Optimization of curtain gas injection position and flow rate in a conical reaction
chamber for Si nanoparticle synthesis by inductively coupled thermal plasmas
M. Boselli2, V. Colombo1,2, E. Ghedini1,2, M. Gherardi1, P. Sanibondi1
Alma Mater Studiorum – Università of Bologna
1
Department of industrial engineering (DIN)
2
Industrial Research Center for Advanced Mechanics and Materials (C.I.R.I.-M.A.M.)
Via Saragozza 8-10, 40123 Bologna, Italy
Abstract: In this paper, we report on design oriented modelling for the optimization of gas
injection in a reaction chamber for silicon nanoparticle synthesis by inductively coupled
thermal plasmas. The number of injection points, their position along reaction chamber walls,
the gas flow rate and the direction of injection has been investigated, with the final aim of
controlling particle size while maintaining high process yield. A computational approach is
adopted to describe plasma thermo-fluid dynamics, electromagnetic field, precursor
trajectories and thermal histories, and nanoparticle nucleation and growth, being the latter
modelled using the moment method.
Keywords: Thermal plasmas, Nanoparticle synthesis, Modelling
1. Introduction
Increasing attention has been devoted to nanoparticle
production technology in the last decades as a
consequence of the increasing interest for nanoparticle
properties, such as modified physical properties with
respect to bulk materials and high area to volume ratio,
that allow their successful use in biomedical, optical,
energy and electronic applications [1].
Inductively coupled thermal plasma technology, whose
distinctive features are high energy density, high process
purity, large plasma volume and long residence time, has
proven to be a viable means for nanoparticle synthesis.
Productivity, product quality control and affordability are
the main challenges still to be solved for this technology
[2]. Over the last few years, many studies have been
directed towards the optimization of the synthesis of
nanoparticles by inductively coupled thermal plasma,
intended for the production of nanoparticles of specific
size and with a narrow PSD [3]. Also, the use of conical
reaction chamber geometry and of a curtain gas to protect
the reaction chamber walls from nanoparticle deposition
has been suggested to increase the yield of the process,
defined as the ratio of nanoparticles mass flow rate at the
outlet of the reaction chamber and precursor feed rate [4].
In this paper, we report on design oriented modelling
for the optimization of a process for silicon (Si)
nanoparticle synthesis in an inductively coupled plasma
system. In particular, the optimization of gas injection in
the reaction chamber is addressed: the number of curtain
gas injection points in a conical reaction chamber, their
position along reaction chamber walls, the gas flow rate
and the direction of injection has been investigated, with
the final aim of controlling particle size while maintaining
high process yield. A computational approach is adopted
to
describe
plasma
thermo-fluid
dynamics,
electromagnetic field, precursor trajectories and thermal
histories, and nanoparticle nucleation and growth and to
predict process yield and mean nanoparticle diameter at
the reaction chamber outlet.
2. Modelling approach
A 2-D model for the plasma torch and reaction chamber
has been implemented in the ANSYS FLUENT©
environment in an axisymmetric geometry. The model
include the following hypothesis:
Plasma is in local thermodynamic equilibrium
(LTE);
Combined diffusion approach of Murphy is used to
model the diffusion in a mixture of argon and
hydrogen;
Turbulent effects are taken in account through either
standard k-ε model;
Plasma is optically thin and radiative losses are
taken in account considering only the presence of
argon in the mixture; resonance lines are neglected
in the computation of radiative losses;
Composition is computed taking in account six
species: Ar, Ar+, H2, H, H+ and electrons.
Mass, momentum and energy equations are solved as in
[4] in coupling with electromagnetic field equations
written in the vector potential form. Precursor trajectory
and thermal histories have been modelled using a
Lagrangian approach, with the final aim of calculating
precursor evaporation. Precursor vapours have been
tracked by means of an additional an advection-diffusion
equation for the vapour mass fraction, considering no
influence of the vapours on the plasma properties. The
nucleation, growth and transport of nanoparticles have
been modelled using the moment method for the solution
of the General Dynamics Equation (GDE) for aerosols. In
this method, the aerosol GDE is mathematically
reformulated in order to obtain a system of equations that
is easier to solve; the first three moments of the
nanoparticle size distribution function are handled. The
zero-th moment represents the total concentration of the
generated nanoparticles, while the first moment
corresponds to their total volume. Meanwhile, the second
moment is proportional to the light scattered by the
nanoparticles in case their size is much smaller than the
wavelength of the incident light. Transport equations for
the first three moments are solved, assuming a log-normal
shape of the particle size distribution and including
turbulent effects in the diffusion term of transport
equations, as done in [4].
The 2-D domain analysed in this work included a
PL-35 Tekna plasma source and an axisymmetric reaction
chamber with multiple gas injection points, schematically
shown in Fig. 1.
Fig. 1 Detail of the computational domain: torch region
(left) and reaction chamber (right). Dimensions in mm.
The origin of x-axis is located at the top of the reaction
chamber. Working gases are supplied through three
different inlet regions located in the head of the torch:
carrier gas from the probe tip (6 slpm pure Argon),
primary gas from the gap between the probe and the
quartz tube (12 slpm pure Argon) and sheath gas from the
inlet between the quartz and ceramic tubes (60 slpm Ar +
6 slpm H2). Additional argon gas is supplied to the
reaction chamber to influence the synthesis process,
details are reported in Table 1. A no-slip boundary
condition is applied on all the internal walls, while a 300
K temperature has been fixed at the external walls of the
torch and the internal walls of the chamber. The operating
pressure has been fixed at 40 kPa. The electromagnetic
field equations are solved in an enlarged domain
extending 40 mm outside of the torch in the y-direction,
using the extended field approach [3]. The coupled power
has been set to 10 kW, which corresponds to typical
lab-scale generator plate power of 18. The precursor is set
to be solid micrometric silicon characterized by a particle
size distribution with mean diameter equal to 10 m and
by a feed rate equal to 3.5 g/min.
