Method and apparatus for controlling electron density distribution

Abstract

1. A method for controlling a density distribution of electrons provided by an electron source for use in hard x-ray, soft x-ray and / or extreme ultraviolet generation, the method comprising: generating a plurality of electrons from a pattern of ultra-cold excited atoms inside a cavity using an ionizing laser, the electrons having a density distribution determined by at least one of the pattern of excited atoms and the ionizing laser; and accelerating the electrons exiting the cavity using a non-static acceleration profile, the acceleration profile controlling the density distribution of the electrons as they exit the cavity.

Description

[Technical Field]

[0001] Cross-reference of related applications

[0001] This application claims priority to European Patent Application No. 20216083.4, filed on 21 December 2020, which is incorporated herein by reference in whole.

[0002]

[0002] The present invention relates to a method, assembly and apparatus for controlling electron density distribution for use in radiation generation. Specifically, the present invention relates to the control of electron density distribution as electrons exit a cavity for use in hard X-ray, soft X-ray and / or extreme ultraviolet generation. [Background technology]

[0003]

[0003] A lithography apparatus is a machine built to apply a desired pattern to a substrate. Lithography apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A lithography apparatus can project a pattern (often called a "design layout" or "design") located on a patterning device (e.g., a mask) onto a radiative-sensitive material (resist) layer provided on a substrate (e.g., a wafer).

[0004]

[0004] A lithography apparatus may use electromagnetic radiation to project a pattern onto a substrate. The wavelength of this radiation determines the minimum size of the feature that can be formed on the substrate. Typical wavelengths currently in use are 365 nm (i-line), 248 nm, 193 nm, and 13.5 nm. A lithography apparatus using extreme ultraviolet (EUV) radiation with wavelengths in the range of 4 to 100 nm, for example 6.7 nm or 13.5 nm, can form smaller features on the substrate than a lithography apparatus using radiation with a wavelength of 193 nm, for example.

[0005]

[0005] For processing features having dimensions smaller than the classical resolution limit of a lithographic apparatus, low k1 lithography can be used. In such a process, the resolution equation can be expressed as CD = k1 × λ / NA, where λ is the wavelength of the radiation used, NA is the numerical aperture of the projection optical system of the lithographic apparatus, CD is the "critical dimension" (generally the smallest feature size to be printed, but in this case the half pitch), and k1 is an empirical resolution factor. Generally, the smaller k1 is, the more difficult it becomes for the circuit designer to replicate on the substrate a pattern that resembles the shape and dimensions planned to achieve a particular electrical functionality and performance. To overcome such difficulties, advanced fine-tuning steps can be applied to the lithographic projection apparatus and / or the design layout. Such steps include, for example, optimization of NA, customization of the illumination mode, use of a phase-shifting patterning device, various optimizations of the design layout, such as optical proximity effect correction (OPC, sometimes also referred to as "optical and process correction") in the design layout or other methods generally defined as "resolution enhancement techniques" (RET), but are not limited thereto. Instead, a strict control loop for managing the stability of the lithographic apparatus can be used to improve pattern replication at low k1.

[0006]

[0006] Metrology tools can be used to perform measurements and inspections of patterns and devices generated using a lithography apparatus. Due to the pattern dimensions in the lithography process, there is an increasing need for high-throughput optical metrology tools that operate using short-wavelength probe radiation. High throughput can limit the amount of time and cost of inspection during the lithography process. Short-wavelength probe radiation is necessary to achieve the required resolution and penetration depth, both of which are wavelength-dependent. Conventional tools (such as optical metrology tools that use visible wavelengths) may be insufficient to resolve patterned lithography structures. Short-wavelength tools can include, for example, EUV as well as X-ray radiation (including soft X-ray and hard X-ray radiation), thereby achieving higher resolution.

[0007]

[0007] Radiation sources with shorter wavelengths can address the resolution challenges. However, at shorter wavelengths, there is a lack of high-brightness radiation sources necessary for metrology in high-volume production applications. This application addresses this problem by describing methods, assemblies, and devices for achieving a radiation source with increased brightness.

Summary of the Invention

[0008]

[0008] An object of the present invention is to provide a method for controlling the density distribution of electrons provided by an electron source for use in hard X-ray, soft X-ray, and / or extreme ultraviolet generation. The method includes generating a plurality of electrons from a pattern of cryogenically excited atoms inside a cavity using an ionization laser, wherein the electrons have a density distribution determined by at least one of the pattern of excited atoms and the ionization laser. The electrons exiting the cavity are accelerated using a non-static acceleration profile. The acceleration profile controls the density distribution of the electrons as they exit the cavity.

[0009]

[0009] Optionally, the acceleration profile can control the velocity of electrons within the cavity so that the velocity of electrons is substantially equal as they leave the cavity.

[0010]

[0010] Optionally, the electron density distribution may include multiple electron bunches.

[0011]

[0011] Optionally, the acceleration profile can reduce chirp in the density distribution of electrons leaving the cavity.

[0012]

[0012] Optionally, acceleration may include a non-static electromagnetic field.

[0013]

[0013] Optionally, the non-static electromagnetic field may include components that change over time.

[0014]

[0014] Optionally, the non-static electromagnetic field may include a component that varies depending on the position within the cavity.

[0015]

[0015] Optionally, the electron density distribution can be matched with the pattern of ultracold excited atoms.

[0016]

[0016] Optionally, the electron density distribution can be determined by a structured ionization laser.

[0017]

[0017] Optionally, the cavity may be a resonant microwave structure.

[0018]

[0018] Optionally, hard X-ray, soft X-ray and / or extreme ultraviolet radiation generation can be achieved using inverse Compton scattering.

[0019]

[0019] According to another aspect of the present disclosure, there is provided an apparatus for controlling the density distribution of electrons provided by an electron source for use in hard X-ray, soft X-ray and / or extreme ultraviolet radiation generation, the apparatus configured to perform the method described above.

[0020]

[0020] According to another aspect of the present disclosure, a radiation source including the above-described apparatus is provided.

[0021]

[0021] According to another aspect of the present disclosure, a metrology apparatus including the apparatus described above is provided.

[0022]

[0022] According to another aspect of the present disclosure, a lithography cell including the apparatus described above is provided.

[0023]

[0023] According to another aspect of the present disclosure, a method is provided for compressing a density distribution including electron bunches for the generation of coherent hard X-rays, soft X-rays and / or extreme ultraviolet radiation. The method comprises receiving a plurality of electron bunches having a density distribution and compressing the plurality of electron bunches such that the distances between the bunches along the propagation direction of the electron bunches correspond to the wavelengths of the hard X-rays, soft X-rays and / or extreme ultraviolet radiation to be generated.

[0024]

[0024] Optionally, the electron bunch can be compressed using echo-enhanced harmonic generation.

[0025]

[0025] Optionally, the electronic bunch can be compressed using an electro-optical device.

[0026]

[0026] Optionally, coherent hard X-ray, soft X-ray and / or extreme ultraviolet radiation generation can be achieved using inverse Compton scattering.

[0027]

[0027] According to another aspect of the present disclosure, an assembly is provided for compressing a density distribution including an electron bunch for the generation of coherent hard X-rays, soft X-rays and / or extreme ultraviolet radiation. The assembly is configured to perform the method for compressing the density distribution described above.

[0028]

[0028] According to another aspect of the present disclosure, an echo-enhanced harmonic generation method for coherent hard X-ray, soft X-ray and / or extreme ultraviolet generation is provided. The method includes receiving a plurality of electron bunches, each bunch including momentum spreading. Electrons are provided through a dispersion section and a skew is introduced along the propagation direction in phase space. Periodic momentum modulation along the propagation direction is applied to the electron bunches using an optical modulator. Electrons are propagated through a second dispersion section and a second skew is introduced along the propagation direction in phase space. The second skew modifies the modulated momentum of the bunches in order to provide the plurality of bunches with reduced separation along the propagation direction compared to the plurality of received bunches.

[0029]

[0029] Another aspect of the present disclosure provides a method for generating attosecond hard X-rays, soft X-rays and / or extreme ultraviolet pulses. The method includes obtaining a plurality of electron bunches, introducing chirps in the separation between the plurality of bunches, and irradiating the chirp bunches with back-excited chirp radiation pulses for generating hard X-rays, soft X-rays and / or extreme ultraviolet radiation. The chirps in the separation between bunches are matched with the chirps of the radiation pulses according to resonance conditions, thereby generating attosecond hard X-rays, soft X-rays and / or extreme ultraviolet pulses.

[0030]

[0030] Optionally, the chirp in the separation between bunches and the chirp in the radiation pulse may be positive.

[0031]

[0031] Optionally, the kinetic energy chirp can be configured to control the bandwidth of the generated hard X-rays, soft X-rays, and / or extreme ultraviolet radiation.

[0032]

[0032] Optionally, introducing chirp in the separation between multiple bunches may include controlling the rate of change of at least one forward-backward change of the kinetic energy of the electron bunches and the pitch of the electron bunches.

[0033]

[0033] Hereinafter, embodiments of the present invention will be described merely as examples with reference to the attached schematic drawings. [Brief explanation of the drawing]

[0034] [Figure 1]

[0033] A general overview of the lithography apparatus is shown. [Figure 2]

[0033] A general overview of the lithography cell is shown. [Figure 3]

[0033] A schematic diagram of holistic lithography is shown, illustrating the coordination between three key technologies for optimizing semiconductor manufacturing. [Figure 4]

[0033] A schematic diagram of the scantometry apparatus is shown. [Figure 5]

[0033] A schematic diagram of a transmissive scatometry apparatus is shown. [Figure 6]

[0033] A schematic representation of exemplary inverse Compton scattering hard X-ray, soft X-ray and / or extreme ultraviolet radiation sources is shown. [Figure 7a]

[0033] A schematic representation of the steps of a method for generating ultra-low temperature electron pulses is shown. [Figure 7b]

[0033] A schematic representation of the steps of a method for generating ultra-low temperature electron pulses is shown. [Figure 7c]

[0033] A schematic representation of the steps of a method for generating ultra-low temperature electron pulses is shown. [Figure 7d]

[0033] A schematic representation of the steps of a method for generating ultra-low temperature electron pulses is shown. [Figure 8]

[0033] An exemplary setup of two electrodes for accelerating the electron pulses exiting the cavity is shown. [Figure 9]

[0033] A flowchart of the steps of a method for controlling the electron density distribution or the generation of hard X-rays, soft X-rays and / or extreme ultraviolet rays is shown. [Figure 10a]

[0033] An illustrative simulation graph of electron pulses exiting a cavity accelerated by a non-static acceleration profile is shown. [Figure 10b]

[0033] An illustrative simulation graph of electron pulses exiting a cavity accelerated by a non-static acceleration profile is shown. [Figure 10c]

[0033] An illustrative simulation graph of electron pulses exiting a cavity accelerated by a non-static acceleration profile is shown. [Figure 11a]

