Design of a heated micro-cantilever optimized for thermo-capillary driven printing of molten polymer nanostructures

Abstract

Here we present an atomic force microscope (AFM) cantilever design capable of patterning millions of polymer nanostructures with integrated mass flow sensing and control. The micro-cantilever has two embedded joule heaters connected via a microchannel, where thermo-capillary forces induced by the temperature gradient between heaters can deliver 40ng of polymer to the tip. We used multi-physics finite element analysis to optimize the thermo-mechanical and thermo-fluidic performance of the device. A modal analysis of the cantilever vibration during operation show the resonant frequencies of the first four cantilever modes are sensitive to the location of the advancing polymer meniscus within the channel, where the frequency shifts by 1.7%, 0.2%, 0.4%, and 1.8% for modes 1–4, respectively. The cantilever frequency shift thus provides a facile measure of mass flow rate within the channel. We further model the temperature rise in each heater, showing that the heaters can reach temperatures exceeding 400°C with a temperature gradient along the channel between the two heaters tunable from −2,000,000 to 2,000,000°C/m. Computational fluid dynamics simulations of molten polymer flowing in the microchannel shows the leading edge advances as t according to Washburn’s equation, and the velocity of the leading edge depends significantly on the imposed temperature gradient. Large temperature gradients in the direction of polymer imbibition serve to increase the leading edge velocity for faster channel filling, while large temperature gradients opposing capillary filling can decrease filling speeds, hold the leading edge still, and even reverse polymer flow. Thus, the cantilever tip can be inked, cleaned, and re-inked by controlling the temperature of the integrated heaters. The design presented here provides a platform for wafer scale polymer nanostructure fabrication with mass flow control required for nano-manufacturing complex polymer-based devices.