A conventional x-ray transmission grating (TG) consists of alternating transmissive and opaque nanometer structures, and is used in spectrometers to analyze the x-ray spectra radiated from high-energy-density processes, such as those in inertial confinement fusion and astrophysics.^[1–6] According to the grating equation derived by Fraunhofer, it disperses x-rays not only in the first-order diffractions but also higher-order diffractions.^[7] Unfortunately, the higher-order diffractions with various wavelengths may overlap each other in continuous or broadband spectra. Hence, a complex unfolding process must be performed to extract usable first-order diffractions,^[2,5,6] which reduces the accuracy of the spectral data.

Sinusoidal transmission grating (STG) generates only one pair of conjugate first-order diffractions. Thus, they can be used to efficiently suppress higher-order diffractions in the optical region,^[7] but they do not extend to x-ray region because of the inherent phase problem in material. In 2001, Kipp et al.^[8] proposed a new zone plate, or photon sieve, with a large number of pinholes distributed appropriately over the Fresnel zones that focused soft x-rays to a sharp focal spot and suppressed higher orders. Other x-ray gratings that can suppress higher-order diffractions were developed, such as the binary sinusoidal transmission grating (BSTG),^[9] the quantum-dot-array diffraction grating (QDADG),^[10–12] and the quasi-sinusoidal single-order diffraction transmission grating (QSTG).^[13] Unfortunately, the BSTG and the QDADG do not have line densities greater than 1000 lines/mm. Although a 1000-line/mm gold QSTG is fabricated, the x-ray-absorbing polymer membrane substrates must be used to support the periodic holes, which is also the case the BSTG and the QDADG encounter.

Here in this study, a two-dimensional (2D) diffraction grating that behaves as a spectroscopic photon sieve (SPS) is discussed. Because it has a large number of nanoscaled circular pinholes on a gold substrate, the SPS can be free-standing while suppressing higher-order diffraction components. An SPS with a spatial frequency of 1000 lines/mm is fabricated via electron-beam and x-ray lithography. The diffraction quality is calibrated with soft x-ray synchrotron radiation, and the results accord well with theoretical calculations. This grating offers new opportunities for improving the x-ray spectroscopy, monochromatization, and beam splitting.

As shown in Fig. 1, the SPS consists of many nanoscale circular pinholes distributed on an opaque screen. The thin substrate (such as gold) was opaque to x-rays and was diced uniformly into N × N small squares with side length d, which was the period of this square dispersive device. In each square, a circular hole that transmits x-rays was randomly located within its area. Generally, the diameter (a) of the holes was half the value of d and was much larger than the wavelengths of the incident x-rays. Thus, the SPS was a 2D array of many quasi-randomly distributed transmissive holes on a thin substrate that was opaque to x-rays.

Fig. 1

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	Fig. 1 SPS design, showing (a) design route, (b) one period of SPS, and (c) transmission function of SPS and STG within a period, with intensity being normalized with respect to x = d/2.

For a plane wave given by A₀ exp (2πix/λ) incident on a TG with transmittance varying along the x axis, the classical Fourier optics theory predicts that the far-field diffraction pattern in the coordinate system shown in Fig. 2 can be written as

Fig. 2

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	Fig. 2 Coordinate system for SPS geometry.

For the distribution along the ξ-axis, equation (1) is reduced to

If the incident x-rays are transmitted only through the circular pinholes, the SPS transmittance is a real step function that is equal to one within the pinholes and zero on the substrate. In such a case, the variation of the SPS transmission function along the x axis can be written as

Figure 1(c) illustrates the amplitude transmission profile of the SPS within a period. It has a quasi-cosine transmission peculiarity similar to that of an STG. Thus, only zero-order and first order diffractions will exist after being modulated by an SPS, and higher-order diffractions will be eliminated.

Based on the above discussion, the SPS suggested here has approximately the same transmission function as that of an STG. When the number of circular pinholes N along the y axis is large enough, the SPS has the same amplitude transmission profile as the scenario along the x axis and will exhibit quasi-single-order diffraction as an ideal STG. Thus, the SPS will exhibit an approximate 2D single-order diffraction.

To verify the SPS single-order diffraction property for soft x-rays, its far-field diffraction pattern was numerically simulated with Fresnel–Kirchhoff diffraction theory.^[7] Parameters used in the simulation are given in Table 1.

Table 1.

Table 1.

Table 1. Parameters for diffraction pattern simulation of SPS. . Incident wavelength λ/nm 1 Incident angle/(°) 90 Period of SPS d/μm 1 Number of pinholes N 10000 Distance between the SPS and receiving screen Z/m 1.22 Pixel used in the receiving screen Δ x/μm 5 Hits on the receiving screen M × N 2048 × 2048 The thickness of the SPS h/μm 0.4

Table 1. Parameters for diffraction pattern simulation of SPS. .

