- Email: [email protected]
Charge transfer: a key issue in silicon thermal oxidation growth
Computational Materials Science 24 (2002) 241–245 www.elsevier.com/locate/commatsci
Charge transfer: a key issue in silicon thermal oxidation growth A. Esteve a
a,*
, M. Djafari Rouhani
a,b
, D. Esteve
a
Laboratoire d’Analyse et d’Architecuture des Systemes (LAAS)–CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse Cedex, France b Laboratoire de Physique des Solides, 118 Route de Narbonne, 31062 Toulouse Cedex, France
Abstract A novel atomic scale model of thermal oxidation of Si(1 0 0) has been developed based on a kinetic Monte Carlo approach. This method is particularly useful to investigate atomic scale experimental data by linking them to the kinetics and energetics of atomic scale elementary mechanisms, i.e. migration, adsorption, desorption and reaction. We will focus on two recent experimental observations where we will qualitatively demonstrate that the oxidation process is partly driven by charge transfer arising from the ionic Si–O bond formation during oxidation induced by oxygen electronegativity. In conclusion we will show that our method is suitable to any further first principles investigation of reaction pathways in a multi-scale approach. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Over the years, silicon dioxide remains one of the most widely used and studied materials despite its scaling limitations recently established in the frame of ultimate gate oxide generation of MOS transistors [1]. Beyond the traditional SiO2 gate oxide, alternative higher K dielectric materials have also been shown to generate an interfacial ultra-thin SiOx transition region. In both cases, there is a need to control the very first interfacial layer of Si–Ox growth. Considering the nanometric device dimensions, aspects of interest such as microroughness, homogeneity of the grown layers, substrate morphology; . . . ; continuum approaches become obsolete independently of the inherent problems associated with the well known ano*
Corresponding author. Tel.: +33-561-336985; fax: +33-561336802. E-mail address: [email protected] (A. Esteve).
malous initial oxidation growth regime under dry oxidation. In the last decade, atomistic approaches, advanced experimental techniques [2–9] as well as first principles calculation efforts [10–19] have been engaged to understand basic phenomena of oxide growth. Although these methods have proved very useful to understand basic properties of silicon oxide [21], we are far from any predictive modelling tool associated with technological process design in the spirit of the Deal and Grove approach towards the engineer [22]. In this paper, we present a novel atomic scale approach in the field of silicon oxidation named kinetic Monte Carlo (KMC) that makes it possible to deal with complex oxidation mechanistic processes. Specifically, it provides a framework to introduce any new atomic jump and simulate the impact of this mechanism on the formation of oxide species as a function of experimental conditions (temperature, pressure, annealing time duration). Experimental evidence of a layer by layer
0927-0256/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 5 6 ( 0 2 ) 0 0 2 0 1 - X
242
A. Esteve et al. / Computational Materials Science 24 (2002) 241–245
growth mode and surface agglomeration of oxygen atoms in the initial oxidation stage still need to be addressed and will be qualitatively discussed in the result subsections of this paper [2,4,5,21]. 2. Method In the KMC procedure, sequences of atomistic elementary mechanisms or ‘‘events’’, i.e. migrations, chemical reactions, etc., are performed in a manner to reproduce the complete growth process. These events are discrete movements or ‘‘jumps’’ of atoms from site to site, i.e. using a lattice-based formalism. Each single jump ‘‘i’’ has its own occurrence probability determined by an activation energy DEi which is a function of the type of jump. This probability of the event i per unit of time is assumed to have an Arrhenius form: ki ¼ m expðDEi =kT Þ where m is a vibration (or attempt) frequency. The temporal progress of the simulation is assumed to be, for each single event, of the following Poisson form: t ¼ ð1=ki Þ ln zi
with zi 2 0; 1
The random sampling introduces a stochastic aspect that makes the simulation closer to a real experiment. The pertinence of the simulated growth is therefore due to the list of events considered in the model as well as the associated activation barriers. 3. Results: layer by layer growth mode Under O2 exposure, the implemented mechanisms are twofold, emanating from ab initio and experimental considerations described elsewhere [19,20]. The major point of our mechanistic model is to consider the ability for an oxygen atom to extract a silicon atom from the network Si generating SiO mobile molecules and subsequent dangling bonds. The second important point is to use these dangling bonds as intermediate positions where mobile species (SiO, O, H, . . .) are able to adsorb as strands, i.e. atom or chain of atoms at-
