Influence of Image Charge Potential on High Current Field Emitted Electron Flows in a Nano-Diode

In recent years, it is of interest to extend the classical models of space charge limited (SCL) flows to quantum regime. It was found that the classical value of the 1D Child-Langmuir (CL) law is enhanced by a large factor due to quantum effects. Similar effects were also found in the SCL bipolar flow. A review of the quantum CL law can be found in a recent review paper. Recently, a model has been developed to study the transition of electron field emission to quantum CL law in a nanogap . In this paper, we study the importance of the image charge potential in a nanogap to show that the classical form of the image charge potential is no longer valid if the vacuum gap is too small. Thus, we will present a correction to the image charge potential and calculate the IV characteristics of electron emission in a nano-diode over a wide range of voltage biases, which includes the space charge effects.