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doi.org/10.26434/chemrxiv.9943964.v2
A Systematic Method for Predictive in-silico Chemical Vapour DepositionÖrjan Danielsson, Matts Karlsson, Pitsiri Sukkaew, Henrik Pedersen, Lars Ojamäe
Submitted date: 11/02/2020 • Posted date: 12/02/2020Licence: CC BY-NC-ND 4.0Citation information: Danielsson, Örjan; Karlsson, Matts; Sukkaew, Pitsiri; Pedersen, Henrik; Ojamäe, Lars(2019): A Systematic Method for Predictive in-silico Chemical Vapour Deposition. ChemRxiv. Preprint.https://doi.org/10.26434/chemrxiv.9943964.v2
A comprehensive systematic method for chemical vapour deposition modelling consisting of seven welldefined steps is presented. The method is general in the sense that it is not adapted to a certain type ofchemistry or reactor configuration. The method is demonstrated using silicon carbide (SiC) as model system,with accurate matching to measured data without tuning of the model. We investigate the cause of severalexperimental observations for which previous research only have had speculative explanations. In contrast toprevious assumptions, we can show that SiCl2 does not contribute to SiC deposition. We can confirm thepresence of larger molecules at both low and high C/Si ratios, which have been thought to cause so-calledstep-bunching. We can also show that high concentrations of Si lead to other Si molecules than the onescontributing to growth, which also explains why the C/Si ratio needs to be lower at these conditions to maintainhigh material quality as well as the observed saturation in deposition rates. Due to its independence ofchemical system and reactor configuration, the method paves the way for a general predictive CVD modellingtool.
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1
A Systematic Method for Predictive in-silico Chemical Vapour
Deposition
Örjan Danielsson1,3 *, Matts Karlsson2, Pitsiri Sukkaew1, Henrik Pedersen1, and Lars Ojamäe1
1 Department of Physics, Chemistry and Biology, Linköping University, Sweden
2 Department of Management and Engineering, Linköping University, Sweden
3 Physicomp AB, Liljanstorpsvägen 20, Västerås, Sweden
* e-mail: o.danielsson@physicomp.se
Abstract
A comprehensive systematic method for chemical vapour deposition modelling consisting of
seven well defined steps is presented. The method is general in the sense that it is not adapted
to a certain type of chemistry or reactor configuration. The method is demonstrated using
silicon carbide (SiC) as model system, with accurate matching to measured data without
tuning of the model. We investigate the cause of several experimental observations for which
previous research only have had speculative explanations. In contrast to previous
assumptions, we can show that SiCl2 does not contribute to SiC deposition. We can confirm
the presence of larger molecules at both low and high C/Si ratios, which have been thought to
cause so-called step-bunching. We can also show that high concentrations of Si lead to other
Si molecules than the ones contributing to growth, which also explains why the C/Si ratio
needs to be lower at these conditions to maintain high material quality as well as the observed
saturation in deposition rates. Due to its independence of chemical system and reactor
configuration, the method paves the way for a general predictive CVD modelling tool.
2
1. Introduction
Chemical vapour deposition (CVD) processes comprise a vast range of physical and chemical
phenomena acting at different time and length scales extending over 10-15 orders of
magnitude; from chemical reactions to fluid flow and heat transfer, all influencing the
properties and quality of the final coating1. This complex interaction, along with the
challenges to perform in situ measurements, makes it difficult to obtain a detailed
understanding of the CVD process2. Thus, developing new processes and/or improving
existing ones, are undertaken using experimental trial-and-error methods with the resulting
coating as the only measurable output, while the details of the actual deposition mechanism
remain largely unknown. Consequently, the CVD process is in many aspects a black box,
where tuning of input parameters like precursor flow rates and temperature settings control
the final deposition output.
This black box can, however, be unlocked through modelling and simulations that provide
detailed information impossible to obtain experimentally2, 3. Simulation data can often be
presented as distributions rather than (a few) points as in the case of measurements and
combining simulation data from a complete and detailed model with experimental data
enables enhanced analysis possibilities and a deeper understanding, moving towards a
knowledge-based process development.
The CVD related phenomena, widely spread in time and length, require different modelling
methods found in different disciplines of physics, chemistry and engineering. CVD modelling
studies have therefore mainly focused on either the chemistry4, 5 or the fluid flow
characteristics6, using simplified descriptions of the other parts of the CVD process.
3
Simplified reactor geometries are good in that they can significantly reduce the computational
time needed for the simulation. However, in reality, a CVD reactor often has a complex
design to facilitate transport and distribution of both precursors and heat to the deposition
area. If this design is too much simplified the simulated heat and mass distributions will be
significantly different from the real case, giving non-realistic predictions of gas mixture
compositions and species concentrations at the deposition surface, ultimately leading to
wrong conclusions being drawn from the simulation work.
Simplified descriptions of the chemistry on the other hand, often makes it necessary to
introduce some kind of tuning parameter to fit the simulation results to experimental data,
leading to a model that predicts what you already know but is less useful for predicting
deposition at other process conditions or in a different reactor geometry.
When detailed kinetic models are developed, surprisingly few employ a systematic approach
to ensure the model is adequate for its purpose. Two of the earliest and maybe most thorough
work on developing reaction mechanisms for CVD were done by Coltrin et al4 for Si and by
Mountziaris and Jensen5 for GaAs. Coltrin et al4 constructed a relatively large system of 120
elementary reactions for silane decomposition, which then was reduced to 20 reactions based
on a sensitivity analysis. Mountziaris and Jensen5 built a reaction mechanism for GaAs
consisting of 17 reaction steps based on a combination of equilibrium computations and
spectroscopic measurements in specially designed reactors. However, in neither of these
studies is the selection of reaction mechanisms fully motivated or explicitly validated.
Many of the studies that have followed, including those for SiC7, 8, 9, AlGaN10 and GaN11, are
based on either of these two models, with some additions taken from other literature sources.
But none of them use a systematic method for selecting which reactions shall be included.
This points to the problem: when data from different literature sources are compiled into a
4
new model, how can one be sure that the resulting chemical model is accurate and relevant for
its purpose?
Here, we present a systematic method for CVD modelling where input kinetic data, from
literature or from quantum chemical modelling, is combined with computational fluid
dynamics to generate a map of the CVD chemistry that can mimic experimental data without
applying correction factors.
2. A concept for systematic CVD modelling
A complete model of a CVD process requires detailed descriptions of all phenomena, from
the flow of gases, heat generation and distribution, to the chemical reactions in the gas phase
and at the surfaces, i.e. a combination of different modelling methods must be used. To enable
in-depth studies of CVD through modelling, we suggest a systematic approach as summarized
in Table 1, with the details given in the Methods section.
Table 1 A seven-step protocol for systematic CVD modelling
1. Identify controlling phenomena/factors through a system and time scale analysis
2. Construct a model for the gas phase reaction mechanisms and determine reaction rate
constants utilizing quantum-chemical (QC) computations or other methods
3. Validate the gas phase kinetic model by performing gas phase kinetics simulations
4. Evaluate species concentration trends from the kinetic model and compare with
experiments to determine growth species
5. Construct a surface reaction mechanism and determine reaction rate constants
6. Set up and run a simulation of the CVD process using Computational Fluid Dynamics
(CFD), where the gas phase and surface kinetics are included.
7. Validate the CFD model against experiments
This comprehensive, yet straight forward, modelling strategy can be used to build robust
models independent of reactor geometry, choice of precursors or process conditions. Even
5
though some of the individual steps may be well known, and also frequently used in CVD
modelling, each step only gives a fraction of the information needed for the full model.
Therefore, the order in which each step is performed also becomes important. Our method is
constructed so that the information needed for one step is obtained in the previous one. This
systematic approach certifies not only that the correct information is used in the model, but
also that it is not tuned or adjusted to fit into any predetermined case. Although this might
seem obvious, it is not the common way of modelling CVD. Many studies on CVD modelling
seen in literature simply starts at step 6, with no validation or relevance check of the chemical
reaction models used12.
It should be noted that validation of the surface reaction mechanism between step 5 and step 6
would make sense. However, at present we lack good methods for this, besides checking the
resulting growth rate. Therefore, the validation of the surface reaction mechanism is done
implicitly via the CFD simulation.
To show the strength and potential of the proposed modelling strategy, it is here applied to
CVD of hexagonal silicon carbide (SiC), a wide bandgap semiconductor material of great
importance for the transition to more energy efficient high-power electrical systems13, 14. As
SiC is a compound material, its CVD process is more complex than that of e.g. silicon, thus
increasing the need for modelling as a tool for better understanding. Previous attempts to
compile a complete and general model for SiC CVD are few9, 15, 16, 17, and mainly based on the
model for heteroepitaxial growth of cubic SiC (3C-SiC) on silicon substrates at 1400°C by
Allendorf and Kee8, a process quite different from that of homoepitaxial growth of hexagonal
SiC on SiC substrates at approximately 1600°C.
6
3. Methods
Our systematic approach to CVD modelling consists of the seven steps presented above
(Table 1).
3.1 System and time scale analysis
To find suitable approximations for modelling, one must understand the system, its
dominating phenomena and limiting factors. A first overview is obtained via dimensionless
numbers that give the ratio between different phenomena. The most useful ones for CVD
processes, with typical values, are given in Table 2.
Table 2 Dimensionless numbers to characterise fluid flow and mass transfer in CVD systems.
