The influence of mask substrate thickness on exposure and development times for the LIGA process

Optimizing mask substrate thickness is an important practical concern in the X-ray exposure of PMMA resists for LIGA. An overly thick substrate necessitates long exposure times due to excessive beam filtering, while a substrate too thin leads to long development times due to low absorbed doses at the PMMA bottom surface. To assist in this optimization, we have developed numerical models describing both the exposure and development of a PMMA resist. These exposure and development models are coupled in a single interactive code, permitting automated adjustment of mask substrate thickness to yield the minimum of a prescribed cost object function that depends on both the exposure and development times. Results are presented for several synchrotron sources and over a wide range of the PMMA thickness.