Saturation of field emission caused by space charge and substrate resistance effects using a self-consistent modeling

Saturation of field emission under a strong applied electric field has been observed experimentally and studied theoretically for decades. Basically, the saturation can be attributed to a substrate effect characterized by a resistance or a space charge effect featured with a reduced surface electric field. In this work, a self-consistent model based on the particle-in-cell method coupled with a circuit modeling is employed to study the saturation of field emission due to these two effects in order to understand the electrical properties influenced and different characteristics caused. Based on the particle-in-cell simulations, the saturation effects from either space charge or substrate resistance can be determined self-consistently. From the FN plots of the simulation results, one can see, significantly, at a lower current density regime, the saturation is caused by the external or substrate resistance effect while at a higher current density regime, the saturation due to the space charge effect can be seen. The saturation due to the combined effects can be differentiated and quantified using the self-consistent approach. Space charge effect cannot be ignored at high current density operation of field emission. Detailed model and simulation results will be presented and discussed.