Focus position and depth of two-dimensional patterning by Talbot effect lithography

•Analytical expressions of the Talbot effect for self-imaging from low-order diffraction rays were derived.•The depth of focus based on Rayleigh’s criterion was analytically a quarter of the Talbot distance.•In a hexagonal array of a fine pitch, the Talbot distance derived from 2nd-order approximation was not accurate. The Talbot distance of hexagonal array was derived from the accurate analytical expression.

The Talbot effect is a self-imaging phenomenon enabling lens-less imaging. The interval of the focus position is called the Talbot distance. To maintain pattern fidelity, the accurate focus position of the self-imaging needs to be known. The depth of focus based on Rayleigh’s criterion is analytically a quarter of the Talbot distance. In a hexagonal array of a fine pitch, the Talbot distance derived from 2nd-order approximation is inaccurate. The analytically accurate expression of the Talbot distance for hexagonal arrays is shown in imaging of low-order diffraction rays.

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