Thin Solid Films 520 (2012) 4734–4740

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Defect generation during silicon oxidation: A Kinetic Monte Carlo study

A. Ali-Messaoud a, A. Chikouche b, A. Estève c,d,⁎, A. Hemeryck c,d, C. Lanthony c,d,C. Mastail c,d, M. Djafari Rouhani c,d

a Université Saad Dahlab, Faculté des Sciences, 09000 Blida, Algeriab Unité de Développement des Equipements Solaires U.D.E.S, Alger 16000, Algeriac CNRS; LAAS; 7 avenue du colonel Roche, F-31077 Toulouse, Franced Université de Toulouse; UPS, INSA, INP, ISAE, UT1, UTM, LAAS; F-31077 Toulouse, France

⁎ Corresponding author at: CNRS, LAAS, 7 avenue du coFrance.

E-mail address: aesteve@laas.fr (A. Estève).

0040-6090/$ – see front matter © 2011 Published by Eldoi:10.1016/j.tsf.2011.10.207

a b s t r a c t

a r t i c l e i n f o

Available online 10 November 2011

Keywords:Kinetic Monte Carlo simulationDFTSiO2

Multi-scale simulationProcess simulationSilicon oxidation

We present a synthetic review of elementary chemical mechanisms source of the oxidation of pure silicon(100) surfaces. These mechanisms are then discussed from their ability to build a mesoscale model of theKinetic Monte Carlo type dedicated to the process simulation of silicon thermal oxidation. We show thatoxidation is driven by two main processes: (i) charge transfer arising from the formation of Si\O bonds incontact to pure silicon at the interface, (ii) destructive oxidation in which SiO building blocks rearrange atthe interface to form a hexagonal-based oxide network directly in contact to cubic Si layers. Based on theseconsiderations, simulations at the process scale exhibit epitaxial behavior within the interfacial domain.The resulting oxide layers are analyzed in terms of local to more extended defects. We observe two typesof defects: (i) “intra-domain defects” which are related to local distortion of the elementary hexagonaloxide pattern Si6O6 (ii) “inter-domain defects”, which are related to global oxide structural transitionsfrom one orientation to another.

© 2011 Published by Elsevier B.V.

1. Introduction

Silicon and its oxide remain at the heart of microelectronics indus-try after being at the source of one major technological breakthroughenabling massive production as well as miniaturization of the MetalOxide Semiconductor Field Effect Transistors for more than 40 years.The remarkable properties of the Si/SiO2 interface have allowed itsscaling from the submicron down to the nanoscale in the frame ofthe Very Large Scale Integration technologies. Despite a huge mobili-zation of researchers and engineers throughout the years, the basicunderstanding of the oxidation of silicon is still facing major contra-dictions and difficulties including oxidation elementary chemistry, in-terface growth kinetics at early oxidation stages, and finally, detailedinterface atomic arrangement. To date, there is still no model at theatomic scale of the technological process of oxidation. Moreover, theformation of defects in close relation with the experimental set uphas never been simulated….

From its early technological developments, silicon oxidation hasbeen accompanied with macroscopic types of phenomenologicalmodels more or less based on chemical rate equations to unravel ox-idation growth kinetics as a function of processing conditions (partialpressures, temperatures…). The most famous and invariably quoted

lonel Roche, F-31077 Toulouse,

sevier B.V.

without contest is the “linear-parabolic” model of Deal and Grovebased on oxygen diffusion through the oxide followed by reactionsat the silicon/silicon dioxide interface [1]. Because of the originallimitation of the model to predict the growth of films below 20 nm,a number of candidate models have been proposed and pushedbeyond their macroscopic conceptual limits [2,3]. In the last twodecades, the goal of reaching the atomic scale information has beenhelpfully enriched by the use of ab initio codes, quasi exclusively ofthe Density Functional Theory (DFT) type [4]. Interestingly, theymade it possible to investigate a number of fundamental silicon oxi-dation issues on the characterization of local oxide defects of interestfor the device operation [5–8] and on the silicon/silicon dioxide inter-face structural aspects through quantum-based molecular dynamics[9,10]. In this field, a number of articles have been dedicated to thestudy of the oxygen adsorption [11,12], active oxidation [13–15], ox-ygen diffusion modes [16,17] and more interestingly, oxygen incor-poration into the silicon surface [18–21]. Recently Hemeryck andcoworkers have shed light into the mechanisms of oxygen incorpora-tion exhibiting non incorporated “strand-like” oxygen precursors be-fore oxide nucleation under nominal oxygen coverage to arrive at acrystalline semi-hexagonal pattern onto cubic silicon [21]. This theo-retical observation echoed a widely discussed experimental work ofthe late eighties in which a local ordered silicon dioxide was observedat the interface [22].

