Plasma simulations are widely used in both academic and industrial settings to gain insights into fundamental plasma physics and optimise plasmas processes. Their success not only hinges on a robust physical model but also on the availability of data describing the chemical processes in a discharge. These data can be in the form of:

• Collision cross-sections, mostly for electron processes

• Rate coefficients, mostly for heavy particle processes

• Lifetimes and de-excitation channels of excited states

• Probabilities for surface reactions

• Species properties such as the enthalpy of formation

For rather simple or common gas mixtures such as argon or oxygen, sufficient data can usually be found in existing publications or databases; however, for more complex gas mixtures, especially ones including gases which have not been extensively studied yet, these data are usually not available for all species and reactions of interest. Furthermore, even in quite well known gas mixtures so far unknown or neglected phenomena can become important under specific process conditions. Hence, it is of vital importance to generate new data in a timely fashion.

We have developed a series of software tools to address the issue of missing data for plasma simulation purposes and to give easy access to existing data. These include:

• The calculation of missing electron – molecule collision cross sections [1].

• An online database QDB [2] of existing plasma chemistry data including both cross-sections and rate coefficients as well as some surface chemistry data

• Machine learning algorithms for the quick estimation of species and reaction data [3]

• A database of radiative lifetimes for excited states tailored to the needs of plasma modellers [4].

• A global plasma model with additional tools such as a chemistry set reduction [5] to tailor a chemistry set to specific process conditions.

• A collisional-radiative model to calculate the emission spectrum of a plasma discharge based on the densities of the excited states and the neutral gas temperature.

We will present the latest additions to these tools and examples to showcase their use and their impact on plasma simulations such as adding reactions with formerly unknown cross-sections or rate coefficients to chemistry sets or the impact of adding the radiative decay of vibrational states to a plasma model.

[1] B Cooper at al 2019 Atoms7 97

[2] J Tennyson et al 2022 Plasma Sources Sci. Technol.31 095020

[3] M Hanicinec at al 2023 J Phys D, in press, doi:10.1088/1361-6463/acd390

[4] A Owens et al 2023 Plasma Sources Sci. Technol., submitted

[5] M Hanicinec et al 2020 Plasma Sources Sci. Technol.29 125024

There has been recent interest in the spatial afterglow of plasmas because of its potential role in charging and agglomeration of aerosol particles as well as neutralization and dosing of surfaces. In general, the spatial afterglow is analogous to a temporal afterglow, characterized by a decay of charge resulting from a change in the applied power, except that the charge decay occurs in space rather than in time. However, the nature of the charge decay has been much less studied than temporal afterglows, perhaps because of the challenge of performing experiments at higher pressures and in smaller dimensions.

Here, we performed double Langmuir probe (DLP) measurements, which enable spatial measurements of the plasma density, and developed a one-dimensional advection-diffusion-recombination model that describes the charge decay in the spatial afterglow. Our results show excellent agreement between experimental measurements and model outputs over different pressures. Experimental measurements were limited to a pressure of 300 Torr at which point the DLP traces no longer exhibited known shapes and could not be analyzed to extract plasma parameters. By validating the model at the lower pressures, we were then able to extend the model to predict behavior at higher pressures, up to atmospheric. At pressures above ~75 Torr, the rate of charged species decay is primarily influenced by pressure, as three-body recombination becomes increasingly dominant over diffusional losses, and is secondarily influenced by gas flow velocity and temperature. Importantly, our findings reveal a transition from ambipolar diffusion to free diffusion at some distance from the bulk plasma within the spatial afterglow. First studied in temporal afterglows, apparent diffusivities of charged species vary as the plasma decays, eventually reaching a critical point where the ambipolar field becomes too weak and charged species begin to diffuse freely. The shift to free diffusion could lead to negatively-charged electrons being lost and positively-charged ions remaining, which has been previously reported to explain how aerosol particles that leave a bulk plasma negatively charged become neutralized or even positively charged after their transit through the spatial afterglow.

Inductively Coupled Plasmas (ICPs) are extensively used for materials processing in the semiconductor industry, typically with the addition of an RF bias [1]. For these reactors, it is assumed that the majority of plasma generation comes from the inductive power while the bias can independently control the flux and energy of ions needed for processing. In reality, the interaction between the multiple power sources is difficult to isolate and computational modeling becomes a necessity. Typically ICPs are modeled using a fluid approach, which does not correctly model the collision processes at lower pressures (~1-10 mTorr) nor the sheath that forms near the wafer. In this work, we discuss multiple techniques using the particle-in-cell software package VSim [2,3] that can be used for reactor-scale modeling of mixed inductive and capacitive discharge systems to accurately characterize the ion energies impacting a wafer for processing. One method is to use a global model to first compute a near-steady-state system composed of neutrals and plasma. The fluxes and densities from the global model serve as initial conditions for a high-resolution electrostatic capacitively coupled plasma (CCP) simulation to correctly model the sheath near the wafer and ion fluxes onto the wafer. Another approach is to model both the inductive and capacitive power sources in one simulation using a newly developed implicit electromagnetic scheme. We discuss differences between the CCP-only and coupled ICP/CCP systems found in ion energies, ion fluxes and the ion distribution function impacting the wafer, as well as the computational costs of the two methods.

