Field Enhancement of Full-3D Carbon Nanotube Arrays Evaluated in an Axisymmetric 2D Model

Abstract

Center for Information Technology Renato Archer, Rod. D. Pedro I km 146.3, 13069-901, Campinas-SPIn field emission studies of parallel-oriented carbon nanotube (CNT) arrays, there is the necessityto model experimental data using simulations in a large variety of cases, of which only a smallnumber are covered in the literature. Arrays of CNTs are, fundamentally 3D systems, but simulationin full 3D-geometry is time and memory consuming and is also less accurate than simulating in2D-geometry. Here we show an alternative that overcomes these hurdles. We describe the fieldenhancement factor ( ) of CNTs in a 2D-rotationally-symmetric coordinate system and compare theresults with square and hexagonal 3D arrays. We find that the deviation between the 2D rotationalmodel and the 3D-models is at most 25%. Moreover, values of calculated in the 2D-geometry canbe corrected with a factor that is a function of the aspect ratio and spacing in the array. We applythe axis symmetric model to open tip CNT arrays, which are notoriously difficult to simulate in 3D.