We investigated the oxidation reaction of the O2 molecule at the Si(100)-SiO2 interface by using a constrained ab initio molecular dynamics approach. To represent the Si(100)-SiO2 interface, we adopted several model interfaces whose structural properties are consistent with atomic-scale information obtained from a variety of experimental probes. We addressed the oxidation reaction by sampling different reaction pathways of the O2 molecule at the interface. The reaction proceeds sequentially through the incorporation of the O2 molecule in a Si-Si bond and the dissociation of the resulting network O2-species. The oxidation reaction occurs nearly spontaneously and is exothermic, regardless of the spin state of the O2 molecule. Our study suggests a picture of the silicon oxidation process entirely based on diffusive processe

Bongiorno, A.

Pasquarello, A.

RERO DOC Digital Library

ELEVENTH INTERNATIONAL CONFERENCE ON INTERGRANULAR AND INTERPHASE BOUNDARIES 2004J O U R N A L O F M A T E R I A L S S C I E N C E 4 0 (2 0 0 5 ) 3047 – 3050O2 oxidation reaction at the Si(100)-SiO2interface: A first-principles investigationA. BONGIORNO∗, A. PASQUARELLO∗∗Institut de The´orie des Phe´nome`nes Physiques (ITP), Ecole Polytechnique Fe´de´rale deLausanne (EPFL), CH-1015 Lausanne, Switzerland; Institut Romand de RechercheNume´rique en Physique des Mate´riaux (IRRMA), CH-1015 Lausanne, SwitzerlandE-mail: Alfredo.Pasquarello@epfl.chWe investigated the oxidation reaction of the O2 molecule at the Si(100)-SiO2 interface byusing a constrained ab initio molecular dynamics approach. To represent the Si(100)-SiO2interface, we adopted several model interfaces whose structural properties are consistentwith atomic-scale information obtained from a variety of experimental probes. Weaddressed the oxidation reaction by sampling different reaction pathways of the O2molecule at the interface. The reaction proceeds sequentially through the incorporation ofthe O2 molecule in a Si Si bond and the dissociation of the resulting network O2-species.The oxidation reaction occurs nearly spontaneously and is exothermic, regardless of thespin state of the O2 molecule. Our study suggests a picture of the silicon oxidation processentirely based on diffusive processes. C© 2005 Springer Science + Business Media, Inc.1. IntroductionPresent-day metal-oxide-semiconductor devices de-mand gate oxide films thinner than 2 nm [1]. In thisregime, a significant fraction of the full oxide film isoccupied by the transition layer at the Si(100)-SiO2 in-terface, resulting in gate oxides with degraded dielectricproperties [2, 3]. Optimal device performance requirescontrolling the oxide growth at the atomic scale. Furtherprogress therefore requires a detailed understanding ofthe fundamental atomic-scale processes responsible forsilicon oxidation [2, 3].The silicon oxidation process is commonly describedby adopting the physical picture presented by Deal andGrove several decades ago [4]. According to this pic-ture, the silicon oxidation process is assumed to pro-ceed through two sequential steps: (i) the O2 diffusionthrough the oxide network toward the Si SiO2 inter-face, and (ii) an activated O2 reaction with the Si sub-strate at the interface. The diffusion process has beenextensively investigated both experimentally [3, 5] andtheoretically [6] and its description nowadays meetsa large consensus. At variance, the oxidation reactionprocess appears far less characterized and understood.This is mainly related to the fact that the Deal-Grovemodel fails in describing the oxidation kinetics of thinfilms, the regime dominated by the oxidation reactionat the interface [4]. More recently, elaborate kineticsmodels have been designed to account for the thin-filmregime [7–9]. However, such models remain only lim-ited at reproducing the kinetics of the silicon oxida-tion process. No direct information is available about∗Present address: Georgia Institute of Technology, School of Physics, 837 State Street, Atlanta, GA 30332-0430.