[0033] A schematic representation of random electrons is shown. [Figure 11b]

[0033] A schematic representation of the electron bunch is shown. [Figure 12]

[0033] A flowchart of the steps of a method for compressing a density distribution including electron bunches for the generation of coherent hard X-rays, soft X-rays and / or extreme ultraviolet rays is shown. [Figure 13]

[0033] An exemplary phase space plot representing the steps in beamline conversion for electron pulse compression is shown. [Figure 14]

[0033] A schematic representation of horizontal and vertical skew in the front-to-back phase space is shown. [Figure 15a]

[0033] A schematic representation of the steps of electron pulse compression using echo-enhanced harmonic generation is shown. [Figure 15b]

[0033] A schematic representation of the steps of electron pulse compression using echo-enhanced harmonic generation is shown. [Figure 15c]

[0033] A schematic representation of the steps of electron pulse compression using echo-enhanced harmonic generation is shown. [Figure 15d]

[0033] A schematic representation of the steps of electron pulse compression using echo-enhanced harmonic generation is shown. [Figure 16]

[0033] A graph is shown illustrating an exemplary electron density along the propagation direction of a compressed electron pulse containing multiple bunches. [Figure 17]

[0033] An exemplary particle tracking simulation for echo-enhanced harmonic generation compression using an optical modulator is shown. [Figure 18]

[0033] Exemplary representations of kinetic energy, bunch spacing, and their forward and backward derivatives in phase space are shown. [Modes for carrying out the invention]

[0035]

[0034] In this document, the terms “radiation” and “beam” are used to encompass all types of electromagnetic and particle radiation, including ultraviolet radiation (e.g., having wavelengths of 365, 248, 193, 157, or 126 nm), EUV (e.g., extreme ultraviolet radiation having wavelengths in the range of approximately 5 to 100 nm), X-ray radiation, electron beam radiation, and other particle radiation.

[0036]

[0035] As used herein, the terms “reticle,” “mask,” or “patterning device” may be broadly interpreted to mean a general patterning device that can be used to provide an incident radiation beam with a patterned cross section corresponding to a pattern to be created on a target portion of a substrate. In this context, the term “light bulb” may also be used. In addition to classic masks (transmissive or reflective masks, binary masks, phase-shift masks, hybrid masks, etc.), other examples of such patterning devices include programmable mirror arrays and programmable LCD arrays.

[0037]

[0036] Figure 1 schematically shows a lithography apparatus LA. The lithography apparatus LA includes an illumination system IL (also called an illuminator) configured to adjust a radiation beam B (e.g., UV radiation, DUV radiation, EUV radiation, or X-ray radiation), a mask support (e.g., a mask table) T built to support a patterning device (e.g., a mask) MA and connected to a first positioner PM configured to precisely position the patterning device MA according to specific parameters, a substrate support (e.g., a wafer table) WT built to hold a substrate (e.g., a resist-coated wafer) W and connected to a second positioner PW configured to precisely position the substrate support according to specific parameters, and a projection system (e.g., a refractive projection lens system) PS configured to project the pattern applied to the radiation beam B by the patterning device MA onto a target portion C of the substrate W (e.g., including one or more dies).

[0038]

[0037] During operation, the illumination system IL receives a radiant beam from the radiation source SO (for example, via the beam delivery system BD). The illumination system IL may include various types of optical components for induction, shaping and / or control of the radiation, including, for example, refractive, reflective, diffracting, magnetic, electromagnetic, electrostatic and / or other types of optical components or any combination thereof. The illuminator IL may be used to adjust the radiant beam B so that the radiant beam B has a desired spatial intensity distribution and angular intensity distribution in its cross-section on the surface of the patterning device MA.

[0039]

[0038] The term “projection system” PS as used herein should be interpreted broadly to encompass a variety of projection systems. Such systems may include refractive, reflective, diffractive, reflector-refracting, anamorphic, magnetic, electromagnetic, and / or electrostatic-optical systems or any combination thereof, depending on the requirements of the exposure radiation used and / or other factors (e.g., the use of immersion liquid or vacuum). Where the term “projection lens” is used herein, they may all be considered synonymous with the more general term “projection system” PS.

[0040]

[0039] The lithography apparatus LA may be of a type in which at least a portion of the substrate is covered with a liquid (e.g., water) with a relatively high refractive index so as to fill the space between the projection system PS and the substrate W, which is also called immersion lithography. Details of the immersion technique are shown in U.S. Patent No. 6,952,253, which is incorporated herein by reference in its entirety.

[0041]

[0040] The lithography apparatus LA may be of a type having two or more substrate support units WT (also called a "dual-stage"). In such a "multi-stage" machine, the substrate support units WT may be used in parallel, and / or, while a substrate W on one of the substrate support units WT is being used to expose a pattern onto that substrate W, procedures for preparing another substrate W on the other substrate support unit WT for subsequent exposure of that other substrate W may be performed.

[0042]

[0041] In addition to the substrate support WT, the lithography apparatus LA may include a measurement stage. The measurement stage is configured to hold sensors and / or a cleaning device. The sensors may be configured to measure the characteristics of the projection system PS or the characteristics of the radiation beam B. The measurement stage may hold multiple sensors. The cleaning device may be configured to clean a part of the lithography apparatus, for example, a part of the projection system PS or a part of the system that supplies the immersion fluid. The measurement stage may move under the projection system PS when the substrate support WT is away from the projection system PS.

[0043]

[0042] During operation, the radiant beam B is incident on the patterning device (e.g., a mask MA held on a mask support T) and patterned by the pattern (design layout) on the patterning device MA. After the radiant beam B crosses the mask MA, it passes through the projection system PS, which focuses the beam onto a target portion C on the substrate W. With the assistance of a second positioner PW and a position measuring system IF, the substrate support WT can move precisely, for example, so that various target portions C are positioned to be focused and aligned along the path of the radiant beam B. Similarly, a first positioner PM and possibly another position sensor (not shown in Figure 1) may be used to precisely position the patterning device MA relative to the path of the radiant beam B. The patterning device MA and the substrate W may be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. The substrate alignment marks P1 and P2 occupy dedicated target areas as shown in the figure, but may also be placed in the space between target areas. When the substrate alignment marks P1 and P2 are placed between target areas C, they are called scribe line alignment marks.

[0044]

[0043] As shown in Figure 2, the lithography apparatus LA may be part of a lithography cell LC (sometimes called a lithocell or (litho)cluster), which often includes equipment for performing pre-exposure and post-exposure processes on the substrate W. Conventionally, such equipment includes a spin coater SC for depositing a resist layer, a developer DE for developing the exposed resist, a cooling plate CH and a bake plate BK (these, for example, regulate the temperature of the substrate W, which is done, for example, to regulate the solvent in the resist layer). A substrate handler (i.e., robot) RO picks up the substrates W from input / output ports I / O1 and I / O2, moves the substrates W between various process equipment, and delivers the substrates W to the loading bay LB of the lithography apparatus LA. The devices within a lithography cell are often collectively referred to as tracks and may be under the management of a track control unit (TCU). The TCU itself may be controlled by a monitoring and control system (SCS), which in turn may control the lithography apparatus (LA) (for example, via a lithography control unit (LACU)).

[0045]

[0044] In the lithography process, it is desirable to frequently measure the created structure (for example, for process control and verification). Tools used to perform such measurements may be called metrologic tools (MT). Various types of metrologic tools (MT) are known to perform such measurements, such as scanning electron microscopes or various forms of scattrometer metrologic tools (MT). A scattrometer is a multi-purpose instrument that enables the measurement of parameters in the lithography process, and the measurements are performed by having a sensor on or near the pupil or conjugate plane of the objective lens of the scattrometer (usually called a pupil-based measurement), or by having a sensor on or near the image plane or conjugate plane of the image plane (in this case, usually called an image-based or field-based measurement). Such scatorometers and related measurement techniques are described in detail in U.S. Patent Applications Publications 20100328655, 2011102753A1, 20120044470A, 20110249244, 20110026032 or European Patent Application Publication 1,628,164A, which are incorporated herein by reference as a whole. The aforementioned scatorometers can measure gratings using light from hard X-rays (HXR), soft X-rays (SXR), extreme ultraviolet (EUV), visible light to near-infrared (IR), and IR wavelength ranges. When the radiation is hard X-rays or soft X-rays, the aforementioned scatorometers may optionally be small-angle X-ray scattering metronomes.

[0046]

[0045] It is desirable to inspect the substrate to measure the characteristics of the patterned structure, such as overlay errors between consecutive layers, line thickness, critical dimension (CD), and structural shape, so that the substrate W is exposed accurately and consistently by the lithography apparatus LA. For this purpose, inspection tools and / or metronome tools (not shown) may be included in the lithocell LC. If an error is detected, adjustments can be made, for example, to the subsequent exposure of the substrate or other processing steps to be performed on the substrate W, which can be done in particular if the inspection is performed before other substrates W of the same batch or lot are subsequently exposed or processed.

[0047]

[0046] Inspection equipment, sometimes called metrology equipment, is used to determine the properties of a substrate W, in particular how the properties of different substrates W change, or how the properties associated with different layers of the same substrate W change layer by layer. Alternatively, inspection equipment can be constructed to identify defects on the substrate W, and can be, for example, part of a lithocell LC, integrated into a lithography apparatus LA, or even a standalone device. Inspection equipment can measure properties related to latent images (images in the resist layer after exposure), semi-latent images (images in the resist layer after a post-exposure bake step PEB), developed resist images (where the exposed or unexposed parts of the resist have been removed), or even etched images (images after a pattern transfer step such as etching).

[0048]

[0047] In the first embodiment, the scatorometer MT is an angle-resolved scatorometer. In such a scatorometer, a reconstruction method that reconstructs or calculates the properties of the grating may be applied to the measured signal. Such reconstruction may be the result of, for example, simulating the interaction between scattered radiation and a mathematical model of the target structure and comparing the simulation results with the measured results. The parameters of the mathematical model are adjusted by the simulation of the interaction until a diffraction pattern similar to the diffraction pattern observed from the actual target is produced.

[0049]

[0048] In a second embodiment, the scatorometer MT is a spectrometer MT. In such a spectrometer MT, radiation emitted from a radiation source is directed toward a target, and radiation reflected, transmitted or scattered from the target is directed toward a spectrometer detector, which measures the spectrum of the spectrometer-reflected radiation (i.e., measures the intensity as a function of wavelength). From this data, it is possible to reconstruct the structure or profile of the target that is causing the detected spectrum, which can be done, for example, by exact coupled wave theory and nonlinear regression, or by comparison with a library of simulated spectra.

