Transition from Fowler-Nordheim to Child-Langmuir Law in the quantum regime

A detailed quantum mechanical analysis of the current-voltage characteristics of a 1D planar nanodiode showing the transition from Fowler-Nordheim to quantum Child-Langmuir (CL) law in high current regime is presented. Results reveal that at 1000 nm gap spacing (D), the transition follows the classical CL law that the saturation limit at high electric field approaches the normalized self-consistent field emission current density. The influence of different cathode materials with different work functions and temperature is presented