QDB: a new database of plasma chemistries and reactions

Realistic plasma models of many processes rest on the availability of reliable atomic and molecular data, so that the models are able to replicate the processes that drive the plasma at the submicroscopic level. Particularly for low-temperature plasmas, which are substantially molecular in composition, the set of possible processes, which we refer to as reactions below, can be very large. For low-temperature plasmas, accurate and comprehensive reaction datasets enable complex modeling of plasma-using technologies that empower our technology-based society [1]. Assembling appropriate datasets is therefore of critical importance.

For a given plasma composition, there are sets of species that are present in the plasma and a set of processes, generally called reactions, that will link the species or different states of the species. This reaction set is described as the 'chemistry' for that plasma. For anything but the simplest molecular plasma, the number of possible reactions that could make up a chemistry can be very large [2]. The important reactions in a given plasma will be a subset of all these possible reactions, although it is not always possible to say in advance precisely which these reactions will be. In this context it is appropriate to characterize a useful chemistry as one which has three attributes: (1) The chemistry should be complete, that is contain all the important reactions for the given plasma. (2) It should be consistent, that is the reactions should not be unbalanced, thus resulting in the plasma composition being driven away from the true composition. (3) Finally, the plasma chemistry should be correct; this criterion cannot be demonstrated on theoretical grounds alone and requires validation against experimental measurements made in plasmas.

Assembling plasma chemistries is far from straightforward. While there may be several chemistries available for relatively simple systems such as molecular nitrogen plasmas [3–7], they generally do not exist for more complex problems such as the chemical mixtures typically used in etching and other technological plasmas. Indeed, given that reactions involving molecular radicals frequently remain completely uncharacterized [8], it is often a challenge to assemble a complete reaction set for these chemistries.

Here we present the QDB. There are a growing number of databases aimed at supplying the needs of plasma modellers. For example, the recent LXCat project of Pitchford et al [9] aims to provide a web-based platform for data needed to model low-temperature plasmas. In practice LXCat considers electron collision processes but not heavy-particle (chemical) reactions. While both QDB and LXCat are set up to accept and provide multiple datasets for a single process if they are available, QDB aims to recommend a dataset for a particular application while LXCat leaves this choice to its users. The Phys4Entry database provides (ro)vibrationally resolved collisional data, including heterogeneous processes, for modeling re-entry plasmas [10]. For low-temperature, astronomical plasmas KIDA [11, 12] and BASECOL [13] provide data on chemical reactions and collisional excitation, respectively.

QDB aims to provide a repository for cross sections and/or rates for key reactions needed for models of low-temperature, i.e. molecular, plasmas. QDB collects data on both electron scattering and heavy-particle reactions and aims to facilitate and encourage peer-to-peer data sharing by its users. At present the data provided are largely for two-body reactions and hence are appropriate for low-pressure plasmas, but this will change in the future. Given sets of reactions, QDB then assembles these sets in chemistries for important plasma mixtures. If there are suitable experimental data available, these chemistries can be validated.

The following section gives an overview of QDB, with a technical specification of the data model given in the appendix. Section 3 catagorises the process types included in the database while section 4 summarizes the data sources used. A list of the reactions with a complete set of references is given as supplementary data to this article. Section 5 explains our chemistry construction and validation procedure; this is illustrated for two chemistries, those comprising SF₆/CF₄/O₂ and SF₆/CF₄/N₂/H₂, respectively. These chemistries were selected due to their importance in silicon etching. Section 6 discusses future developments planned for the database, and the last section provides a summary and conclusions.

QDB provides reaction rates, cross sections and chemistries. The basic data item is the species, which can be state-specified, e.g. N(⁴S), or not, e.g. N₂. At present QDB considers three generic species: the electron, the photon, and M, the third body in three-body reactions, plus 405 other atomic and molecular species. This total rises to 904 species when state-specified species are counted separately.

Species can undergo a series of processes called reactions. These includes, for example, elastic scattering or momentum transfer that are not generally regarded as chemical reactions. These processes are considered in more detail below. At present the database contains data on 4099 distinct reactions, comprising 2888 energy-dependent cross sections and 2259 temperature-dependent rate coefficients in Arrhenius form. Note that QDB allows multiple datasets for the same reaction, and for some reactions we have distinct data which are available as both cross sections and rate coefficients.