Dimensionless
number
Description Typical values
in CVD
Reynolds (Re) inertial forces vs. viscous forces
laminar to turbulent flow transition for Re > 2300
100 – 1000
Nusselt (Nu) convective vs. conductive heat transfer
if of the order of 1 => laminar flow
1 – 10
Knudsen (Kn) mean free path vs. physical length scale
if ≳ 1, the continuum assumption is not valid
<< 1
Prandtl (Pr) momentum vs. thermal diffusivity ~1
Schmidt (Sc) momentum vs. mass diffusivity ~1
Lewis (Le) thermal vs. mass diffusivity ~1
Péclet (Pemass) convective mass transfer vs. mass diffusivity > 100
Péclet (Petherm) convective heat transfer vs. thermal diffusivity > 100
Damköhler (Da) flow time scale vs. chemical time scale
estimation of the degree of conversion
Da < 0.1 => less than 10% conversion expected. Da >
10 => more than 90% conversion expected.
We find that many CVD processes have laminar flows, work in the continuum regime, and
that momentum, mass and thermal diffusivities are about equally important. The relation
between the flow and chemistry time scales (the Damköhler number) give indications on how
to model the chemistry. At high temperatures, gas phase reactions become fast and in
comparison, the residence time of the gas in a CVD reactor, i.e. the time for the gas to pass
7
through the reactor and during which chemical reactions take place, is orders of magnitude
longer. A rough estimate of the residence time is calculated simply by dividing the reactor
volume by the volumetric flow, while a more detailed analysis can be made using
Computational Fluid Dynamics (CFD) (see Supplement). For a typical CVD process, the
Damköhler number is usually very high, indicating that the residence time is important. This
does not come as a surprise since the main idea behind CVD is to allow sufficient time for the
chemical reactions.
For laminar flow, transport of species towards the surface occurs mainly by diffusion through
the fluid flow boundary layer. The time for diffusion, tDiff, can be expressed as
𝑡𝐷𝑖𝑓𝑓 =𝜆𝐷𝑖𝑓𝑓
2
4𝐷𝑖
Eq. 1
where Di is the mass diffusion coefficient and λDiff the diffusion length (which could be taken
to be equal to the thickness of the boundary layer above the surface, 𝛿 ≈ 4.99𝑥
√𝑅𝑒, where Re
is the Reynolds number and x is the distance along the flow direction). The mass diffusion
coefficient is
𝐷𝑖 =1 − 𝑋𝑖
∑𝑋𝑗
𝐷𝑖𝑗𝑗≠𝑖
Eq. 2
Where Xi is the molar fraction of species i, and Dij is the binary diffusion coefficient given
by18
𝐷𝑖𝑗 =3
16
√2𝜋𝑅3
𝑁𝑎𝑝𝜋
𝑇3/2
𝜎𝑖𝑗2 Ω𝑖𝑗
(1,1)∗(
1
𝑀𝑖+
1
𝑀𝑗)
1/2
Eq. 3
8
R is the gas constant, Na Avogadro’s number, Mi the molecular mass of species i, p the
pressure and T the temperature. σij is the combined collision diameter of the two species:
𝜎𝑖𝑗 =𝜎𝑖+𝜎𝑗
2, and Ω𝑖𝑗
(1,1)∗ the collision integral whose values can be found in tables18. For
diluted mixtures Di ≈ Dij.
The time for diffusion of adsorbed species on the surface can be estimated by19
𝜏𝐷 =𝐿2
16𝐷𝑠
Eq. 4
where L = terrace length and Ds = surface diffusivity. The surface diffusivity is approximately
𝐷𝑠 = 𝜈𝑎02𝑒−𝐸𝑑/𝑅𝑇
Eq. 5
where ν = lattice vibration frequency (of the order of 1012 Hz), a0 = lattice parameter, Ed =
diffusion activation energy. Ed is approximately half of the bond strength, Ed = 0.5Eb.
3.2 Gas phase reaction mechanism
A gas phase reaction mechanism that describe the decomposition of precursors and reactions
between by-products is necessary when modelling CVD. A minimum requirement for a
general model, that is independent of a specific process or reactor geometry, is to include
those species that would be present at thermodynamic equilibrium in the mechanism. Any
closed chemical system, held at constant temperature and pressure, will eventually reach a
state of thermodynamic equilibrium. Thus, a general reaction mechanism should contain
reactions that eventually lead to the equilibrium species. The equilibrium composition is
determined through minimization of the Gibbs free energy for a system that allows formation
of all species that can be formed by combinations of the atoms contained in the precursors and
9
in the carrier gas. When making these calculations there is a risk that the results are biased by
the set of molecules chosen for the study, and that wrong conclusions are drawn if the set is
too limited. A combinatorial approach can be used to build the set of molecules to be included
– molecules made from combinations of atoms from the precursors and the carrier gas. The
necessary properties (enthalpy and entropy) of each molecule are then calculated using
quantum chemical calculations, or when applicable, found in standard reference databases.
For CVD processes it is reasonable to limit the set of molecules to those having a maximum
of four or five of the precursor atoms (e.g. hydrocarbons up to C4H10 or C5H12), since we
expect larger molecules to thermally decompose.
When the equilibrium set of species has been determined, the next step is to systematically
find reaction paths from common sets of precursors towards these species. This will add
several other (intermediate) species to the reaction scheme. Also here, a combinatorial
approach can be used as a start to write up the set of reactions, i.e. every type of molecule
may react with any other type of molecule. By analysing Gibbs reaction energies, reactions
that likely will occur can be found (a negative Gibbs reaction energy indicates that the
reaction could proceed spontaneously). Reactions unlikely to occur or reactions leading to
highly improbable products, such as very large or unstable molecules, are then removed from
the set.
Once the reaction mechanism is set up, the individual reaction rates need to be determined.
Transition state theory can be used to derive rate constants for each elementary reaction20 and
the energy profiles along the reaction coordinates are obtained by quantum-chemical
computations. For a reaction with no transition state, the barrier height can be approximated
to be equal to the reaction energy when the energy is positive, and to be zero when the energy
is negative.
10
In our study, all quantum-chemical calculations were done using the Gaussian 09 software21.
Ground state and transition state structures for each reaction were optimized using the hybrid
density functional theory (DFT) B3LYP22, 23 and Dunning’s cc-pVTZ basis set24 together with
the dispersion energy correction (D3) from Grimme et al25. Harmonic frequencies were
calculated at the same level of theory. Transition states were verified by either visualizing the
displacement of the imaginary frequencies or by tracing the reaction path from the transition
state to the product and reactant states using the intrinsic reaction coordinate (IRC)
computation21. The electronic energies were calculated using CCSD(T) single point
calculations26, 27 and cc-pVnZ basis sets from Dunning24, 28 for n = D, T and Q before
extrapolated to the values at the complete basis set limit using eq. (2) in29.
The choice of QC method has been discussed in the papers30, 31. The error in the computed
activation energies will be reflected in the uncertainties of the rate constants, e.g. an error of
5 kJ/mol in the transition state energy would give an error in the rate constant of about 40% at
1900 K, which should be kept in mind.
For some of the reactions the optimization procedure could not predict any transition state due
to a change of the spin states, e.g. the sum of the spin states of the reactants is triplet, while
that of the products is singlet. To make accurate calculations of reaction rates for these
reactions, more advanced methods are needed, which is beyond the scope of this paper.
Instead we used collision theory to determine these reaction rates. The use of collision theory
is obviously a simplification, but it can be motivated in cases when the CVD process is mass
transport limited, which allows for larger deviations in the reaction rates without altering the
overall result.
11
3.3 Validation of the gas phase reaction mechanism
The final chemical kinetic reaction model should after “infinite” time lead to a gas phase
composition equal to the equilibrium state, which means that the equilibrium composition of
the gas also can be used to validate the reaction mechanism. Here, we set up a 1D transient
model using the reaction mechanism to simulate the evolution of the gas composition with
time by numerically integrating the coupled rate law equations of the elementary reaction
steps. In practice, this was done using a commercial CFD software, but it could equally well
be done via some more specialized software for chemical kinetics, or a relatively simple
home-made computer code.
If the validation should fail, it is likely that some reaction paths are missing, and we should go
back to step 2 to find additional ones and also make sure there are paths connecting all
reacting species.
3.4 Evaluate species concentration trends to determine growth species
The number of moles of a species striking the surface per unit area and unit time
(impingement rate) is estimated through the commonly used expression derived from the
Maxwell-Boltzmann velocity distribution for ideal gases:
Φ𝑖 =𝑝𝑖
√2𝜋𝑀𝑖𝑅𝑇
Eq. 6
where pi is the partial pressure of species i, Mi its molar mass, R the gas constant and T the
temperature. The partial pressures are given as results from the kinetic simulations in step 3.
For faster computations, one could use thermodynamic equilibrium calculations to obtain the
partial pressures, if the reactions are fast enough and residence times are long enough, since
we at this stage only are interested in how the species concentrations change (i.e. the trends)
12
when varying process conditions and not the exact concentration. Comparing the trends for
each species to the variation in deposition rates from experimental data will enable
determination of active growth species. It is useful to have access to experimental data
covering a broad parameter space for this evaluation.
3.5 Construct a surface reaction mechanism and calculate/determine reaction rates
Once the growth species have been determined, surface reaction mechanisms containing these
species are constructed similarly as for the gas phase reaction mechanisms.
A common and simple way of describing the reaction rate is by defining a probability for the
adsorption, also called sticking coefficient. Then the reaction rate is this probability times the
species flux to the surface, i.e. each species that hits the surface will adsorb with a certain
probability.
