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Sensitivity of SiC Grain Boundaries to Oxidation Cheng Liu, Jianqi Xi, and Izabela Szlufarska J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b00068 • Publication Date (Web): 17 Apr 2019 Downloaded from http://pubs.acs.org on April 18, 2019

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The Journal of Physical Chemistry

Sensitivity of SiC Grain Boundaries to Oxidation Cheng Liu†, Jianqi Xi‡, Izabela Szlufarska*†‡ †

University of Wisconsin-Madison, Department of Engineering Physics, 1500 Engineering Dr.,

Madison, WI, 53706, U.S.A. ‡

University of Wisconsin-Madison, Department of Material Science and Engineering, 1509

University Ave., Madison, WI, 53706, U.S.A. *

Corresponding author with email: [email protected]

Abstract Molecular dynamics simulations of dry oxidation of bicrystals with incoherent and coherent grain boundaries (GBs) in 3C-SiC are performed at 2000 K and the results are compared to oxidation of single crystal SiC. Oxidation near incoherent GBs is found faster than that in single crystals and in coherent GBs, whereas oxidation of coherent GBs is comparable to that of single crystal. The accelerated oxidation near incoherent GBs is attributed to strain and the presence of under-coordinated Si within the GB region, which both reduce the positive charge on silicon atoms, making them more reactive with oxygen. Although atoms with similar properties are found in dislocation cores of coherent GBs, dislocation cores are isolated from each other by crystalline regions, which in turn control the rate of oxidation.

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1. Introduction Silicon carbide is known to have outstanding high-temperature strength, wide bandgap, high radiation resistance, good thermal conductivity, and low thermal expansion, making it an attractive material for multiple industrial applications. For example, SiC has been used in high temperature, high power and high frequency semiconductor applications, such as Schottky diodes and field-effect transistors

1–3.

SiC/SiC ceramics matrix composites have been tested as

structural components in advanced engines, gas turbines and aerospace vehicles thermal protection layers

4–7.

In addition, SiC has been considered for use in reactor cores for such

components as tristructural-isotropic coating of fuel particles, control rod sheath in high temperature gas-cooled reactors, and fusion reactor blanket structural materials 8–13.

Oxidation of SiC is relevant for many of the above applications. For instance, efforts have been reported to make SiC metal-oxide-semiconductor-field-electric-transistors using a simple thermal oxidation step

14,15,

where SiO2 is formed on SiC substrate. In both aerospace and

nuclear application, SiC is subject to high temperature and oxidizing environments, which make SiC prone to degradation by either active or passive oxidation. Oxidation of SiC results in degradation of its properties, such as fracture toughness, and creep and fatigue resistance, which in turn increases the instability of systems that are based on SiC components

16–20.

In

general, environmental degradation and recession of SiC during operation are a major hurdle in broadening the range of applications of SiC 21–25.


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There have been two general areas of research aimed at increasing control over oxidation of SiC. One set of studies focused on understanding of fundamental mechanisms of oxidation of this material

1,2,26.

Another set of studies has been focused on tailoring the microstructure of SiC,

e.g., distribution of grain boundary (GB) types, to suppress oxidation 27. For example, a number of first principle calculations 1,2,28 have been carried out to identify the energetics and reaction pathways for oxygen adsorption and carbon desorption on different SiC surfaces during the early stages of oxidation. Simulations using classical molecular dynamics (MD)

29–31

have also

been reported where formation and breaking of atomic bonds was tracked during the growth of the first few nanometers of oxide, providing a deeper understanding of the dependence of the oxidation rate on crystal orientation, surface atomic composition, and crystal structure. Experiments have been conducted both in dry and in wet environments to evaluate oxidation rate under a wide range of conditions 19,20,31,32. In general it was found that GBs and interfaces in SiC were more vulnerable to oxidation

21,32–34.

In cases where preferential corrosion of GBs

was observed, it was also found that such corrosion could result in detachment of entire grains and in acceleration of the oxidation rate. Detailed analysis

27,33,34

revealed that accelerated

oxidation only occurred along specific GB types. For example, Tan et al. 33 found after exposing SiC to 500 °C and 25 MPa supercritical water, that only incoherent GBs show accelerated oxidation. However, it is still not clear why coherent GBs and incoherent GBs have different sensitivities to oxidation, and whether the vulnerabilities of GBs to oxidation under wet conditions are also present during dry thermal oxidation.


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Here, we use MD simulations based on reactive potentials to determine the dependence of oxidation on the GB type in SiC. Specifically, we use the ReaxFF force field for SiC oxidation developed by van Duin et al. 29. We compare oxidation rates and mechanisms in single crystals with different orientations, as well as bicrystals with incoherent and coherent GBs. The underlying reasons for vulnerabilities of incoherent GBs and stability of coherent GBs are elucidated based on the mechanisms of the early stage of oxidation, GB atomic volume, and charge distribution.

