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arXiv:2406.16543 · Nanoscale Advances

Atomic diffraction by nanoholes in hexagonal boron nitride

Eivind Kristen Osestad, Ekaterina Zossimova, Michael Walter, Bodil Holst, Johannes Fiedler

Published Jan 1, 2024• 2 citations
arXivHTMLPDF

Abstract

Fabricating patterned nanostructures with matter waves can help to realise new nanophotonic devices. However, due to dispersion effects, designing patterns with nanoscale features is challenging. Here, we consider the propagation of a helium matter wave through different holes in hexagonal boron nitride (h-BN) as a case study for the weakest dispersion interaction and the matter wave's diffraction as it passes through the holes. We use a quantum-mechanical model to calculate the polarisability of edge atoms around the holes, where we observe polarisation ripples of enhanced and reduced polarisabilities around the holes. We use these values to calculate van der Waals dispersion coefficients for the scattered helium atoms. We find that the resulting diffraction patterns are affected by the shape and size of the holes, where the smallest holes have a radius of just 6 Å. These results can be used to predict the resolution limits of nano-hole patterns on nanophotonic materials.

DOI
10.1039/d4na00322e

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Fabricating patterned nanostructures with matter waves can help to realise new nanophotonic devices. However, due to dispersion effects, designing patterns with nanoscale features is challenging. Here, we consider the propagation of a helium matter wave through different holes in hexagonal boron nitride (h-BN) as a case study for the weakest dispersion interaction and the matter wave's diffraction as it passes through the holes. We use a quantum-mechanical model to calculate the polarisability of edge atoms around the holes, where we observe polarisation ripples of enhanced and reduced polarisabilities around the holes. We use these values to calculate van der Waals dispersion coefficients for the scattered helium atoms. We find that the resulting diffraction patterns are affected by the shape and size of the holes, where the smallest holes have a radius of just 6 Å. These results can be used to predict the resolution limits of nano-hole patterns on nanophotonic materials.
Abstract The diffraction of atoms and molecules through tiny, sub-nanometre holes in atomically thin membranes is a promising approach for advancing atom interferometry sensing and atomic holography. However, dispersion interactions, such as the Casimir-Polder force, pose a significant challenge by attracting diffracting particles to the membrane, limiting the minimum hole size. This paper presents a numerical simulation of helium matter-wave diffraction through sub-nanometre holes in hexagonal boron nitride by solving the time-dependent Schrödinger equation. Our results show that the transmission rates in the quantum approach are significantly higher than those predicted by the commonly used semi-classical approach. This suggests that significantly smaller holes can be used in the design of diffractive masks, provided that fabrication techniques can meet the atomic-level precision to realise such holes. Furthermore, we observe notable differences in diffraction patterns, even for atom velocities that are much greater than the expected convergence threshold between semi-classical and quantum computational models.
Abstract Fast, large area patterning of arbitrary structures down to the nanometre scale is of great interest for a range of applications including the semiconductor industry, quantum electronics, nanophotonics and others. It was recently proposed that nanometre-resolution mask lithography can be realised by sending metastable helium atoms through a binary holography mask consisting of a pattern of holes. However, these first calculations were done using a simple scalar wave approach, which did not consider the dispersion force interaction between the atoms and the mask material. To access the true potential of the idea, it is necessary to access how this interaction affects the atoms. Here we present a theoretical study of the dispersion force interaction between an atom and a dielectric membrane with a hole. We look at metastable and ground state helium, using experimentally realistic wavelengths (0.05–1 nm) and membrane thicknesses (5–50 nm). We find that the effective hole radius is reduced by around 1–7 nm for metastable helium and 0.5–3.5 nm for ground-state helium. As expected, the reduction is largest for thick membranes and slow atoms.
