Dimensional errors in LIGA-produced metal structures due to thermal expansion and swelling of PMMA

Numerical methods are used to examine dimensional errors in metal structures microfabricated by the LIGA process. These errors result from elastic displacements of the PMMA mould during electrodeposition and arise from thermal expansion of the PMMA when electroforming is performed at elevated temperatures and from PMMA swelling due to absorption of water from aqueous electrolytes. Both numerical solutions and simple analytical approximations describing PMMA displacements for idealized linear and axisymmetric geometries are presented and discussed. We find that such displacements result in tapered metal structures having sidewall slopes up to 14 µm per millimetre of height for linear structures bounded by large areas of PMMA. Tapers for curved structures are of similar magnitude, but these structures are additionally skewed from the vertical. Potential remedies for reducing dimensional errors are also discussed. Here we find that auxiliary moat-like features patterned into the PMMA surrounding mould cavities can reduce taper by an order of magnitude or more. Such moats dramatically reduce tapers for all structures, but increase skew for curved structures when the radius of curvature is comparable to the structure height.