Multi-frequency capacitively coupled plasmas (CCPs) are widely used for thin film etching and deposition in the semiconductor industry. When operated at low pressures, kinetic effects dominate electron dynamics and, therefore, fluid assumptions are inaccurate for electrons in plasma models. Most industrial applications are, however, done using complicated gas mixtures with a variety of ions and neutral species. These plasmas are often electronegative with large concentrations of negative ions. Kinetic modeling for all the species, e.g., by solving the Boltzmann equation or using particle-based techniques, is impractical due to the high computational cost. A hybrid model for multi-frequency CCPs is described in this paper where the electrons are modeled as particles (using the particle-in-cell technique) while the ions and neutral species are treated as a fluid. The equations governing the kinetics of electron pseudo-particles, continuity and momentum equations for ions, Poisson equation for the electric field, and the continuity equations for neutral species are coupled at each time-step, with the time-step typically governed by the light electrons. This model is used to examine plasmas of Ar/CF₄ and c-C₄F­₈/O₂ in a parallel plate CCP reactor with a high frequency (40 MHz sinusoidal) and a low frequency (400 kHz tailored voltage waveform) source. A combination of 1-dimensional, 2-dimensional (2D) Cartesian geometry, and 2D axisymmetric cylindrical geometry simulations is used to examine the effect of the low-frequency duty cycle on plasma chemistry and spatial structure of the plasma. The relative flows of the gases in the mixture are varied to understand the dynamics of both electropositive and electronegative discharges. Due to the long electron mean free path (relative to the inter-electrode gap), the plasma spreads out far from the region where the electrons absorb energy. This has major consequences on plasma uniformity in the 2-dimensional model. It is also found that, at a lower duty cycle, the time-averaged sheath at the powered electrode is thinner and the plasma occupies a larger volume. Consequently, for a given HF power and LF voltage, charged and neutral specie densities are higher at a lower duty cycle.

Current microelectronic device architectures are continuing to trend towards 3-dimensional devices for higher functionality.A consequence of fabricating 3D devices is the need to plasma etch high aspect ratio (HAR) features of ARs > 100.An example of HAR plasma etching is deep trench isolation (DTI) which is used to isolate 3D logic structures and imaging cells from interfering with each other.These DTI etches are performed in halogen-based mixtures (e.g., HBr/Cl₂) for a Si wafer in inductively coupled plasma (ICP) reactors.

At HARs, the primary etch mechanisms deep within the profile are ion/hot neutral chemical and physical sputtering. In-order to reduce the etch time for these features while maintaining critical dimensions, plasma etching with narrow-angular distributions of incident ions is required.By lowering the bias frequency (100s kHz), ion transit through the sheath is in the thin-sheath limit.(The thin sheath limit refers to ions being able to transit the sheath in a fraction of the RF period.) While this is helpful for ions incident across the majority of the wafer, ion distributions are typically broader and perhaps skewed at these lower frequencies near the edge of the wafer.This is primarily due to charging of the focus ring (FR) due to the longer period exceeding the RC time constant for such charging leading to greater sheath curvature at the edge of the wafer. To maintain critical dimensions of HAR structures at the wafer edge, modifying the FR geometry and/or electrical properties may be necessary to take advantage of lower bias frequencies.

In this work, results from a computational investigation of an ICP using very low bias frequencies for different FR parameters will be discussed.The simulations were conducted with the Hybrid Plasma Equipment Model (HPEM), investigating an ICP sustained in Ar/O₂/Cl₂.IEADs, uniformity of fluxes to the wafer and sheath structure for these systems will be discussed.Consequences on etch profiles will also be discussed.

Work was supported by Samsung Electronics Co. and the US National Science Foundation.

Low-pressure multi-frequency capacitively coupled plasmas (CCP) are used for numerous etch and deposition applications in the semiconductor industry.Pulsing of the radio-frequency (RF) sources enables control of neutral and charged species in the plasma on a millisecond timescale.In this work, the synchronous (i.e., simultaneous, in-phase) pulsing of both power sources in a dual frequency CCP is examined.To resolve kinetic effects at low gas pressure, modeling has been done using the electrostatic Particle-in-cell/Monte Carlo collision method.The objective of this work is to investigate the sensitivity of the plasma properties to small changes in timing during synchronous pulsing of the 2 RF sources.It is demonstrated that small deviations in the on and off times of the 2 RF sources can lead to major changes in the plasma characteristics. In the simulations, the pulsing parameters (on and off times and ramp rates) are varied and the temporal evolution of plasma characteristics such as electron density,ion energy, ion energy flux, species current at the electrode, and electron temperature are examined.It is demonstrated that if the low-frequency (LF) source is turned on (or off) a few μs before (or after) the high-frequency source, plasma density during the off-state (or on state) undergoes sharp variations due to the frequency coupling effect. Similarly, turning on the LF source with a small delay results in a sharp increase in the plasma density when the HF source is turned on. The study demonstrates the importance of synchronization of RF pulsing in dual frequency CCPs and discusses methods to finetune plasma properties further.