Abstract
It is found that the Langmuir-Blodgett solutions for the space charge limited current density, for both cylindrical and spherical diodes, may be approximated by over a wide range of parameters, where is the surface electric field on the cathode of the vacuum diode and is the anode-cathode spacing. This dependence is valid whether is greater than or less than unity, where and are, respectively, the anode and cathode radius. Minor empirical corrections to the above scaling yield fitting formulas that are accurate to within 5% for . An explanation of this scaling is given. An accurate transit time model yields the Langmuir-Blodgett solutions even in the Coulomb blockade regime for a nanogap, where the electron number may be in the single digits, and the transit time frequency is in the THz range.
- Received 31 January 2013
DOI:https://doi.org/10.1103/PhysRevLett.110.265007
© 2013 American Physical Society