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Scripta Materialia 62 (2010) 654–657

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The rate-limiting step in the thermal oxidation of silicon carbide

Junjie Wang,a,* Litong Zhang,a Qingfeng Zeng,a Gerard L. Vignoles,b

Laifei Chenga and Alain Guetteb

aNational Key Laboratory of Thermostructure Composite Materials, Northwestern Polytechnical University,

Xi’an 710072, People’s Republic of ChinabLaboratory for Thermostructural Composites, UMR 5801, CNRS-CEA-Snecma-Universite Bordeaux l, F-33600 Pessac, France

Received 17 December 2009; revised 11 January 2010; accepted 11 January 2010Available online 14 January 2010

Using first-principles density-functional calculations of the total energy, we performed a systematic study of the diffusion acti-vation energies of O2 and CO in SiO2 and Si1�xCxO2. Our results suggest that the dense Si1�xCxO2 (e.g., Si2CO6) layer may playa critical role in the SiC thermal oxidation process. The out-diffusion of CO through SiO2 or Si2CO6 is the controlling step of the SiCthermal oxidation. Known experimental data are explained well by our results.� 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: SiC oxidation; O2; CO; Diffusion; Deal–Grove model

Silicon carbide (SiC) has attracted growing inter-est over the past few decades as a promising candidatematerial for the next generation of high-power, high-temperature electronic devices [1,2]. Thermal oxidationof SiC is among the most fundamental processes in thefabrication of MOS (metal–oxide-semiconductor) de-vices. Many studies [3–13] have been carried out onthe oxidation of SiC, and several models have beendeveloped to explain its mechanism [4,9,10]. Thermaloxidation of SiC is considerably more complicated thanthat of Si. It includes the production of SiO2 and the re-moval of product gases (e.g., CO) from the SiO2/SiCinterface. Therefore, the out-diffusion of CO is a distinc-tive feature in SiC thermal oxidation.

A silicon oxycarbide layer below the SiO2 layer wasdetected in a former study [14]. Da Silva et al. [15] stud-ied hypothetical crystalline phases of silicon oxycarbide(Si1�xCxO2) by using variable cell ab initio moleculardynamics [16]. They found that silicon oxide remainedenergetically stable with respect to carbon incorporationand achieved two possible crystalline phases for Si2CO6.This compound could be a candidate for a Si1�xCxO2

accommodation layer at the SiC/SiO2 interface, assketched in Figure 1.

Recently, Watanabe et al. [17] proposed a new per-spective on the thermal oxidation of Si by considering

1359-6462/$ - see front matter � 2010 Acta Materialia Inc. Published by Eldoi:10.1016/j.scriptamat.2010.01.017

* Corresponding author. E-mail: pro_junjie@yahoo.com.cn; pro_jun-jie @mail.nwpu.edu.cn

a strained oxide region near the SiO2/Si interface, wherediffusion is strongly hindered. By assuming that the oxi-dant diffusivity is strongly decreased in the thin strainedlayers, a new linear–parabolic rate equation for the ther-mal oxidation of silicon was derived. This suggests thatthe silicon oxycarbide layer at the SiC/SiO2 interfacemay also have an important influence on the thermaloxidation of SiC.

In this letter we report on variable cell shape first-principles molecular dynamics calculations for studyingstructures of Si1�xCxO2. We then provide estimates ofthe diffusion activation energies of O2 and CO in SiO2

(including a-quartz, b-quartz, cristobalite and tridymite)and in the obtained Si1�xCxO2 crystals. Our resultsshow that the activation energies of O2 in-diffusion aresmaller than those of CO out-diffusion. Moreover, theSi2CO6 layer has a lower permeability to CO than SiO2.

