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Acta Physica Sinica

Method of identifying the relative position between standing wave of laser light and substrate in atom lithography

Wang Jian-Bo, Qian Jin, Yin Cong, Shi Chunying, Lei Ming

Published Jan 1, 2012• 2 citations
Publisher

Abstract

Standing wave of laser light acts as an array of lenses to focus the moving atoms in atom lithography. The position between standing wave and substrate plays an important role in determining the quality of depositional nanometer lines. Using the rule of Gaussian beam, a method of accurately identifying the position of standing wave of laser light is reported. By adjusting accurately the displacement stage which carries the beam focus lens and reflective mirror, the laser beam is subsequently shielded by depositional substrate. Signal of photoelectric detector is changed because of shielding the standing wave, so we can convert the displacement of standing wave into electrical signal. Positioning the standing wave against substrate is achieved by using the value of waist diameter of standing wave of laser light. Theoretical model is developed according to the experimental process. The result of numerical computation coincides well with the experimental record. This method realizes accurately positioning standing wave of laser light against substrate, and it provides the experimental basic for deeply studying the influence of the distance between standing wave and substrate on the quality of depositional nanometer lines.

DOI
10.7498/aps.61.190601

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Standing wave of laser light acts as an array of lenses to focus the moving atoms in atom lithography. The position between standing wave and substrate plays an important role in determining the quality of depositional nanometer lines. Using the rule of Gaussian beam, a method of accurately identifying the position of standing wave of laser light is reported. By adjusting accurately the displacement stage which carries the beam focus lens and reflective mirror, the laser beam is subsequently shielded by depositional substrate. Signal of photoelectric detector is changed because of shielding the standing wave, so we can convert the displacement of standing wave into electrical signal. Positioning the standing wave against substrate is achieved by using the value of waist diameter of standing wave of laser light. Theoretical model is developed according to the experimental process. The result of numerical computation coincides well with the experimental record. This method realizes accurately positioning standing wave of laser light against substrate, and it provides the experimental basic for deeply studying the influence of the distance between standing wave and substrate on the quality of depositional nanometer lines.
The effect of a Gaussian laser standing wave on 23Na atoms was simulated by CRANK-NICOLSON numerical algorithm based on quantum-mechanical method.It was found that atoms focus on wave nodes in standing wave light field with a period of λ/2 when the laser is positive-detuned.The focusing results are in accord with thin lens regime,thick lens regime and channeling regime,respectively,as the optical potential is deepened or the longitudinal velocity of atoms is increased.In thick lens regime,the focal plane shifts backward and the full width at half maximum(FWHM)increases,along the z direction,as the atomic longitudinal velocity increases.With increasing laser power or decreasing beam waist,the FWHM of atomic density peak at the focal plane decreases,both the peak value and the contrast increase.
Atom lithography uses standing wave light fields as arrays of lenses to focus neutral atom beams into line patterns on a substrate. Laser cooled atom beams are commonly used, but an atom beam source with a small opening placed at a large distance from a substrate creates atom beams which are locally geometrically collimated on the substrate. These beams have local offset angles with respect to the substrate. We show that this affects the height, width, shape, and position of the created structures. We find that simulated effects are partially obscured in experiments by substrate-dependent diffusion of atoms, while scattering and interference just above the substrate limit the quality of the standing wave lens. We find that in atom lithography without laser cooling the atom beam source geometry is imaged onto the substrate by the standing wave lens. We therefore propose using structured atom beam sources to image more complex patterns on subwavelength scales in a massively parallel way.
Atom lithography is a technique to structure layers of atoms during deposition, using interactions of near-resonant light fields with neutral atoms. The basic scheme uses a standing wave light field, aligned just above a substrate, while a beam of atoms impinges perpendicularly on the standing wave light field. The interaction of the light field and the atoms focuses the atoms towards the crests or troughs of the standing wave intensity, dependent on the tuning of the light field. The focused atoms are subsequently deposited on the substrate, resulting in an array of lines, whose periodicity is determined by the wavelength of the light field. The standing wave light field can therefore be seen as an array of lenses, focusing the atom beam into an array of lines. The first experiments on atom lithography were performed in the 1990s with sodium and chromium. In this thesis experiments with iron are described, which is a magnetic element and thus allows for the creation of magnetic nanostructures. To focus atom beams into structures using atom lithography, well-colimated atom beams are required. The most common technique to create collimated atom beams is transverse laser cooling, but iron has no closed optical transition suitable for laser cooling. Fortunately Smeets and Te Sligte found that even then atom lithography of iron is possible. If the standing wave light field is considered to be an array of lenses, the focusing of the atom beam on a single lens is determined by the local collimation of the atom beam at that position. This local collimation is determined by the geometry of the beam source and the distance of the beam source to the standing wave lens. Using a small beam source (e.g. 1 mm diameter) positioned far from the standing wave (e.g. 1 m), the geometrically collimated atom beam is suitable for atom lithography. Chapter 3 shows what the implications of geometric collimation are on the structure formation in atom lithography. The geometric effects that locally collimate the atom beam on the sample also introduce local offset angles of