Dependence of the O-2 diffusion rate on oxide thickness during silicon oxidation

We address the rate of O-2 diffusion through the oxide layer at Si-SiO2 interfaces using an atomic-scale approach. In particular, we investigate the combined effect of a percolative diffusion mechanism and of a dense oxide layer located close to the silicon substrate. We first extend our atomic-scale description of O-2 diffusion in amorphous SiO2 to the case of a densified oxide. This yields an activation energy which compares well with the experimental result. Next, we investigate the dependence of the O-2 diffusion rate on oxide thickness at Si-SiO2 interfaces using Monte Carlo simulations. We consider both homogeneous and nonhomogeneous oxide layers. The nonhomogeneous oxide is composed of two layers, a normal and a densified one. The thickness and the mass density of the densified layer are taken from experiment. In the case of a normal oxide, we find that the O-2 diffusion rate increases with decreasing thickness, as a result of the percolative nature of the diffusion mechanism. When a densified layer is inserted, the diffusion coefficient drops below its value for bulk amorphous SiO2, for oxide thicknesses larger than 2 nm. This result is consistent with the experimental behaviour of the oxidation kinetics.

Simulation of atomistic processes during silicon oxidation

Angelo Bongiorno

Silicon dioxide (SiO2) films grown on silicon monocrystal (Si) substrates form the gate oxides in current Si-based microelectronics devices. The understanding at the atomic scale of both the silicon oxidation process and the properties of the Si(100)-SiO2 interface is of significant importance in state-of-the-art silicon microelectronics manufacturing. These two topics are intimately coupled and are both addressed in this theoretical investigation mainly through first-principles calculations. We first address the atomic structure at the interface. We construct atomistic models of the Si(100)-SiO2 interface accounting for the density of coordination defects, the amount and location of partially oxidized Si atoms, and the mass density profile, as measured in electron-spin-resonance, photoemission, and X-ray reflectivity experiments, respectively. A variety of model interfaces are obtained, differing by the degree of complexity in the transition region. The nature of the transition structure at Si(100)-SiO2 interface is investigated by addressing the inverse ion-scattering problem. In particular, we refer to a new set of ion-scattering measurements carried out in the channeling geometry to achieve sensitivity to Si displacements at the interface. To interpret these experimental data, we perform ion-scattering simulations on a selected set of model interfaces presenting different atomic-scale features in the transition region at the Si(100)-SiO2 interface. Silicon displacements larger than 0.09 Å are found to propagate for three layers into the Si substrate. Transition structures consistent with these distortions include Si-Si in-plane dimers, O-protrusion, and/or disordered bond patterns at the Si(100)-SiO2 interface. A transition structure with regularly ordered O bridges results inconsistent with experiments. We then address the silicon oxidation process. We first focus on the diffusion limited regime occurring during the growth of thick oxide films. In particular, we provide an atomic-scale description of the long-range oxygen migration through the disordered SiO2 oxide. The O2 molecule is firmly identified as the transported oxygen species and is found to percolate through interstices without exchanging oxygen atoms with the network. The associated activation energy is found in agreement with experimental values. Then, we address the O2 diffusion rate through the thin oxide layer at the Si-SiO2 interface. In particular, we investigate the combined effect of a percolative diffusion mechanism and of a dense oxide layer located close to the silicon substrate. We find that when a thin densified layer is present at the Si(100)-SiO2 interface, the O2 diffusion rate drops below its value for bulk amorphous SiO2 for oxide thicknesses larger than 2 nm. These results support the blocking layer model introduced to explain the failure of the Deal and Grove model in describing the oxidation kinetics of thin oxide films. Finally, the atomic scale mechanisms responsible for oxidation at the Si(100)SiO2 interface are addressed. First we focus on the properties of negative oxygen species in amorphous SiO2. We initially focus on the relative energetics of neutral and negative oxygen species in both the atomic and the molecular state. The energy landscape and the dissociation properties of the O2- and O22- are also considered. We find that, in amorphous SiO2, the negative oxygen species incorporate in the oxide network and are accommodated by significant network distortions. The investigation of the dissociation processes of the negatively charged molecular oxygen species in amorphous SiO2 highlights the dependence of the dissociation energies on the disordered nature of the network and on the charge carried by the oxygen molecule. In a second stage, we address the atomistic processes occurring at the Si(100)SiO2 interface. We consider the neutral O2 molecule and the negatively charged molecular species. In the case of the neutral O2 molecule, different spin states are investigated. For all these species we study sequentially the network incorporation and the dissociation process. We find that at the Si(100)-SiO2 interface all these species incorporate in the network either spontaneously or by crossing small energy barriers. In the vicinity of the interface, the neutral O2 molecule attacks and penetrates into Si-Si bonds. This process is favored by the charge transfer from the Si-Si bonds to the molecular species. The triplet spin state of the O2 molecule narrows the channels for network incorporation. Indeed, molecules in the triplet spin state preferentially incorporate in the network in correspondence of the upper layer of the Si substrate. Negatively charged species spontaneously incorporate in any Si-Si bond of the oxide, regardless from distance from the interface. Their incorporation is often associated to the formation of network defects, confirming their ability to modify the network. After the incorporation process, the dissociation and hence the oxidation of Si-Si bonds is spontaneous. We find either vanishing or very small dissociation energies. The energy required for crossing the small barriers is provided by the energy gained during the incorporation process. These results are consistent with a variety of experimental observations.

