Effective and flexible modeling approach to investigate various 3D Talbot carpets from a spatial finite mask

Abstract

We present an effective modeling approach for a fast calculation of the Talbot carpet from an initially 2-dimensional mask pattern. The introduced numerical algorithm is based on a modified angular-spectrum method, in which it is possible to consider the border effects of the Talbot region from a mask with a finite aperture. The Bluestein's fast Fourier transform (FFT) algorithm is applied to speed up the calculation. This approach allows as well to decouple the sampling points in the real space and the spatial frequency domain so that both parameters can be chosen independently. As a result an extended three-dimensional Talbot-carpet can be calculated with a minimized number of numerical steps and computation time, but still with high accuracy. The algorithm was applied to various 2-dimensional mask patterns and illumination setups. The influence of specific mask patterns to the resulting field intensity distribution is discussed.

Flexible mask illumination setup for serial multipatterning in Talbot lithography

“…In Talbot lithography deviations from the addressed fundamental periodicity occur because of the mask's boundary that causes edge effects in the Talbot carpet [6,14]. Additionally, a variation of the periodicity is also related to the mask's manufacturing technology where, e.g., disturbing stitching effects have to be minimized.…”

“…Using Talbot lithography, local variations in the attained groove shape are mainly caused by deviations in the distance between mask and photoresist-the maximum tolerable distance error is dependent on the specific mask structure and the illumination wavelength spectrum, and can be estimated by calculating the intensity carpet behind the mask [6,14], as was done in, e.g., [8]. Besides the residual tilting error between mask and substrate, which is below 2 arcmin in our setup, the minimal attainable distance error between mask and resist surface is given by the flatness of the mask, the substrate, and the resist layer.…”