NL2019961A - Radiation Source - Google Patents

Abstract

An electron bunch modulator comprises: an energy modulator; a first dispersive electron optics; a chirp module; and a second dispersive electron optics. The energy modulator is for receiving a bunched electron beam and is operable to produce an energy modulation within each bunch of the bunched electron beam at a first distance scale λ1. The first dispersive electron optics is arranged to receive the bunched electron 5 beam output by the energy modulator, disperse the electron bunches and subsequently recombine them such that the distance travelled by an electron within a given electron bunch is dependent on its energy. The chirp module is operable to receive the bunched electron beam output by the first dispersive electron optics and to produce a longitudinal phase space correlation in each electron bunch. The second dispersive electron optics is arranged to receive the bunched electron beam output by the chirp module, disperse the 10 electron bunches and subsequently recombine them such that the distance travelled by an electron within a given electron bunch is dependent on its energy in an opposite sense to the first dispersive electron optics.

Description

FIELD [0001] The present invention relates to a radiation source. The radiation source may, for example, form part of a lithographic system. In particular, the present invention may relate to a radiation source that uses inverse Compton scattering and may incorporate apparatus and methods for imposing a density modulation on electron bunches.

BACKGROUND [0002] A lithographic apparatus is a machine constructed to apply a desired pattern onto a substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus may for example project a pattern from a patterning device (e.g. a mask) onto a layer of radiation-sensitive material (resist) provided on a substrate.

[0003] The wavelength of radiation used by a lithographic apparatus to project a pattern onto a substrate determines the minimum size of features which can be formed on that substrate. A lithographic apparatus which uses EUV radiation, being electromagnetic radiation having a wavelength within the range 4-20 nm, may be used to form smaller features on a substrate than a conventional lithographic apparatus (which may for example use electromagnetic radiation with a wavelength of 193 nm).

[0004] A lithographic system may comprise one or more radiation sources, a beam delivery system and one or more lithographic apparatus. The one or more radiation sources may comprise a radiation source that uses inverse Compton scattering wherein bunches of electrons interact with pulses of radiation at a first wavelength to form a beam of radiation at a second wavelength.

[0005] It is an object of the present invention to obviate or mitigate at least one problem of prior art techniques.

SUMMARY [0006] According to a first aspect ol’ the invention there is provided an electron bunch modulator comprising: an energy modulator for receiving a bunched electron beam, the energy modulator operable to produce an energy modulation within an electron bunch of the bunched electron beam at a first distance scale λι; a first dispersive electron optics arranged to receive the bunched electron beam output by the energy modulator, disperse the electron bunch and subsequently recombine it such that the distance travelled by an electron within the electron bunch is dependent on its energy; a chirp module operable to receive the bunched electron beam output by the first dispersive electron optics and to produce a longitudinal phase space correlation in the electron bunch; and a second dispersive electron optics arranged to receive the bunched electron beam output by the chirp module, disperse the electron bunch and subsequently recombine it such that the distance travelled by an electron within the electron bunch is dependent on its energy in an opposite sense to the first dispersive electron optics.

[0007] It will be appreciated that the distance travelled by an electron within a given electron bunch the second dispersive electron optics being dependent on its energy in an opposite sense to the first dispersive electron optics may mean that, for example, higher energy electrons travel a shorter distance than lower energy electrons within the first dispersive electron optics and higher energy electrons travel a greater distance than lower energy electrons within the second dispersive electron optics. Alternatively, higher energy electrons may travel a greater distance than lower energy electrons within the first dispersive electron optics and higher energy electrons may travel a shorter distance than lower energy electrons within the second dispersive electron optics.

[0008] It will be appreciated that the energy modulator may be operable to produce an energy modulation within a plurality of electron bunches of the bunched electron beam at the fust distance scale λι. The first dispersive electron optics may be arranged to disperse each of the plurality of electron bunches and subsequently recombine them such that the distance travelled by an electron within a given electron bunch is dependent on its energy. The chirp module may be operable to produce a longitudinal phase space correlation in each of die pluarlity of electron bunches. The second dispersive electron optics may be arranged to disperse each of the plurality of electron bunches and subsequently recombine them such that the distance travelled by an electron within a given electron bunch is dependent on its energy in an opposite sense to the first dispersive electron optics.

[0009] The first aspect of the invention is advantageous since it allows spatial electron density modulation to be applied to a bunched electron beam at a second distance scale λ2, which is smaller than the first distance scale λι, as now explained.

[0010] First an initial energy modulation is applied to each bunch by the energy modulator. As a result of this energy modulation, the longitudinal phase space distribution of each bunch may, for example, be generally sinusoidal. The relative energy or momentum of the electrons within the bunch oscillates as a function of longitudinal position within the bunch. The longitudinal phase space distribution of the bunches is such that at any given longitudinal position, the relative energy or momentum of the electrons within the bunch is substantially constant.

[0011] Subsequently, the energy modulation is converted into a second, higher frequency spatial electron density modulation by the first dispersive electron optics, the chirp module and the second dispersive electron optics in combination. Together, the first dispersive electron optics, the chirp module and the second dispersive electron optics mat be considered to be a bunch compressor which is arranged lo spatially compress electron bunches to which an energy modulation has been applied. In particular, the first dispersive electron optics, the chirp module and the second dispersive electron optics may be considered to be a bunch compressor which is arranged to achieve longitudinal compression of the bunches whilst maintaining the modulation of longitudinal phase space distribution of the bunches that is created by the energy modulator. In this way, the first dispersive electron optics, the chirp module and the second dispersive electron optics compress bunches so as to create an energy modulation that is of a smaller scale k₂ than the scale λι of the modulation imposed by the energy modulator. This two stage process therefore allows a higher frequency spatial electron density modulation to be applied to the electron bunches. First the first dispersive electron optics skews the longitudinal phase space distribution of the bunches; next the chirp module stretches the longitudinal phase space distribution of the bunches in a direction that is inclined at a non-zero angle relative to the longitudinal direction; and then the second dispersive electron optics compresses the longitudinal phase space distribution of the bunches so as to produce the density modulation. The net result of this skewing, stretching and compression of the longitudinal phase space distribution of the bunches results in the second, higher frequency spatial electron density modulation. [0012] In some embodiments, within the first dispersive electron optics, the highest energy electrons within each bunch may move relative to a centre of mass of the bunch by a distance greater than a quarter of the first distance scale λι/4. With such an arrangement, the longitudinal phase space distribution of each bunch is skewed such that each maximum of the distribution moves past at least one adjacent minimum. For such an arrangement, after the first dispersive electron optics the longitudinal phase space distribution of the bunches is such that at any given longitudinal position, the relative energy or momentum of the electrons within the bunch has a plurality of different values.

[0013] The chirp module may be operable to produce a generally linear longitudinal phase space correlation in each electron bunch. It will be appreciated that the longitudinal phase space distribution of the bunches as they leave the first dispersive electron optics has already been modulated by the energy modulator and that the chirp module imposes a longitudinal phase space correlation or chirp on top of this modulation.

[0014] As a result of the energy modulation at the first distance scale λι, the density of the bunches could also be modulated at the first distance scale λι. For a generally sinusoidal energy modulation, this could be achieved by a suitable dispersive electron optics that is arranged to disperse the electron bunches and subsequently recombine them such the highest energy electrons within each bunch move relative to a centre of mass of the bunch by a distance of the order of a quarter of the first distance scale λι/4. However, the electron bunch modulator according to the first aspect of the invention allows the energy modulation at the first distance scale λι that was applied by the energy modulator to be converted to a spatial density modulation at a smaller scale. For example, it may allow an energy modulation at a scale of the order of

200 nm to be converted into a spatial density modulation at a wavelength in the EUV range (for example ol' the order of 13.5 nm).

[0015] The first electron optics may apply a R56 transformation and may, for example, comprise a magnetic arc or magnetic chicane. Similarly, the second electron optics may apply a R56 transformation and may, for example, comprise a magnetic arc or magnetic chicane. In one embodiment, the first electron optics applies a positive R56 and comprises a magnetic arc and the second electron optics applies a negative R?6 and comprises a magnetic chicane.

[0016] It is particularly beneficial that the energy modulation is applied to each electron bunch before the bunch compression stage that is provided by the second dispersive electron optics. This is in contrast to, for example, a two stage spatial electron density modulation wherein the electron bunches are first compressed and then subsequently a spatial electron density modulation is applied. This is because the arrangement of the first aspect reduces the effects of space charges and therefore can result in a stronger spatial electron density modulation al relatively high frequencies. For example, it may allow a strong spatial electron density modulation at a wavelength in the EUV range (for example of the order of 13.5 nm).

[0017] Note that, together, the first dispersive electron optics, the chirp module and the second dispersive electron optics are arranged to spatially compress the bunched electron beam with an oscillating longitudinal phase space distribution whilst maintaining the oscillation or modulation of the longitudinal phase space distribution. This is in contrast to known bunch compressors of the type that are operable to compress a bunched electron beam that has a generally linear longitudinal phase space distribution.

[0018] As the bunches exit the second dispersive electron optics the longitudinal phase space distribution of the bunches is generally sinusoidal, but has a sufficient amount of residual skew to create a density modulation. To achieve this, the relative strengths of the first and second dispersive electron optics may be generally matched such that the phase space distribution of the bunches as they exit the second dispersive electron optics has a sufficient amount of residual skew to result in a density modulation. This may be achieved by ensuring that the ratio of the R56 value of the first dispersive electron optics to the R56 value of the second dispersive electron optics is approximately equal to a compression factor imposed by the second dispersive electron optics.

[0019] It will be appreciated that as used herein, a first component (for example the first dispersive electron optics) being arranged to receive a bunched electron beam from a second component (for example the energy modulator) should be considered to mean that the bunched electron beam is output by the second component and subsequently received by the first component, whether or not the bunched electron beam passes through one or more intermediate components in between.

[0020] The electron bunch modulator may further comprise a second chirp module operable to receive the bunched electron beam output by the second dispersive electron optics and to reduce a longitudinal phase space correlation in the electron bunch.

[0021] The second chirp module may result in a reduction in the energy spread within the bunches. In turn, this may result in a more efficient generation of radiation if the bunched electron beam is to be subsequently used as part of a radiation source.

[0022] The energy modulator may be operable to produce a periodic magnetic field arranged so as to guide the bunched electron beam along an oscillating path so as to produce the energy modulation within each bunch of the bunched electron beam at the first distance scale λι.

[0023] The energy modulator may be an optical undulator. Such an arrangement allows the undulator period to be reduced further than would be practicable for an undulator formed from permanent magnets. In turn, for a given electron beam energy, this reduces the scale of the energy modulation that can be achieved.

[0024] The first dispersive electron optics, the chirp module and the second dispersive electron optics may be arranged such that as a bunched electron beam exits the second dispersive electron optics it has a longitudinal electron density modulation at a second distance scale.

[0025] The first dispersive electron optics, the chirp module and the second dispersive electron optics may be arranged such that a ratio of an R₅6 value of the first dispersive electron optics to an Ra, value of the second dispersive electron optics is approximately equal to a compression factor imposed by the combination of the first dispersive electron optics, the first chirp cavity and the second dispersive electron optics.

