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arXiv:2201.03845 · Journal of Physics B Atomic Molecular and Optical Physics

An atom passing through a hole in a dielectric membrane: impact of dispersion forces on mask-based matter-wave lithography

Johannes Fiedler, Bodil Holst

Published Jan 13, 2022• 13 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1361-6455/ac4b41

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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.
Mask-based pattern generation is a crucial step in microchip production. The next-generation extreme-ultraviolet- (EUV) lithography instruments with a wavelength of 13.5 nm are currently under development. In principle, this should allow patterning down to a resolution of a few nanometers in a single exposure. However, there are many technical challenges, including those due to the very high energy of the photons. Lithography with metastable atoms has been suggested as a cost-effective, less-complex alternative to EUV lithography. The great advantage of atom lithography is that the kinetic energy of an atom is much less than that of a photon for a given wavelength. However, until now no method has been available for making masks for atom lithography that can produce arbitrary, high-resolution patterns. Here we present a solution to this problem. First, traditional binary holography is extended to near-field binary holography, based on Fresnel diffraction. By this technique, we demonstrate that it is possible to make masks that can generate arbitrary patterns in a plane in the near field (from the mask) with a resolution down to the nanometer range using a state-of-the-art metastable-helium source. We compare the flux of this source with that of an established EUV source (NXE:3100, ASML) and show that patterns can potentially be produced at comparable speeds. Finally, we present an extension of the grid-based holography method for a grid of hexagonally shaped subcells. Our method can be used with any beam that can be modeled as a scalar wave, including other matter-wave beams such as helium ions, electrons, or acoustic waves.
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.
Mask based pattern generation with photolithography is a crucial step in microchip production. The next generation Extreme Ultra Violet (EUV) lithography instruments with a wavelength of 13.5 nm is currently under development. In principle this allows patterning down to a few nm resolution in a single exposure. However, there are many technical challenges due to the very high energy of the photons among others. Lithography with metastable atoms has been suggested as a cost effective, less complex alternative to EUV lithography. The big advantage of atom lithography is that the kinetic energy of an atom is much smaller than that of a photon for a given wavelength. However up till now no method has been available for making masks for atom lithography that can produce arbitrary, high resolution patterns. Here we present a solution to this problem. We show that it is possible to make masks based on binary holography that can generate arbitrary patterns down to a few nm resolution using a state of the art metastable helium source. We compare the flux of this source with that of an established EUV source (ASML, NXE:3100) and show that patterns can potentially be produced at comparable speeds. Finally we present an extension of the grid based holography method for a grid of hexagonally shaped subcells. Our method can be used with any wave beam, including other matter wave beams such as helium ions or electrons.
Mask-based pattern generation is a crucial step in microchip production, but there are many technical challenges in scaling current techniques down to nanometer resolution. Lithography using metastable atoms has been suggested as a cost-effective, less complex alternative to conventional techniques, including extreme ultraviolet (EUV) photolithography. This study presents a method based on binary holography that can be used to shape atom beams into arbitrary patterns. Simulations demonstrate the potential for state-of-the-art helium sources to produce patterns with nanometer resolution.
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.
Due to their very short de Broglie wavelengths, matter waves could be used for high-resolution patterning, competing with e.g.e.g.e.g. e-beam or helium-ion lithography for producing features smaller than 10 nm. Binary holography is presently the only method available for mask-based atom lithography, but its theoretical framework has remained quite limited. The authors present an optimal method for making binary holograms that can shape atom beams arbitrarily, allowing for free selection of the geometrical properties of the generated masks, and the resulting structures.