Transport limitations on development times of LIGA PMMA resists

Abstract

Analytical and numerical methods are employed to investigate the role of PMMA fragment transport in resist development for the LIGA process. We demonstrate that the overall development time can be expressed as the sum of the kinetic-limited development time and a time for fragment transport. The kinetic-limited time depends only on the resist thickness, dose profile and development temperature and is independent of feature size. The transport time grows as the square of the resist thickness and falls inversely with the Sherwood number. A new analytical model describing the Sherwood number for forced convective transport in deep cavities is also developed. This model, applicable to both resist development and electroforming, is compared with numerical simulations and with data previously reported. Based on this model, we find that forced convective transport can significantly reduce development times only for features having an aspect ratio less than about five. Acoustic agitation is also discussed, and sample calculations of the development time are presented for both forced convective transport and acoustic agitation over a wide range of feature sizes.