Two dimensional numerical modeling of TWIN-LIBWE method for interpretation of submicrometer grating fabrication in fused silica

Full text: The periodically structured transparent materials have a wide range of application possibilities: these can be applied as transmission gratings, in sensing and special spectroscopy techniques (OWLS), etc. The two-beam interferometric laser-induced backside wet etching (TWIN-LIBWE) method is a well suited, competitive procedure for structuring of these materials (especially for grating fabrication in fused silica surface) due to the achievable high resolution (reachable minimum grating period is ≈100 nm) and good controllability. The reachable minimum grating period is limited in TWIN-LIBWE by optically: the applied laser wavelength, the incident angle and the relevant refractive indexes determined the achievable minimum grating period. Beside this obvious optical limitation, the thermal effects also limit the achievable resolution. If the heat diffusion length is comparable with the grating constant, the material can be removed not only from the intensity maximums of the interference pattern, but from the minimums, too. This could be the reason that the modulation depth of structure drastically decreased if the period reach the magnitude of the heat diffusion length. However, the heat diffusion length does not describe completely the lateral heat diffusivity. Therefore our motivation was to simulate numerically the grating fabrication during TWIN-LIBWE procedure to verify our above described assumptions. We aimed to study the effects of lateral heat diffusion in this periodical irradiation pattern on the resulted grating structure. To achieve this objective, we extended our previously published one dimensional LIWBE model to two dimensional, including the lateral heat diffusion. The material removal during LIBWE procedure can be attributed to basically thermal (high temperature target surface), chemical (modification of hydrocarbon absorber and the carbon contamination of target surface) and mechanical (high pressure jet and bubble) effects. The latter one was not taken into account in this model. During our calculation the two-dimensional heat flow equation was solved by the finite differences method. The phase changes and the temperature-dependent thermal parameters of the relevant materials are included. The absorption of thin, carbon contaminated fused silica film and the removal of boiled layer from the transparent target surface are also taken into consideration. The incoming laser intensity has sinusoidal profile: one grating period was taking into account with the consideration of proper boundary conditions. In our model the heat can propagate both perpendicularly to the liquid-target boundary and parallel to the surface (perpendicularly the grooves). The average laser fluence and the grating periods were swept in the following ranges: fluence: 200-600 mJ/cm²; period: 100-1000 nm. The etched profiles were perfectly calculated with our model. The results were similar as we expected: in the smaller period cases (𝑝=100 and 200 nm) the lateral heat diffusion become dominant and the modulation depth decreases, while for higher periods (p>5-600 nm) the decreasing of modulation depth is not significant. (author)