2. Methods We performed MD simulations of oxidation of cubic (β) SiC, using a single crystal sample, as well as of bicrystals with incoherent and coherent GBs. Incoherent GBs were created by combining two single crystals with different crystallographic orientations along the z directions (see Figure 1). These orientations were selected from the group of (100), (110), and (111). The interface at GBs formed using a (100) single crystal can be either carbon rich or silicon rich, depending on the termination of the surface that forms a GB. Therefore, we considered two kinds of incoherent GBs. Carbon rich GBs formed by (100) and (111) crystals were labeled [111100] C rich and the corresponding Si-rich GBs were labeled [111-100] Si rich. The top surfaces (exposed to oxygen) of (111) and (100) single crystals can also be terminated by either carbon or silicon atoms. As the purpose of this simulation is to investigate GB vulnerability, to simplify our simulation, we only considered top (100) and (111) surfaces that are Si terminated. Other incoherent GBs analyzed in this study were formed by combining single crystals with (100) and


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(110) orientations, and with (110) and (111) orientations. These GBs are labeled [100-110] and [110-111], respectively. We found that [111-100] bicrystals with Si- or C-rich GB both show an accelerated oxidation near incoherent GB, and therefore to save computational time we only simulate Si-rich GB in the [100-110] bicrystal. Coherent GBs were formed following methods described in Ref.

35.

We prepared two coherent GBs by tilting single crystal with a (110)

orientation around the x direction (which corresponds to [100]) to angles of 11.3° and 4.4°. The resulting coherent GBs had coincident site lattices 13 and 85, and are referred to as Σ13 and Σ 85 GBs, respectively.

As shown in Figure 1, each GB was placed in the middle of a simulation box. In each case, the dimensions of the SiC sample are 30 Å and 50 Å, along the x and z directions, respectively. The dimension of SiC sample along the y direction was 60 Å and 120 Å for single crystal and bicrystal geometry, respectively. After constructing each sample, it was equilibrated at 300K for 2.5 ps, relaxed at 500K for ps and then quenched to 300 K for 5 ps in isothermal-isobaric (NPT) ensemble at zero pressure. We are not aware of published experiments showing detailed structures of either coherent or incoherent GBs in SiC. However, the structures of coherent GBs obtained at the end of our equilibration simulations are the same as those previously reported in MD simulations with a different SiC potential35,36. They have similar units as GBs in diamond37 and cubic-Si38, as determined from MD simulations and validated against electron microscopy images39. Using the same optimization procedures, we obtained equilibrated structure of incoherent GBs.


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After the system was equilibrated, oxygen molecules with the number density of 0.02/Å3 were randomly and uniformly inserted into a 40 Å thick space above the SiC surface, which is consistent with dry air conditions in thermal oxidation. The corresponding vapor pressures at 300 K and 2000 K are 82.9 MPa and 552.5 MPa, respectively. They are significantly higher than pressures used in dry and wet thermal oxidation experiments, which are generally around a few tens of kPa40,41 and MPa33,42, respectively. The high pressures used in our simulations are necessary to observe reactions on the time scales of MD simulations. Similar pressures were used in earlier MD simulations of SiC oxidation,29,30,43,44 where it was shown that such simulations give a reasonable description of chemical reactions. The surfaces of SiC were initially not passivated, as the passivation of surfaces could potentially affect the investigation of orientation dependence of oxidation growth rates

29,31.

Periodic boundary conditions were

applied along all three directions. We placed a reflective boundary at the top of the simulation box (the top z boundary) to prevent oxygen from leaving the simulation cell and from interacting with the bottom surface of SiC. The bottom 10 Å layer of SiC was kept fixed during oxidation (i.e., the atoms were not allowed to move) to maintain the GB structure.

After SiC and oxygen were prepared, oxidation simulations were performed in the canonical ensemble with the Nose-Hoover thermostat Parallelized Simulator (LAMMPS)

48

45–47.

code and ReaxFF

Large-scale Atomic/molecular Massively 29

potential were used in all simulations.

This ReaxFF force field has been previously shown to correctly reproduce quantum mechanical calculations of binding energy, equation of state, and heat of formation of SiC crystal. ReaxFF


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potential is very well suited for describing bond formation and breaking in general and, in the case of SiC, it has been demonstrated to describe correctly bond evolution during combustion and aqueous reactions 49–53. After a random placement of O2 molecules above the SiC surface, the entire system was equilibrated at 300 K for 2.5 ps. Subsequently, the system was heated to 2000 K within 2.5 ps, and finally annealed at 2000 K for 200 ps. The time step of 0.25 fs and the temperature damping constant of 25 fs were used in all MD simulations. Single crystals with (100), (110) and (111) crystallographic orientations interacting with oxygen were chosen as reference samples to show the effects of GBs.