[0050]

[0049] In a third embodiment, the scatometer MT is an ellipsoscalometer. The ellipsoscalometer makes it possible to determine the parameters of the lithography process by measuring the scattered or transmitted radiation for each polarization state. Such a metronome device emits polarized light (e.g., linearly polarized light, circularly polarized light, or ellipsoscalometer) using a suitable polarizing filter, for example, in the illumination section of the metronome device. A suitable source for the metronome device can also be polarized radiation. Various embodiments of existing ellipsoscalculometers are described in U.S. Patent Applications Publications 11 / 451,599, 11 / 708,678, 12 / 256,780, 12 / 486,449, 12 / 920,968, 12 / 922,587, 13 / 000,229, 13 / 033,135, 13 / 533,110, and 13 / 891,410, which are incorporated herein by reference as a whole.

[0051]

[0050] In one embodiment of the scatrometer MT, the scatrometer MT is adapted to measure the overlay of two misaligned grids or periodic structures by measuring the asymmetry of the reflectance spectrum and / or the detection configuration, where the asymmetry relates to the degree of overlay. The two (possibly overlapping) grid structures can be applied in two different layers (not necessarily continuous layers) and can be formed at substantially the same location on the wafer. The scatrometer may have a symmetric detection configuration, such as described, for example, in the jointly owned European Patent Application Publication No. 1628164A, so that any asymmetry can be clearly distinguished. This provides a straightforward method for measuring grid misalignment. Further examples for measuring overlay errors between two layers containing periodic structures, when the target is measured through the asymmetry of the periodic structure, can be found in the PCT Patent Application Publication International Publication No. 2011 / 012624 or the US Patent Application No. 20160161863, which are incorporated herein by reference in whole.

[0052]

[0051] Other parameters of the subject may be focus and dose. Focus and dose can be determined simultaneously by scantometry (or by scanning electron microscopy) as described in U.S. Patent Application No. 2011-0249244, which is incorporated herein by reference as a whole. A single structure can be used which has a unique combination of critical dimension and sidewall angle measurements for each point of the focus energy matrix (FEM, also called the focus exposure matrix). If these unique combinations of critical dimension and sidewall angle are available, the focus and dose values ​​can be uniquely determined from these measurements.

[0053]

[0052] A metrologic target can be an assembly of composite gratings, mostly formed by the lithography process in the resist, but also formed, for example, after the etching process. The pitch and linewidth of the grating structure may depend heavily on the measurement optics (specifically, the NA of the optics) so that the diffraction order obtained from the metrologic target can be captured. As previously shown, the diffraction signal can be used to determine the shift between two layers (also called "overlay") or to reconstruct at least a portion of the original grating as produced by the lithography process. This reconstruction can be used to provide guidance on the quality of the lithography process and can be used to control at least a portion of the lithography process. The target may have smaller subsegmentations configured to mimic the dimensions of the functional parts of the design layout in the target. These subsegments cause the target to behave more like the functional parts of the design layout so that the total process parameter measurements closely resemble those of the functional parts of the design layout. The target can be measured in underfill mode or overfill mode. In underfill mode, the measurement beam generates a spot smaller than the entire target. In overfill mode, the measurement beam generates a spot larger than the entire target. In such overfill mode, it may be possible to measure different targets simultaneously, and therefore, to determine different processing parameters at the same time.

[0054]

[0053] The overall quality of a measurement of a lithography parameter using a particular target is determined, at least in part, by the measurement recipe used to measure that lithography parameter. The term “substrate measurement recipe” may include one or more parameters of the measurement itself, one or more parameters of the one or more patterns measured, or both. For example, if the measurement used in the substrate measurement recipe is a diffraction-based optical measurement, one or more parameters of this measurement may include the wavelength of the radiation, the polarization of the radiation, the angle of incidence of the radiation on the substrate, and the orientation of the radiation on the pattern on the substrate. One criterion for selecting a measurement recipe may be, for example, the sensitivity of one of the measurement parameters to process variations. Further examples are given in U.S. Patent Application No. 2016-0161863 and the published U.S. Patent Application No. 2016 / 0370717A1, which are incorporated herein by reference in whole.

[0055]

[0054] The patterning process in the lithography apparatus LA can be one of the most critical steps in a process that requires high precision in dimensionalizing and positioning structures on the substrate W. To ensure this high precision, three systems can be combined in a so-called "holistic" control environment, as schematically shown in Figure 3. One of these systems is the lithography apparatus LA, which is (virtually) connected to the metrologic tool MT (second system) and the computer system CL (third system). The key to such a "holistic" environment is to optimize the coordination between these three systems to reinforce the entire process window and provide a strict control loop, thereby ensuring that the patterning performed by the lithography apparatus LA stays within the process window. The process window defines a range of process parameters (e.g., dose, focus, overlay) within which a particular manufacturing process produces a defined result (e.g., a functional semiconductor device), and within this range the process parameters of the lithography or patterning process can vary.

[0056]

[0055] The computer system CL can use (part of) the design layout to be patterned to predict which resolution enhancement techniques should be used, and can perform simulations and calculations of computational lithography to determine the mask layout and lithography apparatus settings that achieve maximization of the entire process window of the patterning process (indicated in Figure 3 by the bidirectional arrows on the first scale SC1). The resolution enhancement techniques can be configured to suit the patterning capabilities of the lithography apparatus LA. The computer system CL can also be used to detect where the lithography apparatus LA is currently operating within the process window (for example, using input from the metrology tool MET) to predict whether defects may exist, for example, due to suboptimal processing (indicated in Figure 3 by the arrow pointing to "0" on the second scale SC2).

[0057]

[0056] The Metrology Tool MT can provide input to the computer system CL to enable accurate simulation and prediction, for example, it can provide feedback to the lithography apparatus LA to identify possible drift in the calibration status of the lithography apparatus LA (shown in Figure 3 by multiple arrows on the third scale SC3).

[0058]

[0057] An example of a metronome device such as a scatrometer is shown in Figure 4. It may include a broadband (e.g., white light) radiation projector 2 that projects radiation 5 onto a substrate W. The reflected or scattered radiation 10 is sent to a spectrometer detector 4, which measures the spectrum 6 of the specularly reflected radiation (i.e., the measurement of the intensity I as a function of wavelength λ). From this data, the structure or profile 8 that gives rise to the detected spectrum can be reconstructed by a processing unit (PU), for example by exact coupled wave analysis and nonlinear regression, or by comparison with a library of simulated spectra, as shown at the bottom of Figure 4. Generally, for reconstruction, the general form of the structure is known, and several parameters are assumed from knowledge of the process by which the structure was made, thereby leaving only a few parameters of the structure to be determined from the scatrometry data. Such a scatrometer may be configured as a normal incidence scatrometer or an oblique incidence scatrometer.

[0059]

[0058] A transmission version of an example of a metronome device (such as a scatrometer shown in Figure 4) is shown in Figure 5. The transmitted radiation 11 is passed to a spectrometer detector 4, which measures the spectrum 6 as discussed with respect to Figure 4. Such a scatrometer can be configured as a normal-incident scatrometer or an oblique-incident scatrometer. The transmission version uses hard X-ray radiation having wavelengths of optionally <1 nm, optionally <0.1 nm, and optionally <0.01 nm.

[0060]

[0059] As an alternative to optical metronome methods, the use of hard X-rays, soft X-rays, or EUV radiation has also been considered, such as radiation having at least one wavelength range of <0.01 nm, <0.1 nm, <1 nm, 0.01 nm to 100 nm, 0.01 nm to 50 nm, 1 nm to 50 nm, 1 nm to 20 nm, 5 nm to 20 nm, and 10 nm to 20 nm. An example of a metronome tool that operates in one of the wavelength ranges presented above is transmitted small-angle X-ray scattering (T-SAXS, such as U.S. Patent Application Publication No. 2007224518A, the content of which is incorporated herein by reference in whole). Profile (CD) measurements using T-SAXS are discussed in Lemaillet et al, “Intercomparison between optical and X-ray scatterometry measurements of FinFET structures”, Proc. of SPIE, 2013, 8681. The use of laser-generated plasma (LPP) X-ray sources is described in U.S. Patent Application Publication 2019 / 003988A1 and U.S. Patent Application Publication 2019 / 215940A1, which are incorporated herein by reference in their entirety. Reflectivity techniques using graze-incident X-rays (GI-XRS) and extreme ultraviolet (EUV) radiation can be used to measure the properties of stacks of films and layers on a substrate. Within the general field of reflectivity methods, angle measurement and / or spectroscopic techniques can be applied. Angle measurement methods can measure variations in the reflected beam at different incident angles. Spectroscopic reflectivity methods, on the other hand, measure the spectrum of wavelengths reflected at a given angle (using broadband radiation). For example, EUV reflectivity is used to inspect mask blanks before the manufacture of reticles (patterning devices) for use in EUV lithography.

[0061]

[0060] Depending on the scope of application, for example, the use of wavelengths in the hard X-ray, soft X-ray, or EUV region may be insufficient. U.S. Patent Application Publication No. 20130304424A1 and U.S. Patent Application Publication No. 2014019097A1 (Bakeman et al / KLA) describe a hybrid metrologic technique that combines optical measurements with measurements performed using X-rays at wavelengths in the range of 120 nm to 2000 nm to obtain measurements of parameters such as CD. CD measurements are obtained by combining one or more common and by X-ray mathematical models and optical mathematical models. The contents of the cited U.S. patent applications are incorporated herein by reference in their entirety.

[0062]

[0061] Many different forms of metrologic tools MT for measuring structures produced using a lithography patterning apparatus can be provided. Metrologic tools MT can use electromagnetic radiation to examine structures. The properties of the radiation (e.g., wavelength, bandwidth, power) can affect the different measurement properties of the tool, and generally, the shorter the wavelength, the greater the resolution. The radiation wavelength affects the resolution that the metrologic tool can achieve. Therefore, a metrologic tool MT equipped with a short-wavelength radiation source is preferred in order to enable the measurement of structures with features having small dimensions.

[0063]

[0062] Another way in which radiation wavelength can affect measurement characteristics is the penetration depth and transmittance / opacity of the material to be inspected at the radiation wavelength. Depending on the opacity and / or penetration depth, radiation can be used for measurements in transmission or reflection. The type of measurement can affect whether information about the structure / substrate surface and / or bulk interior can be obtained. Therefore, penetration depth and opacity are another factor to consider when selecting a radiation wavelength for the metrology tool.

[0064]

[0063] To achieve higher resolution for measuring structures patterned by lithography, a metrology tool MT having a short wavelength is preferred. This may include wavelengths shorter than the visible wavelength, such as the UV, EUV, and X-ray portions of the electromagnetic spectrum. Hard X-ray methods (HXR), such as transmitted small-angle X-ray scattering (TSAXS), can utilize the high resolution and high penetration depth of hard X-rays (wavelength < 0.1 nm) and therefore can operate in transmission mode. On the other hand, soft X-rays and EUV (wavelength > 0.1 nm) do not penetrate deep into the target but can induce rich optical responses in the material to be probed. This may be a legitimate optical property of many semiconductor materials and may be due to a structure of a size equivalent to the probe wavelength. As a result, EUV and / or soft X-ray metrology tools MT can operate in reflection mode, for example by imaging or analyzing diffraction patterns from structures patterned by lithography. Soft X-rays may have wavelengths in the range of 0.1 to 1 nm.

