Mater. Res. Soc. Symp. Proc. Vol. 996 © 2007 Materials Research Society 0996-H01-03 Oxidation of Silicon: How to deal with a Kinetic Monte Carlo Approach Anissa AliMessaoud1, Anne Hémeryck2, Alain Estève2, Mehdi Djafari Rouhani2, and Georges Landa2 1 University Saad Dahlab, Lasicom, BLIDA, 09000, Algeria 2 LAAS, CNRS, TOULOUSE, 31000, France ABSTRACT A Kinetic Monte Carlo procedure dealing with the growth of the Si/SiO2 interface is presented. We show how this general procedure, usually dedicated to well defined epitaxial growth processes can be used for an oxide material exhibiting a complex chemistry and producing highly defective layers. In particular, we discuss the balance that has to be found to monitor diffusion mechanisms with regard to slower events such as reaction mechanisms occurring at the surface/interface. Finally we detail the growth and structuring of the first interface layers as a function of the process and chemical parameters. Keywords: Kinetic Monte Carlo, oxidation, silica growth, ab initio. INTRODUCTION The interface between silicon and silicon dioxide displays the best electronic characteristics of all known semiconductor/oxide interfaces. Yet, the exact interfacial structure remains subject to much controversy. The general trend in microelectronics industry to downscale the devices, in particular the MOSFET (Metal Oxide Semiconductor Field Effect Transistor), has led to a point where it is no more possible to reproduce the qualities of the bulk silicon dioxide. This happens below 0.7 nm for the traditional SiO2 gate oxide [1]. Several emerging ideas are proposed from using higher k materials to modifying the MOS architecture. In both cases, the problem of silicon oxidation remains a key point in the context of a Silicon based technology. From the modelling side, design tools used for years by engineers are also facing the limitations of their poorness with regard of the effective microscopic mechanisms (Deal and Grove [2]) acting at the nanoscale growth regime. Their increasing obsolescence is pleading for the emergence of a new generation of tools having their fundaments based on the atomic scale phenomena. In this trend, we demonstrate that it is feasible to treat the atomic scale modelling of complex technology processes such as silicon dioxide thermal growth using a Kinetic Monte Carlo (KMC) technique. The simulations include several aspects such as the process parameters, the fact that the system is out of equilibrium, the time duration… In the following, we show how the major technical difficulties of the Kinetic Monte Carlo for this complex system are overcome. We then give simulation examples illustrating the potential applications of such models. TECHNICAL ISSUES While traditional Thermodynamic and Kinetic models deal with average physical quantities, Kinetic Monte Carlo is able to consider a wide range of possible configurations at the atomic scale and to choose only one random path out of all possible ones. This corresponds to an actual experiment. The path is determined according to transition probabilities between configurations. Obviously, the transition probability depends also on the local configuration, activation barriers and on the experimental conditions such as pressure and temperature. Moreover the role of each mechanistic step on an ensemble of interacting species makes it feasible to proceed to process-dependent type of growth with deep understanding of the kinetics and their associated atomic arrangements. A classic Kinetic Monte Carlo model can be divided into four parts: 1. the list of elementary mechanisms and associated activation barriers. The mechanisms can emanate from Density Functional Theory (DFT) calculations or directly be drawn from experimental investigations, 2. the temporal dynamics that can be derived from the activation barriers, 3. the lattice site based model to describe the atom location and 4. the implementation of configurations to link a site location and its chemical nature (Oxygen, Silicon, Contaminants). The lattice site description must be chosen with respect to crystallographic data. Point 1, the basic chemical mechanisms of oxidation, and point 3, the matching of lattice structures, make the KMC difficult to use in the context of oxidation modelling. Actually, most of the chemical reactions are not known or controversial and the oxide layers are amorphous. Point 1 - we demonstrate that the understanding of the Silicon oxidation chemistry emanating from intensive Density Functional Theory calculation is now mature enough to draw a list of events to be introduced in the KMC procedure [3-6]. In particular, we indicate how to monitor slow versus fast mechanisms via either a mesoscopic or semi-atomic diffusion algorithm. Point 2 – A crystallographic investigation shows that the description of the SiO2 layers on top of the cubic Silicon Structure can be operated by a tridymite hexagonal structure. TECHNICAL DISCUSSION Silicon