3. Results and discussion 3.1 Evolution of oxide thickness Similar to what has been observed in simulations on single crystal SiC reported in Refs. 29–31, in our MD simulations oxygen molecules quickly approach SiC surface, the bonds between silicon and carbon atoms are broken, and new bonds such as Si-O and C-O are formed. As times goes on, a thick SiOxCy layer forms on top of SiC. This layer becomes protective as it suppresses oxygen diffusion into SiC and slows down further oxidation. To understand the oxidation process, we analyzed the thickness of the oxide layer formed on surfaces of the different samples. In our simulations of dry oxidation, we found that some of the carbon atoms can form CO and CO2 molecules and dissociate from the SiC surface whereas all silicon atoms are left in the solid matrix. This observation is consistent with the results reported in Ref.

29,

where

oxidation of SiC by O2 was simulated at temperatures that ranged from 500 K to 5000 K. We


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define oxide thickness as the difference between the average height of the top three silicon atoms and the average height of the deepest three oxygen atoms. Choosing a number of molecules different than 3 does not change the qualitative trends reported in this paper.

Oxidation of SiC has been often described using an empirical Deal-Grove model

54–57,

in which

oxide thickness has linear-parabolic dependence on time. The linear and parabolic regimes have been attributed to reaction- and diffusion-controlled oxidation, respectively. However, both experimental

58–60

and computational

31

observations corroborate that the Deal-Grove model

fails to predict the time-dependent thickness of oxide during initial oxidation phase, i.e., when oxide thickness is smaller than several nanometers.

Time evolution of oxide thickness during the early stages of oxidation is shown in Figure 2 for all of our simulated samples. The growth of oxide layers during the entire simulation time (200 ps) follows a logarithmic time dependence (the function is clearly linear when plotted on a logarithmic scale). Such logarithmic relationship between oxide thickness and time has been found in early oxidation of many metallic materials, such as Al 61, Fe 62–64, Pt 65–68. Logarithmic relationship was usually attributed to a place-exchange mechanism, which can be described as follows: (i) oxygen molecules are absorbed onto the metal surface, (ii) oxygen molecules dissociate to produce chemisorbed atomic oxygen and form covalent bonds with the substrate atoms, (iii) after more than half of the surface has been covered with oxygen, oxygen atoms begin to switch places with the surface atoms they are bonded to. After several monolayers of


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oxide have been formed, a new mechanism becomes dominant, where ions diffuse in an electric field developed across the oxide.

The inset in Figure 2, which shows evolution of oxide thickness on linear time scale, reveals that oxide thickness grows quickly in the first 100 ps and then the growth rate slows down. This transition in the growth rate is consistent with previous simulations of oxidation of single crystal SiC with different temperatures and oxygen concentrations 29,31,43. It can be attributed to the fact that oxide layer formed on top of the crystal affects the in-diffusion of O2 and outdiffusion of gas products. The gas products block the SiC surface from chemically reacting with oxygen, and thereby they decelerate the oxidation process 31. After about 100 ps, the growth rate decreases, and the dependence of oxide growth on time becomes close to linear. It is likely that oxide growth in SiC follows a logarithmic-linear-parabolic dependence on time and that the logarithmic behavior occurs in the very early stages of oxidation, not yet resolved in experiments. Similar findings were reported for oxidation of iron

62–64,69,70.

Specifically,

experimental studies of iron oxidation (on the time scales of hours) found a parabolic kinetics after a short period of linear oxidation 69,70. In contrast, early oxidation simulation 62 (time scale on the order of hundreds of picoseconds) and experiments 63,64 (time scale on the order of tens of seconds and thickness scale less than 5 nm) of iron found a logarithmic oxide growth kinetics.

In order to highlight the differences in oxide evolution among the three types of samples, all oxide evolution curves were colored with red, black, and blue, which correspond to oxide development on single crystal, coherent GBs, and incoherent GBs bicrystals. Within the first 200


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ps of the simulations, there was little difference between oxide evolution in single crystals and bicrystals with coherent GBs. In contrast, we found the oxide grew much faster in bicrystals with incoherent GBs. These observations are similar to the experimental results in Ref.

33,

where 3C-SiC was exposed to supercritical water. The authors found accelerated corrosion only in incoherent GBs whereas there was a negligible difference between coherent GB and bulk SiC. In the following two sections, the reasons for the preferential oxidation of incoherent GBs and lack of preference for oxidation of coherent GBs will be analyzed. In our simulations, the difference in oxide thickness between bicrystals with incoherent GBs and single crystals continued to increase until ~100 ps, at which point the difference remained relatively constant. A likely reason is that after 100 ps, oxidation becomes limited by the supply of oxygen atoms, which need to pass through oxide layer formed on top of SiC crystals and therefore oxidation rates is less sensitive to the underlying structure of SiC The similarities in oxide growth rates within 100-200 ps imply that the differences among the three types of systems mainly stem from the growth before 100 ps. Therefore, the following analysis will focus on the early stage of oxidation.