tached on one side to the network and free on the other side. Stoichiometric oxide is then produced via junction of strands. Fig. 1 provides the simulated interface morphology of several oxides grown at 720 °C temperature under low 102 Pa pressure. A 10 10 Si atoms substrate is used with periodic boundary conditions. In the top left morphology, extraction of silicon is hindered (by using a high activation barrier for the dedicated mechanism). Thus, only adsorption of oxygen atoms is possible. Therefore, oxidation stops as soon as the surface dangling bonds are oxygen saturated. In the top right morphology, extraction is allowed with no distinction of the attacked silicon environment (presence of other oxygen atoms or dangling bonds nearby). The roughness as well as the interface propagation is drastically increased. A higher pressure would result in an explosive oxidation process (where surface and bulk are oxidized simultaneously). In the bottom left morphology, oxidation induced charge transfer (CT) is allowed. This means that silicon atoms which are first neighbours of oxidized silicon atoms have their Si–Si bonds weakened due to the polar Si–O bond. In concrete terms, extraction activation barriers are lowered in these configurations. These Si atoms are, in turn, more susceptible of being extracted compared to a bulk Si covalently Si–Si bonded. We then observe a planarization of the interface due to lateral growth of the oxide. At the atomic scale, once the Si layer is oxygen nucleated (extraction of a Si atom and further adsorption of O and SiO on the subsequent dangling bonds), lateral extraction becomes easier than extraction normal to the surface. In bottom right morphology, we introduce other CT of Si–Si bonds towards dangling bonds that generates a hierarchy in the extraction process as a function of Si–Si remaining bonds, i.e. a surface silicon atom is easier to extract compared with a bulk silicon atom. The interface microroughness is again abrupt for the same reason as before. The change comes from the kinetics which is lowered in this last case indicating that refinement of the CT procedure allows one to monitor the oxidation kinetics, and thus, to obtain and control a layer by layer growth mode.
A. Esteve et al. / Computational Materials Science 24 (2002) 241–245
243
Fig. 1. Si/SiO2 interface morphologies as a function of CT parameters: top left––no CT, no extraction mechanism, top right––extraction mechanism without CT, bottom left––same as before with CT arising from Si–O bonding, bottom right––same þ CT arising from dangling bond presence.
4. Results: oxygen agglomeration In the following experiment, Si(1 0 0)-(2 1) is exposed. Then sequences of annealing steps are performed without any addition of oxidizing species under ultra-high vacuum condition. Along these steps, in situ infrared measurements and quantum cluster calculations suggest agglomeration of oxygen atoms to finally form epoxides, i.e. three or five inserted oxygen atoms within a same surface dimer unit [4,5] (see Fig. 2). In this particular subsection the list of KMC implemented mechanisms is reduced to oxygen atom surface movements from bond to bond as shown in Fig. 3. To be consistent with our strand formalism, any silicon dangling bond is authorised to trap some atomic oxygen migrating species as an intermediate unstable state which leads to a more stable dimer or backbond position (Fig. 3). In order to be consistent qualitatively with the
Fig. 2. Cluster view of oxidized surface silicon dimer unit (epoxides). The dimer bond remains around Si–O–Si bonds (oxygen ¼ dark grey balls).
experimental oxidation with water, at t ¼ 0 s, one atomic oxygen per dimer is placed on top of one of the surface dimer dangling bonds giving a single oxygen atom by surface dimer unit as produced experimentally. We ignore the hydrogen atoms by considering a temperature higher than the
244
A. Esteve et al. / Computational Materials Science 24 (2002) 241–245
1. a relative stability of agglomerated species, i.e. the migration activation energy of an oxygen atom leaving an agglomerated configuration such as Si–O–Si–O–Si is increased; 2. an oxygen atom performing long-range migration is attracted locally by agglomerated oxygen within a dimer. This is done by lowering the associated migration activation barrier.