Many of these reactions are compiled into chemistries. Currently QDB has 29 chemistries, which are tabulated and discussed below. These chemistries can be validated, provided appropriate experimental data are available. Currently QDB contains 8 chemistries with some degree of validation; two of these chemistries are considered in detail below. Notes on the validation procedure are provided in the form of a datasheet for each validated chemistry. Chemistries are awarded a star rating that reflects how far they have been shown to satisfy the criteria of being complete, consistent, and correct. QDB is structured as a MySQL relational database; the data model used is discussed in the appendix to this article.

Users can upload new data using the interface on the QDB website (www.quantemoldb.com) and download data using a choice of file formats, which is being expanded. Currently supported formats are comma-separated text for each reaction, provided as a zip file or in qdat format, which facilitates input for Kushner's Hybrid Plasma Equipment Model (HPEM) [14, 15] code. The zip format contains all the cross sections, as individual comma-separated text files, and the rate coefficients that are needed for the specific chemistry. It also includes a manifest file listing all the files provided in the zip archive, a readme file, and a set of citations in bibtex format. The online view of each dataset contains data sheets and a form allowing users to provide feedback. Figure 1 shows a sample screen shot from QDB giving a comparison between various cross sections for electron-impact ionization of methane. Note that for some reactions, cross sections for the process are obtained from two different sources; in these cases the agreement is excellent.

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Development of QDB is performed with input from the Advisory Board whose members are co-authors of this paper.

Each reaction dataset in QDB is classified as containing cross sections or rate coefficients. The latter can be generated from the cross sections. The rate coefficients are expressed in Arrhenius form stored in the form of three parameters (A, n, and E), which can be used to compute the rate coefficients at the desired temperatures. For electron-impact reactions the Arrhenius formula is

$$\begin{eqnarray}&&A{\left(\displaystyle \frac{{T}_{e}}{1\mathrm{eV}}\right)}^{n}\exp \left(-\displaystyle \frac{E}{{T}_{e}}\right),\end{eqnarray} \tag{ 1 }$$

where T_e is the electron temperature in eV and E is the activation energy in eV. For heavy-particle reactions the Arrhenius formula employed is

$$\begin{eqnarray}&&A{\left(\displaystyle \frac{{T}_{g}}{300{\rm{K}}}\right)}^{n}\exp \left(-\displaystyle \frac{E}{{T}_{g}}\right),\end{eqnarray} \tag{ 2 }$$

where T_g is the gas temperature in K and E is the activation energy in K. In both cases, A is the Arrhenius coefficient whose units depend on the order of the reactions. First-order reactions such as photodissociation and photoexcitation are expressed in s⁻¹; second-order reactions, such as electron-impact reactions or two-body heavy-particle reactions, are expressed in cm³ s⁻¹; and three-body reactions use cm⁶ s⁻¹. Cross sections, e.g. for electron-neutral-molecule scattering, are given in units of cm² as a function of electron energy in eV.

Each reaction is classified according to the process considered. These processes are listed in tables 1, 2, and 3 which consider electron collision processes, heavy-particle reactions and processes involving photons, respectively. Note that some heavy-particle processes, in particular HAS and HIR, also involve a third body, generically denoted M in the database. The process label does not depend on the presence of M which is therefore not included in the process description.

Table 1.  Classification of electron collision processes considered in QDB.