3.2 Oxidation of incoherent GBs In order to highlight differences between samples containing incoherent GBs and single crystals, in Figure 3 we plot the thickness of oxides in bicrystals with incoherent GBs and in single crystals that constitute these bicrystals. In Figure 3(a), we compare oxide growth on single crystal (100) face and (111) face, and on bicrystals with GBs that are either carbon or silicon rich.


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Although oxygen has a higher affinity to silicon than to carbon 2, oxidation rate of bicrystal with carbon rich incoherent GB is still faster than the oxidation rates of single crystals with (100) and (111) faces. Similarly, oxidation rates in the other two bicrystals with incoherent GBs, namely [100-110] and [110-111], are also found to be faster than those of the corresponding single crystals (see Figures 3(b) and 3(c)). In the insets of Figure 3 we show the same data as in the corresponding panels but in the inset the data is restricted to the early oxidation stage, where the differences between samples are most pronounced.

We confirmed that the acceleration of oxidation in bicrystals with incoherent GBs is due to the presence of the GBs, by plotting position of the oxide front as a function of time (see Figure 4). The oxide front was determined in the following way: (i) simulation boxes were divided into bins with 3 Å length along the y direction, whereas the bin size along the x and z directions were equal to the size of the entire simulation box; (ii) three oxygen atoms with the lowest z coordinates were identified in each bin, then the average of their z coordinates was calculated and treated as the oxide front in a given bin; (iii) at a given time, positions of the oxide front in each bin were plotted with hollow markers and connected with a solid line with markers as shown in Figure 4. In Figure 4, the horizontal axis is the distance to the center of the sample in the case of a single crystal or to the incoherent GB in a bicrystal sample. The vertical axis shows the difference between the oxide front at the given point in time and the position of the original (pre-oxidation) interface between SiC and oxygen molecules.


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In single crystal SiC (Figures 4 (a) and (b)), the lines representing oxide fronts at different times are relatively flatter compared to those in bicrystals with GBs. In contrast, oxide front in bicrystal with incoherent GBs develops a concave upward shape near GBs, as shown in Figures 4 (c) and (d). This localization of oxidation at incoherent GBs is consistent with the overall faster oxidation rate of bicrystals with incoherent GBs (Figures 2 and 3). In addition, it is noticeable that the (100) side of the oxide front lines in Figures 4 (c) and (d) are lower (i.e., the oxide is thicker) than the (111) side, which can be explained by a faster oxidation of single crystals with (100) surface than with (111) (as shown in Figures 4 (a) and (b)). These results are also consistent with oxidation rates reported in Ref.

30,

where MD simulations of oxidation on SiC

single crystals with (100) and (111) faces at 1000 K, 3000 K, and 5000 K were reported. In Ref. 30 the authors fitted oxidation activation energies and diffusion coefficients for single crystals with different surfaces based on oxidation model developed by Newsome et al. 43. According to the fitted parameters, at 2000 K oxidation on Si terminated (100) face should be 5% faster than on Si terminated (111) face.

To understand the mechanisms underlying accelerated oxidation of incoherent GBs, we analyzed atomic-level details of the early stage of oxidation of single crystals with (100), (111) faces and of bicrystals [111-100] with silicon rich GBs. We found that the place-exchange oxidation mechanism reported for metals

61–68

can be modified and used to describe early

oxidation in SiC, as shown in Figure 5. Specifically, the oxidation steps can be described as: (1) Oxygen approaches SiC surface. (2) Oxygen molecules adsorb onto SiC and form Si-O-O-Si bridges with Si atoms in the first (topmost) layer. (3) Si-O-O-Si bridge dissociates into two


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separate Si-O-Si bridges. (4) C from the second subsurface layer switches places with Si from the third layer. Simultaneously O and Si in a Si-O-Si bridge switch places so that O can now bind to the Si atom that swapped places with C. In other words, counting from the surface into the bulk, the initial sequence of layers O-Si-C-Si transforms to Si-O-Si-C. The swapping mechanism reported in Figure 5 is very common in our simulations and a similar mechanism of attack on SiC has been reported in published ab initio simulations of SiC corrosion in molten salts71. Other reactions can also be possible, particularly at the later stages of oxidation where the surface is no longer intact.

In our simulations O first attacks Si because it has a stronger affinity to it2 and also because the top surface is Si terminated. Throughout simulations, we also observe O binding to C and forming CO and CO2 molecules. Some of these molecules diffuse out through the oxide layer into the gas phase. However, most of the C atoms in the early stages of oxidation stay near the SiC/oxide interface, leading to formation of oxycarbide SiOxCy instead of SiO2. The presence of oxycarbide near the SiC surface has been previously reported from both computational31 and experimental15,25,72,73 observations.