[0065]

[0064] In the case of hard X-rays, soft X-rays, and EUV radiation, their application in high-volume manufacturing (HVM) applications may be limited due to the lack of high-brightness radiation sources available at the required wavelengths. In the case of hard X-rays, radiation sources commonly used in industrial applications include X-ray tubes. X-ray tubes (including advanced X-ray tubes, e.g., those based on liquid metal anodes or rotating anodes) are relatively readily available and compact, but may lack the brightness required for HVM applications. High-brightness X-ray sources such as synchrotron lasers (SLS) and X-ray free electron lasers (XFELs) currently exist, but their size (>100m) and high cost (hundreds of millions of euros) make them prohibitively large and expensive for metrology applications. Similarly, there is a lack of availability of sufficiently bright EUV and soft X-ray radiation sources.

[0066]

[0065] A promising class of alternative radiation sources with the potential to provide high-brightness X-rays or EUV is the inverse Compton scattering (ICS) radiation source. Figure 6 shows a schematic overview of the main components of an exemplary ICS radiation source 400. In (a), the pulsed electron source 402 provides electron pulses to the electron accelerator 404. The electrons to be accelerated are accelerated and then irradiated by the pulsed laser 406 for emission radiation generation. The emission radiation may include wavelengths in the extreme ultraviolet, soft X-ray and / or hard X-ray portions of the electromagnetic spectrum. The emission radiation may include one or more wavelengths in the ranges of less than 1 nm, less than 0.1 nm, less than 0.01 nm, 0.01 nm to 100 nm, 0.1 nm to 100 nm, 0.1 nm to 50 nm, 1 nm to 50 nm and 10 nm to 20 nm. The operation of the ICS radiation source is described in more detail here.

[0067]

[0066] The pulsed electron source 402 may be a photoelectron emission source, and by emitting a laser pulse, which may be a UV laser pulse, toward the cathode, an electron pulse can be ejected from the cathode. The laser beam from the pulsed laser 406 may have a propagation direction that includes a component propagating opposite to the propagation direction of the electron pulse. Alternatively or in addition to this, the propagation direction of the pulsed laser 406 may have a component perpendicular and / or co-moving to the propagation direction of the electron pulse. A back-excited laser pulse may collide with the electron pulse. Electrons can travel at speeds close to the speed of light. Due to the relativistic Doppler effect, laser photons reflected by electrons may be converted into emitted radiation (e.g., X-ray photons), which are used as examples in the text below. This constitutes a narrow X-ray beam traveling in the same direction as the electrons. At present, the brightness demonstrated by the ICS emission source is still 10 9 ~10 11 photons / s / mm 2 / mrad 2 The brightness is approximately 0.1% BW. This brightness is several orders of magnitude lower than the desired brightness for metronome applications intended for HVM setups. HMV X-ray metronome setups require at least 10 12 ~10 14 photons / s / mm 2 / mrad2 A radiation source with a brightness of / 0.1%BW may be required, and the required brightness depends on the specific application. The low brightness of the above-described ICS radiation source may be partly due to the fact that the X-rays generated by individual electrons are added incoherently. Incoherent addition means that the brightness of the conventional ICS radiation source 400 is linearly proportional to the number N of electrons. In contrast, when X-ray photons are added coherently, the brightness will increase quadratically (proportional to N 2 ). As described in this description, this can be achieved, for example, when individual electrons emit in-phase X-ray photons and their intensities are added coherently.

[0068]

[0067] One possible method for achieving coherent emission of X-ray photons in an ICS radiation source is to use an ultracold electron source (UCES), which enables a multiple-digit increase in the emission brightness of the ICS radiation source. In the setup, an ultracold electron source is used instead of the conventional photoelectron emission electron source. This is shown in image (b) of Figure 6, where the ICS radiation source 408 has an ultracold electron source 410. An important advantage of using UCES is that the electron density distribution (also called the electron cloud) of the generated electron pulses can be adjusted together. In Figure 6(b), the density distribution is controlled such that electrons are concentrated into a series of narrow-spaced bunches 412 when the electrons exit the UCES. How bunching can be achieved is described in more detail in International Publication No. 2020 / 089454 and Franssen, J. G. H., et al. “From ultracold electrons to coherent soft X-rays.” arXiv preprint arXiv:1905.04031 (2019), which are incorporated herein by reference.

[0069]

[0068] One way to coherently sum the generated X-ray photons may be to make the spacing between electron bunches in the pulse approximately equal to the wavelength of the generated X-ray radiation. This can be partially achieved, for example, by the accelerator 414 before the electron pulse reaches the laser pulse 416 for X-ray generation. As described above, this coherent summation is achieved when a significant portion of the brightness of the ICS radiation source is N 2 This can mean that the intensity becomes proportional to the resulting X-rays, leading to an increase of several orders of magnitude in brightness. This increase in brightness makes the radiation source suitable for higher-brightness applications, such as in HVM lithography metrology tools (MT). Another benefit of UCES-driven ICS radiation sources is that they produce spatially perfectly coherent X-ray pulses, a key characteristic in several applications.

[0070]

[0069] To explain how coherent X-ray generation can be achieved, it is helpful to understand the operating principle of the cryogenic electron source, which will be explained in relation to Figure 7. In image (a), a cloud of cryogenic atoms 500 may be generated. The cloud may be generated in an area called a cavity 501. Cavity 501 may include, for example, a magneto-optical trap with a combination of a laser beam and a magnetic field, a technique well known in atomic physics. In one embodiment, cavity 501 is a microwave cavity or radio frequency (RF) cavity, which is a special type of resonator consisting of a closed (or mostly closed) metallic structure that restricts the electromagnetic field to the microwave region of the spectrum. The structure is hollow or filled with dielectric material. Microwaves travel back and forth between the walls of the cavity many times. At the resonant frequency of the cavity, the microwaves intensify the formation of standing waves within the cavity. Thus, the cavity functions similarly to organ pipes or the soundbox of a musical instrument, preferentially vibrating at a set of frequencies that are its resonant frequencies. RF cavities can also be used in particle accelerators and microwave vacuum tubes (klystrons and magnetrons) to manipulate charged particles passing through them by applying an accelerating voltage. Next, in image (b), atoms 502 can be excited by two back-excited lasers 504 to form a standing wave. Alternative techniques (e.g., the use of a spatial light modulator) can be used to generate intensity patterns such as standing waves. The characteristics of the standing wave may be that the local intensity is modulated every half wavelength between maximum intensity and zero. Atoms are excited to high-energy states where the intensity is high, and atoms are not excited where the intensity is low. This can generate a pattern of excited atom bunches. The spacing between bunches 506 may be equal to half the wavelength of the excitation laser 504. For example, in Figure 7, the spacing between excited atom bunches 506 may be 390 nm when generated by an excitation laser 504 having a wavelength of 780 nm. In image (c), an ionization laser pulse 508 may be applied. The photon energy of pulse 508 is high enough to ionize excited atoms, but not high enough to ionize unexcited atoms.Therefore, this can generate an electron cloud 510 having substantially the same bunch structure as the excited atoms 506 generated by the standing wave pattern. The electron cloud can be referred to as an electron pulse in this description. Electrons can be generated where both a high excitation laser intensity and a high ionization laser intensity combination is present. Therefore, alternative embodiments for generating an electron cloud may include a combination of a structured ionization laser (e.g., standing wave or SLM generation) and an unstructured excitation laser, or a combination of a structured excitation laser and a structured ionization laser. In the latter embodiment, more complex electron cloud patterns can be generated, for example, by combining an excitation laser and an ionization laser having different intensity patterns. In image (d), the structured electron cloud 510 emanating from the cavity 501 can be accelerated by a static electric field 512 between electrodes 514(a) and 514(b).

[0071]

[0070] The inventors have identified a problem associated with the cryogenic electron generation method described in relation to Figure 7. That is, in the above image (d), electrons are accelerated by an electrostatic field. Such a field can typically be generated by applying a static voltage between a back electrode and a front electrode surrounding the atomic cloud 506 within the cavity 501, as shown in Figure 7. However, a problem with this scheme is that electrons generated from atoms closer to the back electrode 514(a) may spend more time in the accelerating field 512 than electrons generated from atoms closer to the front electrode 514(b) before exiting through the aperture of the front electrode 514(b). As a result, electrons generated at the back of the cavity 501 may exit the cavity 501 at a greater speed than electrons generated at the front. Electrons generated at the back may begin to catch up with and / or overtake electrons generated at the front.

[0072]

[0071] Figure 8 shows an exemplary setup of two electrodes for accelerating the electron cloud exiting cavity 601. The electrodes generate an electric field E, which can be substantially constant throughout the cavity and can be obtained by E = V0 / L, where V0 is the voltage applied across the ends of the electrodes and L is the length of cavity 601 between the two electrodes. In Figure 8, the velocity v obtained by the electron at position z relative to the center of the electron cloud is proportional to its initial distance z0-z to the front electrode, and as a result, v(z) = v0 + This is the result.

[0073] Here, z0 is the distance from the cloud center to the forward electrode. v0 is the velocity obtained by the cloud center. The constant h<0 can be called the electron cloud chirp.

number

[0074] As a result, the electron cloud, after propagating along a short distance d as shown in image (b) of Figure 8, can self-compress to a very short length.

number

[0075]

[0072] As described above and shown in Figure 8(b), the electron cloud is generated at time t0 and accelerates out of cavity 601, but the electrons have varying velocities. Due to the varying velocities, the cloud can be compressed as it accelerates away from the outlet 602, as shown at t1. At time t2, the electrons reach their most compressed state. The point at which the electron cloud reaches its most compressed state can be called the self-compression point. The distance d between the outlet 602 of cavity 601 and the self-compression point can typically be a few millimeters. As the electron cloud passes the self-compression point, electrons generated near the rear of the cavity can overtake electrons generated at the front of cavity 601 and near the outlet 602. This is shown at time t3, and the size of the electron cloud has expanded compared to its size at the compression point. One object of this disclosure is to provide a method and apparatus for overcoming the problem of self-compression.

[0076]

[0073] According to a first aspect of the present invention, as shown in Figure 9, a method is provided for controlling the density distribution of electrons supplied by an electron source for use in X-ray generation. The method may include generating a plurality of electrons from a pattern of ultracold excited atoms inside a cavity (702). The electrons may have a density distribution corresponding to the pattern of excited atoms. The electrons leaving the cavity can be accelerated using a non-static acceleration profile (704). The acceleration profile can control the density distribution of electrons as they leave the cavity.

[0077]

[0074] The advantage of the above method is that the non-static acceleration profile can overcome the problems described in relation to Figure 8 above. Instead of using a static electric field to accelerate and giving electrons different velocities to exit the cavity depending on where the electrons originate within the cavity, the non-static acceleration profile can be designed to mitigate this effect. By applying various accelerations to electrons inside the cavity, it may be possible to control the velocity across the density distribution of electrons exiting the cavity. It may also be possible to control the shape and / or size of the electron density distribution as the electrons exit the cavity.

