† Corresponding author. E-mail:
Project supported by the National Natural Science Foundation for Young Scientists of China (Grant No. 11805179).
A single-order diffraction transmission grating named spectroscopic photon sieve (SPS) for soft x-ray region is proposed and demonstrated in this paper. The SPS consists of many circular pinholes located randomly, and can realize both free-standing diffractions and the suppression of higher-order differations. In this paper, the basic concept, numerical simulations, and calibration results of a 1000-lines/mm SPS for soft x-ray synchrotron radiation are presented. As predicted by theoretical calculations, the calibration results of a 1000-lines/mm SPS verify that the higher-order diffractions can be significantly suppressed along the symmetry axis. With the current nanofabrication technique, the SPS can potentially have a higher line density, and can be widely used in synchrotron radiation, laser-induced plasma diagnostics, and astrophysics.
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.
![]() | 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
For the distribution along the ξ-axis, equation (
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
![](cpb_29_5_054101/cpb_29_5_054101_ieqn3.gif)
Figure
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
![]() | 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.
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
![]() | 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
Figure
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.
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