Nanoscale to Microscale Monte Carlo Modeling of
Plasma Processing with FPS-3D.
Paul Moroz
Tokyo Electron U.S. Holdings Ltd.
37 Manning Rd., Billerica, MA 01821, USA
Abstract: Predictive modeling of etching, deposition, and surface modification at
nanometer to micrometer scales is very important for advancing nanotechnology
and semiconductor industry to the next level. Such modeling often includes
various competing etching and deposition processes, where final results depend
on many factors, often counteractive or competing with each other such, for
example, as simultaneously going on etching and deposition. The processing
results could be reasonably assessed only experimentally or due to detailed
numerical techniques. The FPS-3D feature profile simulator pushes forward this
task and allows modeling of materials processing at very different scales ranging
from a few nanometers to a few micrometers.
Keywords: plasma, simulation, etching, deposition, materials processing
1. Introduction
2. FPS-3D description
Reliable and predictive modeling for materials
processing would allow significant saving of
time and resources otherwise spent for design
experiments directed to finding proper
chemistries and conditions in a multidimensional parameter space of search for
advanced processing. However, creating a fast,
general, and dependable 2D and 3D
computational modeling simulator, possessing
predictive capability, is a very difficult task.
FPS-3D [12] is a Monte Carlo code, where
launched particles (corresponding to the
specified fluxes, each particle typically
consisting of many gas molecules, or radicals,
or ions, or electrons) interact with solid
materials of the target. A cellular model is used
for presenting solid materials. Each cell has the
same volume but contains different number of
molecules depending on the density of the
corresponding material. A cell is a complex
object consisting of a body and a deposition
layer, each typically including many molecules.
Many attempts have been made in the past (see,
for example, [1-11]) to develop numerical
techniques allowing reliable feature profile
simulations, and significant progress was made
to date. Still it is a long way to go to the final
goal of reliable and predictive simulations that
could be applied to processing in various
conditions used in nanotechnology and
semiconductor industry.
As input parameters, FPS-3D requires that the
fluxes of all reactive species to the surface be
provided. Those fluxes, and their energy-angle
distributions, can be generated by the
corresponding plasma codes. Among those,
which we often use for this purpose, are HPEM
[2,13] or SHEATH-PIC [14]. Incoming fluxes
could also be generated internally by FPS-3D if
the user specifies a corresponding set of
parameters in the input file.
Incoming fluxes are represented by particles.
Each particle is characterized by the kind of
species, as well as by the energy and direction
of flight. The Monte Carlo launcher generates
those species in correspondence with specified
fluxes, so when many particles are launched the
result closely corresponds to the specified
distribution of fluxes on energy and angle.
A size of a Monte Carlo particle (how many
molecules it contains) is typically significantly
smaller than the size of a material cell, so
numerical statistical artifacts could be reduced.
However, too small particles lead to increased
time of simulations. The user has an option to
select a proper compromise between these two
effects by adjusting proper control parameters in
the input file.
All material properties and all reaction
mechanisms are specified in the chemistry file.
The Monte Carlo treatment of gas and ion
reactions is defined by the reaction probability
(or by reaction yield), which might depend on
particle energy and the angle of incidence to the
cell’s normal, as well as on the surface
temperature. There might be a few different
reactions initiated by the same reactants. In this
case, the Monte Carlo algorithm selects a
particular reaction depending on its coefficient
of probability (or yield).
FPS-3D has no limitation on the number of
chemical reactions, or on the number of solid
and gaseous products produced in each reaction.
Whenever there is a reactive gaseous product, it
is put in the list of particles to be tracked.
Because reaction yields could be greater than 1,
and because of a few gaseous reaction species
might be produced from a single reaction, the
code makes sure to track all the reactive gaseous
species until they disappear due to interaction
with surfaces or due to leaving the simulation
volume.
Each chemical reaction includes particular
coefficients for probabilities (or for yields).
Correspondingly, there are many coefficients
which the user should specify before the
simulation can start. It is not an easy task to
properly choose those coefficients, especially
because there could be many reactions and
because there might be reaction with limited
data available. Also, actual process rates depend
not only on energy, angle, or surface
temperature, but also, for example, on the ratio
of neutral to ion fluxes. A specific methodic was
developed for FPS-3D, which recommends how
to select the proper reactions such that a singular
set of reactions can encompass all those
changing conditions. We see this as the only
way to make the code to possess a predictive
capability to different and changing conditions.
3. Results of calculations
Below we present results of calculations for the
case of Si and SiO2 etching by plasma or by
beams of Cl, Cl+, or Ar+. The most detailed and
straightforward tuning of reaction coefficients
can be done when the results of calculations are
compared with the results of beam experiments,
where the species fluxes, the direction of
incident particles and their energies can be
accurately estimated.
FPS-3D could be used for the wide range of
scales, and could simulate features with sizes
varying from a few nanometers to a few
micrometers. This is demonstrated in Figs. 1-3,
where the same case of Si/SiO2 etching by Cl+
ions is presented. Of course, simulation for large
features usually takes significantly more time,
especially if one wants to use small-size cells
for large-size features. In Fig. 1, the feature size
is 0.5 x 1 μm, while it is smaller -- 50 x 100 nm
in Fig. 2, and very small -- 5 x 10 nm in Fig. 3.
One could see different degrees of chlorination
at the bottom and at the sidewalls of the
features. Separate cells are shown in Figs 2 and
3, but not in Fig 1 where the number of cells is
too many to show. The size of a cell in Fig. 3 is
just 3 x 5 Angstroms, but still each cell contains
many molecules. The possibility to consider
small sizes opens an option of tuning FPS-3D
with well-known Molecular Dynamics models,
which are computationally efficient only at
small scales.
Figure 2. Si etching for a feature sized 50 x 100 nm. The cells
are shown. Different materials have different colors.
Finite penetration depth of ions into solid
materials is included in FPS-3D. However, we
do not discuss it here. Correspondingly, to avoid
significant ion penetration deeper than the size
of the cell, we limit ion energy to 120 eV for the
case of Fig. 2 and to 50eV for the case of Fig. 3.
Figure 3. Si etching for a feature sized 5 x 10 nm. A cell size is
about 3 x 5 Angstroms. Different level of chlorination is seen on
the surface.
Figure 1. Si etching for a feature sized 0.5 x 1 μm.
To demonstrate FPS-3D operation in a 3D
mode, Fig. 4 shows trench etching, while Fig. 5
shows via etching. Those are the big-scale
models, and both cases represent Si etching by
Cl/Ar+ plasma. 3D simulations usually take
significantly more time than corresponding 2D
simulations, but in cases such, for example, as
via etching or any other essentially 3D features,
or estimating roughness effects, the 3D option is
the only one capable of properly addressing the
issues.
Conclusions
FPS-3D is a fast, general, and dependable 2D
and 3D feature profile simulator possessing
predictive capability. It can be used for the wide
range of scales, from a few nanometers to a few
micrometers.
Acknowledgments
The author is thankful to Dr. S.-Y. Kang of TEL
TDC for valuable discussions.
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