Narrowband and tunable anomalous transmission filters for spectral monitoring in the extreme ultraviolet wavelength region

We present the first experimental demonstration of a novel type of narrowband and wavelength-tunable multilayer transmission filter for the extreme ultraviolet (EUV) region. The operating principle of the filter is based on spatially overlapping the nodes of a standing wave field with the absorbing layers within the multilayer structure. For a wavelength with a matching node pattern, this increases the transmission as compared to neighboring wavelengths where anti-nodes overlap with the absorbing layers. Using Ni/Si multilayers where Ni provides strong absorption, we demonstrate the proper working of such anomalous transmission filter. The demonstration is carried out at the example of 13.5 nm wavelength and at normal incidence, providing a 0.27 nm-wide transmission peak. We also demonstrate wavelength tunability by operating the same Ni/Si filter at different wavelengths by varying the angle of incidence. As the multilayer filter is directly deposited on the active area of an EUV-sensitive photodiode, this provides an extremely compact device for easy spectral monitoring in the EUV. The transmission spectrum of the filter is modeled and found to be in good agreement with the experimental data. The agreement proves that such filters and compact monitoring devices can be straightforwardly designed and fabricated, as desired, also for other EUV wavelengths, bandwidths and angles of incidence, thereby showing a high potential for applications. c © 2017 Optical Society of America OCIS codes: (120.2440) Filters; (130.7405) Wavelength filtering devices; (230.4170) Multilayers; (340.0340) X-ray optics; (340.7480) X-rays, soft X-rays, extreme ultraviolet (EUV). References and links 1. V. Bakshi, EUV Sources for Lithography (SPIE, 2006). 2. U. Stamm, I. Ahmad, V. M. Borisov, F. Flohrer, K. Gäbel, S. Götze, A. S. Ivanov, O. B. Khristoforov, D. Klöpfel, P. Köhler, J. Kleinschmidt, V. 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Introduction
The development of extreme ultraviolet (EUV) lithography tools demands improved and simplified approaches for on-line spectral monitoring of available EUV sources, as well as for source metrology and standardized characterization.Advanced EUV sources, such as based on laser-produced plasmas and discharge-produced plasmas, are capable of generating powerful radiation at the next generation lithography wavelengths, e.g., at 13.5 nm within a 2% spectral bandwidth [1][2][3][4], which matches the bandwidth of a typical Mo/Si 10-mirror optical system designed for high numerical aperture [5].However, as EUV generating plasmas are based on excitation to extremely high temperatures, emission occurs at multiple atomic and ionic transitions.Therefore the emitted spectrum comprises a significant amount of out-of-band radiation, ranging from soft x-rays to the infrared.Although much undesired radiation does not pass through the reflective mirror system due to the finite bandwidth of EUV mirror reflectivity, spectral monitoring with sufficient resolution is required to determine the amount of in-band and residual out-of-band radiation in the EUV lithography system.
A related problem of high importance for EUV lithography is that the overall amount of radiation and also the shape of the overall spectrum is critically dependent on maintaining specific excitation conditions, such as for the drive laser intensity and pulse duration [6,7], or the spatial distribution and density of the target material [8].Thereby, even smaller changes in these conditions can lead to significant variations of the in-band power over time.This cannot be tolerated because maintaining a stable power in the 13.5 nm-band is crucial to avoid over or under-exposure of the resist leading to loss of resolution [9].In-situ spectrally resolved monitoring of the power emitted across any relevant EUV ranges and, particularly, an output monitoring at 13.5 nm wavelength might then be used for a tight control of the plasma excitation parameters.
What would be desired for both metrology and monitoring of EUV sources is a solution which can isolate the relevant spectral intervals while being compact and requiring minimum alignment efforts and installation time, so that a monitoring device can, e.g., be readily transferred from one source to another.Most straightforward seems to be monitoring with grating spectrometers [10,11], but such devices are usually optimized for high resolution with an accordingly large size, and need careful alignment after installation at a matching vacuum port.A much simpler and versatile approach would be monitoring with a highly compact device (e.g.one-cm dimensions) as can be formed with a narrowband and tunable transmission filter in front of an EUV photodiode, to be placed inside the existing vacuum (source) vessel and requiring only electrical feedthrough.Due to filtering in transmission, rather than in reflection or with diffractive spectrometers, there are minimum efforts in alignment and, due to a compact size, installation could be done in multiple locations, near the source and further along the beam line.