[0026] According to a second aspect of the invention there is provided a radiation source comprising: an electron source operable to produce a bunched electron beam; the electron bunch modulator of any preceding clause arranged to receive the bunched electron beam, modulate a spatial density of at least one bunch of the bunched electron beam and output an output beam; and a laser operable to produce radiation of a first wavelength arranged to interact with the output beam so as to produce a beam of radiation of a second wavelength.

[0027] The radiation source of the second aspect produces radiation via inverse Compton scattering. [0028] The spatial electron density modulation achieved by the electron bunch modulator of the first aspect of the invention results in an increase in the power of the beam of radiation of the second wavelength. In particular, as explained above, it allows a relatively strong spatial electron density modulation to be achieved at relatively high frequencies. For example, it may allow a strong spatial electron density modulation at a wavelength in the EUV range (for example of the order of 13.5 nm), such that the radiation source of the second aspect of the invention can be an EUV radiation source.

[0029] The laser may comprise a second undulator arranged to receive the bunched electron beam output by the bunch compressor and wherein the radiation of the first wavelength is produced as the output radiation beam propagates through it. For such embodiments, the laser may be considered to be a free electron laser. The second undulator may comprise permanent magnets.

[0030] The laser may comprise a con ventional laser operable to emit radiation of the first wavelength.

[0031] The radiation source may further comprise a second undulator arranged to receive the bunched electron beam output by the bunch compressor and to guide it along a periodic path so as to produce a radiation beam. The second undulator may comprise permanent magnets.

[0032] The radiation source may further comprise mirrors disposed at opposed ends of the second undulator to form a resonant cavity.

[0033] At least a portion of the radiation produced as the output radiation beam propagates through the second undulator may be used by the optical undulator.

[0034] An interaction point at which the radiation of a first wavelength interacts with the output beam may be disposed between the electron bunch modulator and the second undulator. This can minimise the distance travelled by the output beam following bunch compression and before the interaction. In turn, this reduces the effect that space charge effects have on the spatial electron density modulation before the interaction, which can increase the power of the beam of radiation of the second wavelength.

[0035] The radiation source may further comprise a beam dump arranged to receive and at least partially absorb the bunched electron beam.

[0036] The radiation source may comprise an energy recovery linear accelerator.

[0037] According to a third aspect of the invention there is provided a radiation source comprising: an electron source operable to produce a bunched electron beam; the electron bunch modulator arranged to receive the bunched electron beam, modulate a spatial density of at least one bunch of the bunched electron beam and output an output beam; and a laser operable to produce radiation of a first wavelength arranged to interact with the output beam so as to produce a beam of radiation of a second wavelength; wherein the electron bunch modulator comprises: an energy modulator for receiving the bunched electron beam, the energy modulator operable to produce an energy modulation within the at least one bunch of the bunched electron beam at a first distance scale λι; and a bunch compressor arranged to receive the bunched electron beam output by the energy modulator and to spatially compress the at least one electron bunch so as to produce the spatial density of the at least one bunch of the bunched electron beam at a second distance scale λ?.

[0038] The radiation source of the third aspect produces radiation via inverse Compton scattering.

[0039] The third aspect provides a particularly efficient arrangement, as now discussed. The third aspect of the invention is advantageous since it allows spatial electron density modulation to be applied to a bunched electron beam at a second distance scale λ?, which is smaller than the first distance scale λι, as now explained. First an initial energy modulation is applied to each bunch by the energy modulator. Subsequently, the energy modulation is converted into a second, higher frequency spatial electron density modulation by the bunch compressor. This two stage process allows a higher frequency spatial electron density modulation to be applied to the electron bunches. For example, it may allow an energy modulation at a scale of the order of 200 nm to be converted into a spatial density modulation at a wavelength in the EUV range (for example of the order of 13.5 nm).

[0040] It is particularly beneficial that the energy modulation is applied to each electron bunch before the bunch compression stage that is provided by the bunch compressor. This is in contrast to, for example, a two stage spatial electron density modulation wherein the electron bunches are first compressed and then subsequently a spatial electron density modulation is applied. This is because the arrangement of the third aspect reduces the effects of space charges and therefore can result in a stronger spatial electron density modulation at relatively high frequencies. For example, it may allow a strong spatial electron density modulation at a wavelength in the EUV range (for example of the order of 13.5 nm).

[0041] The electron bunch modulator may comprise the electron bunch modulator of the first aspect of the invention.

[0042] The radiation source may further comprise a beam dump arranged to receive and at least partially absorb the bunched electron beam.

[0043] The radiation source may comprise an energy recovery linear accelerator.

[0044] According to a fourth aspect of the invention there is provided an electron bunch modulator comprising: an energy modulator for receiving the bunched electron beam, the energy modulator operable to produce an energy modulation within an electron bunch of the bunched electron beam at a first distance scale λρ and a bunch compressor arranged to receive the bunched electron beam output by the energy modulator and to spatially compress the electron bunch so as to produce a spatial density modulation within the electron bunch at a second distance scale λ?.

[0045] The electron bunch modulator of the fourth aspect may be used within the radiation source of the third aspect.

[0046] It will be appreciated that the energy modulator may be operable to produce an energy modulation within a plurality of electron bunches of the bunched electron beam at the first distance scale λ]. The bunch compressor may be arranged to spatially compress the electron bunch so as to produce a spatial density modulation within each of the plurality of electron bunches at the second distance scale λ-, [0047] According to a fifth aspect of the invention there is provided a radiation source comprising: an electron source operable to produce a bunched electron beam; an electron bunch modulator arranged to receive the bunched electron beam, modulate it and output an output beam, the electron bunch modulator comprising an optical undulator for receiving the bunched electron beam, the undulator operable to produce a periodic magnetic field arranged so as to guide the bunched electron beam along an oscillating path so as to produce an energy modulation within at least one bunch of the bunched electron beam; a laser operable to produce radiation of a first wavelength arranged to interact with the output beam so as to produce a beam of radiation of a second wavelength; and a second undulator arranged to receive the output beam by the electron bunch modulator and to guide it along a periodic path so as to produce a radiation beam and wherein at least a portion of the radiation produced as the output radiation beam propagates through the second undulator is used by the optical undulator, [0048] The radiation source of the fifth aspect produces radiation via inverse Compton scattering.

[0049] The fifth aspect provides a particularly efficient arrangement, as now discussed. The bunched radiation beam is used to interact with the radiation of the first wavelength to produce the beam of radiation of the second wavelength, which is the output of the radiation source. In addition, the bunched radiation beam is also used to provide radiation, via the second undulator, to provide power to the optical undulator. This optical undulator produces an energy modulation in the electron bunches, which in turn results in an increase in the power of the beam of radiation of the second wavelength.

[0050] The laser may comprise the second undulator such that the radiation of the first wavelength is produced as the output radiation beam propagates through the second undulator. For such embodiments, the laser may be considered to be a free electron laser. This is a particularly efficient arrangement since it does not require any additional, external lasers to drive the inverse Compton scattering.

[0051] The radiation source may further comprise a beam dump arranged to receive and at least partially absorb the bunched electron beam.

[0052] The radiation source may comprise an energy recovery linear accelerator.

[0053] According to a sixth aspect of the invention there is provided an electron bunch modulator for echo enabled harmonic generation comprising: a bunch compressor arranged to receive a bunched electron beam and to spatially compress the bunched electron beam; a first optical undulator arranged to receive the bunched electron beam from the bunch compressor and to guide the bunched electron beam along an oscillating path so as to produce a first spatial electron density modulation within an electron bunch of the bunched electron beam; first dispersive electron optics arranged to receive the bunched electron beam output by the first optical undulator, disperse the electron bunch and subsequently recombine it such that the distance travelled by an electron within the electron bunch is dependent on its energy; a second optical undulator arranged to receive the bunched electron beam from the first dispersive electron optics and to guide the bunched electron beam along an oscillating path so as to produce a second spatial electron density modulation within the electron bunch of the bunched electron beam; and second dispersive electron optics arranged to receive the bunched electron beam output by the second optical undulator, disperse the electron bunch and subsequently recombine it such that the distance travelled by an electron within the electron bunch is dependent on its energy.

[0054] It will be appreciated that the first optical undulator may be arranged to produce a first spatial electron density modulation within a plurality of electron bunches of the bunched electron beam. The first dispersive electron optics may be arranged to disperse each of the pluarlity of electron bunches and subsequently recombine them such that the distance travelled by an electron within a given electron bunch is dependent on its energy. The second optical undulator may be arranged to produce a second spatial electron density modulation within each of the plurality of electron bunches of the bunched electron beam. The second dispersive electron optics may be arranged to disperse each of the plurality of electron bunches and subsequently recombine them such that the distance travelled by an electron within a given electron bunch is dependent on its energy.

[0055] According to a seventh aspect of the invention there is provided a radiation source comprising: an electron source operable to produce a bunched electron beam; an electron bunch modulator arranged to receive the bunched electron beam, modulate a spatial density of the bunched electron beam and output it as an output beam; and a laser operable to produce radiation of a first wavelength arranged to interact with the output beam so as to produce a beam of radiation of a second wavelength, wherein the beam of radiation of the second wavelength comprises EUV radiation.

[0056] The radiation source of the seventh aspect produces radiation via inverse Compton scattering. [0057] The electron bunch modulator may comprise the electron bunch modulator of any one of the first, fourth or sixth aspects of the invention.

[0058] According to an eighth aspect of the invention there is provided a lithographic system comprising: the radiation source of the second, third, fifth or seventh aspect of the invention, which is operable to produce a radiation beam; and a lithographic apparatus arranged to receive at least a portion of the radiation beam.

[0059] Various aspects and features of the invention set out above or below may be combined with various other aspects and features of the invention as will be readily apparent to the skilled person.

BRIEF DESCRIPTION OF THE DRAWINGS [0060] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings, in which:

Figure 1 is a schematic illustration of a lithographic system according to an embodiment of the invention;

Figure 2 is a schematic illustration of a lithographic apparatus tha t may form part of the lithographic system of Figure I;

Figure 3 is a schematic illustration of an inverse Compton scattering radiation source;

Figure 4 is a schematic illustration of tin electron source that forms part of the radiation source of

Figure 3;

Figure 5 is a schematic illustration of a radiation source according to a first embodiment of the invention that may form part of the lithographic system of Figure 1;

Figures 6A to 6D show the longitudinal phase space distribution of electron bunches at four different locations within of the radiation source of Figure 5;

Figures 7A to 7D show the longitudinal electron density distribution of electron bunches at the same four different locations within of the radiation source of Figure 5;

Figure 8 is a schematic illustration of a first variant of the radiation source shown in Figure 5;

Figure 9 is a schematic illustration of a second variant of the radiation source shown in Figure 5;

Figure 10 is a schematic illustration of a third variant of the radiation source shown in Figure 5; and

Figure 11 is a schematic illustration of a radiation source according to a second embodiment of the invention that may form part of the lithographic system of Figure 1.

DETAILED DESCRIPTION [0061] Figure 1 shows a lithographic system LS according lo one embodiment of the invention. The lithographic system LS comprises a radiation source SO, a beam delivery system BDS and a plurality of lithographic apparatus LA„-LA_fl. The radiation source SO is configured to generate an extreme ultraviolet (EUV) radiation beam RB (which may be referred to as a main beam).