∗∗Author to whom all correspondence should be addressed.the fundamental processes responsible for the oxidegrowth at the Si SiO2 interface. The understanding ofthese atomic-scale processes appears at present onlyaccessible within density-functional investigations[10–12]. However, difficulties in modelling the struc-ture of the Si(100)-SiO2 interface have hitherto pre-vented the study of the oxidation reaction directly atthe interface.In this work, we use a constrained first-principlesmolecular dynamics approach [13] to address the oxida-tion reaction at the Si(100)-SiO2 interface. We employmodel interface structures reproducing atomic-scalefeatures consistent with a broad range of experimen-tal probes [14, 15]. The O2 reaction is found to proceedsequentially through (i) the incorporation of the molec-ular species in the network and (ii) the dissociation ofthe network O2-species in two neighboring Si O Siunits. Since the calculated energy barriers are of theorder of a few tenths of eV, the reaction is expectedto proceed readily at the temperatures generally usedduring thermal oxidation. Our results suggest that thekinetics of the silicon oxidation process are dominatedsolely by the oxygen transport through the oxide.2. MethodThe electronic structure and the atomic forces inour simulations [13] were obtained within density-functional theory. The exchange and correlation energywas accounted for within a spin-polarized generalizedgradient approximation [16]. We expanded the electron0022–2461 C© 2005 Springer Science + Business Media, Inc. 3047ELEVENTH INTERNATIONAL CONFERENCE ON INTERGRANULAR AND INTERPHASE BOUNDARIES 2004wave functions and density on plane-wave basis sets de-fined by energy cutoffs of 24 and 150 Ry, respectively.Core-valence interactions were described by a norm-conserving pseudopotential for Si [17] and an ultrasoftone for O [18]. The Brillouin zone of our simulationcell was sampled at the  point.To represent the Si(100)-SiO2 interface, we usedthree interface models taken from previous work[14, 15]. In particular, we adopted the models labelledB, C, and C′ in Ref. [15]. These models consist of dis-ordered, topologically perfect oxide networks match-ing the Si substrate without coordination defects [14].The transition region at the interface extends overabout two Si monolayers and shows several in-planeSi Si dimers [15]. These model interfaces reproducethe mass density profile, the amount and location ofpartially oxidized Si atoms, and the degree of distor-tions propagating in the Si substrate, as measured inX-ray reflectivity [19], photoemission [20], and ion-scattering experiments [15], respectively. The modelinterfaces used in the present study consist of an oxidelayer about 6 ˚A thick and a Si substrate of 7 mono-layers. The extremities were saturated by H atoms. Thestructures are periodic in the plane of the interface, witha√8 × √8 Si repeat unit.Pathways and energy profiles for the O2 oxidationreaction are obtained using a constrained moleculardynamics approach. In particular, during the molec-ular dynamics simulations we favor the course of theoxidation reaction by varying an appropriate reactioncoordinate. All the other coordinates are free to vary ac-cording to the calculated atomic forces. During the evo-lution, we prevented the system from leaving the Born-Oppenheimer energy surface by damping the electronicdegrees of freedom [21]. Using this procedure we gen-erated, for each model interface, 15 different reactionpathways for the O2 molecule in both the triplet and sin-glet spin state. The results of this study do not dependon the specific model used for the calculations. Hence,hereafter we will not refer to a specific model interface.3. ResultsThe lowest-energy electronic configuration for the O2molecule in both the vacuum and the interstitials ofthe oxide corresponds to a triplet spin state [6, 22].Hence, we started our simulations by locating the O2molecule in the triplet state on top of the oxide compo-nent, at the oxide-vacuum interface. At this stage, wefavored the progress of the oxidation reaction by grad-ually decreasing the distance between the O2 moleculeand the Si(100)-SiO2 interface. Our simulations showthat the O2 molecule approaches the interface by diffus-ing through neighboring interstices (Fig. 1, top panel)[6]. In the proximity of the Si(100)-SiO2 interface, theO2 molecule attacks a Si atom in an intermediate oxida-tion state and incorporates in the corresponding Si Sibond near the Si substrate. Our simulations show thatnetwork incorporation corresponds to an exothermicprocess with an energy release ranging between 1.0and 1.5 eV and proceeds by crossing energy barriers ofonly 0.1–0.2 eV.Figure 1 Neutral O2 molecule in the