In order to answer the question why bicrystal with incoherent GBs oxidize faster, we analyzed properties of atoms in the different regions of bicrystals. We focused on Si atoms because they are preferentially attacked by O. We found that the charges on Si atoms within GBs are less positive than on Si atoms within crystalline grains, which means that it will be easier for Si atoms in the GBs to donate electrons to O and therefore these Si atoms will be more reactive.


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In our study we identified two reasons for decreased charges on Si: these are broken bonds (undercoordinated atoms) and strain (free volume), as explained below.

Broken bonds can be quantified by analyzing coordination number. To calculate coordination number, we use 2.10 Å as a cut-off for Si-C bonds, which is 7.7% larger than the average bond length of single crystal SiC at 300K predicted by ReaxFF potential and 11% larger than the bond length predicted by density functional theory (DFT) calculations74. For Si-Si and C-C bond, we used cut-off lengths of 2.62 Å and 1.71 Å, respectively, which correspond to 11% of the equilibrium bond lengths predicted by DFT calculations for single crystal Si and diamond, respectively75,76. We found that within 5 Å from incoherent [111-100] Si rich GB, 28.4% of all (Si and C) atoms are under-coordinated, while 0.3% atoms are over-coordinated. That means that many Si atoms in the GB have dangling bonds and can react with O more easily than fully coordinated Si atoms in the bulk.

Local strain in the GB results from the presence of homonuclear (Si-Si and C-C) bonds as well as from structural disorder. We quantify strain by calculating free volume associated with Si atoms in a single crystal and in a bicrystal [111-100] and for this purpose we used the Voronoi cell method. The average atomic volumes of silicon atoms within 2 Å wide region centered at GBs are 11.46 Å3. That means that these volumes are around 3.8% larger for Si than the corresponding volumes in a single crystal. Moreover, 31.5% of silicon atoms from the 2 Å wide region centered at GBs had atomic volume larger than 11.65 Å3, which was the highest atomic volume of Si atoms in a single crystal. The aforementioned 31.5% of silicon atoms from a GB


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have an average volume of 12.1 Å3, which is 9.2% larger than the corresponding silicon atomic volume in single crystals. In order to confirm that strain can speedup oxidation, we performed additional oxidation simulations on single crystals that were subjected to 5% of hydrostatic tensile strain. Our simulations confirmed that the oxide front was proceeding faster in strained samples. For example, after 100 ps of simulations, oxide thickness in single crystal strained to 5% is 2.5 Å thicker than that the oxide in the unstrained sample. This difference is similar to the thickness difference between oxides grown on single crystals and on bicrystals in Figure 2. Although the atomic volume of carbon atoms is also increased in the strained sample relative to C atomic volume in single crystal, these simulations qualitatively support the conclusion that the excess silicon free volume can contribute to fast oxidation near incoherent GBs. The effect of free volume/strain on oxidation is likely not direct because for the thin oxides considered in our simulations, oxidation is controlled by surface reactions rather than by O diffusion. Strain has indirect effect on oxidation because it leads to a decrease of the positive charge on Si, making it more reactive. We confirmed it by performing simulations of single crystal SiC subjected to volumetric strain and by calculating charges (see Figure 6).

Figure 7 shows charge state distribution of carbon and silicon atoms near incoherent GBs in the silicon rich [111-100] bicrystal before oxidation. Charges in carbon rich [111-100] bicrystal have the same qualitative features. Specifically, the charges on carbon atoms near incoherent GB is more positive than in the crystalline grains. Charges on silicon atoms near incoherent GB and on top surface are less positive than in the crystalline grains. Since during oxidation, oxygen prefers to interact with silicon2 and since it accepts electrons from silicon, silicon on the top


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surface and near the GB will be more likely to attract oxygen than silicon in the bulk. As shown in Figure 7, an incoherent GB provides a continuous path of Si atoms with decreased charge (increased reactivity), which facilitates faster oxidation.

