초록
The LIGA X-ray exposure step was modelled into three inequalities, by assuming that the X-ray energy attenuated within a resist is deposited only in the localized range of the resist. From these inequalities, equations for the minimum and maximum exposure times required for a good quality microstructure were obtained. Also, an equation for the thickness of an X-ray mask absorber was obtained from the exposure requirement of threshold dose deposition. The calculation method of the synchrotron radiation power from a synchrotron radiation source was introduced and applied to an X-ray exposure step. A power from a synchrotron radiation source was introduced and applied to an X-ray exposure step/ A power function of photon energy, approximating the attenuation length of the representative LIGA resist, PMMA, and the mean photon energy of the XZ-rays incident upon an X-ray mask absorber were applied to the above mentioned equations. Consequently, the tendencies of the minimum and maximum exposure and with respect to mean photon energy and thick ness of PMMA was obtained. Additionally, the tendencies of the necessary thickness of PMMA and photon energy of the X-ray mask absorber with respect to thickness of PMMA and photon energy of the X-rays incident upon an X-ray mask absorber were examined. The minimum exposure time increases monotonically with increasing mean photon energy for the same total power density and is not a function of the thickness of resist. The minimum exposure time increases with increasing mean photon energy for the same total power density in the case of the general LIGA process, where the thickness of PMMA is thinner than the attenuation length of PMMA. Additionally, the minimum exposure time increases monotonically with increasing thickness of PMMA. The maximally exposable thickness of resist is proportional to the attenuation length of the resist at the mean photon energy with its proportional constant of ln $(Dd_m/D_{dv})$. The necessary thickness of a gold X-ray mask absorber due to absorption edges of gold, increases smoothly with increasing PMMA thickness ratio, and is independent of the total power density itself. The simplicity of the derived equations has made clearly understandable the X-ray exposure phenomenon and the correlation among the exposure times, the attenuation coefficient and the thickness of an X-ray mask absorber, the attenuation coefficient and the thickness of the resist, and the synchrotron radiation power density.