Fig. 3. Si(1 0 0)-(2 1) top view showing oxygen possible migration pathways.
desorption barrier (873 K). The purpose is therefore to understand how oxygen agglomerates. To perform agglomeration/epoxide formation, long-range oxygen migration is required. For instance, a 2 eV barrier is used for oxygen incorporation into either dimer or backbond from the strand positioning. A barrier of 2.3 eV is used for backbond to backbond migration and backbond/ dimer bond to strand hopping. This allows such long-range migration at 873 K temperature. The simulation is performed on 30 30 atoms substrate with 2 min for the annealing time duration. Results give essentially single oxygen atom within a dimer unit (31% of all dimers), and a few percent of agglomerated species as shown in Table 1. This observation clearly indicates that CT is required to introduce:
Table 1 gives a picture of the CT key role during this oxidation experiment. It also shows the population of 1O, 2O in the backbond, and 5O epoxide species as a function of the extra energy given for stabilizing the agglomeration of oxygen atoms (according to previous remark (1)). As seen experimentally, three oxygen atoms bonded to the same silicon atom are stabilized by considering an additive term for the dissociation barrier. We can see that, as in the case where we neglect CTs, overestimating them gives rise to 2O within a dimer that is not observed experimentally. Furthermore, the ultimate agglomerated species, the 5O epoxide, is created with less efficiency. Clearly an intermediate value gives reasonable good qualitative adjustment with efficient agglomeration giving 8.5– 5.5% of 5O epoxide. The addition of the CT effect (2) allows to monitor the 1O species by lowering it in favour of agglomerated configurations. 5. Conclusion In conclusion, we show that the atomic scale KMC method is a powerful tool to investigate experimental processes where atomistic information can be derived from experiment. Recently, surface agglomeration of oxygen atoms after water-exposed Si(1 0 0)-(2 1) and layer by layer growth mode have been observed. With crude
Table 1 1O (either dimer or backbond incorporated), 2O in the backbond, 3O, 4O and 5O agglomerated within a dimer (% of all dimers) as a function of extra stabilizing energy limiting oxygen migration
0 eV 0.25 eV 0.3 eV 1 eV
1O (%)
2O (%)
3O (%)
4O (%)
5O (%)
31 10 8 3.5
3.5 12 9.5 22
2 1 1.5 5
4 4 9 6
0.5 8.5 5.5 1
A. Esteve et al. / Computational Materials Science 24 (2002) 241–245
elementary considerations, our KMC simulation procedure demonstrates that CT arising from the polarisation of the Si–O bond locally modifies activation energies of oxygen incorporation or migration. This constitutes a key issue of these observed oxidation behaviour. In future work, direct quantitative calibration of mechanisms will be done by considering the exact kinetics of the layer by layer growth mode and by integrating infrared spectra to quantify the surface species as a function of annealing steps. This work will serve as an unprecedent guideline for further first principles investigation of oxidation chemical reaction and migration pathways avoiding non-pertinent calculations.
References [1] D.A. Muller, T. Sorsch, S. Moccio, F.H. Baumann, K. Evans-Lutterodt, G. Timp, Nature 399 (1999) 758. [2] J.M. Gibson, M.Y. Lanzerotti, Nature (London) 340 (1989) 128. [3] B.B. Stefanov, A.B. Gurevitch, M.K. Weldon, K. Raghavachari, Y.J. Chabal, Phys. Rev. Lett. 81 (1998) 3908. [4] M.K. Weldon, B.B. Stefanov, K. Raghavachari, Y.J. Chabal, Phys. Rev. Lett. 79 (1997) 2851.
