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Journal of the Optical Society of America B

Calculation of atomic positions in nanometer-scale direct-write optical lithography with an optical standing wave

Karl K. Berggren, Mara Goff Prentiss, Gregory L. Timp, Robert E. Behringer

Published Jul 1, 1994• 46 citations
Publisher

Abstract

Recent experiments have shown that the light pressure force that is due to an optical standing wave (SW) focuses an atomic beam to submicrometer dimensions. We calculate some theoretical limits on the focusing of a sodium atomic beam by a SW optical field.
DOI
10.1364/josab.11.001166

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We passed a transversely cooled sodium atomic beam through an optical standing wave, which channeled the atoms into the intensity minima (maxima) for light tuned below (above) the sodium 32S1/2 → 32P3/2 resonance frequency. The channeled atoms retained their spatial distribution when they were deposited onto the silicon surface. The surface was thus covered by a permanent periodic sodium grating with an area of 1 x 0.1 cm2 and a period of d = 294.3 ±0.3 nm, which is half the wavelength of the standing wave field. The entire grating was completed in 10 min. We measured the period of the grating by backscattering weak probe light. The probe light had a wavelength λ, which we varied between 5580 and 5800 Å, and was incident at an angle ϕ relative to the normal. There is constructive interference when the angle θ with respect to the normal to the grating is such that λ = d(sin θ + sin ϕ). The dependence of θ on ϕ allowed us to measure d. Semiclassical theory suggests the width of the lines in the grating could be of the order of 100 Å.

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Journal of the Optical Society of America B•Oct 1, 1995•89 citations
Recent experiments have demonstrated that the light pressure force from an optical standing wave (SW) focuses an atomic beam to sub-micrometre dimensions. We start from a two-dimensional time-dependent Schrödinger equation and reduce it to a one-dimensional equation by a paraxial approximation. We calculate some theoretical limits on the focusing of an atomic beam by an SW optical field. It is found that two parameters, the atomic velocity and the intensity of the laser beam, play an important role in determining the deposition quality.
Recent experiments have demonstrated that the light pressure force from an optical standing wave (SW) focuses an atomic beajm to sub-micrometre dimensions.We start from a two-dimensional time-dependent Schrodinger equation and reduce in to a one-dimensional equation by a paraxial approximation.We calculate some theoretical limits on the focusing of an atomic beam by an SW optical field.It is found that two parameters,the atomic velocity and the intensity of the laser beam,play an important role in determining the deposition quality.
Summary form only given. Recently it has been demonstrated that neutral atomic beams can be focused by use of a laser as an atom-optical lens. Standing wave atom-optical (SW) lenses have been of particular interest because of the potential for both high-resolution and high-throughput lithography. In this paper, using sub-Doppler optical cooling schemes in conjunction with mechanical collimation, and a SW with /spl sigma/=56 /spl mu/m, we have been able to achieve <20 nm resolution with contrast of at least 10:1, focusing a thermal atomic sodium beam using 589-nm light corresponding to the D/sub 2/ transition.
The light pressure force from an optical standing wave (SW) can focus an atomic beam to submicrometer dimensions. To make the best of this technique it is necessary to find a set of optimal experimental parameters. In this paper we consider theoretically the chromium atoms focusing and demonstrate that the focusing performance depends not only on the strength of but also on the time atoms take to traverse the force field. The general conclusions drawn can easily be applied to other atoms. To analyze the problem we numerically integrate a coupled time-dependent Schro¨dingerSchr{\"{o}}dingerSchro¨dinger equation over a wide range of experimental parameters. It is found that an optimal atomic beam speed-laser intensity pair does exist, which could give substantially improved focusing over the one with the experimental parameters given in the literature. It is also shown that the widely used classical particle optics approach can lead to erroneous predictions.
We passed a transversely cooled sodium atomic beam through an optical standing wave, which channeled the atoms into the intensity minima (maxima) for light tuned below (above) the sodium 32S1/2 → 32P3/2 resonance frequency. The channeled atoms retained their spatial distribution when they were deposited onto the silicon surface. The surface was thus covered by a permanent periodic sodium grating with an area of 1 x 0.1 cm2 and a period of d = 294.3 ±0.3 nm, which is half the wavelength of the standing wave field. The entire grating was completed in 10 min. We measured the period of the grating by backscattering weak probe light. The probe light had a wavelength λ, which we varied between 5580 and 5800 Å, and was incident at an angle ϕ relative to the normal. There is constructive interference when the angle θ with respect to the normal to the grating is such that λ = d(sin θ + sin ϕ). The dependence of θ on ϕ allowed us to measure d. Semiclassical theory suggests the width of the lines in the grating could be of the order of 100 Å.
The focusing of atoms to nanometer-scale dimensions by a near-resonant standing-wave light field is examined from a particle optics perspective. The classical equation of motion for atoms traveling through the lens formed by a node of the standing wave is derived and converted to a spatial trajectory equation. A paraxial solution is obtained, which results in simple expressions for the focal properties of the lens, useful for estimating its behavior. Aberrations are also discussed, and an exact numerical solution of the trajectory equation is presented. The effects on focal linewidth of angular collimation and velocity spread in the atomic beam are investigated, and it is shown that angular collimation has a much more significant effect than velocity spread, even when the velocity spread is thermal.