the phase difference between the sine wave component and the square wave component of the control signal, and determining a discontinuous jump boundary phase difference at which the dependence occurs; determining a slope of a dependence of the jump boundary phase on the minimum; determining a drag coefficient based on the slope; and determining a transfer function at the frequency of the sine wave component based on the minimum value and the drag coefficient.

According to another aspect of the embodiments, a method of optimizing the coalescence behavior of a flow of EUV target material from a target material distributor comprising an electrically actuatable element arranged to cause a velocity disturbance in the flow in response to an applied control signal is disclosed, the method comprising the steps of: determining a minimum value of the amplitude of the sine wave component of the control signal for which the stream does not include satellites; determining a dependence of the coalescence length on the phase difference between the sine wave component and the square wave component of the control signal, and determining a discontinuous jump boundary phase difference at which the dependence occurs; determining a slope of a 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 a difference between the jump boundary phase difference and the designed phase delay.

According to another aspect of the embodiments, there is disclosed a method of controlling the coalescing behaviour of a flow of EUV target material from a target material distributor, the target material distributor comprising an electrically actuatable element arranged to cause a velocity disturbance in the flow in response to an applied control signal having a sine wave component and a square wave component, the method comprising the steps of: determining a width L of a maximum range of the stream excluding adjacent values of phase differences between sinusoidal and square wave components of the satellite_n(ii) a Determining a width L of a stream comprising a maximum of adjacent values of a phase difference between a sine wave component and a square wave component of a satellite₂(ii) a Determining the value S_mAs having a width L_nA statistical measure of the variation of the stream crossing interval within a range of (a); determine the value YStabilty as the vector [ ry_m，rz_m]Wherein ry is_mIs a statistical measure of the stability of the flow in the y-direction, rz_mIs a statistical measure of the stability of the flow in the z direction; and determining a cost function

Wherein W₁、W₂、W₃、W₄Are some positive real numbers; and the parameters of the sinusoidal and square wave components are adjusted to minimize the cost function.

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

According to another aspect of the embodiments, a method of operating a target material distributor in an EUV source is disclosed, the method comprising the steps of: generating a 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; applying a waveform to an electrically actuatable element mechanically coupled to a target material dispenser having a nozzle to provide a stream of target material that breaks up into first droplets after exiting the nozzle and then coalesces into second droplets larger than the first droplets in one or more stages within a coalescence distance from the nozzle; scanning, for a plurality of amplitudes, a plurality of phase differences to identify a jump boundary combination of amplitude and phase differences at which a sudden change in coalescence distance occurs, generating a jump boundary curve; and using a combination of amplitude and phase difference based at least in part on the jump boundary curve during operation of the EUV source.

According to another aspect of the embodiments, a method is disclosed, comprising: releasing a stream of initial droplets of a first size from a droplet generator under the control of an electrical signal, the stream of initial droplets undergoing at least one coalescence to become a stream of final droplets of a second size larger than the first size after having traveled a coalescence length, the electrical signal having a first periodic component and a second periodic component that is out of phase with the first periodic component; operating the drop generator if the phase difference is at a value where the stream of final drops does not include any satellite drops smaller than the second size; the value of the phase difference phase is varied until satellites appear in the stream of final drops to detect a jump boundary of the functional dependence of the coalescence length on the value of the phase difference. In the case where the phase difference is at a value where the stream of final droplets does not include any satellite droplets smaller than the second size, operating the droplet generator may include: operating the drop generator with the phase difference at a value expected to be lower than the value at which the satellite drops appear in the stream of final drops, and varying the value of the phase difference phase until the satellite drops appear in the stream of final drops, to detect a jump boundary of the functional dependence of the coalescence length on the value of the phase difference may comprise: the value of the phase difference phase is increased until a satellite droplet appears in the stream of final droplets to detect a jump boundary of the functional dependence of the coalescence 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 that is an integer multiple of the first frequency, the integer multiple comprising one. One of the first and second periodic components may be sinusoidal while the other of the first and second periodic components is a square wave.

According to another aspect of the embodiments, there is disclosed a method of controlling the coalescing behaviour of a flow of EUV target material from a target material distributor, the target material distributor comprising an electrically actuatable element arranged to cause a velocity disturbance in the flow in response to an applied control signal having a sine wave component and a square wave component, the method comprising the steps of: determining a first number of ranges of adjacent values of phase difference between the sinusoidal and square wave components of the stream excluding the satellite; determining a second number of ranges of adjacent values of the phase difference between the sinusoidal and square wave components of the satellite for which the stream does include; and determining that the coalescence behavior of the flow of EUV target material is acceptable if the first number and the second number are equal to one.

Further embodiments, features, and advantages of the present inventions, as well as the structure and operation of the various embodiments, are described in detail below with reference to the accompanying drawings.

Drawings

The accompanying drawings, which are incorporated herein and form a part of the specification, illustrate by way of example, and not of limitation, methods and systems of embodiments of the present invention. Together with the detailed description, the drawings further serve to explain the principles of and to enable a person skilled in the pertinent art to make and use the methods and systems presented herein. In the drawings, like reference numbers can indicate identical or functionally similar elements.

FIG. 1 is a simplified schematic diagram of an EUV light source coupled to an exposure apparatus.

FIG. 2 is a schematic diagram of a droplet generation subsystem for an EUV light source.

FIG. 3 illustrates a technique for coupling one or more electrically actuatable elements with a fluid to create a disturbance in the flow exiting an orifice;

fig. 4 is a diagram showing a state of coalescence in the droplet stream.

Fig. 5A and 5B illustrate components of a composite blended waveform such as may be used in accordance with an aspect of an embodiment.

FIG. 6 is a diagram of satellite formation as a function of phase difference in accordance with an aspect of an embodiment.

Fig. 7 is a diagram of satellite formation behavior as a function of cross-over spacing and a ratio of a length of a region with satellites to a region without satellites in accordance with an aspect of an embodiment.

FIG. 8 is a graph of coalescence length dependence on phase difference in accordance with an aspect of an embodiment.

