Child–Langmuir law in the Coulomb blockade regime

The one-dimensional (1D) classical Child–Langmuir (CL) law has been extended to the Coulomb blockade (single to few electrons) regime, including the effect of single-electron charging. It is found that there is a threshold of voltage (Vth) equals to one-half of the single-electron charging energy for electron injection assuming zero barrier at the interface. For voltage in the range of 1electron inside the gap, and the time-averaged single-electron injected current is equal or higher than the 1D CL current.