Ab Initio MD Study of the Mechanism of Carbonization of Si(001) Surfaces with Methane at High Temperatures

Abstract

This study employs ab initio metadynamics to simulate the carbonization of Si(001) surfaces with chemical vapor deposition at a temperature of 1423 K. We reveal the complete reaction mechanism, including the beginning of silicon carbide crystal formation. The existence of surficial native oxide is incorporated into the theoretical model. The mechanism determination includes clarification of all intermediate products and transition states. The free-energy surface of the reaction chain has been found. Carbonization initiates with alkylated surface products and continues with consecutive dehydrogenation steps. Carbon is integrated in the volume, near the crystal surface, only if no covalent interactions with hydrogen atoms remain. The native oxide was not found to prohibit the process of carbonization. The oxygen atoms have certain surface mobility at high temperatures. It was revealed that hypervalency of carbon atoms is possible in transition state structures. The theoretical activation free energy of the rate-determining step was found to be only 166 kJ/mol. This work sheds light on the advantage of the practical use of Si(001) substrates for the synthesis of silicon carbide and Si-O-C glasses using direct carbonization via chemical vapor deposition. We also aim to enable more methodical designs of future synthetic routes and better-informed decisions for experimental investigations.

1. Introduction

Silicon carbide (SiC) has many interesting properties for use in practice, such as oxidation resistance, very high hardness, high creep resistance, and excellent resistance to chemical attack and thermal shock [1,2,3,4]. Its outstanding IR-transmittance with a cutoff beyond 5.5 μm makes it a natural choice for applications in optics and laser technology [5,6,7]. Moreover, SiC has been successfully utilized as a single crystalline substrate in graphene synthesis—the method for the so-called epitaxial deposition of graphene [8] was developed practically in parallel with micromechanical exfoliation [9].

SiC crystals are most often synthesized using three methods: physical vapor deposition (PVD), chemical vapor deposition (CVD), or high-temperature solution melts [10]. Various substrates are normally used for deposition using CVD methods, e.g., single-crystal Si or SiC wafers and polycrystalline Si or SiC. There are several fundamental problems in depositing a thin layer on silicon with CVD; the main ones are related to lattice mismatch, the precursor used, the oxygen present in the reaction space, and the native oxide. The lattice parameters of the two crystal forms, Si and SiC, have a notable mismatch. On the other hand, the thermal expansion coefficients of the two materials are different, reaching a 20% difference at temperatures around 1450 K. As a result, the concentration of the formed structural defects in the deposited films is far from optimal. A working solution to these problems is proposed by Nishino et al. [11] with the so-called “multi-step method” including (i) direct carbonization of the Si substrate, with the CVD process of thermally stimulated decomposition of propane in a hydrogen gas flow, and (ii) secondary deposition of SiC through the reaction of SiH₄ and C₃H₈, both steps occurring at around 1673 K. About a decade ago, Severino et al. introduced additional steps in the multi-step method (etching at high temperature in a reductive gas flow and deposition of a thin protective carbon film at temperatures lower than the carbonization temperature) for reproducible deposition of SiC thin films on up to 6 inches of Si substrates with different orientations [12,13].

The interactions between SiH₂ and SiCl₂ with H-terminated SiC clusters have been investigated with hybrid Generalized Gradient Approximation (h-GGA) of the Density Functional Theory (DFT) [14]. For example, the first step in synthesizing the popular silicon carbide polytype 4H-SiC is modeled with static calculations for the following reactants: ·CH₃, CH₄, C₂H₂, and C₂H₄ [15]. These static calculations can only examine assumed chemical changes, do not account for temperature, and have a qualitatively poor way of predicting entropy. Kinetic Monte Carlo simulations of SiC growth [16] have also been carried out. However, the performed simulations are of limited practical importance as the C and Si source reagents are represented unrealistically as isolated atoms. Moreover, the substrate is geometrically fixed, which introduces additional inaccuracy.

