Velocity and charge of the nanoparticles produced by a gas aggregation
cluster source
J. Kousal1, O. Polonskyi1, J. Blažek2, O. Kylian1, J. Pesicka1, H. Biederman1
1
Charles University in Prague, Faculty of Mathematics and Physics, V Holešovičkách 2, 18000 Prague 8, Czech
Republic
University of South Bohemia, Pedagogical faculty, Jeronýmova 10, 371 15 České Budějovice, Czech republict
2
Abstract: A simple and compact gas aggregation cluster and nanoparticle source
based on a planar magnetron (Haberland type) without mass separation was
designed and characterized.
Size, speed and charge of nanoparticles have been determined using combination
of TEM micrographs, electrostatic deflection setup and numeric modelling.
Using the electrostatics model and the TEM micrographs, the velocity of
particles was experimentally found to be 30-200 m.s-1 in dependence on their
size, in an agreement with the simulations.
The charging of nanoparticles was modelled. It was found that the most of the
initial charge of the particle is lost in the afterglow part of the plasma, in general
agreement with experiment.
Keywords: nanoparticles, velocity, charge
1. Introduction
Gas phase production of clusters and nanoparticles
[1] and their deposition became very popular within
the last two decades and various gas aggregation
nanoclusters and/or nanoparticle sources have been
designed (e.g. reviews [2,3]). One should stress the
idea of Haberland et al. [4] to use a planar
magnetron as a source of the material. This approach
made it possible to produce a large number of
charged clusters in relatively simple way. In order to
increase the deposition rate of the particles we
decided to design simple and compact nanoparticle
source similar to the Haberland concept that could
be placed into a high vacuum chamber. Silver target
was chosen as a model metal. The basic parameters
of the source in terms of size distribution of the
deposited particles and the ratio of negatively and/or
positively charged to neutral particles in dependence
on the working parameters were studied [5]. The
presented study is aimed at the characterization of
the velocity and charge of the nanoparticles.
2. Theory
In our gas aggregation source the material is
sputtered from the target and forms nanoparticles
that are dragged by the flow of the carrier gas. These
nanoparticles are then extracted from the source
through an orifice into the deposition chamber with a
substantially lower pressure.
Since the pressure inside the source is usually from
several Pa to several hundred Pa and the velocity of
the carrier gas flow inside the source is some tens of
cm/s, the carrier gas can be treated as viscous
laminar flow in the cylindrical part of the source. At
such conditions the nanoparticles are flying inside
the source with velocity equal to the drift velocity of
the gas.
However, this is not true in the area near the orifice,
where a pressure drop of several orders of magnitude
occurs over the length of several millimeters. This is
accompanied by a strong acceleration of the carrier
gas flow due to the expansion. Since the mass to the
crossection ratio of the nanoparticle increases with
its diameter and the carrier gas density decreases
during expansion, the particles do not undergo
enough collisions with light gas atoms to equalize
their velocity and direction with the gas. This effect
is more pronounced for heavier particles that leads
e.g. to the so called aerodynamic lensing [6].
Analytical theory of the acceleration of nanoparticles
near in the conical orifice with purely conical walls
is nicely treated in [7]. For a particular pressure and
temperature in the source it leads to the dependency
of the final velocity v of the nanoparticle on its mass
m in the form v  m-2/9.
The simulation of gas dynamics also shows that
influence of the carrier gas on the nanoparticles after
leaving the source is negligible. This enables
manipulation of the trajectory of the charged
nanoparticle is manipulated by an electrostatic field.
The basic idea of this experiment is shown in
Figure 1. The beam of the nanoparticles enters a
region with electrostatic field and particles that are
charged are deflected. The deflection y is
proportional to
y  q / m v02
where q is the charge of the particle, m is its mass
and v0 is its velocity.
The particle velocity can be then, under the
assumption of specific charge, determined from
measured particle deflection and its mass. The
particles of the same mass can have certain velocity
distribution. By measurement of the smallest and
largest particles deflected into given position it is
possible to determine the maximal and minimal
velocity for the given mass, respectively.
Figure 1. Scheme of the setup for the measurement of the
nanoparticle (NP) velocities using their mass/charge separation
and histogram of their size obtained from TEM micrographs.