3.3 Oxidation of coherent GBs In order to investigate oxidation behavior of coherent GBs, in Figure 8 (a) we directly compare time-resolved oxide thicknesses on single crystals, and on two bicrystals containing a tilt GB formed by misorienting single crystal (110) by 11.3° (Σ13) and 4.4° (Σ85). In the first 3-4 ps, oxides on bicrystals grow slightly faster than those in single crystals. This trend can be attributed to the fact that in our simulations bicrystals with tilt GB have surfaces terminated with high-index planes (as would be created for instance during polishing). Atoms on such surfaces form a zigzag pattern (creating more open space for oxygen) and are generally less stable than atoms on low-energy surfaces. This difference in surface structure impacts the initial oxidation rate, however after the first 3-4 ps, the oxidation rate of bicrystals and of single crystals proceeds at comparable rate. There is no evidence that the presence of a coherent GB changes the oxidation rate. To verify that, we analyzed oxidation fronts for coherent GBs (Σ13 and Σ85) and in Figure 8 (b) we show results for Σ13 as a representative example. Comparison of Figure 4 and Figure 8 (b) reveals that there are no obvious differences between single crystals and bicrystals containing tilt GBs. Plus, there is no evidence of accelerated oxidation (a concave up shape) near an incoherent GB, such as was observed earlier in coherent GBs (see Figure 4).


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Coherent low-angle tilt GBs consist of GB dislocations separated by strained crystalline regions. We found that atoms in the dislocation cores have a larger atomic volume and are undercoordinated. However, the regions between dislocations have properties very similar to bulk crystal and they limit the rate of oxidation. For instance, in GB Σ13 , the average atomic volume of silicon atoms at the dislocation cores of coherent Σ13 GB is 11.32 Å3. The atomic volume of atoms in the regions between dislocations is 11.05 Å3, which is the same as of atoms in a single crystal. Silicon atoms from the entire bicrystal had atomic volume that followed a normal distribution (with the mean of 11.06 Å3 and the standard deviation is 0.25 Å3). However, only a small number (0.4% and 0.2% in Σ13 and Σ85, respectively) of silicon atoms had atomic volume larger than 11.65 Å3, which is the upper limit of the atomic volume for silicon in a single crystal. Similarly, there are 30.6 % of atoms that are undercoordinated in dislocation cores and 0.4 % in the GB regions between dislocations.

Charge distribution on carbon and silicon atoms in a bicrystal with a coherent GB Σ13 is plotted in Figure 9. Charges on carbon near coherent GB were similar to those in incoherent GB (Figure 7) and they were higher (less negative) than the corresponding values in the crystalline bulk. However, charges on silicon atoms near coherent GBs were comparable to the charges on silicon atoms in bulk, in contrast to the reduced positive charge present on Si atoms in incoherent GBs. The reason the increase/decrease of charge is not symmetric for Si and C atoms is that there are slightly more C atoms in the dislocation cores of incoherent GBs. Such structure and chemistry of GBs have been found to be most stable in calculations reported in Ref.

35.

Although silicon atoms at the core of GB dislocation have the charge state (0.54)


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increased (i.e., less positive) than silicon in the bulk (charge state of 0.57), the regions of increased charge state in the GB are separated by crystalline regions between dislocation cores, where charge state of Si atoms is also 0.57. As a result, although silicon atoms at coherent GBs dislocation core may have a stronger tendency to react with oxygen, their effect was damped by the crystalline regions between dislocation cores. As a result, oxidation acceleration near coherent GBs is much less obvious compared with that near incoherent GB.

4. Conclusion We performed MD simulations of the dry oxidation of single crystal 3C-SiC, bicrystals with incoherent GBs and with coherent GBs at 2000 K. Incoherent GBs were more vulnerable to oxidation than single crystals, whereas oxidation of bicrystals with coherent GBs proceeded at a similar rate to that on single crystals. The accelerated oxidation along incoherent GBs can be attributed to the presence of a connected network of Si atoms with increased reactivity (a less positive charge). The reasons underlying the change in the charge states of Si atoms in the GB are strain (free volume) and under-coordination (dangling bonds). Although atoms with similar features were found in coherent GBs, they were localized within dislocation cores and did not form a continuous network along the GB. Oxidation front was arrested by the crystalline regions between dislocation cores. Our simulations suggest that GB provide preferential sites for oxidation of SiC and that it might be possible to reduce oxidation rate of polycrystalline SiC by GB engineering.


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Acknowledgment The authors gratefully acknowledge financial support from the US Department of Energy Basic Energy Science Grant # DE-FG02-08ER46493.


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Figures

Reflective Wall O2 SiC

Evolution Layer z

GB x

y

Frozen Layer Figure 1. Schematic of a simulation cell with a GB. Along the z direction, SiC has the height of 50 Å and O2 layer is 40 Å thick. SiC and O2 regions have the same dimensions along the x and the y directions. Along the x direction the width is approximately 30 Å. Along the y direction, it is approximately 60 Å for a single crystal and approximately 120 Å for a bicrystal. Precise dimensions of the all crystals are listed in Table 1 and they depend on the crystal orientations. The density of O2 layer is 0.02 molecules/Å3.