[0062] The beam delivery system BDS comprises beam splitting optics and may optionally also comprise additional beam expanding optics and/or beam shaping optics. The main radiation beam RB is split into a plurality of radiation beams B,,-B_n (which may be referred to as branch beams), each of which is directed to a different one of the lithographic apparatus LA_a-LA_n, by the beam delivery system BDS.

[0063] The beam delivery system BDS may comprise beam expanding optics that are arranged to increase a cross section of the main radiation beam RB and/or the branch radiation beams B_a-B_n· Advantageously, this decreases the heat load on mirrors downstream of the beam expanding optics, for example mirrors within the lithographic apparatus LA_a-LA_n. This may allow these mirrors to be of a lower specification, with less cooling, and therefore less expensive. Additionally or alternatively, it may allow the downstream mirrors to be nearer to normal incidence.

[0064] In an embodiment, the branch radiation beams B_a-B_n are each directed through a respective attenuator (not shown). Each attenuator may be arranged lo adjust the intensity of a respective branch radiation beam B_a-B_n before the branch radiation beam Ba-Bn passes into its corresponding lithographic apparatus LA_a-LA_n.

[0065] The radiation source SO, beam delivery system BDS and lithographic apparatus LA_a-LA„ may all be constructed and arranged such that they can be isolated from the external environment. A vacuum may be provided in at least part of the radiation source SO, beam delivery system BDS and lithographic apparatuses LA_a-LA_n so as to minimise the absorption of EUV radiation. Different parts of the lithographic system LS may be provided with vacuums at different pressures (i.e. held at different pressures which are below atmospheric pressure).

[0066] Referring to Figure 2, a lithographic apparatus LA_a comprises an illumination system IL, a support structure MT configured to support a patterning device MA (e.g. a mask), a projection system PS and a substrate table WT configured to support a substrate W. The illumination system IL is configured to condition the branch radiation beam B_a that is received by that lithographic apparatus LA_a before it is incident upon the patterning device MA. The projection system PS is configured to project the radiation beam B_a’ (now patterned by the patterning device MA) onto the substrate W. The substrate W may include previously formed patterns. Where this is the case, the lithographic apparatus aligns the patterned radiation beam B_a’ with a pattern previously formed on the substrate W.

[0067] The branch radiation beam B_a that is received by the lithographic apparatus LA_a passes into the illumination system IL from the beam delivery system BDS though an opening 8 in an enclosing structure of the illumination system IL. Optionally, the branch radiation beam B_a may be focused to form an intermediate focus at or near to the opening 8.

[0068] The illumination system IL may include a facetted field mirror device 10 and a facetted pupil mirror device 11. The faceted field mirror device 10 and faceted pupil mirror device 11 together provide the radiation beam B_a with a desired cross-sectional shape and a desired angular distribution. The radiation beam B_a passes from the illumination system IL and is incident upon the patterning device MA held by the support structure MT. The patterning device MA reflects and patterns the radiation beam to form a patterned beam B_a’. The illumination system IL may include other mirrors or devices in addition to or instead of the faceted field mirror device 10 and faceted pupil minor device 11. The illumination system IL may for example include an array of independently moveable mirrors. The independently moveable mirrors may for example measure less than 1 mm across. The independently moveable mirrors may for example be microelectromechanical systems (MEMS) devices.

[0069] Following redirection (e.g. reflection) from the patterning device MA the patterned radiation beam B_a’ enters the projection system PS. The projection system PS comprises a plurality of mirrors 13, 14 which are configured to project the radiation beam B_a’ onto a substrate W held by the substrate table WT. The projection system PS may apply a reduction factor to the radiation beam, forming an image with features that are smaller than corresponding features on the patterning device MA. A reduction factor of 4 may for example be applied. Although the projection system PS has two mirrors in Figure 2, the projection system may include any number of mirrors (e.g. six mirrors).

[0070] The lithographic apparatus LA_a is operable to impart a radiation beam B_a with a pattern in its cross-section and project the patterned radiation beam onto a target portion of a substrate thereby exposing a target portion of the substrate to the patterned radiation. The lithographic apparatus LA_a may, for example, be used in a scan mode, wherein the support structure MT and the substrate table WT are scanned synchronously while a pattern imparted to the radiation beam B_a’ is projected onto a substrate W (i.e. a dynamic exposure). The velocity and direction of the substrate table WT relative to the support structure MT may be determined by the demagnification and image reversal characteristics of the projection system PS. The patterned radiation beam B_a’ which is incident upon the substrate W may comprise a band of radiation. The band of radiation may be referred to as an exposure slit. During a scanning exposure, the movement of the substrate table WT and the support structure MT are such that the exposure slit travels over a target portion of substrate W in a scan direction, thereby exposing the target portion of the substrate W to patterned radiation. It will be appreciated that a dose of radiation to which a given location within the target portion of the substrate W is exposed depends on the power of the radiation beam B_a’ and the amount of time for which that location is exposed to radiation as the exposure slit is scanned over the location (the effect of the pattern is neglected in this instance). The term “target location” may be used to denote a location on the substrate which is exposed to radiation (and for which the dose of received radiation may be calculated).

[0071] Referring again to Figure 1, the radiation source SO is configured to generate an EUV radiation beam RB with sufficient power to supply each of the lithographic apparatus LA_a-LA_n.

[0072] hi an alternative embodiment, the lithographic system LS may comprise a single lithographic apparatus. For such embodiments, the single lithographic apparatus may be generally of the form of lithographic apparatus LA_a shown in Figure 2. For such single lithographic apparatus embodiments, beam delivery system BDS may not comprise beam splitting optics and may transport the main radiation beam RB output by the radiation source SO to the single lithographic apparatus. Optionally, the main radiation beam RB may be focused to form an intermediate focus at or near to the opening 8 (see Figure 2) of the lithographic apparatus.

[0073] Figure 3 is a schematic depiction of a radiation source 20 according to an embodiment of the invention that may form part of the lithographic system LS of Figure 1. The radiation source 20 uses inverse Compton scattering to generate a radiation beam B_out. The radiation source 20 comprises electron source 22 operable to produce a bunched electron beam E and a radiation source 24 operable to produce a radiation beam 26.

[0074] The bunches of the bunched electron beam E and the pulses of radiation beam 26 interact at an interaction point 28. In particular, at the interaction point 28, photons from the radiation beam 26 and electrons from electron beam E scatter inelastically, via inverse Compton scattering, to produce radiation beam B_out and outgoing electron beam E’. A photon from the radiation beam 26 may interact with an electron from electron beam E. It will be appreciated that not all of the photons from radiation beam 26 and electrons from electron beam E interact. Each photon from radiation beam 26 and electron from electron beam E that do interact results in a final state electron in outgoing electron beam E’ and a final state photon in radiation beam B_out. As used herein the term “initial state’’ generally refers to a particle (either a photon or electron) before the interaction (i.e. electrons in the bunched electron beam E and photons in the radiation beam 26) and the term “final state’’ generally refers to a particle (either a photon or electron) after the interaction (i.e. electrons in the outgoing electron beam E’ and photons in radiation beam B_out) [0075] It will be appreciated that in the centre of mass frame of each electron and photon pair, the outgoing final state electrons and photons will propagate away from the interaction point 28 in a range of directions. However, as shown schematically in Figure 3, the electrons in electron beam E have significantly higher momentum that the photons in radiation beam 26. Due to this large Lorentz boost factor from the center of mass frame, the outgoing electrons and photons are both highly collimated in the direction of the initial state electron beam E and therefore form electron beam E’ and radiation beam B_out respectively. In general, the electron beam E is highly relativistic, the initial radiation beam 26 comprises relatively low energy photons and the output radiation beam B_out comprises relatively high energy photons. [0076] The number of high-energy photons produced in the output radiation beam B_om is dependent on the density of the electrons in the bunches of electron beam E, the photon density of initial radiation beam 26, the repetition rate of the initial radiation beam 26 and the repetition rate of the bunched electron beam E.

[0077] As shown in Figure 3, optionally, the radiation source 20 may comprise electron optics 30 arranged to steer the final state electron beam E’ to a beam dump 32 or the like, which may be arranged to absorb the final stale electron beam E’.

[0078] As shown in Figure 4, the electron source 22 comprises an injector 34, a particle accelerator 36, and an electron bunch modulator 38.

[0079] The injector 34 is arranged to produce a bunched electron beam E and may, for example, comprise a thermionic cathode or a photo-cathode arranged to emit electrons and an accelerating electric field arranged to accelerate said electrons so as to form an electron beam. Said electric field may comprise a static electric field, an alternating electromagnetic field or a combination of both. In one embodiment, electrons may be initially accelerated away from a cathode through a static electric field and then may be subsequently accelerated further in a booster that uses alternating fields. The thermionic cathode or a photocathode may be operable to produce a bunched electron beam E (e.g. by emitting bursts of electrons from the cathode). Alternatively, the thermionic cathode or photo-cathode may be operable to produce a continuous electron beam and the injector 34 may further comprise an electron beam chopper arranged to convert the continuous electron beam into a bunched electron beam.

[0080] Electrons in the electron beam E are further accelerated by the particle accelerator 36. The particle accelerator 36 comprises one or more accelerator modules. Each of the accelerator modules may comprise a linear accelerator. In an example, each accelerator module may comprise a plurality of radio frequency cavities, which are axially spaced along a common axis, and one or more radio frequency power sources, which are operable to control the electromagnetic fields along the common axis as bunches of electrons pass between them so as to accelerate each bunch of electrons. The cavities may be superconducting radio frequency cavities. Advantageously, this allows: relatively large electromagnetic fields to be applied at high duty cycles; larger beam apertures, resulting in fewer energy losses due to wakefields; and for the fraction of radio frequency energy that is transmitted to the beam (as opposed to dissipated through the cavity walls) to be increased. Reducing the amount of energy dissipated through the cavity walls (for example by heat) is beneficial since this heat can cause physical damage to parts of the accelerator. The reduction in wakefield generation that is achieved by the larger beam apertures also reduces degradation of the quality of the electron beam as it passes through the accelerator. Alternatively, the cavities may be conventionally conducting (i.e. not superconducting), and may be formed from, for example, copper. Other types of linear accelerators may be used such as, for example, laser wake-field accelerators or inverse free electron laser accelerators.

[0081] The electron bunch modulator 38 is arranged to modulate the longitudinal electron density distribution of electron bunches in the electron beam E. In particular, the electron bunch modulator 38 is arranged to cause the electrons within each bunch to bunch together into microbunches, modulated at the wavelength of output radiation beam B_0llt.

[0082] In general, photons generated by the interaction between an electron from electron beam E and a photon from radiation beam 26 at interaction point 28 are incoherent and the intensity of the output radiation beam B_out is proportional to the number of electrons in each bunch of electron beam E. However, if the longitudinal electron density distribution of electron bunches in the electron beam E bunches is modulated at the wavelength of output radiation beam B_out so as to form microbunches then photons generated by the interaction between different electrons from electron beam E and radiation beam 26 are coherent and the intensity of the output radiation beam B_out is proportional to the square of number of electrons in each bunch of electron beam E. Therefore, the provision of the electron bunch modulator 38 can result in a significant increase in the gain of the radiation source 20.

