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arXiv:quant-ph/0011088 · Physical Review A

Quantum-interferometric optical lithography: Towards arbitrary two-dimensional patterns

Pieter Kok, Agedi N. Boto, Daniel S. Abrams, Colin P. Williams, Samuel L. Braunstein, Jonathan P. Dowling

Published May 9, 2001• 127 citations
arXivHTMLPDF

Abstract

As demonstrated by Boto et al. [Phys. Rev. Lett. 85, 2733 (2000)], quantum lithography offers an increase in resolution below the diffraction limit. Here, we generalize this procedure in order to create patterns in one and two dimensions. This renders quantum lithography a potentially useful tool in nanotechnology.
DOI
10.1103/physreva.63.063407

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As demonstrated in Boto et al. [quant-ph/9912052], quantum lithography offers an increase in resolution without an upper bound. This procedure makes use of the entangled state (| n ,0〉+ e inϕ |0, n 〉)/√2. It allows us to write evenly spaced lines with sub-wavelength resolution. Here we generalise this procedure in such a way that it enables us to create arbitrary patterns in one dimension. We distinguish two methods: the ‘Fourier method’ and ‘the superposition method’. The Fourier method is conceptually easier since it depends on Fourier series, but it also involves a minimal finite amount of unwanted exposure of the substrate. The superposition method gets around this problem and gives generally better results, but lacks the intuitive clarity of the Fourier method. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Classical optical lithography is diffraction limited to writing features of a size lambda/2 or greater, where lambda is the optical wavelength. Using nonclassical photon-number states, entangled N at a time, we show that it is possible to write features of minimum size lambda/(2N) in an N-photon absorbing substrate. This result allows one to write a factor of N2 more elements on a semiconductor chip. A factor of N = 2 can be achieved easily with entangled photon pairs generated from optical parametric down-conversion. It is shown how to write arbitrary 2D patterns by using this method.
Based on our previous scheme [Hemmer et al., Phys. Rev. Lett. 96, 163603 (2006)] we show the procedures to obtain any one- or two-dimensional pattern by multiple exposures. A key modification to the resonance condition is made to achieve subwavelength pattern resolution. The level separation of the substrate does not pose an upper limit to the frequency summation. So the fundamental frequency can be high and the number of Fourier terms can be large, making our scheme very suitable for subwavelength arbitrary patterns.