Numerical study of the electrostatic field gradients present in various planar emitter field emission configurations relevant to experimental research

Abstract

The generally assumed validity of the V∕dCA approximation for the cathode surface electric field under commonly employed electron field emission configurations was studied. Using appropriate typical dimensions for each configuration, the magnitude of the electric field over the cathode area under the probe was obtained, and especially near critical (i.e., sharp) regions that could lead to residual gas ionization, dielectric breakdown and emission of electrons from unintended areas. The results indicate that the V∕dCA approximation is far from being universally applicable to all the field emission measuring configurations. In particular, the cylindrical probe anode with flat tip gives the most uniform ES, which nearly equals V∕dCA over most of the cathode area under the probe. Spherical and hemispherical probes, on the other hand, result in ES close to V∕dCA only locally near the center, and much lower anywhere around the center. Moreover, the parallel-plate configurations lead to significantly detrimental field enhancement effects near the edges that discourage their use. These results have important implications in the correct evaluation of cold cathode materials for applications requiring large emitting areas or large current densities.

Effects of adsorbates on field emission reproducibility of sulfur-incorporated nanocomposite carbon films

“…For the configuration employed, the macroscopic surface electric field ͑E S ͒ on the sample ͑i.e., cathode͒ can be estimated accurately by E S = V / d CA , where V is the voltage applied to the anode and d CA is the distance between the anode and the cathode. 7 All the measurements were taken at d CA = 100± 2 m and at a pressure of ͑1-2͒ ϫ 10 −7 Torr. Currents lower than 1 ϫ 10 −12 A were considered at the background noise level.…”

Effects of a nanocomposite carbon buffer layer on the field emission properties of multiwall carbon nanotubes and nanofibers grown by hot filament chemical vapor deposition

“…By using this field emission configuration, we can accurately approximate the macroscopic electric field on the surface of the sample ͑i.e., cathode͒ as E = V / d C-A . 12 All the measurements were done at d C-A of 100± 2 m and at a high vacuum of 10 −7 Torr ͑1.33ϫ 10 −5 Pa͒. The turn-on field ͑E C ͒ was defined as the field required to produce a current density of 1 A/cm 2 .…”

Silicon Encapsulated Carbon Nanotubes

“…The emitted current is measured with a Keithley 6517A electrometer. For the configuration employed, the macroscopic surface electric field ( E S ) on the sample (i.e., cathode) can be estimated accurately by E S = V / d CA , where V is the voltage applied to the anode and d CA is the distance between the anode and the cathode [10]. All the measurements were taken at d CA = 100 ± 2 μm, and at a pressure of 1–2 × 10 −7 Torr (1.3–2.7 × 10 −7 mbar).…”

“…Currents lower than 1 × 10 −12 A was considered at the background noise level. The current density was calculated by dividing the current over the area of the sample subjected to E S = V / d CA , which, in our specific configuration, is well-approximated by using the area of the anode (0.071 cm 2 ) [10]. The turn-on field ( E t ) was defined as the electric field necessary to emit a current density of 10 μA/cm 2 [11].…”