Thermal oxidation of silicon
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A conventional multi-levels modeling approach has been applied until then, where DFT calculations are used as input parameters for the parametrization of a kinetic Monte Carlo code developed in our team. But at our stage, i.e. from a fully oxidized surface of a silicon substrate identified in our previous studies [1-8], the space of atomistic configurations becomes too complex (abundance of diffusions, subjective choice due to human intervention) and consequently, DFT reaches its limits. To overcome this limitation, we use the Activation Relaxation Technique (ART) developed by Prof. Normand MOUSSEAU from Université de Montréal, Canada. This technique allows the automatized search of diffusion path in complex systems without the pre-knowledge of the arrival state .
METHODOLOGICAL DEVELOPMENT: COUPLING DFT WITH ART METHOD
As ART uses traditionally empirical potentials, none empirical potential can well describe the chemistry at the Si/SiO2 interface. A coupling between DFT code (here VASP) and ART was achieved, to keep the quantum precision to take into account correctly the tricky chemistry encountered in the case of the silicon oxidation, and notably to deal with specific event at the Si/SiO2 interface.
Ce coupling is operational but appears to be highly expensive in terms of computational resources.
ARTn-VASP Coupling 
Different pre-oxidized surface structures have been considered to conduct our study. These structures have been built on the basis of our previous results [1-8].
We modeled partially (Configuration A) and fully (Configurations B and C) oxidized surfaces by using an elementary pattern that can be depicted as alternate 4-O atom and 6-O atom rings.
As the DFT methodology does not allow to determine the exact deformation of the electronic density around a given atom, the Keating’s formalism  is used to evaluate the local strain associated with dioxygen adsorption and diffusion. On these modeled substrates, oxygen coverage is increasing by adsorbing one or several oxygen molecules.
First obtained results using ARTn/DFT coupling exhibit progressive reconstructions of the Si/SiO2 interface. New interesting diffusions are found enabling the propagation of the oxidation front following a layer-by-layer mode, as refered in the literature. Two diffusions are detailed below in terms of energetics as a function of the oxygen coverage:
- An oxygen diffusion below the oxidized surface as an intralayer diffusion (surface -1)
- An oxygen diffusion toward a deeper layer as an interlayer diffusion (surface -1 à surface-2)
Here, the energy gains are 0.87 eV, 0.50 eV et -0.28 eV respectively. Associated to the decrease of the activation energies, the diffusion becomes also energetically favorable, stabilizing the total energy of the system by releasing the accumulated strain energy (-1.00 eV, -1.40 eV and -3.67 eV, respectively).
As long as the oxygen coverage increases, the energy strain in the interfacial layer becomes so high that an atomic rearrangement becomes necessary to release the accumulated strain energy and reduce the local structural deformation. The local energy strain reduces thus the activation barriers, enhancing the diffusion and leading to a stabilization of the atomic system. The strain energy appears here as a catalyst for the atomic diffusion.
This study highlights a correlation between the energetics typical of an atomic diffusion (energy gains, and activation barriers) with the local strain energy i.e. the local atomic deformation and the oxygen coverage. This study demonstrates a logical approach of the layer-by-layer growth mode observed experimentally.
This work has been performed by Nicolas SALLES during his post-doc fellow between 2015 and 2016.
This work has been published in 2017 in Journal of Chemical Physics.
Strain-driven diffusion process during silicon oxidation investigated by coupling Density Functional Theory and Activation Relaxation Technique - Nicolas Salles, Nicolas Richard, Normand Mousseau and Anne Hemeryck, Journal of Chemical Physics 147 (2017) 054701 - doi: 10.1063/1.4996206
 Fundamental steps towards interface amorphization during silicon oxidation - Anne Hémeryck, Alain Estève, Nicolas Richard, Medhi Djafari Rouhani, Yves J. Chabal - Physical Review B 79 (2009) 035317 - doi: 10.1103/PhysRevB.79.035317
 A kinetic Monte Carlo study of the initial stage of silicon oxidation: basic mechanisms-induced partial ordering of the oxide interfacial layer - Anne Hémeryck, Alain Estève, Nicolas Richard, Mehdi D Djafari Rouhani, Georges Landa - Surface Science 603 (2009) 2132 - doi: 10.1016/j.susc.2009.04.014
 Étude ab initio des premières étapes de l’oxydation du silicium - Anne Hémeryck, Alain Estève, Nicolas Richard, Mehdi Djafari Rouhani and Yves J. Chabal - Chocs Avancées (2009) 24
 Difficulty for oxygen to incorporate into the silicon network during initial O2 oxidation of Si(100)-(2x1) - Anne Hémeryck, Andrew Mayne, Nicolas Richard, Alain Estève, Yves J. Chabal, Mehdi Djafari Rouhani, Gérald Dujardin, Geneviève Comtet - Journal of Chemical Physics 126 (2007) 114707 - doi: 10.1063/1.2566299
 Diffusion of oxygen atom in the topmost layer of the Si(100) surface: Structures and oxidation kinetics - Anne Hémeryck, Nicolas Richard, Alain Estève, Mehdi Djafari Rouhani - Surface Science 601 (2007) 2339 - doi : 10.1016/j.susc.2007.03.038
 Active oxidation: silicon etching and oxide decomposition basic mechanisms using Density Functional Theory - Anne Hémeryck, Nicolas Richard, Alain Estève, Mehdi Djafari Rouhani - Surface Science 601 (2007) 2082 - doi : 10.1016/j.susc.2007.03.008
 Multi-scale modeling of oxygen molecule adsorption on a Si(100)-p(2x2) surface - Anne Hémeryck, Nicolas Richard, Alain Estève, Mehdi Djafari Rouhani - Journal of Non-Crystalline Solids 353 (2007) 594
 Oxidation of silicon: how to deal with a Kinetic Monte Carlo approach - Anissa Ali Messaoud, Anne Hémeryck, Alain Estève, Mehdi Djafari Rouhani, Georges Landa - Material Research Society Symposium Proceedings 996 (2007)
 Strain-driven diffusion process during silicon oxidation investigated by coupling Density Functional Theory and Activation Relaxation Technique - Nicolas Salles, Nicolas Richard, Normand Mousseau and Anne Hemeryck, Journal of Chemical Physics 147 (2017) 054701 - doi: 10.1063/1.4996206
 P.N. Keating, Phys. Rev. 145, 637 (1996)