However, standard approaches for spectral filtering in transmission, such as absorptive filters and interference filters, are not suitable here.Absorptive filters usually have wide transmission bands, whose spectral location are intrinsically determined by the absorption edge of the filter material, and thus cannot be shifted to a desirable wavelength.Bandpass interference filters, such as commonly used in the infrared [12,13], would theoretically work also for the EUV region [14], and would provide both high resolution and tunability.However, the design of such a filter requires that the thickness of the layers varies strongly with the location in the stack.Such strong variations in layer thickness render the fabrication of an EUV interference filter very critical, because nanolayers deposited at very different thicknesses, even if nominally made of the same materials, easily end up displaying different optical properties, due to difference in density, crystallinity, interlayers thickness, or layer roughness.In comparison, fabricating a multilayer stack with periodically repeating layer thicknesses is much preferable, because each bilayer in the multilayer stack will have the same optical, i.e., largely predictable, properties.
Here we present the first realization of a novel type of filter for achieving narrowband and tunable EUV transmission by exploiting the effect of anomalous transmission [15][16][17], as was suggested earlier by one of us [14].Using this principle, we show how to devise such an anomalous transmission (AT) filter and create a transmission window at a specific, desired wavelength, here, as an example, around 13.5 nm.We describe the fabrication of such an AT filter, based on the deposition of Ni/Si multilayer structures, and experimentally demonstrate narrowband transmission that is in agreement with the theoretical model.Importantly, to realize a highly compact monitoring device, the multilayer structure forming the AT filter is deposited directly onto an EUV photodiode, thereby opening a new avenue for easy monitoring of EUV light sources.

Anomalous transmission
The effect of anomalous transmission was discovered by Borrmann upon x-ray diffraction in quartz [15] and calcite crystals [16], and first explained by von Laue [17].In the range of hard x-rays (tens of keV to MeV photon energy) where a matching natural periodicity of crystalline materials is available, the effect has been exploited for realizing x-ray polarizers [18][19][20], for x-ray monochromatization and signal enhancement [21], for detection of micro-defects [22], for spectroscopy of quadrupole transitions [23], or for the measurement of thermal diffuse scattering [24,25].Anomalous transmission was predicted by one of us to occur also in amorphous multilayer structures [14], but there is no experimental observation so far.Of particular relevance would be to demonstrate anomalous transmission in the EUV range, using multilayer systems similar to EUV multilayer mirrors.This promises to provide a new approach towards narrowband transmission filters for the EUV range operating close to normal incidence, offering to set the transmission to pre-selectable wavelengths or offering angle tuning to scan a certain wavelength band.
The underlying physical mechanism leading to anomalous transmission can be explained using Fig. 1, which shows a multilayer structure subject to EUV radiation of a given wavelength, λ 0 , incident under normal incidence.The multilayer structure, if optimized for maximum reflectivity, is formed by a periodic stack of nanolayers using two different materials that provide the best compromise between a maximum index contrast (to maximize reflection) and a minimum of absorption (to maximize the number of material interfaces contributing to the reflection).In the EUV range this is typically achieved with alternating layers of a high-Z material and a low-Z material, for instance, Mo and Si for maximizing the reflectivity at 13.5 nm wavelength [26], or LaN and B for maximizing the reflectivity near 6.7 nm [27].For brevity, the high-Z material providing an increased index, indicated in opaque dark red in Fig. 1, is often named absorber, due to the strong absorption associated to a high-Z material as well.Although absorption forms a fundamental limitation for reflective EUV optics, we show that here absorption is highly desired because it gives rise to an increased transmission within a narrow spectral interval.The low-Z material of lower index and absorption, indicated in transparent light yellow in Fig. 1, is often named spacer.Fig. 1.A multilayer structure, comprising a periodic stack of an absorber material (dark opaque red) and a spacer material (light transparent yellow), is subject to EUV radiation under normal incidence with a given wavelength, λ 0 .The interference between the incoming and reflected waves creates a standing wave pattern inside the multilayer stack, represented by the electric field envelope E(z).The geometrical parameters of the multilayer structure are fine-tuned such that the wave field nodes overlap with the absorber layers.As this reduces the amplitude of the electric field within the absorber layers, the incident radiation experiences a decreased absorption, and thus an increased transmission, compared to other, neighboring wavelengths that do not fit the periodic structure.
Given such a multilayer structure, achieving anomalous transmission can be seen in two steps.First, the absorber and spacer thicknesses, d A and d S , are chosen to maximize the reflection of the multilayer structure for a given wavelength, λ 0 .This creates an intensity pattern inside the stack that resembles a standing wave.The intensity pattern is indicated in Fig. 1 as an electric field envelope E(z) that varies sinusoidally and decreases throughout the stack along the coordinate z.Maximum reflection, and thus a pronounced standing wave with a large contrast between nodes and antinodes, is achieved when the Bragg condition is satisfied, i.e., when the optical thicknesses of the bilayer is close to half the wavelength of the incident radiation (at normal incidence).In the second step, while staying in the vicinity of the Bragg condition, the thicknesses of the layers are fine-tuned with the goal to overlap the field nodes, where the intensity is small, with the center of the absorber layers.
