Surface Science 603 (2009) 2132–2137

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Surface Science

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A kinetic Monte Carlo study of the initial stage of silicon oxidation:Basic mechanisms-induced partial ordering of the oxide interfacial layer

Anne Hémeryck a,b,*, Alain Estève a,b, Nicolas Richard c, Mehdi Djafari Rouhani a,b, Georges Landa a,b

a CNRS, LAAS, 7 Avenue du colonel Roche, F-31077 Toulouse Cedex, Franceb Université de Toulouse, UPS, INSA, INP, ISAE, LAAS, F-31077 Toulouse, Francec CEA-DAM-DIF, Bruyères-le-Châtel, F-91297 Arpajon Cedex, France

a r t i c l e i n f o a b s t r a c t

Article history:Received 18 December 2008Accepted for publication 8 April 2009Available online 18 April 2009

Keywords:Crystalline–amorphous interfacesGrowthSilicon oxidesMonte Carlo simulations

0039-6028/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.susc.2009.04.014

* Corresponding author. Address: CNRS, LAAS, 7F-31077 Toulouse Cedex, France. Tel.: +33 0 5613362

E-mail address: ahemeryc@laas.fr (A. Hémeryck).

A kinetic Monte Carlo study of the early stage of silicon oxidation is presented. The model assembles themost recently published dedicated surface mechanisms: oxygen incorporations, migrations, charge trans-fer effects. Simulations of the thermal oxidation at typical manufacturing temperature and pressure con-ditions are discussed. As revealed recently through Density Functional Theory investigations, we observehexagonal patterns that can be here extended over the surface giving rise to a new model system of theSi/SiO2 interface as well as new associated specific defects. We show that our simulator is able to repro-duce correctly the oxidation states of the silicon atoms which are specific of the Si/SiO2 interface.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

The growth of the amorphous silicon dioxide on crystalline sil-icon substrate results on a nearly perfect silicon/oxide interface,with a low density of defects [1,2]. In the current trend of the de-vice downscaling, the use and control of ultrathin silicon dioxidefilms below the nanometre scale is mandatory, and the under-standing of the microstructural characteristics of these films be-comes crucial [3,4]. Despite many studies devoted to elucidatethe formation of the silicon dioxide film [5–18], the structure ofthe Si/SiO2 interface is still a controversial topic. It is known thata transition layer at the Si/SiO2 interface enables the amorphoussilicon dioxide to adapt itself to the crystalline silicon network[19]. Experiments reveal that the transition interfacial layer isone or two monolayers thick [19,20], has a crystalline structure,at least a partial ordering [21,22], and contains silicon atoms inintermediate oxidation states [23–25]. Several large scale modelssimulating the oxidation process exist. In these models, an artificialinterface is formed, by inserting oxygen atoms into the SiASi bondsof the silicon network. The structure is then rearranged by hand orthrough molecular dynamics. An alternative way is to adjust aknown silica phase on top of the silicon substrate to create a super-cell containing the desired interface [13].

In order to establish a direct relation between the oxidation realprocessing conditions and the obtained oxide microstructure, we

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adopt a multiscale strategy. A set of hierarchical models used in se-quence is employed, each one providing structural and energeticparameters to the higher modelling level. Here we detail a partof this work: a novel predictive tool (Oxcad) for the atomic scalemodelling of silicon dry thermal oxidation process. This time-con-tinuous lattice-based kinetic Monte Carlo simulation package hastwo main characteristics which make it apart from other meso-scale models. First, the resulting Si/SiO2 interface is not a hand-builtinterface: the interface is generated from a non-oxidized siliconsubstrate. Oxygen atoms are then inserted according to quantummechanical considerations of oxygen molecule dissociation andincorporation [16–18]. Second, the simulator is based on kineticand thermodynamic considerations in opposition to the sole ener-getic factor [26,27]. Beyond the modelling level, the purpose of thepresent work is to collect, confront the most recently publishedoxidation basic mechanisms and to evaluate, to the best of ourknowledge for the first time their impact on the oxide growth.

