Electrical characterization of rf plasmas Page: 2 of 11
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The groups felt that V-l comparisons would be a good starting point for characterizations because those
comparisons would be easier and less expensive for all to perform than alternatives such as electron-
density mesurements or quantitative optical-emission measurements. The workers thought that
agreement in V-I data was a necessary condition for achievement of similar plasmas. Of course,
agreement in V-I data does not guarantee that the plasmas are identical. As a result of this work, a
variety of experimental and analytical methodologies have been developed that have been shown to be
applicable to industrial reactors as well as to laboratory plasma systems. In this paper we summarize
several of those techniques as applied to the GEC Cell. First, we describe V-I measurement techniques
and problems, and then we use equivalent-circuit models to convert measured V and I to plasma V and
I. Next, we describe nonlinear interactions between the plasma and the external electrical circuit that
provides the rf excitation to the plasma. Finally, we present selected data on harmonic behavior that
indicate the richness of nonlinear phenomena that can occur in rf discharges.
2. V-I MEASUREMENT
V-I measurement begins with voltage and current probes (sensors). Most of the initial data from the
GEC Cell were taken with commercial probes. Their use is advantageous because they are relatively
inexpensive and readily available to all collaborating groups. In order to obtain accurate, absolute
measurements of voltage and current, one must determine amplitude and phase responses of the probes
as functions of freo jency. Absolute accuracy is perhaps not important in some applications, such as
control systems where one needs only a relative signal that is reproducible from run to run. However,
accuracy is certainly important in comparing GEC-Cell data between groups unless all groups use
probes with identical errors. Accuracy also might be useful in control systems so that information from
differen; reactors and information gathered over a long time period could be used, for . mple, to
identify hardware, recipe, or gas-flow differences.
As an alternative to the commercial probes, we developed "derivative" probes as shown in Fig. 1 to
measure voltage and current. This technology is based on similar techniques used in other areas of
physics and engineering.^ > 8 These probes are advantageous because their components are rugged and
very inexpensive, they have perfect linearity and excellent frequency response, and they are very
compact. Their main disadvantage is that they need amplitude calibration (unless special procedures are
used in design and fabrication). Calibration often is performed at low frequency by reference to a
calibrated commercial probe.
These probes function as follows. The derivative voltage probe has a pickup element that is
capacitivelv coupled to the power lead, but the pickup element is held close to ground potential because
it is connected to ground by a "low" terminating resistance (Rj = 50 H in Fig. 1). A capacity Cc couples
the pickup element to the power lead and a stray capacity Cs couples the element and ground. The
pickup element’s voltage Vp and the voltage of the power lead V are related to a displacement current
Ip to the probe by Ip = Cc d(V-Vp)/dt. If the time constant RtCs is much shorter than times of
interest, then Ip will flow through Rt and Vp = IpRt. If the time constant RtCc is similarly short
(0.15 ns in Fig. 1), then Vp<<V, and we obtain Vp = RtCc dV/dt. Thus the probe’s voltage is
proportional to the derivative of the voltage on the power lead.
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Miller, P.A. Electrical characterization of rf plasmas, article, August 1, 1991; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc1071608/m1/2/: accessed April 26, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.