Nonuniform Space Charge Limited Current for 2-D Bipolar Flow in Vacuum Diode

• Published in: IEEE transactions on electron devices 2021-12, Vol.68 (12), p.6538-6545
• Main Authors: Zhu, Ying Bin, Liao, Mei Yan, Zhao, Pan, Yao, Ruo He
• Format: Article
• Language: English
• Subjects: Bipolar flow; Current density; Differential equations; Edge effect; Electric potential; Electrons; Geometry; Ions; Space charge; space-charge-limited (SCL); Two dimensional flow; Two dimensional models
• ISSN: 0018-9383; 1557-9646
• DOI: 10.1109/TED.2021.3125286

This article presents a self-consistent model to study the space charge limited (SCL) bipolar flow for the 2-D nonuniform and uniform currents injection. This model can simultaneously determine the unknown current densities and the potential distribution. By considering a planar diode with a gap spacing {D} and a finite-width beam {W} , the enhancement over the 2-D unipolar flow model is investigated as a function of {W}/{D} . Due to the edge effect, the nonuniform current density profiles for both the electron and ion are observed. We also found that the 2-D total SCL electron current is universally given by {F} \times {I}_{\mathrm {2D\_{}unipolar}} , where {F} and {I}_{\mathrm {2D\_{}unipolar}} , respectively, denote the 2-D enhancement factor due to the influence of the geometry and ions, and 2-D total SCL electron current in the absence of ions. The enhancement factor {F} follows a {W}/{D} scaling and gradually converges to the 1-D enhancement factor {\Gamma } with the increasing of the ratio {W}/{D} .