Optimal Design of Grid-Based Binary Holograms for Matter-Wave Lithography

Abstract

Grid based binary holography (GBH) is an attractive method for patterning with light or matter waves. It is an approximate technique in which different holographic masks can be used to produce similar patterns. Here we present an optimal design method for GBH masks that allows for freely selecting the fraction of open holes in the mask from below 10% to above 90%. Open-fraction is an important design parameter when making masks for use in lithography systems. The method also includes a rescaling feature that potentially enables a better contrast of the generated patterns. Through simulations we investigate the contrast and robustness of the patterns formed by masks generated by the proposed optimal design method. It is demonstrated that high contrast patterns are achievable for a wide range of open-fractions. We conclude that reaching a desired open-fraction is a trade-off with the contrast of the pattern generated by the mask.

Nanometer-Resolution Mask Lithography with Matter Waves: Near-Field Binary Holography

“…Furthermore, which value the field will have depends on the configuration of open and closed subcells that the cell has; this is explained in great detail in Ref. [24]. For instance, the total area of the open subcells determines the magnitude of the field associated with a cell.…”

“…Since this approach was recently presented in great detail in Ref. [24], here we will limit ourselves and give only the main steps that the method involves; for the necessary details and the mathematics, we refer the reader to Ref. [24].…”

“…[24], here we will limit ourselves and give only the main steps that the method involves; for the necessary details and the mathematics, we refer the reader to Ref. [24]. The method for generating masks that are able to transform the incident field, after passing through them, into the mask field, is based on the seminal work on binary holography of Lohmann and Paris [20] and Onoe and Kaneko [21].…”

“…Because the phase of the atoms when they arrive at the image plane (target plane) is not important, only the intensity is, many different hole distributions can create the same intensity pattern. In a recent publication it was shown how it is possible to vary the number of open holes in a mask over a large range without changing the final pattern [24]. Coverage differences of up to 83 % were demonstrated.…”

Wave scattering from two-dimensional self-affine Dirichlet and Neumann surfaces and its application to the retrieval of self-affine parameters

“…Since then much progress has been made on the experimental and theoretical aspects of the problem [2][3][4][5][6][7][8][9]. Today surfaces with well controlled statistical roughness can be manufactured to facilitate the comparison between experimental and theoretical predictions [10,11], and the full angular distribution of the scattered intensity can be measured [12,13] and calculated for both metallic and dielectric surfaces [14][15][16][17][18][19][20]. Initially, the theoretical treatment was concentrated around various perturbation theories [4,[21][22][23][24] and single scattering approximations, like the Kirchhoff approximation [25][26][27][28][29], methods that are expected to be accurate for weakly rough surfaces and/or surfaces of small slopes.…”