FIG. 9 is a graph of coalescence length as a function of sinusoidal amplitude and square phase in accordance with an aspect of the embodiments.

FIG. 10 is a graph illustrating the effect of resistance magnitude on the relationship between (1) the product of the nozzle transfer function and the sine amplitude and (2) the square phase, in accordance with an aspect of an embodiment.

FIG. 11 is a graph illustrating the effect of time lapse on the relationship between (1) the product of the nozzle transfer function and the sine amplitude and (2) the square phase, in accordance with an aspect of an embodiment.

Fig. 12 is a diagram illustrating a configuration of a satellite-free operating region as a function of square phase and blocker sine amplitude in accordance with an aspect of an embodiment.

Fig. 13 is a diagram illustrating a relationship of a jump boundary slope and a drag coefficient in accordance with an aspect of an embodiment.

FIG. 14 is a graph illustrating a drag coefficient versus nozzle transfer function and blocking sine amplitude in accordance with an aspect of an embodiment.

Fig. 15 is a flow diagram illustrating a process for inferring a presence or absence of a satellite drop using skip boundary data in accordance with an aspect of an embodiment.

FIG. 16 is a diagram illustrating certain conventions in a coordinate system used to describe EUV radiation generation in accordance with an aspect of an embodiment.

FIG. 17 is a diagram illustrating a relationship between drop locations in accordance with an aspect of an embodiment.

FIG. 18 is a diagram illustrating a relationship of a square phase and drop position relative to a nozzle transfer function in accordance with an aspect of an embodiment.

FIG. 19 is a flow diagram illustrating a process for determining a transfer function of a drop generator in accordance with an aspect of an embodiment.

FIG. 20 is a diagram illustrating a relationship between drop locations in accordance with an aspect of an embodiment.

FIG. 21 is a diagram illustrating relationships between drop locations in accordance with an aspect of an embodiment.

Further features and advantages of the invention, as well as the structure and operation of various embodiments of the invention, are described in detail below with reference to the accompanying drawings. Note that the present invention is not limited to the specific embodiments described herein. Such embodiments are presented herein for illustrative purposes only. Other embodiments will be apparent to persons skilled in the relevant art(s) based on the teachings contained herein.

Detailed Description

Various embodiments are now described with reference to the drawings, wherein like reference numerals are used to refer to like elements throughout. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of one or more embodiments. It will be apparent, however, that in some or all cases, any of the embodiments described below may be practiced without employing the specific design details described below. In other instances, well-known structures and devices are shown in block diagram form in order to facilitate describing one or more embodiments. The following presents a simplified summary of one or more embodiments in order to provide a basic understanding of such embodiments. This summary is not an extensive overview of all contemplated embodiments, and is intended to neither identify key or critical elements of all embodiments nor delineate the scope of any or all embodiments.

Before describing these embodiments in more detail, however, it is helpful to present an example environment in which embodiments of the invention may be implemented. In the description and claims that follow, the terms "upward," "downward," "top," "bottom," "vertical," "horizontal," and the like may be used. These terms are intended to refer only to relative orientation, and not to any orientation relative to gravity.

Referring initially to FIG. 1, a schematic diagram of an exemplary EUV radiation source (e.g., a laser-produced plasma EUV radiation source 10) is shown in accordance with an aspect of an embodiment of the present invention. As shown, the EUV radiation source 10 may include a pulsed or continuous laser source 22, and the laser source 22 may be, for example, a pulsed gas discharge CO that produces a radiation beam 12 having a wavelength typically below 20 μm (e.g., about 10.6 μm or about 0.5 μm or less)₂A laser source. Pulsed gas discharge of CO₂The laser source may have DC or RF excitation operating at high power and high pulse repetition rate.

The EUV radiation source 10 further comprises a target delivery system 24 for delivering the source material in the form of droplets or a continuous stream of liquid. In this example, the source material is a liquid, but may also be a solid or a gas. The source material may be made of tin or a tin compound, but other materials may 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 where the source material may be irradiated to generate plasma. It should be noted that, as used herein, an irradiation region is a region where irradiation of a source material can occur, and is an irradiation region even when irradiation does not actually occur. The EUV light source may also include a beam focusing and steering system 32, which will be explained in more detail below in conjunction with fig. 2.

In the system shown, the assembly is arranged so that the droplets 14 travel substantially horizontally. The direction from the laser source 22 towards the irradiation region 28 (i.e. the nominal direction of propagation of the optical beam 12) may be taken as the Z-axis. The path taken by the droplet 14 from the source material delivery system 24 to the irradiation region 28 may be taken as the X-axis. The view of fig. 1 is thus perpendicular to the XZ plane. Further, while a system is depicted in which the droplets 14 travel substantially horizontally, one of ordinary skill in the art will appreciate that other arrangements may be used in which the droplets travel vertically or at some angle between 90 degrees (horizontal) and 0 degrees (vertical) with respect to gravity, inclusive.

The EUV radiation source 10 may further include an EUV light source controller system 60, and the EUV light source controller system 60 may further include a laser emission control system 65 and a beam steering system 32. The EUV radiation source 10 may also include a detector, such as a droplet position detection system, which may include one or more droplet imagers 70, the droplet imagers 70 generating outputs indicative of the absolute or relative position of the droplets (e.g., relative to the irradiation region 28) and providing the outputs to the target position detection feedback system 62.

The drop position detection feedback system 62 can use the output of the drop imager 70 to calculate drop position and trajectory, from which drop position errors can be calculated. The drop placement error may be calculated on a drop-by-drop basis, or averaged, or otherwise calculated. The drop position error may then be provided as an input to the light source controller 60. In response, the light source controller 60 may generate a control signal, such as a laser position, orientation, or timing correction signal, and provide the control signal to the laser beam steering system 32. Laser beam steering system 32 may use the control signal to change the position and/or power of the laser beam focal spot within chamber 26. Laser beam steering system 32 can also use the control signal to change the geometry of the interaction of beam 12 and droplet 14. For example, beam 12 may be made to strike drop 14 off-center or at an angle of incidence other than directly on-head.