the atom beam with respect to the focusing light field. Structure formation has been observed with lines of up to 7 nm high on a background layer of 15 nm average height, over areas of up to 400 µm × 6 mm. This indicates that the offset angles can vary over an 8 mrad range, which is more than an order of magnitude larger than the local angle of collimation. The offset angle influence the local geometry of the deposited structures: an increasing offset angle decreases the local line height, increases the width and creates a skewness in the local line shape. The local geometry of the lines has been modelled with a Monte Carlo particle tracking model and the results were compared to experiments. It was found that the highest and narrowest lines suffer from significant broadening due to surface diffusion in experiments, limiting the achievable structure width of iron on SiOx samples to about 80 nm. We have also found that in atom lithography without laser cooling, each standing wave lens is effectively imaging the source geometry onto the substrate. We therefore propose using structured atom beam sources to image more complex patterns on sub-wavelength scales in a parallel way. The reason to use iron in atom lithography, is the option to create magnetic nanostructures. However, in previous experiments no clear magnetic signature of the atom lithographic structuring of iron was found. Therefore in Chapter 4 firstly the magnetic properties of unstructured layers of iron (Fe), nickel (Ni) and FexNi1-x are investigated. These layers are all ferromagnetic, but with a reduced magnetic moment compared to bulk values due to contaminations and crystal growth effects. As a reference for periodic atom lithography structures, periodic line structures are created with interference lithography in a polymer layer and onto these structures thin layers of FexNi1-x are shadow deposited, thereby creating a layer periodically modulated in both height and elemental composition. This periodic modulation in composition has been observed with SEM-EDX on sub-micron scales. The structures showed a clear magnetic anisotropy with an easy axis along the direction of the lines, in accordance with expectations. In Chapter 5, the magnetic properties of atom lithographic iron line structures are presented. Using MOKE microscopy, direct comparison of structured and unstructured parts of a sample is possible, which allows for the observation of clear magnetic signatures due to the atom lithographic structuring. In layers of an average thickness of about 15 nm, no anisotropy is induced by the line structures, while a magnetic easy axis along the direction of the lines is expected. The line structures introduce an isotropic increase in the coercivity of the layers, indicating that the line structures can be considered as isotropic corrugations instead of directional line structures. For layers of 30 nm average thickness and thus higher line structures, a clear magnetic anisotropy is observed for the highest line structures. This anisotropy can be seen as a magnetic easy axis along the direction of the lines, as expected for line structures. However, we also observe a sharp increase in coercivity for applied fields perpendicular to the lines. This phenomenon is intriguing and may be explained by a pinning of head-to-head domain walls along the direction of the lines. In Chapter 5, we also report on the first results of co-deposition of FexNi1-x, where the Fe is structured into lines using atom lithography, while the Ni is deposited uniformly, thereby creating an alloy of modulating composition. Magnetic analysis of these structures indicates that these structures are anisotropic, both the coercivity and the shape of domain walls is dependent on the angle of the applied field relative to the line structures. Finally in Chapter 6, we investigate the possibilities to focus a thermal beam of atoms into a single 100 nm spot using light fields, thereby creating a nanopencil suitable for deposition of nanostructures. A Monte Carlo particle tracking program was developed to model the all optical focusing or funneling of 10 µm sized atom beams to a 100 nm spot. This model included effects of initial beam divergence, magnetic substructure, laser cooling, and spontaneous as well as stimulated diffusion and it was applied to a number of promising light field configurations. The best results obtained for experimentally realistic settings are a beam focused to a full width at half maximum of FWHM = 0.55 µm in a blue detuned hollow beam where atoms are focused towards the dark center, or a FWHM = 0.31 µm in a red detuned axicon light field, where atoms are focused towards the maximum intensity at the heart line. However, in the latter case the focused beam has a flux only 25 times larger than the background flux, which is unpractical for applications. The limiting factors of all schemes are heating due to stimulated diffusion and the limited interaction time available for a thermal beam of atoms. A nanopencil could be possible if it were based on the focussing of a slow and / or monochromatic atom beam, but this would seriously complicate the practical application of such a device.
Atom lens generated by a laser standing wave can be used to focus an atomic beam to nanometer dimensions. Aberrations exist in atom lens owing to the influence of velocity spread, beam spread, wave nature of atoms and so on. Two theoretical models were built to describe atom lens. Spherical aberration, chromatic aberration and the aberration caused by angular spread were analyzed with semi-classical model, and diffractive aberration was analyzed using quantum model. Simulation results show that aberration originates mainly from beam spread, and diffractive aberration is larger than spherical aberration and chromatic aberration. Three solutions of optimization of experimental parameters, adding beam mask and using etching technologies for improving atom lithography quality are presented.
We start from the intensity distribution of a standing wave (SW) laser field and deduce the classical equation of atomic motion. The image distortion is analyzed using transfer function approach. Atomic flux density distribution as a function of propagation distance is calculated based on Monte-Carlo scheme and trajectory tracing method. Simulation results have shown that source imperfection, especially beam spread, plays an important role in broadening the feature width, and the focus depth of atom lens for real atomic source is longer than that for perfect source. The ideal focal plane can be easily determined by the variation of atomic density at the minimal potential of the laser field as a function of traveling distance.