2. Methodology

The kinetic Monte Carlo (KMC) approach is a phenomenologicaltype of model coupled with a random number sampling that altersthe sequence of basic mechanisms and therefore introduces a sto-chastic aspect in order to make the simulation closer to a realexperiment (for more details on the KMC method, see [28,29]).The kinetic parameters associated to the structural features arethe keys for the understanding of the silicon oxidation. Each basicatomistic mechanism is associated to an activation energy, deter-mined from ab initio Density Functional Theory (DFT) calculations,

Fig. 1. Three topview snapshots of the silicon substrate at chronological stages ofthe oxidation. (a) one oxygen molecule is adsorbed, (b) after twenty-eightadsorptions and (c) at the end of the simulation when the first monolayer is fullyoxidized. Silicon atoms are shown in gray (blue in color) and oxygen atoms in black(red in color). Encircled zones are zoomed, respectively, in Fig. 2a–d. (Forinterpretation of the references to colour in this figure legend, the reader isreferred to the web version of this article.)

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and joined to a probability. A time of occurrence is also associatedto each of these mechanisms. This time of occurrence correspondsto the reaction rate derived from energy activation barriers, pro-viding a realistic time evolution for our simulations. The drivingidea is to use a large number of ab initio calculations in order tocharacterize correctly each elementary mechanism, which then isimplemented into Oxcad. These ab initio results provide the struc-tural and energetic parameters, used as input data for the MonteCarlo simulation package. The pertinence of the simulations resultsfrom the number and pertinence of these mechanisms. The major-ity of the mechanisms have already been published [16–18]. Wepreviously performed ab initio calculations on Si(1 0 0) � p(2 � 2)surface highlighting channel and dimer rows and the buckling ef-fect [30], their relative role in adsorption and incorporation havebeen addressed in preceding work by the authors [16–18]. How-ever, a simple (2 � 1) reconstruction is used in the kinetic MonteCarlo (KMC) representation, since we have chosen to average theO2/buckling effect into our restricted lattice based methodologythat actually does not explicitly reproduce the buckling as wellas dimer distortion or surface rearrangements. This can be seenin Figs. 1 and 2, schematic views of dimer construction are pro-vided in Figs. 2e, 3 and 6 to help the reader.

The structure of the system evolves by mixing stochastically thefollowing four types of mechanisms:

1/ ‘‘Arrival mechanism”: the dissociative adsorption of the oxy-gen molecule resulting in two oxygen atoms in ‘‘strand” or ‘‘ontop” configurations (i.e. Si@O type of bonding) [6,16].2/ The incorporation of this strand oxygen atom into silicon tocreate SiAOASi bonds [17,18].3/ The atomic oxygen migration from SiASi bonds to otherSiASi bonds [17,18].4/ The back-reactions of the incorporation and migration mech-anisms [17,18].

Mechanisms 2/ and 3/ above actually describe a large number ofelementary mechanisms grouped into two generic ones, for moreconcision. In fact, all pathways determined in Ref. [18] via DFT cal-culations, with associated activation barriers, are reported hereaf-ter in Table 1. They all have been taken into consideration in ourKMC simulations. Basically, we observe that surface migration bar-riers are dependent on the local distribution of oxygen atoms [17].Therefore, in the KMC procedure, the local presence of oxygenatoms is systematically explored to consequently modify the prob-ability of occurrence of the current migration mechanism.

To summarize, after dissociation, each oxygen atom moves intothe silicon substrate by hops following its own occurrence proba-bilities. These probabilities depend on the local environment, theactivation energies and the experimental conditions.