[0083] It will be appreciated that Figure 4 is schematic and that in alternative embodiments the order of the particle accelerator 36 and the electron bunch modulator 38 may be reversed. Furthermore, although shown in Figure 4 as two separate components, the particle accelerator 36 and the electron bunch modulator 38 may be combined. For example, in some embodiments the particle accelerator 36 may comprise two or more accelerator modules and at least some parts of the electron bunch modulator 38 may be provided between said two or more accelerator modules.

[0084] Figure 5 is a schematic illustration of a specific embodiment of a radiation source 40 according to a first embodiment of the invention that is of the general form of the radiation source 20 shown in Figure 3 and which may form part of the lithographic system LS of Figure 1. Features which are common to both radiation source 40 of Figure 5 and radiation source 20 of Figures 3 and 4 share common reference numerals.

[0085] Radiation source 40 comprises an injector 34, a first particle accelerator module 36a, an energy modulator 42, a second particle accelerator module 36b, a first dispersive electron optics 44, a first chirp module 46, a second dispersive electron optics 48, a second chirp module 50, an undulator 52, a pair of mirrors 54a, 54b and a beam dump 32.

[0086] The injector 34 is arranged to produce a bunched electron beam. The first particle accelerator module 36a is arranged to receive the bunched electron beam and to accelerate it to 5 MeV.

[0087] The energy modulator 42 is arranged to receive the bunched electron beam from the first particle accelerator module 36a and to produce an energy modulation within each bunch of the bunched electron beam at a first distance scale λι. In the present embodiment, the energy modulator 42 comprises an optical undulator which is operable to produce a periodic magnetic field arranged so as to guide the bunched electron beam along an oscillating path so as to produce the energy modulation within each bunch of the bunched electron beam at a first distance scale λι, [0088] Generally, an undulator comprises at least one module suitable for guiding a relativistic electron beam E along a periodic path. Some undulator modules comprise a periodic magnet structure which may, for example, be formed from permanent magnets. Alternatively, some undulators are optical undulators wherein the periodic magnetic field is provided by a radiation beam.

[0089] The periodic magnetic field produced by an undulator module causes the electrons to follow an oscillating path about a central axis. As a result, within each undulator module, the electrons radiate electromagnetic radiation generally in the direction of the central axis of that undulator module. The path followed by the electrons may be sinusoidal and planar, with the electrons periodically traversing the central axis. Alternatively, the path may be helical, with the electrons rotating about the central axis.

[0090] As electrons move through an undulator module, they interact with the electric field of the radiation, exchanging energy with the radiation. In general the amount of energy exchanged between the electrons and the radiation will oscillate rapidly unless conditions are close to a resonance condition. Under resonance conditions, the interaction between the electrons and the radiation causes the electrons to bunch together into microbunches, modulated at the wavelength of radiation within the undulator, and coherent emission of radiation along the central axis is stimulated. For an optical undulator the resonance condition may be given by:

(1) where is the wavelength of the radiation, is the undulator period for the undulator module that the electrons are propagating through (i.e. the wavelength of the radiation that is providing the alternating magnetic field that guides the electrons) and γ is the Lorentz factor of the electrons. For an undulator formed from permanent magnets the resonance condition may be given by:

(2) where λ_α„ is the wavelength of the radiation, λ» is the undulator period for the undulator module that the electrons are propagating through, γ is the Lorentz factor of the electrons and K is the undulator parameter. A is dependent upon the geometry of the undulator: for a helical undulator that produces circularly polarized radiation A=1, for a planar undulator A-2, and for a helical undulator which produces elliptically polarized radiation (that is neither circularly polarized nor linearly polarized) 1<A<2. In practice, each bunch of electrons will have a spread of energies although this spread may be minimized as far as possible (by producing an electron beam E with low emittance). The undulator parameter K is typically approximately 1 and is given by:

_{K =} ,

2mnc (3) where q and m are the electric charge and mass of the electrons respectively, Bo is the amplitude of the periodic magnetic field, and c is the speed of light.

[0091] As previously explained, the energy modulator 42 comprises an optical undulator. The energy modulator 42 is provided with a first radiation beam 41, which provides the periodic magnetic field that causes the electrons to follow an oscillating path. The undulator period λ,, is therefore given by the wavelength of radiation beam 41, in this example it is 77 pm. The energy modulator 42 is further provided with a second radiation beam 43, which acts as seed radiation, which is amplified by stimulated emission within the energy modulator 42. hi this example, the wavelength of radiation beam 43 is 193 nm. This is a convenient wavelength since commercial lasers with a wavelength of 193 nm are available. Note that in order to ensure resonance, the energy of the electron beam entering the energy modulator 42 (or, equivalently, the Lorentz factor of the electron beam), the wavelength of the first radiation beam and the wavelength of the second radiation beam are constrained by Eq. (1). Therefore, for a fixed value of the wavelengths ol' the first radiation beam and the second radiation beam, the energy to which the first particle accelerator module 36a should accelerate the bunched electron beam is constrained by Eq. (1).

[0092] As a result of the interaction between the electron bunches and the second radiation beam 43 within the energy modulator 42, the energy of each bunch of the bunched electron beam is modulated at a first distance scale λι (see Figure 6A), which is equal to the wavelength of the second radiation beam 43. As a result of this energy modulation, the longitudinal phase space distribution of each bunch is generalij' sinusoidal.

[0093] The second particle accelerator module 36b is arranged to receive the bunched electron beam from the energy modulator 42 and to accelerate it to 19 MeV. The bunched electron beam is then guided to the interaction point 28 via the first dispersive electron optics 44, the first chirp module 46, the second dispersive electron optics 48, the second cliirp module 50, and the undulator 52.

[0094] The first dispersive electron optics 44 is of the form of an arc and is arranged to receive the bunched electron beam output by the second particle accelerator module 36b, disperse the electron bunches and subsequently recombine them such that the distance travelled by an electron within a given electron bunch is dependent on its energy.

[0095] The first chirp module 46 is operable to receive the bunched electron beam output by the first dispersive electron optics 44 and to apply a longitudinal phase space correlation to each electron bunch. As will be discussed further below, with reference to Figures 6A-6D, it will be appreciated that the longitudinal phase space distribution of the bunches as they leave the first dispersive electron optics 44 is modulated by the energy modulator 42 and that the first chirp module 46 imposes a longitudinal phase space correlation or chirp on top of this modulation.

[0096] The second dispersive electron optics 48 is generally of the form of a magnetic chicane and is arranged to receive the bunched electron beam output by the first chip module 46, disperse the electron bunches and subsequently recombine them such that the distance travelled by an electron within a given electron bunch is dependent on its energy. The first and second electron optics 44,48 therefore each cause a change in the longitudinal position of at least some of the electrons within each bunch relative to the centre of the bunch. The first and second electron optics 44, 48 may each be considered to apply a R56 transformation, as will be discussed further below. In particular, the second dispersive electron optics 48 is arranged to apply such a transformation in an opposite sense to the first dispersive electron optics 44 (i.e. the R56 value of the second dispersive optics 48 has an opposite sign to that of the first dispersive optics 44). For example, the first electron optics 44 may apply a positive R.% and the second electron optics 48 may apply a negative R56.

[0097] The second chirp module 50 is operable to receive the bunched electron beam output by the second dispersive electron optics 44 and to apply a longitudinal phase space correlation to each electron bunch. In particular, the second chirp module 50 is arranged to apply a longitudinal phase space correlation to each electron bunch in an opposite sense to the first chirp module 46 such that the phase space distribution of the electron bunches exiting the second chirp module 50 has substantially no longitudinal phase space correlation.

[0098] The radiation source 40 also comprises a radiation source that is operable to produce a radiation beam 26 which interacts with the bunches of the bunched electron beam at the interaction point 28. This radiation source (referred to as radiation source 24 in Figure 3) is of the form of a free electron laser and comprises an undulator 52. The radiation source further comprises and a pair of mirrors 54a, 54b, the undulator 52 being formed between the pair of mirrors 54a, 54b, which form an optical cavity.

[0099] The undulator is a linear' undulator formed from permanent magnets and has an undulator period λ„ of 110 mm. As the bunched electron beam passes through the undulator 52, it generates the radiation beam 26.

[00100] A portion of the radiation beam 26 passes through one of the mirrors 54a, 54b, exits the cavity and is supplied to the energy modulator 42 as the first radiation beam 41.

[00101] The beam dump 32 may comprise a sufficient quantity of material to absorb the electron beam E. The material may have a threshold energy for induction of radioactivity. The threshold energy for induction of radioactivity may be referred to as the activation energy. Electrons entering the dump 32 with an energy below the threshold energy may produce only gamma ray showers but will not induce any significant level of radioactivity. The material may have a high threshold energy for induction of radioactivity by electron impact. For example, the beam dump may comprise aluminium (Al), which has a threshold energy of around 17 MeV. It may be desirable to reduce the energy of electrons in the electron beam E before they enter the dump 32. This removes, or at least reduces, the need to remove and dispose of radioactive waste from the dump 32. This is advantageous since the removal of radioactive waste may require the radiation source 40 to be shut down periodically and the disposal of radioactive waste can be costly and can have serious environmental implications.

[00102] In combination, the energy modulator 42, the first dispersive electron optics 44, the first chirp module 46 and the second dispersive electron optics 48 may be considered to form the electron bunch modulator 38 shown in Figure 4 and described above, as now explained with reference to Figures 6A-6D and Figures 7A-7B.

[00103] An electron beam may be characterized by a six-dimensional phase space comprising three spatial position coordinates (e.g. x, y and z) and the rate of change of each of those spatial coordinates i.e. the velocities in each of those directions. At a given point in time each electron within an electron bunch will occupy a position in this phase space. Similarly, at any given point in time a bunch of electrons may be described by a density distribution within this phase space.

[00104] In the following, it will be appreciated that, unless otherwise stated, the term “longitudinal·’ refers to a direction parallel to a direction along with a bunched electron beam propagates and that the term “transverse” may refer to a direction generally perpendicular to the direction along with the bunched electron beam propagates. In the following, unless otherwise stated, for bunches of electrons that generally propagate in a given direction the z direction will be used to describe the longitudinal direction of the bunches (i.e. the direction in which the bunch is generally moving) and the x and y directions will be used to define the transverse directions (i.e. the plane which is perpendicular to the direction of the bunch). The phase space may be split or projected into different planes (or hyperplanes) within the six-dimensional phase space. For bunches of electrons which generally propagate in a given direction it may be convenient to project the phase space into a transverse phase space and a longitudinal phase space. The transverse phase space describes the transverse size of the bunches (i.e. the x and y coordinates) and the divergence of the bunches (or, equivalently, the momentum in the x and y directions). The longitudinal phase space describes the longitudinal position within the bunch (the z coordinate) and the velocity, or equivalently momentum, in the longitudinal direction. Note that for highly relativistic electron bunches, the momentum of each electron is equal to its energy (in natural units where the speed of light equals 1). Furthermore, for a well collimated bunch of electrons the velocity or momentum of each electron in the transverse plane is negligible compared to the momentum of that electron in the longitudinal direction. Therefore, for such bunches, the momentum of each electron in the longitudinal direction is equivalent to its energy. Note that the longitudinal and transverse phase spaces are generally coupled to each other by electron optics within electron beam transport systems.