With such a reduced overlap of the intensity pattern and the absorber layers, the incident radiation at the wavelength λ 0 experiences a much reduced absorption, compared to slightly different wavelengths because, for the latter, the intensity pattern is phase-shifted and overlaps more strongly with the absorber layers.The result is a higher transmission at the wavelength λ 0 compared to other wavelengths near the Bragg condition for reflection.We note that such formation and phase-shifting of standing waves for controlling optical transmission has recently gained additional interest also with single absorptive layers, for the purpose of controlling light by light without optical nonlinearity [28].Here, we control the transmission of EUV radiation through an entire stack of absorbing layers arranged periodically, by carefully selecting the geometrical parameters with sub-nanometer precision.This way, it is possible to devise an AT filter with a narrow bandpass centered at any selected EUV wavelength.
The reflectance and transmittance spectra of multilayer structures can be calculated with many methods.A well-known approach is the recursive formalism developed by Parratt [29] which models a layer stack as a sequence of Fabry-Perot resonators in the slowly varying envelope approximation.Numerically solving the equations has been conveniently implemented by Windt, in the form of the software IMD, which also incorporates comprehensive optical data for a large number of materials [30].We use this approach below to calculate anomalous transmission spectra from multilayer design parameters and material properties.The calculations show that the absolute value of transmittance decreases with the number of layers, because an increasing part of the incident radiation is to be reflected to form a standing wave with a high contrast between nodes and antinodes.On the other hand, increasing the number of layers, and thus the contrast, leads to a narrowing of the spectral bandwidth of transmittance.
For analytically calculating the transmittance of a given multilayer structure, we introduce the following parameters: A and S the complex dielectric constants of the absorber and the spacer materials, respectively, d the multilayer period (d , N the number of bilayers, L the thickness of the multilayer structure (L = N d), λ the incident wavelength, and θ the angle of incidence.The transmittance of a periodic multilayer structure in the vicinity of the first order Bragg peak can then be written as [31,32]: in which we have used the following parameters: for s-polarization cos(2θ), for p-polarization . ( The parameter 1/S characterizes the depth of penetration of EUV radiation into the multilayer structure, B is the strength of the index modulation in the multilayer structure in terms of the dielectric constants and the gamma ratio, characterizing the reflectivity of a bilayer, b describes the deviation from the Bragg condition of reflection, and σ is a polarization parameter. From (1), assuming the total thickness of the multilayer structure to be large compared to the penetration depth so that SL 1, and for a given angle of incidence, θ, we obtain the wavelength of maximum transmittance, λ T [14]: where the parameter η is defined as: For maximizing the transmittance at λ T as compared to the background (transmittance outside the Bragg peak), it can be shown that the thickness ratio γ has to be chosen to assume an optimum value, γ o pt , fulfilling the following equation [14]: As a result, when the thickness ratio takes this optimum value, γ o pt , the expression for η given in ( 4) can be simplified as η = cos(πγ o pt ).Note that fulfilling (5) also maximizes the reflectivity of multilayer mirrors [31,32].Inspecting the equation shows that the optimum thickness ratio decreases with a decreasing value of g, i.e., with an increasing ratio of absorptivities of the high and low-Z materials.
Designing an AT filter with this set of equations and conditions can be done in three steps.First, the desired transmission wavelength, λ T , has to be chosen.The second step is then to choose two appropriate materials that provide a well-pronounced AT effect.Finally, as the third step, the desired angle of incidence, θ, and a suitable value for the peak transmittance, T ( 1), are chosen, after which all geometrical parameters of the AT filter (the period d, the thickness ratio γ, and the number of bilayers N) can be determined via Eqs.( 1)- (5).