In the following sections, we show how this basic mechanisticknowledge can be translated into elementary events allowing adescription of thermal oxidation of silicon through a Kinetic Monte

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Carlo (KMC) technique. This multi-scale approach is, to the best of ourknowledge, the only existing opportunity to model the oxidationtechnological process at the atomic scale. As suggested in previouswork [23] in which only surface mechanisms, i.e. surface migrationsand dimer or backbond oxygen incorporation are mixed in the KMCapproach, a partial ordering of the surface oxide is found throughthe extension of the oxide nucleus pattern discussed above upon ox-ygen agglomeration. In this paper, we provide additional interfacemechanisms making it possible to address the simulation of theoxide growth toward the silicon bulk as a function of the experimen-tal conditions. In Section 2, we describe our methodological approachand we detail atomistic mechanisms which serve as ingredients inour calculations. Simulation results related to the nature of defectsgenerated in the oxide films are then reported and discussed inSection 3.

2. Materials and methods

In many cases, the multi-scale simulation is essential for under-standing the formation of mesoscopic structures, from local atomisticordering to global layer arrangement across time scale [24]. We haveperformed KMC simulations of dry oxidation of silicon on a 2D peri-odic cell composed of (100×100) atoms representing a (100) orient-ed silicon surface. Simulations have been performed under realisticexperimental conditions, namely a substrate temperature T of 993 Kand an oxygen partial pressure PO2 of 10 Pa. For more clarity andease of expertise, the oxidation is artificially stopped after the oxida-tion of three silicon layers.

As described in [24], the main ingredients for the set up of ourlattice-based KMC simulator are threefold: (i) crystallographic datato account for the lattice description, (ii) events that describe theoxidation process and (iii) the temporal dynamics sequencing themicroscopic events.

It has been experimentally shown that the first atomic layers ofthe oxide films present the crystalline structure of the tridymite lat-tice [22]. Based on this assumption, a coincidence between the twolattices of silicon and tridymite has been found. Here, the [001] andthe [010] axes of tridymite are aligned with [011] and [01-1] axes ofSi(100) substrate. In this lattice based frame, all predefine sites ofour KMC can be explicitly addressed as cubic silicon or hexagonal tri-dymite as these two lattices are superimposed. Therefore, the localmechanisms and associated chemistry decide if a specific latticeposition turns to be either silicon dioxide, silicon or interstitial (orempty site). The main concern and originality of our present investi-gation is the implementation of new mechanisms allowing oxidationof the deep silicon layers, beyond already investigated surface oxida-tion processes [23].

As already pointed out above, quantum calculations have offered areal opportunity to elucidate atomistic mechanisms of silicon oxida-tion [9–21,23,24]. Despite this considerable research effort, the stateof the art of silicon oxidation basic mechanisms remains limited tothe understanding of the initial stage of oxidation: dissociation andincorporation of the first oxygen atoms into the silicon surface toform Si\O\Si bonds. The most remarkable property derived fromthese results is the inability of the oxygen atoms to be systematicallyintegrated into Si\Si bonds between first neighbors of the silicon net-work. This basic assumption made it possible to describe surface oxi-dation limited to the formation of the first oxide monolayer [23].Nucleation is shown to occur when the surface is exposed to nominalmolecular oxygen coverage and results into oxide nuclei which aresemi-hexagonal [21], involving atomic structures that are stronglydistorted with respect to the initial pure silicon lattice. This observa-tion implies that the crystalline to amorphous transition, as observedin SiO2/Si films, is initiated in the very first stages of oxidation. Furtheroxidation toward the bulk necessitates other basic mechanisms whichhave not been revealed, to date, by DFT calculations. Despite this fact,