Recently, single-atomic-layer SiC has been experimentally prepared and characterized [17]. Huang et al. [18] have employed molecular dynamics to reveal the mechanism of thermo-mechanical coupling, governing thermal conductivity in two-dimensional SiC, thus improving the understanding of processes governing these characteristics.

In our previous research, we combined a theory and an experiment to elucidate the mechanisms of CVD carbon deposition on ordered carbon surfaces [19]. We established that phases with sp³ hybridization are energetically favored if the precursor is methane, while sp² structures are preferred in the presence of dicarbon. A major factor in the study was accounting for the presence of native oxide on an untreated Si substrate surface. It was determined that, generally, an intermediate thin layer of SiC or a C-enriched film of SiO₂ usually appears on the Si surface.

In a recent study, we successfully simulated the total synthesis of SiC with methane and a Si(111) wafer at a temperature of 1423 K [20]. Investigation of the mechanism included all intermediate products and transition states. We discovered that the presence of native oxide does not prohibit the process and that the carbon atoms are incorporated in the Si wafer only after the total loss of hydrogen atoms. At high temperatures, reconstruction of the crystal surface was found to take place and no substitution reaction was necessary for the carbon incorporation in the silicon structure. Two mechanisms of native oxide reduction were also revealed. To our knowledge, similar studies for Si(001) surfaces have not been reported.

Here, we present a theoretical model of the CVD of crystalline SiC on Si(001) surfaces, aiming to establish chemical mechanisms in this step-wise synthesis. Our study includes all covalent interactions between methane and a silicon slab at a temperature of 1423 K. The relatively low temperature and hydrogen-rich alkane inhibit the formation of an undesired pure carbon phase. Our model also considers the presence of native oxide, as it is well known that traces of oxygen are very often observed, regardless of the methods for the reduction/removal of native oxides from the surface of Si wafers. To our knowledge, regarding theoretical research, the only previous study that accounted for oxygen passivation of silicon is also ours [20]. All synthetic steps are simulated with quantum metadynamics. All transition states and intermediates have been found. Energetic effects and reaction barriers are predicted in terms of free energy (FE). Our work demonstrates the advantage of using Si(001) substrates for synthesizing SiC and Si-O-C glasses by direct carbonization via CVD processes. Our results contribute to the detailed understanding of the studied processes at an atomic scale. This knowledge will help make a more systematic design for future synthetic routes.

2. Methods

All calculations are performed with the CP2K/Quickstep package [21,22]. The self-consistent field iterations are carried out at a DFT level, employing the GGA Perdew–Burke–Ernzerhof (PBE) functional [23]. Atomic orbitals are modeled according to the double-zeta quality basis set DZVP-MOLOPT-SR-GTH, which is optimized for gasses and condensed phase systems [24]. The Gaussian Plane Wave method is used for electronic wavefunction expansion [25,26]. Valence electrons are computed explicitly. Goedecker–Teter–Hutter pseudopotentials, which are optimized for PBE, are used to represent the core electronic shells [27,28]. The finest grid level has a charge density cutoff of 400 Ry. In total, five multigrids are used. All systems are modeled in the unrestricted Kohn–Sham formalism. Dispersion interactions are taken into account for all calculations. The latest D3 revision of the DFT + D method is applied with enabled three-body terms [29]. A recent study has concluded that the accuracy of the combination of PBE, D3, and a large basis set is relatively high for reaction energetics, including barriers. The MAE was found to be only 6.7 kJ/mol [30], outperforming even the highly popular hybrid GGA functional B3LYP.

Born–Oppenheimer Molecular Dynamics is used in all simulations [31]. Metadynamics is usually applied to study chemical changes and their mechanism [32,33]. It is a state-of-the-art simulation method that guides processes to simulate a selected chemical reaction. Collective variables (colvars, CV) are set according to critical degrees of freedom to bias the system towards the desired changes. To increase FE and reach unexamined geometries in the CV space, penalty potentials (hills) are generated periodically for the current values in the CV space. As a TS is crossed over, a systematic examination of a new energy well begins. The FES of the reaction, i.e., the relative stability of each geometry, is obtained by reversing the bias of the potential peaks. While FE increases, unguided changes can freely occur in the system, providing a realistic insight into the studied processes.

