Diffraction gratings with high efficiency and high groove density are required for EUV and soft x-ray spectroscopy
techniques (such as Resonant Inelastic X-ray Scattering, RIXS) designed for state-of-the-art spectral resolution and
throughput. A multilayer coated blazed grating (MBG) fabricated by deposition of a multilayer on a saw-tooth substrate
could address these challenges. In order to obtain high diffraction efficiency one should provide perfect triangular
grooves on a substrate and perfect replication of the groove profile during the multilayer deposition. However,
multilayers trend to smooth out the corrugated surface of the substrates, resulting in the main limiting factor for
efficiency of ultra-dense MBGs. Understanding of the growth of multilayers on saw-tooth substrates is a key for further
grating improvement. In this work we investigate growth behavior of Al/Zr multilayers on saw-tooth substrates with a
groove density of 10,000 lines/mm. We apply existing growth models to describe an evolution of Power Spectral
Density functions of a grating surface during the multilayer deposition, and identify a main smoothing mechanism. We
found that growth of flat multilayers is well modeled with surface diffusion caused by surface curvature as a main
relaxation mechanism, while growth of the multilayer on saw-tooth substrates obeys different kinetics. Limitations of the
linear approach and possible model improvements by accounting for an additional component of the surface diffusion
flux, caused by a gradient of adatom concentration on a corrugated surface are discussed.
KEYWORDS: Modulation transfer functions, Calibration, Transmission electron microscopy, Scanning electron microscopy, Electron microscopes, Binary data, Interferometers, Profilometers, Spatial frequencies, Microscopes
A modulation transfer function (MTF) calibration method based on binary pseudorandom (BPR) gratings and arrays has been proven to be an effective MTF calibration method for interferometric microscopes and a scatterometer. Here we report on a further expansion of the application range of the method. We describe the MTF calibration of a 6 in. phase shifting Fizeau interferometer. Beyond providing a direct measurement of the interferometer's MTF, tests with a BPR array surface have revealed an asymmetry in the instrument's data processing algorithm that fundamentally limits its bandwidth. Moreover, the tests have illustrated the effects of the instrument's detrending and filtering procedures on power spectral density measurements. The details of the development of a BPR test sample suitable for calibration of scanning and transmission electron microscopes are also presented. Such a test sample is realized as a multilayer structure with the layer thicknesses of two materials corresponding to the BPR sequence. The investigations confirm the universal character of the method that makes it applicable to a large variety of metrology instrumentation with spatial wavelength bandwidths from a few nanometers to hundreds of millimeters.
KEYWORDS: Modulation transfer functions, Transmission electron microscopy, Scanning electron microscopy, Calibration, Binary data, Interferometers, Electron microscopes, Silicon, Spatial frequencies, Interferometry
A modulation transfer function (MTF) calibration method based on binary pseudo-random (BPR) gratings and arrays
[Proc. SPIE 7077-7 (2007), Opt. Eng. 47(7), 073602-1-5 (2008)] has been proven to be an effective MTF calibration
method for a number of interferometric microscopes and a scatterometer [Nucl. Instr. and Meth. A 616, 172-82 (2010].
Here we report on a significant expansion of the application range of the method. We describe the MTF calibration of a
6 inch phase shifting Fizeau interferometer. Beyond providing a direct measurement of the interferometer's MTF, tests
with a BPR array surface have revealed an asymmetry in the instrument's data processing algorithm that fundamentally
limits its bandwidth. Moreover, the tests have illustrated the effects of the instrument's detrending and filtering
procedures on power spectral density measurements. The details of the development of a BPR test sample suitable for
calibration of scanning and transmission electron microscopes are also presented. Such a test sample is realized as a
multilayer structure with the layer thicknesses of two materials corresponding to BPR sequence. The investigations
confirm the universal character of the method that makes it applicable to a large variety of metrology instrumentation
with spatial wavelength bandwidths from a few nanometers to hundreds of millimeters.
Multilayer coated blazed gratings with high groove density are the best candidates for use in high resolution EUV and
soft x-ray spectroscopy. Theoretical analysis shows that such a grating can be potentially optimized for high dispersion
and spectral resolution in a desired high diffraction order without significant loss of diffraction efficiency. In order to
realize this potential, the grating fabrication process should provide a perfect triangular groove profile and an extremely
smooth surface of the blazed facets. Here we report on recent progress achieved at the Advanced Light Source (ALS) in
fabrication of high quality multilayer coated blazed gratings. The blazed gratings were fabricated using scanning beam
interference lithography followed by wet anisotropic etching of silicon. A 200 nm period grating coated with a Mo/Si
multilayer composed with 30 bi-layers demonstrated an absolute efficiency of 37.6% in the 3rd diffraction order at 13.6
nm wavelength. The groove profile of the grating was thoroughly characterized with atomic force microscopy before and
after the multilayer deposition. The obtained metrology data were used for simulation of the grating efficiency with the
vector electromagnetic PCGrate-6.1 code. The simulations showed that smoothing of the grating profile during the
multilayer deposition is the main reason for efficiency losses compared to the theoretical maximum. Investigation of the
grating with cross-sectional transmission electron microscopy revealed a complex evolution of the groove profile in the
course of the multilayer deposition. Impact of the shadowing and smoothing processes on growth of the multilayer on the
surface of the sawtooth substrate is discussed.