indirect interpretation of older calculations [8,15,20] including resultsof an oxygen atom inserted into bulk Si, in addition to the precedingconclusions on surface oxidation allows us to consider some interfacialmechanisms to be introduced in our KMC model. These new mecha-nisms include: (i) molecular oxygen diffusion through the oxide, (ii)active oxidation, i.e. extraction of silicon atoms from their lattice posi-tion to generate SiO molecules as building blocks for the creation ofthe oxide network, this process is enhanced by the local presence ofinserted oxygen atoms (charge transfer), (iii) generation of Si intersti-tials to account for the difference in Si concentration between bulk Siand SiO2. According to these assumptions, a typical oxidation scenariocan be described in terms of the following steps. This complex scenariois pictured in Fig. 1a and b: a. Surface oxidation: accounting for thedissociation of O2 that does form a (SiO)i interstitial molecule throughextraction of a surface Si atom, the second oxygen atom then reactswith the dangling bonds left or right after (SiO)i formation. (SiO)i thenreacts with either the left Si dangling bond or the Si\O surface strandto end up with the formation of a Si\O\Si surface configuration. b.Subsurface/interface oxidation: because of subsurface Si\Si bondweakening after surface oxidation, a subsurface Si atom can be moreeasily extracted upon O2 dissociation. In this process, at each SiO crea-tion, a Si interstitial atom is also created. The upper part (initial surface)rearranges to form a trydimite network. Mobile and reactive SiO and Ospecies can then drive the tridymite network growthwithin the interfa-cial region via an epitaxial type of growth. In their side, the created sil-icon atoms can migrate as interstitials toward the bulk and theinterface.

Another important issue to be considered in the KMC model is thecharge transfer mechanism. Charge transfers occur between siliconand oxygen atoms which are always negatively charged. This ioniccharacter of oxygen depletes the neighboring Si\Si bonds. They areresponsible for the local weakening of Si\Si bonds which are theneasily oxidized in the presence of oxygen molecules. These effectshave been identified in DFT calculations during the investigation ofsurface migration and agglomeration of oxygen atoms onto silicon[17]. In our KMC model, the activation barriers of the reaction mech-anism described above is assumed to be environment dependent, inorder to take charge transfers and bond weakening into account.This environment dependence is implemented by reducing the acti-vation barrier of the reaction mechanism, at a given site, by the frac-tion of energies QO and QDB taken respectively, as a function of thepresence of oxygen or dangling bonds on neighboring sites. Thus, ona given site, the overall elementary oxidation activation energy forreaction mechanism is given by the following expression:

Ea reactð Þ ¼ nVSi�Si–Δz

where n is the number of Si\Si bonds on a given silicon network siteto be broken through oxidation (n=2 for Si surface atoms and n=4for the subsurface/bulk atoms), VSi\Si is set to be 2.3 eV, the Si\Sibond energy of the Si crystal. Δz is a parameter which is adjusted tomodulate the activation barrier for the mechanisms of reaction, as afunction of the oxidative environment. In our KMC simulation, Δzhas been parameterized in terms of QO and QDB as follows:

z ¼ QDB:NDB siteð Þ þ QO:NO 1st neighb:ð Þ

where NDB (site) is the number of created dangling bonds in a given“site” of reaction, NO (1st neighb.) is the number of bridging oxygenconnected to the four first neighbors of the given reaction site. QO

and QDB are adjusted, in our model, to be 1.5 eV and 2.0 eV respec-tively, in order to reproduce the layer-by-layer oxidation mode seenexperimentally. All the other activation energies of mechanisms thatoccur on surface or in silicon bulk, described above, are adjusted to0.07 eV, including reconstructionmechanisms associatedwith tridymitegrowth: SiO, O adsorptions, Si\O strand recombinations.