On a general form the surface reaction can be described by
∑ 𝛼𝑖𝐴𝑖(𝑔) +
𝑁𝑔
𝑖=1
∑ 𝛽𝑖𝐵𝑖(𝑠)
𝑁𝑠
𝑖=1
+ ∑ 𝛾𝑖𝐶𝑖(𝑏)
𝑁𝑏
𝑖=1
= ∑ 𝛼𝑖′𝐴𝑖(𝑔) +
𝑁𝑔
𝑖=1
∑ 𝛽𝑖′𝐵𝑖(𝑠)
𝑁𝑠
𝑖=1
+ ∑ 𝛾𝑖′𝐶𝑖(𝑏)
𝑁𝑏
𝑖=1
Eq. 7
where g, s, and b denote gas-phase, surface adsorbed, and bulk (deposited) species,
respectively. The rate of the surface reaction is
�̇� = 𝑘𝑓 ∏[𝐴𝑖(𝑔)]𝑤𝛼𝑖
𝑁𝑔
𝑖=1
∏[𝐵𝑖(𝑠)]𝛽𝑖
𝑁𝑠
𝑖=1
− 𝑘𝑟 ∏[𝐴𝑖(𝑔)]𝑤𝛼𝑖
′
𝑁𝑔
𝑖=1
∏[𝐵𝑖(𝑠)]𝛽𝑖′
𝑁𝑠
𝑖=1
Eq. 8
where kf and kr are the forward and reverse rate expressions, and [X] is the molar
concentration of molecule X. It is assumed that the reaction rate is independent of the bulk
species concentration.
13
The rate expressions, often expressed in the Arrhenius form, are calculated using transition
state theory and quantum-chemical calculations on cluster models, as described in the
supplementary information.
3.6 Set up and run a simulation of the CVD process using Computational Fluid Dynamics
(CFD)
Computational Fluid Dynamics (CFD) solves the equations for conservation of mass,
momentum and energy at the macroscopic scale by numerical methods. Since most
experimental data are measured at the reactor length scale, CFD is a useful method to model
CVD processes. The inclusion of gas phase and surface chemical reaction mechanisms in the
CFD model is a way to couple the quantum chemistry scale to the reactor continuum scale.
Results from the CFD simulation give distributions of deposition, species concentrations, as
well as temperatures and flow velocities, which are used for analysing and increasing the
understanding of the CVD process.
The concentrations of individual species in the gas are given by
𝜕𝜌𝑌𝑖
𝜕𝑡+ ∇ ∙ (𝜌𝐯𝑌𝑖) + ∇ ∙ 𝐉i = 𝑀𝒊 ∑ 𝜈𝑖𝑗(𝑅𝑗
𝑓− 𝑅𝑗
𝑟)
𝑁𝑟𝑒𝑎𝑐𝑡
𝑗=1
Eq. 9
where ρ is the gas density, Yi the mass fraction of species i, v the velocity vector, Ji the
diffusive flux, Mi the molar mass and νij the stoichiometric coefficient of species i in reaction
j. 𝑅𝑗𝑓 and 𝑅𝑗
𝑟 are the forward and reverse reaction rates of reaction j, respectively. For the
simple and general reaction αA + βB → C, the forward reaction rate is
𝑅𝑗𝑓
= 𝑘𝑗[𝐴]𝛼[𝐵]𝛽 Eq. 10
14
where [A] and [B] are the concentrations of species A and B, respectively. kj is the rate
constant that e.g. can be calculated by quantum-chemical calculations, see step 2 above. The
rate constant is often expressed as an Arrhenius equation, 𝑘𝑗 = 𝐴𝑇𝑛𝑒−𝐸𝑎/𝑅𝑇, where Ea is the
activation energy for the reaction. The reverse reaction rate can be calculated from
equilibrium, using
𝑘𝑗𝑟 =
𝑘𝑗𝑓
𝑘𝑗𝑒𝑞
Eq. 11
where
𝑘𝑗𝑒𝑞 = (
𝑝0
𝑅𝑇)
∑ (𝜐𝑖′′−𝜐𝑖
′)𝑖
𝑒− ∑ (𝜐𝑖′′−𝜐𝑖
′)𝑖 Δ𝑟𝐺𝑖0/𝑅𝑇 Eq. 12
𝜐𝑖′′ and 𝜐𝑖
′ are the stoichiometric coefficients of species i on the reactant and product side of
the reaction, respectively. p0 is the standard state pressure (100 kPa) and Δ𝑟𝐺𝑖0 is the Gibbs
free energy change per mole of reaction for unmixed reactants and products at standard
conditions.
Reactions at surfaces are implemented in the CFD model as boundary conditions at the solid-
fluid interfaces. The mass flux to the surface equals the rate at which the gas phase species is
consumed by the reaction on the surface. The species flux balance, J, for the simple reaction
αA(g) + βB(s) → products is
𝐽 = 𝛼𝑀𝑅𝑎𝑑𝑠 Eq. 13
and the change in surface species concentration is
𝑑[𝐵(𝑠)]
𝑑𝑡= 𝛽𝑅𝑎𝑑𝑠 Eq. 14
15
The adsorption reaction rate is
𝑅𝑎𝑑𝑠 = 𝑘𝑓[𝐴(𝑔)]𝑤 [𝐵(𝑠)] = 𝑘𝑓
𝜌𝑤𝑌𝐴,𝑤
𝑀𝐴𝜌𝑠𝑋𝐵
Eq. 15
where the subscript w indicates the value taken at the wall. The concentration of the species
[𝐴(𝑔)]𝑤 =𝜌𝑤𝑌𝐴,𝑤
𝑀𝐴 and [𝐵(𝑠)] = 𝜌𝑠𝑋𝐵 , where YA is the mass fraction of species A, and XB is
the surface site fraction of species B. ρw is the gas phase density at the surface, MA is the
molar mass of species A, and ρs is the surface site density. The surface site density depends on
the crystal structure of the surface and may be calculated from the lattice parameters of the
substrate. kf may be written as an Arrhenius expression, 𝑘𝑓 = 𝐴𝑇𝑛𝑒−𝐸𝑎/𝑅𝑇, with the units
[𝑚3
𝑘𝑚𝑜𝑙
1
𝑠], so that the units of 𝑅𝑎𝑑𝑠 become [
𝑘𝑚𝑜𝑙
𝑚2 𝑠].
For reactions between two adsorbed surface species, the reaction rate is
𝑅𝑠𝑢𝑟𝑓 = 𝑘𝑓[𝐵1(𝑠)][𝐵2(𝑠)] = 𝑘𝑓𝜌𝑠𝑋𝐵1𝜌𝑠𝑋𝐵2 = 𝑘𝑓𝜌𝑠2𝑋𝐵1𝑋𝐵2
Eq. 16
For the reaction to take place, the surface species need to be next to each other, so the
expression should in principle take into account the fraction of surface occupied by an
adjacent pair of B1(s) + B2(s), i.e. XB1+B2. However, we can assume (according to step 1
above) that diffusion on the surface is much faster than the reactions, making the
approximation XB1+B2 = XB1∙XB2 valid. The units of kf are in this case [𝑚2
𝑘𝑚𝑜𝑙
1
𝑠], so that the units
of 𝑅𝑠𝑢𝑟𝑓 also become [𝑘𝑚𝑜𝑙
𝑚2 𝑠].
3.7 Validate the CFD model against experiments
Experimental data in the literature is not always accompanied by a detailed description of the
CVD reactor used, and it could therefore be challenging to set up a CFD model for validation
16
even if there is enough deposition data available. Nevertheless, without validation one cannot
determine the accuracy and generality of the model, which is necessary if the model shall be
used as a predictive tool. Access to own CVD reactors, or close collaboration with a CVD lab
could then be crucial. It should be stressed that the CFD model has to be carefully
constructed, avoiding simplifications that could affect the simulation results.
The validation could preferably be made in steps; first against temperature (without chemistry
added) and then against deposition rates. This is to make sure that the resolution (grid size) of
the CFD model and other assumptions are good enough to render accurate temperature results
before adding the chemical reactions. If the validation should fail, even if the model can
predict the temperature distributions correctly, we should go back to step 5 and re-examine
the surface reaction mechanism.
4. Applying the seven-step protocol: modelling of SiC CVD
4.1 System and time scale analysis
CVD of semiconductor grade SiC is performed at around 1600 °C at reduced pressures
around 0.1 bar with precursors, like SiH4 and C3H8, heavily diluted (concentrations < 1%) in
the H2 carrier gas. Characterising the fluid flow and mass transfer by dimensionless numbers
(Methods) indicate a laminar flow where momentum, thermal and mass diffusivities are about
equally important. The residence time of the gas in a typical CVD reactor32 is of the order of
0.1 – 1.0 seconds as evaluated by Computational Fluid Dynamics (CFD) (Supplement). A
typical value of the diffusion coefficient, Di, (calculated from Eq. 2 and Eq. 3) is of the order
of 10-2 m2/s. With a diffusion length, λDiff, of the order of millimetres (the thickness of the
boundary layer above the surface, i.e. 𝛿 ≈ 4.99𝑥
√𝑅𝑒, with x of the order of centimetres and Re
17
of the order of 100 – 1000), the corresponding time for diffusion of species from the gas to the
surface, tDiff, is then of the order of milliseconds. The time for diffusion of adsorbed species,
τD is in the range 10 – 1000 ns. These are considerably longer times than the mean time for
chemical reactions to occur at the surface. Our model system is therefore mass transport
limited when it comes to the actual growth. However, chemical reactions occur all the way
along the path towards the growth zone, and the composition of the gas at the growth surface
depends on what happens upstream. It is therefore important to model the chemical reactions
as accurately as possible.
4.2 Gas phase reaction mechanism
The species (end products) that must, as a minimum, be included in the reaction mechanism,
are found through calculations of thermodynamic equilibrium for a wide range of
temperatures and precursor concentrations, including up to 190 different species (Supplement,
Table S1). No condensed phases were allowed to from, a common approach for probing the
gas phase composition before it reaches the substrate. At the same time, the larger Si and Si-C
molecules (such as Si6 or Si5C) could be thought of as embryos to solid particles in the gas.
