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arXiv:1006.2250 · New Journal of Physics

On the efficiency of quantum lithography

Christian Kothe, Gunnar G. Bjork, Shuichiro Inoue, Mohamed Bourennane

Published Apr 19, 2011• 11 citations
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Abstract

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.

DOI
10.1088/1367-2630/13/4/043028

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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.
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.
The working principle of quantum lithography has been demonstrated a few years ago: entangled N-photon systems can improve the spatial resolution of an imaging system by a factor of N, despite the classical Rayleigh limit. Recently, a number of experiments successfully simulated certain features of quantum imaging and two-photon interference-diffraction by using chaotic light in coincidence detection experiments. Can classical light simulate the effect of imaging type quantum lithography? This article attempts to provide an answer to this currently debated question.
At the end of last century, the name of “quantum lithography” has been emerged. This exciting approach was proposed for making a resolution two times higher than that of the conventional optics without changing a wavelength and a numerical aperture. For those who want optical lithography to last long, this has been thought to be a great technology. However, an applicability of the proposed method to the current exposure system i.e., reduced projection exposure system has not yet been examined clearly. We have investigated the proposed quantum lithography to apply into the current exposure system using reticle. For simplicity, coherent illumination i.e. sigma is zero condition is used for calculation. Our quantum lithography compatible to mask exposure system explains probability of one and two photon absorption on the image plane i.e. on wafer. We have shown that the half-wavelength quantum lithography using conventional mask exposure system is impossible because diffraction at the mask makes biphoton into two photon. We have found that there is still super-resolution quantum lithography using mask exposure, however, there is little possibility of quantum lithography practically today because biphoton light source is as dark as stars. To realize quantum lithography practically, further development of not only biphoton light source but also two-photon absorption resist is indispensable.