The far-field diffraction pattern of the 1000-lines/mm SPS for an incident wavelength of 1 nm is shown in Fig. 3(a). The middle peak at the maximum intensity is the zero-order diffraction, and the others are all first-order diffractions. Along the η axis and the ξ axis, the SPS diffraction pattern has just a pair of first-order diffractions and one zero-order diffraction. In addition, according to the intensity profile in Fig. 3(b), even-order diffractions are eliminated and higher-order diffraction components are suppressed by about three orders of magnitude relative to that of the 1 : 1 TG. Although the relative diffraction efficiency (energy ratio of first-order to zero-order diffraction) of the SPS is only 21 %, its application is acceptable for implementing the precise spectrum measurements and serving as a monochromatic source.

Fig. 3

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	Fig. 3 (a) Calculated far-field SPS diffraction pattern at 1 nm, and (b) intensity profile of typical diffraction patterns of 1 : 1 TG and SPS at 1 nm.

A hybrid of electron-beam and x-ray lithography were used to fabricate a high-line-density SPS for x-rays. First, the master mask for the SPS pattern was made by using the electron-beam direct-writing lithography. The task was implemented by the following steps: (i) SiC membrane with a thickness of 2 μm was used as substrate; (ii) a Cr (5 nm)/Au (10 nm) plating base was deposited on the substrate by using electron beam evaporation; (iii) after electron beam resist (ZEP520A) was spin-coated and baked, the SPS patterns were written in the electron beam resist by using the electron beam lithography system; (iv) the resist patterns were transferred into Au layer with a thickness of 300 nm by electroplating process. The second key step is the x-ray lithography, and the main steps are as follows: i) transfer the mask patterns into a positive ZEP520 A resist layer on a 0.2-μm-thick SiC membrane containing a Cr (5 nm)/Au (10 nm) plating base; ii) the x-ray lithography was carried out at beamline 3B1B1 of Beijing Synchrotron Radiation Facility with a resist thickness of 600 nm; iii) the resist patterns were transferred to the Au layer with a thickness of 550 nm by using the electroplating process and the resist mold was removed by using acetone followed by deionized water rinse; iv) the Cr/Au plating base and the SiC film beneath the resist mold were removed by ion beam etching and ICP etching, respectively.

Figure 4 shows the microstructure of a 1000-lines/mm SPS where the red lines indicate the periods. Because there were no isolated points on the opaque substrate, the SPScould be free-standing with no additional polymer membrane substrate for large areas. In addition, the apertures that transmit x-rays are circle. With 2-nm positioning accuracy^[14] and 20-nm–40-nm resolution,^[15] the technique could be used to fabricate an SPS with resolution reaching up to 5000 lines/mm.

Fig. 4

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	Fig. 4 Microstructure of fabricated SPS, with gold substrate thickness being 400 nm, the period 1000 nm, and the hole diameter nearly 500 nm.

The diffraction pattern of the fabricated SPS was characterized with a soft x-ray beam at the Beijing Synchrotron Radiation Facility. A cylinder mirror and flat-field grating were used as a monochromator to isolate single wavelengths in a range of 50 eV–1500 eV. The energy resolution of the monochromator was ΔE/E = 10^–2, and the divergence of the monochromatic x-ray beam was about 5.3 mrad in the axial direction. Figure 5(a) shows a schematic of the calibration arrangement. Various filters were used to eliminate high-order components in the quasi-monochromatic soft x-rays. An ultrafast mechanical shutter was used to control the luminous flux and to avoid trailing the source along columns of the detector. The x-ray detector was a back-illuminated charge-coupled device without an anti-reflection coating (Princeton Instruments, PIXIS-XO:1024B).

Fig. 5

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	Fig. 5 Calibration of SPS. (a) Schematic diagram of experimental arrangement, with SPS being 100-μm wide and 200-μm high; (b) diffraction pattern recorded by CCD at 800 eV; (c) intensity profiles across η axis in Fig. 5(b), where red plot is in Cartesian coordinates, and black plot is log-scaled, and red plot is normalized to the peak intensity of zero-order diffraction.

Figure 5(b) shows the 2D SPS diffraction pattern imaged with an x-ray CCD at a photon energy value of 800 eV. Nine diffraction peaks appear, which are correlated with the calculated diffraction shown in Fig. 3(a). The rectangular diffraction spots arose from the rectangular shape of the SPS. Figure 5(c) shows the plots of one-dimensional intensity profiles across the η axis in Fig. 5(b). The red plot is in Cartesian coordinates, while the black plot has a log scale. As predicted by the theoretical calculation plotted in Fig. 3(b), only three diffraction peaks exist along the symmetry axis. Higher-order diffraction components have intensities that are only 0.47 % of those for the first-order diffractions; they can be as low as the background radiation noise. The relative diffraction efficiency is 21.33 %, which accords well with the theoretical value.

A new single-order diffraction transmission grating for the soft x-ray region is demonstrated. This spectroscopic photon sieve is comprised of many circular apertures, it is free-standing, and it can potentially have a higher linear density obtained by using the current nanofabrication technique. As predicted by theoretical calculations, the calibration results of a 1000-lines/mm SPS verify that higher-order diffractions can be significantly suppressed along the symmetry axis. It thus may become an alternative to conventional transmission gratings for high-accuracy x-ray spectroscopy.