[00105] It will be appreciated that throughout this specification, the term “correlated energy spread” relates to a spread of energies for an electron bunch that has a longitudinal phase space correlation (i.e. a correlation between the energy of an electron and its longitudinal position with the bunch). By convention, a longitudinal phase space correlation of an electron bunch may be described as a positive correlation if electrons towards the front of the bunch generally have greater energy than electrons towards the rear of the bunch. Such a positive longitudinal phase space correlation may be referred to as a positive chirp. Similarly, by convention, a longitudinal phase space correlation of an electron bunch may be described as a negative correlation if electrons towards the front of the bunch generally have lower energy than electrons towards the rear of the bunch. Such a negative longitudinal phase space correlation may be referred to as a negative chirp.

[00106] The position of an electron within an electron bunch in phase space may be represented by a six component vector. In one basis, the components of this vector may be (x, x’, y, y’, z, 5p), where x, y and z are the x, y and z positions respectively of the electron relative to the centre of mass of the electron bunch, x’ and y’ are the velocities in the x and y directions respectively and δρ is the relative longitudinal momentum (i.e. the difference between the longitudinal momentum of an electron and the average longitudinal momentum of the bunch).

[00107] In general, as an electron bunch propagates through an electron optic, individual electrons within the electron bunch will move from one position in phase space to another. As a result, in general, the density distribution of the bunch in phase space will change. Each phase space co-ordinate of an electron as it exits the electron optic can, at least to a first order approximation, be expressed as a linear combination of each of the (six) phase space co-ordinates of the electron as it enters the electron optic. Such a first order or linear approximation may only be appropriate for some electron optics and a more accurate model may take into account higher order terms. For such linear electron optics, the phase space position vector (whose components are the six phase space co-ordinates) of an electron as it exits the election optic can be expressed as the product of a 6x6 transport matrix and the phase space position vector of the electron as it enters the electron optic. The off-diagonal elements of this transport matrix quantify how one component of the initial phase space (as the electron bunch enters the electron optic) is converted into, or changes, another component of the final phase space (as the electron bunch exits the electron optic). Two special cases are now discussed.

[00108] A dispersive electron optic (for example a magnetic arc or a magnetic chicane) may be arranged to receive a bunched electron beam, disperse the electron bunches and subsequently recombine them such that the distance travelled by an electron within a given electron bunch is dependent on its energy. Such a dispersive electron optic has a non zero off-diagonal element, Rs.>. which maps the relative longitudinal momentum δρ onto the longitudinal position z. Such a dispersive electron optic may be considered to apply an Rs6 transformation. If an electron bunch passes through such a dispersive electron optic, the longitudinal position z’ of an electron (relative to the centre of mass of the electron bunch) as the bunch exits the dispersive electron optic is given by:

(4) where z and δρ are, respectively, the longitudinal position of an electron (relative to the centre of mass of the electron bunch) and the relative longitudinal momentum of the electron as the bunch enters the dispersive electron optic. For a positive R,% value, higher energy electrons travel a shorter distance than lower energy electrons, whereas for a negative Rse value, higher energy electrons travel a longer distance than lower energy electrons.

[00109] A chirp cavity may be arranged to receive a bunched electron beam and to change a correlation between the longitudinal position and relative longitudinal momentum electrons in the bunch. Such a chirp cavity has a non-zero off-diagonal element, Rös, often referred to as h which maps the longitudinal position z onto the relative longitudinal momentum δρ. If an electron bunch passes through such a dispersive electron optic, the relative longitudinal momentum δρ’ of an electron as the bunch exits the dispersive electron optic is given by:

(5) where z and δρ are, respectively, the longitudinal position of an electron (relative to the centre of mass of the electron bunch) and the relative longitudinal momentum of the electron as the bunch enters the dispersive electron optic. A positive h (or Rss) value results in a positive chirp, whereas a negative h (or Res) value results in a negative chirp.

[00110] Figures 6A to 6D show a schematic representation of the longitudinal phase space distribution of the electron bunches at four different parts of the radiation source 40 shown in Figure 5. In general, a longitudinal phase space distribution is a two-dimensional distribution of energy and longitudinal position. The schematic representations of longitudinal phase space distributions shown in Figures 6A to 6D only show the shape of the of the electron bunches in this longitudinal phase space, i.e. the region of longitudinal phase space defined by the edge of the electron bunches. It will be appreciated that the electron bunches do not have a sharp and clearly defined edge and therefore the edge of the electron bunch (as schematically shown in Figures 6A to 6D) may be defined as the locus of points where the electron density drops below a threshold value.

[00111] The longitudinal phase space distributions shown in Figures 6A to 6D show the relative longitudinal momentum δρ (i.e. the difference between the longitudinal momentum of an electron and the average longitudinal momentum of the bunch) against the longitudinal position within the bunch (the z coordinate).

[00112] Figures 7A to 7D show the longitudinal electron density distributions of electron bunches at four different parts of the radiation source 40 shown in Figure 5. In particular, each of Figures 7A to 7D shows the longitudinal electron density distribution of electron bunches at the same part of the radiation source 40 shown in Figures 6A-6D respectively. The longitudinal electron density distributions are one-dimensional distributions, which show how the electrons are distributed within the bunch in the longitudinal direction.

[00113] Figure 6A shows a schematic representation of the longitudinal phase space distribution 60 of the electron bunches as they exit the energy modulator 42. Figure 7A shows the longitudinal electron density distribution 61 ofthe electron bunches as they exit the energy modulator 42. Figure 6B shows a schematic representation of the longitudinal phase space distribution 62 for electron bunches after the first dispersive electron optics 44. Figure 7B shows the longitudinal electron density distribution 63 of the electron bunches after the first dispersive electron optics 44. Figure 6C shows a schematic representation of the longitudinal phase space distribution 64 for electron bunches after the first chirp module 46. Figure 7C shows the longitudinal electron density distribution 65 of the electron bunches after the first chirp module 46. Figure 6D shows a schematic representation of the longitudinal phase space distribution 66 for electron bunches after the second dispersive electron optics 48. Figure 7D shows the longitudinal electron density distribution 67 of the electron bunches after the second dispersive electron optics 48.

[00114] The radiation source 40 is advantageous since it allows a spatial electron density modulation to be applied to the bunched electron beam at a second distance scale λι, which is smaller than the first distance scale λ], as now explained.

[00115] First an initial energy modulation is applied to each bunch by the energy modulator 42. As a result of this energy modulation, the longitudinal phase space distribution 60 of each bunch is generally sinusoidal. The relative energy or momentum of the electrons within the bunch oscillates as a function of longitudinal position within the bunch. That is, the longitudinal phase space distribution 60 of each bunch oscillates about a line which is aligned with the longitudinal position within the bunch. As can be seen from Figure 7A, as the electron bunches exit the energy modulator 42 there is substantially no longitudinal electron density modulation and the longitudinal electron density distribution 61 of the electron bunches is generally flat.

[00116] Subsequently, the energy modulation is converted into a second, higher frequency spatial electron density modulation by the first dispersive electron optics 44, the first chirp module 46 and the second dispersive electron optics 48 in combination. This two stage compression allows a higher frequency spatial electron density modulation to be applied to the electron bunches.

[00117] First the first dispersive electron optics 44 skews the longitudinal phase space distribution of the bunches; next the first chirp module 46 stretches the longitudinal phase space distribution of the bunches in a direction that is inclined at a non zero angle relative to the longitudinal direction (z direction); and then the second dispersive electron optics 48 compresses the longitudinal phase space distribution of the bunches so as to produce the density modulation. The net result of this skewing, stretching and compression of the longitudinal phase space distribution of the bunches results in the second, higher frequency energy and spatial electron density modulation.

[00118] In combination, the first dispersive electron optics 44, the first chirp module 46 and the second dispersive electron optics 48 may be considered to be a bunch compressor. In particular, the first dispersive electron optics 44, the first chirp module 46 and the second dispersive electron optics 48 may be considered to be a bunch compressor which is arranged to achieve longitudinal compression of the bunches whilst maintaining the modulation of longitudinal phase space distribution of the bunches that is created by the energy modulator 42. hi this way, the first dispersive electron optics 44, the first chirp module 46 and the second dispersive electron optics 48 compress the bunches so as to create an energy modulation that is of a smaller scale λζ than the scale λι of the modulation imposed by the energy modulator 42. The first chirp module 46 imposes a correlation on the longitudinal phase space distribution of the bunches. The spatial compression of the bunches is achieved by the second dispersive electron optics 48, which exploits this longitudinal phase space distribution correlation to compress the bunches. Since the longitudinal phase space distribution of the bunches has been modulated (by the energy modulator 42), in addition to spatially compressing the bunches, the second dispersive electron optics 48 also skews the phase space distribution of the bunches. The first dispersive electron optics 44 is arranged to “pre-skew” the phase space distribution of the bunches in an opposite sense such that after the second dispersive electron optics 48 the energy modulation is preserved (although reduced in scale).

[00119] Within the first dispersive electron optics, the highest energy electrons within each bunch move relative to a centre of mass of the bunch by a distance greater than a quarter of the first distance scale λι/4. As can be seen in Figure 6B, with such an arrangement, the longitudinal phase space distribution 62 of each bunch is skewed such that each maximum 62a (also referred to herein as a peak) of the distribution moves past at least one adjacent minimum 62b (also referred to herein as a trough). For clarity, only three maxima 62a and three minima 62b are labelled in Figure 6B.

[00120] As a result of the energy modulation at the first distance scale λι, the density of the bunches could also be modulated at the first distance scale λι. This could be achieved by propagation of the bunches over a sufficiently large distance and/or by a suitable dispersive electron optics that is arranged disperse the electron bunches and subsequently recombine them such the highest energy elections within each bunch move relative to a centre of mass of the bunch by a distance of the order of a quarter of the first distance scale λι/4. Such dispersive electron optics would cause electrons with a positive relative longitudinal momentum 5p to move relative to the centre of mass of the bunch in one direction and electrons with a negative relative longitudinal momentum δρ to move relative to the centre of mass of the bunch in an opposite direction. For a sinusoidal oscillation, each peak and trough is separated by half of the distance scale of the oscillation (see, for example, Figure 6A). Therefore, an arrangement that causes the highest energy electrons within each bunch move relative to a centre of mass of the bunch by a distance of the order of a quarter of the first distance scale λι/4 would result in each peak moving such that it is at approximately the same longitudinal position as an adjacent trough, resulting in a density modulation. W'ith such an arrangement, the energy modulation remains but has been skewed by a sufficient amount lo create a density modulation. However, in contrast to this, the first dispersive electron optics 44 is arranged such that the highest energy electrons within each bunch move relative to a centre of mass of the bunch by a distance greater than a quarter of the first distance scale λι/4 (see Figure 6B). As a result, any such density modulations are washed out by the first dispersive electron optics 44. Therefore, as can be seen from Figure 7B, as the electron bunches exit the first dispersive electron optics 44 there is substantially no longitudinal electron density modulation and the longitudinal electron density distribution 63 of the electron bunches is generally Hat.