[0078]

[0075] The acceleration profile can be designed to control the velocity of electrons within the cavity so that the velocity of electrons is substantially equal as they exit the cavity. This substantially equal velocity of electrons in the cloud allows electrons to move away from the cavity while substantially maintaining the electron density distribution at the cavity exit. The electron density distribution can also be called the electron cloud and / or electron pulse.

[0079]

[0076] Acceleration profiles can reduce chirp in the electron density distribution. A potential definition of chirp is provided in relation to Figure 8 above. Chirp can be caused by differences in velocity between electrons at different positions in the density distribution, thereby resulting in a change in the shape of the density distribution as electrons propagate. In cases where the velocities of all electrons in the density distribution are substantially equal as the electrons leave the cavity, chirp can be substantially eliminated (i.e., chirp can be reduced to zero). An acceleration profile that results in a collimated density distribution in the forward and backward directions (i.e., a zero-chirp density distribution) where all electrons have substantially the same velocity can also be called an acceleration profile that avoids self-compression of the density distribution.

[0080]

[0077] The non-static acceleration profile may include an electromagnetic field. The field may be, for example, a non-static electric field E(z,t). The field may change with time t, and the field at any given location within the cavity will change over time. The field may also change with position along the propagation direction z, and different positions along z within the cavity may experience different electric field strengths at any given time. The electric field strength may vary over the period during which the electron cloud exiting the cavity is accelerated.

[0081]

[0078] The cavity can be a volume from which electrons are generated. The cavity can be a resonant structure to support the generation of a high electric field strength (e.g., an electric field of several tens of MV / m, which can result in pulsed electron bunches with kinetic energies in the range of several tens of keV to several MeV). The cavity can be a sealed (partially) space or an open space. The cavity can include at least one outlet from which electrons can be extracted from the cavity. The cavity can be a resonant microwave structure to enable the generation of electrons from a pattern of ultracold atoms. The cavity can include an aperture that acts as an outlet for electrons to exit the cavity. The cavity can include, for example, forward and backward electrodes to accelerate electrons generated within the cavity. The forward electrode can include an aperture that acts as an outlet for the electron cloud. The cavity can have a rectangular shape, or a more complex non-rectangular shape to achieve a non-static acceleration profile.

[0082]

[0079] The cavity may be an RF cavity, for example, which may include a metal enclosure on which RF waves can generate an oscillating field. The field may oscillate at frequencies in the range of 1 to 12 GHz, which may correspond to one or more standardized frequencies of the L, S, C, and X bands. The RF cavity may be powered by a klystron RF radiation source. The RF cavity may operate in pulse mode. The pulse frequency can be determined by the rate at which the cryogenic atomic cloud inside the cavity is replenished. This may typically be in the kHz range. Any device suitable for confining atoms of a sufficiently high density in the gas phase to a small volume can be used to form the cryogenic atomic cloud and pattern. This may include, for example, a magneto-optical trap.

[0083]

[0080] As described above, accelerating the electron cloud exiting the cavity with a non-static acceleration profile can be achieved using a time- and position-dependent electric field E(z,t). The electric field strength can vary over a range of values ​​from the time the electron cloud is generated until it moves towards the cavity exit. The range of values ​​experienced by the electrons can depend on the initial position z of the electrons when they are generated inside the cavity. This variation for electrons generated at different locations inside the cavity can make it possible to modify the electron velocity distribution. Specifically, it can be possible to modify chirp within the electrons.

[0084]

[0081] To modify the electric field and control the electron velocity through a non-static acceleration profile, the electric field distribution E(z,t) can change considerably during the time it takes for the electron cloud to leave the cavity. The electric field distribution E(z,t) can have a field gradient strong enough to allow for considerably different field values ​​to be observed in electrons at different positions along the propagation direction z. In this context, the magnitude of a sufficiently strong field gradient dE / dz can be as large as E / L, where E is the electric field strength in the cavity and L is the length of the electron cloud. The intensity of the gradient may depend on E and L for the specific application, but is MV / m 2 ~GV / m 2It can be within a certain range. Furthermore, the electric field distribution E(z,t) can be very strong, capable of accelerating the electron cloud emanating from the Bessel to a considerable speed. In this context, a considerable speed means a speed sufficient to inject the electron cloud into the accelerator so that X-rays are generated after the electron cloud passes through the accelerator. This speed can be, for example, at least 10% of the speed of light. Moreover, a higher speed is preferable for electron velocities because it reduces Coulomb interactions (collisions). These Coulomb collisions can be detrimental, as they can lead to bunching decomposition. Therefore, reducing these Coulomb collisions by increasing the speed (beam energy) can be an advantage of increasing electron velocities. An electric field with the properties described in this paragraph can be achieved, for example, in an RF cavity where a strong oscillating electromagnetic field can be established.

[0085]

[0082] An exemplary electric field suitable for use as a non-static acceleration profile may be as follows:

number

number

number

[0086]

[0083] Figure 10 shows an exemplary simulation in which the electron cloud exiting the cavity is accelerated by the field E(z,t) given by equation (1) above. For this exemplary simulation, the following parameters were used: an electron cloud measured to have a length of 1 mm along the z propagation direction, a 2 GHz RF cavity with a length of L = 3 cm, and an electric field E0 = 9 MV / m. In Figure 10, the solid line corresponds to electrons behind the pulse, i.e., electrons generated near the back electrode, further away from the cavity exit. The dashed line corresponds to electrons ahead of the pulse, i.e., electrons generated near the front electrode, near the cavity exit. Figure 10(a) shows the electric fields experienced by both exemplary electrons during the acceleration of electrons exiting the cavity. In the initial stages, up to 100 ps on the graph, the back electrons are always closer to the maximum field than the front electrons. This situation is similar to the case of static field acceleration. However, since the field oscillates over time (see equation (1)), the field can be set in the opposite direction before the electrons leave the cavity. This is seen, for example, at 100 ps to 200 ps in Figure 10(a). As shown in Figure 10(b), the reversing electric field can partially decelerate the electrons, thereby canceling out some of their acquired velocity.

[0087]

[0084] An advantage of this setup is that, for example, the field inversion can be tuned by selecting and setting appropriate values ​​for the parameters E0, φ and z0 so that the velocity differences between electrons cancel each other out. As shown in Figure 10(a), forward electrons have greater acceleration (0 ps to 100 ps) and also greater deceleration (100 ps to 200 ps). The net effect is that, as shown in Figure 10(b), it can be tuned so that both forward and backward electrons exit the cavity at the same velocity. Having the same exit velocity for all electrons in a pulse is equivalent to tuning the chirp h for this electron pulse to zero. As a result, no self-compression point occurs in the pulse. Moreover, during the process of accelerating electrons in and out of the cavity, electrons at different positions along the z direction do not have their trajectories intersecting. As shown in Figure 10(c) (where the positions of electrons relative to the center of the pulse are shown), forward and backward electrons can exit the cavity at separate positions. As shown in Figure 10(c), the electron pulse may exit the cavity somewhat compressed compared to its size at the time of generation.

[0088]

[0085] Electrons can be a cloud of electrons that form a single pulse generated by a pulsed electron source. Electrons can be generated, for example, as described in relation to Figure 7 above. The pulse may consist of multiple bunches.

[0089]

[0086] The electron density distribution can be a generated electron pulse, which includes multiple electron bunches. An electron pulse may include multiple electron bunches that are spatially separated from each other along the z direction. Each bunch may contain multiple electrons with a higher density compared to lower density electrons located in the area between the bunches. Multiple bunches can be generated from a pattern of ultracold atoms present inside the cavity, for example, as described in relation to Figure 6 above.

[0090]

[0087] According to the acceleration profile described in relation to Figure 10 above, separation between bunches of electron pulses can be maintained. Different bunches of pulses can be accelerated out of the cavity without overlapping with each other. As the bunches are accelerated out of the cavity, they are compressed in size and may move closer to each other as part of the pulse compression. The separation of electron pulse bunches may be in the range of, for example, 0.39 to 10 μm. The electron pulse length may be about 1 mm. The number of pulse bunches may be in the range of 100 to 2500.

[0091]

[0088] Although the acceleration profile has been described in relation to tuning the electron pulse chirp to zero, the above method can be used to set other chirp and / or velocity configurations. The chirp can be controlled independently of the electron velocity, although this is not possible in a stationary field. Specifically, the beam chirp is intentionally increased to a large value so that the self-compression point can be passed in a very short time. This can shorten the duration of the space charge effect enough to limit microstructure resolution, thus providing an alternative method to avoid the harmful reduction in Coulomb interaction at the self-compression point.

[0092]

[0089] Static electric fields and RF cavities may be used in series. Multiple RF cavities may also be used in series. Although a rectangular cavity shape containing two electrodes is described above, the method may also use more general cavity shapes. Equation (1) shows a single standing wave field distribution (i.e., the lowest-order mode of the cavity), but generally, an RF cavity can support multiple different modes. Thus, the final velocity distribution can be further tuned by using combinations of RF cavity modes. Rather than standing wave modes of the RF cavity, an RF traveling wave structure may also be used.

[0093]

[0090] The control of the density distribution discussed above focuses on control along the pulse propagation direction (z direction). Furthermore, regardless of whether the accelerating field is static or RF, or which RF cavity mode (and RF cavity shape) it is, it can also affect the velocity distribution of electrons in the up, down, left, and right directions of the electron pulse along the x and y directions. Any electric field has the property that a forward-backward gradient induces field components in the up, down, left, and right directions. This results in electron pulses that diverge in the up, down, left, and right directions in the case of a negative chirp, and electron pulses that converge in the up, down, left, and right directions in the case of a positive chirp. When operating in an RF cavity, the beam size and / or electron beam divergence in the up, down, left, and right directions can be controlled by additional electro-optical equipment (e.g., solenoids, quadrupole magnets, electro-optical equipment for electrostatic or static magnetic fields in the up, down, left, and right directions, or time-dependent electro-optical equipment for the up, down, left, and right directions). Such electro-optical equipment can be provided, for example, near the cavity exit.

[0094]

[0091] The electron density distribution can be used for X-ray generation. Specifically, electrons can be used to generate X-rays through inverse Compton scattering. The methods for controlling the electron density distribution described above can be carried out by apparatus. The apparatus can form part of a radiation source, such as an X-ray radiation source, or be connected to a radiation source. The apparatus can be provided for use in or with a metrology apparatus, for example, for measuring and / or inspecting lithographic structures. The apparatus may be for use in lithography applications, for example, an apparatus can be provided for controlling the electron density distribution in a lithography cell.