All systems are modeled in the NVT ensemble. The thermostat uses canonical sampling via a velocity rescaling (CSVR). The temperature is set to 1423 K in all metadynamics simulations [34,35]. The time resolution is 1 fs. The Gaussian penalty potential height is 5.251 kJ/mol. The scale factor (Gaussian width) is 0.2 for every CV. Hills are generated every 50 fs. The walls are quadratic, having a potential constant of 83.68 kJ/mol. The temperature tolerance is set to 100 K. The shortest distances between C–Si and H–Si are above 300 pm in all initial steps. Before each metadynamics run, a system equilibration is performed in the NPT ensemble. A simultaneous cell and geometry optimization of the systems precedes each equilibration run. The resulting converged cell dimensions are utilized for equilibration. The final cell dimensions obtained from the equilibration are used in productive runs of the metadynamics simulations.

Distance CVs are given in units of pm. The coordination formula for CVs can be found on the CP2K website [36]. All variable values are in arbitrary units. A value of 1.00 denotes the product-type covalent bonding between the central/“coordinating” atom and all “ligands”; a value of 0.00 denotes “ligand” distances, which are too long for covalent interactions.

All TSs are located through metadynamics as critical structures, connecting the FE pits of reagents and products. In each saddle point, the reaction coordinate is at its energy maximum. Their geometries are representative of moments in time (usually below 5 femtoseconds), in which the old bonds are not entirely cleaved and new bonds have not completely emerged.

3. Results and Discussion

The formation of a SiC crystalline seed near the Si(001) surface of a silicon crystal is modeled with quantum metadynamics. The carbon source reagent is methane. The system is simulated as 2D supercells of a single orthorhombic cell in 3D periodic boundary conditions (PBC). To emulate 2D periodicity, the dimension perpendicular to the surface is set to a length of vanishing dispersion forces between the Si slabs. In the unit cell, the 48 Si atoms are arranged in the cubic $Fd\overline{3}m$ space group. The “bottom” side of the slab is terminated with 12 H atoms to prohibit undesired covalent interactions. The crystal’s reactive “top” side does not contain dangling bonds, because of the present native oxide. In particular, each two neighboring silicon atoms, which would have a free valence in the pristine slab surface, are now bound covalently to an oxygen atom.

The high temperature during equilibration causes significant reconstruction of the crystal surface. Most atoms still assume tetrahedral configurations with their neighbors, but others have become centers of pyramidal and semi-planar geometries. The equilibrated system contains dangling bonds, as mono-, di-, and trivalent Si atoms are present on the system’s surface.

The geometry of the system after equilibration is shown in Figure 1.

3.1. Building a SiC Crystallite Seed Through the Si(001) Surface with Native Oxide

The main purpose of this study is to model the hetero-epitaxial formation of a SiC seed on a Si(001) slab. The ultimate goal is the synthesis of a -Si-C-Si-C-Si-C-Si- nucleus, because it marks the beginning of crystal growth.

This desired crystalline motif has been achieved in three metadynamics simulations. In the first frame of the initial simulation, the methane molecule is sufficiently apart from the oxidized Si(001) slab to ensure no initial covalent interactions (Figure 1). Bias is applied with two CVs: C-Si distance with an inner Si atom and C-H coordination.