For a subsequent experimental investigation and due to its relevance for state-of-the-art lithography, we start describing the design considerations for an AT filter at a wavelength of 13.5 nm.For this wavelength, the choice of a proper spacer material that minimizes absorption is straightforward.Here we chose Si as spacer material due to its relatively low absorption at a wavelength of 13.5 nm.The choice of an appropriate absorber material is, however, not straightforward.To illustrate the problem more clearly, we discuss the consequences of choosing two different absorber materials.The first example is Mo, which is the standard high-Z material in multilayer mirrors for 13.5 nm.The other example is Ni, which provides a much higher absorptivity at 13.5 nm.For discussing the consequences of choosing either material, we introduce the parameter f defined as: As explained earlier, an AT peak can only be observable if the AT wavelength lies in the vicinity of the Bragg peak.First, for finding the wavelength of maximum Bragg reflection, λ B , we recall the Bragg condition for maximum reflectance at λ B at the same angle of incidence, θ, as in (3), taking into account the effects of both refraction and absorption [32]: Then, from Eqs. ( 3) and ( 7), we determine the relative offset between the Bragg wavelength, λ B , where the maximum reflectance is observed, and the AT wavelength, λ T , where the maximum transmittance is observed: In order to verify whether the AT wavelength remains inside the Bragg peak such that an AT peak can be observed, the offset needs to be compared with the spectral width of the Bragg peak, ∆λ B .For a multilayer stack with | f | 1, the relative spectral bandwidth of the Bragg peak, ∆λ B /λ B , is [32]: Therefore, for | f | 1, the comparison between the Bragg-AT offset, (λ T − λ B ), and the spectral width of the Bragg peak, ∆λ B , can be written as: On the other hand, for multilayer stacks with | f | ≤ 1, one obtains ∆λ B /λ B as [32]: Therefore, for | f | ≤ 1, the comparison between the Bragg-AT offset, (λ T − λ B ), and the spectral width of the Bragg peak, ∆λ B , can be written as: When designing an optimum multilayer mirror (and not an AT filter), the absorber material is chosen with the objective to provide a maximum reflectance at the desired wavelength.This is achieved by choosing a high contrast of the indices of refraction with simultaneously the lowest possible absorptivity, i.e., by maximizing the ratio Re( A − S )/ Im( A ). Indeed, choosing Mo as absorber material in Mo/Si multilayer mirrors maximizes this ratio, which is why Mo/Si mirrors provide the reflectivity record for multilayers at 13.5 nm wavelength [33].
However, for inspecting whether an excellent Mo/Si EUV mirror is simultaneously also the best choice for an AT filter, considering the dielectric constants of Mo and Si, we obtain from (10) that (λ T − λ B )/∆λ B ≈ 1.25, with the thickness ratio taking the optimum value for a Mo/Si multilayer mirrors, γ o pt = 0.38.Hence, with Mo as absorber, the AT wavelength, λ T , lies outside of the Bragg peak where no standing wave is present such that no AT peak is observed.This example shows that designing a multilayer AT filter is quite different from designing a multilayer mirror.The example also shows that anomalous transmittance is usually not present in multilayer mirrors, even though the design of those is quite similar in some respects.
Designing a multilayer AT filter is based on a different principle.For maximizing the standing wave contrast, by minimizing (λ T − λ B ) in (8), the optimum thickness ratio, derived from (5), should be as small as possible, i.e., the absorptivity of the absorber should be as high as possible.The highest absorptivity in the wavelength range around 13.5 nm is found with Ni and Ag [34,35].Here, for an experimental demonstration, we choose to discuss Ni because this material is technologically more suitable for fabrication.Using the dielectric permittivity of Ni and Si, we calculate the optimum absorber thickness ratio for a Ni/Si AT filter to be γ o pt = 0.19, which is almost a factor two smaller than for a Mo/Si multilayer mirror.Then, taking into account this optimum thickness ratio, we find that for Ni/Si, the comparison between the Bragg-AT offset, (λ T − λ B ), and the spectral width of the Bragg peak, ∆λ B , calculated with (12), is (λ T − λ B )/∆λ B ≈ 0.23, which means that the AT wavelength lies almost in the center of the Bragg reflection peak, providing a strong standing wave contrast.Hence, anomalous transmission should be clearly observable in a Ni/Si multilayer transmission filter.

Design of an AT filter for 13.5 nm wavelength
Choosing Ni and Si as the absorber and spacer materials, respectively, and using Eqs.( 3)-( 5), we have determined the optimum design parameters of an AT filter that should provide a narrowband transmission peak near a wavelength λ T = 13.5 nm at normal incidence.For the calculations, we have used the optical constants for Ni and Si available in the CXRO database [34][35][36], which the software IMD uses as well.We obtain the thicknesses of the Ni and Si layers as d Ni = 1.3 nm and d Si = 5.4 nm, respectively, i.e., the multilayer period is d = 6.7 nm and the thickness ratio is γ o pt = 0.19.The number of bilayers N can be chosen to achieve a desired value for the peak transmittance T. Here, as an example, we chose T = 1%, which requires then N = 74 bilayers.We note that the absolute value of the transmittance is not a crucial parameter due to the extreme intensities of EUV sources intended for EUV lithography.Using these design parameters in [30] we obtain the transmission spectrum for this Ni/Si AT filter as shown in Fig. 2. As can be seen within the displayed relatively narrow range from 12 to 16 nm, the spectrum exhibits a single and dominant AT peak with a small bandwidth of ∆λ T = 0.23 nm (full-width at half-maximum, FWHM), centered at 13.5 nm.This corresponds to a relative bandwidth of 1.7% and is thus matching well the desired 2% source bandwidth.We note that a 1.7% bandwidth is comparable with what can be obtained via reflective multilayer mirrors [37,38].However, as we show below, because this bandwidth is available in transmission, it can be used to realize extremely compact spectral monitoring devices.Towards shorter wavelengths, between 12.4 and 13.1 nm, in the far wing of the dominant transmission peak, the transmittance is somewhat rising again, up to T = 0.05%, which is about 20-times smaller than the transmittance of the main peak, before the Si L-absorption edge at 12.4 nm blocks all shorter wavelengths (T < 10 −4 to 10 −7 ).However, when considering the filter transmission across a wider wavelength range, additional transmission peaks might be present that would need to be blocked as well for optimum filter performance.To identify additional transmission peaks, Fig. 3 shows as the red curve the calculated transmission spectrum of the same filter over a much wider wavelength range, from 10 nm to 1 µm (on a logarithmic wavelength scale).It can be seen that there are indeed also other important transmission peaks, particularly in the 20-40-nm range and in the visible (400-1000-nm).Emission that lies further in the infrared is of less concern due to the limited detector responsivity in that range.For instance, when using Si-photodiodes for detection, light transmitted at wavelengths beyond 1 µm will not yield a photocurrent because there the photon energy does not reach across the bandgap of Si.