For the arrival mechanism of the oxygen molecule (event 1/)which does not need any activation energy, the probability obeysthe Maxwell–Boltzmann statistics in gas phase: C1PS=

ffiffiffiffiffiffiffiffi

MTp

, whereC1 is a constant, P the pressure, S the elementary cell area as de-fined by the symmetry of the silicon surface (3.84 � 3.84 Å2), Mthe considered species molar mass and T the temperature. For allother events schematized in Table 1 (2/ to 4/), the probabilitiesare determined by an Arrhenius Law: C2 exp (�DEac/kBT) whereC2 is a constant dynamic prefactor, DEac is the activation energyof the mechanism and kB the Boltzmann constant. Thus, the activa-tion energy for each mechanism has an important role in the prob-ability determination: the larger DEac is, the less the event occurs.This way, due to intensive performed ab initio calculations, a largenumbers of activation energies have been implemented in themodel allowing the implementation of barrier dependence on thesurface concentration; these activation barriers take into account

the neighbouring surface species such as already inserted oxygenatoms or already formed oxide seed into the silicon surface, that af-fects considerably the energetic of insertion (for an illustration ofneighbouring influence see Ref. [18] and Table 1).

Each possible event is subject to a random sampling, accordingto its occurrence probability, in order to balance the competitionbetween events. An occurrence time, estimated from the Poissonprobability law, is then associated to each event: ti ¼ �1=k: ln zwhere ti is the time of occurrence associated to the mechanism

Fig. 2. Closed views of encircled parts of the snapshots in Fig. 1. highlighting (a) asilanone structure obtained in Fig. 1a, (b) an ADB site of an isolated oxide nuclei getin Fig. 1b, (c) large oxide nuclei and (d) grain boundaries extracted from Fig. 1c.Silicon atoms are shown in gray (blue in color) and oxygen atoms in black (red incolor). (e) Is a schematic representation of (d) in order to help the reader tounderstand the ADB configuration as obtained in (b) and the grain boundary; blacklines are the dimer bonds and whites spheres are the oxygen atoms. (Forinterpretation of the references to colour in this figure legend, the reader isreferred to the web version of this article.)

ig. 3. Schematic representation of Si/SiO2 interface at two stages of the oxidation.) Initially perfect parallel dimers, (b) illustration of the hexagonal nuclei as

btained at the end of the simulation. Dimer bonds are shown in black lines andDB in gray (green in color). (For interpretation of the references to colour in thisgure legend, the reader is referred to the web version of this article.)

2134 A. Hémeryck et al. / Surface Science 603 (2009) 2132–2137

number i, where k is the probability of occurrence and z, a randomnumber distributed between ]0, 1].

To avoid the probability calculation of all possible mechanismsat each step of the simulation, an event filtering is used. This eventfiltering consists in considering that only the possible mechanismsoccurring in the vicinity of the last realized event, i.e. the nearestneighbours, get a modified probability. In such a way, the simula-tion time is drastically reduced.

The operating cycle of the Monte Carlo consists in three steps: i/the initial atomistic configuration is scanned through the wholesample to detect all the possible mechanisms on each surfaceand bulk sites. The event calendar is then updated: a probabilityand an occurrence time are calculated for each possible mecha-nism. ii/ The minimum time is sought leading to iii/ the occurrenceof the corresponding mechanism. This elementary occurrence timeis then added to the whole simulation time. The procedure returnsagain to step i/. In this way, each Monte Carlo cycle leads to a stepby step evolution of the atomistic configuration, according to ther-modynamic and kinetic parameters, and taking the stochastic nat-ure of the mechanisms into account. An accurate description of theinterface formation is deduced from repeated Monte Carlo cycles.

In our model, the silicon oxidation phenomenon is driven by anexposure of the surface to oxygen species: oxygen molecules intro-duced one by one from a thermodynamic reservoir, atomic oxygenresulting from the dissociative adsorption of molecules and hop-

F(aoAfi

ping from site to site [16–18]. Silicon and oxygen atoms have coor-dination numbers of 4 and 2, respectively. The bonds created areSiAO bonds, no OAO bond is allowed after dissociation of oxygenmolecules. As our study is restricted to the silicon surface oxida-tion, only the FCC-diamond structure with a (2 � 1) reconstructionis used to describe the silicon lattice. No desorption process isimplemented in the simulation package due to the large activationenergies required, although we have shown that SiO desorptionmay occur at higher temperatures [31].

