Estimation of line dimensions in 3D direct laser writing lithography

Two photon polymerization (TPP) based 3D direct laser writing (3D-DLW) finds application in a wide range of research areas ranging from photonic and mechanical metamaterials to micro-devices. Most common structures are either single lines or formed by a set of interconnected lines as in the case of crystals. In order to increase the fidelity of these structures and reach the ultimate resolution, the laser power and scan speed used in the writing process should be chosen carefully. However, the optimization of these writing parameters is an iterative and time consuming process in the absence of a model for the estimation of line dimensions. To this end, we report a semi-empirical analytic model through simulations and fitting, and demonstrate that it can be used for estimating the line dimensions mostly within one standard deviation of the average values over a wide range of laser power and scan speed combinations. The model delimits the trend in onset of micro-explosions in the photoresist due to over-exposure and of low degree of conversion due to under-exposure. The model guides setting of high-fidelity and robust writing parameters of a photonic crystal structure without iteration and in close agreement with the estimated line dimensions. The proposed methodology is generalizable by adapting the model coefficients to any 3D-DLW setup and corresponding photoresist as a means to estimate the line dimensions for tuning the writing parameters.