The full reaction scheme is constructed from elementary reaction steps that involve
precursors, intermediate species and/or end products (Supplement, Table S2-Table S4). For
SiC there are three sub-sets of reactions: hydrocarbons, silicon hydrides/chlorides and
organosilicons. The hydrocarbon reactions are well studied in previous literature33, 34, 35, 36, 37,
while kinetic reaction rates for the silicon-containing part are calculated using thermodynamic
reaction profile results obtained from QC computations (Methods).
In the development of a reaction scheme for SiC CVD, we made the following considerations:
18
• A reaction scheme without Si-C molecules will not accurately predict the gas phase
composition at “infinite” time. In the literature the reaction schemes for SiC CVD
have been decoupled to one silicon side and one carbon side, based on the arguments
from Stinespring and Wormhoudt7 that the formation of molecules containing both
silicon and carbon is unlikely. However, they considered only two different reaction
paths – SiH2 + CH4 ⟶ H3SiCH3 and Si2 + CH4 ⟶ Si2CH4 – and thereby neglected
several other possibilities, which are included here.
• For reactions leading to species containing both Si and C atoms, we take as reactants
those molecules that have high concentrations at standard CVD conditions, i.e. C2H2,
CH4, SiH2, and Si.
• The reaction SiH2 + C2H2 → SiC2H4 was suggested in38 where one of the triple bonds
in C2H2 breaks and the Si-atom of the SiH2 is inserted there. A similar situation could
be plausible for the gaseous Si atom: Si + C2H2 → SiC2H2 as a first step to form SiC2.
• The SiC CVD process uses large amounts of hydrogen as carrier gas. When
chlorinated precursors are used, reactions leading to HCl are therefore more likely
compared to reactions leading to atomic chlorine or chlorine gas.
• At thermodynamic equilibrium, chlorinated carbon species are not found at all, and
species containing both Si, C plus chlorine have very low concentrations in this
environment, at any temperature. They are therefore not considered as important
intermediate species. Unless such species are used as precursors (e.g. CH3Cl), their
reactions can be excluded.
• Reactions among hydrocarbons are well described in the literature33, 34, 35, 36, 37. We
have chosen to include reactions involving H, H2, CH3, CH4, C2H2, C2H3, C2H4, C2H5,
C2H6, C3H6, i-C3H7, n-C3H7 and C3H8.
19
The resulting silicon-containing part of the reaction scheme is illustrated in Fig. 1, where the
values on the arrows are the Gibbs reaction energies at the process temperature (T = 1900 K).
Some reactions are simplified so that reaction sequences where e.g. two or more H2 molecules
split off is represented by a single reaction step.
20
Fig. 1 Proposed reaction scheme for the silicon-containing part in the Si-C-H-Cl system. The
values indicated on the arrows are the Gibbs reaction energies at T = 1900 K.
21
4.3 Validation of the gas phase reaction mechanism
The chemical kinetic reaction scheme is validated by performing kinetics simulations, using a
one-dimensional transient model to compute the gas phase composition with respect to time at
constant temperature and constant pressure. Fig. 2 compares two different sets of precursors
for the Si-C-H-Cl chemistry (for the standard Si-C-H chemistry, see Supplement, Fig. S3).
After ”infinite” time, the model predicts species concentrations close to the equilibrium state,
as obtained by independent Gibbs free energy minimization calculations, for all species
involved, regardless of precursors. This is very important and shows that, even though the set
of species included in the equilibrium calculations was much larger (Supplement, Table S1),
the proposed reaction scheme reproduces the gas phase composition at equilibrium, and thus
there are no dead-ends or infinite loops in the scheme.
a)
22
Fig. 2 Species molefraction vs time for a) C2H4 + SiH4 + HCl as precursors and b) C3H8 +
SiCl4 as precursors. T = 1600°C, total pressure, p = 100 mbar, and partial pressure ratios
Si/H2 = 0.25%, C/Si = 1.0, Cl/Si = 4.
Within the timeframe for CVD, i.e. in less than 0.5 seconds, all relevant species reach
concentrations of the same order of magnitude as in equilibrium. Hence, for a more extensive
analysis of the species concentration trends, equilibrium calculations are used to scan a much
larger parameter space of different process conditions, allowing faster calculations and a
broader range of process conditions to be analysed. It should be noted that in this way it is
only possible to study concentration and relation trends and not the real species
concentrations.
4.4 Evaluate species concentration trends to determine growth species
For the chemical systems Si-C-H and Si-C-H-Cl, changes in species concentrations with the
commonly used experimental parameters temperature, input C/Si ratio, input Cl/Si ratio and
b)
23
input Si/H2 ratio39, are simulated (Fig. 3, and Supplement Fig. S4, Fig. S5 and Fig. S7,
respectively). Impingement rates (Methods) are calculated to evaluate the abundance of
different species at the growth surface, to explain experimentally observed trends (Table 2)
and to find the main growth species.
Fig. 3 Impingement rates of the most abundant species at equilibrium in the temperature
interval 1000 – 1700°C. a) hydrocarbons, b) silicon and silicon hydrides, c) Si-C molecules,
and d) silicon-chlorides. For the CVD systems Si-C-H – dash-dotted lines and Si-C-Cl-H –
solid lines.
c) d)
a) b)
24
Table 3 Experimental observations and simulated species trends for common experimental
parameters.
Parameter Experimental observation Simulated species trends
T Growth rate increases with higher temperature40, 41.
Nitrogen doping is constant for temperatures between
1500-1600 °C 42, indicating that the concentrations of
active carbon species are constant, or slightly decreasing
to compensate for the higher growth rate.
Si-C and Si-H species increase with
temperature.
SiCl2 decrease with temperature.
C2H2 and CH3 constant between
1400-1700°C, while CH4 and C2H4
decrease.
C/Si High C/Si leads to higher surface roughness43.
Step bunching occurs both at low and high C/Si –
suggested to be caused by either Si or C clusters on the
surface44.
Si3-Si6, and SinCm decreases with
higher C/Si.
C4H2 increases to significant levels
at high C/Si.
Cl/Si Cl/Si > 2 is needed to keep good surface morphology
(low surface roughness) – suggested reason is increased
SiCl2 and thereby decreased effective C/Si45. However,
the growth rate decreases with higher Cl/Si – not
matched by potentially increased etching by HCl46 –
indicating less active Si species.
Nitrogen doping increases for Cl/Si = 2-4 47, also
indicating lower C/Si, but then decreases for Cl/Si = 3-7 46.
All Si-Cl species increase with
increasing Cl/Si. SiCl2 increases
more than others do, while Si-C and
Si-H species decrease.
Both C2H2/SiCl2 and C2H2/SiCl
ratios decrease over the whole
range Cl/Si = 0 – 8.
C2H2/(Si+SiCl) decreases at low
Cl/Si, and increases slowly at high
Cl/Si, with a minimum at Cl/Si = 5,
which is in fair agreement with the
experiments.
Si/H2 The growth rate saturates at high Si/H2 48.
High Si/H2 requires lower C/Si to maintain material
quality49, and consequently it is suggested that a rough
surface is caused by an increased effective C/Si at
higher Si/H2.
Nitrogen doping decreases more than explained by
higher growth rates42, i.e. more carbon is competing
with the nitrogen when Si/H2 ratio is increased, also
indicating that the “effective” C/Si increases with
increasing Si/H2.
Concentrations of Si and SiH1-3
saturates at Si/H2 > 0.1%.
The ratios C2H2/Si and C2H2/SiHn
(n = 0-3) increases with increasing
input Si/H2.
C2H2/SiCl2 decreases in the whole
range studied.
SiCl2 has been assumed to be the main active silicon species in SiC CVD with Cl
addition50, 51, due to its high concentration at relevant process conditions. Experimentally, the
growth rate increases with temperature (i.e. more active Si species are produced)40, 41, and
decreases with increasing Cl/Si41, 46, while the concentration of SiCl2 show opposite trends
25
(Fig. 3, and Supplement, Fig. S5). Recent findings even suggest a plausible inhibiting effect
of halogen atoms52. In addition, the effective C/Si ratio is shown to increase with higher
Si/H249, whereas the simulations show an opposite trend for e.g. the ratio C2H2/SiCl2
(Supplement Fig. S6). In epitaxial growth of silicon, SiCl2 was also once suggested as the
main growth species, but due to its high desorption rate other species are more likely to be the
active ones53, while SiCl2 remains in the gas phase54, 55. Based on these results, in
contradiction to most previous assumptions, we conclude that SiCl2 does not play a positive
role in the SiC growth process, but rather acts to keep silicon in the gas phase.
Nitrogen is a dopant in SiC that competes with carbon for the same lattice sites56. Thus,
changes in doping can be used as an indicator of the active carbon concentration trends, or the
effective C/Si ratio. In addition, the surface morphology can be used as an indicator of the
C/Si ratio, as high carbon concentrations result in a rough surface43.
Experiments show no or small changes in nitrogen doping and growth rate between 1500°C –
1600°C42. Therefore, the total concentrations of active carbon species should remain constant,
or just slightly decrease, in that same range. CH3 and C2H2, as well as Si3C and SiCH2,
matches this criterion (Fig. 3). A combination of species with increasing/decreasing
concentrations, such as CH4 + Si2C, could possibly also result in a constant total carbon
supply to the growth surface, nonetheless less reactive30.
