Nexus Theory: Electron Emission Regime Transitions Across Length, Pressure, and Temperature Scales

Abstract

Modern electron device design necessitates fully characterizing the transitions between electron emission mechanisms to optimize device operation and reliability. These transitions have been studied ad hoc, usually in pairs, for decades. Recent efforts have linked multiple mechanisms to determine when detailed numerical solutions or simulations are necessary rather than the well-known simple equations. One study incorporated collisions into the transition from space-charge-limited emission (SCLE) to field emission to link the Child-Langmuir (CL), Mott-Gurney (MG), and Fowler-Nordheim (FN) laws, defining nexuses where two or three asymptotes intersect <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> . Another study included quantum SCLE and Paschen's law (PL) law to these conditions <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . More recently, we have incorporated thermo-field emission to link the Richardson-Laue-Dushman law to CL and FN, and then demonstrate additional nexuses with MG and Ohm's law <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> . Here, we summarize these approaches and demonstrate their importance for determining the appropriate emission condition for various scenarios. Generally, a mechanism significantly influences current-voltage curves for approximately an order of magnitude from a nexus. We further demonstrate the applicability of this theory to experimental data linking FN, MG, CL, and PL for atmospheric nanoscale gaps. We conclude by conjecturing on the behavior of nanodiodes at other temperatures and pressures.