[0095]

[0092] Once an electron density distribution is provided outside the cavity using a controlled velocity profile, pulses can be directed to the destination for X-ray generation. As described above, the density distribution may include multiple bunches. Applying bunch patterns in an inverse Compton scattering X-ray source may have the advantage of increasing the brightness and / or temporal coherence of the X-ray source. The setup may be more compact than other types of X-ray sources that achieve similar brightness performance. This is shown, for example, in Figure 11, which shows an electron distribution. Figure 11(a) shows randomly distributed electrons. The X-ray radiation generated from these electrons may be emitted incoherently due to the random distribution. This can result in an X-ray source brightness proportional to the number of electrons N, as described in relation to Figure 6 above.

[0096]

[0093] Figure 11(b) shows electrons clustered in bunches. When irradiated with a laser pulse, the resulting density distribution of bunches can lead to increased coherent emission of X-ray radiation. However, in order to increase the coherence of the generated X-ray radiation, the spacing between bunches should approximate the wavelength of the generated X-ray radiation. The spacing between bunches in the density distribution as the bunches exit the cavity may be approximately the period of the standing wave pattern of the excitation laser 504 and / or the ionization laser, as explained in relation to Figure 7. This spacing may be several orders of magnitude larger than the desired spacing. Therefore, in order to achieve a spacing of the X-ray wavelength, further control and manipulation of the density distribution of the electron pulse may be necessary after the pulse exits the cavity where the pulse was generated. The purpose of this explanation is to achieve a further increase in source brightness by manipulating the spacing between electron bunches to be approximately equal to the X-ray wavelength. To reduce the spacing between bunches, the beamline can be provided to compress the electron pulse in the forward and backward directions along the z-propagation direction.

[0097]

[0094] Figure 12 shows a flowchart of a method for compressing a density distribution including electron bunches for coherent X-ray generation. Specifically, the X-rays to be generated may be soft X-rays. The method includes receiving a plurality of electron bunches having a density distribution (1002). The plurality of electron bunches are compressed such that the distance between bunches along the propagation direction of the electron bunches corresponds to the wavelength of the X-ray radiation to be generated (1004).

[0098]

[0095] As described above, the distance or spacing between electron bunches before compression may be on the order of several hundred nanometers. Reducing the spacing between electron bunches to match the X-ray wavelength may have the advantage of increasing coherent X-ray generation through inverse Compton scattering, thereby increasing the brightness of the X-ray source.

[0099]

[0096] The criteria for improving coherence in ICS-generated X-rays are: k mod =k x +k0cosθ0 This is possible, and in the formula,

number

number

number

number

[0100]

[0097] Compression methods can be performed by beamlines. To describe the beamline content, it may be useful to consider the velocity and positional distribution of electron pulses in phase space. A useful method for visualizing the forward and backward dynamics of electron bunches may be to plot the so-called forward and backward phase space, which represents the particle momentum p in the propagation direction. z This is a plot of the electron bunch particles against their forward / backward position z. An exemplary forward / backward phase space plot is shown in Figure 13, sketching the phase space for different locations along the beamline. Dark lines indicate high particle density, and light backgrounds indicate low particle density. The electron bunch is at position z n =nλ mod High electron densities can occur at certain locations, and low electron densities can occur between those locations. In this context, the meanings of high and low densities can be evaluated in comparison to one another. Ideally, a low electron density is an electron deficiency (1m). 3 (There are 0 electrons per unit area). An example of a high electron density is in a radiation source, at 1 m 3 10 16 ~10 18 It can be in the range of electrons. At the interaction site, the density is high, 1m 3 10 16 ~10 18 It can be within the range of electrons / M, where M is the scaling factor introduced above, and it is assumed that the size in the up, down, left, and right directions is constant.

[0101]

[0098] In phase space representation, bunching may appear as a series of vertical lines. Plot (i) may represent the state of electron bunches at the exit of a radiation source. Overall electron bunches may have a specific finite length and a specific particle momentum spread, which can be represented in the graph by the width and height of an elliptical contour in phase space, called a phase space ellipse. In phase space, the goal of the beamline may be to manipulate the electron bunches so that the final phase space (iv) shows a pattern of vertical lines that are more closely spaced by a coefficient of 1 / M than those at the radiation source. Mathematically, this final phase space can be obtained from the initial phase space by a linear transformation. For example, the density distribution in graph (i) containing multiple bunches can be horizontally reduced in graph (iv) by a coefficient of 1 / M. This result can be obtained, for example, by combining two elementary linear transformations available in an accelerator beamline. These may be horizontal skew in phase space and vertical skew in phase space. The meaning of skew in phase space is shown in Figure 14. The top row shows positive and negative horizontal skew in z-dimensional. The bottom row shows positive and negative vertical skew in z-dimensional.

[0102]

[0099] At low electron pulse energies, horizontal skew can be obtained by propagating the pulse over a certain distance, thereby constituting drift. This is because particles at the top of the phase space ellipse, with slightly higher momentum, overtake electrons at the bottom of the phase space ellipse, with slightly lower momentum. For higher electron pulse energies, horizontal skew can be obtained by moving faster particles over longer or shorter paths than slower particles. This can be achieved, for example, by applying one or more magnetic fields. Standard magnetic devices for doing this may include, for example, so-called chicanes, doglegs, and / or alpha magnets. Any arrangement that causes horizontal skew in phase space can be more generally called a dispersion section. The magnitude of the skew is R 56It can be shown as follows: In this notation, the numbers 5 and 6 are indices in the transfer matrix, and 5 and 6 represent the 5th row and 6th column. This is because the x and y directions (up, down, left, and right) use the first four rows and columns of the transfer matrix, and the z direction is the third direction included in the transformation.

[0103] [000100] A vertical skew in phase space can be obtained by applying a z-dependent modification of the particle momentum. In phase space, this can be done by moving one end of a phase space ellipse upward and the other end downward. Such a vertical skew can be achieved, for example, by propagating an electron pulse through an RF cavity structure. Within an RF cavity structure, the phase of the oscillating electric field may be such that the field is accelerating when the forward (or backward) end of the pulse crosses the cavity, and decelerating when the backward (or forward) end of the electron pulse crosses the cavity. More generally, any beamline element that produces a vertical skew in phase space can be called a chirper. The magnitude of the skew is R 65 This can be shown as follows (see Figure 14 for coding conventions).

[0104] [000101] From the viewpoint of elementary skew operation, a beamline may include a series of beamline elements that apply desired transformation steps in a desired size and order. These beamline elements may include electron-optical equipment as described above. As shown in Figure 13, the operation to achieve compression along the propagation direction is as follows: between the initial pulses (i) and (ii), R 1 56 It may include a distributed section >0. This can be formed by any of the horizontal skew methods described above. Between (ii) and (iii), R 65 It may include a chirper of <0. This can be obtained, for example, by many RF cavities arranged in series. Between (iii) and (iv), R 2 56 A second distribution section >0 may be provided. To achieve compression of coefficient M, the following relationship must be satisfied:

number

[0105] [000102] Alternative versions of the beamline can be provided to achieve reduction M. For example, any three beamline elements satisfying equations (2) and (3) above. Furthermore, the compression can be distributed over multiple stages (for example, using more than three transformation elements). In a multi-stage beamline, each stage may be similar to the beamline described above. The product of the reduction coefficients of all stages may be equal to the total compression M. Such multi-stage reduction may be advantageous when a large compression M (M≪1) is required. This is because, in the case of a large compression, the overall length of the beamline can be shortened by using multiple smaller compression stages in series. Any beamline that results in a reduction of phase space in the z direction can be used as a beamline. A beamline can be characterized by a transfer matrix T. The transfer matrix is ​​the phase space coordinates z and p z This can show how the beamline transforms the beam. Besides compression, the beamline can also be used to achieve expansion. Therefore, the coefficient M can be called either / both an expansion coefficient and a compression coefficient.

number

number

[0106] [000103] Optionally, a dechirper (i.e., R opposite to that of the first chirper) may be placed at the end of the beamline. 65 Add the second chirper to the final bunch and z and p zThe remaining correlation between them can be eliminated. Optionally, the accelerator can be placed at any position on the beamline to increase the total bunch energy. This may be advantageous for further increasing the photon energy of the X-rays generated by the ICS.

[0107] [000104] In a beamline, the complexity can increase considerably in that the electrons in the electron pulse repel each other. This can cause the pulse bunches to expand, reducing the spacing between bunches due to the higher density of electrons in the bunches. In addition, there may be a nonlinear relationship between velocity and momentum, which is characteristic of mildly relativistic electron pulses. This nonlinear relationship can lead to deformation of phase space. Due to these phenomena, not all beamlines satisfy the equation. 2 and 3 work equally well. Detailed particle tracking simulations that explain space charge and relativistic effects in detail show that the exemplary beamline in Figure 13 can work well for electron pulses containing up to 3000 electrons. In the exemplary beamline, the chirper may be designed as a series of multiple consecutive RF cavities rather than a single RF cavity. This may be to limit the required electric field strength per cavity.

[0108] [000105] In an exemplary beamline, an increase in the number of particles can have a significant impact on the bunching structure of the electron pulses, and this increase can be prevented by a bottleneck associated with parasitic compression. Parasitic compression can be a point in the beamline where the pulse length is minimized. This point is R 1 56 If >0, it can occur between the chirper and the interaction point by the ICS laser. Therefore, an alternative beamline that could be the target is one where the first dispersion section is R 1 56 It may have values ​​< 0. In addition, the absolute value of the size of this section can be large when considering equation 3, requiring a large reduction ratio. In practice, this section is

number

[0109] [000106] An alternative form of beamline using the above-described electron-optical equipment may be to achieve compression using echo-enhanced harmonic generators (EEHGs). EEHGs can obtain local regions with narrow-pitch bunches within a pulse that initially has a broad-pitch bunching structure. The principle of using EEHGs for pitch compression is shown in Figure 15. An electron pulse (shown in 15(a)) with multiple bunches whose inter-bunch spacing is compressed can be transmitted through the dispersion section 1302. This can lead to a horizontal skew phase space (shown in 15(b)). The initial horizontal skew can be strong.

[0110] [000107] In the next step, modulator 1304 can be applied, thereby modulating the periodic electron momentum in the z-direction, which is the direction of pulse propagation. The magnitude of the momentum modulation in this example can be considerably larger than the initial momentum spread of the pulse. This may have the advantage that the modulated phase space exhibits a region having multiple narrowly spaced lines with a negative slope at any modulation time p1, as shown in 15(c). The modulated pulse can be transmitted through a second dispersion section 1306 to introduce a second horizontal skew. This may result in a band of lines (1308) with a negative slope oriented vertically (see 15(d)). The electron density along the z-direction corresponding to this final phase space is shown in Figure 16. As shown, the EEHG procedure may result in a region having very narrowly spaced bunches separated by a distance p1, where the spacing is λ mod It can be controlled. Alternative implementations of the distributed section can be used. Section 1302 may be provided with a positive or negative sign. Selectively, section 1306 may be provided with a negative sign, in which case the region with a large positive slope in Figure 15(c) may be oriented vertically.

