Direct Simulation Monte Carlo Analysis of Microscale Field Emission and Ionization of Atmospheric Air

Ionic winds are formed when air ions are drawn through the atmosphere by applied electric and/or magnetic fields. The ions collide with neutral air molecules, exchanging momentum, causing the neutral molecules to move. Continued collisions and momentum exchanges generate a net flow called an ionic wind [1]. Ionic winds formed near flat plates can produce local boundary layer distortion in the presence of a bulk flow. This concept has been studied experimentally at the macroscale as a method for drag reduction [2] and has been suggested at the microscale for convective cooling enhancement [3]. Specifically, microfabricated ion wind engines can be integrated onto electronic chips to provide additional local cooling at “hot-spot” locations. In our previous work, continuum modeling of the ionic wind phenomena showed an approximately 50% increase in the local heat transfer coefficient at the location of the ion wind engine [3]. However, in that work, ionization physics were not modeled, rather assumptions for ion current and concentrations were used as a basis for modeling ion transport. At the microscale, ionization occurs when fieldemitted electrons from closely spaced electrodes collide with neutral air molecules, stripping away electrons and forming molecular ions. Geometric enhancement of the electrodes using nanostructured materials enables low ionization voltages conducive to microelectronic devices. Understanding the microscale ionization process is necessary to accurately predict the ensuing ionic wind and cooling. Direct Simulation Monte Carlo (DSMC) is used in the present work to predict field emission between two planar electrodes and the consequent ionization of the interstitial air. NUMERICAL SIMULATION Figure 1 shows a cross-sectional schematic of an ion wind engine in the presence of a bulk flow. Previous experimental work by Schlitz on microscale ionic winds suggests that ions are often trapped on the dielectric surface between the electrodes, reducing the ion density in the air and the ensuing body force on the bulk flow [4]. The two electrodes depicted in Figure 1 are elevated above the surface in order to reduce ion trapping. The DSMC simulation predicts ion and electron currents to the electrodes and to the flat plate, thus quantifying ion trapping. anode cathode ionic wind boundary layer profile upstream of ionic wind boundary layer profile downstream of ionic wind ionized air emitted electrons ion trapping at the plate due to random processes e Figure 1 Cross-sectional view of microscale ion wind engine. Boundary layer distortion due to the ionic wind is depicted with the downstream profile. The electrodes are 20 μm wide by 1 μm high and spaced 10 μm apart. The electrodes are elevated 10 μm above the flat plate. (Not to scale.) DSMC techniques simulate many particles (hundreds of thousands or more) in groups in order to represent a much larger number of real particles. A potential is applied between the two electrodes, and the resulting electric field, determined by Poisson’s equation, causes electron field emission from the cathode. The electrons are accelerated through the gap between electrodes by the electric field, and collisions (including ionizations) with neutral air molecules are simulated and tracked statistically. Any generated electrons from ionization processes and the movement and collisions of the air ions are also traced. Field emission is modeled using Fowler-Nordheim theory [6] in which the surface current density is given by 1 Copyright © 2006 by ASME Proceedings of IMECE2006 2006 ASME International Mechanical Engineering Congress and Exposition November 5-10, 2006, Chicago, Illinois, USA