## 18. Atomic and molecular data for plasma science

N J Mason¹ and J Tennyson²

¹ The Open University

² University College London

**Status.** The physical and chemical processes of any plasma are inextricably linked with the underlying atomic and molecular (A+M) physics. Therefore, a better understanding of such physics has the potential to provide mechanisms for the manipulation and control of the plasma. To date, the plasma industry has largely been developed through incremental change, framed by engineering and commercial considerations. This has been a successful strategy and, for example, underpins the successful implementation of ‘Moore’s law’ in the fabrication of semiconductor chips. However, it is now broadly recognised that we are entering a new era in which technological advances in plasma processing and the exploitation of plasmas in general, from material processing to plasma medicine, will be based upon the manipulation of the plasma properties, which in turn places renewed emphasis on establishing a thorough understanding of the A+M processes within those plasmas [172].

In the last decade, our knowledge of the electron, ion and photon interactions with A + M species within the plasma and evaluation of cross-sections and reaction rates for such collisions, both in the gaseous phase and on the surfaces of the plasma reactor, has greatly increased [173]. The development of new experimental methodologies, such as velocity map imaging (VMI), has provided new insights into the dissociation dynamics and energy transfer in plasma feed gases, while advances in theoretical calculations of fundamental collision processes, in part led by continued improvements in computational speed, has provided data on many targets, which have proven to be impractical for experimental study (e.g. short-lived or very reactive chemical species).

Databases that compile, curate and disseminate A+M data are an important requirement in many scientific communities. For example, the virtual atomic and molecular data centre (VAMDC) [174]. VAMDC federates A+M databases through an e-science infrastructure and recently has added databases from the plasma community. Within the plasma community the Plasma Data Exchange Project has created the LXcat open-access website [175] for collecting, displaying and downloading electron and ion scattering cross sections, swarm parameters (e.g. mobility and diffusion coefficients), reaction rates, energy distribution functions and other data required for modelling low temperature plasmas. Such databases are now routinely exploited by both academic and industrial communities, with the data being used to build models of such plasmas and calibrate many diagnostic tools used for in situ monitoring of these plasmas.

<figure><img src="image_40.png" /><figcaption>**Figure 34.** Summary of recommended cross section for electron collisions with methane: TCS—total scattering, ES—elastic scattering, MT—momentum transfer, ION—partial ionization, TICS—total ionization, VE—vibrational excitation, RE—rotational excitation, ATT—dissociative attachment, TACS—total dissociative attachment. Reprinted from [177], with the permission of AIP Publishing.</figcaption></figure>

**Current and future challenges.** Despite advances in our understanding of A+M processes and the widespread acceptance of the need for appropriate databases, several challenges remain. The ever expanding range of species used in different plasmas, for example, the replacement of ‘traditional’ fluorocarbons used in plasma etching with new compounds that have lower global warming potentials and the growing use of new hydrocarbons in CVD have emphasized the need for compilation of A+M datasets for such species. Unfortunately, while the need for such data is recognized, the funding for the collection of such data remains limited and the international A+M community has declined over the past decade. Our knowledge of many A+M processes remains poor [176]. Indeed, recent reviews of electron collision data (figure 34) with relatively simple molecules, such as methane ($CH_4$) [177], have highlighted the lack of reliable data for electron impact dissociation. The ever growing use of atmospheric plasmas (e.g. in plasma medicine) has highlighted our poor knowledge of collision processes and chemical reactivity in/with A+M clusters, which are observed to dominate such plasmas. Similarly, the interactions on surfaces provides a challenge, since, unlike the gas phase, unique cross sections and rate constants are hard to define, as they are dependent on a multitude of parameters, such as the morphology, nature and thickness of surface films. Within the gas phase, there are still many targets for which little or no data is available including: (i) atomic species, such as B, Be, C, Cl, Dy, F, Hg, N, Na, O and W, important in fusion plasmas (particularly in edge plasmas), arc plasmas and the lighting industry, (ii) neutral molecular species formed by dissociation of plasma feed gases (e.g. $CH_x CF_x NH_x$ $x = 1, 2, 3, OH$), formed in semi-conductor and CVD plasmas and (iii) ionic species where, for example, quantifying (for cations) dielectric recombination remains rudimentary and ion pair formation (also called dipolar dissociation) remains
largely unexplored, even though it may be the major source of anions in some plasmas. Furthermore, direct experimental measurements of collisions involving unstable molecules, often called radicals, which are prevalent in plasmas, remain extremely scarce.

