22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Modulation of the plasma properties by direct current sources in capacitively
coupled argon discharges
Y.R. Zhang1,2, F. Gao1, Y.-H. Song1, A. Bogaerts2 and Y.N. Wang1
1
Key Laboratory of Materials Modification by Laser, Ion, and Electron Beams (Ministry of Education), School of
Physics and Optoelectronic Technology, Dalian University of Technology, 116024 Dalian, P.R. China
2
Research group PLASMANT, Department of Chemistry, University of Antwerp, 2610 Antwerpen-Wilrijk, Belgium
Abstract: In this paper, a one dimensional fluid model has been employed to investigate
the plasma characteristics, especially the plasma density and the flux above the wafer, in a
hybrid dc/RF (direct current/radio frequency) capacitively coupled discharge. The results
indicate that the dc source has different influences on the plasma properties under various
discharge conditions.
Keywords: hybrid dc/rf discharges, fluid model
1. Introduction
Capacitively coupled radio frequency discharges are
widely used for industrial applications, such as etching
and deposition processes. Recently, the combined dc/RF
(direct current/radio frequency) plasma source has
received increased attention due to the energetic electrons
generated in the dc sheath, which may alleviate charging
of the bottom of high aspect ratio features etched in
insulators[1-4].
Indeed, the positive charges are
accumulated at the trench bottom of the dielectric, and
this accordingly distorts the electric field and gives rise to
the formation of the notch. When a negative bias is
applied to the top electrode, the ions are accelerated and
bombard the dc electrode. Subsequently, secondary
electrons are generated, and they have enough energy to
travel a large distance towards the bottom electrode, and
neutralize the positive ions accumulated there. Therefore,
in this work, we investigate the influence of the dc source
on the discharge properties of capacitively coupled
discharges under various conditions.
2. Fluid model
In this work, a one dimensional fluid model has been
employed to investigate the plasma characteristics,
especially the plasma density and the flux above the wafer,
in a hybrid dc/RF capacitively coupled discharge. For the
purpose of studying the physical mechanisms, argon is
adopted as the working gas. In the simulation, electron
impact ionization, excitation, de-excitation, stepwise
ionization, metastable pooling and quenching are included,
and more details of the reaction set can be found in table
3.3 of [5]. The discharge is sustained between two
parallel plate electrodes, both of which are assumed to be
infinite. The top electrode is driven by a negative dc
source, and another RF source is applied on the bottom
electrode.
In the fluid model, the plasma can be treated as a
continuum, and the behaviour of the species can be
described by continuity equations, momentum balance
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equations and energy balance equations. Since the
electron mass is very small, the inertial term can be
ignored, so the electron flux can be presented in the driftdiffusion form. Because the ions can be assumed at room
temperature, no energy balance equation is needed for
them. Besides, the potential and the electric field are selfconsistently obtained by solving the Poisson equation.
3. Results and Discussions
We have varied the dc voltage from 0 V to -400 V, to
investigate the influence of the dc source on the plasma
properties. The pressure is set to 50 mTorr, and the
frequency and voltage of the RF source are 60 MHz and
250 V, respectively.
The different influences of the dc source on the peak
value of the electron density, calculated for various
secondary electron emission coefficients γ, are apparent
from Fig. 1. It is clear that when the secondary electrons
are not included, i.e., γ=0, the electron density decreases
with increasing dc voltage. This is because when the dc
source is switched on, an electron-free sheath is generated
near the dc electrode, and therefore this reduces the bulk
plasma width. When γ increases to 0.05, the electron
density shows a strikingly different trend with rising dc
voltage. Indeed, the peak value of the electron density
first increases slightly when adding a small dc bias, and
then it decreases, with the minimum appears at a dc
voltage of -300 V. As the dc voltage increases further,
the plasma density increases again. For γ = 0.1, the
electron density exhibits a similar evolution with dc
voltage, except that the minimum of the electron density
appears at -160 V, and the density increases significantly
to 1.3×1011 cm-3 at -400 V. This trend can be explained
because when a small dc voltage is applied, although the
bulk region is suppressed by the dc source, the ionization
enhanced due to the secondary electrons plays a dominant
role in the discharge, and this gives rise to an increase in
the electron density. When the bias voltage becomes
higher, the bulk region is significantly reduced, and so is
1
the ionization rate. As the bias voltage increases further,
more energetic secondary electrons are generated, and the
α−γ discharge mode transition occurs under this condition.
For γ = 0.15, the peak value of the electron density
increases monotonically with the bias voltage, which
indicates that the secondary electron induced ionization
plays a dominant role under all the selected dc voltages.
at lower frequencies, the discharge is mainly sustained by
the secondary electron induced ionization rather than the
ionization by the bulk plasma. As the dc voltage
increases, more energetic secondary electrons are
generated, and they collide with neutral species, and
consequently this causes a remarkable ionization. As the
frequency increases to 60 MHz and 100 MHz, the
electron density first rises slightly, but then it drops, and
finally it rises again more significantly with dc voltage.
Especially at 100 MHz, the decreasing trend is obvious.
This is explained by the strong competition between the
bulk plasma heating and the secondary electron heating at
higher frequencies.
Figure 1. Peak values of the electron density, as a
function of dc voltage, for various secondary electron
emission coefficients.
By fixing γ = 0.1, the influence of the dc voltage on the
electron density has also been investigated under various
pressures, as shown in Fig. 2. When the pressure varies
from 50 mTorr to 200 mTorr, the peak value of the
electron density first increases (slightly), then decreases
(slightly), and finally increases again with dc voltage.
However, the influence of the dc source on the electron
density becomes different at 400 mTorr. Indeed, the
electron density first increases rapidly, then slightly, and
finally it increases significantly again, due to the stronger
secondary electron effect at higher pressures.
Figure 2. Peak values of the electron density, as a
function of dc voltage, for various pressures.
Finally, the dc source effect on the plasma properties is
examined at different radio frequencies, with the pressure
at 50 mTorr. In the range of low frequency, i.e.,
13.56 MHz and 27.12 MHz, the peak value of the electron
density increases monotonically with dc voltage. Indeed,
2
Figure 3. Peak values of the electron density, as a
function of dc voltage, for various radio frequencies.
4. Conclusion
In this paper, a one dimensional fluid model has been
employed to investigate the influence of the dc source on
the plasma characteristics, for various secondary electron
emission coefficients, pressures and radio frequencies.
The results indicate that the peak value of the electron
density decreases with dc voltage when the secondary
electrons are not included. As the secondary electron
emission coefficient becomes higher, the electron density
first increases, then decreases, and finally increases again.
Moreover, when the secondary electron effect becomes
dominant, i.e., at higher pressures and lower radio
frequencies, the discharge is mainly sustained by
secondary electrons, and the electron density increases
monotonically with dc voltage. This study is important
for controlling the profile of high aspect ratio features
during plasma etching. Indeed, by adding a negative dc
source on the top electrode, the electron density can be
modulated by adjusting the dc voltage, and the
modulation is different for various secondary electron
emission coefficients, pressures and radio frequencies. In
practical etching processes, the higher electron flux above
the wafer could neutralize the positive charge
accumulated at the trench bottom, and this gives rise to a
better etching profile.
5. Acknowledgments
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This work was supported by the National Natural
Science Foundation of China (No. 11405019, 11335004,
11275038, 11205025), the Important National Science &
Technology Specific Project (No. 2011ZX02403-001),
the International Science and Technology Cooperation
Program of China (No. 2021DFG02150), and the joint
research project in the framework of the agreement
between MOST and FWO.
[2]
[3]
[4]
[5]
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