On the Schwarzschild Effect in 3D Two-Photon Laser Lithography

The two-photon Schwarzschild effect in photoresists suitable for 3D laser lithography is revisited. The study ranges over seven orders of magnitude in exposure time (from 1 mu s to 10 s) and investigates a wide variety of different photoresist compositions. For short exposure times (regime I), the laser power at the polymerization threshold can scale with the inverse square root of the exposure time, as naively to be expected for two-photon absorption. Substantial deviations occur, however, for low photoinitiator concentrations. For intermediate exposure times (regime II), a Schwarzschild-type of behavior is found, as discussed previously. For very long exposure times (regime III), an unexpected deviation from regime II is found. By presenting numerical solutions of the coupled 3D reaction-diffusion equations, this behavior is explained in terms of the diffusion of oxygen and photoinitiator molecules, respectively.