Abbreviation	Types of reaction	Description
EDX	deexcitation	$e+{A}^{* }\to e+A$
EEL	elastic scattering	$e+A\to e+A$
EIN	ionization	$e+A\to e+{A}^{+}+e$
EMT	momentum transfer
ERR	radiative recombination	$e+{A}^{+}\to A+h\nu$
EDR	dissociative recombination	$e+{{AB}}^{+}\to A+B$
EDS	dissociation	$e+{AB}\to e+A+B$
EDA	dissociative attachment	$e+{AB}\to A+{B}^{-}$
EDE	dissociative excitation	$e+{AB}\to {A}^{* }+B+e$
EDI	dissociative ionization	$e+{AB}\to {A}^{+}+B+2e$
EEX	electron-impact electronic excitation	$e+A\to e+{A}^{* }$
ECX	change of excitation	$e+{A}^{* }\to e+{A}^{* * }$
ERC	recombination (general)	$e+{A}^{+z}\to {A}^{+(z-1)}$
EDT	electron attachment	$e+A+B\to A+{B}^{-}$
EVX	electron-impact vibrational excitation	$e+A\to e+A[v=* ]$
ETS	electron total scattering	$e+A\to e+{\rm{\Sigma }}A$
ETI	electron total ionization	$e+A\to e+e+{\rm{\Sigma }}{A}^{+}$
ETA	electron total attachment	$e+A\to {\rm{\Sigma }}{A}^{-}$

Table 2.  Classification of heavy-particle processes considered in QDB.

Abbreviation	Types of reaction	Description
HGN	associative electron detachment	${A}^{-}+B\to {AB}+e$
HCX	charge transfer	${A}^{+}+B\to A+{B}^{+}$
HIR	heavy-particle interchange	$A+{BC}\to {AB}+C$
HAS	association	$A+B\to {AB}$
HIN	heavy-particle collisional ionization	$A+B\to A+{B}^{+}+e$
HIA	heavy-particle association and ionization	$A+B\to {{AB}}^{+}+e$
HPI	Penning ionization	$A+{B}^{* }\to {A}^{+}+B+e$
HNE	neutralization	$e+{B}^{-}\to B+2e$
HMM	ions recombination	${A}^{-}+{B}^{+}\to A+B$
HDS	heavy-particle collisional dissociation	${AB}+C\to A+B+C$
HDX	heavy-particle collisional deexcitation	$A+{B}^{* }\to A+B$
HDN	heavy-particle dissociative neutralization	${{AB}}^{-}+{C}^{+}\to A+B+C$
HDC	heavy-particle dissociation and charge transfer	${AB}+{C}^{+}\to {A}^{+}+B+C$
HDI	heavy-particle dissociation and ionization	${AB}+{C}^{* }\to {A}^{+}+B+C+e$
HEX	heavy-particle excitation	$A+B\to A+{B}^{* }$
HED	heavy-particle electron detachment	${A}^{-}+B\to A+B+e$

Table 3.  Classification of photon processes considered in QDB.

Abbreviation	Types of reaction	Description
PDS	photodissociation	${AB}+h\nu \to A+B$
PEX	photoexcitation	$A+h\nu \to {A}^{* }$
PRD	radiative decay	${A}^{* }\to A+h\nu$

The scientific literature contains many measurements and calculations of reaction data that provide potentially useful input to plasma models. However, the task of extracting these data is far from straightforward. So far our strategy has been to focus on major data compilations and data sources. A list of those included so far is given in table 4. In addition a variety of data was taken from models performed by Kushner and co-workers [18–34]. These sources were augmented with individual reactions taken directly from the original scientific literature. Where no suitable data could be found, internal (Quantemol) electron collision cross sections were generated using the Quantemol-N [35] implementation of the UK Molecular R-matrix code (UKRMol) [36]. As implied by table 4, only a few of these cross sections have been published, although some have already been made available via LXCat [9] and the Virtual Atomic and Molecular Data Centre [37]. The process of adding new data to QDB is a continuous one. The present results represent a snapshot of the situation as of November 2016.

A complete list of all reactions currently given in QDB with appropriate bibliographic references is provided in the supplementary data. Tables 5 and 6 summarize the sources of the data currently available in QDB by process type. At present there are relatively few radiative process in the database; the only ones involve radiative decay (PRD) in atoms [21, 92, 93].

The chemistry sets are assembled starting from reactions already present in QDB; missing reactions are then extracted from the literature and added to QDB where possible. In cases where important reactions have not been previously studied, the missing reaction data are calculated using appropriate methods, such as Quantemol-N [35] for electron-molecule scattering reactions, or by scaling laws, or estimated to provide the necessary data. These data are added to QDB. This allows us to provide complete and self-consistent chemistry sets that form the starting point for validation. Figure 2 illustrates the network of 196 reactions assembled to characterize the chemistry of CF₄ and O₂. Table 7 lists the chemistries avaible in QDB as of November 2016.