As shown in fig. 1, 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 drop position error described above or some quantity derived from the drop position error provided by the system controller 60) to adjust the path of the source material through the irradiation region 28. This may be accomplished, for example, by repositioning the point at which the source material delivery mechanism 92 releases the droplet 14. The droplet release point may 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 externally supplied with source material and connected to a gas source to place the source material under pressure in the source material delivery mechanism 92.

Continuing with FIG. 1, 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 is also applicable to other optical elements. The collector 30 may be a normal incidence reflector, e.g. implemented as an MLM with an additional thin barrier layer, e.g. B₄C、ZrC、Si₃N₄Or C, a thin barrier layer is 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. The collector 30 may be in the form of an oblong ellipsoid with a central hole to allow the laser radiation 12 to pass through and reach the irradiation region 28. Collector 30 may be, for example, an elliptical shape with a first focus at irradiation region 28 and a second focus at a so-called intermediate point 40 (also referred to as intermediate focus 40), where EUV radiation may be output from EUV radiation source 10 and input to, for example, an integrated circuit lithography scanner or stepper 50, which processes a silicon wafer workpiece 52 using, for example, a reticle or mask 54 in a known manner using radiation. The mask 54 may be transmissive or reflective. For EUV applications, the mask 54 is typically reflective. The silicon wafer workpiece 52 is then additionally processed in a known manner to obtain integrated circuit devices.

Figure 2 shows the droplet generation system in more detail. The source material delivery system 90 delivers droplets to the irradiation site/primary focus 48 within the chamber 26. Waveform generator 230 provides a drive waveform to electrically actuable elements in drop generator 90 that causes velocity disturbances in the stream of drops. The waveform generator 230 operates under the control of the controller 250 based at least in part on data from the data processing module 252. The data processing module receives data from one or more detectors. In the example shown, the detector includes a camera 254 and a photodiode 256. The droplets are irradiated by one or more lasers 258. In this typical arrangement, the detector detects/images the droplet at a point in the stream where coalescence is expected to have occurred.

Figure 3 shows in schematic form the components of a simplified droplet source 92. As shown, the droplet source 92 may include a container 94 containing a fluid 96 (e.g., molten tin) under pressure. Also shown, the container 94 may be formed with a nozzle 98 that allows the pressurized fluid 96 to exit the container 94, forming a continuous stream that subsequently breaks into a plurality of droplets. The waveform generated by the waveform generator 230 is used to drive the electrically actuatable element 150 to produce droplets for EUV output. Electrically actuable element 150 creates a perturbation in the fluid that generates droplets having different initial velocities causing at least some adjacent pairs of droplets to coalesce together before reaching the irradiation region. The ratio of initial droplets to coalesced droplets may be any number, for example, in the range of about 10 to about 500.

The entire droplet coalescence process can be thought of as a series of multiple coalescence steps or states that evolve as the distance from the nozzle changes. This is shown in fig. 4. For example, in the first state I, i.e. when the target material first leaves the orifice or nozzle, the target material is in the form of a laminar fluid jet with a velocity disturbance. In a second state II, the fluid jet breaks up into a series of droplets with different velocities. In the third state III, the droplets coalesce into medium size droplets, called sub-coalesced droplets, having different velocities from each other, measured in time-of-flight or by distance from the nozzle. In the fourth state IV, the sub-coalesced drops coalesce into drops having the desired final size. The number of sub-coalescence steps may vary. The distance from the nozzle to the point where the droplets reach their final coalesced state is the coalescence distance or length L. Ideally, the coalescence distance of the droplets is as short as possible. As the droplets coalesce into larger droplets, they are less sensitive to source conditions such as hydrogen flow and ion impact.

Thus, when controlled with an excitation signal, the coalescence process can thus be understood as having: an initial partially coalesced or sub-coalesced state that produces medium size droplets (higher frequency (typically 500kHz) droplets) with a pitch of about 2 μ s; and main coalescence, in which the sub-coalesced drops coalesce into a main drop having a pitch (50kHz) of about 20 μ s, although other pitches are produced in other embodiments.

Thus, control of the splitting/coalescing process involves controlling the droplets so that they are sufficiently coalesced before reaching the irradiation region and have a frequency corresponding to the pulse rate of the laser used to irradiate the coalesced droplets. The blended waveform can be provided to an electrically actuatable element to control the coalescence process of the Rayleigh split droplet into fully coalesced droplets having a frequency corresponding to the laser pulse rate. In essence, the blended waveform may be comprised of a combination of a first low frequency periodic waveform and a second high frequency periodic waveform. For example, the mixed waveform may be composed of a low frequency sine wave and a higher frequency square or block wave. However, it should be understood that the higher frequency periodic waveform need not be a square wave, and the teachings herein relating to implementations using square waves may be considered context-permitting, which is equally applicable to implementations in which the second high frequency periodic signal is not a square wave. Thus, the mixed waveform signal may be composed of a low-frequency sine wave (such as 50kHz) shown in fig. 5A and a high-frequency block wave (such as 500kHz) shown in fig. 5B. In the figure, the scale of the time axis and the amplitude axis is arbitrary. Such a hybrid waveform can be characterized by reference to five adjustable parameters, including a) the amplitude of the sine wave, b) the square phase, i.e., the phase difference between the sine wave and the square wave, c) the amplitude of the square wave, d) the uptime (duty cycle) of the square wave, and d) the frequency of the square wave. The main coalescence process depends mainly on the sinusoidal amplitude and the square phase, and may further depend on the other three adjustable parameters mentioned above.

As previously mentioned, if complete coalescence is not achieved, the droplet stream will comprise smaller droplets, referred to as satellites or microsatellites. The presence of satellite droplets may be detected by any one or a combination of several methods, for example, using a Droplet Detection Module (DDM), a crossover spacing, a Droplet Formation Camera (DFC), or even by monitoring changes in the EUV signal. Systems and methods for monitoring the flow of droplets are disclosed, for example, in U.S. patent No. 9,241,395 entitled "System and Method for Controlling drop Timing in an LPP EUV Light Source," issued at 19/1/2016, which is incorporated herein by reference in its entirety. However, with monitoring devices that are relatively far from the flow, it is difficult to directly view the satellites or measure the coalescence distance. It would be useful to have a way to infer conditions such as the presence or absence of satellites or the length of a conglomerate from more directly determinable parameters.

