Modeling acoustic agitation for enhanced development of PMMA resists

Abstract

Although acoustic agitation is known to enhance the development rate of LIGA resists, the operative physical mechanism is not well understood. Analytical and numerical models presented here suggest that the observed enhancement results from steady acoustic streaming and associated polymer fragment transport induced by the high frequency sound waves. The computed steady flow within the feature is torroidal with downflow along the feature walls and upflow in the center. The numerically calculated enhancement of fragment transport is shown to be well approximated by a closed-form expression based on a pair of asymptotic formulas for weak and strong agitation. These transport models are combined with a model of PMMA dissolution kinetics and used to predict development rates for a range of LIGA feature sizes. The results are in good agreement with experimental data from Forschungszentrum Karlsruhe.

Development of a sonovoltammetric cell for mass transport investigations in the LIGA-process under megasonic agitation

“…The simulation of mass transport rate enhancement under megasonic agitation in microstructures is presented in [14,15] for the resist development process step in the LIGA process. This simulation was made assuming that of acoustic streaming is generated by megasonic agitation within microstructures.…”

“…Pe is the Peclet number, a ratio that indicates the relative strength of convective transport compared to transport by diffusion. For a system with ultrasonic activation Peclet number is proportional to acoustical intensity [14,15]:…”

Visualization of the development process in deep X-ray lithography

“…The coupled PMMA dissolution and fragment transport has been described based on a semi-empirical model of polymer dissolution kinetics [2,3]. Secondly, gel-formation and gel-transfer into the developer-phase play an important role in the development process [4].…”

Development rate of PMMA exposed to synchrotron x-ray radiation for LIGA applications

“…This paper expands upon the prior work by thoroughly comparing different developer solutions, comparing different synchrotron sources, and by investigating different sources of PMMA. Various enhancements to obtain a faster or more uniform development have been proposed [16,[19][20][21], but these techniques were not investigated in this paper.…”