For suppressing additional transmission peaks, without much effecting the anomalous transmission at 13.5 nm, we identified Zr as a suitable material to be used as an additional absorbing thin film.For a quantitative inspection of the effect of an additional Zr film, Fig. 3 shows the comparison between the transmittance of the Ni/Si AT filter discussed above (red curve) and the transmittance of a Zr-coated Ni/Si AT filter (blue curve) calculated with [30].The thickness of the zirconium layer is chosen as d Zr = 200 nm because our calculations showed that this value offers the best compromise between suppression of the additional transmission peaks and preservation of the absolute value of transmission in the AT peak.In order to obtain the same AT peak transmittance, T = 1%, for making both spectra directly comparable, the number of bilayers in the Zr-coated Ni/Si AT filter was adjusted to N = 61, whereas the other parameters of the Ni/Si AT filter remained the same.It can be seen in the insert of Fig. 3 that the strong, narrowband transmission peak remains of approximately same shape when intending to have the same peak transmittance with and without the Zr layer.The transmittance outside the 13.5 nm-band drops to at least 0.1% (at λ = 12.4 and 19 nm) or lower (below 0.02%, from 20 nm to 1 µm).With the Zr-coated Ni/Si AT filter, the bandwidth of the AT peak is slightly increased to ∆λ T = 0.30 nm (FWHM), due to the reduced number of bilayers.A bandwidth of 0.23 nm can be achieved as before with N = 71 layers if desired, with a peak transmittance of 0.5% due to the Zr layer.
Having transmission filters available at an entire set of pre-determined wavelengths can be desired for a more comprehensive source monitoring.For this purpose, AT filters that all work at normal incidence but each transmitting at a different wavelength might be fabricated by giving each filter a different multilayer period.An easier solution might be to make use of the property of AT filters that they can be tuned via the angle of incidence for obtaining anomalous transmission at adjustable wavelengths.To illustrate how the AT wavelength and AT peak transmittance can be modified by tuning the angle of incidence or choosing a different multilayer period, Fig. 4 shows the AT wavelength, λ T , and the AT peak transmittance, T, as a function of the angle of incidence, θ, for a range of multilayer periods, d.The calculations show that for a given multilayer period, increasing the angle of incidence allows to shift the AT peak toward shorter wavelengths, while the transmittance somewhat decreases.Different from angle-tuning, narrowing the AT bandwidth (FWHM) cannot be done in situ, but can be achieved via the number of bilayers during fabrication.This tuning of the AT bandwidth via the number of bilayers is illustrated in Fig. 5 which shows the AT bandwidth, ∆λ T , and the AT peak transmittance, T, as a function of the number of bilayers, N, for a range of multilayer periods, d.The calculations show that for a given multilayer period, increasing the number of bilayers, and thereby reducing the AT peak transmittance, allows to decrease the AT bandwidth.
It should be noted that the previous calculations were made considering perfectly collimated incident radiation, while, in reality, the radiation collected from an EUV source has a small but non-zero divergence.Therefore, the radiation arriving at the AT filter will subtend a small but non-zero spread in angle of incidence, causing a slight spectral broadening of the transmittance.Taking as a typical example a 13.5 nm radiating plasma plume with 300 µm size to be monitored at a distance of 1 m [39,40], with the Ni/Si filter shown in Fig. 2 placed in front of a photodiode of 1 cm size, the spectral broadening is indeed small, less than 0.001 nm at normal incidence, or less than 0.04 nm at an angle of incidence of 20 • .
We also note that the calculations and arguments for the best choice of materials were based on the optical properties of pure materials assuming sharp interfaces, i.e., on the absence of intermixing.A more detailed discussion and choice of materials would therefore ultimately include also soft interfaces and diffusion barriers [33,41].
