Matthew J. Goeckner

The Stochastic Weighted Particle Method (SWPM) of Rjasanow and Wagner is a generalization of the Direct Simulation Monte Carlo method for computing the probability density function of the velocities of a system of interacting particles for applications that include rarefied gas dynamics and plasma processing systems. Key components of a SWPM simulation are a particle grouping technique and particle reduction scheme. These are periodically applied to reduce the computational cost of simulations due to the gradual increase in the number of stochastic particles. A general framework for designing particle reduction schemes is introduced that enforces the preservation of a prescribed set of moments of the distribution through the construction and explicit solution of a system of linear equations for particle weights in terms of particle velocities and the moments to be preserved. This framework is applied to preserve all moments of the distribution up to order three. Numerical simulations are performed to verify the scheme and quantify the degree to which even higher-order moments and tail functionals are preserved. These results reveal an unexpected trade off between the preservation of these higher-order moments and tail functionals.

Modeling and forecasting the dynamics of complex systems, such as moderate pressure capacitively coupled plasma (CCP) systems, remains a challenge due to the interactions of physical and chemical processes across multiple scales. Historically, optimization for a given application would be accomplished via a design of experiment (DOE) study across the various external control parameters. Machine learning (ML) techniques show the potential to “forecast” process conditions not tested in a traditional DOE study and thereby allow better optimization and control of a plasma tool. In this article, we have used standard DOE as well as ML predictions to analyze I-V data in a moderate-pressure CCP system. We have demonstrated that supervised regression ML techniques can be a useful tool for extrapolating data even when a plasma system is undergoing a transition in the heating mode, in this case from the alpha to gamma mode. Classification analysis of control parameters is another possible application of ML techniques that can be deployed for system control. Here, we show that given a large set of measured data, the models can identify the gas ratio in the feed gas as well as correctly identify the operating pressure and electrode gap in almost all the cases.

Most in situ plasma diagnostics are only reliable for low-pressure systems, e.g., systems where the collision frequency, νen, is small compared to the plasma frequency, ωpe. In this article, we describe a novel diagnostic technique for simultaneous measurement of the plasma density, ne; electron temperature, Te; and νen in systems in which νen approaches ωpe. We illustrate the operational setup of our probe system along with an analytical framework for ascertaining ne, Te, and νen. Furthermore, we show experimental results from argon capacitively coupled plasma operating in the 0.5–1 Torr pressure range.

This study examines the transition of 13.56 MHz, capacitively coupled plasmas (CCP) from low to intermediate pressure regimes. Here, we investigate power deposition/plasma production in argon, nitrogen, and oxygen discharges as a function of pressure. These three feed gases were chosen as they provide a set of electropositive and electronegative gases and they are widely discussed in the existing literature. Experiments were conducted for all combinations of pressures: 0.5, 1.5, and 2.5 Torr, and nominal power density between 0.1 and 0.7 W/cm2 for each feed gas at a fixed electrode gap of 24 mm, a commonly employed gap in many industrial processes. Our study shows that increasing pressure results in an increase in current at a given electrode bias in argon and oxygen discharges, while there is no discernible pressure-induced change in nitrogen discharges. We attribute this increase to an increase in plasma density, which might result from a change in power deposition or ionization processes. It is likely that heating via secondary electrons becomes more important at intermediate pressures, resulting in increased plasma density and current. Specifically, based on our measurements, it appears that the mechanisms through which power is deposited into the plasma change with increasing pressure for both argon and oxygen discharges but not for nitrogen discharges. Our experimental results align with the outcomes of our simulations and the simulation results of CCP discharges conducted by other researchers under similar conditions.

Phase resolved optical emission spectroscopy (PROES) measurements were combined with measurements of the optical emission intensity (OEI) and electrical characteristics (RF current and voltage, power, and DC bias voltage) as a function of time during the re-ignition of Ar plasmas pulsed at 100 Hz and 10 kHz. The OEI exhibits a large overshoot at the 100 Hz pulsing rate even though no such overshoot is present in any of the electrical characteristics. The OEI overshoot occurs at a point in time when the RF power, voltage, DC bias voltage, and electron density are all smaller than they become later in the glow. PROES measurements in combination with the time resolved electrical characteristics indicate that the heating mechanism for the electrons changes during the time of the overshoot in the OEI from stochastic heating to a combination of stochastic and ohmic heating. This combination appears to enable a more efficient transfer of the electrical energy into the electrons.

The authors report on phase resolved optical emission spectroscopy (PROES) measurements of pulsed capacitive coupled plasmas (CCPs) through argon. The PROES results indicate that under some conditions, the electron heating mechanism can be changed substantially from that dominant in continuous CCPs. The normally dominant α heating mode of electropositive plasmas can be aided by a drift-ambipolar (DA) heating mode during the early portion of the reignition. The DA heating mode is ordinarily only found in electronegative discharges. The authors found that Ar discharges pulsed at 10 kHz only exhibited the α heating mode throughout the reignition process, while those pulsed at 0.1 kHz exhibited a mixed α and DA heating mode during the reignition. The differences in the two heating modes cause substantial differences in the spatial pattern of the light emission from the plasma in addition to an overshoot in the light emission intensity.

Fluorocarbon species (CxFy) are commonly used in plasma etch processes. Trifluoroiodomethane (CF3I) might also be used as an etch gas, but there is a limited understanding as to how it will react. In this article, the authors examine the creation of CxFy daughter species from CF3I under different plasma conditions. Here, Fourier transform infrared spectroscopy (FTIR) was used to measure the concentration of various gas species. Readings were taken at different plasma powers and different chamber pressures. Outside the parent gas, both CF3 and CF4 were found under all operating conditions. CF3I density decreases monotonically with increasing plasma power. In comparison, CF3 densities peaked at moderate plasma powers (200 W), while CF4 densities increased with power. Above 300 W, small levels of C2F6 were also observed. At high powers, a large fraction of gas phase chemistry is not observable via FTIR spectrometry, suggesting the presence of significant quantities of I, I2, F, and F2. A greater understanding of CF3I could yield better methods for large scale semiconductor etching and help to add clarity to the creation of CxFy species.