Similarity Theory and Scaling Networks for Vacuum and Gaseous Electronics Devices

Similarity theory can establish parameter correlation and thus enable cross-comparison among devices of different dimensional scales [1-3]. In this talk, we review the development of similarity laws and recent advances in scaling networks for electron-emission driven vacuum diodes [4,5] and gaseous discharge plasmas [6]. First, we present the first-principles derivation of the similarity relation from the Boltzmann equation, with coupling to the full Maxwell equations. The similarity factors are given for the distribution function of electrons and ions and macroscopic parameters, including current density, electric potential, and field parameters. Second, we demonstrate the similarity properties for electron-beam-driven diodes when the gap dimension, emission current, and gap voltage are proportionally scaled. The space charge oscillation frequencies in compared diodes of different sizes are shown to be scale-invariant. Then, we show two kinds of symmetry for the spatial distributions of the electric potential, virtual cathode position, and the electron phase space parameters. Third, we summarize the similarity theory and scaling networks, which have been recently developed for low-pressure radio frequency plasmas in electropositive (e.g., argon) and electronegative (e.g., carbon tetrafluoride) gases. The results from the fully kinetic particle-in-cell simulations confirmed that similarity relations hold rigorously when the discharge is dominated by electron impact neutral ionizations [6]; however, for the radio frequency plasma in electron negative gases, the similarity laws are valid with relatively small scaling factors. This study offers a comprehensive understanding of the similarity theory and scaling network, providing valuable guidance for designing and optimizing vacuum and gaseous electronics devices.