The process begins with a transition state connecting the combination of the Si slab and the gas phase methane in the reagent state to methyl silicon and hydrogenated Si in the product formation (5569 fs, Figure 2a). We can notice a five-valent carbon atom in the TS. Both short-lived and stable molecules with hypervalent carbon are experimentally known [37,38,39]. The alkylated surface product is shown in Figure 2b. The next step in the process is the formation of methylene silicon, which starts with a TS at 33645 fs (Figure 2c). The next intermediate is either the diradical -Si-C•(H)-Si•- or the significantly more stable -Si-C(H)=Si-, considering that one of the Si atoms is engaged in only two σ-bonds. A hybrid structure that is a superposition of both resonance forms can exist at the simulated temperature. The TS leading to this product occurs at 52669 fs (Figure 2e). A reaction representing a Si addition with a TS at 53286 fs (Figure 2g) stabilizes the structural motif into methine silicon (-Si-C(H)(Si)-Si-). The remaining methane hydrogen atom is abstracted by a surface Si atom via a TS structure at 66738 fs (Figure 2i). First, the product assumes a semi-planar configuration (Figure 2j). Since -Si-C•(Si)-Si- would have a pyramidal shape, this intermediate SiC moiety must be recognized as -Si-C(Si)=Si-. Finally, a Si addition reaction, with a TS at 70492 fs (Figure 2k), results in Si₄C (Figure 2l).

The silicon carbide structures in Figure 3b,d are formed in two additional metadynamics simulations. Figure 3d represents the final crystalline seed of SiC.

A free (non-interacting) oxygen atom can be noticed in Figure 2l. In Figure 3b–d, this O atom is incorporated into the SiC moiety with a direct, covalent bond. The result correlates with the Si-C-O motives, discovered in our previous experimental research on the growth of thin carbon layers on a Si substrate [19].

3.2. Free Energy Surface

The FES of the carbonization of the Si(001) surface is shown in Figure 4. Five distinct FE pits are visible due to the decrease in the H content in organic residue during the simulations. The funnels correspond to structures with the following motifs (in order of decreasing C-H coordination): CH₄ + Si_slab, -Si-CH₃, -Si-CH₂-Si-, -Si-C(H)=Si-, -Si-C(H)(Si-)-Si-, Si₃C•, and Si₄C. The CV2 values, corresponding to the first four structures, are 1.00, 0.75, 0.50, and 0.25. The CV2 value for the fifth moiety is also 0.25. The sixth and the seventh structures correspond to a value of 0.00. The intermediate values of this CV belong to steep portions of the FES, due to the abrupt cleavage of the C-H bonds. The forward FE barriers of the reaction steps in the process are given in

Table 1. Major reagents, products and activation FE of the reaction steps in the carbonization process of the Si(001) surface with methane at 1423 K.

Reagent	Product	Activation FE [kJ/mol]
Sislab + CH4	-Si-CH3 + -Si-H	45
-Si-CH3	-Si-CH2-Si- + -Si-H	166
-Si-CH2-Si-	-Si-C(H)(Si-)-Si- + -Si-H	164
-Si-C(H)(Si-)-Si-	Si4C + -Si-H	144

. The formation of methylene silicon from methyl silicon is the rate-determining reaction. It has an activation FE of 166 kJ/mol, which makes the theoretically modeled CVD process attractive from economic and environmental perspectives.

3.3. Overall Remarks and Discussion

According to our study, the most prevalent reaction (the one with the lowest activation FE) in the CVD process is the surface alkylation of the Si slab (Table 1). In our previous theoretical investigation on Si(111) surfaces [20], we found that the FE barrier of the corresponding reaction, not including native oxide and with the same CV setup, is approximately the same (51 kJ/mol). The rate-determining reaction in the modeled SiC synthesis is displayed as Equation (1). Equation (2) shows that, at a given temperature, the rate of the next reaction step in the mechanism will be almost the same.

$$Me-{Si}_s+{2Si}_s \stackrel{E_A=166 kJ/mol}{\to }{Si}_s-{CH}_2-{Si}_s+H-{Si}_s$$

(1)

$${Si}_s-{CH}_2-{Si}_s+{2Si}_s\stackrel{E_A=164 kJ/mol}{\to }{Si}_s-C(H)({Si}_s)-{Si}_s+H-{Si}_s$$

(2)

where ${Si}_s$ designates a Si atom at the crystal surface.