245
[5] M.K. Weldon, K.T. Queeney, Y.J. Chabal, B.B. Stefanov, K. Raghavachari, J. Vac. Sci. Technol. B 17 (1999) 1795. [6] S. Fujita, H. Watanabe, S. Maruno, M. Ichikawa, Appl. Phys. Lett. 71 (1997) 885. [7] H. Watanabe, K. Kato, T. Uda, K. Fujita, M. Ichikawa, T. Kawamura, K. Terakura, Phys. Rev. Lett. 80 (1998) 345. [8] Y. Enta, Y. Miyanishi, H. Irimachi, M. Niwano, M. Suemitsu, N. Miyamoto, E. Shigemasa, H. Kato, J. Vac. Sci. Technol. A 16 (1998) 1716. [9] K. Ohishi, T. Hattori, Jpn. J. Appl. Phys. 33 (1994) L675. [10] B.B. Stefanov, K. Raghavachari, Appl. Phys. Lett. 73 (1998) 824. [11] B.B. Stefanov, K. Raghavachari, Surf. Sci. Lett. 389 (1997) L1159. [12] Y. Miyamoto, A. Oshiyama, Phys. Rev. B 41 (1990) 12680. [13] T. Uchiyama, M. Tsukada, Phys. Rev. B 53 (1996) 7917. [14] K. Kato, T. Uda, K. Terakura, Phys. Rev. Lett. 80 (1998) 2000. [15] D. Hamman, Phys. Rev. Lett. 81 (1998) 3447. [16] A. Pasquarello, M.S. Hybertsen, R. Car, Nature 396 (1998) 5. [17] K.-O. Ng, D. Vanderbilt, Phys. Rev. B 59 (1999) 10132. [18] Y. Tu, J. Tersoff, Phys. Rev. Lett. 84 (2000) 4393. [19] A. Esteve, M. Djafari Rouhani, D. Esteve, J. Non-Cryst. Solids 245 (1999) 150. [20] A. Esteve, M. Djafari Rouhani, D. Esteve, Mater. Sci. Semicond. Process. 3 (2000) 47. [21] Y.J. Chabal, R. Hull, R.M. Osgood, H. Sakaki, A. Zunger (Eds.), Springer Series in Materials Science, vol. 46, Springer-Verlag, Berlin, Heidelberg, New York, 2001. [22] B.E. Deal, A.S. Grove, J. Appl. Phys. 36 (1965) 3770.
Charge transfer: a key issue in silicon thermal oxidation growth A. Esteve a
a,*
, M. Djafari Rouhani
a,b
, D. Esteve
a
Laboratoire d’Analyse et d’Architecuture des Systemes (LAAS)–CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse Cedex, France b Laboratoire de Physique des Solides, 118 Route de Narbonne, 31062 Toulouse Cedex, France
Abstract A novel atomic scale model of thermal oxidation of Si(1 0 0) has been developed based on a kinetic Monte Carlo approach. This method is particularly useful to investigate atomic scale experimental data by linking them to the kinetics and energetics of atomic scale elementary mechanisms, i.e. migration, adsorption, desorption and reaction. We will focus on two recent experimental observations where we will qualitatively demonstrate that the oxidation process is partly driven by charge transfer arising from the ionic Si–O bond formation during oxidation induced by oxygen electronegativity. In conclusion we will show that our method is suitable to any further first principles investigation of reaction pathways in a multi-scale approach. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Over the years, silicon dioxide remains one of the most widely used and studied materials despite its scaling limitations recently established in the frame of ultimate gate oxide generation of MOS transistors [1]. Beyond the traditional SiO2 gate oxide, alternative higher K dielectric materials have also been shown to generate an interfacial ultra-thin SiOx transition region. In both cases, there is a need to control the very first interfacial layer of Si–Ox growth. Considering the nanometric device dimensions, aspects of interest such as microroughness, homogeneity of the grown layers, substrate morphology; . . . ; continuum approaches become obsolete independently of the inherent problems associated with the well known ano*
Corresponding author. Tel.: +33-561-336985; fax: +33-561336802. E-mail address: [email protected] (A. Esteve).
