Enhanced space charge limited current for curved electron emitters

Abstract

The maximum current that can be transported across a vacuum diode is limited by forces arising due to space charge. In a planar diode configuration, the space charge limited (SCL) current density from a planar emitting patch is given by the Child-Langmuir (CL) law $J_{CL}\sim V_g^{3/2}/D^2$ where $V_g$ is the potential difference across the diode and $D$ is the separation between the anode and cathode. We show here analytically using the nonlinear line charge model that for a curved emitter in a planar diode configuration, the limiting current obeys the scaling relationship $J_{SCL}\sim {\gamma }_a{V}_g^{3/2}/D^2$ where ${\gamma }_a$ is the apex field enhancement factor of the curved emitter. For an emitter with large height ($h$) to apex radius of curvature ($R_a$) ratio, the limiting current far exceeds the planar value. The result is verified using the particle-in-cell code PASUPAT for two curved emitters shapes.

arXiv comment5 pages, 4 figures

References in corpus (8)

• A universal formula for the field enhancement factor
• Shielding effects in random large area field emitters, the field enhancement factor distribution and current calculation
• Generalization of Child-Langmuir Law for Non-Zero Injection Velocities in a Planar Diode
• Verification of shielding effect predictions for large area field emitters
• Electrostatic shielding versus anode-proximity effect in large area field emitters
• The anode proximity effect for generic smooth field emitters
• The Child-Langmuir law in the quantum domain
• Boundary conditions for the solution of the 3-dimensional Poisson equation in open metallic enclosures

Cited by in corpus (4)

• Predicting space-charge affected field emission current from curved tips
• Simulating multiscale gated field emitters -- a hybrid approach
• Interpreting the empirical field emission equation for large area field emitters
• Approximate universality in the electric field variation on a field-emitter tip in the presence of space charge