We approached the problem of identifying stableSi1�xCxO2 structures by using the variable cell shapefirst-principles molecular dynamics method [16]. Thecases of x = 1/3 and x = 1/2 were both considered. Cris-tobalite and a-quartz were adopted as the referencestructures for x = 1/3 and x = 1/2, respectively. Thenhypothetical cristobalite (SiCO4) and a-quartz (Si2CO6)silicon oxycarbides were generated by replacing Si atomswith C ones. The molecular dynamics calculations werecarried out using the CASTEP package [18]. The elec-tronic structure calculations were carried out withinthe generalized gradient approximation (GGA) with

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Figure 1. Illustration of the SiC/S2CO6/SiO2 interface. Grey, yellowand red spheres indicate carbon, silicon and oxygen atoms, respec-tively. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)

J. Wang et al. / Scripta Materialia 62 (2010) 654–657 655

ultrasoft pseudopotentials, a 340 eV plane wave energycutoff and a 5 � 5 � 5 regular Monkhorst–Pack meshto sample the Brillouin zone. The stable structures andlattice parameters of SiCO4 and Si2CO6 are shown andlisted in Figure 2 and Table 1, respectively. The struc-ture of Si2CO6 that we found to be stable and henceadopted in the following diffusion activation energy cal-culations is the phase A of Ref. [15], which could act as amore suitable accommodation layer in the SiC/SiO2 [15].

The diffusion energy barriers of O2 and CO in SiO2

and the silicon oxycarbides SiCO4 and Si2CO6 werestudied using first-principles density-functional calcula-tions, which were performed within GGA as imple-mented in the DMOL3 package [19,20]. The GGAfunctional adopted here is PW91 [21]. For all atoms,the “double numerical plus polarization” basis set,which is comparable to the 6-31G** basis of Hehreet al. [22], was used. Real space cut-offs for Si and C

Figure 2. Lattice models and simulated X-ray diffraction patterns of SiCO4 (aand oxygen atoms, respectively. (For interpretation of the references to coloarticle.)

atoms were 4.6 and 3.7 A, respectively. In the structuraloptimization, the convergence criteria for energy and en-ergy gradient were 1 � 10�5 and 1 � 10�3 a.u., respec-tively. The k-point numbers depend on the actual sizesof the superlattices used in the calculations. The mini-mum-energy paths and activation energies for O2 andCO diffusions were obtained with the generalized syn-chronous transit method approach [23].

Previous experiments have shown that O2 diffuses inSiO2 in molecular form and does not react with theSiO2 network [24]. Moreover, the diffusion barrier foroxygen molecules seems to be highly sensitive to thestructure of the oxide [25,26]. Therefore, a-quartz,b-quartz, cristobalite and tridymite were all included inthe present study.

Table 2 gives the diffusion energy barriers of O2 andCO between neighboring cages (interstitial sites) in dif-ferent kinds of crystals. It can be seen that the energybarriers for CO diffusion are higher than the corre-sponding barriers for O2 diffusion in all SiO2 and Si–C–O structures. Moreover, Si2CO6 has the highest en-ergy barrier for the CO diffusion. Conversely, the energybarriers of O2 and CO diffusion are both very low inSiCO4.

This result is not consistent with the sizes of O2 andCO molecules, since O2 is larger than CO. This can beexplained by the fact that CO has a larger Lewis basecharacter, which makes it much more reactive with re-spect to the surrounding atoms when inserted in thesesolid structures. Although our calculations show thatCO molecules diffuse in all the structures through inter-stitial diffusion instead of reaction diffusion, there arestronger interactions between the CO molecule and thesurrounding diffusion structures. These interactionscould make the CO molecule more “sticky”.

The Si thermal oxidation is limited by the in-diffusionof O2 through the SiO2 layer. Our calculation resultsshow that the out-diffusion of CO may be an importantlimiting factor of the SiC thermal oxidation. The largedifference between the diffusion energy barriers of O2

) and Si2CO6 (b). Grey, yellow and red spheres indicate carbon, siliconr in this figure legend, the reader is referred to the web version of this

Table 1. Space groups, lattice parameters and densities of two kinds of silicon oxycarbide.

Si–C–O Space group Density (g cm�3) Length (A) Angles (�)

a b c a b c

SiCO4 I-4 2.574 4.51 4.51 6.62 90.00 90.00 90.00Si2CO6 C2 2.964 7.57 4.80 9.02 90.00 145.81 90.00

Table 2. O2 and CO diffusion barriers in different kinds of SiO2 crystals and Si–C–O.

