Quantum Treatment of the Current through Plasma-Metal Junction: Fundamentals

We study the quantum nature of current through plasma-probe junction from the viewpoint of the metal probe. The intrinsic material properties of the metal and their influence on the nature of the observed current are theoretically worked out. The novel idea is that the plasma-sheath at the plasma-probe junction is treated as a potential barrier, and in analogy with the current conduction through a metal-metal junction, the current through the plasma-sheath is treated as a quantum barrier penetration problem. Essentially, we obtain an expression for the electron-current as a function of the bias voltage in its full range, thereby unlocking the intricate dependency of the current on the material properties of the probe.