Physical modeling and analysis of microlens formation fabricated by a modified LIGA process

In this paper, we present the physical modeling and analysis method of microlens formation using deep x-ray lithography followed by the thermal treatment of a polymethylmethacrylate (PMMA) sheet. According to the modeling, x-ray irradiation causes a decrease of the molecular weight of PMMA, which in turn decreases the glass transition temperature and consequently causes a net volume increase during the thermal cycle, resulting in a swollen microlens. In this modeling, the free volume theory including volume relaxation phenomena was considered during the thermodynamically non-equilibrium cooling process. Based on this modeling, an analysis method has been proposed to predict the shape of the microlens with the surface tension effect taken into account. The analysis results are favorably compared with experimental data. The present analysis method enables us to predict the fabricated microlens shapes and the variation pattern of the maximum heights of the microlens, which depend on the conditions of the thermal treatment. The prediction model could eventually be used in determining the detailed thermal treatment conditions for a desired microlens shape fabricated by a modified LIGA process.