For high silicon concentrations (high Si/H2) the growth rate saturates, while the surface
morphology becomes rougher48. For chlorinated chemistries, this growth rate saturation
occurs at higher Si/H2, making it possible to obtain higher growth rates. This behaviour is
well explained by the simulation results, showing a concentration saturation above
Si/H2 = 0.1 % for Si and SiH1-3 (Supplement, Fig. S7). SiCl increase throughout the interval
studied, and the concentrations level out beyond Si/H2 > 1.0 %. The conclusion is therefore
26
that Si and SiH1-3 are most likely active Si species, with additional contributions from SiCl
(and possibly SiHCl) for the chlorinated chemistry. The active carbon species continue to
increase linearly with higher Si/H2 (when maintaining the input C/Si ratio), and thus, the
effective C/Si ratio increases, eventually causing surface roughening, in accordance with
experiments.
Homogeneous gas phase nucleation is assumed to cause silicon droplets deteriorating the
surface at high Si/H245. In the simulations, the larger Si species (Si6 and Si5C) increase with
higher Si concentrations. These molecules can be said to represent larger clusters of silicon,
since we have limited our model to molecules up to this size. Adding chlorine, less Si6 is
formed in favour of chlorinated silicon species, thus reducing the risk of gas phase nucleation.
So-called step-bunching has been suggested to be caused by immobile clusters of either
carbon or silicon that sits on surface terraces44. The highest levels of the larger Si species (Si3
– Si6) occur at low input C/Si, while one of the larger hydrocarbons included in the study
(C4H2) increases to significant levels at high input C/Si (see Supplementary material, Fig. S4).
Thus, we expect step-bunched growth to be caused by Si clusters at low C/Si ratios, and by C
clusters at high C/Si ratios.
4.5 Construct a surface reaction mechanism and calculate/determine reaction rates
Based on the conclusions above, the main active growth species are CH3, C2H2, Si, SiH and
SiCl, possibly with some contributions from CH4 and Si2C. Reaction mechanisms for
adsorption of these species on the SiC surface were determined using quantum chemical
methods based on density functional theory (DFT), and the results have been published
elsewhere30, 31, 57. A full surface reaction scheme is given in the Supplement, Table S5.
27
For the sake of simplicity here, only adsorption on terraces is accounted for, i.e. adsorption at
step edges is not included. It has been observed that the growth rate of SiC depends on the
miscut angle of the substrate58. Therefore, further refinements of the surface reaction model to
include the effect of step edges, e.g. using the approach used by Yanguas-Gil and Shenai59
may improve the accuracy. Also, the model set up here only allow stoichiometric SiC to form.
This means that the Si-rich and C-rich deposition zones that are known to exist will not be
accounted for.
4.6 Set up and run a simulation of the CVD process using Computational Fluid Dynamics
(CFD)
For a CVD process, the reactor itself may be designed and optimised with the aid of CFD
simulations, provided that the desired output parameters can be achieved (e.g. growth rates
and distributions). Generally, CFD solves the equations for mass and heat transport by
numerical methods. These equations may also include the change in species concentrations by
chemical reactions (Methods). A small experimental reactor9, for which measured data exists
outside the usual sweet spots at the wafer area, was used here as our test model.
4.7 Validate the CFD model against experiments
The simulated deposition rates can now be compared to the growth rates measured along the
gas flow direction in the entire susceptor9, Fig. 4. For the main part of the susceptor, the
model is accurately mirroring the experimental results, i.e. growth rates of a few micrometres
per hour and a decreasing trend for the growth rate along the gas flow direction. We note that
in the experiment the material deposited upstream (< 20 mm) is not considered to be
stoichiometric SiC, but rather either Si-rich or C-rich9. The present model was simplified and
does not consider Si-rich and C-rich deposits, and the effect of a miscut angle of the substrate
28
is not included, as pointed out in section 4.5 above. Nevertheless, the obtained growth rates
and deposition profile along the gas flow direction are in good agreement with experiments.
It is here worth pointing out that no adjusted parameters have been used – the entire model is
systematically built step by step using existing theoretical framework for chemistry and fluid
dynamics. The deviation from experiments is reasonable considering the complexity of the
process and the uncertainties in both reaction rates (as stated in section 3.2), and the full scale
CFD model.
Fig. 4 Growth rate vs. distance along the gas flow direction in a SiC CVD reactor, comparing
experiments (black dots) [9] and CFD simulation results (red line).
0,0
1,0
2,0
3,0
4,0
5,0
6,0
7,0
0 10 20 30 40 50 60 70 80 90 100
Gro
wth
rat
e (µ
m/h
)
Distance along gas flow direction (mm)
29
5. Conclusions
The more complex process to model, the more meticulous one must be setting up the model.
However, surprisingly few studies in the literature use a systematic approach when modelling
CVD. We have therefore devised a systematic method for in-silico CVD making it possible to
perform in-depth studies of any CVD process. Even though the individual steps of the
presented method may be well-known, their combined use in the context of CVD modelling
has not previously been discussed. The presented method enables creation of models free
from tuning parameters that have the potential of being truly predictive tools for next
generation materials and processes.
Specifically, applied to CVD of SiC, we have determined the main active growth species for
SiC, and species acting as inhibitors to growth. In contrast to previous assumptions, we have
shown that SiCl2 does not contribute to SiC deposition. Further, we have confirmed the
presence of larger molecules at both low and high C/Si ratios, which have been thought to
cause so-called step-bunching. We have also shown that at high enough concentrations of Si,
other Si molecules than the ones contributing to growth are formed, which also explains why
the C/Si ratio needs to be lower at these conditions to maintain high material quality. On the
reactor scale we have shown that the thickness distribution can be accurately predicted in
comparison to measured data.
The modelling method has already been used to predict the process behaviour for previously
untested combinations of precursor gases52.
Due to its bottom-up approach and independence of chemical system and reactor
configuration, the method paves the way for a general predictive CVD modelling tool for
future materials and processes.
30
Acknowledgement
This work was supported by the Swedish Foundation for Strategic Research project "SiC - the
Material for Energy-Saving Power Electronics" (EM11-0034) and the Knut & Alice
Wallenberg Foundation (KAW) project "Isotopic Control for Ultimate Material Properties".
L.O. acknowledges financial support from the Swedish Government Strategic Research Area
in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO
Mat LiU No 2009 00971) and from the Swedish Research Council (VR). Supercomputing
resources were provided by the Swedish National Infrastructure for Computing (SNIC) and
the Swedish National Supercomputer Centre (NSC).
Author contributions
Ö.D. carried out all kinetic and equilibrium calculations and all CFD simulations, and wrote
the manuscript. P.S. and L.O. derived reaction mechanisms, modelled energetics and
computed reaction rates based on QC computations and contributed to the evaluations. All
authors contributed to interpretation of the results and commented on the manuscript.
Supporting information
Supplementary material is provided free of charge on the ACS Publications website. The
supplement includes reaction rate constants for both the gas phase and surface reactions, and
additional results on impingements rates calculated from equilibrium concentrations.
31
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download fileview on ChemRxivA_method_for_in-silico_Chemical_Vapour_Deposition_rev... (1.17 MiB)
1
A Systematic Method for Predictive
in-silico Chemical Vapour Deposition
Örjan Danielsson1, 3, Matts Karlsson2, Pitsiri Sukkaew1, Henrik Pedersen1, and Lars Ojamäe1
1 Department of Physics, Chemistry and Biology, Linköping University, Sweden
2 Department of Management and Engineering, Linköping University, Sweden
3 Physicomp AB, Liljanstorpsvägen 20, Västerås, Sweden
Supplementary material
CFD SIMULATION OF FLUID FLOW AND TEMPERATURE DISTRIBUTION
Computational Fluid Dynamics (CFD) can be used to obtain detailed information of fluid flow and heat
distributions in the actual CVD equipment. An example is shown here, where CFD was used to study the flow and
temperature distributions in a horizontal hot-wall CVD reactor commonly used for SiC epitaxial growth. The
model included all relevant parts of the reactor, without any major simplifications with respect to geometry or
boundary conditions, (e.g. temperature dependent material properties were used for all solid parts, inductive
heating was taken into account, rotation of the satellite disc that holds the SiC wafer was modelled, etc.)
Fig. S1 A part of the complete CFD model. The temperature distribution is shown on the graphite susceptor and
in the gas flow. Each line in the gas corresponds to 100°C, while each line on the graphite susceptor corresponds
to 20°C.
The results reveal a temperature homogeneity over the rotated satellite disc of 3 K, and a temperature gradient in
the gas flow close to the satellite surface between 15 and 56 K/mm, with the highest gradient at the upstream
position (Fig. S1).
2
The maximum gas flow velocity is about 30 m/s in the centre of the gas flow (Fig. S2), with the gas accelerating
along the flow direction due to the heating. The velocity gradient over the satellite disc is about 3 (m/s)/mm in the
vertical direction, and the residence time for the gas inside the susceptor, closest to the surface (up to 1 mm above),
is of the order of 0.1 s.
Fig. S2 Velocity contour plot on a vertical plane through a horizontal hot-wall CVD reactor. Flow direction is
from left to right.
3
SPECIES
Table S1 Species included in the thermodynamic equilibrium calculations.
