A Novel Setup For Realization of Periodic Arbitrary Patterns Through Interference Lithography

The two-dimensional (2D) Fourier series expansion technique is a fundamental tool for generating arbitrary 2D patterns in interference lithography. Indeed, this article is 2D extension to our previous work for 1D interference lithography, introduced in our previous paper. In this approach, an inequality on the magnitude of electric field on the surface of photoresist is addressed. Since an analytic solution to this inequality is complicated, we present an estimated solution with two degrees of freedom. Furthermore, an intuitive perspective on the general case of interference lithography is provided, elucidating the relationship between the number of interfering plane waves and the achievable resolution, and showing that a relatively small number (e.g., 9-11) is sufficient to reproduce sub-wavelength features. Finally, a new optical configuration is proposed to enable the practical implementation of our interference lithography approach for generating 2D periodic arbitrary patterns. By combining the proposed formulation and optical configuration, this study demonstrates that interference lithography can be systematically extended to generate almost any arbitrary 2D patterns using a limited number of plane waves. The capability of the proposed approach in producing complex 2D periodic patterns is demonstrated using two examples. In the first case, a unit cell of 12λ × 12λ containing concentric circular features with widths as small as one wavelength (λ) was successfully reconstructed using 11 plane waves (M = N = 5). In the second example, a 10λ × 10λ pattern composed of a 1.5λ-wide strip, a circular feature of radius 1.5λ, and a ring with inner and outer radii of 2λ and 3.5λ, respectively, was reproduced using only 9 plane waves (M = N = 4). The method can achieve feature sizes down to approximately 150 nm under UV exposure (λ​​​​0 = 365 nm) when 10-15 plane waves are used.