The amount of data required has placed greater emphasis on the use of accurate theoretical calculations of the required cross sections and rate constants. Theory is the major source of cross sections or rate coefficients for radical species, but there is a lack of data against which to benchmark calculations; just because a method gives good results for stable (closed-shell) molecules, it does not guarantee that the same procedure will work equally well for the more complicated electronic structures found in a radical. Several semi-empirical methods have been developed to provide electron scattering cross sections (particularly ionization and elastic scattering cross sections) with accuracies of some 10%, but, for accurate evaluation of electron excitation (leading to dissociation), it is necessary to exploit more detailed models incorporating quantum chemical descriptions of the target [178, 179]

*Advances in science and technology to meet current challenges.* Several advances in methodology have the potential to provide benchmark A+M data for the plasma community. For electron-atom collisions, the development of sophisticated methods based on the use of a very extensive basis set of expansions has led to benchmark results for such processes with a high degree of predictability [180].

Unfortunately, computational studies on electron-molecule collisions, while increasingly supplying data on key processes, cannot yet be performed with complete confidence for many key problems [180], in particular leading to the dissociation of the molecule, for example, by low energy dissociation electron attachment (DEA). More than a dozen international groups are now pursuing VMI studies to quantify the dissociation dynamics of DEA and dipolar dissociation. The inauguration of the next generation of storage rings (e.g. Desiree in Sweden) will provide further data on dielectric recombination. Although many plasmas are electronegative, the data available for anion interactions with neutrals, cations and surfaces is sparse. Exploiting techniques developed within the cold atom community, the first 'anion traps' have been developed; by introducing A+M species into the trap and looking at the rate of anion loss, anion reaction rates may be evaluated.

Despite these new experimental techniques and the establishment of new laboratories to study A+M processes

(particularly in nations where the research community is growing and new facilities are being built), theoretical methods will still provide the bulk of the A+M data for the plasma community in the coming decades. Experimentally derived data is routinely quoted with assessed 'error bars' but, in contrast, theoretical data with 'uncertainty estimates' are rare. A recent initiative provides guidelines on estimating uncertainties for compilations of structure and scattering data [181].

Having calculated and measured many of the fundamental A+M processes necessary for plasma studies, the cura-
tion and dissemination of these data is crucial. The methods
for incorporating, interrogating and extracting the data
from the databases have been the subject of considerable
research and review with the adoption of SQL as a stand-
ard. With the development of 'big data' initiatives, further
progress and standardization of database protocols may be
expected. Automation of data transport from databases to
modelling code through the use of APIs (application pro-
gramming interfaces) will become essential as the datasets
grow. However, it is not sufficient to just acquire and col-
late data; it is also necessary to provide recommendations on
the data, preferred cross sections and rate constants, spec-
troscopic constants etc. The method and, indeed, ethics by
which such recommendations are made and presented have
yet to be established and they must be accepted by the whole
international community.

*Concluding remarks.* Access to large amounts of A+M data is now required by the plasma community, which has diverse applications from plasma medicine, water and waste treatment to the more traditional semiconducting and materials processing industries. The plasma community has recognized the need to both compile and curate A+M data, while also identifying missing data. This is leading to a step change in the way in which A+M data is evaluated. While new experiments are used for benchmarking and to provide new insights into the mechanisms of A+M collisions, the majority of the data are expected to be derived from theoretical calculations. The recent work on establishing uncertainty estimates in theoretical methods that will be complimentary to the established errors assigned to experimental results will be an important part of the delivery of A+M data to the wider plasma community. However, the compilation, assessment and, above all, accuracy of entire sets of data required by the plasma physics community are challenges that are only beginning to be met.
# 19. Plasma chemistry: mechanisms, validation and distribution

L C Pitchford<fnref n="1" /> and Miles M Turner<fnref n="2" />

**Status.** The terms ‘mechanisms,’ ‘validation’ and ‘distribution’ in the title of this contribution are intended to imply plasma chemical kinetics models with associated reaction rates, the validation by comparison of model predictions with target experiments and the distribution in an open-access electronic format, respectively. The low temperature plasma (LTP) community generally recognizes the need to establish, validate and distribute some standard reaction mechanisms, at least for a few common gas mixtures. Discussions are now underway to define a strategy to make progress, as a community, towards these goals. In the following, we outline the nascent consensus and our conclusions.