Since the nanoparticle source used in this study is
equipped with cylindrical orifice in order to suppress
the effects of aerodynamic focusing, we have made a
direct 2D Monte Carlo simulation of the carrier gas
flow near the orifice using the DS2V code [8]. We
have simulated a domain from 13 mm before the
orifice plane to 50 mm after it.
Since our source produces relatively narrow beam of
nanoparticles (half-angle of about 6 degrees), we
treated in this work the acceleration region as
basically a 1D problem. Using the data from the gas
flow simulation, we can numerically integrate the
momentum transfer equation [7] along the axis of
the orifice to obtain the final velocity of a particle
with particular diameter and mass.
This calculation predicts 2-3 times higher velocities
of nanoparticles in comparison with the analytical
theory, from 80 m/s for 5 nm particles to 30 m/s for
40 nm particles.
To improve the accuracy of the velocity estimation,
a 2D electrostatic model of the setup was made
using QuickField software [9]. The velocity of the
particles was then found using numerical calculation
of their trajectories.
It is known that the Haberland type source produces
neutral particles and charged particles of both
polarities [5, 10, 11]. In so called "dusty plasma" the
particles obtain a negative charge proportional to
their diameter of about 103 elementary charges per
micrometer [12]. On the contrary, experiments with
Haberland type source are consistent with the
assumption of only unit charge of the nanoparticle,
regardless of its size. It can be attributed to the fact
that the particles in the gas aggregation source are
not suspended in the homogeneous plasma as the
carrier gas flow transports them through the
aggregation chamber. Some model of nanoparticle
charging is provided in [7].
We have developed another model using a set of
kinetic equations. The charge of nanoparticles was
investigated in the frame of standard continuous
charging model as well as in a model, which takes
into account statistical distribution of discrete
charge. The suggested statistical model is based on a
set of unlimited kinetic equations with solution
obtained recurrently.
It can be assumed that the nanoparticles are formed
near the magnetron erosion track and the gas flow
transports them through the afterglow region out of
the aggregation chamber. Thus the problem can be
treated as a charging of static particle in the plasma
with time dependent density.
For simplicity both models were divided into two
parts, with the first part concerning the active plasma
and the second one concerning the afterglow plasma.
In the active plasma the charge distribution is spread
in negative region. In the afterglow plasma the
negative charges quickly tend to zero. The final
charges are symmetrically distributed around zero,
i.e. both positive and negative values are equally
present. The particles are mostly neutral or singly
charged.
Knowing almost all the input parameters (initial
angle of the flight, deflection, mass of the particle,
geometry of the setup, electric potentials) and
assuming single charge of the particles, the initial
velocity (limits of velocity) for the particular case
was found.
4. Results and discussion
Both theoretical and experimental values of the
velocity of the nanoparticles of given mass are
shown in the Figure 2.
The velocity of the bigger (>15 nm) particles is in a
general agreement with the simulations and their
velocities are strongly dependent on their mass.
Some reason for the observed discrepancy with the
smaller particles can be the error in the estimation of
the size of the particle, which may be due to limited
resolution of TEM. . However, in all cases the
kinetic energy of the particles is well below the
0.1 eV/atom what confirms that the particles hit the
surface in soft-landing regime [15].
3. Experimental
d [nm]
The description of the nanoparticle source used in
this study can be found in [5, 13].
10
20
30
40
50
300
experiment
The deflection plates were placed 10 mm from the
orifice of the source. The length of the plates was
20 mm and their distance was 12 mm. The voltage
difference between the plates was 30-400 V (in both
polarities). The total distance from the orifice of the
source to the sample plane was 50 mm. The diameter
of the beam of the particles at this distance was
10 mm. The carbon foil sample for TEM
micrographs was placed about 10 mm from the
center of the beam.
The TEM samples were investigated using Jeol
2000FX electron microscope and the images were
processed using imageJ software [14]. From each
sample a histogram of diameters (masses) of the
nanoparticles was obtained. The histogram was then
used as described in the previous section.
200
(q= 1e assumed)
simulation
-1
v [m.s ]
The nanoparticles were prepared at the pressure of
75 Pa of argon in the aggregation chamber and
0.1 Pa in the deposition chamber. The magnetron
current was 0.2 A.
