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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Theoretical consideration on quantum lithography with conventional projection

Tôru Fujii, Naoki Fukutake, Hisao Osawa, Hiroshi Ooki

Published Jun 25, 2003• 4 citations
Publisher

Abstract

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.

DOI
10.1117/12.485335

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•Jul 28, 2014•0 citations
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.
It is well known that entangled-photon pairs generated by spontaneous parametric down-conversion exhibit a property that is analogous to that of ordinary incoherent lights. We formulate an image-forming optical theory of quantum lithography that comprehends the both conceptions of partial coherence and partial entanglement by extending a classical image-forming optical theory. Our optical system consists of an image-forming system, an illumination system with a second-order nonlinear medium, and two-photon absorbing materials. We evaluate the resolution of the quantum lithography system by using the optical transfer function and show a special case to be a super-resolving system.
The concept of performing quantum lithography with classical, instead of entangled, light is of great interest for practical implementation. One recent proposal [Hemmer, Muthukrishnan, Scully, and Zubairy, Phys. Rev. Lett. 96, 163603 (2006)] to accomplish this was based on the use of frequency selective multiphoton transitions in a two-level atom. To analyze this possibility we investigate a four-level system theoretically and show that a high-resolution lithography is possible. We quantitatively identify conditions under which high-contrast lithography can be performed without sacrificing high resolution. The approach is a perturbative density matrix method. This model identifies the tradeoff between resolution and contrast as being due to higher-order terms from intermediate-level Rabi oscillations. We propose using positive and negative one-photon detunings to suppress this effect. Allowing higher Rabi frequencies means that shorter interaction time can be used, and this overcomes the degradation in contrast due to population decay. Finally, we generalize our scheme to $\mathbit{N}$-photon lithography.
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.
We formulate an image-forming optical theory of quantum lithography in which Entangled-photon pairs generated by spontaneous parametric down-conversion play an important role. Our optical system consists of an image-forming system, an illumination system with a second-order nonlinear medium, and two-photon absorbing materials. We evaluate the resolution of the quantum lithography system by using the optical transfer function and show a super-resolving condition which is, however, difficult to achieve.
The advantages of using nonclassical states of light for optical imaging are discussed, with special emphasis on the new field of quantum optical lithography. The classical resolution limit given by the Rayleigh criterion is approximately half of the optical wavelength. However, it has been argued that, by using special quantum states of light and a multiphoton-sensitive material or detector, this limit can be broken. Here, a brief and rigorous overview of this problem is provided, some particularly widespread misconceptions are addressed, and turning quantum lithography into a practical technology is discussed.
The resolution of traditional optical microscope and optical lithography is limited by about half wavelength of the light source, which is well known as the diffraction limit or Abbe limit. The resolution limit is due to the missing of high spatial frequency components in the far-field. One way to achieve high resolution is to move the detector into the near-field region where the evanescent wave can be collected. However, these methods are surface-bound and usually very slow which have limited applications. It has long been an interesting and important question about how to overcome the diffraction limit in the far-field.\n\nFor optical lithography, a number of methods have been proposed to overcome the diffraction limit such as multi-photon scanning, quantum entanglement, quantum inspired process (e.g., dopperlon), and quantum dark state. However, these methods either require multi-photon absorber, quantum entanglement, or multi-energy levels, which restrict them from extending to higher resolution in practice. In this thesis, we showed that sub-diffraction-limited resolution can be generated by the coherent Rabi gradient. This method does not require multi-photon absorber or quantum entanglement but just quantum coherence of the medium. Extension from lower resolution to higher resolution is very straightforward where we just need to increase the pulse intensity or pulse duration. We also proposed two atom lithography experiments based on the Rabi gradient. The first one uses Rubidium Rydberg atom and microwave where we showed that sub-micrometer line spacing is possible. The second one uses Chromium atom and optical field where we showed that sub-10nm line spacing is possible while the wavelength of the light is about 400nm.\n\nFor optical imaging, a number of methods have also been proposed to achieve super-resolution such as multi-photon microscope, stimulated-emission-depletion, structured illumination microscopy, centroid-based techniques and metamaterial-based lens. Here, we will show a new method to achieve resolution beyond the diffraction limit which we called it resonance fluorescence microscopy. Resonance fluorescence has been proposed to localize a single atom with resolution beyond the diffraction limit. The separation between two atoms can also be extracted from the resonance\nfluorescence spectrum. To develop it as microscopy, we need to evaluate the resonance fluorescence spectrum of multiple-atom system. We analytically solved the general feature of the spectrum when the Rabi frequency is much larger than the dipole-dipole interaction and showed how to extract the spatial information of the atoms with resolution far beyond the diffraction limit. This method is entirely based on far-field techniques and it does not require point-by-point scanning.