Molecules Energy barrier (in eV)

SiO2 Si–C–O

a-Quartz b-Quartz Cristobalite Tridymite SiCO4 Si2CO6

O2 1.22 0.67 1.67 1.13 0.82 1.62CO 1.82 1.87 1.83 1.52 1.34 2.57

656 J. Wang et al. / Scripta Materialia 62 (2010) 654–657

and CO explains the fact that the oxidation of SiC isabout one order of magnitude slower than that of Si un-der the same conditions.

If there is a Si1�xCxO2 accommodation layer at theSiC/SiO2 interface, the oxidation of SiC could proceedthrough the following eight steps (Fig. 3): (i) the insertionof oxygen species from the vacuum into a pre-existingSiO2 layer; (ii) the diffusion of the oxygen through theoxide network toward the SiO2/Si1�xCxO2 interface;(iii) the decomposition of silicon oxycarbide at the SiO2/Si1�xCxO2 interface, where the new SiO2, CO (COdecomp)and O2 (O2-decomp) are formed; (iv) the in-diffusion of oxy-gen (including O2-decomp) through the silicon oxycarbidefilm; (v) the reaction with SiC at the Si1�xCxO2/SiC inter-face and production of new silicon oxycarbide; (vi) theout-diffusion of product gases (here, CO) through the sil-icon oxycarbide film; (vii) the out-diffusion of productgases (including COdecomp) through the oxide film; and fi-nally (viii) the removal of product gases from the oxidesurface.

From experiments, we know that the Si1�xCxO2 layershould be very thin; its thickness is a constant in the oxi-dation process. Moreover, two kinds of typical condi-tions are included in our model based on the differentstructures of Si1�xCxO2 layer. If the Si1�xCxO2 is SiCO4,the SiCO4 layer has a higher permeability to O2 and CO

Figure 3. The eight steps of thermal oxidation of SiC.

than SiO2; therefore, the thermal oxidation of SiC withparabolic–linear character is controlled by the out-diffu-sion of CO through SiO2.

In the Si2CO6 case, the silicon oxycarbide layer has acritical influence on the thermal oxidation of SiC. Theoxidation rate can be limited by the out-diffusion ofCO in the silicon oxycarbide layer. This explains thatwhy some experiments [4] cannot find a carbon monox-ide gradient in the SiO2 layer, as one would expect if COdiffuses outward slowly. Moreover, Vickridge et al. [5]investigated the thermal growth of silicon oxide filmson silicon carbide using oxygen isotopic substitutionand narrow resonance nuclear reaction profiling. Theirinvestigation shows that the limiting steps of the thermaloxide growth are different in Si and SiC. The oxidationof Si is limited by the oxygen diffusion. However, thegrowth kinetics of SiO2 on SiC is very sensitive to thestructure of the interface region. This experiment in factstrongly supports our calculation results. This meansthat different SiC/SiO2 interface structures (e.g., Si2CO6

and SiCO4) could have different influences on the oxida-tion of SiC due to their different barrier effects on thediffusions of O2 and CO molecules.

According to the Deal–Grove model of silicon oxida-tion, the growth rate obeys the following relation:

X 2 þ AX ¼ Bðt þ sÞ ð1Þwhere X is the thickness of oxide and t the oxidationtime. s is related to the initial thickness. B and B/A arethe parabolic and linear rate constant, respectively. Byincluding the CO out-diffusion, Song et al. [10] devel-oped a modified Deal–Grove model for the oxidationof SiC. According to their model, diffusion of O2 orCO could be the rate-controlling step in the parabolicgrowth regime. If oxygen diffusion through silica is therate-controlling step, then

B �C�O2

1:5N 0

DO2ð2Þ

where C�O2is the equilibrium concentration of oxygen

gas, N0 is the number of oxidant molecules incorporatedinto an unit volume of the oxide layer and DO2 is the dif-fusion constant of O2. In this case, the activation energyof the parabolic rate constant will be the same as thatfor the oxidation of Si. Conversely, if the CO out-diffu-

J. Wang et al. / Scripta Materialia 62 (2010) 654–657 657

sion is the rate-controlling step, the parabolic rate con-stant will be:

B �C�O2

K f

N 0Kr

DCO ð3Þ

where DCO is the diffusion constant of CO, and Kf andKr are, respectively, the forward and reverse reactionrate constants.