100
90
80
70
60
50
40
30
20
10000
100000
1000000
n
Figure 2. Predicted and experimentally determined velocity of
both positively and negatively charged nanoparticles vs. number
of atoms in the particle resp. the diameter of the particle.
These data also show that the assumption of single
charge of the particles (both for positive and
negative ones) is quite reasonable, since the
calculated value of the nanoparticle velocity scales
with its expected charge as v0  q1/2.
These findings can be explained in a following way:
The nanoparticle (nanocluster) is formed near the
erosion track of the magnetron in dense plasma and
mostly obtains a high negative charge. The particle
is then dragged by the carrier gas flow through the
afterglow region of the plasma where the charge of
the particle is being quickly lost. However, the
negative charge is lost quicker than the positive one.
In the end a mixture of neutral and singly charged
positive a negative nanoparticles is expelled from
the source. Such process was in general numerically
modeled and a qualitative agreement with
experiment was obtained. However, the more
detailed description of nanoparticles charging and
de-charging is a subject of ongoing study [16].
5. Conclusions
The velocity of the nanoparticles was found to be
dependent on their size. The velocity increased from
30 m.s-1 for 50 nm particles up to about 70 m.s-1 for
15 nm particles. However, velocity of smaller
nanoparticles
(≤7 nm) can reach more than
200 m.s-1. The numerical simulation of their
acceleration in the carrier gas is in reasonable
agreement with experiment.
The experimental results are also consistent with
zero or single positive or single negative charge of
the nanoparticles. The model of their charging is
being successfully developed.
Acknowledgement
This work is a part of the research plan
MSM0021620834 financed by the Ministry of
Education of Czech Republic and was partly
supported by the Grant Agency of the academy of
Sciences of the Czech Republic under contract
KAN101120701.
[4] H. Haberland, M. Karrais, M. Mall, Y. Thurner,
J.Vac.Sci.Technol.A. 10 (1992) 3266.
[5] O. Polonskyi, P. Solař, O. Kylián, M. Drábik,
A. Artemenko, J. Kousal, J. Hanuš, J. Pešička,
I. Matolínová,
E. Kolíbalová,
D. Slavínská,
H. Biederman, Thin Solid Films, (2011), in press,
DOI: 10.1016/j.tsf.2011.04.100
[6] F. Di Fonzo,
A. Gidwani,
M. H. Fan,
D. Neumann, D. I. Iordanoglou, J. V. R. Heberlein,
P. H. McMurry,
S. L. Girshick,
N. Tymiak,
W. W. Gerberich, N. P. Rao, Appl.Phys.Lett. 77
(2000) 910-912
[7] B. M. Smirnov,
I. Shyjumon,
Phys.Rev. E, 75, 2007
[8] G. A. Bird, Molecular Gas Dynamics and the
Direct Simulation of Gas Flows, Oxford University
Press (1994) gab.com.au
[9] QuickField, www.quickfield.com
[10] I. Shyjumon, M. Gopinadhan, C. A. Helm,
B. M. Smirnov, R. Hippler, Thin Solid Films 500,
(2006) 41
[11] S. Pratontep,
S. J. Carroll,
C. Xirouchaki,
M. Streun, R. E. Palmer, Rev.Sci.Instrum. 76 (2005)
045103
[12] M. Bonitz,
C. Henning,
Rep.Prog.Phys. 73 (2010) 066501
[1] K. Sattler, J. Mühlback, E. Recknagel, Phys.
Rev. Lett. 45 (1980), 821.
[2] C. Binns, Surface Sci. Rep. 44 (2001)
[3] K. Wegner,
P. Piseri,
H. Vahedi Tafreshi,
P. Milani, J. Phys. D: Appl. Phys. 39 (2006) R439–
R459
D. Block,
[13] O. Polonskyi, O. Kylián, J. Kousal, P. Solař,
A. Artemenko,
A. Choukourov,
D. Slavínská,
th
H. Biederman, Proc. of 20 ISPC, 2011
[14] ImageJ, http://rsb.info.nih.gov/ij/
[15] H. Haberland,
Z. Insepov,
Phys.Rev.B 51 (1995) 11061
[16] J. Blažek, in preparation
References
R. Hippler,
M. Moseler,