EPFL2003

Multiscale modeling of oxygen diffusion through the oxide during silicon oxidation

Angelo Bongiorno, Alfredo Pasquarello

We investigate at the atomic scale the oxygen diffusion process occurring during silicon oxidation. First, we address the energetics of several oxygen species in the oxide using density-functional calculations. Our results support the interstitial O-2 molecule as the most stable oxygen species. We then adopt a classical scheme for describing the energetical and topological properties of the percolative diffusion of the O-2 molecule through the interstitial network of the oxide. By studying a large set of disordered oxide structures, we derive distributions of energy minima, transition barriers, and the number of connections between nearest-neighbor minima. These distributions are then mapped onto a lattice model to study the long-range O-2 diffusion process by Monte-Carlo simulations. The resulting activation energy for diffusion is found to be in agreement with experimental values. We also extend our atomic-scale approach to an oxide of higher density, finding a significant decrease of the diffusivity. To address the O-2 diffusion directly at the Si-SiO2 interface, we construct a lattice model of the interface which incorporates the appropriate energetic and connectivity properties in a statistical way. In particular, this lattice model shows a thin oxide layer of higher density at the interface, in accord with x-ray reflectivity data. We carry out Monte-Carlo simulations of the O-2 diffusion for this model and obtain the dependence of the diffusion rate on oxide thickness. For oxide thicknesses down to about 2 nm, we find that the presence of an oxide layer of higher density at the Si-SiO2 interface causes a drop of the O-2 diffusion rate with respect to its value in bulk SiO2, in qualitative agreement with the observed oxidation kinetics.

2004

On the relationship between the microstructure and the mechanical properties of an ODS ferritic/martensitic steel