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The self-consistency of each chemistry set is checked using a range of models including Kushner's zero-dimensional GlobalKin model [29, 32, 291, 292] as implemented in Quantemol-P. GlobalKin couples molecular data (i.e. reaction probabilities) with plasma models to determine plasma properties, such as equilibrium concentrations of species. A variety of plasmas can be simulated using this software, such as etching and atmospheric pressure plasma reactors. HPEM, as implemented in Quantemol-VT, is also used.

Initial validation is achieved by using a chemistry set as the basis for the modeling of different industrial reactors. Comparison of the model output with measurement is the principal means by which validation is achieved. For higher-dimensional simulation, the behavior of the species and the surface parameters across the wafer, such as etching or deposition rates, can also be used for comparison. Chemistry sets are given a reliability rating on the basis of these comparisons; see table 8. Of course, we recognize that the partial validations presented below only give agreement in the general trends for a given parameter under one set of specific conditions. Therefore, we cannot guarantee (i) that the given chemistry set produces right results under different operation conditions, nor (ii) that every plasma parameter is reproduced correctly at this stage of validation. Continually improving the offered chemistry sets by extending the validation process to other operating conditions and plasma parameters is one of the goals of QDB. Indeed, it is hoped that the community-driven nature of the QDB website will inspire new, relevant validation tests which can be carried out to further improve the database.

We now illustrate this process using two chemistry sets: those for SF₆/CF₄/O₂ and SF₆/CF₄/N₂/H₂ gas mixture etching Si. As discussed below, these sets comprise subsets of mixtures, which provide important chemistries as well. These were also validated as part of the validation process. The chemistries were validated using GlobalKin and compared with experimental data provided by Infineon. Unfortunately the data available for complex reactions sets such as the ones considered is often very limited and so only partial validation can be expected for these cases: we consider these examples to meet only the lowest level of validation—that is, agreement in the general trends between simulation and experiment for one discharge, as discussed above.

The Infineon tool consists of two parts. The first part is a coaxial microwave plasma discharge. In this part the electromagnetic wave propagates along the interface between the plasma column and the surrounding dielectric tube and the plasma column is sustained by electromagnetic energy. Free radicals are formed in this chamber with high efficiency. This chamber is connected to a larger vessel where the flux of particles propagates and where the remote wafer to be etched is located. Our GlobalKin models only attempted to model the second, larger chamber. GlobalKin performs a spatially homogeneous plasma chemistry simulation which are coupled with surface reaction modules. The model uses a Boltzmann solver to obtain electron impact reaction rate coefficients. These models assumed a plasma volume of 90 000 cm³, an area around the plasma of 10 700 cm². The models, which used an assumed diffusion length of 8.3 cm, were initiated using the feedstock gases. They were run for 500 iterations, corresponding to a total of 1 s, which proved sufficient to reach steady state.

5.1. SF₆/CF₄/O₂

Initially, distinct sets of chemistries for SF₆/O₂ and CF₄/O₂ were constructed and validated separately. These chemistries were then merged and missing reactions, such as SF₆ + ${\mathrm{CF}}_{3}^{+}\to$ SF₅⁺ + CF₄ [293] or SF_x⁻ + ${\mathrm{CF}}_{y}^{+}\,\to$ SF_x + CF_y, were identified and added. We then set up separate surface chemistries for SF₆ and CF₄, with a focus on silicon etching by F-radicals in the case of SF₆ and CF₄. Surface chemistry parameters were taken from Kokkoris et al [294]. Since CF₄ formed a smaller percentage of the mixture, see table 9, we did not include the polymer deposition by CF_x radicals. In addition to the F atom reactions, we added reactions of SF_x radicals using the same reaction scheme as Kokkoris et al [294], see also comments on this work by Nelson et al [295].

Table 9.  Conditions assumed in the model of SF₆–CF₄–O₂ etching.

