Space charge effects in field emission: One dimensional theory

Abstract

The current associated with field emission is greatly dependent on the electric field at the emitting electrode. This field is a combination of the electric field in vacuum and the space charge created by the current. The latter becomes more important as the current density increases. Here, a study is performed using a modified classical 1D ChildLangmuir description that allows for exact solutions in order to characterize the contributions due to space charge. Methods to connect the 1D approach to an array of periodic 3D structures are considered.

Time evolution of electron flow in a model diode: Non-perturbative analysis

“…The stabilization process almost finishes after t > T 1 + T 2 and j(t) asymptotically approaches to the stationary [9] value. For 0 ≤ a ≤ 3.5 the asymptotic values of j for a = 1, 2, 3, 3.5 are found at corresponding t = T 1 + T 2 + T 3 to be 0.367, 0.417, 0.432, 0.434 respectively.…”

“…Surprisingly T 1 is quite close to 2 though the space charge pushes forward the first bunch of electrons while the anode attracts them. Starting from the second step all T j stay close (T 2 = 2.66, T 3 = 2.75) to the asymptotic stationary value T as = 2.732 [9] as well as the current density j as → 0.431. These quantities for a = 3 are not far away from the Child-Langmuir ones: T CL = 3, j CL = 0.444 when the emissivity is infinite, a = ∞.…”

“…Keeping intact the main features of a field emitted current we will simplify Eqs. (9) to some degree and use other functions of the flow found above, like (4b),(8a) and (8c), to help us find an approximate solution. In particular, using Eqs.…”

“…There are two unknown functions f (t) and T (t) in (9) whose initial values at t = 0 are determined by the IC. One could consider a situation with an non-zero voltage in the initial state V (t−) which makes a sudden jump ∆V at t = 0+ and a simultaneous jump ∆V /x a of the cathode field.…”

Room temperature fabrication of 1D carbon-copper composite nanostructures directly on Cu substrate and their field emission properties

“…This would be also due to the space charge effect at high current density at confined emission area. 28 In conclusion, we have demonstrated the morphological control of C-Cu composite nanostructures on highly conductive Cu substrate at room temperature without any catalyst. The research was conducted by simultaneously supplying C on the Cu substrate at room temperature by using the ion irradiation method.…”