Amuthan Ramar

In the quest of materials for the first wall of the future fusion reactor, it has been shown that oxide dispersion strengthened (ODS) ferritic / martensitic (F/M) steels appear to be promising candidates. The inherent good mechanical properties supported by a good thermal conductivity, swelling resistance and low radiation damage accumulation of the base material, such as EUROFER97, are further enhanced by the presence of a fine dispersion of nanometric oxide particles. They would allow in principle for a higher operating temperature of the fusion reactor, above 550°C, which improves its thermal efficiency. In effect, their strength remains higher than the base material at high temperatures. There are however limitations to their application in the reactor, which relate to the intimate link between the microstructure and the mechanical properties. These limitations, such as an increased ductile to brittle transition temperature above room temperature relative to the base material, come directly from the role played by the oxide particles but also from their indirect impact on the overall microstructure, stemming from the procedure of elaboration of these materials. In addition, there is a lack of knowledge on their response to irradiation, which, even though it appears to be promising with a reduced irradiation induced hardening, is not very well understood. In this work we have developed and evaluated ferritic/martensitic steel, EUROFER97, strengthened by a dispersion of yttria particles. (1) The powder metallurgical process used to obtain it was optimized, (2) the basic mechanisms of hardening were identified and (3) the impact of irradiation on its microstructure and mechanical properties were investigated. In order to understand the behaviour of this class of material other oxide dispersion strengthened (ODS) ferritic/martensitic steels based on EUROFER97 and model alloys were also investigated. For the elaboration of the ODS steel the powders of atomized EUROFER97 and yttria are ball milled in a planetary ball mill and the material is compacted by hot isostatic pressing (HIP). The mechanical properties are evaluated by uniaxial tensile test, Charpy test and micro-indentation while the microstructure is investigated by optical microscopy, scanning electron microscopy and transmission electron microscopy. The focused ion beam (FIB) technique is also used. In the study of the ball milling it appears that the optimal time is 20 hours, as the X-ray peak broadening, crystallite size and hardness of the particles remain unchanged at longer times. Yttria nanoparticles clusters are no more detectable by X-ray after 2 hrs of milling, which is attributed here to their incorporation in the matrix, as opposed to dissolution in the matrix as is often suggested in the open literature. HR-TEM performed on the yttria particles before and after incorporation in the steel by ball milling shows that the yttria maintain its bcc equilibrium structure throughout the process. This could suggest that they are not dissolved during ball milling. We have clarified this point by a cross sectional examination of the EUROFER97 ball milled particles with 0.3wt% of yttria in an FIB. By X-ray EDS analysis it shows nanometric regions reach in yttrium and oxygen, which are the yttria particles embedded in the EUROFER97 particles, proving that they are not dissolved by ball milling. The mechanism at the origin of the alloy compaction during HIP was elaborated. The alloy compaction was done through HIPing at 1150°C for 2.5 hrs at a pressure of 190 MPa. This condition is shown to provide the highest bulk density, to a value close to 99.9%. In the optimization process, it is found that temperature plays a larger role than pressure for alloy compaction. The compaction appears to be mainly due to diffusion. Also, it appears that the ball milled particle size plays a major role in the alloy compaction. It is shown that smaller particles size induces better compaction, provided that the densification proceeds through diffusion flow. This further suggests to terminate the ball milling process by 20 hrs as the particles size reaches its minimum. The impact of the ball milling process on the mechanical properties was evaluated. EUROFER97 with and without ball milling, with and without oxide addition presents an average density around 99.8%. In the as received state, casted EUROFER97, atomized EUROFER97, ball milled EUROFER97 and ODS Yttria present microstructure morphology typical of tempered martensite, whereas ODS Ti presents a nano sized grain microstructure with an average grain size of 200 nm. Ball milling and HIPping does have a slight influence up to 400°C, due to the higher dislocation density induced by ball milling relative to casted EUROFER97. It becomes negligible above 400°C, since both casted and ball milled EUROFER97 present similar hardness and microstructure. In ODS Yttria, yttria presents an average particle size of 25 nm. In ODS Ti, Y-Ti-O presents an average particle size of 7 nm. In the following the identification of the hardening mechanisms in ODS F/M steels. A new model was developed to quantify the collective hardening due to different obstacles, assuming that they provide independent hardening mechanisms. The model helped identifying the dominating source of hardening in ODS F/M steels. The base of the model is the dispersion barrier strengthening model, which is given by Δσsparticle or defects = Mαμb(Nd)1/2 for the hardening due small defects or oxide particles and is given by Δσd-d = Mαμb(ρ)1/2 for the hardening due to dislocations. In this approximation, the total hardening is then given by Δσtotal = {(Δσd-d)2 + (Δσparticle or defects)2}1/2 . The model is used to explain the hardening due to oxides, dislocations and irradiation induced defects. It appears that dispersed oxides is dominating hardness up to 800°C, while following a heat treatment at 1000°C it is the dislocations that then dominate the hardness. Deformation mechanisms were investigated using differential strain rate experiments. The activation parameters, i.e. the activation volume and activation energy, were calculated. It appears that there is a decrease in the activation volume from room temperature to 400°C, which is less than 3%. At about 500°C there is a sudden drop in the activation volume that reaches a minimum at 600°C. With further increase in temperature, there is a significant raise in the activation volume. This abrupt decrease between 400°C and 600°C hints at a change in dislocation-rate controlling mechanism, marking two regimes, a low temperature one and a high temperature one. In situ TEM observations show that at low temperature the deformation is mainly due to the formation of the Orowan loops around the particle. At high temperature the activation energy is about 3.4 eV for ODS, whereas it is 1.3 eV for EUROFER97. The calculated activation energy corresponds well to the one of dislocation climb mechanism. This indicates that at high temperature the yttria particles could be overcome by climb, while at low temperature they are overcome by the Orowan mechanism. The peculiar response of the yield stress to irradiation for this class of material was rationalized using the total hardening model we developed. At a dose of 2 dpa, irradiation induced defects are higher in number density than the dispersed yttria particles, which although they are weaker than the yttria particles they can explain the significant hardening observed in the material. Conversely, the shallow impact of irradiation on ODS F/M steels at low doses, relative to base F/M steels, is explained by the fact that the amount of dispersoid is found to be higher than the density of irradiation induced defects.