Document 180340

Mater. Res. Soc. Symp. Proc. Vol. 996 © 2007 Materials Research Society
Oxidation of Silicon: How to deal with a Kinetic Monte Carlo Approach
Anissa AliMessaoud1, Anne Hémeryck2, Alain Estève2, Mehdi Djafari Rouhani2, and Georges
University Saad Dahlab, Lasicom, BLIDA, 09000, Algeria
LAAS, CNRS, TOULOUSE, 31000, France
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.
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.
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.
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
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
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.
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:
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.
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
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.
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