malous initial oxidation growth regime under dry oxidation. In the last decade, atomistic approaches, advanced experimental techniques [2–9] as well as first principles calculation efforts [10–19] have been engaged to understand basic phenomena of oxide growth. Although these methods have proved very useful to understand basic properties of silicon oxide [21], we are far from any predictive modelling tool associated with technological process design in the spirit of the Deal and Grove approach towards the engineer [22]. In this paper, we present a novel atomic scale approach in the field of silicon oxidation named kinetic Monte Carlo (KMC) that makes it possible to deal with complex oxidation mechanistic processes. Specifically, it provides a framework to introduce any new atomic jump and simulate the impact of this mechanism on the formation of oxide species as a function of experimental conditions (temperature, pressure, annealing time duration). Experimental evidence of a layer by layer
0927-0256/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 5 6 ( 0 2 ) 0 0 2 0 1 - X
242
A. Esteve et al. / Computational Materials Science 24 (2002) 241–245
growth mode and surface agglomeration of oxygen atoms in the initial oxidation stage still need to be addressed and will be qualitatively discussed in the result subsections of this paper [2,4,5,21]. 2. Method In the KMC procedure, sequences of atomistic elementary mechanisms or ‘‘events’’, i.e. migrations, chemical reactions, etc., are performed in a manner to reproduce the complete growth process. These events are discrete movements or ‘‘jumps’’ of atoms from site to site, i.e. using a lattice-based formalism. Each single jump ‘‘i’’ has its own occurrence probability determined by an activation energy DEi which is a function of the type of jump. This probability of the event i per unit of time is assumed to have an Arrhenius form: ki ¼ m expðDEi =kT Þ where m is a vibration (or attempt) frequency. The temporal progress of the simulation is assumed to be, for each single event, of the following Poisson form: t ¼ ð1=ki Þ ln zi
with zi 2 0; 1
The random sampling introduces a stochastic aspect that makes the simulation closer to a real experiment. The pertinence of the simulated growth is therefore due to the list of events considered in the model as well as the associated activation barriers. 3. Results: layer by layer growth mode Under O2 exposure, the implemented mechanisms are twofold, emanating from ab initio and experimental considerations described elsewhere [19,20]. The major point of our mechanistic model is to consider the ability for an oxygen atom to extract a silicon atom from the network Si generating SiO mobile molecules and subsequent dangling bonds. The second important point is to use these dangling bonds as intermediate positions where mobile species (SiO, O, H, . . .) are able to adsorb as strands, i.e. atom or chain of atoms at-
tached on one side to the network and free on the other side. Stoichiometric oxide is then produced via junction of strands. Fig. 1 provides the simulated interface morphology of several oxides grown at 720 °C temperature under low 102 Pa pressure. A 10 10 Si atoms substrate is used with periodic boundary conditions. In the top left morphology, extraction of silicon is hindered (by using a high activation barrier for the dedicated mechanism). Thus, only adsorption of oxygen atoms is possible. Therefore, oxidation stops as soon as the surface dangling bonds are oxygen saturated. In the top right morphology, extraction is allowed with no distinction of the attacked silicon environment (presence of other oxygen atoms or dangling bonds nearby). The roughness as well as the interface propagation is drastically increased. A higher pressure would result in an explosive oxidation process (where surface and bulk are oxidized simultaneously). In the bottom left morphology, oxidation induced charge transfer (CT) is allowed. This means that silicon atoms which are first neighbours of oxidized silicon atoms have their Si–Si bonds weakened due to the polar Si–O bond. In concrete terms, extraction activation barriers are lowered in these configurations. These Si atoms are, in turn, more susceptible of being extracted compared to a bulk Si covalently Si–Si bonded. We then observe a planarization of the interface due to lateral growth of the oxide. At the atomic scale, once the Si layer is oxygen nucleated (extraction of a Si atom and further adsorption of O and SiO on the subsequent dangling bonds), lateral extraction becomes easier than extraction normal to the surface. In bottom right morphology, we introduce other CT of Si–Si bonds towards dangling bonds that generates a hierarchy in the extraction process as a function of Si–Si remaining bonds, i.e. a surface silicon atom is easier to extract compared with a bulk silicon atom. The interface microroughness is again abrupt for the same reason as before. The change comes from the kinetics which is lowered in this last case indicating that refinement of the CT procedure allows one to monitor the oxidation kinetics, and thus, to obtain and control a layer by layer growth mode.