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24

24 18

21

Oxide Thickness (Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


12 6

18

0

0

50

100

150

200

15 12 9

Single Crystals Coherent GBs Incoherent GBs

6 3 0

1

10

100

1000

Time (ps)

Figure 2. Evolution of oxide thickness on single crystals, bicrystals with coherent GBs, and bicrystals with incoherent GBs. Oxide thickness for single crystals with (100), (110) and (111) faces are shown in red. Oxide thickness for coherent GB ∑13 and ∑85 are shown in black and for incoherent GBs – in blue. The inset shows oxide thickness data from 50 ps to 200 ps after manually shifted along vertical axis to minimize the variance.


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(a)

[100] [111] Inco [111-100] Si rich Inco [111-100] C rich

24 21 18 15 12

12

9

8

6

4

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Oxide Thicness (Å)

(b)

[100] [110] Inco [100-110]

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(c)

[110] [111] Inco [110-111]

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Oxide Thicness (Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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18 15 12

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Figure 3. Evolution of oxide thickness on single crystal with (100), (110) and (111) faces to oxygen and bicrystals with incoherent GBs. (a) Comparison of oxide thickness evolution in single crystals (100), (111) and bicrystal [111-100]. Incoherent GBs formed by (100) and (111) were divided into Si rich and C rich based on the termination of the surface at the GB interface. Since (111) and (110) interface are always stoichiometric, dominant atom specie finally depends on the interface from (100) was Si terminated or C terminated. (b) Comparison of oxide thickness evolution in single crystals (100), (110) and bicrystal [100110]. (c) Comparison of oxide thickness evolution in single crystals (110), (111) and bicrystal [110-111]. Oxidation early stage from 0 - 20 ps are depicted in right bottom corner panels in each figure.


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Position of oxide front (Å)

0

0

(a)

2

2

4

4

6

0

8

[111] -20

-10

(c)

6

5 fs 15 fs 25 fs

8

10


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0

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20

(b)

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2

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[111-100] Si Rich GB -20

-20

-10

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-10

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(d)

[100] 10

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[111-100] C Rich GB 10

20

Distance from center of single crystal (Å)

10

-20

-10

0

10

20

Distance from GB (Å)

Figure 4. Evolution of the oxide front in single crystals (100), (111), and bicrystals with Si and C rich [111-100] incoherent GBs. Time interval between lines is 10 ps. The horizontal axis represents distance to the center of a single crystal or to the GB in a bicrystal. Position of the oxide front it calculated with respect to the original position of the SiC surface.


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a.1

a.2

a.3

a.4

b.1

b.2

b.3

b.4

Figure 5. Top view (a) and side view (b) of mechanisms of early oxidation on single crystal with (100) face can be broken down into four steps: (a.1 and b.1) Oxygen approaches SiC surface. (a.2 and b.2) Oxygen molecules adsorb onto SiC and form Si-O-O-Si bridges with Si atoms in the first (topmost) layer. (a.3 and b.3) Si-O-O-Si bridge dissociates into two separate Si-O-Si bridges. (a.4 and b.4) C from the second subsurface layer switches places with Si from the third layer. Simultaneously O and Si in a Si-O-Si bridge switch places so that O can now bind to the Si atom that swapped places with C. The simulation system is much larger than what is shown here.


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-0.545 Si Charge C Charge

-0.550

0.565

-0.555

0.560

-0.560

0.555

-0.565

0.550

-0.570

0.545

-0.575 0

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8

C Charge

0.570

Si Charge

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10

Volume Expansion (%) Figure 6. Charge states on silicon and carbon atoms in single crystal SiC as a function of volumetric strain.


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(a) [111-100] C

-0.45

(b) [111-100] Si

-0.55

0.6

0.0

Figure 7. Charge distribution of carbon (a) and silicon (b) atoms in silicon terminated bicrystal with silicon rich incoherent GB [111-100].


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Coherent GB-13 Coherent GB-85 [100] [110] [111]

20 16 12

(a)

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8

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(b)

2

4

6

5 fs 15 fs 25 fs

8

20

200

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-20

Time (ps)

-10

0

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20

Distance to GB-13 (Å)

Figure 8. (a). Oxide thickness evolution in single crystal with (100), (110), (111) faces, and bicrystals with coherent GBs ∑13 and ∑85. (b). Evolution of the oxide front in bicrystals with coherent ∑13 from 0 to 25 ps. Time interval separating each line is 10 ps. The horizontal axis represents distance to the center of a single crystal or to the ∑13 in a bicrystal. Position of the oxide front it calculated with respect to the original position of the SiC surface


38

Page 39 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(a) Σ13 – C

-0.45

(b) Σ13 – Si

-0.55

0.6

0.0

Figure 9. Charge distribution of carbon and silicon atoms in bicrystal with coherent GBs ∑13. Color code is same to the one in Figure 7.


39


Page 40 of 51

Tables Table 1. SiC crystal dimensions in oxidation simulations.

