Modeling of space charge limited current - Zhu, Yingbin (2014)
Space-charge-limited (SCL) electron flow describes the maximum current density allowed for steady-state electron beam transport across a diode. It is central to the studies of high current diodes, high power microwave sources, vacuum microelectronics, and sheath physics in plasma processing, etc. It is also of interest to the contemporary studies of the nanogap and nanodiode. This thesis presents recent development and application of SCL current.Recently, various studies were conducted in using ultrafast lasers to excite localized photofield electron emission from metallic nanotips, where a finite number of emitted electrons per pulse can be obtained. Based on a time of flight model, the one-dimensional classical Child-Langmuir (CL) law has been extended to the Coulomb blockade regime, including the effect of single-electron charging. It is found that there is a threshold of voltage equals to one-half of the single-electron charging energy for electron injection assuming zero barrier at the interface. The time-averaged single-electron injected current is equal to or higher than the 1D CL current.The traditional Langmuir and Blodgett (LB) law for SCL current in cylindrical and spherical geometries remains numerically tabulated form. We develope a transit time model to obtain a uniform analytical form for LB law. It is found that the LB solutions may be approximated by a scaling law using the surface electric field on the cathode of the vacuum diode. With the help of data fitting, minor empirical corrections to the scaling law is obtianed and a new formula within 5% error comparied with the LB law is given. We also find that the electron transport through a 100 nm gap at THz frequency. The transit time model is then used for the problem of SCL current injection into solid. The same expression for tranditional theory is obtained.Due to the development of nanotechnology, many experiments about the transport properties through nanowire and nanorod whose injection area is compareable or much smaller than the transport length were performed. In order to understand the experiment observed current enhancement, we propose a 2D model for SCL nonuniform injection. Large current density enhancement is observed due to the edge effect. The trap effect is also considered.