Bipolar Quantum Child-Langmuir Law

摘要: Summary form only given. The classical Child-Langmuir (CL) law has been the subject of interest for many years. Since it was first derived in early twentieth century, modifications have made recently to include multi-dimensional, relativistic, and quantum effects. Including effects ion flows, bipolar CL relativistic theory developed . However, scaling flow a nano-sized diode is still unknown. In this paper, we present consistent mechanical model based on mean field theory. model, consider electron, but including space-charge ions consistently. From our calculations, see that no longer valid regime, when electron tunneling exchange-correlation become important. Smooth transition between regimes demonstrated