A 20 � 20 silicon atoms with periodic boundary conditions con-stitutes the substrate surface. The aim of the simulations is to de-scribe accurately the structure of the ultrathin oxide layer as afunction of the manufacturing conditions, and to propose an or-dered structure for the Si/SiO2 interface. We therefore determinethe amount and the localization of the intermediate oxidationstates and we identify the defect creation. The simulations arestopped when the first monolayer at the top of the silicon substrateis fully oxidized. Conventional manufacturing temperature andpressure of 900 �C and 2 Pa are applied on a 20 � 20 simulationcell; this is the minimum required box size in order to simulateeffectively the surface phenomenon and surface mechanistic rear-rangements at the medium range. Going into to more extendedsurfaces wouldn’t change the presented conclusions because ofthe local impact of the oxygen influence [32].

3. Results

Fig. 1 represents, a set of three chronological snapshots ob-tained during one simulation. Only one oxygen molecule is ad-sorbed in Fig. 1a. The resulting 2-oxygen atoms structure is asilanone configuration, as defined in Refs. [6,16] (see Fig. 2a): oneoxygen atom is in a strand configuration while the second one isinserted in the backbond; this configuration is obtained after threesuccessive events: one partially dissociative adsorption on top of asingle surface silicon atom leading to both oxygen atoms in strandconfigurations following by two atomic migrations: the first to-wards the dimer bond and the second in the backbond. This struc-ture is predominant at the earlier stages of the oxidation process asexperimentally observed [6]: with only ten oxygen molecules ad-

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sorbed on the silicon surface, nine silanone structures are formed.It is remarkable at this point to see that the full incorporation ofoxygen atoms into the silicon surface is not obtained, expressingthe difficulty of oxygen material to adapt to the silicon surface,even at the early oxidation stage. Then, we see that, while the sila-none specie is very useful to oxidize the SiASi backbonds of thefirst monolayer, it enhances the oxide growth: the first oxide nucleiare rapidly created from the silanone locations (Fig. 1b). Indeed,the presence of the silanone configuration introduces charge trans-fers on the surface, in its neighbourhood, as shown in Refs.[18,31,33]. This drastic influence of the charge transfers are imple-mented in the model: the activation barriers of the diffusion mech-anisms occurring around the silanone structure, or around an oxideseed, are affected tremendously (See in Table 1). The most notableillustration is the change in the diffusion mechanism to form the‘‘Adjacent-Dimer Bridging” (ADB), whose barrier is reduced from0.89 eV in the case of the diffusion of an oxygen atom on a non-oxi-dized part of the silicon surface [17] (Table 1 diffusion 1 ? 2), to0.09 eV in the neighbourhood of an already inserted oxygen atomson the silicon surface [18] (see Fig. 2b and Table 1 diffusion11 ? 12). This weighty breakeven point is observed when the localcoverage exceeds 0.5. These oxide nuclei exhibit an ADB betweentwo adjacent dimer units. This ADB, referred to as ‘‘surface BridgingOxygen” in Ref. [34], bridges silicon atoms positioned on two sep-arate dimer units and is the main way to aggregate adjacent oxidenuclei. The silicon atoms are therefore slightly extracted from theircrystalline positions to come close together to form a SiAOASibond. (Fig. 3b). This process involves a rotation of the danglingbonds by a full 90 degree angle leading to a distortion of the two

Fig. 4. Temporal evolution of oxygen structures at the Si/SiO2 interface: vacantempty dangling bonds (DB in black and triangles), oxygen atoms on-top configu-ration (OT in red and crosses), oxidized dimer bonds (OD in green and squares),oxygen atoms inserted into a backbond (BB in blue and circles) and oxygen atoms inan ADB configuration (ADB in turquoise and lozenges). (For interpretation of thereferences to colour in this figure legend, the reader is referred to the web version ofthis article.)

