<title>Applications of nondiffracting beams</title>

Abstract

Non-diffracting beams represent a group of fields whose radial intensity distributions do not change during their propagation. In 1987 Durnin showed that the field described by E(r, z, t) = A . Jo(k1r) . ei11t) (1) is an exact solution of the wave equation, where k + k = w2/c2, and J0 is the zero order Bessel function of the first kind. The field described by Eq. (1) represents a non-diffracting beam because the transverse intensity distribution is independent of the propagation distance (z). However, such an ideal beam cannot be realized experimentally over large values of z and r, since this would represent a beam with infinite energy and spatial extent. In the last twelve years several experimental arrangements have been proposed21 to create nearly non-diffracting Bessel beams and apply them in different domains of physics. In 1997 a new approach was suggested by the authors [3,4J for enhancing both the critical dimension (CD) and depth of focus (DOF) in optical microlithography based on Bessel beams. A Fabry-Perot etalon placed between the mask and the projection lens creates multiple images of the original mask pattern along the optical axis. The distance and the exact phase between these virtual images can be controlled by the separation of the etalon mirrors. The projection lens produces perfect images of the virtual mask patterns, shifted in position along the optical axis, in contrast with the conventional projection process, which produces a single image at the wafer surface. Preliminary theoretical and experimantal results showed that an etalon with optimized mirror separation is capable of enhancing the CD and DOF by 60% and 400%, respectively, using a single on-axis contact hole. In order to evaluate this technique for more complex, and realistic extended mask patterns, a microlithographic simulation tool must be employed. This software, however, is not configured in such a way that it can be immediately adapted to simulate the Fabry-Perot approach. An elegant and efficient method to model this Fabry-Perot technique is to represent the effect of the etalon with an appropriate pupil-plane filter. Such filters with a complex amplitude-phase transmission can be easily implemented in any simulation tool. In this work Prolith/2, a commercially available simulation software, was used to evaluate the aerial image of contact hole arrays and line-space patterns with different pitch sizes. Figure 1 depicts a typical 2D intensity distribution for an off-set hole array with and without filter. The resolution enhanced by 25%, while the filter shifted the optimum focal position by 5 microns towards the lens. Due to constructive interference between the diffraction rings, secondary maxima appeared between the main peaks. These peaks can be eliminated by means of controlling the spatial coherence of the illumination, or using a phase shifting mask that introduces a r phase difference between the adjacent holes. The filter with a narrow bandwidth introduces a pitch sensitivity and light loss into the system. A pattern can be imaged if the filter transmits the cardinal spatial Fourier components of the mask patterns. Missing components degrade the image quality. Application of such filters requires a complex optimization process that contains the evaluation of light loss, pitch sensitivity, and technical feasibility.