The activation FE of the most widely used industrial method for SiC production (the Acheson process) is 440 kJ/mol [40]. The most common reagent in the CVD preparation of SiC is methyltrichlorosilane (MTS). The FE barrier of the rate-determining step for methods involving MTS is 233–254 kJ/mol [41,42]. High activation energies are also found for processes involving unsubstituted silanes, such as SiH₄ and Si₂H₆, at 259 and 243 kJ/mol, respectively [43,44]. A theoretical study based on SiF₂, SiHF, and SiF, as silicon sources, determines FE barriers of 503, 413, and 347 kJ/mol, respectively [45]. Here, in the revealed mechanism of the CVD process, the activation FE of the rate-determining reaction of 166 kJ/mol is significantly lower than the abovementioned values. There is clear potential for the synthesis we propose to become the operative CVD process. Furthermore, the energy barrier implies that the method can be successful even at lower temperatures. The rate-determining reaction in the CVD carbonization of a Si(111) wafer (from our previous theoretical research [20]) has a similar value—173 kJ/mol. All reactions appear to have comparable activation energies.

The already mentioned thermal rearrangement of the Si atoms close to the crystal surface is accompanied by an additional structural reconstruction due to the rise in FE during the metadynamics simulations. The mobility of Si atoms is high enough to change their positions. The closer to the surface the Si atom is, the higher the chance it will alter its typically tetrahedral geometry configuration with four neighbors into a pyramidal or semi-planar arrangement. Surface Si atoms can also be mono- or bi-coordinated. The reconstruction is so evident that the crystal structure of the Si(001) surface is lost.

The Si-bound oxygen atoms do not enter the Si slab or the gas phase. Si atoms also do not enter the vacuum space of the system.

The methane carbon atom is only adsorbed within the solid phase after the complete loss of hydrogen atoms. Substitution of Si atoms is not necessary for SiC formation, because, at high temperatures, the flexibility of the structure is sufficiently high.

The first reaction step has the highest rate. The activation FE of the following three dehydrogenations is similar and approximately three times higher.

4. Conclusions

In the present research, the mechanism of CVD crystal growth of SiC on a Si(001) slab has been modeled with PBE metadynamics with methane as the carbon source. The formation of an initial SiC crystallite seed with three C atoms (-Si-C-Si-C-Si-C-Si- motif) has been successfully modeled at 1423 K. Reconstruction of the slab surface at this temperature results in the loss of local lattice symmetry characteristics for Si(001) surface orientation. Carbonization occurs in a particular sequence with intermediate products. The mechanism initializes with surface alkylation of the Si(001) wafer and progresses through the loss of hydrogen atoms. The first product is methyl silicon, followed by methylene silicon. The next intermediate is methine silicon. The carbon atom is integrated into the volume of the Si slab (to a Si₄C motif) only after the complete loss of hydrogen atoms. The initializing reaction step has the highest rate. The activation FE of the next three dehydrogenation steps is similar and approximately three times higher than the value for the first one. In conclusion, removing hydrogen atoms from the attacking C species is crucial for carbonization. The presence of native oxide does not prohibit the synthesis of SiC.

At the simulation temperature, the native oxygen atoms exhibit significant surface mobility without immersing into the bulk or evaporating in the gas phase. According to our model, oxygen atoms can be trapped in a glassy Si-C-O layer between the underlying Si atoms and the SiC layer.

The present work demonstrates that methane can be an attractive carbon source reagent for the CVD process of silicon carbonization. The SiC phase remains hydrogen-free since the carbon atoms integrate into the crystal after total hydrogen loss. As far as we are concerned, this is the first theoretical study that models the entire carbonization mechanism of widely used Si(001) wafers. The prevalence of consecutive reaction steps has been assessed based on energetics. The activation FE of the rate-determining reaction in the modeled CVD process of SiC synthesis is significantly lower (166 kJ/mol) than the corresponding highest barriers in alternative methods.