Fig. 5. Temporal evolution of oxidation states of the surface silicon atoms: the blackand triangles curve represents the non-oxidized silicon atoms (Si0), the Si1+ statesare in red and crosses one, the Si2+ states are in green and squares, the Si3+ states arein blue and circles and the Si4+ states are in turquoise and lozenges, respectively.(For interpretation of the references to colour in this figure legend, the reader isreferred to the web version of this article.)

adjacent dimers, in opposition to the initially perfect parallel dimerrows (Fig. 3a), thus leading to a semi-hexagonal oxide pattern onthe surface. This ADB configuration is a particular surface structure,expected at relatively high oxide coverage [34] as well as coveragesdown to 0.5 ML [18], involves the non incorporation of the oxygenatoms into the SiASi bonds of the original silicon network pointingthe specific arrangement of Si/SiO2 interface through combustionof the original silicon network. We show here that it is possibleto form oxide nuclei at the initial stages of the silicon oxidationprocess [35–37], even at very low coverage, by migration of oxygenatoms and their incorporation into islands using the ADB configu-ration. Then, the growth of the small isolated hexagonal nuclei,containing one ADB, leads to larger oxide nuclei (see Figs. 1c and2c). Finally the ADB and the sequence of the distorted dimers resultin an extended hexagonal pattern on the silicon surface as illus-trated on Fig. 3b [18]. This hexagonal pattern constitutes a logicaltransition between an ordered crystalline substrate and an amor-phous silica, this viewpoint is compatible with what has been iden-tified and discussed many times in literature on an orderedinterface: tridymite or cristobalite phases [18,22,38].

A more detailed structural aspect is addressed next. If we lookat the SiAO bond-types in the first monolayer (Fig. 4), we observethat the vacant dangling bonds (DB curve in black) are rapidly oxi-dized leading to oxygen atoms in strand configurations (OD in red).These O-strand atoms are immediately inserted in dimer bonds(OT in green) or into SiASi backbonds (BB in blue), consistent withthe silanone configuration. Nearly all dimer bonds are oxidized anda great amount of adjacent dimer bridges are obtained (ADB curve)at the end of the simulation (170 out of 200 dimers on the surface).

Fig. 5 shows the variations of the silicon atoms oxidation stateson the surface. The red curve representing the Si1+ states, corre-sponding to the dissociated oxygen atoms attached in strand posi-tion on the surface, shows a peak. This peak is associated with thedisappearance of the black line corresponding to the non-oxidizedsilicon atom Si. In less than 1 ms, all the silicon atoms have at least

Fig. 6. Schematic representation of Si/SiO2 interface exhibiting grain boundaries ascould be obtained (a) from a perfect parallel dimers from a p(2 � 2) surface, (b) froma surface with terraces and (c) from a surface with a non aligned dimersreconstruction. Dimer bonds are shown in black lines and ADB in gray (green incolor). (For interpretation of the references to colour in this figure legend, the readeris referred to the web version of this article.)

Table 1List of the main diffusion processes implemented into Oxcad. The direction of the diffusion starting from one configuration to another and the associated activation barrier (in eV)are given. Reduced slab top view configurations are shown where the atoms of oxygen are in white and of Si in gray. All the activation barriers have been determined using abinitio calculations; the given references correspond to the already published results.

Configurations Diffusion DEac (eV) Diffusion DEac (eV) Configurations

1 1 ? 2 [17] 0.11 2 ? 1 [17] 1.11 9

2 1 ? 3 [17] 0.38 3 ? 1 [17] 1.34

3 1 ? 4 [17] 0.89 4 ? 1 [17] 0.58 10

4 3 ? 4 [17] 1.86 4 ? 3 [17] 0.575 ? 7 0.08 7 ? 5 1.5 11

5 6 ? 7 [16] 0.08 7 ? 6 4.1

6 7 ? 8 [16] 0.27 7 ? 8 [16] 0.94

7 9 ? 10 0.40 10 ? 9 0.7 12

8 11 ? 12 [18] 0.09 12 ? 11 0.74

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one oxygen atom as first neighbour. This peak, followed by the veryfast increase of the Si2+ curve, is the evidence of the immediateincorporation of the oxygen atoms in the bonds of the silicon net-work. We can observe that the Si2+ states constitute the majority ofcases at the beginning of the simulation, showing evidence of thefavourable formation of the silanone structure.