[00121] The first chirp module 46 is operable to produce a generally linear longitudinal phase space correlation in each electron bunch. It will be appreciated that the longitudinal phase space distribution 62 of the bunches as they leave the first dispersive electron optics 44 has already been modulated by the energy modulator 42 and that the first chirp module 46 imposes a longitudinal phase space correlation or chirp on top of this modulation so as to produce the longitudinal phase space distribution 64 shown in Figure 6C. As shown in Figure 6C, the first chirp module 46 has the effect of stretching the longitudinal phase space distribution of the bunches in a direction that is inclined at a non-zero angle relative to the longitudinal direction (z direction). As a result, adjacent maxima or peaks 64a of the longitudinal phase space distribution 64 are at different relative longitudinal momentum δρ values and, similarly, adjacent minima or troughs 64b of the longitudinal phase space distribution 64 are at different relative longitudinal momentum δρ values. For clarity, only three maxima 64a and three minima 64b are labelled in Figure 6C. [00122] As can be seen from Figure 7C, as the electron bunches exit the first chirp module 46 there is substantially no longitudinal electron density modulation and the longitudinal electron density distribution 65 of the electron bunches is generally flat.

[00123] The second dispersive electron optics 48 is arranged such that the distance travelled by an electron within a given electron bunch in the second dispersive electron optics 48 is dependent on its energy in an opposite sense to the first dispersive electron optics 44. That is, whereas in the first dispersive electron optics 44 higher energy electrons travel a shorter distance than lower energy electrons, within the second dispersive electron optics 48 higher energy electrons travel a greater distance than lower energy electrons. It will be appreciated that, in alternative embodiments, within the first dispersive electron optics 44 higher energy electrons may travel a greater distance than lower energy electrons, and within the second dispersive electron optics 48 higher energy electrons may travel a shorter distance than lower energy electrons.

[00124] As a result, the second dispersive electron optics 48 unskews the longitudinal phase space distribution of the bunches such that the longitudinal phase space distribution 66 of the bunches is generally sinusoidal, having a second distance scale λ?. Although as the bunches exit the second dispersive electron optics 48 the longitudinal phase space distribution 66 of the bunches is generally sinusoidal, it does have a sufficient amount of residual skew to create a density modulation. As discussed above, it will be appreciated that a sufficient amount of skew to create a density modulation is a skewing of the phase space distribution such that each peak is at approximately the same longitudinal position as an adjacent trough. It will be further appreciated that an alternative way of expressing this is that a sufficient amount of skew to create a density modulation is a skewing of the phase space distribution such that each peak is at approximately the same longitudinal position as a zero point crossing of the distribution. It can be seen from Figure 6D that as the bunches exit the second dispersive electron optics 48, although the longitudinal phase space distribution 66 ofthe bunches is generally sinusoidal, it is skewed such that each ofthe maxima or peaks 66a is at approximately the same longitudinal position as an adjacent minima or trough 66b. For clarity, only three peaks 66a and three troughs 66b are labelled in Figure 6D. For example, as can be seen from Figure 6D one of the peaks (labelled 66a’) is at approximately the same longitudinal position as an adjacent trough (labelled 66b’), both the peak 66a’ and the trough 66b’ being approximately at a longitudinal position of z=0.

[00125] As can be seen from Figure 7D, as the electron bunches exit the second dispersive electron optics 48 there is a longitudinal electron density modulation. In particular, the longitudinal electron density distribution 67 of the electron bunches as they exit the second dispersive electron optics 48 comprises a plurality of regularly spaced peaks 67a. For clarity, only three peaks 67a are labelled in Figure 7D. The longitudinal spacing between each pair of adjacent peaks 67a is the second distance scale X2. Each peak 67a in the longitudinal electron density distribution 67 of the electron bunches as they exit the second dispersive election optics 48 corresponds to a peak 66a and trough 66b of die longitudinal phase space distribution 66 that are at substantially the same longitudinal position. For example, as can be seen from Figures 6D and 7D, one of the peaks (labelled 67a’) in the longitudinal electron density distribution 67 is at approximately the same longitudinal position as the peak 66a’ and trough 66b’ in the longitudinal phase space distribution 66 that are approximately at a longitudinal position of z=0.

[00126] To achieve a sufficient skewing of the longitudinal phase space distribution 66 of the bunches so as to create a density modulation as shown in Figure 7D, the relative strengths of the first and second dispersive electron optics 44, 48 are generally matched such that die phase space distribution 66 of the bunches as they exit the second dispersive electron optics 48 has a sufficient amount of residual skew to create a density modulation. This may be achieved by ensuring that the ratio of the R.·^ value of the first dispersive electron optics 44 to the Rs6 value of the second dispersive electron optics 48 is approximately equal to the compression factor imposed by the combination of the first dispersive electron optics 44, the first chirp cavity 46 and the second dispersive electron optics 48, as now described.

[00127] In order for there to be no net skewing of the longitudinal phase space distribution by the first dispersive electron optics 44, the first chirp cavity 46 and the second dispersive electron optics 48, the amount of skewing of the phase space distribution by the second dispersive electron optics 48 should cancel the amount of skewing of the phase space distribu tion by the first dispersi ve electron optics 44. The amount by which the longitudinal phase space distribution is skewed by the first dispersive electron optics 44 is proportional to the Rs<, value of the first dispersive electron optics 44 and the variation in the energy within the bunches as they enter the first dispersive electron optics 44 (i.e. the amplitude of the energy modulation created by the energy modulator 42). The amount by which the longitudinal phase space distribution is skewed by the second dispersive electron optics 48 is proportional to the R56 value of the second dispersive electron optics 48 and the variation in the energy within the bunches as they enter the second dispersive electron optics 48. In turn, the variation in the energy within the bunches as they enter the second dispersive electron optics 48 is dependent on the amplitude of the energy modulation created by the energy modulator and the chirp value of the first chirp cavity 46.

[00128] In order for there to be no net skewing of the longitudinal phase space distribution by the first dispersive electron optics 44, the first chirp cavity 46 and the second dispersive electron optics 48, the net change in the longitudinal position of an electron within a bunch should be independent of its energy (or, equivalently, its relative longitudinal momentum δρ) and should be linearly proportional to its initial longitudinal position within the bunch. In order to achieve this, the parameters of the first dispersive electron optics 44, the first chirp cavity 46 and the second dispersive electron optics 48 should be tuned such that:

where R^(bs6 is the Rs(1 value of the first dispersive electron optics 44, h is the chirp value of the first chirp cavity 46, and R^<2,56 is the R.v> value of the second dispersive electron optics 48. When the parameters of the first dispersive electron optics 44, the first chirp cavity 46 and the second dispersive electron optics 48 are tuned to satisfy Eq. (6), the compression factor C of the bunch compressor formed by the first dispersive electron optics 44, the first chirp module 46 and the second dispersive electron optics 48 (which is given by the first distance scale λι to the second distance scale λ2) is given by:

= ¹

Λ 1 + (7)

From Eqs. (6) and (7), it can be seen that in order for there to be no net skewing of the longitudinal phase space distribution by the first dispersive electron optics 44, the first chirp cavity 46 and the second dispersive electron optics 48 the ratio of the Rv, value of the first dispersive electron optics 44 to the Rv, value of the second dispersive electron optics 48 should be equal to the magnitude of the net compression factor C imposed by these components (which is given by the first distance scale λι to the second distance scale λ₂).

[00129] A possible design method for selecting the parameters of the first dispersive electron optics 44, the first chirp cavity 46 and the second dispersive electron optics 48 is now described.

[00130] First, the R><> value of the second dispersive electron optics 48 and the chirp value h of the first chirp cavity 46 are chosen in combination to achieve a desired compression factor C. As can be seen from Eq. 67), this constrains the product of these two parameters. In turn, there may be additional constraints on these two parameters, since there may only be a practicably achievable range for each of the R56 value of the second dispersive electron optics 48 and the chirp value h of the first chirp cavity 46. For example, the practicably achievable chirp value h of the first chirp cavity 46 may be limited to be less than a maximum value and the R.% value of the second dispersive electron optics 48 may be chosen, in combination with this maximum value (or a lower value of the chirp value h) to achieve the desired compression factor C.

[00131] Next, the R v, value of the first dispersive electron optics 44 is chosen so as to achieve a sufficient net skewing of the longitudinal phase space distribution of the bunches as they exit the second dispersive electron optics 44 so as to create a density modulation (as shown in Figure 7D). This may be achieved by ensuring that the ratio of the R.% value of the first dispersive electron optics 44 to the R56 value of the second dispersive electron optics 48 is approximately equal to the compression factor C imposed by the combination of the first dispersive electron optics 44, the first chirp cavity 46 and the second dispersive electron optics 48. As described, exactly meeting this condition would result in no net skewing of the longitudinal phase space distribution. Therefore, in practice the R56 value of the first dispersive electron optics 44 is slightly detuned (such that Eq. (6) is no longer satisfied) to obtain the desired residual skew. It will be appreciated that in practice, particularly for large compression factors, the amount by which the longitudinal phase space distribution is skewed by the first dispersive electron optics 44 and the amount by which the longitudinal phase space distribution is skewed (in the opposite sense ) by the second dispersive electron optics 48 may be significantly larger than the desired net residual skew. For such arrangements, the amount by which the Rss value of the first dispersive electron optics 44 is detuned such that Eq. (6) is no longer satisfied is relatively small and, therefore, Eq. (6) is still approximately satisfied.

[00132] Note that although the longitudinal phase space distribution 66 of the bunches is generally sinusoidal, it retains some residual positive phase space correlation or chirp. The second chirp module 50 is arranged to remove this positive chirp so as to reduce the spread of energies within each bunch. This may increase the efficiency of the radiation source 40.

[00133] Note that the first chirp module 46 being disposed between the first and second dispersive electron optics 44, 48, in combination with the relative strengths of the R56 values of the first and second dispersive electron optics 44, 48 ensures that the scale /2 of the modulation after the second dispersive electron optics 48 is different from the scale λι of the modulation after the energy modulator 42. That is, this arrangement allows the energy modulation to be compressed to a different scale and skewed by a sufficient amount so as to create a density modulation at a scale λ? which is different from the scale λι of the energy modulation after the energy modulator 42.

[00134] It will be appreciated that the specific values of the electron beam energies and radiation beam energies described above in relation to the radiation source 40 shown in Figure 5 are merely examples. In particular, the electron beam that interacts at the interaction point 28 may have an energy other than 19 MeV and the radiation beam 26 that interacts with this electron beam may have a wavelength other than 77 pm. Furthermore, the electron beam that enters the energy modulator 42 may have an energy other than 5 MeV and, similarly, the first and second radiation beams 41, 43 that are provided to the energy modulator may have any wavelength, subject to the energy of the electron beam entering the energy modulator 42, the wavelength of the first radiation beam 41 and the wavelength of the second radiation beam 43 generally satisfying the resonance (see Eq. (1)).

[00135] Furthermore, it will be appreciated that the first and second dispersive electron optics 44, 48 may take different forms to those shown in the radiation source 40 of Figure 5. For example, in the radiation source 40 of Figure 5, the first dispersive electron optics 44 is an arc and the second dispersive electron optics 48 is a chicane. It will be appreciated that, in alternative embodiments the first and second dispersive electron optics 44, 48 may take any form provided that the second dispersive electron optics 48 is arranged such that the distance travelled by an electron within a given electron bunch in the second dispersive electron optics 48 is dependent on its energy in an opposite sense to the first dispersive electron optics 44. Either or both of the first and second dispersive electron optics 44, 48 may comprise an arc, a chicane or some other combination of dispersive electron optics or magnets.

