Invariance of the r²-ln(F) relationship and attainable precision in ultrafast laser ablation experiments

Pursuing ever-smaller feature size in laser-based lithography is a research topic of vital importance to keep this technique competitive with other micro-/nano-fabrication methods. Features smaller than the diffraction-limited spot size can be obtained by "thresholding", which utilizes the deterministic nature of damage threshold with ultrashort laser pulses and is achieved by precisely tuning pulse energies so that only the central portion of the focal spot produces permanent modification. In this paper, we examine the formulation commonly used to describe thresholding and show that the relationship between feature size (r) and laser fluence (F) is invariant with respect to the nature of laser absorption. Verified by our experiments performed on metal, semiconductor, and dielectric samples, such invariance is used to predict the smallest feature size that can be achieved for different materials in a real-world system.