Fig. 1. a: Schematic representation of the surface oxidation scenario: O2 dissociates to form Si\O strands plus molecular SiO. Recombination of these species gives a surface bridgingoxygen. In red and dashed lines we represent the weakening of the Si\Si bonds due to local Si oxidation states. b: Schematic detailed representation of the subsurface oxidationscenario: upon O2 dissociation and reaction, a molecular SiO plus one atomic oxygen plus one extracted Si atom are generated. In this process, SiO and O are used to grow thetridymite network which is now formed through the Si/oxide disconnection. The silicon atom is considered as a diffusing interstitial.

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3. Results and discussion

Results reported in this section concern general features of thegrowth, but mainly the description of the defects observed in thethin oxide layer. Simulations have been carried out on (100×100)atoms on Si(100) substrates at T=993 K under an oxygen pressureof 10 Pa. They have been deliberately limited to the growth of 2SiO2 layers (i.e. 4 silicon layers) in order to identify accurately the dif-ferent types of defects and their formation mechanisms. Indeed, it iswell known that the SiO2 layer has an amorphous structure, except-ing a few molecular layers close to the interface, which are well orga-nized in tridymite phase [22,25]. Given the mismatch between the Silattice and the tridymite structure, it is expected that the oxide con-tains a large number of defects. Such a layer will rapidly transforminto an amorphous material, after relaxation of the film around thedefects. For this reason, only a minor fraction of the abundant litera-ture on SiO2 characteristics addresses individual defects. On themodeling side, growth of multiple SiO2 layers results in more andmore complex defects, needing also a structural relaxation of theoxide film. In the absence of such a relaxation in our model, whichprobably leads to an amorphization of the layers, we estimate thattwo SiO2 layers are sufficient for our identification purpose.

Examining the oxide growth, we can first observe that once anoxide nucleus is formed, it propagates rapidly along a dimer row.This propagation kinetics, already reported in the literature [17,23],is due to the fact that electron transfers to oxygen atoms weakenneighboring Si\Si bonds. The oxidation kinetics on adjacent rowsare only weakly correlated to each other, since two adjacent rowsare mainly linked through subsurface Si atoms, not oxidized at thisstage of growth. Therefore, the orientations of the tridymite nucleiare not correlated from one dimer row to the adjacent ones. The ab-sence of correlation is clearly seen in Fig. 2 where a top view of theoxidized surface is shown. In this figure, different orientations of the

tridymite elementary hexagonal patterns are represented with differ-ent colors. The absence of correlation results in a large number ofseparate domains with boundaries parallel to the dimer rows.

Looking along a single dimer row, we can still observe few domainboundaries. These boundaries result from the coalescence of twopropagating nuclei, not aligned in the same tridymite lattice direc-tion. To observe this mechanism, the size of the simulation cell shouldbe large enough so that the propagation time along the cell is largerthan the nucleation time along the same line. In a proper simulationthis condition should bemet in order to observe these domain bound-aries. The (100×100) atom cell used in our simulations meets there-fore this condition.

In the following, we have distinguished between intra-domainand inter-domain defects, respectively illustrated starting fromFig. 2.

3.1. Intra-domain defects in SiO2/Si(100)-2×1

3.1.1. Oxygen vacanciesIntra-domain defects are generally constituted of isolated point de-

fects. The predominant type of point defect formed at the end of oursilicon dry oxidation process is the oxygen vacancy. This defect is, byfar, one of the most discussed and studied among silicon dioxidedefects. Its ability to fix charges is a crucial issue of the overall deviceoperation. In Fig. 3, we reference all oxygen vacancies that are charac-teristic of our oxide intra-domain structure. We do observe singleoxygen vacancies, noted as O-MV (Oxygen Mono-Vacancies) andagglomerated oxygen vacancies, noted as ODV (Oxygen Di-Vacancies).

3.1.2. Peroxy linkage defectThe second intra-domain localized defect in silicon dioxide is the

O\O peroxy linkage (PL). This defect arises from propagation of

Fig. 2. (a) Grid representation of TDB on a 100×100 square lattice of SiO2/Si(100)-2×1; (b) ball-and-stick model representation of SiO2/Si(100) with hexagonal unit cells ofSiO2(β-Tridymite). Each color corresponds to one orientation of the periodic hexagonal cells of SiO2. The atomic structures of the defects are denoted O-MV and O-DV in the intra do-mains section, TDB, KS and SF in the inter domains section.