triplet spin state (top) diffusingthrough the oxide and (bottom) incorporating in a Si Si bond.Network incorporation of the O2 molecule in thetriplet spin state gives rise to network O2 species rang-ing from the peroxyl linkage to a non-bridging O2 com-plex accompanied by a Si dangling bond (Fig. 1, bottompanel). These structures all correspond to metastablestates. In fact, our electronic structure calculations showthat spin conversion to the singlet spin state alwayslowers the energy, with energy gains ranging between0.1 and 1.0 eV. Furthermore, upon spin conversion theatomic structure generally undergoes an important re-laxation favoring the formation of a more symmetricperoxyl linkage (Fig. 2, bottom panel).To further investigate the role of spin, we repeated ourset of 15 simulations setting the O2 molecule in the spinsinglet state from the outset, while keeping otherwiseidentical conditions. In this case, the trajectories of themolecule through the oxide are very similar to thosefollowed by the O2 molecule in the triplet spin stateand the incorporation in the Si Si bond directly gives a3048ELEVENTH INTERNATIONAL CONFERENCE ON INTERGRANULAR AND INTERPHASE BOUNDARIES 2004Figure 2 The spin conversion to the singlet state is energetically fa-vorable and drives (top) the O2 molecule incorporated in the networktowards the completion of the incorporation process by forming a per-oxyl linkage (bottom). The top panel corresponds to the transition statefor the incorporation process of an O2 molecule in the singlet spin state.symmetric peroxyl linkage (Fig. 2, bottom panel). Alsothe energetic profile is very similar to the triplet spincase. The triplet-singlet crossing occurs in the neighbor-hood of the transition state (Fig. 2, top panel). Hence,regardless of the spin carried by the O2 molecule, theoxidation reaction proceeds through barriers that caneasily be overcome under the usual thermal conditionsof silicon oxidation [4] and results in the formation ofa peroxyl linkage.To further investigate the oxidation reaction, we fa-vored the dissociation of the network molecular speciesby taking the bond length of the molecule as the new re-action coordinate. The dynamics was constrained untilthe transition barrier was overcome (Fig. 3, top panel)and evolved freely afterwards. We observed that thenetwork O2 species dissociates by having one of theO atoms oxidize a neighboring Si Si bond. For ourFigure 3 The top panel shows the transition state associated to the dis-sociation process of the network O2 species in the bottom panel of Fig. 2.Dissociation gives two neighboring Si O Si units (bottom).set of 15 simulations, we found transition barriers ofat most 0.4 eV. These barriers are noticeably smallerthan the energy released during the incorporation of theO2 molecule, suggesting that the dissociation proceedsreadily. The uptake of oxygen at the interface finally re-sults in two neighboring Si O Si units (Fig. 3, bottompanel).4. ConclusionsIn conclusion, we used constrained ab initio moleculardynamics simulations to investigate the reaction of theO2 molecule at the Si(100)-SiO2 interface. Our studyshows that the oxidation reactions occurs in two se-quential steps: (i) the incorporation in the network ata Si Si bond, and (ii) the dissociation of the networkO2 species in two neighboring Si O Si units (Fig. 4).Both processes are activated with energies of a fewtenths of an eV and are highly exothermic. Therefore,our study provides strong evidence against an activatedO2 reaction at the interface which severely influences3049ELEVENTH INTERNATIONAL CONFERENCE ON INTERGRANULAR AND INTERPHASE BOUNDARIES 2004Figure 4 Schematic energy profiles during the incorporation (left) anddissociation (right) processes of the oxidation reaction. For the incorpo-ration, the energy is given with respect to the distance between the O2molecule and the Si Si bond at the interface. For the dissociation, theenergy is given with respect to the O2 bond length. EI , ED , BI , and BDrefer to the energy gains and the energy barriers for the incorporationand dissociation process, respectively.the kinetics of the oxidation process [4]. Our results areconsistent with kinetics models fully relying on diffu-sion [9]. However, to match kinetic data in the thinoxide regime, such a description should account for adecrease of the diffusion rate near the interface [7]. Ac-cording to a recent theoretical investigation [23], suchan effect is achieved by the occurrence of a thin inter-facial oxide layer of higher density, which has indeedbeen observed in X-ray reflectivity experiments [19].AcknowledgmentsWe acknowledge support from the Swiss National Sci-ence Foundation (Grant No. 620-57850.99) and theSwiss Center for Scientific Computing.References1. J . W A N G, P . R O M A N, E . K A M I E N I E C K I and J .R U Z Y L L O , Electrochem. Solid-State Lett. 6 (2003) G63.2. Y . J . C H A B A L (ed.) “Fundamental Aspects of Silicon Oxidation”(Springer, Berlin, 2001).3. E . P . G U S E V, H. C . L U, T . G U S T A F S S O N and E .G A R F U N K E L , Phys. Rev. B 52 (1995) 1759.4. B . E . D E A L and A. S . G R O V E , J. Appl. Phys. 36 (1965)3770.5. E . R O S E N C H E R, A. S T R A B O N I , S . R I G O and G.A M S E L , Appl. Phys. Lett. 34 (1979) 254.6. A . B O N G I O R N O and A. P A S Q U A R E L L O , Phys. Rev. Lett. 88(2002) 125901.7. N . F . M O T T, S . R I G O, F . R O C H E T and A. M.S T O N E H A M , Philos. Mag. B 60 (1989) 189.8. L . V E R D I and A. M I O T E L L O , Phys. Rev. B 51 (1995) 5469;S . D I M I T R I J E V and H. B . H A R R I S O N , J. Appl. Phys. 80(1996) 2467; A . S T O C K H A U S E N, T . U . K A M P E N and W.M O¨ N C H , Appl. Surf. Sci. 56 (1992) 795; J . W E S T E R M A N N,H. N I E N H A U S and W. M O¨ N C H , Surf. Sci. 311 (1994) 101;K . -Y. P E N G, L . -C . W A N G and J . C . S L A T T E R Y , J. Vac.Sci. Technol. B 14 (1996) 3316; D . R . W O L T E R S and A. T . A .Z E N G E R S V A N D U I J N H O V E N , Microelect. Reliab. 38 (1998)259; R . M. C . D E A L M E I D A, S . G O N C¸ A L V E S, I . J .R . B A U M V O L and F . C . S T E D I L E , Phys. Rev. B 61 (2000)12992.9. R . H . D O R E M U S and A. S Z E W C Z Y K , J. Mater. Sci. 22 (1987)2887; R . H . D O R E M U S , J. Appl. Phys. 66 4441 (1989).10. A . P A S Q U A R E L L O, M. S . H Y B E R T S E N and R. C A R ,Nature 396 (1998) 58; in Ref. [2] p. 107.11. W. O R E L L A N A, A. J . R . D A S I L V A and A. F A Z Z I O ,Phys. Rev. Lett. 90 (2003) 16103.12. B . B . S T E F A N O V and K. R A G H A V A C H A R I , Surf. Sci. 389(1997) L1159; K . K A T O, T . U D A and K. T E R A K U R A , Phys.Rev. Lett. 80 (1998) 2000; Y . T U and J . T E R S O F F , ibid. 89 (2002)086102; T . A K I Y A M A and H. K A G E S H I M A , Appl. Surf. Sci.216 (2003) 270; T . Y A M A S A K I , K . K A T O and T . U D A ,Phys. Rev. Lett. 91 (2003) 146102.13. A . P A S Q U A R E L L O, K. L A A S O N E N, R . C A R, C .L E E and D. V A N D E R B I L T , ibid. 69 (1992) 1982; K .L A A S O N E N, A. P A S Q U A R E L L O, R . C A R, C . L E E andD. V A N D E R B I L T , Phys. Rev. B 47 (1993) 10142.14. A . B O N G I O R N O and A. P A S Q U A R E L L O , Appl. Phys. Lett.83 (2003) 1417.15. A . B O N G I O R N O, A. P A S Q U A R E L L O, M. S .H Y B E R T S E N and L . C . F E L D M A N , Phys. Rev. Lett. 90 (2003)186101.16. J . P . P E R D E W and Y. W A N G , Phys. Rev. B 46 (1992) 12947.17. A . D A L C O R S O, A. P A S Q U A R E L L O, A.B A L D E R E S C H I and R. C A R , ibid. 53 (1996) 1180.18. D . V A N D E R B I L T , Phys. Rev. B 41 (1990) 7892.19. N . A W A J I et al., Jpn. J. Appl. Phys. 35 (1996) L67; S . D .K O S O W S K Y et al., Appl. Phys. Lett. 70 (1997) 3119.20. F . R O C H E T, C H. P O N C E Y, G. D U F O U R, H. R O U L E T,C . G U I L L O T and F . S I R O T T I , J. of Non-Crystal. Solids 216(1997) 148; J . H . O H, H. W. Y E O M, Y. H A G I M O T O, K.O N O, M. O S H I M A, N. H I R A S H I T A, M. N Y W A and A.T O R I U M I , Phys. Rev. B 63 (2001) 205310.21. R . C A R and M. P A R R I N E L L O , Phys. Rev. Lett. 55 (1985) 2471;F . T A S S O N E, F . M A U R I and R. C A R , Phys. Rev. B 50 (1994)10561.22. W. O R E L L A N A, A. J . R . D A S I L V A and A. F A Z Z I O ,Phys. Rev. Lett. 87 (2001) 155901.23. A . B O N G I O R N O and A. P A S Q U A R E L L O , J. Phys.: Condens.Matter 15 (2003) S1553.Received 29 July 2004and accepted 31 January 20053050

O2 oxidation reaction at the Si(100)-SiO2 interface: A first-principles investigation

http://doc.rero.ch/record/309853/files/10853_2005_Article_2663.pdf

O2 oxidation reaction at the Si(100)-SiO2 interface: A first-principles investigation

Abstract

Similar works

Full text

Available Versions

RERO DOC Digital Library