Thermal instability of field emission from carbon nanotubes studied using multi-physics simulation by considering space charge effect

Thermal instability is an important concern for practical use of high-current field emitters in display, X-ray generation, Hall thruster, and microplasma generation. Carbon nanotubes (CNTs) and their bundles have high thermal conductivity and offers great promise in this aspect. A wide-range of experiments has recently been performed with CNT-based emitters containing single or a bundle of nanotubes. Analysis of these experiments is executed using the classical Fowler-Nordheim (FN) equation and the heat equation with no self-consistency. The space-charge effect – one of the most important aspect of high-current field emission – is often ignored in these theoretical analyses. In this work, we use a numerical framework to study thermal instability in the CNT-based emitters by solving electrostatics, space-charge effect, quantum-mechanical tunneling (with FN equation as the limiting case), thermionic emission and heat flow in a self-consistent manner. Simulation compares well with the experimental results and allows study of temperature rise – the root cause of thermal instability – for the emitter in a wide range of conditions. Our analysis suggests that higher thermal conductivity and/or electrical conductivity and their reduced temperature dependence are beneficial for the field emitters, as these improve the thermal stability of the emitter by reducing temperature rise.