A critical condition in Fresnel diffraction used for ultra-high resolution lithographic printing

Abstract

The adoption of a novel method for producing fine features by 1 nm proximity x-ray lithography would solve all of the current technical limitations to its extensibility. These limitations include the fabrication of fine features on masks and the maintenance of narrow mask-wafer gaps. Previously, with demagnification by bias, we described line features of 43 nm width produced with comparatively large clear mask features and large mask-wafer gaps. The method is generally applicable and has been shown to be extensible to beyond 25 nm printed features sizes on the wafer. The demagnification, ×1-×6, is a result of Fresnel diffraction and occurs without lenses or mirrors. The method takes advantage of the modern control of resist processing and has good exposure stability. We now expand on the optimization of the process by defining and explaining the critical condition and by demonstrating the consistency of various types of simulation. The simulations demonstrate the effects of the gap width, non-symmetric rectangular masks, spectral bandwidth, outriggers, T junctions, blur, etc. In two-dimensional images, the spectral bandwidth allows sharp features due to interference and effectively eliminates ripple parallel to the longer dimension. Demagnification by exposure near the critical condition extends the most mature of the next generation lithographies which we define generically-following actual current lithographic practice-in terms of the departure from the classical requirement for fidelity in the reproduction of masks. Specifically, for 1 nm proximity lithography, demagnification of critical features greatly facilitates the printing of fine features.

Proximity correction simulations in ultra-high resolution x-ray lithography

“…Typical 1-2 kV incident beam energies (1.2-0.6 nm wavelengths) were used and demagnification up to 9×-through two-sided bias, without lenses or mirrors-was obtained with correspondingly large mask feature sizes and comparatively large mask−wafer gaps. The technique, called ultra-high resolution lithography (UHRL), which uses Fresnel diffraction positively near a 'critical condition' (CC) (see below and [1]) results in demagnification by bias. The demagnification is not generally uniform because the bias is more or less constant around the edge of the image so that the bias is subtracted from the size of the mask aperture when the print is developed.…”

“…Previously we have reported the results of simulations [1] which have shown the effects of (a) varying the mask-wafer gap about the critical condition, (b) the distortion observed in non-symmetric features, and (c) high frequency ringing parallel to longer dimensions. The simulations have been performed for both monochromatic incident radiation and for the wide band of wavelengths typically used in PXL.…”

“…As is illustrated in figure 1, which represents parallel illumination passing through a clear mask feature forming an The off-axis ray suffers a phase lag proportional to 2πs 2 λ −1 whose phase is represented on the Cornu spiral (see [1]), and where λ is the wavelength of the radiation.…”

“…For a one-dimensional line feature, the construction of wave amplitudes at the image plane (on the wafer) can be represented by means of the well-known Cornu spiral [10], the phases of individual rays being represented by infinitesimal arrows lying on the spiral. When the size of a clear mask feature v is equal to 2.42, the wave amplitude at the wafer on the axis of the mask feature is maximum [1] and the aerial image sharpest. This is the 'critical condition' and for a given s and λ , the CC depends on G. The clear mask feature then covers just less than two and a half Fresnel half zones.…”

Voids in the Hall Effect; Excitons in HiT<sub>c</sub>

“…Clarity requires that wave mechanics be distinguished from quantum mechanics, not only in the description of the Hall Effect, but generally in physics [3] [4] [31] [32] [33] 9 . The prior wave mechanics was developed by Huygens, Fraunhofer, Fresnel and others.…”