# Surface Potential Measurements with the Kelvin Probe Diagnostic

## Surface Potential Measurements with the Kelvin Probe Diagnostic

Charging of components immersed within plasma occurs according to the fluxes of positive and negative plasma species. We study this phenomenon with a Trek 6000B-8 non-contacting voltmeter. During operation, the voltmeter is positioned over a charged substrate and reports surface voltages in the range of 0 to ±3000 Volts in 1 Volt increments.

The probe operates under the principle of an oscillating capacitor. As the probe’s needle-point tip oscillates in space, the voltage difference V between the tip and the surface is maintained by a current I delivered to the probe tip. The time rate of change of the probe-surface capacitance is given by

\frac{dQ}{dt} = \frac{dC}{dt}V \implies I = - \frac{\varepsilon \varepsilon_0 A}{\left(D_0 + D_1(t)\right)^2 }\frac{dD_1(t)}{dt}V

where D_0 is the mean distance between the surface and probe, D_1(t) is the oscillation distance of the probe tip, A the area of the probe tip, and \varepsilon and \varepsilon_0  the permittivity of the surrounding media and free space. By observing the current supplied to the probe and driving the oscillation, the voltage V of the surface relative to the probe can be calculated.

In one setup (Fig. 1) we measure the charge delivered to a dielectric substrate by a DC glow discharge. Results of one such measurement are given in Figure 2.

Figure 1a: System when plasma is ignited and charging the substrate. Diagram (top), image during operation (bottom).

Figure 1b: System when plasma is off and voltmeter probe is measuring surface charge. Diagram (top), image during operation (bottom).

Figure 2: Example of a surface charge measurement in a 200 mTorr Plasma. This capability is located at the Princeton Plasma Physics Laboratory.