A fully developed ‘mechanism’ in this sense is more than an assembly of rate constants. A mechanism is designed to predict certain species densities under specified conditions, and will have been tested (‘validated’) by comparison with suitable experiments (‘targets’). These aims will inform the selection of both the species and reactions represented in the mechanism, as well as the choice of target experiments. A basic mechanism for helium, suitable for ionization balance calculations, is shown in figure 35. In this mechanism, all excited states are represented by either He\* or He\*₂, where the arrows represent the individual processes considered for which rate coefficients must be defined. If the aims included predictions of, for example, the density of specific atomic metastable state densities, then an appreciably more elaborate mechanism would be called for [182].

The LTP literature is replete with discussions of mechanisms for many different gas mixtures, but intercomparisons are generally difficult because of the disparity in discharge conditions considered. Also, given the level of detail involved, it is not surprising that errors have crept into the literature, as has been discussed recently [183] in the case of He/O₂ mixtures. Although some mechanisms from previous work have become de facto ‘standards’, the situation at present is that the LTP community lacks recommended mechanisms. For researchers who aim to develop new mechanisms or to corroborate those previously published, resources are available, some of which we mention here. In 1992, Kossyi *et al* [184] published a detailed review of reactions and recommended rate coefficients in N₂/O₂ mixtures. Beginning in 1980 and under the auspices of the IUPAC task group on atmospheric chemical kinetic data evaluation, a number of papers were published<fnref n="39" /> which provide some recommended rate coefficient data for species of interest in developing and emerging LTP applications. VAMDC (virtual atomic and molecular data center) [174] is another resource and, although developed mainly for astrophysics, it provides a common portal to a

<figure><img src="image_41.png" /><figcaption>**Figure 35.** Illustration of a simplified mechanism in helium. A rate must be associated with each arrow to fully define the mechanism.</figcaption></figure>

number of electronic databases containing recommended data relevant to modeling LTPs.

The identification of rate coefficients for processes involving electrons is complicated by the fact that in most LTPs, the electrons—the vector through which most of the energy from the electromagnetic fields sustaining the plasmas is transferred to excitation in the neutral gas—generally do not have Maxwellian energy distribution functions (EDF). The EDF (and hence rate coefficients versus mean electron energy or versus local field strength) can be calculated *if* a full set of electron-neutral scattering cross sections is available. To this end, the LXCat project [185] (www.lxcat.net) was established in 2010 as a means for exchanging data needed for modeling the electron and ion components of LTPs, and it includes compilations of data for cross sections for electron collisions with atoms/molecules in their ground state, which are accessible through VAMDC. We regard LXCat as, in many relevant ways, a model for future efforts to distribute plasma chemistry models.

In spite of these and other resources too numerous to mention here, coming up with a *coherent* set of rate coefficients for a mechanism is the cause of the largest uncertainties in the predicted plasma species concentrations in different types of plasma sources. In general, there is both irreducible uncertainty in the basic data, combined with contradictory evidence. Expert knowledge is often needed to extract a preferred datum from this information. For plasma chemistry with complex molecules of interest to the microelectronics industry, for example, very little guidance can be found in the literature and recourse must be made to theory or to making estimates.