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nuclei which meet and coalesce in good lattice fit but with an excessof oxygen on the top Si\Si bond, as shown in Fig. 3(a).

Some vacancies O-MV (or O-DV) have been created close to PLdefects. This result is in good agreement with experimentalobservation of H. Guo and co-workers [26] and I. Kitagawa and T.

Maruizumi [27]. These authors have reported that oxygen vacanciesin silicon dioxide are not located on the surface as has been inter-preted by Calliari [28] but are close to the surface of the oxide andform with PL one pair of defect considered as a new type of intrinsicdefect [29].

(a)

(b) (c)

[0-11]

[011]

Z

Z=0 (atoms onSurface)

Z=-2 (atoms onSubsurface)

Fig. 3. Structure of 2 ML of SiO2 in beta-tridymite configuration viewed along two orthogonal silicon crystal axes [0-11] and [011]. (a) OMV defect along the silicon directions [0-11]and (b) along [011], in the subsurface of SiO2/Si-2×1; (c) ODV defect formed by two OMV. The z value indicate the oxide layer normal to the surface, - signifies layers pointingtoward the subsurface.

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3.2. Inter-domain defects in SiO2/Si(100)_2×1 surface: twin domain

Inter domain defects are generated by coalescence of growingislands with different crystal orientations. At these domain bound-aries, we can observe Twin Domain Boundaries (TDB), and edge dis-locations, noted as (ED) (see Fig. 4). TDB are characterized by mirrorsymmetry. They can be localized on a single dimer row, or extendedalong the dimer row. Two extended TDB along two adjacent dimerrows may intersect to give rise to a Kink Site, noted as (KS). KinkSites are localized imperfections that include vacancies and stackingfaults, noted as (SF).

After this defect inventory, one another level is to study the char-acteristic of the defect structures and their spatial distribution as afunction of the applied experimental conditions of temperature andpressure. Continuous effort is still to be done along this line whichis the subject of on-going investigations.

4. Conclusion

In this work, we make a brief overview of the elementaryphysico-chemical mechanisms that have been identified through

first principles calculations of the Density Functional Theory type.These mechanisms are introduced in a Kinetic Monte Carlo proce-dure allowing atomic scale simulation of the silicon oxidation pro-cess. We report on the atomic scale simulation of the oxidation oftwo silicon layers under conventional experimental conditions ofpressure and temperature. The resulting grown oxide layers areanalyzed in terms of generated defects. These defects are structurallydefined and discussed in the light of experimental knowledge. Theirformation mechanisms are specified in relation to the elementaryoxidation chemistry. We observe the formation of oxide domainswith specific crystalline orientation along the dimer rows of the sili-con (100)-2×1 surface. At the domain boundaries we identify andcharacterize several defects such as twin boundary defects, andKink Site defects. Beyond these inter-domain defects, we show theformation of intra-domain local defects, mainly oxygen vacancies,more or less agglomerated, and peroxy bridges. Although furthereffort is needed to characterize more accurately these defects, partic-ularly their concentration as a function of experimental conditions,we have provided an atomic scale process simulation capable ofgenerating a Si/SiO2 interface description that includes intrinsicdefect formation.

d

TDB

TDB

Domain 1

Domain 2

TDB

Domain 1

Domain 2

Domain 1

Domain 2

ED

TDB

Kink Site

Edge Dislocation

2 dd

KS

(a)

(b)

(c)

Fig. 4. Ball-and-stick model of the inter-domains defects, as a transition zone, observed on the surface of the SiO2/Si(100)-2×1, by KMC simulation: (a) TDB development betweenthe two domains symmetrically related by rotation of 180°, (b) periodic SF and O-MV at the TDB, (c) ED with KS at the boundaries (transition zones) formed by the coupling of thetwo twin domains.

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Acknowledgments

The work was supported by CEA-DAM and CALMIP supercomput-er resources.

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