After 1 ms, the Si3+ curve (in blue) overtakes the Si2+ curve: thisobservation reveals and confirms that originating from the sila-none structure (Si2+), hexagonal oxide nuclei are formed at the ear-lier stages of the silicon oxidation. The mechanism involves theaddition of an ADB oxygen on a silicon atom engaged in the sila-none configuration. The same conclusion can be drawn from theturquoise ADB curve, corresponding to the ADB configuration onFig. 4, which increases like the one relative to Si3+ state on Fig. 5.Around 150 hexagonal nuclei are obtained when the simulationis over, leading to a partial ordering at the interface, between thecrystalline substrate and the first monolayer of silicon oxide. InFig. 1c, we observe that some dimer rows are fully oxidized, orhave at least large oxide nuclei formed.

The Si4+ oxidation state are also obtained in lower proportionthan Si2+ and Si3+ oxidation states. This observation reveals the

preference of the oxygen atom to build bridge between two dimerunits compared to the maximal oxidation of the silicon atoms.

Finally, we obtain a Si/SiO2 interface, containing all the siliconoxidation states with a larger proportion for Si3+ and Si2+, as ob-served experimentally [23]. The total oxidation of the first mono-layer of the silicon substrate is performed in 6 ms in theexperimental conditions of 900 �C and 2 Pa oxygen partialpressure.

Looking at the interface defects, Oxcad has further been used toidentify them. We have already mentioned that some dimer unitsare not oxidized. They constitute the first precursor sites for theformation of defects. Another type of defect is attributed to theoxygen atom stabilized in strand configuration. This oxygen atomin strand configuration is present notably on silicon atoms in Si4+

oxidation state. These oxygen atoms, not inserted into the SiASibond, act as ‘‘seeds” towards the amorphization of the siliconoxide. We also find few dangling bonds at the interface, in agree-ment with experimental observations. The last type of defects ob-served with Oxcad are the grain boundaries schematicallyrepresented in Fig. 6 in many conformations following the surfacestarting topology. They form wherever two existing oxide nuclei

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cannot coalesce into one, because of different orientations of thetwo hexagonal nuclei. In this situation, it becomes impossible tojoin the two nuclei by creating an ADB between them, giving riseto a grain boundary. These grain boundaries limit the full oxidationand lead to partial ordering on the silicon surface.

4. Conclusion

A kinetic Monte Carlo code (Oxcad) is presented that performsthe atomic scale simulation of the initial stage of the thermal oxi-dation of silicon as a function of the processing conditions. The ki-netic Monte Carlo procedure is used here to evaluate the state ofthe art basic oxidation mechanisms emanating from Density Func-tional Theory calculations produced these last years (dissociationof O2, incorporation onto silicon, migrations). In this multi-modelframework, we reveal the potential impact of local basic chemicalmechanisms on the atomic arrangement of the first oxide mono-layer. These considerations lead us to the observation of new med-ium range interface structures that are discussed at the light ofdefect formation: local defects, oxygen vacancies, dangling bonds,as well as extended defect such as grain boundaries. These obser-vations are confronted with state of the art experimental and the-oretical knowledge. We have successfully reproduced silanoneformation and subsequent stabilization of the oxide through ADBsites under oxygen exposure. We have further analyzed the oxida-tion states and the partial ordering at the interface. This model sys-tem exhibits a semi-hexagonal pattern at the interface, in goodagreement with: (i) an abrupt interface between silicon and silicondioxide, (ii) the desired transition between a crystal and an amor-phous material. Finally, beyond local defects such as danglingbonds or located oxygen vacancies, the obtained partial orderingof the oxide allows the formation of specific defect, grain bound-aries separating misoriented hexagonal oxide domains. From ourunderstanding, these domains may be considered as a signatureof low temperature (<800 �C) thermal oxides. We believe thatthese results will initiate some attempts to generate new model-structure of the silicon/silicon dioxide interface where electronicstructure calculations will be connected to real processing-basedstackings.

Acknowledgments

The authors want to thank the OSiGe_Sim, ANR-05-NANO-004and LN3M, ANR-05-CICG-0003-02 grants for financial supports.

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