Table 1. Parameters for the injection of gas in the reaction
chamber for different cases.
Total chamber
Injection
Injection
Cases
flow rate
points
direction
[slpm]
Case 0
0
None
None
Case 1A
260
P1-P6
Axial
Case 1B
520
P1-P6
Axial
Case 1C
260
P4-P6
Axial
Case 1D
260
P1-P3
Axial
Case 1E
260
P2
Axial
Case 1F
260
P4
Axial
Case 1G
260
P6
Axial
Case 2A
260
P1-P6
Radial
Case 2B
520
P1-P6
Radial
Case 2C
260
P4-P6
Radial
Case 2D
260
P1-P3
Radial
Case 2E
260
P2
Radial
Case 2F
260
P4
Radial
Case 2G
260
P6
Radial
3. Results
First, the case with no injection of gas in the reaction
chamber will be analysed and considered as a reference
case (case 0). In figure 1, the contours for gas temperature
and for streamlines are reported: plasma temperature is
maximum in the torch region (11000 K), whereas in the
reaction chamber the gas is rapidly cooled by conduction
of heat to the water cooled chamber walls; a recirculation
flow pattern is formed in the conical part of the chamber.
The vapour consumption distribution is shown in figure 2,
together with the predicted nanoparticle mean diameter:
the vapour is consumed during its conversion to
nanoparticles in the upper part of the chamber, which
results in a mean nanoparticle diameter increase or
increasing axial positions, leading to a mean diameter at
outlet equal to 92 nm. However, most of nanoparticles are
deposited to the walls before reaching the chamber outlet,
with a predicted yield of 25%.
With an injection of gas from six different points in the
axial direction (case 1A), the plasma is more rapidly
cooled with respect to case 0 and the recirculating flow
pattern is avoided. The region where vapour consumption
occurs (figure 3) is slightly shifted towards the chamber
axis and the diameter at outlet is greatly reduced due to
lower nanoparticle residence time in the reaction chamber.
For this case, the yield is improved as a consequence of
wall protection by the injected gas.
Fig. 2 Temperature and stream function for cases 0
(left), 1A (center) and 2A (right).
Fig. 3 Vapour consumption and nanoparticle mean
diameter for cases 0 (left), 1A (center) and 2A (right).
In case 2A, the six radial injections points induce a
stronger cooling of the plasma tail (figure 2) and the
vapour is converted to nanoparticle at an upper position in
the chamber with respect to case 0 and 1A. The higher
quenching rate results in mean diameter at outlet lower
than case 1A.
The injection of gas with a higher flow rate in axial
direction (cases 1B) results in a higher yield (85%),
whereas in radial direction (case 2B) induces a higher
quenching rate and the production of nanoparticles with
smaller mean diameters (see figure 4).
The use of only three injection points in axial direction
(cases 1C and 1D) results in a yield of 65-70%, but the
mean diameter of particles at outlet is slightly increased
(up to 60 nm). On the contrary, injecting the chamber gas
with three points P1-P3 in radial direction (cases 2D)
results in a stronger quenching of the plasma tail, which
can be deducted from the upper position of the region
where vapour consumption is significant (see figure 5),
leading to the production of smaller nanoparticles (35 nm).
Radial injection of gas from points P4-P6 (case 2C) is not
effective for quenching and for the production of smaller
particles, because in this case the cooling affects a spatial
region that is downstream the region with higher vapour
consumption rate.
Injection of gas from one single point strongly modifies
the flow patterns in the reaction chamber as can be seen
from vapour consumption fields reported in figures 6 and
7.
Fig. 4 Contours of vapour consumption and
nanoparticle mean diameter for cases 1B, 1C and 1D.
producing a stronger cooling and a reduction of mean
nanoparticle size (30 nm at outlet for case 2E). However,
for these cases the yield is lower than 55%.
Case 2E is the one with lowest mean diameter at outlet for
a total flow rate of 260 slpm, whereas case 1B is the one
with highest process yield.
Fig. 5 Contours of vapour consumption and
nanoparticle mean diameter for cases 2B, 2C and 2D.
Fig. 7 Contours of vapour consumption and
nanoparticle mean diameter for cases 2E, 2F and 2G.
4. Conclusions
Design oriented modelling for the optimization of gas
injection in a reaction chamber for silicon nanoparticle
synthesis by inductively coupled thermal plasmas has
been carried out. For the cases investigated, it is shown
that injection of gas in the reaction chamber induces a
higher yield of the process and a lower mean diameter at
reaction chamber outlet. A radial injection results in lower
nanoparticle mean diameter, whereas the axial injection
along reaction chamber walls is more effective in
producing a higher process yield.
Fig. 6 Contours of vapour consumption and
nanoparticle mean diameter for cases 1E, 1F and 1G.
Cases with axial injection (cases 1E, 1F, 1G) are
characterized by a yield of 40-55% and a mean
nanoparticle diameter at outlet of 60 nm. The radial
injection from a single point is more effective in
References
[1] M. Shigeta and A. B. Murphy, J. Phys. D: Appl. Phys.
44, 174025 (2011)
[2] M. I. Boulos, Pure Appl. Chem. 57, 1321 (1985)
[3] V. Colombo, C. Deschenaux, E. Ghedini, M. Gherardi,
C. Jaeggi, M. Leparoux, V. Mani and P. Sanibondi
Plasma Sources Science and Technology, 21, 045010
(2012)
[4] V. Colombo, E. Ghedini, M. Gherardi, P. Sanibondi
and M. Shigeta, Plasma Sources Science and
Technology, 21, 025001 (2012)