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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High Growth Rate Epitaxy. Material Science Forum 2015, 821-823, 141-144.

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2009, 311, 1321-1327.

48 Tanaka, T.; Kawabata, N.; Mitani, Y.; Sakai, M.; Tomita, N.; Tarutani, M.; Kuroiwa, T.;

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823, 133-136.

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Growth by Chlorine Addition, Material Science Forum 2009, 615-617, 55-60.

36

50 Veneroni, A.; Omarini, F.; Masi, M. Silicon Carbide Growth Mechanisms from SiH4,

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37

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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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