In atom optics a material structure is commonly regarded as an amplitude mask for atom waves. However, atomic diffraction patterns formed using material gratings indicate that material structures also operate as phase masks. In this study a well collimated beam of sodium atoms is used to illuminate a silicon nitride grating with a period of 100 nm. During passage through the grating slots atoms acquire a phase shift due to the van der Waals interaction with the grating walls. As a result the relative intensities of the matter-wave diffraction peaks deviate from those expected for a purely absorbing grating. Thus a complex transmission function is required to explain the observed diffraction envelopes. An optics perspective to the theory of atomic diffraction from material gratings is put forth in the hopes of providing a more intuitive picture concerning the influence of the vdW potential. The van der Waals coefficient C3=2.7±0.8meVnm3C_{3} = 2.7\pm 0.8{meV nm}^{3}C3​=2.7±0.8meVnm3 is determined by fitting a modified Fresnel optical theory to the experimental data. This value of C3C_{3}C3​ is consistent with a van der Waals interaction between atomic sodium and a silicon nitride surface.
In atom optics a material structure is commonly regarded as an amplitude mask for atom waves. However, atomic diffraction patterns formed using material gratings indicate that material structures also operate as phase masks. In this study a well collimated beam of sodium atoms is used to illuminate a silicon nitride grating with a period of 100 nm. During passage through the grating slots atoms acquire a phase shift due to the van der Waals interaction with the grating walls. As a result the relative intensities of the matter-wave diffraction peaks deviate from those expected for a purely absorbing grating. Thus a complex transmission function is required to explain the observed diffraction envelopes. An optics perspective to the theory of atomic diffraction from material gratings is put forth in the hopes of providing a more intuitive picture concerning the influence of the vdW potential. The van der Waals coefficient C3=2.7pm0.8meVnm3C_{3} = 2.7\\pm 0.8{meV nm}^{3}C3​=2.7pm0.8meVnm3 is determined by fitting a modified Fresnel optical theory to the experimental data. This value of C3C_{3}C3​ is consistent with a van der Waals interaction between atomic sodium and a silicon nitride surface.
In atom optics a material structure is commonly regarded as an amplitude mask for atom waves. However, atomic diffraction patterns formed using material gratings indicate that material structures also operate as phase masks. In this study a well collimated beam of sodium atoms is used to illuminate a silicon nitride grating with a period of 100 nm. During passage through the grating slots atoms acquire a phase shift due to the van der Waals (vdW) interaction with the grating walls. As a result the relative intensities of the matter-wave diffraction peaks deviate from those expected for a purely absorbing grating. Thus a complex transmission function is required to explain the observed diffraction envelopes. An optics perspective to the theory of atomic diffraction from material gratings is put forth in the hopes of providing a more intuitive picture concerning the influence of the vdW potential. The van der Waals coefficient ${C}_{3}=2.7\ifmmode\pm\else\textpm\fi{}0.8\phantom{\rule{0.3em}{0ex}}\mathrm{meV}\phantom{\rule{0.3em}{0ex}}{\mathrm{nm}}^{3}$ is determined by fitting a modified Fresnel optical theory to the experimental data. This value of C3{C}_{3}C3​ is consistent with a van der Waals interaction between atomic sodium and a silicon nitride surface.
The resonant metastability-exchange process is used to obtain a metastable atom beam with intrinsic properties close to those of a ground-state atom nozzle beam (small angular aperture, narrow velocity distribution). The estimated effective source diameter (15 µm) is small enough to provide at a distance of 597 mm a transverse coherence radius of about 873 nm for argon, 1236 nm for neon and 1660 nm for helium. It is demonstrated both by experiment and numerical calculations with He*, Ne* and Ar* metastable atoms, that this beam gives rise to diffraction effects on the transmitted angular pattern of a silicon-nitride nano-slit grating (period 100 nm). Observed patterns are in good agreement with previous measurements with He* and Ne* metastable atoms. For argon, a calculation taking into account the angular aperture of the beam (0.35 mrad) and the effect of the van der Waals interaction—the van der Waals constant C 3 = 1.83 +0.1 −0.15 au being derived from spectroscopic data—leads to a good agreement with experiment.