Space-Charge Limited Current from Plasma-Facing Material Surface

We have derived an exact theoretical expression for the space-charge limited current from the solid surfaces adjacent to plasmas that is applicable for an arbitrary sheath voltage. Our expression shows that the space-charge limited current tends to saturate with the sheath voltage. This new formula is evaluated by 1-D Particle in Cell (PIC) simulation and experiment, and is in a good agreement with the simulation and experimental results. We have also obtained an analytical equation fitted to the new formula based on conventional Child-Langmuir formula by taking into account a more sophisticated dependence of the electrode potential and the plasma density through the effect of Debye shielding and a sheath expansion due to increased voltage across the sheath.