A conclusion from the calculations, such as presented in Figs.2-5, is that AT filters are rather flexible in adjustment of their spectral properties via the choice of design and fabrication parameters, and via the tuning of the angle of incidence.This provides a significant potential for an easy adaptation to the requirements of a lithographic setup or of a spectroscopic characterization and standardization of EUV sources.For instance, a set of AT filters with their transmission set to a single wavelength can be fabricated for monitoring the amount of source radiation in a narrow spectral region and, still, the AT wavelength can be tuned via the angle of incidence during monitoring.Or a set of AT filters with various different multilayer periods can be fabricated, each yielding maximum transmission at normal incidence for different target wavelengths, allowing for parallel monitoring.

Fabrication of AT filters
We fabricated a Ni/Si AT filter for λ T = 13.5 nm with the design parameters chosen as discussed in the previous section.The AT filter was deposited directly on an EUV silicon photodiode, and also on freestanding silicon nitride membranes, in order to investigate the viability of both approaches.The type of silicon photodiode (AXUV100G, 10 × 10 mm active area, Opto Diode Corp.) was chosen to offer a sufficiently large area and a high quantum efficiency [42].Silicon nitride membranes (Si 3 N 4 , 5 × 5 mm area, 50 nm thickness, Silson Ltd.) were chosen as the freestanding substrates.For a detailed analysis and characterization of the multilayer structure with X-ray Photoelectron Spectroscopy (XPS) and Grazing Incidence X-ray Reflectometry (GIXR), the same Ni/Si AT filter was also deposited on flat silicon substrates (20 × 20 mm area, 512 µm thickness).
The Ni/Si AT filter was deposited with a magnetron sputtering system.Ultrahigh purity (> 99.5%) argon was used as a process gas at a pressure of 8 × 10 −4 mbar.The base pressure in the vacuum chamber before deposition was set to 2 × 10 −8 mbar.The temperature was kept at ambient value (21 • C).During the deposition process, each photodiode was covered by a mask with a 5 × 5 mm square aperture, in order to prevent the deposition material from coating the wire bonds and the pins of the photodiode, which might otherwise adversely affect the performance of the photodiodes by increasing the dark current or creating a short circuit.An alternative approach would be to cover the perimeter of the active area by a nonconducting epoxy [43].The mask-covered photodiodes, the Si 3 N 4 membranes and the flat silicon substrates were held upside down on a large rotating holder over the sputtering sources, and the deposited layer thickness was computer-controlled by variation of the rotational velocity of this holder.A photograph of a silicon photodiode and a silicon nitride membrane, after coating with the Ni/Si AT filter, is presented in Fig. 6.On the photodiode, in Fig. 6(a), the Ni/Si coating is visible as the central, approximately square area with rounded edges, the shape of which results from the square mask used to protect the wire bonds and contact pins (on either sides of the active area) from being coated.The surface of the membrane, in Fig. 6(b), is entirely coated with the Ni/Si filter.It can be seen that the surface is not flat but forms wrinkles over its whole area.We address these distortions to significant mechanical stress introduced with the deposition of the Ni/Si filter, in combination with the extremely low thickness of the membrane (50 nm).To verify the realization of the intended fabrication parameters, we first performed an XPS analysis using the coated Si substrate samples.These measurements allow to determine the chemical species present and thus to assess the extent of intermixing in the deposited Ni/Si filters.Real multilayer systems often show an intermixing of materials at the interfaces.Specifically, if a transition metal and Si are used as absorber and spacer materials, such as is the case here, this may translate in the formation of silicides.These silicides have different dielectric constants than their constituents, such that the ratio Im( S )/ Im( A ) is increased, which would influence the effect of anomalous transmission.
The results from the XPS analysis were calibrated by measuring also a sample of pure Ni, deposited from the same target used for the Ni/Si AT filter, and by comparing the results to literature values.The measurements showed that pure Ni was not present anymore, or in a quantity below the experimental uncertainty.Instead, only a specific nickel silicide, NiSi, was present, indicating that all of the Ni had been consumed to form NiSi. We attempted to evaluate the XPS data for obtaining more details about the quantitative shape of the Ni concentration profile vs. depth.However, evaluating the obtained depth-profiles remained unreliable due to the relatively low quantity of Ni compared to Si, and due to the limited depth resolution of XPS measurements.Nevertheless, the conclusion is that the anomalous transmission spectra expected from our samples cannot be calculated assuming pure Ni as the absorber material, as was initially shown in Fig. 2, but should instead be calculated using nickel silicide NiSi as absorber material.
For enabling the calculation of the expected transmission spectra for our samples, we determined the multilayer period, d, and the absorber thickness ratio, γ, of the deposited AT filters via GIXR measurements (Empyrean, PANalytical) at the Cu-Kα emission line (λ = 0.154 nm).By considering nickel silicide as the absorber material (i.e., NiSi/Si as the multilayer structure with sharp interfaces) and by fitting calculated GIXR spectra [30] to the experimental data, the multilayer period was obtained as d = 6.67 ± 0.05 nm and the absorber thickness ratio as γ = 0.42 ± 0.01.For comparing with the measured transmission of the fabricated multilayer filters in the next section, it can be expected that calculations have to make use of these values for d and γ again, assuming nickel silicide as the absorber material.