[00136] Figure 8 is a schematic illustration of a first variant of the radiation source shown in Figure 5. The radiation source 70 shown in Figure 8 shares many elements in common with the radiation source 40 shown in Figure 5. In the following only the differences will be described in full and corresponding elements of radiation source 70 shown in Figure 8 and the radiation source 40 shown in Figure 5 which are substantially the same share common reference numerals.

[00137] In radiation source 70, the energy of electrons in the electron beam is reduced before they enter the dump 32. This is achieved by operating the second particle accelerator module 36b as an energy recovering linear accelerator (ERL), as now described.

[00138] Electron beam optics 72 are provided to transport the bunched electron beam from the interaction point 28 to the entrance of the second particle accelerator module 36b.

[00139] This electron beam which is transported from the interaction point 28 is decelerated by passing the electrons back through the second particle accelerator module 36b with a phase difference of approximately 180 degrees relative to the electron beam produced by the injector 34. The RF fields in the second particle accelerator module 36b therefore serve to decelerate the electrons which are output from the interaction point 28 and to accelerate electrons output from the injector 34. As the electrons decelerate in the second particle accelerator module 36b some of their energy is transferred to the RF fields in the second particle accelerator module 36b. Energy from the decelerating electrons is therefore recovered by the second particle accelerator module 36b and may be used to accelerate the electron beam output from the injector 34. Such an arrangement is known as an energy recovering linear accelerator. Arranging the phases such that the bunches of decelerating electrons enter the second particle accelerator module 36b approximately 180° ou t of phase with the accelerating electrons ensures that the energy recovered by second particle accelerator module 36b is approximately equal to the amount of energy required to accelerate the accelerating electrons. However, in practice, the phase difference between the accelerating and decelerating electron bunches may not be 180° and may, for example, be up to of the order of 10° above or below 180° (i.e. between 170° and 190°). There may be some advantage to such a small offset from a phase difference of 180°.

[00140] The radiation source 70 also comprises a merger 74 and a splitter 76. The merger 74 is provided proximate to an entrance to the second particle accelerator module 36b. The merger 74 is arranged to alternately direct bunches from the injector 34 and the electron optics 72 towards the entrance to the second particle accelerator module 36b. The merger 74 may, for example, comprise a plurality of dipole magnets that are arranged to receive bunches of electrons from both the injector 34 and the electron optics 72 along different initial trajectories and to exploit the difference in the energies of the electron bunches so as to bend their trajectories by different amounts such that electron bunches from both the electron optics 72 and the injector 34 pass into the second particle accelerator module 36b along substantially the same trajectory. [00141] The splitter 76 is provided proximate to an exit of the second particle accelerator module 36b. The splitter 76 is arranged to direct bunches of electrons exiting the second particle accelerator module 36b alternatively towards the first dispersive electron optics 44 and the beam dump 32. In particular, the splitter 76 is arranged to direct those bunches which have been accelerated by the second particle accelerator module 36b (i.e. their energy has been increased by the second particle accelerator module 36b) towaids the first dispersive electron optics 44 and to direct electron bunches that had been decelerated by the second particle accelerator module 36b (i.e. their energy has been reduced by the second particle accelerator module 36b) towards the beam dump 32. The splitter 76 may comprise a plurality of dipole magnets that are arranged to receive bunches of electrons from the second particle accelerator module 36b and to bend their trajectories by different amounts by exploiting the difference in the energies of the electron bunches.

[00142] Figure 9 is a schematic illustration of a second variant of the radiation source shown in Figure 5. The radiation source 80 shown in Figure 9 shares many elements in common with the radiation source 40 shown in Figure 5. In the following only the differences will be described in full and corresponding elements of radiation source 80 shown in Figure 9 and the radiation source 40 shown in Figure 5 which are substantially the same share common reference numerals.

[00143] The difference between the two embodiments is that the interaction point 28 is disposed adjacent to the second chirp module 50. This is in contrast to the radiation source 40 of Figure 5 wherein the undulator 52 is disposed between the interaction point 28 and the second chirp module 50.

[00144] The arrangement of the radiation source 80 shown in Figure 9 can mini mise the distance travelled by the bunched electron beam following bunch compression by the second dispersive optics 48 and the interaction point 28. In turn, this reduces the effect that space charge effects have on the spatial electron density modulation before the interaction, which can increase the power of the beam of radiation of the second wavelength that is generated via inverse Compton scattering.

[00145] Figure 10 is a schematic illustration of a third variant of the radiation source shown in Figure 5. The radiation source 90 shown in Figure 10 shares many elements in common with the radiation source 40 shown in Figure 5. In the following only the differences will be described in full and corresponding elements of radiation source 90 shown in Figure 10 and the radiation source 40 shown in Figure 5 which are substantially the same share common reference numerals.

[00146] The radiation source 90 comprises a single particle accelerator module 36 that is arranged to receive the bunched electron beam output by the injector 34 and to accelerate it to 7 MeV. This is in contrast to the radiation source 40 of Figure 5 wherein two separate particle accelerator modules 36a, 36b are provided, with the energy modulator 42 disposed between.

[00147] In radiation source 90, the radiation beam 26 which the electron beam interacts with via inverse Compton scattering has a wavelength of 10 pm and is provided by an external laser (not shown). As with the radiation source 40 of Figure 5 a pair of mirrors 54a, 54b are provided on opposite sides of the interaction point 28, said pair of mirrors 54a, 54b forming an optical cavity.

[00148] The radiation source 90 shown in Figure 10 also comprises an undulator 92 arranged to receive the bunched radiation beam so as to generate a radiation beam 96. The undulator 92 is provided between a second pair of mirrors 94a, 94b and at least a portion of the radiation beam 96 passes through one of the mirrors 94a, 94b is supplied to the energy modulator 42 as the first radiation beam 41. In this embodiment, the first radiation beam 41 has a wavelength of 151 pm.

[00149] By providing two separate particle accelerator modules 36a, 36b, with the energy modulator 42 disposed between, advantageously, the radiation source 40 of Figure 5 only uses one input laser, to provide the second radiation beam 43. That is, it does not use a separate laser for generation of the radiation beam 28. In contrast, by providing an additional laser to provide radiation beam 28, advantageously, the radiation source 90 of Figure 10 only uses one particle accelerator module 36.

[00150] Figure 11 is a schematic illustration of a radiation source 100 according to a second embodiment of the invention that is of the general form of the radiation source 20 shown in Figure 3 and which may form part of the lithographic system LS of Figure 1. Features which are common to both radiation source 100 of Figure 11 and radiation source 20 of Figures 3 and 4 share common reference numerals.

[00151] Radiation source 100 comprises an injector 34, a particle accelerator module 36, a bunch compressor 102, a chirp module 104, a first energy modulator 106, a first dispersive electron optics 112, a second energy modulator 114, a second dispersive electron optics 117, an undulator 122, and a beam dump 32.

[00152] The injector 34 is arranged to produce a bunched electron beam. The particle accelerator module 36 is arranged to receive the bunched electron beam and to accelerate it to 7 MeV. The timing of the acceleration of each electron bunch is such that it experiences off crest acceleration within the particle accelerator module 36. As such, the particle accelerator module 36 creates a generally linear chirp or longitudinal phase space correlation.

[00153] The bunch compressor 102 is a magnetic chicane and is arranged to spatially compress the bunches of electrons. The bunch compressor 102 is arranged to exploit the longitudinal phase space correlation generated by accelerator module 36 so as to spatially compress the bunches of electrons.

[00154] The chirp module 104 is operable to receive the bunched electron beam output by the bunch compressor 102. The chirp module 104 is arranged to substantially remove any longitudinal phase space correlation within each electron bunch that is produced by the accelerator module 36.

[00155] Each of the first and second energy modulators 106, 114 is arranged to receive the bunched electron beam and comprises an optical undulator which is operable to produce a periodic magnetic field arranged so as to guide the bunched electron beam along an oscillating path.

[00156] The first energy modulator 106 is provided with a first radiation beam 110, which provides the periodic magnetic field that causes the electrons to follow an oscillating path. The undulator period is therefore given by the wavelength of radiation beam 110, in this example it is 151 pm. The first energy modulator 106 is further provided with a second radiation beam 108 which acts as seed radiation, which is amplified by stimulated emission within the first energy modulator 106. In this example, the wavelength of radiation beam 108 is 193 nm.

[00157] The second energy modulator 114 is provided with a first radiation beam 118, which provides the periodic magnetic field that causes the electrons to follow an oscillating path. The undulator period λ_α is therefore given by the wavelength of radiation beam 118, in this example it is 151 pm. The second energy modulator 114 is further provided with a second radiation beam 116 which acts as seed radiation, which is amplified by stimulated emission within the second energy modulator 114. In this example, the wavelength of radiation beam 116 is 193 nm.

[00158] Each of the first dispersive electron optics 112 and the second dispersive electron optics 117 comprises a magnetic chicane and is arranged to receive the bunched electron beam, disperse the electron bunches and subsequently recombine them such that the distance travelled by an electron within a given electron bunch is dependent on its energy.

[00159] As a result of the interaction between the electron bunches and the second radiation beam 108, within the first energy modulator 106, the energy of each bunch of the bunched electron beam is modulated at a first distance scale λι, which is equal to the wavelength of the second radiation beam 108. As a result of tliis energy modulation, the longitudinal phase space distribution of each bunch is generally sinusoidal.

[00160] Within the first dispersive electron optics 112, the highest energy electrons within each bunch move relative to a centre of mass of the bunch by a distance greater than a quarter of the first distance scale.

With such an arrangement, the longitudinal phase space distribution of each bunch is skewed such that each maximum of the distribution moves past at least one adjacent minimum.

[00161] Electron bunches with this skewed longitudinal phase space distribution are then received by the second energy modulator 114.

[00162] As a result of the interaction between the electron bunches and the second radiation beam 116, within the second energy modulator 114, the longitudinal phase space distribution of the bunches is of the form of a set of nested sine curves. The second dispersive electron optics 117 converts the energy variations of the longitudinal phase space distribution into density variations.

[00163] Such an arrangement is known as echo enabled harmonic generation and produces a longitudinal density distribution that has a plurality of different harmonic contributions, one or which coincides with the wavelength of radiation produced by the inverse Compton scattering at the interaction point 28.

[00164] As in the radiation source 90 shown in Figure 10, the radiation beam 26 which the electron beam interacts with via inverse Compton scattering has a wavelength of 10 pm and is provided by an external laser (not shown). A pair of mirrors 119, 120 is provided on opposite sides of the interaction point 28, said pair of mirrors 119, 120 forming an optical cavity.

[00165] The radiation source 100 shown in Figure 11 comprises an undulator 122 arranged to receive the bunched radiation beam so as to generate a radiation beam 126. The undulator 122 is provided between a second pair of mirrors 123, 124 and at least a portion of the radiation beam 126 passes through one of the mirrors 123, 124 and is supplied to each of the two energy modulators 106, 114 as the first radiation beam 110, 118 respectively.

[00166] Although the above described embodiments show radiation sources based on inverse Compton scattering, it will be appreciated that the electron bunch modulators (as, for example, shown in Figures 5 and 11) may be used for other purposes. For example, in alternative embodiments, the electron bunch modulators may be used as part of a free electron laser so as to enhance the efficiency or gain of the free electron laser. Alternatively, the electron bunch modulators may be used as to enhance the efficiency of transition radiation and/or Cherenkov radiation sources.