Sub-coalescence is an important part of the coalescence process using a mixed waveform excitation signal, because if the sub-coalescence length increases, the main and sub-coalescence processes will interfere with each other, which increases the coalescence length. The increased coalescence length increases the likelihood of satellites caused by plasma pressure from the irradiated region.

In addition, poor sub-coalescence will increase the velocity jitter of the sub-coalesced drops (frequency may be 500kHz), which may cause low frequency satellites (the presence of satellites beside portions of the main drop) or poor drop timing. Satellites and poor timing can affect dose stability and collector lifetime in EUV systems.

It is therefore advantageous to first characterize the sub-coalescence process and use this characterization as at least part of the basis for controlling the time-varying signal that produces pressure variations in the drop generator nozzles. This determination may be performed iteratively, for example, to improve coalescence of droplets (e.g., reduce incidence of satellite droplets). Where such a determination is used to improve the blended waveform, the process may be referred to as blended waveform optimization (HWO).

As described above, one of the main challenges in optimizing the parameters of the blended waveform excitation signal is to determine the characteristics of the sub-coalescence process using low frequency drop metrology devices that can typically be used on EUV systems. In various systems, there may be a setting of image-based low frequency satellite detection at the irradiation region (e.g., the primary focus of the collector). The sampling frequency (rate) of this signal may be less than 20Hz, which is significantly less than the main drop frequency, which may be 50 kHz. There may also be settings that determine the crossover interval (i.e., the timing between two drops). The frequency (rate) of this signal may be the same as the main drop frequency (such as 50 kHz). There may also be an arrangement of image-based position measurements of the drop in the y and z directions: the frequency (rate) of this signal may be 1kHz, which is less than the main drop frequency.

Generally, the signals from these measurements and detections contain only information about the condition of the main droplet, and the measurement equipment may not be able to directly measure quantum coalescence performance. According to one aspect of an embodiment, disclosed herein is a system and method for quantifying sub-coalescence performance using the above-described measurements. This enables the presence of low frequency satellites to be detected after tuning the mixed waveform excitation signal, such as may not be directly observable by typical metrology equipment. It may also use measurements provided by conventional measurement equipment to achieve optimization of the performance of the sub-coalescence. It can also characterize "health metrics" to characterize the performance of the drop generator nozzle in generating stable sub-coalesced drops. It may also enable optimization of sub-agglomerations to improve the robustness of the tuning solution.

According to an aspect of an embodiment, the HWO may be used to optimize a parameter, such as a combination of the above five parameters of the mixed waveform excitation signal. For example, in various implementations of optimization, two of these parameters (square amplitude and square uptime) may be used to control the sub-coalescence process.

In particular, the phase scan data may be used to quantify the sub-coalescence behavior. As used herein, phase scanning refers to the process of scanning a square phase parameter and determining a set of conditions for scanning a particular value of the phase. One of the conditions is whether a satellite is present at the value of the square phase. This is a Boolean yes or no determination that may be used to set the flag. Another of the detected conditions may be a timing spread between two droplets, the timing being referred to asAre cross-over intervals. For example, a statistical measure of the spread, such as three sigma, i.e., an interval within three standard deviations of the mean, may be determined. This may be referred to as a three sigma cross-spacing and is represented by s_iAnd (4) showing. Another condition that can be detected is represented by three sigma of the y and z position of the stream of droplets. In each setting, the three sigma values of the drop position in y and z are determined and represented by ry_iAnd rz_iAnd (4) showing.

This data can then be used to optimize the sub-coalescence performance. First, looking at the presence or absence of a satellite, there will typically be an area of adjacent square phase settings of the yielding satellite, adjacent meaning that the area is not blocked by values of the non-yielding satellite. Note that the area may be determined by satellite detection using DFC. The results are shown in the representative embodiment of fig. 6, fig. 6 being a plot of the three sigma crossover interval as a function of square phase. In fig. 6, the values of the square phases of the non-satellite-producing satellites are represented by pure dots. The value of the square phase of the yielding satellite is represented by the circled point. The area in which the satellites are present (phase range of adjacent phase values) may be referred to as a satellite island SI. Regions without satellites may similarly be referred to as satellite-free islands SFI. According to one technique for analyzing the data, the width L of the square phase of the widest satellite-free island is determined₁. The satellite-free island width for perfect sub-coalescence is denoted L_n. In other words, L_nIs the theoretical value of the island width assuming that the coalescence process starts with uniformly distributed sub-coalesced drops.

Note that L_nIs a function of the product TF (nozzle transfer function at 50kHz) and the sine amplitude (amplitude of the sine wave component) and the drop resistance coefficient. If the measured island width matches L_nThere are uniformly distributed sub coalesced droplets.

Next, the width of the widest satellite island is determined. The width is formed by L₂And (4) showing. In the case of perfect daughter coalescence, this quantity will be equal to 2 π -L_n。

In the next step, a statistical measure, such as the p-norm of the cross-spaced data within the no-satellite region, is determined and denoted S_m。

Next, a statistical measure of the three-sigma p-norm, such as y-stability, is determined as ry _ m, and a statistical measure of the three-sigma p-norm, such as z-stability, is determined as rz _ m. YZStabilty is then determined as the vector [ ry_m，rz_m]Weighted p-norm of (c).

Based on the above determination, the quantifier of a sub-coalescence may be defined as a value that minimizes a cost function, e.g., as follows:

where W1, W2, W3, W4 are some positive real numbers.

The above metric may provide a useful estimate of the likelihood of plasma-induced satellite presence. In other words, the sub-coalescence parameter may be set to the minimum of the above-mentioned cost function numbers. By setting the sub-coalescence parameter to the minimum of the above-mentioned cost function numbers, the presence of satellites can be minimized, thereby optimizing sub-coalescence performance.

