Transition from Fowler-Nordheim field emission to space charge limited current density

Abstract

The Fowler-Nordheim law gives the current density extracted from a surface under strong fields, by treating the emission of electrons from a metal-vacuum interface in the presence of an electric field normal to the surface as a quantum mechanical tunneling process. Child’s law predicts the maximum transmitted current density by considering the space charge effect. When the electric field becomes high enough, the emitted current density will be limited by Child’s law. This work analyzes the transition of the transmitted current density from the Fowler-Nordheim law to Child’s law space charge limit using a one-dimensional particle-in-cell code. Also studied is the response of the emission model to strong electric fields near the transition point. We find the transition without geometrical effort is smooth and much slower than reported previously [J. P. Barbour, W. W. Dolan, J. K. Trolan, E. E. Martin, and W. P. Dyke, Phys. Rev. 92, 45 (1953)]. We analyze the effects of geometric field enhancement and work function on the transition. Using our previous model for effective field enhancement [Y. Feng and J. P. Verboncoeur, Phys. Plasmas 12, 103301 (2005)], we find the geometric effect dominates, and enhancement β>10 can accelerate the approach to the space charge limit at practical electric field. A damped oscillation near the local plasma frequency is observed in the transient system response.

Chemical Ionization Mass Spectrometry Using Carbon Nanotube Field Emission Electron Sources

“…This non-linear phenomenon is not clearly understood. Researchers have attributed it to space charge effects and varying electron transport tunneling mechanisms, with the transition point represented by the Bknee^in the F-N plot [23][24][25]. The device characterized in Figure 2 has a knee between the low and high field behavior at a field of 1.575 V/μm, which closely matches values reported in literature [26].…”

Space charge effects in field emission: One dimensional theory

“…As a result, only the findings summarized in Figure 11 of Ref. [18] for which the work function is 4 eV and the anode-cathode separation is 1 µm are considered.…”

“…[17] and references therein), the usage of Particle-in-Cell codes to treat field emission (Ref. [18] and references therein) and the discussion of numerical issues involved in modeling space-charge-limited flow (even in the 1D case using PIC codes can lead unusual behavior as a consequence of cell-size related problems) [19], that are pertinent.…”

Experimental investigation of transition from Fowler–Nordheim field emission to space-charge-limited flows in a nanogap

“…This in turn reduces the number of electrons emitted by the FN process. Thus a self-regulating system is set up in which a steady state is finally reached when the injected current density is equal to the transmitted current density with typical relaxation time scales 11 of the order of 10 −19 s.…”