Microlenses and microlens arrays were fabricated using a novel fabrication technology based on the exposure of a resist (usually PMMA) to deep x-rays and subsequent thermal treatment. The fabrication technology is very simple and produces microlenses and microlens arrays with good surface roughness (less than 1 nm). The molecular weight and glass transition temperature of PMMA is reduced when it is irradiated with deep x-rays. The microlenses were produced through the effects of volume change, surface tension, and reflow during thermal treatment of irradiated PMMA. The geometry of the microlens was determined by parameters such as the x-ray dose applied to the PMMA, the diameter of the microlens, along with the heating temperature, heating time and cooling rate in the thermal treatment. Microlenses were produced with diameters ranging from 30 to 1500 μm. The modified LIGA process was used to construct not only hemispherical microlenses, but also structures that were rectangular-shaped, star-shaped, etc.

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.