The floating potential of cylindrical Langmuir probes

The formula normally used to calculate the space potential Vs from the measured floating potential V f is derived for plane probes and is erroneous when applied to cylindrical probes in the low-density plasmas (n,10 cm) used in industrial plasma processing. The plasma potential Vs is of interest because it determines the sheath drop which governs the energy of ions bombarding the walls or a silicon wafer, for instance. Since V f is easily measurable, being the potential at which no net current is drawn, it is often used to estimate Vs . The difference Vs2V f can be calculated from the theory of plane probes, in which a ‘‘sheath edge’’ artificially separates the plasma from the sheath region. If Ap is the probe area, n0 the density in the body of the plasma, and the potential Vs there is defined as 0, the electron flux GAp to a floating probe is