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arXiv:quant-ph/0101122 · Physical Review A

Subwavelength lithography over extended areas

Gunnar G. Bjork, Luis Lorenzo Sánchez-Soto, Jonas Söderholm

Published Jun 8, 2001• 28 citations
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Abstract

We demonstrate a systematic approach to subwavelength resolution lithographic image formation on films covering areas larger than a wavelength squared. For example, it is possible to make a lithographic pattern with a feature size resolution of $\ensuremath{\lambda}/[2(N+1)]$ by using a particular 2M-photon, multimode entangled state, where $N<~M,$ and banks of birefringent plates. By preparing such a statistically mixed state, one can form any pixel pattern on a ${2}^{M\ensuremath{-}N}(N+1)\ifmmode\times\else\texttimes\fi{}{2}^{M\ensuremath{-}N}(N+1)$ pixel grid occupying a square with side ${L=2}^{M\ensuremath{-}N\ensuremath{-}1}\ensuremath{\lambda}.$ Hence, there is a trade off between the exposed area, the minimum lithographic feature size resolution, and the number of photons used for the exposure. We also show that the proposed method will work even under nonideal conditions, albeit with somewhat poorer performance.

DOI
10.1103/physreva.64.013811

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We demonstrate a systematic approach to subwavelength resolution lithographic image formation on films covering areas larger than a wavelength squared. For example, it is possible to make a lithographic pattern with a feature size resolution of \ensuremathλ/[2(N+1)]\ensuremath{\lambda}/[2(N+1)]\ensuremathλ/[2(N+1)] by using a particular 2M-photon, multimode entangled state, where N< M,N<~M,N< M, and banks of birefringent plates. By preparing such a statistically mixed state, one can form any pixel pattern on a 2M\ensuremath−N(N+1)\ifmmode×\else\texttimes\fi2M\ensuremath−N(N+1){2}^{M\ensuremath{-}N}(N+1)\ifmmode\times\else\texttimes\fi{}{2}^{M\ensuremath{-}N}(N+1)2M\ensuremath−N(N+1)\ifmmode×\else\texttimes\fi2M\ensuremath−N(N+1) pixel grid occupying a square with side L=2M\ensuremath−N\ensuremath−1\ensuremathλ.{L=2}^{M\ensuremath{-}N\ensuremath{-}1}\ensuremath{\lambda}.L=2M\ensuremath−N\ensuremath−1\ensuremathλ. Hence, there is a trade off between the exposed area, the minimum lithographic feature size resolution, and the number of photons used for the exposure. We also show that the proposed method will work even under nonideal conditions, albeit with somewhat poorer performance.
While it is certainly possible to generate sub wavelength patterns with arbitrary resolution, the exposure efficiency will scale in a very unfortunate manner. The photons in fields with the required N photon entanglement diffract independently, and hence spread out over the exposed area, making the event that all N photons hit the same detector element very rare. If the lithographic film consist of 5 independent detecting elements, then the exposure time τ scale as τ = S~N. For a 500 x 500 pixel image, this means that the exposure time will increase with a factor 250 000 when going from N to N+l photons.
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.
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.
Quantum lithography promises, in principle, unlimited feature resolution, independent of wavelength. However, in the literature, at least two different theoretical descriptions of quantum lithography exist. They differ in the extent to which they predict that the photons retain spatial correlation from generation to absorption, and although both predict the same feature size, they vastly differ in predicting how efficiently a quantum lithographic pattern can be exposed. Until recently, essentially all quantum lithography experiments have been performed in such a way that it is difficult to distinguish between the two theoretical explanations. However, last year an experiment was performed that gives different outcomes for the two theories. We comment on the experiment and show that the model that fits the data unfortunately indicates that the trade-off between resolution and efficiency in quantum lithography is very unfavourable.
Quantum lithography promises, in principle, unlimited feature resolution, independent of wavelength. However, in the literature, at least two different theoretical descriptions of quantum lithography exist. They differ in the extent to which they predict that the photons retain spatial correlation from generation to absorption, and although both predict the same feature size, they vastly differ in predicting how efficiently a quantum lithographic pattern can be exposed. Until recently, essentially all quantum lithography experiments have been performed in such a way that it is difficult to distinguish between the two theoretical explanations. However, last year an experiment was performed that gives different outcomes for the two theories. We comment on the experiment and show that the model that fits the data unfortunately indicates that the trade-off between resolution and efficiency in quantum lithography is very unfavourable.