[100]

[110]

[111]

Co ∑13

Co ∑85

[111-

[111-

[100-

[110-

100]-Si

100]-C

110]

111]

x

31.2

31.2

31.6

31.3

31.2

31.5

31.5

31.2

31.5

y

62.4

59.9

60.3

127.1

120.9

120.8

121.1

120.0

119.1


40

Page 41 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TOC Graphic


41

The Journal of Physical Chemistry Reflective Page 42 of 51 Wall 1 2 3 4 5 6 7 8 9 10 11 12 13

O2 Evolution Layer

SiC

z

GB ACS Paragon Plus Environment

x

y

Frozen Layer

Page 244324of 51 21

18

12 1 2 6 18 3 0 4 5 15 6 7 12 8 9 9 10 11 12 6 13 14 3 15 16 0 17 1 18



0

50

100

150

200

Single Crystals Coherent GBs Incoherent GBs

ACS Paragon Plus Environment 10 100

Time (ps)

1000


[1 0 [1 1 In c In c

2 4

O x id e T h ic k n e s s ( Å )

2 1

(a )

0 ] 1 ] o [1 1 1 - 1 0 0 ] S i r ic h o [1 1 1 - 1 0 0 ] C r ic h

1 8 1 5 1 2

1 2

9 8

6 4

3 0

0

5

1 0

1 5

2 0

0

2 1

O x id e T h ic n e s s ( Å )

(b )

[1 0 0 ] [1 1 0 ] In c o [1 0 0 -1 1 0 ]

2 4

1 8 1 5 1 2

1 2

9 8

6 4

3 0

0

5

1 0

1 5

2 0

0

(c )

[1 1 0 ] [1 1 1 ] In c o [1 1 0 -1 1 1 ]

2 4 2 1

O x id e T h ic n e s s ( Å )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 44 of 51

1 8 1 5 1 2 1 2

9 8

6 4

3 0

0 0

2 5

5 0

7 5

0

1 0 0

5

1 0

1 5

2 0

1 2 5

1 5 0

1 7 5

2 0 0

T im e ( p s )


Page 45 of 0 51

(a )

(c ) 2

4

4

6

6

P o s itio n o f o x id e fr o n t ( Å )

2

5 fs 1 5 fs 2 5 fs 8

8

[1 1 1 - 1 0 0 ] S i R ic h G B

[1 1 1 ]

1 0 -2 0 0

P o s itio n o f o x id e fr o n t ( Å )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56

The Journal of Physical 0 Chemistry

-1 0

0

1 0 1 0

2 0

-2 0 0

(b )

-1 0

0

1 0

2 0

(d )

2

2

4

4

6

6

8

8

[1 0 0 ]

[1 1 1 - 1 0 0 ] C R ic h G B

1 0

1 0 -2 0

D is ta n c e f r o m

-1 0

0

1 0

2 0 Plus Environment ACS Paragon

c e n te r o f s in g le c r y s ta l ( Å )

-2 0

-1 0

0

D is ta n c e f r o m

1 0

G B (Å )

2 0

a.1 1 2 3 4 5 6 7 8 9b.1 10 11 12 13

a.2

b.2

The Journal of Physical a.3Chemistry

b.3 ACS Paragon Plus Environment

a.4

b.4

Page 46 of 51

Page 47 of 51

-0 .5 4 5 0 .5 7 0

S i C h a rg e C C h a rg e

-0 .5 5 0

0 .5 6 5 0 .5 6 0

-0 .5 6 0

0 .5 5 5

-0 .5 6 5

0 .5 5 0

-0 .5 7 0

0 .5 4 5

-0 .5 7 5

C h a rg e

-0 .5 5 5

C

S i C h a rg e

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45


0

2

4

6

8

V o lu m e E x p a n s io n ( % ) ACS Paragon Plus Environment

1 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14

(a) [111-100] C


-0.45

(b) [111-100] Si


-0.55

Page 48 of 51

0.6

0.0

Page 49 of 51

C o h C o h [1 0 0 [1 1 0 [1 1 1

2 0 1 6

0

e r e n t G B - Σ1 3 e r e n t G B - Σ8 5 ] ] ]

1 2

(b )

(a ) P o s itio n o f o x id e fr o n t ( Å )

2 4

O x id e T h ic k n e s s ( Å )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56


1 2 9

8 6 3

4 0

0

0

5 0

0

5

1 0 0

T im e ( p s )

1 0

1 5 0

1 5

2

4

6

5 fs 1 5 fs 2 5 fs 8

2 0

2 0 0

1 0


-2 0

-1 0

0

1 0

D i s t a n c e t o G B - Σ1 3 ( Å )

2 0

1 2 3 4 5 6 7 8 9 10 11 12 13 14

(a) Σ13 – C


-0.45

(b) Σ13 – Si


-0.55

Page 50 of 51

0.6

0.0

Page 51 of 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


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