A. Esteve et al. / Computational Materials Science 24 (2002) 241–245
243
Fig. 1. Si/SiO2 interface morphologies as a function of CT parameters: top left––no CT, no extraction mechanism, top right––extraction mechanism without CT, bottom left––same as before with CT arising from Si–O bonding, bottom right––same þ CT arising from dangling bond presence.
4. Results: oxygen agglomeration In the following experiment, Si(1 0 0)-(2 1) is exposed. Then sequences of annealing steps are performed without any addition of oxidizing species under ultra-high vacuum condition. Along these steps, in situ infrared measurements and quantum cluster calculations suggest agglomeration of oxygen atoms to finally form epoxides, i.e. three or five inserted oxygen atoms within a same surface dimer unit [4,5] (see Fig. 2). In this particular subsection the list of KMC implemented mechanisms is reduced to oxygen atom surface movements from bond to bond as shown in Fig. 3. To be consistent with our strand formalism, any silicon dangling bond is authorised to trap some atomic oxygen migrating species as an intermediate unstable state which leads to a more stable dimer or backbond position (Fig. 3). In order to be consistent qualitatively with the
Fig. 2. Cluster view of oxidized surface silicon dimer unit (epoxides). The dimer bond remains around Si–O–Si bonds (oxygen ¼ dark grey balls).
experimental oxidation with water, at t ¼ 0 s, one atomic oxygen per dimer is placed on top of one of the surface dimer dangling bonds giving a single oxygen atom by surface dimer unit as produced experimentally. We ignore the hydrogen atoms by considering a temperature higher than the
244
A. Esteve et al. / Computational Materials Science 24 (2002) 241–245
1. a relative stability of agglomerated species, i.e. the migration activation energy of an oxygen atom leaving an agglomerated configuration such as Si–O–Si–O–Si is increased; 2. an oxygen atom performing long-range migration is attracted locally by agglomerated oxygen within a dimer. This is done by lowering the associated migration activation barrier.
Fig. 3. Si(1 0 0)-(2 1) top view showing oxygen possible migration pathways.
desorption barrier (873 K). The purpose is therefore to understand how oxygen agglomerates. To perform agglomeration/epoxide formation, long-range oxygen migration is required. For instance, a 2 eV barrier is used for oxygen incorporation into either dimer or backbond from the strand positioning. A barrier of 2.3 eV is used for backbond to backbond migration and backbond/ dimer bond to strand hopping. This allows such long-range migration at 873 K temperature. The simulation is performed on 30 30 atoms substrate with 2 min for the annealing time duration. Results give essentially single oxygen atom within a dimer unit (31% of all dimers), and a few percent of agglomerated species as shown in Table 1. This observation clearly indicates that CT is required to introduce:
Table 1 gives a picture of the CT key role during this oxidation experiment. It also shows the population of 1O, 2O in the backbond, and 5O epoxide species as a function of the extra energy given for stabilizing the agglomeration of oxygen atoms (according to previous remark (1)). As seen experimentally, three oxygen atoms bonded to the same silicon atom are stabilized by considering an additive term for the dissociation barrier. We can see that, as in the case where we neglect CTs, overestimating them gives rise to 2O within a dimer that is not observed experimentally. Furthermore, the ultimate agglomerated species, the 5O epoxide, is created with less efficiency. Clearly an intermediate value gives reasonable good qualitative adjustment with efficient agglomeration giving 8.5– 5.5% of 5O epoxide. The addition of the CT effect (2) allows to monitor the 1O species by lowering it in favour of agglomerated configurations. 5. Conclusion In conclusion, we show that the atomic scale KMC method is a powerful tool to investigate experimental processes where atomistic information can be derived from experiment. Recently, surface agglomeration of oxygen atoms after water-exposed Si(1 0 0)-(2 1) and layer by layer growth mode have been observed. With crude
Table 1 1O (either dimer or backbond incorporated), 2O in the backbond, 3O, 4O and 5O agglomerated within a dimer (% of all dimers) as a function of extra stabilizing energy limiting oxygen migration
0 eV 0.25 eV 0.3 eV 1 eV
1O (%)
2O (%)
3O (%)
4O (%)
5O (%)
31 10 8 3.5
3.5 12 9.5 22
2 1 1.5 5
4 4 9 6
0.5 8.5 5.5 1
A. Esteve et al. / Computational Materials Science 24 (2002) 241–245
elementary considerations, our KMC simulation procedure demonstrates that CT arising from the polarisation of the Si–O bond locally modifies activation energies of oxygen incorporation or migration. This constitutes a key issue of these observed oxidation behaviour. In future work, direct quantitative calibration of mechanisms will be done by considering the exact kinetics of the layer by layer growth mode and by integrating infrared spectra to quantify the surface species as a function of annealing steps. This work will serve as an unprecedent guideline for further first principles investigation of oxidation chemical reaction and migration pathways avoiding non-pertinent calculations.
