The influence of feature sidewall tolerance on minimum absorber thickness for LIGA x-ray masks

Minimizing mask absorber thickness is an important practical concern in producing very small features by the LIGA dagger process. To assist in this minimization, we have developed coupled numerical models describing both the exposure and development of a thick polymethyl methacrylate (PMMA) resist. The exposure model addresses multi-wavelength, one-dimensional x-ray transmission through multiple beam filters, through the mask substrate and absorber, and the subsequent attenuation and photon absorption in the PMMA resist. The development model describes one-dimensional dissolution of a feature and its sidewalls, taking into account the variation in absorbed dose through the PMMA thickness. These exposure and development models are coupled in a single interactive code, permitting the automated adjustment of mask absorber thickness to yield a prescribed sidewall taper or dissolution distance. We have used this tool to compute the minimum required absorber thickness yielding a prescribed sidewall tolerance for exposures performed at the ALS, SSRL and NSLS synchrotron sources. Results are presented as a function of the absorbed dose for a range of the prescribed sidewall tolerance, feature size, PMMA thickness, mask substrate thickness and the development temperature.