As another measure of sub-coalescence performance, if multiple satellite-free regions are found, the sub-coalescence performance may be considered unacceptable. In other words, if sub-coalescence performance is acceptable, the dependence of the three sigma cross-separation as a function of the square phase should have one satellite-free region and one satellite region.

As previously mentioned, satellites may appear when the sub-coalescence behavior fails. Sub-coalescence is related to the high frequency component of the nozzle transfer function. Thus, the metric associated with the sub-coalescence described above gives feedback on this component of the nozzle transfer function.

The above techniques/metrics also provide an objective function for the optimization process of HWO. It also provides a metric to quantify the performance of the drop generator in terms of the sub-coalescence process.

The techniques described herein may also reduce the likelihood of plasma-induced satellites being generated, increase the lifetime (robustness) of the tuning solution determined by the HWO, and provide performance indicators based on the performance of the sub-coalescence to support swap decisions, i.e., decisions for disabling and replacing DGs.

The above metric (more specifically, L) can be calculated for the overall effect of the phase sweep₁And S_m) And can determine which phase scans yield plasma-induced satellites. Phase scans with and without plasma induced satellites can be classified based on a linear combination of these two metrics. In fig. 7, the phase scan with the plasma induced satellites is represented by an asterisk and the phase scan without the plasma induced satellites is represented by an open circle. The probability of plasma induced satellites can be predicted based on the phase scan data. These data can be acquired without plasma while tuning the drop generator.

Based on coalescence simulations and bench testing in vacuum, the coalescence length decreases approximately linearly with increasing sinusoidal amplitude. The minimum coalescence length is centered in the satellite-free region constructed by changing the square phase.

The term "blocking sinusoidal amplitude" is used to refer to the minimum of sinusoidal amplitudes that can generate a satellite-free setting. Which 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 following assumptions: the effect of the resistance on the droplets in the EUV vessel is negligible. In fact, the flow of hydrogen in the container may subject the droplets to a non-negligible resistance. Essentially, the resistance, and hence the blocking sine amplitude, is determined. This results in a corrected transfer function. The transfer function calculation may need to be corrected based on the drag coefficient.

Furthermore, it has been determined that the resistance caused by hydrogen flow in the vicinity of the droplets and stable vessel pressure can have a significant impact on the coalescence process. During the optimization of the mixing waveform parameters, special attention needs to be paid to the resistance acting on the coalesced droplets. The estimation of the transfer function based on the amplitude of the blocking sinusoid during HWO may not be accurate without considering the presence of resistance. Furthermore, in the presence of drag, the center of the satellite-free region (in the square phase space) is not the minimum of the coalescence length.

With regard to resistance, the droplets in the state under consideration can be regarded as spheres each having a diameter d. Also in the considered state, the Reynolds number is relatively small, so the resistance F to a fixed speed of the gas flowing through the sphere_DCan be approximated as follows:

where μ is the gas viscosity, d_pIs the particle diameter, C (Kn) is from 2 lambda/d_pSlip correction factor, V, given Knudsen number_pIs the particle velocity, U is the local velocity of the fluid, C_D(Re_p)Re_pThe/24 is a non-Stokesian correction for fluid inertial effects. See Daniel J.Rader, Anthony S.Geller, "3-Transport and disposition of Aerosol Particles" (Editor(s): RajiV Kohli, K.L.Mittal, Developments in Surface control and cleansing, William Andrew Publishing, 2008, Pages 189 and 266).

One effect of considering the drag is that the location of the minimum in coalescence length becomes partially dependent on the vessel pressure. The coalescence length is a discontinuous function of a parameter of the excitation signal; the minimum value of the coalescence length (close to discontinuity) is not a robust operating point with respect to changes in the nozzle transfer function.

As described above, the HWO process may optimize five parameters of the mixed waveform excitation signal described above. In various implementations of the process, two of these parameters (sinusoidal amplitude and square phase) may be used to control the main coalescence process, and the remaining parameters may be used to control the sub-coalescence. An optimization procedure that takes into account drag offers the possibility of improved performance compared to an optimization that assumes negligible drag. This is particularly the case where the vessel pressure is not negligible and a hydrogen gas stream is present.

Further, as described above, the coalescence length is the minimum distance from the nozzle where all droplets are merged (e.g., a 50kHz drop). A satellite-free setting is obtained if the coalescence length is smaller than the distance between the nozzle and the main focus of the EUV collector. The ideal operating point should have a small coalescence length to provide robustness against hydrogen flow and shock waves originating from the plasma.

In the presence of resistance, the functional dependence of the coalescence length on the square phase has a discontinuity. The discontinuous position is one of the boundaries of the satellite-free area, and is referred to as a jump boundary shown in fig. 8. In a simplified version of the HWO process, the operational square phase may simply be set to the center of the satellite-free region, which is not the minimum value of the coalescence length in the presence of resistance. However, there are advantages to using a HWO process that can determine an operational positive phase value that is robust to nozzle performance variations and can provide a smaller coalescence length. Note that in various implementations, this process may be performed using only the satellite detector target formation metrology device (TFM) and DFC at the primary focus/irradiation zone.

In summary, the coalescence length is a discontinuous function of the square phase for fixed values of sinusoidal amplitude, square uptime, square amplitude and square frequency. That is, a plot of the coalescence length as a function of the positive phase will exhibit discontinuities for certain values of the positive phase. Just prior to the discontinuity, the coalescence length will be at or near a minimum, while at the discontinuity, the coalescence length will be at or near a maximum. This discontinuous location is referred to herein as a jump boundary.

Another approach to this phenomenon is to consider a square phase, which results in a discontinuity as a function of the amplitude of the sinusoidal components. This is shown in fig. 9. In fig. 9, the x-axis is the increasing sinusoidal amplitude and the y-axis is the increasing square phase. The dark to light shades of grey indicate the change in coalescence length, the dark colors indicate shorter and the light colors indicate longer. The resulting boundary between the maximum coalescence length region (brightest) and the minimum coalescence length region (darkest) defines a curve showing the dependence of the position of the jump boundary as a function of sinusoidal amplitude.