Song et al. [10] found that there is a large variation inthe oxidation rate between the different faces, with the(0 0 0 �1) C face oxidizing much faster than the (0 0 0 1)Si face. The activation energies of the overall parabolicrate constant B for the (0 0 0 �1) and (0 0 0 1) surfacesare 1.99 and 3.12 eV, respectively. The large differenceindicates there are different mechanisms in the oxidationprocesses of the (0 0 0 �1) and (0 0 0 1) surfaces. Accord-ing to the calculation results in present work, we inferthat the oxidation of the (0 0 0 �1) surface can be gov-erned by the mechanism involving SiCO4 or no oxycar-bide at all, i.e., the controlling step in the oxidation isthe out-diffusion of CO through SiO2. Here, the activa-tion energy (1.99 eV in Ref. [10]) would be the activationenergy of CO diffusion in SiO2 (about 1.8 eV in the pres-ent work) plus the enthalpy variation of the interfacialoxidation reaction.

In the oxidation process, the silicon oxycarbide layer ismore difficult to produce on a (0 0 0 �1) face because thereis a strong driving force for the C atoms in the first layer tobreak their Si–C bonds and form stable CO molecules[10]. After removing the first layer of C atoms, the Siatoms in the second layer will easily react with oxygento form silica since there is only one broken Si–C bondper Si atom, which is connected to the third layer (Clayer). Following the second layer Si atoms oxidation,the C atoms in third layer will be quickly changed toCO and removed. Consequently, the dense silicon oxycar-bide (Si2CO6) layer is hard to form at the SiO2/SiC inter-face on a (0 0 0 �1) face. A loose silicon oxycarbide (such asSiCO4) thin layer may occur at the SiO2/SiC interface;however, it has no influence on the SiC oxidation process.

For the oxidation of a SiC (0 0 0 1) surface, the slowoxidation rate and the large activation energy (3.12 eV)indicate that there is a new mechanism controlling theprocess instead of CO out-diffusion through SiO2 layer.Here, we propose that the out-diffusion of CO throughSi2CO6 is the controlling step for the thermal oxidationon the SiC (0 0 0 1) face. The structure of the (0 0 0 1) Siface shows that the Si–C bonds are more difficult to breakand be replaced by Si–O since there are three Si–C bondsconnected to the second C layer. Therefore, the C atomsare more easily preserved at the SiO2/SiC interface; theycan form a silicon oxycarbide layer. Since the thicknessof the Si2CO6 layer will be kept as a constant in the SiCthermal oxidation, the thermal oxidation of SiC(0 0 0 1) Si face will proceed in a linear–linear manner in-stead of a linear–parabolic one. The first linear rate is gov-erned by the process of surface reaction; the second isrelated to the CO out-diffusion through Si2CO6. Thisguess should be carefully confirmed in further studies.

In summary, we can draw the following conclusions:(i) there can be a stable Si1�xCxO2 interphase betweenSiC and SiO2, at least in some orientations, like the

(0 0 0 1) Si-terminated surface; (ii) the diffusion activa-tion energies of O2 and CO in SiO2 (various poly-morphs) and Si1�xCxO2 (SiCO4 and Si2CO6) havebeen studied systematically. By comparing the activa-tion energies of O2 and CO in different structures, theout-diffusion of CO in SiO2 or Si2CO6 is seen as the lim-iting step of the SiC thermal oxidation. Experimentaldata can be explained well using our model.

The authors thank Dr. Peter Deak, fromBCCMS in University of Bremen, Germany, for valu-able discussions. We acknowledge the financial supportfrom Snecma Propulsion Solide under contract FPRNo. 0539298A, Flying Star Program of NorthwesternPolytechnical University and NSF of China under theGrant 50802076. We also thank Northwestern Polytech-nical University High Performance Computing Centerfor the allocation of computing time on their machines.

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