**Current and future challenges.** The need to improve the quality of plasma chemistry data available to modelers is well recognized but a concerted effort has not yet been put in place in the LTP community, in contrast to what has been done in several other communities. An example in atmospheric

<footnote n="1">¹ LAPLACE, CNRS and University of Toulouse</footnote>

<footnote n="2">² Dublin City University</footnote>

<footnote n="39">³⁹ A full list of publications is available on the website http://iupac.pole-ether.fr/publications.html</footnote>
<figure><img src="image_42.png" /><figcaption>**Figure 36.** Steps in the process of development and distribution of a validated mechanism.</figcaption></figure>

chemistry was mentioned above. Another example is the multi-decade effort on the GRI-Mech project [186] in the combustion community, which has yielded sets of validated reaction mechanisms for given gas compositions, where rate coefficients have been adjusted within experimental error so as to obtain agreement with key measurements over a range of gas temperatures. The result is a model of the combustion chemistry that is faithful to both the fundamental kinetics and system data, and that can be reliably employed for modeling purposes. Because of the internal consistency, processes/rates should not be individually modified.

The situation in LTPs is more challenging than for the combustion community because there is no single parameter, e.g. gas temperature, which defines both the energy transfer from the charged particles to excitation, dissociation and ionization of the background gas and the subsequent energy transfer reactions among the ion, excited states, and dissociation products. For instance, the electron 'temperature' (or, more properly, electron 'mean energy') cannot be deduced from the translational gas temperature, which itself is usually not the same as the vibrational 'temperature'. This consideration complicates both the modelling and interpretation of basic experiments. An additional consideration is that plasma-surface interactions are sometimes as important as volume processes in the energy transfer sequence, but very few basic data are available to describe these interactions, which are highly dependent on surface conditions. In spite of these difficulties—or rather because of them—it is clear that the LTP community needs to define a strategy to develop, validate (to the extent possible) and distribute reaction mechanisms for some common gas mixtures.

**Advances in science and technology to meet challenges.**

Diagnostic techniques for determining species concentrations are advanced, but measurements of rate coefficients are time-consuming and can reasonably only be made for a few processes. Techniques for model reduction [187] can serve to identify the important reaction pathways in a complicated mechanism. Other techniques are available for performing sensitivity analyses taking into account error bars for each

rate [188]. Hence, numerical analyses can aid the identification of the critically uncertain rate coefficients that need to be measured. It will then be necessary to rely on theory to extend the available results to other systems and other conditions. With a concerted effort on the part of the LTP community, key experiments needed to reduce the uncertainty in reaction mechanisms could be identified and performed. Plasma chemistry can be quite complex, particularly in mixtures with molecular gases when the degree of internal excitation in the neutral gas becomes important. Some data are becoming available for rates for energy transfer between excited states [189], and we refer readers to the section of this Roadmap on atomic and molecular data for further progress in this important area.

**Concluding remarks.** It has been suggested, and we agree, that the community should initiate an effort to establish recommended reaction mechanisms for common gas mixtures, focusing, to begin with, on N₂/O₂ mixtures with argon or helium, because these are relevant to many emerging application areas. Other chemistries are of course very important in different contexts, but some initial focus seems necessary. The steps in the process of developing and distributing a validated reaction mechanism for given gas mixtures are listed in figure 36. Some members of the LTP community have recently undertaken a round-robin exercise for the purpose of comparing calculations of species concentrations for well-defined sets of discharge conditions using the various available codes and previously elaborated mechanisms. Further discussions are underway to initiate a COST action in the European community (to be coordinated by one of the authors of this contribution—MT) to validate mechanisms in simple gas mixtures. We hope that these and other actions planned or underway will provide the impetus and the means for the LTP community to improve the quality of the data available for modeling LTPs.

## ORCID

A Bogaerts https://orcid.org/0000-0001-9875-6460

P J Bruggeman https://orcid.org/0000-0003-3346-7275

V Colombo https://orcid.org/0000-0001-9145-198X

U Czarnetzki https://orcid.org/0000-0002-5823-1501

U Ebert https://orcid.org/0000-0003-3891-6869

P Favia https://orcid.org/0000-0002-5896-895X

U Kortshagen https://orcid.org/0000-0001-5944-3656

N J Mason https://orcid.org/0000-0002-4468-8324

B A Niemira https://orcid.org/0000-0001-9472-1025

Z Lj Petrovic https://orcid.org/0000-0001-6569-9447

Y-K Pu https://orcid.org/0000-0002-9319-4291

S Samukawa https://orcid.org/0000-0003-4971-3290

J Tennyson https://orcid.org/0000-0002-4994-5238
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