[0111] [000108] EEHG is described in Stupakov, Phys. Rev. Lett. 102, 74801 (2009) and Ribic et al., Nature Photonics 13, 555 (2019). The setup described above has several advantages over the EEHG described in those references. The first advantage is that the above EEHG method steps are combined with an electron pulse obtained as described herein. By controlling the velocity and density distribution of electrons in the pulse, the momentum broadening of the pulse is considerably lower than that of conventional electron pulses. This may mean that modulators can be used at considerably lower amplitudes.

[0112] [000109] Secondly, the above references describe EEHG in the context of high-energy accelerators for use as a tool to provide super-relativistic electron pulses with tightly spaced bunches as input to a free-electron laser. However, this description introduces the option of using EEHG in a compact ICS radiation source for X-ray generation. Thus, EEHG can be applied to low-energy electron pulses. An advantage of low-energy application may be that the dispersion section can be implemented as a simple propagation section.

[0113] [000110] Furthermore, an optical modulator can be used instead of a magnetic modulator. The EEHG process described in the above references describes a magnetic modulator used for the modulation step. Conventional magnetic modulators have a pitch λ u It can consist of a magnetic undulator (an arrangement of magnets that alternately change polarity). The magnetic undulator can guide electrons to follow a wave-like path. The undulator has a wavelength λ s It is combined with a forward-excited seed laser pulse having [a specific characteristic]. Due to the wave motion of electrons, they have wavelengths.

number

number

number

[0114] [000111] However, in the case of ICS X-ray sources, the value of γ can be in the range of 2 to 10. This may require combining a conventional seed laser radiation source with a resonant magnetic undulator having a pitch of sub-millimeters. This pitch is small and may be difficult to achieve. This specification proposes that this problem can be overcome by providing an optical modulator. This may be advantageous in ICS X-ray generation applications because the bunch spacing required for improved coherence is on the order of X-ray wavelength radiation. In an optical modulator, the magnetic undulator has a wavelength λ u It can be replaced with a back-pumped laser having a pulsed laser radiation beam. Due to inverse Compton scattering of the back-pumped laser, the electron pulse is wavelength

number

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[0115] [000112] An optical modulator, including the arrangement of a seed laser and a back-pumped laser, can use different incident angles of the lasers. Different angle setups may have corresponding generalized resonance criteria. An advantage of using an optical modulator may be that the required path length in the beamline is shorter than the size required for a magnetic modulator. The path length may be as short as the focal region where the two seed laser beams and the back-pumped laser beam intersect. Another advantage may be that when the optical modulator forms part of the X-ray emission source, one or more lasers may be present in other parts of the setup. As a result, the back-pumped and / or seed laser emission sources can be used multiple times across the entire X-ray source setup. For example, a laser used in another part of the X-ray source can be used simultaneously as the back-pumped emission source of the optical modulator without the need to provide an additional laser.

[0116] [000113] Furthermore, in low-energy electron pulse applications, with respect to ICS-generated X-rays, the required electromagnetic force in the modulator can be sufficiently low (e.g., on the order of μJ) that can be provided by the optical field of the pulsed laser. This is not possible in the case of super-relativistic electron pulses in more conventional high-energy free-electron laser applications. Figure 17 shows the results of an exemplary particle tracking simulation, illustrating the phase space of a small slice of the electron pulse after the application of an optical modulator consisting of two intersecting laser beams. The graph shows the structure of parallel bands with high electron density along the z direction, modulated sinusoidally, as described above. The electromagnetic force in the modulator can be quantified by the laser intensity. A requirement for the modulator may be that the imposed energy modulation is greater than the intrinsic energy spread of the electron pulse. The laser intensity required to satisfy this requirement may be proportional to the product of the electron energy and the electron energy spread. In the case of the cryogenic electron pulses described herein, the energy may be, for example, on the order of a few MeV. The energy spread may be a few eV. Thus, the required laser intensity is 10 17 ~10 19 W / m 2 This can be achieved. This is a typical kHz repetition rate for a cryogenic electron source and can be easily achieved using a commercially available femtosecond laser. In contrast, hyperrelativistic electron pulses can have energies close to 1 GeV and energy broadening close to 1 MeV. This means the required laser intensity is 10 25 W / m 2 This can result in an extremely high intensity that cannot be achieved by lasers available at kHz repetition rates. Therefore, in the case of hyper-relativistic electron pulses, a magnetic modulator may have to be used.

[0117] [000114] The electron pulses using the controlled density and velocity distribution and / or beamline described above can be used to generate X-ray pulses. An electron pulse containing multiple electron bunches has a kinetic energy U and a bunching pitch / spacing λ. mod It can be characterized by U and λ. modBy controlling the average value of, and in addition to or alternatively to, their forward and backward derivatives dU / dz and dλ mod By controlling / dz, it may be possible to achieve a variety of ICS-generated X-ray pulses. Figure 18 shows exemplary effects of controlling these different characterization characteristics. Graph 1601 shows the longitudinal momentum of the bunch along the z direction. The slope indicated by the dashed line may be proportional to the rate of change of kinetic energy along z. Graph 1602 shows the pitch or inter-bunch spacing along the z direction. The slope represents the rate of change of pitch along the propagation direction z of the electron pulse.

[0118] [000115] An electron pulse having a non-zero energy derivative dU / dz can be said to be accompanied by an energy chirp. Non-zero bunching derivative dλ mod An electron pulse with / dz can be said to be accompanied by bunching chirp. The energy chirp of the pulse can be controlled in the electron source, for example, by appropriately selecting the RF phase and position of the atomic cloud. Alternatively, or in addition to this, the energy chirp of the electron pulse can be controlled in the beamline, for example, by using a chirper. The bunching chirp of the electron pulse can be controlled by manipulating standing waves in the electron source. This can be achieved, for example, by crossing strongly diverging excitation laser beams and / or by a spatial light modulator, or by introducing nonlinearity in beamline skew operation.

[0119] [000116] Furthermore, ICS laser pulses used to induce inverse Compton scattering X-ray generation by irradiating with electron pulses can also be intentionally chirp. Laser pulses in which the wavelength gradually decreases from front to back can be called laser pulses having a positive chirp c0>0. By colliding electron pulses with energy chirp and / or bunching chirp with chirp ICS laser pulses, opportunities as described below can be provided.

[0120] [000117] The first opportunity may be the generation of extremely short attosecond X-ray pulses. This can be achieved by colliding an electron pulse with bunching chirp with a chirp laser pulse. This can result in time compression of the generated X-ray pulse. The compression mechanism may be similar to the operating principle of a chirp mirror. The chirp laser pulse can be compressed in the forward and backward directions by different wavelengths penetrating to different depths in the mirror and being reflected. By tuning the path lengths of different wavelength radiation, sections of the laser pulse corresponding to different wavelengths can be made to overlap. This can result in compression of the reflected pulse. Mechanisms for generating very short wave X-ray pulses can be achieved based on the same compression principle.

[0121] [000118] Electron bunch with negative bunching chirp (dλ mod A laser pulse with a back-excited positive chirp (dz < 0) can be collided with it. By inverse Compton scattering, electrons are sent to wavelength λ x (t) = λ(t) / 4γ 2 It may emit X-ray radiation having [a certain characteristic]. Due to the chirpening of the pulse, this emission wavelength varies along the duration of the laser pulse. Only during short time intervals somewhere in the laser pulse, local bunching of electron pulses resonates with the emission wavelength. mod =k x The emitted X-ray radiation can be coherently amplified when the coherence enhancement condition +k0cosθ0 is met. This condition is met at different locations for different parts (slices) of the electron pulse along the z-direction. Therefore, each slice of the electron pulse can emit a short burst of amplified X-ray radiation. Furthermore, because the electron pulse is accompanied by bunching chirp, the resonance time interval can differ for different slices of the electron pulse.

[0122] [000119] By controlling the bunching chirp and laser chirp to create a favorable relationship, the short bursts of X-ray radiation emitted by individual slices of the electron pulse can be made to overlap. As a result, very short, powerful X-ray pulses (e.g., pulses in the attosecond range) can be produced. This concept can be understood by considering pulse slices that resonate near the front of the laser pulse and pulse slices that resonate near the rear of the pulse. The front of the laser should resonate with the falling slice of the pulse, and as a result, the resonant scattered radiation reaches the front slice when it resonates with the rear of the laser.

[0123] [000120] Another opportunity may involve controlling the spectral bandwidth of the X-ray pulse. This can be achieved by selecting a combination of energy chirps for the electron pulse and chirps for the laser pulse. The bunching chirp may be zero or non-zero. Due to inverse Compton scattering, the electrons of the pulse have wavelength λ x (t) = λ(t) / 4γ 2 It can emit X-ray radiation. Due to the chirpening of the laser pulse, this wavelength can vary along the duration of the laser pulse. Because the electron pulse is accompanied by energy chirpping, the bunch spacing resonates with the emission wavelength only during short time intervals somewhere in the laser pulse. As described above, the resonance condition is k mod =k x It can be +k0cosθ0. During the interval in which the resonance condition is satisfied, the emitted X-ray radiation can be coherently amplified. In an approximate view, this is the emitted radiation λ x (t) is the bunching pitch λ mod This can occur when it is equal to λ(t) / 4γ. However, since the energy and thus γ can change over the pulse, 2 =λ mod The specific portion λ(t) of the laser pulse in which resonance and coherent amplification occur can also vary across the electron pulse.

[0124] [000121] For example, if the energy chirp is positive and the laser chirp is negative, the X-ray radiation emitted from the front of the electron pulse may resonate with the bunch spacing when excited by the back of the laser pulse (a large λ is combined with a large γ). The X-ray radiation emitted from the back of the electron pulse may resonate with the bunch spacing when excited by the front of the laser pulse (a small λ is combined with a small γ). As a result, all parts of the electron pulse may resonate within relatively short time intervals. This can result in a shorter overall duration of the X-ray pulse. This can correspond to the X-ray pulse having a wide spectral bandwidth. At the other extreme, for example, if both the energy chirp and the laser chirp are positive, the opposite can occur. The front of the electron pulse may resonate with the front of the laser pulse. The back of the electron pulse may resonate with the back of the laser pulse. Because the forward and backward-excited laser pulses first come into contact with the forward portion of the electron pulse, and only come into contact with the backward portion of the electron pulse some time later, the timing of the emission of coherently amplified radiation from different parts of the electron pulse can be dispersed over relatively long intervals. This can result in relatively long X-ray pulses that can correspond to a narrow spectral bandwidth.