Experimental results
The fabricated Ni/Si filters were experimentally characterized at the PTB synchrotron beamline at BESSY II, which achieves an energy precision below 0.1 eV and an angular precision below 0.01 • [44,45].The spectral responsivity of the silicon photodiodes before and after deposition of the Ni/Si AT filter, as well as the transmittance of the Si 3 N 4 membranes coated with the same Ni/Si AT filter, were measured over a wavelength range from 12 to 14.5 nm, with a radiant power of 0.2 µW in a 2 × 2 mm beam cross section.
For the experimental demonstration of wavelength-tuning, the measurements were performed at three different angles of incidence (0 • , 10 • and 20 • ), the expectation being, as in Fig. 4, that the AT peak will shift toward shorter wavelengths when the angle of incidence is increased.

Ni/Si-coated photodiode
In order to determine the transmittance of the solitary Ni/Si AT filter, T AT (λ), i.e., without the responsivity of the photodiode itself, we divided the responsivity measured after deposition, R(λ), by that of the photodiode before deposition, R 0 (λ): T AT (λ) = R(λ)/R 0 (λ).We note that the used photodiode model was confirmed to be operated in a regime where the response across the entire relevant EUV range investigated here is proportional to the incident power, such that T AT is independent of power as required.The measurement of the spectral responsivity of photodiodes in the EUV range is made at PTB by comparison with their primary detector standard, which is an electrical substitution radiometer (ESR) operated at liquid He temperature [46].
In Fig. 7, the dot symbols show the experimental transmittance, T AT (λ), of the Ni/Si filter deposited on the silicon photodiode.It can be seen that the experimental data show a spectral variation as qualitatively expected, e.g., in Fig. 2, with a clear transmission peak that tunes to shorter wavelengths with increasing angle of incidence.However, a confirmation of anomalous transmission also requires a direct comparison of the experimental data with calculated spectra.For a comparison with theory the transmittance was calculated [30] using the parameters independently determined from the GIXR measurements, d = 6.67 nm and γ = 0.42, and assuming NiSi as absorber material.The angle of incidence was taken as in the experiments (0 • , 10 • and 20 • ).The calculated transmission spectra are presented in Fig. 7 as the solid lines.
It can clearly be seen that the position of the transmission spectra as well as the overall shape are in very good agreement with the theory, which proves that we have observed anomalous transmission in our multilayer stack.Quantitatively, the measured AT wavelengths are 13.4 nm, 13.2 nm and 12.7 nm, for the angles of incidence of 0 • , 10 • and 20 • , respectively.This shift of the AT peak toward shorter wavelength with an increasing angle of incidence demonstrates wavelength-tuning of anomalous transmission.
Comparing the transmittance spectra in Fig. 2 and Fig. 7, it is clear that the formation of nickel silicide results in a decrease of the peak transmittance and thereby also of the peak-to-background ratio, which is a central characteristic of any filter.An important step for increasing this ratio would thus be to reduce interdiffusion at layer boundaries by, e.g., introducing barrier layers such as B 4 C [43].

Ni/Si-coated membrane
A similar set of measurements was performed with the Si 3 N 4 membrane coated with the same Ni/Si AT filter.The experimental transmittance, T AT (λ), of the Ni/Si-coated membrane was obtained as the ratio between the transmitted radiant power, φ t (λ), and the measured incident radiant power, φ 0 (λ): T AT (λ) = φ t (λ)/φ 0 (λ).
The results of the measurements are presented in Fig. 8 with dotted symbols, again for three angles of incidence (0 • , 10 • and 20 • ).It can be seen that now the transmission peaks, with increasing angle of incidence, are found increasingly broadened and shifted as compared to Fig. 7.We address this to the strongly distorted surface contour of the membrane, as seen in Fig. 6, which introduces some wider distribution of the angle of incidence.
For verifying this assumption more quantitatively we modeled the transmission of the membrane, T (λ), via convoluting the angular dependent transmittance spectrum, τ(θ, λ) as in Fig. 7, with a distribution function of the angle of incidence, ρ(θ): The shape of the distribution was taken as Gaussian for simplicity and centered about the respective nominal angle of incidence (0 • , 10 • and 20 • ).The full width of the distribution was taken as ∆θ ≈ 20 • , as obtained from a coarse measurement of the angular spread in reflection from the wrinkled surface when illuminated with a collimated laser beam.The convoluted transmittance spectra are presented in Fig. 8 as solid lines.