The major problem of measurement of a power spectral density (PSD) distribution of surface heights with surface profilometers arises due to the unknown modulation transfer function (MTF) of the instruments, which tends to distort the PSD at higher spatial frequencies. The special mathematical properties of binary pseudo-random patterns make them an ideal basis for developing MTF calibration test surfaces. Two-dimensional binary pseudo-random arrays have been fabricated and used for the MTF calibration of the MicroMapTM-570 interferometric microscope with all available objectives. An investigation into the effects of fabrication imperfections on the quality of the MTF calibration and a procedure for accounting for such imperfections are presented.
We report on recent progress in developing diffraction gratings which can potentially provide extremely high spectral
resolution of 105-106 in the EUV and soft x-ray photon energy ranges. Such a grating was fabricated by deposition of a
multilayer on a substrate which consists of a 6-degree blazed grating with a high groove density. The fabrication of the
substrate gratings was based on scanning interference lithography and anisotropic wet etch of silicon single crystals. The
optimized fabrication process provided precise control of the grating periodicity, and the grating groove profile, together
with very short anti-blazed facets, and near atomically smooth surface blazed facets. The blazed grating coated with 20
Mo/Si bilayers demonstrated a diffraction efficiency in the third order as high as 33% at an incidence angle of 11° and
wavelength of 14.18 nm. This work was supported by the US Department of Energy under contract number DE-AC02-05CH11231.
The major problem of measurement of a power spectral density (PSD) distribution of the surface heights with surface
profilometers arises due to the unknown Modulation Transfer Function (MTF) of the instruments. The MTF tends to
distort the PSD at higher spatial frequencies. It has been suggested [Proc. SPIE 7077-7, (2007), Opt. Eng. 47 (7),
073602-1-5 (2008)] that the instrumental MTF of a surface profiler can be precisely measured using standard test
surfaces based on binary pseudo-random (BPR) patterns. In the cited work, a one dimensional (1D) realization of the
suggested method based on use of BPR gratings has been demonstrated. Here, we present recent achievements made in
fabricating and using two-dimensional (2D) BPR arrays that allow for a direct 2D calibration of the instrumental MTF.
The 2D BPRAs were used as standard test surfaces for 2D MTF calibration of the MicromapTM-570 interferometric
microscope with all available objectives. The effects of fabrication imperfections on the efficiency of calibration are also
discussed.
State of the art soft x-ray spectroscopy techniques like Resonant Inelastic X-ray Scattering (RIXS) require diffraction gratings which can provide extremely high spectral resolution of 105-106. This problem may be addressed with a sliced multilayer grating with an ultra-high groove density (up to 50,000 mm-1) proposed in the recent publication [Voronov, D. L., et al., Proc. SPIE 6705, 67050E (2007)]. It has been suggested to fabricate such a grating by deposition of a soft x-ray multilayer on a substrate which is a blazed saw-tooth grating (echellette) with low groove density. Subsequent polishing applied to the coated grating removes part of the coating and forms an oblique-cut multiline structure that is a sliced multilayer grating. The resulting grating has a short-scale periodicity of lines (bilayers), which is defined by the multilayer period and the oblique-cut angle. We fabricated and tested a Sc/Si multilayer sliced grating suitable for EUV applications, which is a first prototype based on the suggested technique. In order to fabricate an echellette substrate, we used anisotropic KOH etching of a Si wafer. The etching regime was optimized to obtain smooth and flat echellette facets. A Sc/Si multilayer was deposited by dc-magnetron sputtering, and after that it was mechanically polished using a number of diamond pastes. The resulting sliced grating prototype with ~270 nm line period has demonstrated a dispersive ability in the 41-49 nm photon wavelength range with a diffraction efficiency of ~7% for the optimized 38th order assigned to the echellette grating of 10 μm period.
Resonant Inelastic X-ray Scattering (RIXS) is the one of the most powerful methods for investigation of the electronic
structure of materials, specifically of excitations in correlated electron systems. However the potential of the RIXS
technique has not been fully exploited because conventional grating spectrometers have not been capable of achieving
the extreme resolving powers that RIXS can utilize. State of the art spectrometers in the soft x-ray energy range achieve
~0.25 eV resolution, compared to the energy scales of soft excitations and superconducting gap openings down to a
few meV. Development of diffraction gratings with super high resolving power is necessary to solve this problem. In
this paper we study the possibilities of fabrication of gratings of resolving power of up to 106 for the 0.5 - 1.5 KeV
energy range. This energy range corresponds to all or most of the useful dipole transitions for elements of interest in
most correlated electronic systems, i.e. oxygen K-edge of relevance to all oxides, the transition metal L2,3 edges, and the
M4,5 edges of the rare earths. Various approaches based on different kinds of diffraction gratings such as deep-etched
multilayer gratings, and multilayer coated echelettes are discussed. We also present simulations of diffraction efficiency
for such gratings, and investigate the necessary fabrication tolerances.
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