[0125] [000122] Further embodiments are disclosed in the following numbered clauses. 1. A method for controlling the electron density distribution provided by an electron source for use in the generation of hard X-rays, soft X-rays and / or extreme ultraviolet rays, The method involves generating multiple electrons from a pattern of ultracold excited atoms inside a cavity using an ionization laser, wherein the electrons have a density distribution determined by at least one of the excited atom patterns and the ionization laser. Accelerating electrons out of a cavity using a non-static acceleration profile, wherein the acceleration profile controls the electron density distribution as the electrons leave the cavity. Methods that include... 2. The method according to Clause 1, wherein the acceleration profile controls the velocity of electrons within the cavity such that the velocity of electrons is substantially equal as they leave the cavity. 3. The method according to any one of the preceding clauses, wherein the electron density distribution comprises multiple electron bunches. 4. The method of any one of the preceding clauses, wherein the acceleration profile reduces chirp in the density distribution of electrons leaving the cavity. 5. Acceleration is performed in any of the preceding clauses, including a non-static electromagnetic field. 6. The method according to Clause 3, wherein the non-static electromagnetic field includes a component that changes over time. 7. The method according to Clause 5 or 6, wherein the non-static electromagnetic field includes a component that varies depending on the position within the cavity. 8. The method according to any one of the preceding clauses, wherein the electron density distribution is consistent with the pattern of ultracold excited atoms. 9. The method according to any one of the preceding clauses, wherein the electron density distribution is determined by a structured ionization laser. 10. The method according to any one of the preceding clauses, wherein the cavity is a resonant microwave structure. 11. The method of any one of the preceding clauses, wherein hard X-rays, soft X-rays and / or extreme ultraviolet radiation generation is achieved using inverse Compton scattering. 12. An apparatus for controlling the density distribution of electrons provided by an electron source for use in the generation of hard X-rays, soft X-rays and / or extreme ultraviolet radiation, configured to perform the method described in any one of the clauses 1 to 11. 13. Radiation sources including the devices described in Clause 12. 14. Metrology apparatus including the apparatus described in Clause 12. 15. A lithography cell containing the apparatus described in Clause 12. 16. A method for compressing a density distribution including electron bunches for the generation of coherent hard X-rays, soft X-rays and / or extreme ultraviolet rays, Receiving multiple electron bunches with density distributions, Compressing multiple electron bunches so that the distance between bunches along the propagation direction of the electron bunches corresponds to the wavelengths of the generated hard X-rays, soft X-rays, and / or extreme ultraviolet radiation. Methods that include... 17. The method according to clause 16, wherein an electron bunch is compressed using echo-enhanced harmonic generation. 18. The method according to Clause 16 or 17, wherein an electronic bunch is compressed using an electro-optical device. 19. The method according to any one of the clauses 16 to 18, wherein coherent hard X-ray, soft X-ray and / or extreme ultraviolet radiation generation is achieved using inverse Compton scattering. 20. An assembly for compressing a density distribution including an electron bunch for the generation of coherent hard X-rays, soft X-rays and / or extreme ultraviolet radiation, configured to perform the method described in any one of the clauses 16 to 19. 21. An echo-enhancing harmonic generation method for generating coherent hard X-rays, soft X-rays and / or extreme ultraviolet rays, Receiving multiple electron bunches, where each bunch receives including momentum expansion, Propagating electrons through a dispersion section and introducing a skew along the propagation direction in phase space, Applying periodic momentum modulation along the propagation direction to an electron bunch using an optical modulator, The electrons are propagated through a second dispersion section, and a second skew is introduced along the propagation direction in phase space, the second skew being introduced to modify the modulation momentum of the bunches in order to provide the bunches with reduced separation along the propagation direction compared to the received bunches. Methods that include... 22. A method for generating attosecond hard X-rays, soft X-rays and / or extreme ultraviolet pulses, Obtaining multiple electron bunches, Introducing chirp in the separation of multiple bunches, Irradiating a chirp bunch with a back-excited chirp radiation pulse to generate hard X-rays, soft X-rays and / or extreme ultraviolet radiation, wherein the chirp in the separation between bunches matches the chirp of the radiation pulse according to the resonance conditions, thereby generating attosecond hard X-rays, soft X-rays and / or extreme ultraviolet pulses. Methods that include... 23. The method according to Clause 22, wherein the chirp in the separation between bunches and the chirp in the radiation pulse are positive. 24. The method according to clause 22 or 23, wherein the kinetic energy chirp is configured to control the bandwidth of the generated hard X-rays, soft X-rays, and / or extreme ultraviolet radiation. 25. The method according to any one of the clauses 22 to 24, wherein introducing chirps in the separation of a plurality of bunches controls the rate of change of at least one forward-backward change of the kinetic energy of the electron bunches and the pitch of the electron bunches.

[0126] [000123] While this specification specifically refers to the use of lithography equipment in the manufacture of ICs, it should be understood that the lithography equipment described herein may have other applications. Possible other applications include the manufacture of integrated optical systems, guidance patterns and detection patterns for magnetic domain memory, flat panel displays, liquid crystal displays (LCDs), thin-film magnetic heads, and the like.

[0127] [000124] While embodiments may be specifically referenced in relation to lithography apparatus, embodiments may be used in other apparatuses. Embodiments may form part of any apparatus for measuring or processing objects such as mask inspection apparatuses, metrology apparatuses, or wafers (or other substrates) or masks (or other patterning devices). These apparatuses may be collectively referred to as lithography tools. Such lithography tools may operate under vacuum conditions or ambient (non-vacuum) conditions.

[0128] [000125] While this specification may make specific references to embodiments in the context of inspection or metronome apparatus, embodiments may be used in other apparatuses. Embodiments may form part of a mask inspection apparatus, a lithography apparatus, or any apparatus that measures or processes objects such as wafers (or other substrates) or masks (or other patterning devices). The term “metronome apparatus” (or “inspection apparatus”) may also refer to an inspection apparatus or inspection system (or metronome apparatus or metronome system). For example, an inspection apparatus including embodiments may be used to detect defects in a substrate or defects in a structure on a substrate. In such embodiments, the subjective characteristics of the structure on the substrate may relate to defects in the structure, the absence of a particular part of the structure, or the presence of an unwanted structure on the substrate.

[0129] [000126] While the above may contain specific references to the use of embodiments in the context of optical lithography, it will be understood that the present invention is not limited to optical lithography and can be used in other applications, such as imprint lithography, where permitted in the context.

[0130] [000127] The above-described target or target structure (more generally, a structure on a substrate) is a metrologic target structure specifically designed and formed for measurement purposes, but in other embodiments, the properties of a target can be measured in one or more structures that are functional parts of a device formed on a substrate. Many devices have regular, grid-like structures. The terms structure, target grid and target structure, as used herein, do not require that the structure be specifically provided for the measurement being performed. Furthermore, the pitch of the metrologic target may be near or less than the resolution limit of the scatromometer's optical system, but may be much larger than the dimensions of a typical non-target structure (optionally, a product structure) generated by the lithography process in the target portion C. In practice, the lines and / or spacing of the overlay grid within the target structure can be generated to include smaller structures, similar in dimensions to the non-target structure.

[0131] [000128] While specific embodiments have been described above, it will be understood that the present invention can be practiced in ways other than those described. The above description is intended to be illustrative, not restrictive. Accordingly, it will be apparent to those skilled in the art that modifications can be made to the described invention without departing from the claims set forth below.

[0132] [000129] Although specific references have been made to “metrology apparatus / tool / system” or “inspection apparatus / tool / system,” these terms may refer to the same or similar types of tools, apparatus, or systems. For example, an inspection or metrology apparatus including embodiments of the present invention can be used to determine the characteristics of a structure on a substrate or wafer. For example, an inspection or metrology apparatus including embodiments of the present invention can be used to detect defects in a substrate or defects in a structure on a substrate or wafer. In such embodiments, the characteristics of the structure on the substrate may relate to defects in the structure, the absence of a particular part of the structure, or the presence of an unwanted structure on the substrate or wafer.

[0133] [000130] Although specific references are made to SXR and EUV electromagnetic radiation, it will be understood that the present invention can be carried out using all electromagnetic radiation, including radio waves, microwaves, infrared radiation, (visible) light, ultraviolet radiation, X-rays and gamma rays, where permitted in the context. As an alternative to optical metrometry methods, the use of X-rays, optionally hard X-rays (e.g., radiation in the wavelength range of 0.01 nm to 10 nm, or optionally 0.01 nm to 0.2 nm, or optionally 0.1 nm to 0.2 nm) has also been considered for metrometry measurements.

Claims

1. A radiation source for generating emitted radiation including hard X-rays, soft X-rays and / or extreme ultraviolet rays, A pulsed electron source configured to generate electron pulses, A modulator configured to modulate the momentum of the electron pulse, including the arrangement of a seed laser and a back-excited laser, An electronic accelerator configured to accelerate the aforementioned electronic pulse, A pulsed laser configured to generate a laser beam that collides with the accelerated electron pulses for the purpose of generating the emitted radiation, A source of radiation, including

2. The radiation source according to claim 1, wherein the incident angles of the seed laser and the back-excited laser are different.

3. The radiation source according to claim 1 or 2, wherein the propagation direction of the pulsed laser has a codynamic component with respect to the propagation direction of the electron pulse.

4. The radiation source according to any one of claims 1 to 3, wherein the propagation direction of the pulsed laser has a component perpendicular to the propagation direction of the electron pulse.

5. The radiation source according to any one of claims 1 to 4, wherein the propagation direction of the pulsed laser has a back excitation component with respect to the propagation direction of the electron pulse.

6. The radiation source according to any one of claims 1 to 5, wherein the emitted radiation includes coherent radiation.

7. The radiation source according to any one of claims 1 to 6, wherein the accelerated electron pulses include bunches with narrow spacing.

8. Metrology apparatus comprising a radiation source according to any one of claims 1 to 7.

9. A method for compressing a density distribution including electron bunches for the generation of coherent hard X-rays, soft X-rays and / or extreme ultraviolet rays, Receiving multiple electron bunches with density distributions, Compressing the plurality of electron bunches using a modulator including the arrangement of a seed laser and a back-pumped laser such that the distance between the bunches along the propagation direction of the electron bunches corresponds to the wavelength of the generated hard X-rays, soft X-rays and / or extreme ultraviolet radiation. Methods that include...

10. A method for generating emitted radiation including hard X-rays, soft X-rays and / or extreme ultraviolet rays, Generating an electronic pulse, Modulation of the momentum of the electron pulse using a modulator that includes the arrangement of a seed laser and a back-pumped laser, Accelerating the aforementioned electron pulse, To generate the aforementioned emitted radiation, the laser beam is collided with the accelerated electron pulse. Methods that include...

11. The method according to claim 10, wherein the incident angles of the seed laser and the back-excited laser are different.

12. Compressing a plurality of electron bunches of an electron pulse such that the distance between the bunches along the propagation direction of the electron bunches corresponds to the wavelength of the emitted radiation generated. The method according to claim 10 or 11, including the method described in claim 10 or 11.

13. A method for generating emitted radiation including hard X-rays, soft X-rays and / or extreme ultraviolet radiation, comprising compressing a plurality of electron bunches using a modulator including a seed laser and a back-pumped laser arrangement such that the distance between the electron bunches along the propagation direction of the electron bunches corresponds to the wavelength of the emitted radiation to be generated.

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