Silicon hydrides
Hydrocarbons Six, Cx and Si-C “clusters”
Si-C-H Si-H-Cl
C-H-Cl
H-Cl
SiH
SiH2
SiH3
SiH4
Si2H2
Si2H3
H2SiSiH2
H3SiSiH
Si2H5
Si2H6
Si3H2
Si3H4
Si3H6
Si3H8
Si4H2
Si4H4
Si4H6
Si4H8
Si4H10
Si5H6
Si5H8
Si5H10
Si5H12
CH
CH2 (triplet)
CH2 (singlet)
CH3
CH4
C2H
C2H2
C2H3
C2H4
C2H5
C2H6
C3H2
H3CCC
CH3CC
H2CCCH
C3H4-a
C3H4-p
C3H4-c
C3H5-a
C3H5-p
C3H5-s
C3H6
i-C3H7
n-C3H7
C3H8
C4H
C4H2
CH3CHCCH
C4H6
C4H7
i-C4H8
p-C4H9
C4H10
C5H
C5H2
C5H3
H2CCCHCCH
C5H6-c
n-C5H12
Si
Si2
Si3
Si4
Si5
Si6
C
C2
C3
C4
C5
C6
SiC (triplet)
SiC (singlet)
SiC2
SiC3
SiC4
SiC5
Si2C
Si2C2
Si2C3
Si2C4
Si3C
Si3C2
Si3C3
Si4C
Si4C2
Si5C
Si(CH3)4
HSi(CH3)3
H2Si(CH3)2
H3SiCH3
Si(CH3)3
HSi(CH3)2
H2SiCH3
Si(CH3)2
HSiCH3
SiCH3
H2SiC
HSiC
H3SiCCH
H2SiCCH
HSiCCH
SiCCH
H2CCHSiH3
H2CCHSiH2
H2CCHSiH
H2CCHSi
H3SiCH2
H2Si(CH3)CH2
HSi(CH3)2CH2
Si(CH3)3CH2
H2SiCH2
HCH3SiCH2
CH2Si(CH3)2
HSiCH2
SiCH2
H3SiCH
H2SiCH
SiCH
H3SiC
CH3SiH2SiH
SiH3SiH2CH3
CH3SiH2SiH2CH3
SiCl
SiCl2
SiCl3
SiCl4
SiHCl
SiHCl2
SiHCl3
SiH2Cl
SiH2Cl2
SiH3Cl
ClSiSi
ClSiSiCl
Cl2SiSi
Cl2SiSiCl
Cl3SiSi
Cl2SiSiCl2
Cl3SiSiCl
Si2Cl5
Si2Cl6
HSiSiCl
HClSiSi
HCl2SiSiCl2H
H2ClSiSiCl3
Si2Cl5H
Cl3SiCH3
Cl2Si(CH3)2
ClSi(CH3)3
H2ClSiCH3
HCl2SiCH3
HClSi(CH3)2
Cl2SiCH3
ClSi(CH3)2
HClSiCH3
ClSiCH3
Cl2SiCH2
HClSiCH2
Cl(CH3)SiCH2
HClSi(CH3)CH2
Cl2Si(CH3)CH2
ClSi(CH3)2CH2
HCCSiCl2H
CCl
CCl2
CCl3
CCl4
CHCl
CHCl2
CHCl3
CH2Cl
CH2Cl2
CH3Cl
C2Cl
ClCCCl
Cl2C2Cl
C2Cl3
C2Cl4
C2Cl5
C2Cl6
HCCCl
H
H2
Cl
Cl2
HCl
23 39 28 36 41 18 5
4
GAS-PHASE REACTION SCHEMES
Table S2 Reaction scheme for the relevant hydrocarbon species. The forward reaction rate constant is given
by the Arrhenius expression 𝒌𝒇 = 𝑨𝑻𝒏𝒆−𝑬𝒂/𝑹𝑻. Backward rates are calculated from the equilibrium
constant.
Forward reaction rate
(cm3, mol, s)
Ref
Reaction A n Ea/R (K)
1 H + H + H2 ↔ H2 + H2 9.791·1016 -0.60 0 1
2 CH3 + H2 ↔ CH4 + H 1.084·103 2.88 4060 2
3 CH3 + CH3 ↔ C2H5 + H 5.420·1013 0 8080 2
4 CH3 + CH3 + M ↔ C2H6 + M Pressure dependent 2
k0 1.269·1041 -7.00 1390
k∞ 3.613·1013 0 0
Troe parameters a = 0.62, T* = 1180, T*** = 73
5 CH3 + H + M ↔ CH4 + M Pressure dependent 1
k0 6.467·1023 -1.80 0
k∞ 2.108·1014 0 0
Troe parameters a = 0.37, T* = 61, T*** = 3315
6 CH4 + CH3 ↔ C2H5 + H2 1.024·1013 0 11500 3
7 C2H2 + H + M ↔ C2H3 + M Pressure dependent 2
k0 5.802·1027 -3.47 475
k∞ 5.540·108 1.64 1055
Troe parameters a = -0.98, T* = 6000, T*** = 10, T** = 0
8 C2H3 + H ↔ C2H2 + H2 1.204·1013 0.00 0 4
9 C2H4 + H ↔ C2H3 + H2 2.349·102 3.62 5670 2
10 C2H3 + CH3 ↔ C2H2 + CH4 3.914·1011 0 0 5
11 C2H3 + CH3 ↔ C3H6 1.000·1010 1.00 0 6
12 C2H4 + CH3 ↔ C2H3 + CH4 6.022·107 1.56 8370 2
13 C2H3 + C2H3 ↔ C2H4 + C2H2 8.431·1013 0 0 2
14 C2H4 + M ↔ C2H2 + H2 + M 7.950·1012 0.44 44741 5
15 C2H4 + M ↔ C2H3 + H + M 2.589·1017 0 48600 2
16 C2H4 + H + M ↔ C2H5 + M 8.414·108 1.49 499 5
17 C2H5 + H ↔ C2H4 + H2 4.215·1013 0 0 2
18 C2H4 + CH3 ↔ i-C3H7 4.600·104 1.00 2160 6
19 C2H4 + CH3 ↔ n-C3H7 2.200·108 1.00 2916 6
20 C2H4 + C2H4 ↔ C2H5 + C2H3 4.818·1014 0 35961 5
21 C2H5 + H ↔ C2H6 5.446·1013 0.16 0 7
22 C2H6 + H ↔ C2H5 + H2 1.445·109 1.50 3730 4
23 C2H5 + CH3 ↔ C2H4 + CH4 9.033·1011 0 0 2
24 C2H6 + CH3 ↔ C2H5 + CH4 1.506·10-7 6.00 3043 4
25 C2H5 + C2H3 ↔ C2H6 + C2H2 4.818·1011 0 0 5
26 C2H5 + C2H4 ↔ C2H6 + C2H3 4.878·10-7 5.82 6000 2
27 C2H5 + C2H5 ↔ C2H6 + C2H4 1.385·1012 0 0 2
5
28 C3H6 + H ↔ i-C3H7 1.319·1013 0 785 8
29 C3H6 + H ↔ n-C3H7 1.319·1013 0 1636 8
30 C3H6 + C2H4 ↔ i-C3H7 + C2H3 7.226·1015 -0.65 37051 8
31 C3H6 + C2H4 ↔ n-C3H7 + C2H3 6.022·1013 0 37966 8
32 i-C3H7 + H ↔ C3H6 + H2 3.613·1012 0 0 9
33 n-C3H7 + H ↔ C3H6 + H2 1.813·1012 0 0 9
34 i-C3H7 + CH3 ↔ C3H6 + CH4 9.408·1010 0.68 0 9
35 n-C3H7 + CH3 ↔ C3H6 + CH4 1.145·1013 -0.32 0 9
36 i-C3H7 + C2H3 ↔ C3H8 + C2H2 1.520·1014 -0.70 0 9
37 n-C3H7 + C2H3 ↔ C3H8 + C2H2 1.210·1012 0 0 9
38 i-C3H7 + C2H4 ↔ C3H6 + C2H5 2.650·1010 0 3320 9
39 n-C3H7 + C2H4 ↔ C3H6 + C2H5 2.650·109 0 3320 9
40 i-C3H7 + C2H5 ↔ C3H6 + C2H6 2.300·1013 -0.35 0 9
41 n-C3H7 + C2H5 ↔ C3H6 + C2H6 1.451·1012 0 0 9
42 i-C3H7 + C2H5 ↔ C3H8 + C2H4 1.844·1013 -0.35 0 9
43 n-C3H7 + C2H5 ↔ C3H8 + C2H4 1.150·1012 0 0 9
44 i-C3H7 + i-C3H7 ↔ C3H8 + C3H6 2.529·1012 0 0 2
45 i-C3H7 + n-C3H7 ↔ C3H8 + C3H6 5.143·1013 -0.35 0 9
46 n-C3H7 + n-C3H7 ↔ C3H8 + C3H6 1.686·1012 0 0 9
47 C3H8 ↔ C2H5 + CH3 1.100·1017 0 42456 4
48 C3H8 ↔ i-C3H7 + H 7.200·1014 -0.03 47958 6
49 C3H8 ↔ n-C3H7 + H 7.600·1015 -0.34 50356 6
50 C3H8 + H ↔ i-C3H7 + H2 8.700·106 2.00 2518 6
51 C3H8 + H ↔ n-C3H7 + H2 5.600·107 2.00 3877 6
52 i-C3H7 + CH4 ↔ C3H8 + CH3 4.400·1015 1.00 16174 6
53 n-C3H7 + CH4 ↔ C3H8 + CH3 4.400·1015 1.00 16174 6
54 C3H8 + C2H3 ↔ i-C3H7 + C2H4 1.000·1011 0 5237 10
55 C3H8 + C2H3 ↔ n-C3H7 + C2H4 1.000·1011 0 5237 10
56 C3H8 + C2H5 ↔ i-C3H7 + C2H6 1.000·1011 0 5237 10
57 C3H8 + C2H5 ↔ n-C3H7 + C2H6 1.000·1011 0 5237 10
58 C3H8 + i-C3H7 ↔ C3H8 + n-C3H7 8.430·10-3 4.20 4390 9
6
Table S3 Reaction scheme for Si-C-H species. The forward reaction rate constant is given by the Arrhenius
expression 𝒌𝒇 = 𝑨𝑻𝒏𝒆−𝑬𝒂/𝑹𝑻. Backward rates are calculated from the equilibrium constant. Reactions
referenced as ‘coll.’ have their reaction rates calculated from Collision Theory a).