Parameter	Value
Gas Pressure	500 and 700 mTorr
Gas Flow Rate
SF6	800 sccm
CF4	150 sccm
O2	10 sccm
Power	1000 to 2000 W
Substrate	Si

Only just over 1% of oxygen is added to the mixture, as this increases the dissociation of SF₆ and CF₄. Due to its low density, the oxygen-related surface reactions were not included in the model. We also assumed that no significant concentration of CS molecules is formed during plasma processing with a mixture of SF₆ and CF₄, due to the large concentration of the F radicals in the mixture. This results in a much higher probability of formation of C_xF_y and SF_x species. The conditions of the experiments are presented in table 9.

In the validation tests of the chemistry set, the power was varied from 1000 to 2000 W at a fixed pressure of 500 mTorr. As a second test we varied the pressure with power fixed at 2000 W. We used 40% of the experimental power in our simulation, in order to simulate the energy dissipation. This is almost certainly an overestimate of the power reaching the actual plasma in the Infineon device which explains why the simulations give faster etch rates than the measurements, see below.

Our GlobalKin simulations only provide global average values and therefore cannot provide an absolute quantitative comparison. For validation of our global model simulation we therefore compare trends. In particular, we compared the trends in the etching rate with measurements provided by Infineon Technologies, who studied the effect of both power variation and pressure variation. According to these measurements, the etch rate increases with increasing power but decreases with increasing pressure. Figure 3 illustrates the effect of varying power and pressure on the silicon etch rate for a mixture of SF₆/CF₄/O₂. Good agreement in the trends is observed between the results of our simulation and the experimental data of Infineon. By increasing the power in the measurements and simulation we observe an increase in the Si etching rate but the rate drops as the pressure is raised.

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Given the limited nature of the validation tests we have been able to perform for this chemistry we can rate it at only at level 3 (the lowest rating for a validated chemistry) in table 8.

5.2. SF₆/CF₄/N₂/H₂

Initially, two sets of chemistries, for SF₆/CF₄, from the previous validation task, and for N₂/H₂, were constructed and validated separately. These chemistries were then merged. Since there is only a small proportion of N₂/H₂ in the mixture, we excluded species like NF_x and CH_xF_y, as well as the reactions that lead to them. Rates for ion recombination (HMM) reactions such as ${{\rm{N}}}^{+}+{{\rm{F}}}^{-}\to {\rm{N}}+{\rm{F}}$ and ${{\rm{N}}}_{2}^{+}{{\rm{F}}}^{-}\to {{\rm{N}}}_{2}+{\rm{F}}$ were estimated from Moseley et al [271] and added to the chemistry list. The SF₆/CF₄ chemistry was generated using the same assumptions used for the SF₆/CF₄/O₂ mixture. We also dealt with the surface reactions in a similar fashion to SF₆/CF₄/O₂.

Table 10 summarizes the experimental conditions assumed in the model. Figure 4 illustrates the effect of varying power on the silicon etch rate for the SF₆/CF₄/N₂/H₂ mixture. The experimental data from Infineon we tested against compared etch rates, under similar conditions, for the SF₆/CF₄/N₂/H₂ and SF₆/CF₄/O₂ mixtures. According to the measurements, a higher etch rate is found for SF₆/CF₄/O₂ than for SF₆/CF₄/N₂/H₂. As shown in figure 5, due to the lower dissociation in presence of N₂/H₂ compared with O₂, both simulation and experimental results show a higher etch rate for the SF₆/CF₄/O₂ mixtures compared to SF₆/CF₄/N₂/H₂ due to the lower production of F.

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Table 10.  The conditions for processing in the model for SF₆/CF₄/N₂/H₂.

Parameter	Value
Gas pressure	500 mTorr
Gas flow rate
SF6	800 sccm
CF4	150 sccm
N2/H2	10 sccm
Power	1500 W
Substrate	Si

Again, given the limited nature of the validation tests that are possible for this chemistry at this time, we give this chemistry set a 3 star rating (see table 8) indicating agreement only in the general trends relating to a single parameter.

The process of adding both more reactions and chemistries to QDB is continuous and ongoing. We will also progressively improve the validation status of current chemistries and validate more chemistries, although these activities require appropriate experimental data to be available for us to validate against. We have developed an initial rating system for these chemistries, and we have developed this further by allowing users to also submit ratings. At the same time, we plan to implement more formal uncertainty quantification (UQ) procedures [296].