oxidation has for long been difficult due to the chemical complexity of oxygen incorporation into the silicon network. Recent experimental work and intensive simulations of molecular oxygen interacting with Si(100) has led to a deeper understanding of this chemical complexity [6]. Dissociation, incorporation of oxygen atom onto the surface and further surface migration capabilities have been drawn by several research groups [3-7]. In concrete, dissociation is shown to occur within up to two adjacent dimer units: for the KMC, we have considered the barrierless dissociation leading to the formation of two “on top” oxygen atoms distributed between the four silicon atoms that form two adjacent dimer units. This distribution is considered as equi-probable at the moment. Concerning the migrations, table 1 is reflecting the mechanisms as implemented in the KMC code OXCAD (see [7] for more details on these calculations). In particular it is shown how migrations of oxygen atoms are affected by the presence of already inserted oxygen atoms. Beyond these well identified mechanisms, bulk oxidation mechanisms remain controversial and little is known or suggested from a modeling view point [8]. Of course experiment can not directly give detailed mechanisms. Previous work by A. Estève and coworkers has proposed a scheme in which oxygen atoms are able to extract silicon atom from the silicon network to locally re-arrange the elementary SiO generated units to form the Silicon dioxide network. This proposal has two origins: (i) it is shown from DFT calculations that oxygen atoms react strongly with silicon giving rise to drastic charge transfers. In bulk Si, oxygen atom can break Si-Si bonds to form Si-O-Si bridges. On surfaces, there is a great distorsion of the silicon surface and the silicon bond orientation through mobile Si=O intermediate species (see the notion of “strand” SiO in [6]). (ii) Recent calculations on active oxidation process show a propensity of the oxygen atoms to extract non or partially oxidized surface silicon atoms [9]. These high temperature mechanisms are however extrapolated to be chemically pertinent in a simplified KMC procedure Actually, generated SiO units are re-arranged locally and do not desorb to evaporate as in a real experiment. Table 1: Migrations of oxygen atoms within a surface dimer unit or between two adjacent dimer units and associated activation barriers (Density Functional Theory calculations, Nudged Elastic Band Method). The re-arrangement of SiO units is now considered in the frame of a coincidence lattice site study: it is found that the tridymite structure is the most adaptable of all considered SiO2 networks to be matched to the Si(100) surface. A biaxial compression of the (100) tridymite is needed that is not completely compensated by the extension in the normal direction. In the same line, in the late eighties [10], it has been proposed that a portion of the Si/SiO2 interface should be structurally well organized as a tridymite SiO2. Therefore, our lattice based KMC is technically working in the following way. At each silicon site of an actual silicon network is surimposed a silicon atom site of the oxide tridymite network. This is thus the simulation procedure related to the experimental parameters that determines whether we are in the silicon or in the oxide at each considered network site. The distinction is explicitly accomplished thanks to the writing of “configurations” where the site chemical information is centralized. The extraction mechanisms as well as the re-arrangement mechanisms will not be discussed in detail here due to their number and complexity (silicon degree of oxidation, charge transfer, weakening of backbonds…) There last point of this technical discussion is dedicated to the mixing of all these mechanistic steps compared with the axial penetration of molecular oxygen through the silicon layers and particularly through the oxide which is under formation. In particular, when considering the oxidation of multiple silicon layers, the silicon extraction mechanism at the interface is much slower than the diffusion mechanisms. Therefore, we have introduced an alternation of microscopic events (chemical reactions) with macroscopic migration events in the following way. The time duration of the simulated experiment is divided into “dt” time intervals. ”dt” is chosen to satisfy the Poisson criterion, D.dt/d2 <<1: d being the network interlayer distance (silicon or oxide) and D being the associated oxygen diffusion constant. Thus, during dt, microscopic events are performed. At each dt, a diffusion between layers is performed and a average molecular oxygen concentration C(n) is initialized for each network layer (n). The microscopic/macroscopic relation is operated through the molecular reaction occurrence probability written as P=C.