As can be seen, there is a reasonable agreement between the measured and convoluted transmission spectra, confirming that the distortion of the membrane surface contour was causing the measured spectral broadening and shifts.

Conclusion
We presented the first experimental demonstration of anomalous transmission using a multilayer stack made of alternating thin films of amorphous materials.Using this principle of anomalous transmission (AT), where the nodes of a standing wave field are positioned in the absorbing layers within the multilayer structure, we have designed and realized the first narrowband and wavelength tunable transmission filter for the EUV range.The example that we have demonstrated is based on a Ni/Si multilayer structure designed and fabricated for optimum transmission at 13.5 nm and normal incidence, using thicknesses d Ni = 1.3 nm and d Si = 5.4 nm, i.e., a multilayer period d = 6.7 nm and a thickness ratio γ = 0.19.The transmittance spectra of the Ni/Si AT filter were measured in two configurations: as coated directly onto the active area of a silicon photodiode, and as coated on a 50-nm-thick Si 3 N 4 membrane.The experimental data obtained with the coated photodiode show narrow AT peaks, with a spectral bandwidth of 0.27 nm at normal incidence.The AT peak was seen to shift towards smaller wavelengths with increasing angle of incidence, demonstrating the possibility of tuning the transmitted wavelength.While the Ni/Si AT demonstrates a peak transmittance of less than 1%, the value originally chosen for the design, this should not present an issue for monitoring the high brightness EUV sources intended for EUV lithography.The experimental peak transmittance could be brought closer to the originally intended value of 1% by improving the fabrication and structure of the multilayer stack.Indeed, the experimental spectra agree well with calculated spectra, when taking into account the intermixing of Ni and Si in the absorber layers, as independently quantified.This agreement suggests that such AT filters can be further improved, to reduce the transmission bandwidth and increase the peak-to-background transmission ratio, by reducing the intermixing of layers, for instance with interdiffusion blocking layers [43].The spectra obtained with a coated membrane show significant spectral broadening and shifts of the transmission peaks, which can be addressed to a distortion of the membrane due to the presence of stress.For realizing thin membranes with an undistorted, flat surface one might consider to use a supporting grid structure, such as with EUV nano-gratings [47].The successful demonstration of AT filters for the EUV, directly fabricated on the surface of a photodiode, is an important achievement towards spectral monitoring in the EUV range in an extremely compact, cm-sized and technologically convenient format.Designing AT-filter-coated photodiodes could be further improved by the addition of a zirconium layer for the suppression of undesired transmission in other spectral regions.Overall, these results demonstrate a promising new avenue toward applications, specifically for an improved monitoring of EUV lithography sources.
) For a multilayer stack with weaker absorbing materials, such as Mo/Si, we have | f | 1, and for stronger absorbing materials, such as with Ni/Si, we have | f | ≤ 1.For instance, at a wavelength of λ = 13.5 nm, we find | f Mo/Si | = 17.55 and | f Ni/Si | = 0.78.

Fig. 3 .
Fig. 3. Calculated transmission spectra at normal incidence (θ = 0 • ) of the same Ni/Si anomalous-transmission (AT) filter as in Fig. 2 (red curve), and of a Ni/Si AT filter coated with an additional 200 nm-thick Zr film (blue curve).For direct comparison via equal peak transmittances (see insert), the number of bilayers in the Zr-coated Ni/Si AT filter is reduced to N = 61, whereas the multilayer period, d = 6.74 nm, and the thickness ratio, γ = 0.19, remain unchanged.

Fig. 4 .
Fig. 4. Calculated anomalous-transmission (AT) wavelength λ T (black contour lines) and AT peak transmittance T (color scale) for the Ni/Si AT filter described in Fig. 2, upon tuning of the angle of incidence θ, for a range of multilayer periods d.The number of bilayers, N = 74, and the thickness ratio, γ = 0.19, are fixed.

Fig. 5 .
Fig. 5. Calculated anomalous-transmission (AT) bandwidth ∆λ T (black contour lines) and AT peak transmittance T (color scale) for the Ni/Si AT filter described in Fig. 2, upon tuning of the number of bilayers N, for a range of multilayer periods d.The angle of incidence, θ = 0 • , and the thickness ratio, γ = 0.19, are fixed.For each multilayer period, d, the corresponding AT wavelength, λ T , can be obtained from Fig. 4.

Fig. 6 .
Fig. 6.Photograph of (a) the silicon photodiode and (b) a 50nm thin silicon nitride membrane, after deposition of a Ni/Si anomalous-transmission (AT) filter.

Fig. 7 .
Fig. 7. Experimental and calculated transmittance of a Ni/Si anomalous-transmission (AT) filter coated on a silicon photodiode, at three angles of incidence (0 • , 10 • and 20 • ).The sharp decrease in transmittance around 12.4 nm is connected to the L-absorption edge of Si.