The processes currently covered by QDB are listed in tables 1, 2, and 3. These lists do cover all possible low-pressure gas phase processes. For example, inclusion of vibrationally-resolved reactions for molecules, such as in electron collisions with CO₂ [79], is important for a number of plasma studies. QDB has the capability to hold such data but more work on data input and processes considered will be required to make it fully functional. At present QDB does not include processes that occur on surfaces and has only limited data for processes involving a third body. Both of these will be included in the database in the future. The inclusion of three-body reactions will extend the coverage to atmospheric pressure plasmas.

At present the data can be downloaded in two formats: a generic one and one that is appropriate for HPEM. With increasingly large datasets and sophisticated modeling programs, it is desirable for data to be transferred directly from the database to the model using an application program interface (API). We plan to develop APIs for commonly used plasma modeling programs in order to facilitate the use of QDB. We are also currenly implementing facilities for users to self-assemble chemistries in their own basket; in the longer term we plan to facilitate this with an automated chemistry generation tool.

One of the challenging problems when modeling plasmas is the lack of reliable chemistry data. For this purpose, we have developed the Quantemol Database (QDB), which aims to provide a platform for the exchange and validation of reactions that are important in plasmas and plasma chemistry datasets. The database provides data on both electron scattering and heavy-particle reactions, and it aims to facilitate and encourage peer-to-peer data sharing by its users. QDB currently includes almost 5000 reactions and 29 complete sets of chemistries; so far 8 of these sets have undergone some sort of validation. The set of reactions includes more than 2800 cross sections and more than 2100 sets of reaction rate coefficients in Arrhenius format for more than 980 species in different states.

We thank Professor Uwe Czarnetzki, Dr Nobuyuki Kuboi, Professor Satoshi Hamaguchi, Professor Mark Kushner and Professor Leanne Pitchford for helpful discussions during this project. Partial funding was received from the UK STFC under grants ST/M007774 and ST/K004069, and from the Powerbase project. Powerbase has received funding from the Electronic Component Systems for European Leadership Joint Undertaking under grant agreement No 662133. This Joint Undertaking receives support from the European Union's Horizon 2020 research and innovation programme and Austria, Belgium, Germany, Italy, Netherlands, Norway, Slovakia, Spain, United Kingdom.

The QDB is implemented using the MySQL relational database management system. An overview of the principal tables and their relations is given in figure 6.

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Each collision or reaction is considered to take place between one or more reactants to give one or more products. Each of the reactants and products may be an atom, ion, molecule, molecular ion, or particle (such as a photon or an electron), perhaps in a specified quantum state. These species are represented by their chemical formula according to a standard notation (for example, Ar, H2O, NH2+ for atoms and molecules, e^– for electrons $h\nu$ for photons). State information is attached as a number of text strings matching a defined pattern, which can be parsed according to the type of state being considered. A list of some of the state types with examples is given in table 11.

Each reactive or collisional process may be described by more than one DataSet: an experimental measurement or theoretical prediction of rate data relating to the process. There are two principal types of DataSet. Cross sections are represented as a table of (electron energy, cross section value) pairs, stored in an external resource referenced by filename or URL. Rate data expressed according to an Arrhenius-like expression, see equations (1) and (2) are represented by storing separate parameters A, n, and E. The parameters and the columns of any tabular data have associated metadata (name, units, and description) in a linked relational database table.

Different reactive and collisional processes are identified by a three-letter code (process type) (for example: EDR = dissociative recombination). The codes employed are an extended version of those defined in the IAEA document of Humbert et al [297]. A list of codes is given in tables 1, 2 and 3; more extensive descriptions and examples are given on the QDB website at http://quantemoldb.com/reactions/processes/.

The structure of the data model allows the user interface to perform searches of the collisions by species (reactant or product), process type, and citation. Furthermore, additional fields within the DataSet table allow for evaluation comments, quality assessment rating, and validity and usage notes to be stored.

QDB Chemistries are self-contained collections of collisional and reactive processes describing the properties of a plasma under some set of conditions. A table in the relational database holds metadata relating to each Chemistry, evaluation notes and ratings, and the associations with the relevant DataSets; see figure 7.

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