The jump boundary curve in fig. 9 provides a tool for determining the position of the jump boundary for various values of sinusoidal amplitude from measurements of only one position of the jump boundary curve. In other words, once the shape of a portion of a curve is determined, the shape of the other portion of the curve may be determined by extrapolation. By using a look-up table showing the y-displacement of the curve under different resistance conditions, the curve can be calibrated for different resistance conditions.

The skip boundary curve depends on the square uptime, the square amplitude, and may also vary with time (phase drift). However, in general, the shape of the curves defined by this dependence will remain substantially constant over time or changes in resistance, and the effect of these changes will be phase drift, which will shift the curves along the y-axis. This is shown in fig. 10 and 11. Fig. 10 shows three jumping boundary curves: marked as Large F₀The curve of (a) shows a relatively greater resistance curve; marked as small F₀The curve of (a) shows a curve with a relatively smaller resistance; and an unlabeled middle curve for medium-sized drag. It can be seen that the curves have substantially the same shape and are only displaced perpendicularly to each other. The amount of offset is an indication of the amount of resistance. However, fig. 11 shows that the movement of the curve may also be due at least in part to the passage of time.

The resistance function and the transfer function may also be determined from the slope of the blocking sinusoid amplitude and the curve defining the dependence of the skip boundary on the sinusoid amplitude. In fig. 12, the blocking sinusoid amplitude is first determined by recursive phase scanning with different sinusoid amplitudes. Thereby, a curve defining the dependence of the jump boundary on the sinusoidal amplitude is established. Thus, the jump boundary curve can also be used to determine the drag coefficient (fig. 13). The transfer function may be calculated based on the blocking sinusoid amplitude and the drag coefficient (fig. 14). Note that the jump boundary can be determined without determining the crossing interval, since the transfer function is essentially a horizontal scale of the curve of the jump boundary's dependence on the sinusoidal amplitude.

Once the jump boundary is determined, operating conditions may also be selected that will minimize the coalesce length in a manner that does not cause the coalesce length to approach the jump boundary. The coalescence length obtained using this process is less than that obtained using other techniques, which is desirable because it provides a margin with respect to flow and plasma perturbations. The above method also minimizes the possibility of plasma induced satellites being generated.

The above provides a method for estimating the nozzle transfer function, since the transfer function is simply a scale of the horizontal axis. Also a method for optimizing the parameters of a mixed waveform excitation signal. It also provides a new method for determining the vessel pressure and drag coefficient within the vessel.

A statistical measure of the variation of the crossing interval, such as the three sigma value of the crossing interval, will increase near the jump boundary. This is an alternative method to find the position of the hop boundary based on the crossing interval without using satellite detector measurements.

As described above, quantifying these parameters allows characterization of satellite formation, hop boundaries and coalescence length even if the satellite measurements are far from the nozzle and these conditions cannot be directly observed.

According to one aspect, flow conditions such as coalescing length or satellite conditions (presence or absence) may be inferred from the jump boundary data as represented by the flow diagram shown in FIG. 15. In a first step S10, sinusoidal amplitude values are selected. In step S20, the square phase is scanned for the current sinusoidal amplitude, and the jump boundary is determined as a combination of the sinusoidal amplitude and the square phase in which the coalescence length abruptly increases, that is, showing discontinuity. In step S30, it is determined whether a positive phase scan has been performed for all values of the desired sinusoidal amplitude. If so, then in step S40, the jump boundary data is used during operation to infer flow conditions at a given combination of sinusoidal amplitude and square phase (in the figure, satellite conditions are taken as an example). If not, in step S35, the sinusoidal amplitude is changed and the process returns to step S10.

As previously described, when a mixed waveform is used to form droplets, the first droplets, i.e., the droplets that are formed first according to the break-up of the stream exiting the nozzle of the drop generator, coalesce into higher frequency (typically 500kHz) droplets (referred to herein as sub-coalesced droplets). These sub-coalesced droplets then coalesce into fully coalesced droplets of primary frequency (typically 50 kHz). Ideally, none of these droplets or sub-coalesced drops reach the irradiation site during operation. Any of these higher frequency sub-coalesced droplets that reach the primary focus when they do so are referred to herein as sub-coalesced satellite droplets. Any droplet that reaches the primary focus will be referred to as a droplet satellite. Other techniques for optimizing the parameters of the mixed waveform excitation signal use the position and size information of the droplets and satellites.

As described above, in general, for the reference coordinate system, as shown in the conceptual diagram of the EUV system in fig. 16, Z is a direction along which the laser beam 12 propagates, and is also a direction from the collector 30 to the irradiation 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 this a right-hand coordinate system, the trajectory of the stream of droplets 14 is considered to be in the-X direction. The origin is considered as the irradiation site 28. The presence of satellite droplets in the stream at the irradiation site 28 may be detected by any one or a combination of several methods, for example, observing the stream at the irradiation site using DDM or DFC.

As shown in fig. 17, there is a range of sinusoidal amplitudes for each fully coalesced drop 400 in its vicinity with sub coalesced satellite drops 410 from the fully coalesced drop, displaced in the-X direction of propagation of the flow, also referred to herein as the flow direction, as indicated by the arrow. The distance between the droplet and the satellite in the X direction (labeled "a" in the figure) is referred to as STDD (satellite to droplet distance). STDD is a linear function of square phase as shown in fig. 18. In fig. 18, the line labeled 450 shows a simulation of STDD with a square phase, where the sinusoidal amplitude is at a first value, the line labeled 460 shows a simulation of STDD with a square phase, where the sinusoidal amplitude is at a second value, the line labeled 470 shows a simulation of STDD with a square phase, and the sinusoidal amplitude is at a third value. The slope of these lines is a measure of the amplitude of the transfer function sinusoid and can therefore be used to determine the nozzle transfer function.

An analytical expression quantifying the relationship between STDD and the square phase (denoted by phi) is determined as follows:

where TF is the transfer function, LDFC is the streamwise distance between the tip of the drop generator nozzle and the location where the camera used to view the stream captures the stream image, and U0 is the velocity of the primary coalesced drop.