Reaction rate (cm3, mol, s) Ref.
Reaction A n Ea/R (K)
1 SiH4 ↔ SiH2 + H2 1.585·1028 -4.79 30420 11
2 Si + H2 ↔ SiH2 1.653·1013 0.5 0 coll.
3 SiH2 + H ↔ SiH + H2 2.766·1013 0.5 0 coll.
4 SiH2 + CH4 ↔ H3SiCH3 3.011·1013 0 9568 12
5 SiH2 + C2H2 ↔ SiC2 + 2 H2 1.185·1013 0.5 16899 coll. b)
6 H3SiCH3 ↔ SiCH2 + 2 H2 7.413·1014 0 13826 13, c)
7 SiH + H ↔ SiH2 2.646·1013 0.5 0 coll.
8 SiH + CH3 ↔ SiCH2 + H2 1.243·1013 0.5 0 coll.
9 Si + H ↔ SiH 2.042·1013 0.5 0 coll.
10 Si + CH4 ↔ SiCH2 + H2 9.930·1012 0.5 0 coll.
11 Si + C2H2 ↔ SiC2 + H2 9.518·1012 0.5 0 coll.
12 Si2 + C2H2 ↔ Si2C2 + H2 9.178·1012 0.5 0 coll.
13 Si2 + C2H4 ↔ Si2C + CH4 8.974·1012 0.5 0 coll.
14 Si2 + H ↔ Si + SiH 5.150·1013 0 2670 12
15 Si2C + SiH2 ↔ Si3C + H2 8.026·1012 0.5 0 coll.
16 SiCH2 + SiH2 ↔ Si2C + 2 H2 1.051·1013 0.5 0 coll.
17 SiCH2 + C2H2 ↔ SiC2 + CH4 1.216·1013 0.5 0 coll.
18 SiCH2 + Si ↔ Si2C + H2 8.476·1012 0.5 0 coll.
19 SiC2 + Si ↔ Si2C2 8.213·1012 0.5 0 coll.
20 Si2C2 + Si ↔ Si3C2 7.954·1012 0.5 0 coll.
21 Si2C2 + CH4 ↔ Si2C + C2H4 1.275·1013 0.5 0 coll.
22 Si2C3 + CH4 ↔ Si3C + C2H4 1.293·1013 0.5 0 coll.
23 Si + Si ↔ Si2 6.221·1012 0.5 5000 coll. d)
24 Si2 + Si ↔ Si3 6.094·1012 0.5 7500 coll. d)
25 Si3 + Si ↔ Si4 6.258·1012 0.5 10000 coll. d)
26 Si4 + Si ↔ Si5 6.440·1012 0.5 10000 coll. d)
27 Si5 + Si ↔ Si6 6.597·1012 0.5 10000 coll. d)
28 Si2C + Si ↔ Si3C 6.340·1012 0.5 0 coll.
29 Si3C + Si ↔ Si4C 6.845·1012 0.5 0 coll.
30 Si4C + Si ↔ Si5C 7.474·1012 0.5 0 coll.
31 Si2 + CH4 ↔ Si2C + 2 H2 9.988·1012 0.5 5744 coll. b)
32 Si3 + CH4 ↔ Si3C + 2 H2 1.035·1013 0.5 7077 coll. b)
33 Si4 + CH4 ↔ Si4C + 2 H2 1.069·1013 0.5 10487 coll. b)
34 Si5 + CH4 ↔ Si5C + 2 H2 1.098·1013 0.5 14342 coll. b)
a) According to Collision Theory, reactions may occur between two colliding molecules and the forward rate
constant is then given by 𝑘𝑓 = (8𝜋𝑅𝑇
𝑀𝑟𝑒𝑑)1/2
(𝜎1+𝜎2
2)2
𝑁𝑎 ∙ 106, where the factor 106 is used here to convert the
expression from SI units to cm3/mol s. 𝑀𝑟𝑒𝑑 =𝑀1𝑀2
𝑀1+𝑀2 is the reduced molar mass for the two molecules, and σn is
the collision diameter (Lennard-Jones parameter). The Collision Theory has several weaknesses, and is used here
7
only as an approximation motivated by the fact that the process studied is mass transport limited, i.e. the rate of
the chemical reactions are much faster than the mass transport of the species. The error in the rate constants will
therefore not be crucial to the interpretation of the main results.
b) The activation energy, Ea, is approximated by the reaction enthalpy, ∆𝑟𝐻, for reactions with positive Gibbs
reaction energies.
c) The reaction proceeds in two steps: H3SiCH3 → HSiCH3 + H2; HSiCH3 → SiCH2 + H2. It is here assumed that
the first step is the rate limiting one.
d) The activation energies for clustering of atomic Si are merely estimations.
8
Table S4 Reaction scheme for Si-Cl-H species. Reaction rates were calculated by transition state theory
using QC computations and fitted to the Arrhenius expression 𝒌𝒇 = 𝑨𝑻𝒏𝒆−𝑬𝒂/𝑹𝑻. Backward rates are
calculated from the equilibrium constant.
Reaction rate (cm3, mol, s)
Reaction A n Ea/R (K)
1 SiCl4 + H ↔ SiCl3 + HCl 3.031·1010 1.45 10120
2 SiHCl3 ↔ SiCl3 + H 4.319·1013 0.465 44189
3 SiHCl3 ↔ SiCl2 + HCl 1.205·1013 0.48 36070
4 SiHCl3 + HCl ↔ SiCl4 + H2 3.915·103 2.66 21825
5 SiHCl3 + H ↔ SiCl3 + H2 2.303·109 1.62 1574
6 SiHCl3 + H ↔ SiHCl2 + HCl 6.097·109 1.46 10662
7 SiHCl2 ↔ SiCl + HCl 2.262·1012 0.49 26366
8 SiHCl2 ↔ SiCl2 + H 7.194·1012 0.35 22055
9 SiHCl2 + H ↔ SiH2Cl2 4.687·1013 0.52 43643
10 SiHCl2 + HCl ↔ SiCl3 + H2 2.441·103 2.56 14545
11 SiH2Cl2 ↔ SiCl2 + H2 1.479·1012 0.59 37394
12 SiH2Cl2 ↔ SiHCl + HCl 3.699·1012 0.59 36867
13 SiH2Cl2 + HCl ↔ SiHCl3 + H2 4.041·103 2.57 18992
14 SiH2Cl2 + H ↔ SiH2Cl + HCl 3.059·109 1.50 10698
15 SiH2Cl2 + H ↔ SiHCl2 + H2 1.281·109 1.64 1592
16 SiH2Cl ↔ SiCl + H2 5.171·1011 0.58 24893
17 SiH3Cl ↔ SiH2Cl + H 4.541·1013 0.56 43396
18 SiH2Cl + HCl ↔ SiHCl2 + H2 2.883·103 2.49 13282
19 SiH3Cl ↔ SiHCl + H2 2.179·1012 0.54 32184
20 SiH3Cl + H ↔ SiH2Cl + H2 1.645·109 1.66 1636
21 SiH3Cl + HCl ↔ SiH2Cl2 + H2 7.735·103 2.49 16618
22 SiH2Cl ↔ SiHCl + H 6.928·1012 0.43 27592
23 SiHCl + HCl ↔ SiCl2 + H2 1.901·103 2.52 1132
24 SiHCl ↔ SiCl + H 3.599·1011 0.71 35177
25 Si + HCl ↔ SiCl + H 1.096·109 1.63 5264
26 SiH3Cl ↔ SiH2 + HCl 3.581·1012 0.66 37820
27 SiH4 + HCl ↔ SiH3Cl + H2 7.926·104 2.48 18788
28 SiCl2 + H ↔ SiCl + HCl 1.676·109 1.47 7089
29 SiHCl + H ↔ SiCl + H2 2.320·109 1.58 316
30 SiCl3 + H ↔ SiCl2 + HCl 4.538·108 1.36 412
31 SiH2Cl + H ↔ SiHCl + H2 3.156·108 1.67 2214
9
KINETIC RESULTS
One-dimensional transient simulation of the gas phase composition at constant temperature and pressure for
different precursors are shown in Fig. S3. We compare the model from the present study (Fig. S3 a) with the model
presented in ref. 12 (Fig. S3 b). The latter model, or reduced versions of it, is used in most published simulation
studies of SiC CVD up to date. It is clearly seen that the first model predicts a gas phase composition equal to the
equilibrium state after “infinite” time, while the latter model does not. The latter model does not include all relevant
species and is lacking several important reaction paths.
Fig. S3 Species molefraction vs time for C3H8 + SiH4 as precursors. T = 1600°C, p = 100 mbar, Si/H2 = 0.25%,
C/Si = 1.0. a) using the reaction model from the present study, and b) using the model from ref. 12.
a)
b)
10
IMPINGEMENT RATES FROM EQUILIBRIUM CONCENTRATIONS
Fig. S4 Impingement rates of the most abundant species when varying input C/Si ratio from 0.5 to 2.0. a)
hydrocarbons, b) silicon and silicon hydrides, c) Si-C molecules, and d) silicon-halogens. Si-C-H – dash-dotted
lines, Si-C-Cl-H – solid lines.
a) b)
c) d)
11
Fig. S5 Impingement rates of the most abundant species when varying input X/Si ratio from 0 to 8. X = Cl, Br or
F. a) hydrocarbons, b) silicon and silicon hydrides, c) Si-C molecules, and d) silicon-halogens. Si-C-H – dash-
dotted lines, Si-C-Cl-H – solid lines.
