Novel electrical non-linear plasma model with high accuracy and excellent convergence behavior
Fig. 1: Components of the novel non-linear plasma model
Fig. 2: Dual-tone excitation - comparison between measurement and simulation at three different plasma powers, showing also the 2nd resonance
The special features of microwave plasmas are, among others, low plasma temperature, excellent intensity, and increased homogeneity. Therefore, they can be used efficiently for a variety of applications, preferably for surface treatment including activation, coating, and cleaning.
Plasmas are excited by microwave generators. In order to achieve high power output and efficiency, accurate knowledge of the plasma’s electrical behavior is indispensable. For this reason, the FBH has developed a suitable measuring method for precise characterization as well as a novel non-linear plasma model which simplifies and accelerates the design process of plasma sources.
The measurement method used at FBH applies two signals simultaneously. First, a high-power signal of fixed frequency excites the plasma and keeps it burning, and a second signal with significantly lower power measures the frequency-dependent input reflection coefficient Γ = S11 using a network analyzer. With these measurement capabilities, a plasma model for a 2.45 GHz integrated source in the 15 W range was developed, see Fig. 1. The equivalent circuit describes the electrical behavior at the RF feed of the source. Basically, it consists of a series connection of a resistor RPlasma and a capacitance CPlasma, whose power-dependent values can be determined by fitting the loci of the simulation and the measurement results. To obtain a true non-linear model, a Symbolically Defined Device, SDD was used. In the circuit-design software, this stands for an element which allows implementing a general (non-linear) relationship between its currents and voltages. In the present case, the SDD essentially contains the power-dependent elements RPlasma and CPlasma. The non-linear plasma model is completed by a first-order low-pass filter, which allows the description of the dynamic plasma behavior, represented by the time constant t, with sufficient accuracy.
This model developed at FBH can be used in frequency domain simulations as well as in time domain simulations. It shows excellent convergence behavior. In addition, the phenomenon of the 2nd resonance in the measured loci for the input reflection coefficient Γ can be explained, see Fig.2. It is not a measurement artefact, but a true plasma effect in the presence of a two-tone excitation, a kind of multiple mixing of two signals.