ν.exp( -Ea/kbT): ν in the order of the crystal vibrationnal frequency, Ea activation energy of the reaction mechanisms, T temperature, kb boltzman constant. KMC PRELIMINARY SIMULATIONS and VALIDATION On the surface, recent advanced characterization techniques have proposed new insight into the understanding of the initial steps of silicon oxidation [6,11]. From infrared spectroscopy, it has first been demonstrated that silanone structures could be seen at low temperature and low coverage [11]. This Si=O structure having an oxygen atom inserted into the backbond could then be envisaged as a surface intermediate before stoechiometric oxide formation. More recently [6], low temperature STM has demonstrated that this particular structure can be the result of a single oxygen molecule after decomposition onto the clean non-defective silicon surface. For what follows, the KMC code considers the DFT mechanisms shown in table 1 plus the discussed dissociation mechanisms above the surface dimers. The effective sticking of oxygen molecules is considered to be 1, temperature is 200 K, and pressure is 0.005 Pa. The figure 1 presents snapshots of the initial oxidation steps. (a) shows the dissociation of the first molecule on top of a dimer unit: each oxygen atom occupies an “on top” silicon position. In (b), there is two migration leading to the direct formation of a silanone structure as defined in [6,11]: backbond insertion and dimer insertion. (c) is giving a view of the same surface after the dissociation of two other molecules, the diversity of dissociation modes appears, i.e. dissociation between two adjacent dimers. Further steps later, (d) show that four silanone structures have been created. Figure 1: (a) (b) (c) (d) Towards the formation of ultrathin oxide layers, we now consider the mechanisms of extraction followed by further interface re-arrangement of SiO molecules. Figure 2: “stic” top view after oxidation of the first two top layers of Si(100). Oxygen atoms are not represented. These mechanisms have been calibrated in view to reproduce kinetics as well as a layer by layer growth regime as expected experimentally. The temperature is now 993K, the pressure is 2 Pa. The figure 2 shows a top view after oxidation of two silicon layers. The transition between the cubic silicon lattice and the hexagonal sub-units of the tridymite structure is clearly visible. Above the fact that the interface resulting from the simulation exhibits a relatively flat interface, we want here to point out the fact that the local initiation of the tridymite can take several orientations. Due to the lateral expansion of the oxide nuclei, the system is evoluting towards a flat oxide that presents some grain boundaries. This is clear from figure 2 where hexagonal units do not have the same orientation. In this context, many defects are generated by such as-grown films: defects at the interface as well as defects at the grain boundaries. We also want to underline the fact that once initiated on the surface, a specific orientation of a local oxide nuclei also propagates down to the interface: SiO generated at the interface, connect to the SiO2 already existing nearby and having its own specific orientation. CONCLUSION We present an original Kinetic Monte Carlo model designed to simulate the silicon thermal oxidation. We detail intrinsic difficulties facing this modelling procedure, particularly concerning the location of atoms in the context of a lattice based model and concerning the introduction of complex heterogeneous chemical mechanisms. We propose some key elements to allow KMC procedure: sur-imposition of a cubic-tridymite structure, mixing microscopic and macroscopic mechanisms. We demonstrate the potential applications of this model on two aspects: (i) ability to support and complete advanced characterization techniques, (ii) ability to perform process simulation at the atomic scale ACKNOWLEDGMENTS The author wish to thank N. Richard for helpfull discussions, the CALMIP and IDRIS supercomputer centers for computational resources, grants ANR-LN3M and CEA-LAAS for financial support. REFERENCES 1. D.A. Muller, T. Sorsch, S. Moccio, F.H. Baumann, K. Evans-Lutterodt, G. Timp, Nature 399, 758, (1999). 2. B.E. Deal, A.S. Grove, J. Appl. Phys. 36, 3770, (1965). 3. A. Hemeryck, N. Richard, A. Estève, M. Djafari Rouhani, contribution, this conference. 4. N. Richard, A. Estève, M. Djafari Rouhani, Comp. Mat. Sci. 33, 26, (2005). 5. K. Kato and T. Uda, Physical Review B 62, 15978 (2000). 6. A. Hémeryck, A.J. Mayne, N. Richard, A. Estève, Y.J. Chabal, M. Djafari Rouhani, G. Dujardin, G. Comptet, J. Chem. Phys. 126, 114707 (2007). 7. A. Hémeryck, N. Richard, A. Estève, M. Djafari Rouhani, to be published, surf. Sci. lett. 8. A. Bongiorno, A. Pasquarello, Phys. Rev. Lett. 93, 86102, (2004). 9. A. Hémeryck, N. Richard, A. Estève, M. Djafari Rouhani, to be published in Surf. Sci. 10. A. Ourmazd, D.W. Taylor, J.A. Rentschler, J. Bevk, Phys. Rev. Lett. 59, 213, (1987). 11. Y.J. Chabal, K. Raghavachari, X. Zhang, E. Garfunkel, Phys. Rev. B 66, 161315(R) (2002).