The nozzle transfer function is an important indicator of the operating state of the drop generator, as it indicates the amount of voltage required by the drop generator to apply a given relative velocity on the drop. This relative velocity determines how quickly the droplets coalesce. The transfer function may be used to guide switching decisions, for example, to replace a drop generator if the drop generator cannot generate sufficient relative speed at the maximum input voltage to achieve complete coalescence at an acceptable distance before reaching the irradiation region.

According to one aspect, represented in a flow chart as shown in FIG. 9, sinusoidal amplitude values are selected in step S50. In step S60, the functional dependence of the STDD on the square phase is determined at the selected sinusoidal amplitude. In step S70, a transfer function is determined from the slope of the function dependency determined in step S60. In step S80, the drop generator (DG in the figure) is operated according to the determined transfer function, including but not limited to a possible assessment of maintenance or replacement of the drop generator according to the transfer function.

There are a variety of methods to detect sub-coalesced satellite droplets. Another approach is to use an imager such as DFC to determine whether the size of all satellite droplets corresponds to the known size of a sub-coalesced droplet. Here and elsewhere, "correspond" means that the size of the satellites is closer to the size of the sub-coalesced drops than the size of the full coalesced drops or droplets. s equals higher frequency droplets.

Another method of detecting sub-coalescence satellites is based on the coordinates of the position of the satellites in the transverse (Z) direction, which is an indirect measure of the droplet size. The hydrogen flow in the chamber separates the fully coalesced droplets from the smaller droplets in the transverse direction. Thus, for a given flow condition within the chamber, the sub-coalesced satellite drops are displaced in the Z direction from the main full coalesced drops by a certain distance B, as shown in fig. 20.

The position and size information of the droplets and satellites can also be used to measure the sub-coalescence length, i.e. the distance from the nozzle outlet to the position where the droplets have coalesced into sub-coalesced droplets. One technical challenge of hybrid waveform tuning is that increasing the sinusoidal amplitude can cause the main coalescence and sub-coalescence to interfere. As the main coalescence length decreases, the sub-coalescence process is affected by the strong velocity generated by the low frequency (sinusoidal) part of the signal. In other words, as the voltage of the low frequency part of the signal increases, a satellite of droplets will be observed, as shown in fig. 21. The sub-coalescence length may be determined by measuring the minimum sinusoidal amplitude value of the satellite generating droplets. Therefore, the sub-coalescence length can be used as an objective function in the optimization process of the sub-coalescence parameters (square uptime, square amplitude). The 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 assess the operational state of the drop generator.

The invention has been described above with the aid of functional building blocks illustrating the implementation of specific functions and relationships thereof. Boundaries of these functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternate boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed.

The foregoing description of the specific embodiments will so fully reveal the general nature of the invention that others can, by applying knowledge within the skill of the art, readily modify and/or adapt for various applications such specific embodiments, without undue experimentation, without departing from the general concept of the present invention. Therefore, such adaptations and modifications are intended to be within the meaning and range of equivalents of the disclosed embodiments, based on the teaching and guidance presented herein. It is to be understood that the phraseology or terminology herein is for the purpose of description and not of limitation, such that the terminology or phraseology of the present specification is to be interpreted by the skilled artisan in light of the teachings and guidance. The breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims appended hereto and their equivalents.

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

1. An apparatus, comprising:

a target material dispenser having a nozzle and adapted to provide a stream of target material that breaks into first droplets after exiting the nozzle;

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

a waveform generator electrically coupled to the electrically actuatable element and adapted to generate an applied 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, the amplitude and phase difference selected to minimize the coalescence distance while avoiding abrupt changes in the coalescence distance.

2. The device according to clause 1, wherein the electrically actuable element is a piezoelectric element.

3. An apparatus, comprising:

a target material dispenser having a nozzle and adapted to provide a stream of target material that breaks into first droplets after exiting the nozzle;

an electrically actuatable element mechanically coupled to the target material dispenser and arranged to cause a velocity disturbance in the flow based on the applied waveform, the velocity disturbance causing the first drop to eventually coalesce into a second drop larger than the first drop in one or more stages within a coalescence distance from the nozzle, the second drops being spaced apart such that the second drop passes a fixed point at a crossover spacing;

a cross-interval detector arranged to determine a cross-interval of the second droplet and to generate a cross-interval signal; and

a waveform generator electrically coupled to the electrically actuatable element and adapted to generate an applied waveform and to generate the applied waveform based at least in part on the crossing interval signal.

4. A method, comprising:

providing a stream of target material using a target material dispenser, the target material dispenser comprising an electrically actuatable element arranged to cause a velocity disturbance in the stream based on a droplet control signal;

determining whether the stream includes satellite droplets and generating satellite detection signals indicative of whether the stream includes satellite droplets;

generating a waveform based at least in part on the satellite detection signal; and

the waveform is provided to a target material dispenser.

5. The method according to clause 4, further comprising: determining a cross-interval of the flow, and generating a cross-interval signal, and wherein the step of generating a waveform comprises generating the waveform based at least in part on the cross-interval signal.

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

dispensing a stream of EUV target material from a target material dispenser;

applying a waveform to an electrically actuable element, the electrically actuable element being arranged to cause a velocity disturbance in the flow in response to a control signal;

determining a minimum value of the amplitude of the sine wave component of the waveform for which the stream does not include satellites;

determining a dependence of the coalescence length on the phase difference between the sine wave component and the square wave component of the control signal, and determining a discontinuous jump boundary phase difference at which the dependence occurs;

determining a slope of a dependence of the jump boundary phase on the minimum;

determining a drag coefficient based on the slope; and

based on the minimum value and the drag coefficient, a transfer function at the frequency of the sine wave component is determined.

7. A method of optimizing the coalescing behaviour of a flow of EUV target material from a target material distributor, the target material distributor comprising an electrically actuable element arranged to cause a velocity perturbation in the flow in response to an applied control signal, the method comprising:

determining a minimum value of the amplitude of the sine wave component of the control signal for which the stream does not include satellites;

determining a dependence of the coalescence length on the phase difference between the sine wave component and the square wave component of the control signal, and determining a discontinuous jump boundary phase difference at which the dependence occurs;

determining a slope of a 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

the optimum phase difference is determined as the difference between the jump boundary phase difference and the designed phase delay.