References [1] D.A. Muller, T. Sorsch, S. Moccio, F.H. Baumann, K. Evans-Lutterodt, G. Timp, Nature 399 (1999) 758. [2] J.M. Gibson, M.Y. Lanzerotti, Nature (London) 340 (1989) 128. [3] B.B. Stefanov, A.B. Gurevitch, M.K. Weldon, K. Raghavachari, Y.J. Chabal, Phys. Rev. Lett. 81 (1998) 3908. [4] M.K. Weldon, B.B. Stefanov, K. Raghavachari, Y.J. Chabal, Phys. Rev. Lett. 79 (1997) 2851.
245
[5] M.K. Weldon, K.T. Queeney, Y.J. Chabal, B.B. Stefanov, K. Raghavachari, J. Vac. Sci. Technol. B 17 (1999) 1795. [6] S. Fujita, H. Watanabe, S. Maruno, M. Ichikawa, Appl. Phys. Lett. 71 (1997) 885. [7] H. Watanabe, K. Kato, T. Uda, K. Fujita, M. Ichikawa, T. Kawamura, K. Terakura, Phys. Rev. Lett. 80 (1998) 345. [8] Y. Enta, Y. Miyanishi, H. Irimachi, M. Niwano, M. Suemitsu, N. Miyamoto, E. Shigemasa, H. Kato, J. Vac. Sci. Technol. A 16 (1998) 1716. [9] K. Ohishi, T. Hattori, Jpn. J. Appl. Phys. 33 (1994) L675. [10] B.B. Stefanov, K. Raghavachari, Appl. Phys. Lett. 73 (1998) 824. [11] B.B. Stefanov, K. Raghavachari, Surf. Sci. Lett. 389 (1997) L1159. [12] Y. Miyamoto, A. Oshiyama, Phys. Rev. B 41 (1990) 12680. [13] T. Uchiyama, M. Tsukada, Phys. Rev. B 53 (1996) 7917. [14] K. Kato, T. Uda, K. Terakura, Phys. Rev. Lett. 80 (1998) 2000. [15] D. Hamman, Phys. Rev. Lett. 81 (1998) 3447. [16] A. Pasquarello, M.S. Hybertsen, R. Car, Nature 396 (1998) 5. [17] K.-O. Ng, D. Vanderbilt, Phys. Rev. B 59 (1999) 10132. [18] Y. Tu, J. Tersoff, Phys. Rev. Lett. 84 (2000) 4393. [19] A. Esteve, M. Djafari Rouhani, D. Esteve, J. Non-Cryst. Solids 245 (1999) 150. [20] A. Esteve, M. Djafari Rouhani, D. Esteve, Mater. Sci. Semicond. Process. 3 (2000) 47. [21] Y.J. Chabal, R. Hull, R.M. Osgood, H. Sakaki, A. Zunger (Eds.), Springer Series in Materials Science, vol. 46, Springer-Verlag, Berlin, Heidelberg, New York, 2001. [22] B.E. Deal, A.S. Grove, J. Appl. Phys. 36 (1965) 3770.