Fig. S6 Impingement C/Si ratio for different Si molecules when increasing the input Cl/Si ratio.
a) b)
c) d)
12
Fig. S7 Impingement rates of the most abundant species when varying input Si/H2 ratio from 0.001 % to 1.0 %. a)
hydrocarbons, b) silicon and silicon hydrides, c) Si-C molecules, and d) silicon-halogens. Si-C-H – dash-dotted
lines, Si-C-Cl-H – solid lines.
a) b)
c) d)
13
SURFACE REACTION SCHEME
Table S5 Surface reaction mechanism for SiC. (s) denotes a surface adsorbed species and (b) the deposited
bulk material. Open(s) represents a dangling bond at the surface. Reaction rates are taken from the work
in refs. 14 and 15, unless stated otherwise.
Surface reactions Rate constant coefficients a) ∆G°R b)
A (m3/kmol s Kn) n Ea/R (K)
1 H + Open(s) → H(s) c) 1.784·109 0.500 0 -92
2 H + H(s) → H2 + Open(s) c) 2.213·106 1.564 1294 -94
3 H2 + Open(s) → H + H(s) c) 1.918·102 2.495 8059 94
4 CH3 + Open(s) → CH3(s) c) 4.620·108 0.500 0 -5
5 CH4 + Open(s) → H + CH3(s) c) 3.556·10-4 3.699 21829 133
6 C2H2 + Open(s) → CH=CH(s) c) 5.126·100 2.565 911 208
7 C2H4 + Open(s) → CH2-CH2(s) c) 2.872·10-2 3.064 -8 246
8 CH3 + H(s) → H + CH3(s) c) 6.746·10-2 2.724 13507 87
9 H + CH2(s) → CH3(s) c) 1.784·109 0.500 0 -105
10 H + CH3(s) → H2 + CH2(s) c) 2.498·104 1.759 5594 -81
11 H + CH2-CH2(s) → CH3-CH2(s) c) 1.784·109 0.500 0 -98
12 H + CH(s)=CH(s) → CH(s)-CH2(s) c) 4.015·105 1.468 151 59
13 H + CH(s)-CH2(s) → CH2(s) + CH2(s) c) 1.784·109 0.500 0 -96
14 Si + CH2(s) → H2 + Open(s) + SiC(b) d) 3.381·108 0.500 0 -351
15 Si + CH3(s) → H2 + H(s) + SiC(b) d,e) 3.719·108 0.180 -671 -356
16 SiH + CH2(s) → H2 + H(s) + SiC(b) d) 3.321·108 0.500 0 -365
17 SiH + CH3(s) → H2 + H + H(s) + SiC(b) d) 7.473·10-2 3.024 9203 -244
Surface reactions
Rate constant coefficients a) ∆G°R b)
A (m2/kmol s Kn) n Ea/R (K)
18 H(s) + CH2(s) → CH3(s) + Open(s) 2.551·1019 0.129 11269 -13
19 H(s) + CH=CH(s) → CH2=CH(s) + Open(s) 2.551·1019 0.229 3943 -66
20 CH2=CH(s) + Open(s) → CH(s)-CH2(s) 1.359·1019 0.091 7396 9
21 H(s) + CH2-CH2(s) → CH3-CH2(s) + Open(s) 5.664·1019 0.133 5587 -31
22 CH3-CH2(s) + Open(s) → CH2(s) + CH3(s) 1.059·1019 0.685 32109 -33
14
23 CH2(s)-CH2(s) → CH2(s) + CH2(s) c,f) 2.110·109 2.211 58673 381
24 CH=CH(s) +Open(s) → CH(s)=CH(s) 1.026·1018 1 0 -305
25 CH2-CH2(s) +Open(s) → CH2(s)-CH2(s) 1.026·1018 1 0 -197
26 H(s) + H(s) → H2 + 2 Open(s) g) 7.230·1021 0 30767 -2
a) The rate constants are expressed in the form 𝐴𝑇𝑛𝑒𝑥𝑝(−𝐸𝑎 𝑅𝑇⁄ ).
b) Gibbs free energy at 1600 °C and 100 mbar pressure.
c) The reaction rate and Gibbs free energy are calculated using the same method and SiC cluster size as used in ref.
14 (i.e. DFT calculations and 2 SiC bilayer cluster consisting of 19 SiC formula units), with the pressure adjusted
to 100 mbar. For the case where no tight transition state is present along the reaction coordinate, the reaction
probability (sticking coefficient) is assumed to be equal to 1.0.
d) This reaction is simplified from the reaction scheme discussed in Table S6. The Gibbs free energy is derived
from the total change of the Gibbs free energies along the reaction pathway in Table S6.
e) The sticking coefficient is derived following the method used in ref. 14. A small cluster Si(CH3)4 was used to
locate the transition state structure. The geometry optimizations and vibrational calculation are carried out using
the hybrid density functional theory (DFT) B3LYP16, 17 and the cc-pVTZ basis set from Dunning18. The dispersion
correction D3 from Grimme at al.19 is applied to all cases. The B3LYP electronic energies are corrected by the
single-point energy derived from the M06-2X functional20 and the cc-pVTZ basis set from Dunning.
f) This reaction is 1st order, so the units of A are (1/s Kn). The barrier height of the forward rate is approximated
from the Gibbs free energy. The forward rate constant is calculated using 𝑘𝑓 =𝑘𝐵𝑇
ℎ𝑒𝑥𝑝(−∆𝐺𝑟 𝑅𝑇)⁄ .
g) from Allendorf and Kee10.
Table S6 3-step, reaction scheme of R14-R17 in Table S5
3-step, reaction scheme of reaction R14
Rate constant coefficients a)
∆G°R A (m3/kmol s Kn) n Ea/R (K)
R14a Si + CH2(s) ↔ SiCH2(s) 3.381·108 0.50 0 -10
A (m2/kmol s Kn) n Ea/R (K) ∆G°R
R14b SiCH2(s) + CH3(s) ↔ SiH(CH2)2(s) b) 3.871·1018 0.33 11200 -110
R14c SiH(CH2)2(s) + CH3(s) ↔ Si(CH2)3(s) + H2 c) 1.443·1018 0.80 34939 -231
3-step, reaction scheme of reaction R15
Rate constant coefficients a)
∆G°R A (m3/kmol s Kn) n Ea/R (K)
R15a Si + CH3(s) ↔ SiHCH2(s) 3.719·108 0.18 -671 62
A (m2/kmol s Kn) n Ea/R (K) ∆G°R
15
R15b SiHCH2(s) + CH3(s) ↔ SiH2(CH2)2(s) 3.871·1018 0.33 11200 -158
R15c SiH2(CH2)2(s) + CH3(s) ↔ SiH(CH2)3(s) + H2 1.443·1018 0.80 34939 -260
3-step, reaction scheme of reaction R16
Rate constant coefficients a)
∆G°R A (m3/kmol s Kn) n Ea/R (K)
R16a SiH + CH2(s) ↔ SiHCH2(s) 3.321·108 0.50 0 53
A (m2/kmol s Kn) n Ea/R (K) ∆G°R
R16b SiHCH2(s) + CH3(s) ↔ SiH2(CH2)2(s) 3.871·1018 0.33 11200 -158
R16c SiH2(CH2)2(s) + CH3(s) ↔ SiH(CH2)3(s) + H2 1.443·1018 0.80 34939 -260
3-step, reaction scheme of reaction R17
Rate constant coefficients a)
∆G°R A (m3/kmol s Kn) n Ea/R (K)
R17a SiH + CH3(s) ↔ SiH2CH2(s) 7.473·10-2 3.024 9203 132
A (m2/kmol s Kn) n Ea/R (K) ∆G°R
R17b SiH2CH2(s) + CH3(s) ↔ SiH2(CH2)2(s) + H 1.620·1017 0.63 20918 -116
R17c SiH2(CH2)2(s) + CH3(s) ↔ SiH(CH2)3(s) + H2 1.443·1018 0.80 34939 -260
a) The rate constants are expressed in the form 𝐴𝑇𝑛𝑒𝑥𝑝(−𝐸𝑎 𝑅𝑇⁄ ).
b) The forward rate is assumed to be equal to R15b.
c) The forward rate is assumed to be equal to R15c.
A COMPARISON BETWEEN THE 1-STEP AND 3-STEP REACTION SCHEMES.
Methods
The kinetic data R14-R17 in Table S5 and R14a-c to R17a-c in Table S6 are implemented in a kinetic model using
MATLAB SimBiology module21. The calculation is performed at a constant pressure of 100 mbar and constant
temperature of 1600 °C. The gas phase species partial pressures of Si and SiH are kept constant with time to
reproduce the CVD condition where the flow of the gas occurs continuously over the surface and where the
thickness of the stagnant layer (diffusion layer) above the surface is simplified to be zero. The impingement rates
of Si and SiH are assumed to be similar to the results from the CFD calculation in Fig. 3 in the article.
Kinetic results
As shown in Fig. S8, as the equilibrium condition is reached, the results from the 1-step schemes (R14-R17 in
Table S5) can reproduce that of the 3-step schemes (R14a-c to R17a-c in Table S6) within the error bar of ~1%,
0.5%, 3% and 5%, respectively. Therefore, the usage of the simplified 1-step scheme is reliable, and at the same
time can reduce the computational cost and complexity during the CFD simulation.
16
a) R14 (solid line) and R14a-R14c (dashed line)
b) R15 (solid line) and R15a-R15c (dashed line)
c) R16 (solid line) and R16a-R16c (dashed line)
d) R17 (solid line) and R17a-R17c (dashed line)
Fig. S8 Surface fractions derived using the 1-step (solid line) and 3-step (dashed line) reaction schemes. Fig a) to
d) are the results of the reaction scheme for R14 to R17, respectively.
17
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