8. A method of controlling the coalescing behaviour of a stream of EUV target material from a target material distributor, the target material distributor comprising an electrically actuable element arranged to cause a velocity perturbation in the stream in response to an applied control signal having a sine wave component and a square wave component, the method comprising:

determining a width Ln of a maximum range of adjacent values of phase differences between the sinusoidal wave component and the square wave component of the stream excluding the satellite;

determining a width L of a stream comprising a maximum of adjacent values of a phase difference between a sine wave component and a square wave component of a satellite₂；

Determining a value Sm as a statistical measure of the variation of the stream crossing interval over a range having a width Ln;

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

determining a cost function

Wherein W1, W2, W3, W4 are some positive real numbers; and is

The parameters of the sinusoidal and square wave components are adjusted to minimize the cost function.

9. A method, comprising:

providing a stream of target material using a target material dispenser having a nozzle, the stream of target material breaking into first droplets after exiting the nozzle;

using an electrically actuatable element mechanically coupled to the target material dispenser to induce a velocity disturbance in the flow based on the applied waveform, the velocity disturbance causing the first drop to eventually coalesce into a second drop larger than the first drop in one or more stages within a coalescence distance from the nozzle; and

generating an applied waveform using a waveform generator electrically coupled to the electrically actuatable element, the 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, the amplitude and phase difference selected to minimize the coalescence distance while avoiding abrupt changes in the coalescence distance.

10. A method of operating a target material dispenser in an EUV source, the method comprising:

generating a 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;

applying a waveform to an electrically actuatable element mechanically coupled to a target material dispenser having a nozzle to provide a stream of target material that breaks up into first droplets after exiting the nozzle and then coalesces into second droplets larger than the first droplets in one or more stages within a coalescence distance from the nozzle;

scanning, for a plurality of amplitudes, a plurality of phase differences to identify a jump boundary combination of amplitude and phase differences at which a sudden change in coalescence distance occurs, generating a jump boundary curve; and

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

11. A method, comprising:

releasing a stream of initial droplets of a first size from a droplet generator under the control of an electrical signal, the stream of initial droplets undergoing at least one coalescence to become a stream of final droplets of a second size larger than the first size after having traveled a coalescence length, the electrical signal having a first periodic component and a second periodic component that is out of phase with the first periodic component;

operating the drop generator if the phase difference is at a value where the stream of final drops does not include any satellite drops smaller than the second size; and

the value of the phase difference is varied to the value at which the satellite droplets appear in the stream of final droplets to detect a jump boundary of the functional dependence of the coalescence length on the value of the phase difference.

12. The method according to clause 11, wherein

In the case where the phase difference is at a value where the stream of final droplets does not include any satellite droplets smaller than the second size, operating the droplet generator includes: operating the drop generator if the phase difference is at a value that is expected to be lower than the value at which satellite drops appear in the stream of final drops, and

varying the value of the phase difference phase until a satellite droplet appears in the stream of final droplets to detect a jump boundary of the functional dependence of the coalescence length on the value of the phase difference comprises: the value of the phase difference phase is increased until a satellite droplet appears in the stream of final droplets to detect a jump boundary of the functional dependence of the coalescence length on the value of the phase difference.

13. The method of 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 comprising one time.

14. The method of clause 11, wherein one of the first and second periodic components is sinusoidal and the other of the first and second periodic components is a square wave.

15. A method of controlling the coalescing behaviour of a stream of EUV target material from a target material distributor, the target material distributor comprising an electrically actuable element arranged to cause a velocity perturbing component in the stream in response to an applied control signal having a sine wave component and a square wave component, the method comprising:

determining a first number of ranges of adjacent values of phase difference between the sinusoidal and square wave components of the stream excluding the satellite;

determining a second number of ranges of adjacent values of the phase difference between the sinusoidal and square wave components of the satellite for which the stream does include; and

if the first number and the second number are equal to one, the coalescence behavior of the flow of EUV target material is determined to be acceptable.

16. A method, comprising:

providing a stream of droplets of fully coalesced target material using a target material dispenser, the target material dispenser comprising an electrically actuatable element arranged to cause a velocity disturbance in the stream based on a droplet control signal;

determining whether the flow further includes sub-coalesced satellites and generating sub-coalesced drop detection signals indicating whether the flow includes sub-coalesced satellites;

generating a waveform based at least in part on the sub-coalesced drop detection signal; and

the waveform is provided to an electrically actuatable element in the target material dispenser.

17. The method according to clause 1, wherein determining whether the flow includes sub-coalesced satellites includes: it is determined whether the size of any satellite droplets corresponds to the known size of a sub-coalesced droplet.

18. The method according to clause 1, wherein determining whether the flow includes sub-coalesced satellites includes: the magnitude of the displacement of the flow direction of any satellite from a fully coalesced drop is determined.

19. A method, comprising:

providing a stream of coalesced droplets of the target material using a target material dispenser, the target material dispenser comprising an electrically actuatable element arranged to cause a velocity disturbance in the stream based on a droplet control signal, the control signal having a sinusoidal component;

determining a minimum value of a magnitude of an amplitude of a sinusoidal component of a satellite droplet present in the stream;

determining a sub-coalescence length based on the minimum value; and

controlling operation of the target material distributor based on the determined sub-coalescence length.

20. A method, comprising:

providing a stream of coalesced droplets of target material using a target material dispenser, the target material dispenser comprising a nozzle and an electrically actuable element arranged to cause a velocity disturbance in the stream exiting the nozzle to produce a stream that breaks into droplets based on a droplet control signal, the control signal having a sinusoidal component and a square wave component out of phase with the sinusoidal component;

determining a dependence of a magnitude of flow direction displacement of any satellite droplet from the coalesced droplets on a magnitude of the phase difference;

determining a transfer function between the control signal to the velocity disturbance at the outlet of the nozzle based on the dependency; and

controlling operation of the target material dispenser based on the determined transfer function.