[00167] It will be appreciated that in each of the above described embodiments of radiation sources based on inverse Compton scattering the specific values of the electron beam energies and radiation beam energies described above are merely examples. The skilled person will appreciated that these radiation sources may alternalively use different electron beam energies and/or radiation beam energies.

[00168] Many of the above described embodiments of radiation sources comprise dispersive electron optics that are arranged to receive a bunched electron beam, disperse the electron bunches and subsequently recombine them such that the distance travelled by an electron within a given electron bunch is dependent on its energy. Although the above described dispersive electron optics comprise either magnetic arcs or magnetic chicanes, it will be appreciated that any of the dispersive electron optics described above may be embodied by any suitable system of magnets as desired.

[00169] The centre of mass frame of a system of particles (also referred to as the centre of momentum frame) is a reference frame in which the vector sum of the momenta of the system of particles is zero. The centre of mass frame of an electron and photon pair is a reference frame in which the momentum of the electron is equal in magnitude and opposite in direction to the momentum of the photon.

[00170] Lithographic system LS may comprise any number of lithographic apparatus. The number of lithographic apparatus which form a lithographic system LS may, for example, depend on the amount of radiation which is output from a radiation source SO and on the amount of radiation which is lost in a beam delivery system BDS. The number of lithographic apparatus which form a lithographic system LS may additionally or alternatively depend on the layout of a lithographic system LS and/or the layout of a plurality of lithographic systems LS.

[00171] Embodiments of a lithographic system LS may also include one or more mask inspection apparatus MIA and/or one or more Aerial Inspection Measurement Systems (AIMS). In some embodiments, the lithographic system LS may comprise a plurality of mask inspection apparatuses to allow for some redundancy. This may allow one mask inspection apparatus to be used when another mask inspection apparatus is being repaired or undergoing maintenance. Thus, one mask inspection apparatus is always available for use. A mask inspection apparatus may use a lower power radiation beam than a lithographic apparatus. Further, it will be appreciated that radiation generated using a radiation source of the type described herein may be used for applications other than lithography or lithography related applications.

[00172] The term “relativistic electrons” should be interpreted to mean electrons which have relativistic energies. An electron may be considered to have a relativistic energy when its kinetic energy is comparable to or greater than its rest mass energy (511 keV in natural units). In practice a particle accelerator which forms part of a radiation source may accelerate electrons to energies which are much greater than its rest mass energy. For example a particle accelerator may accelerate electrons to energies of >10 MeV, >100 MeV, >1 GeV or more.

[00173] Embodiments of the invention have been described in the context of a radiation source SO which outputs an EUV radiation beam. However the radiation source SO may be configured to output radiation having any wavelength. Some embodiments of the invention may therefore comprise a radiation source SO which outputs a radiation beam which is not an EUV radiation beam.

[00174] The term “EUV radiation” may be considered to encompass electromagnetic radiation having a wavelength within the range of 4-20 nm, for example within the range of 13-14 nm. EUV radiation may have a wavelength of less than 10 nm, for example within the range of 4-10 nm such as 6.7 nm or 6.8 nm. [00175] The lithographic apparatuses LA_a to LA_n may be used in the manufacture of ICs. Alternatively, the lithographic apparatuses LA_a to LA„ described herein may have other applications. Possible other applications include the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat-panel displays, liquid-crystal displays (LCDs), thin-film magnetic heads, etc.

[00176] Different embodiments may be combined with each other. Features of embodiments may be combined with features of other embodiments.

[00177] While specific embodiments of the invention have been described above, it will be appreciated that the invention may be practiced otherwise than as described. The descriptions above are intended to be illustrative, not limiting. Thus it will be apparent to one skilled in the art that modifications may be made to the invention as described without departing from the scope of the clauses set out below. Other aspects of the invention are set out as in the following numbered clauses: 1. An electron bunch modulator comprising:

an energy modulator for receiving a bunched electron beam, the energy modulator operable to produce an energy modulation within an electron bunch of the bunched electron beam at a first distance scale λι;

a first dispersive electron optics arranged to receive the bunched electron beam output by the energy modulator, disperse the electron bunch and subsequently recombine it such that the distance travelled by an electron within the electron bunch is dependent on its energy;

a chirp module operable to receive the bunched electron beam output by the first dispersive electron optics and to produce a longitudinal phase space correlation in the electron bunch; and a second dispersive electron optics arranged to receive the bunched electron beam output by the chirp module, disperse the electron bunch and subsequently recombine it such that the distance travelled by an electron within the electron bunch is dependent on its energy in an opposite sense to the first dispersive electron optics.

2. The electron bunch modulator of clause 1 further comprising a second chirp module operable to receive the bunched electron beam output by the second dispersive electron optics and to reduce a longitudinal phase space correlation in the electron bunch.

3. The electron bunch modulator of clause 1 or clause 2 wherein the energy modulator is an optical undulator.

4. The electron bunch modulator of any preceding clause wherein the first dispersive electron optics, the chirp module and the second dispersive electron optics are arranged such that as a bunched electron beam exits the second dispersive electron optics it has a longitudinal electron density modulation at a second distance scale.

5. The electron bunch modulator of clause 4 wherein the first dispersive electron optics, the chirp module and the second dispersive electron optics are arranged such that a ratio of an R50 value of the first dispersive electron optics to an R56 value of the second dispersive electron optics is approximately equal to a compression factor imposed by the combination of the first dispersive electron optics, the first chirp cavity and the second dispersive electron optics.

6. A radiation source comprising:

an electron source operable to produce a bunched electron beam;

the electron bunch modulator of any preceding clause arranged to receive the bunched electron beam, modulate a spatial density of at least one bunch of the bunched electron beam and output an output beam; and a laser operable to produce radiation of a first wavelength arranged to interact with the output beam so as to produce a beam of radiation of a second wavelength.

7. The radiation source of clause 6 wherein the laser comprises a second undulator arranged to receive the bunched electron beam output by the bunch compressor and wherein the radiation of the first wavelength is produced as the output radiation beam propagates through it.

8. The radiation source of clause 6 wherein the laser comprises a conventional laser operable to emit radiation ofthe first wavelength.

9. The radiation source of clause 8 further comprising a second undulator arranged to receive the bunched electron beam output by the bunch compressor and to guide it along a periodic path so as to produce a radiation beam.

10. The radiation source of either clause 7 or clause 9 further comprising mirrors disposed at opposed ends of the second undulator to form a resonant cavity.

11. The radiation source of any one of clauses 7,9 or 10 when dependent on clause 3, wherein at least a portion of the radiation produced as the output radiation beam propagates through the second undulator is used by the optical undulator.

12. The radiation source of any one of clauses 7, 9, 10 or 11 wherein an interaction point at w'hich the radiation of a first wavelength interacts with the output beam is disposed between the electron bunch modulator and the second undulator.

13. A radiation source comprising:

an electron source operable to produce a bunched electron beam:

the electron bunch modulator arranged to receive the bunched electron beam, modulate a spatial density of at least one bunch of the bunched electron beam and output an output beam; and a laser operable to produce radiation of a first wavelength arranged to interact with the output beam so as to produce a beam of radiation of a second wavelength;

wherein the electron bunch modulator comprises:

an energy modulator for receiving the bunched electron beam, the energy modulator operable to produce an energy modulation within the at least one electron bunch of the bunched electron beam at a first distance scale λβ and a bunch compressor arranged to receive the bunched electron beam output by the energy modulator and to spatially compress the at least one electron bunch so as to produce the spatial density of the at least one bunch of the bunched electron beam at a second distance scale h.

14. The radiation source of clause 13 wherein the electron bunch modulator comprises the electron bunch modulator of any one of clauses 1 to 5.

15. An electron bunch modulator comprising:

an energy modulator for receiving the bunched electron beam, the energy modulator operable to produce an energy modulation within an electron bunch of the bunched electron beam at a first distance scale λι; and a bunch compressor arranged to receive the bunched electron beam output by the energy modulator and to spatially compress the electron bunch so as to produce a spatial density modulation within the electron bunch at a second distance scale fy.

16. A radiation source comprising:

an electron source operable to produce a bunched electron beam;

an electron bunch modulator arranged to receive the bunched electron beam, modulate it and output an output beam, the electron bunch modulator comprising an optical undulator for receiving the bunched electron beam, the undulator operable to produce a periodic magnetic field arranged so as to guide the bunched electron beam along an oscillating path so as to produce an energy modulation within at least one bunch of the bunched electron beam;

a laser operable to produce radiation of a first wavelength arranged to interact with the output beam so as to produce a beam of radiation of a second wavelength; and a second undulator arranged to receive the output beam by the electron bunch modulator and to guide it along a periodic path so as to produce a radiation beam and wherein at least a portion of the radiation produced as the output radiation beam propagates through the second undulator is used by the optical undulator.

17. The radiation source of clause 16 wherein the laser comprises the second undulator such that the radiation of the first wavelength is produced as the output radiation beam propagates through the second undulator.

18. An electron bunch modulator for echo enabled harmonic generation comprising;

a bunch compressor arranged to receive a bunched electron beam and to spatially compress the bunched electron beam;

a first optical undulator arranged to receive the bunched electron beam from the bunch compressor and to guide the bunched electron beam along an oscillating path so as to produce a first spatial electron density modulation within an electron bunch of the bunched electron beam;

first dispersive electron optics arranged to receive the bunched electron beam output by the first optical undulator, disperse the electron bunch and subsequently recombine it such that the distance travelled by an electron within the electron bunch is dependent on its energy;

a second optical undulator arranged to receive the bunched electron beam from the first dispersive electron optics and to guide the bunched electron beam along an oscillating path so as to produce a second spatial electron density modulation within the electron bunch of the bunched electron beam; and second dispersive electron optics arranged to receive the bunched electron beam output by the second optical undulator, disperse the electron bunch and subsequently recombine it such that the distance travelled by an electron within the electron bunch is dependent on its energy.

19. A radiation source comprising:

an electron source operable to produce a bunched electron beam;

an electron bunch modulator arranged to receive the bunched electron beam, modulate a spatial density of the bunched electron beam and output it as tin output beam; and a laser operable to produce radiation of a first wavelength arranged to interact with the output beam so as to produce a beam of radiation of a second wavelength, wherein the beam of radiation of the second wavelength comprises EUV radiation.

20. The radiation source of clause 19 wherein the electron bunch modulator comprises the electron bunch modulator of any one of clauses 1 to 5, clause 15 or clause 18.

21. A lithographic system comprising:

the radiation source of any one of clauses 6 to 16 or clause 19, which is operable to produce a radiation beam; and a lithographic apparatus arranged to receive at least a portion of the radiation beam.

Claims (3)

CONCLUSION A lithography apparatus comprising: an illumination device adapted to provide a radiation beam; 5 a carrier constructed for supporting a patterning device, which patterning device is capable of applying a pattern in a section of the radiation beam to form a patterned radiation beam; a sub-slate table constructed to support a substrate; and a projection device adapted to project the patterned radiation beam onto a The target area of the substrate, characterized in that the substrate table is adapted to position the target area of the substrate in a focal plane of the projection device. 1/11