Download Modeling and experimental studies of radical formation in RF discharges with etching gases

Modeling and Experimental Studies of Radical Formation in RF
Discharges with Etching Gases
Y. Yasaka T. Kawamura, Y. Takada, and A. Tsuji
Dept. Electrical and Electronic Engineering, Kobe University, Kobe 657-8501, Japan
Abstract: Modeling of plasma production combined with gas phase chemical
reaction can be very useful in predicting formation of radical species. However,
knowledges of electron impact cross sections of molecules such as C5F8 are not
enough to construct a set of chemical equations necessary for the modeling.
Quantum chemistry calculations are used to obtain approximate values of the
cross sections of ionization, dissociation, and dissociative ionization. The total
modeling of RF discharges (2D fluid model), which includes RF wave
propagation, plasma transport, and gas phase chemical reaction, is performed and
2D profiles of radicals as well as plasmas are obtained for He/c-C 5F8 discharges.
The calculation results are compared with experimentally measured densities of
radicals by QMS.
Keywords: Modeling, fluid simulation, etching, gas phase reaction.
1. Introduction
Radical species in plasmas used for etching
processes are important in the sense that they
determine the parameters such as etching rate,
anisotropy, and selectivity. In addition to the
conventional SF6/O2 use is made of C4F8, C5F8, and
CHmFn for Si or SiO2 etching to control F/C ratio,
which affects the rates of the bottom etching and
deposition to side walls of a trench. Modeling of
plasma production combined with gas phase
chemical reaction can be very useful in predicting
formation of radical species [1]. However,
knowledges of electron impact cross sections of
molecules such as C5F8 are not enough to construct a
set of chemical equations necessary for the modeling.
We use quantum chemistry calculations [2] by
Gaussian03 [3] to obtain approximate values of the
cross sections of ionization, dissociation, and
dissociative ionization. The total modeling of RF
discharges (2D fluid model), which includes RF
wave propagation, plasma transport, and gas phase
chemical reaction, is performed and 2D profiles of
radicals as well as plasmas are obtained for He/ c-
C5F8 discharges. We also measure densities of
radicals by QMS and compare them with the
modeling results. It is found that the radical species
and their relative amounts are in overall agreement
between the modeling and the experiment.
2. Modeling
2.1 Two-dimensional fluid model
The simulation code numerically analyzes the plasma
maintained by global electric fields via wave
propagation. The code repeatedly calculates wave
propagations, plasma transports, and gas phase
chemical reactions after loading external input files
of configuration setting, parameters, initial condition
and cross section data. The storage spaces are given
to all parameters necessary for the calculation, and
the parameters in storage spaces are successively
updated in each calculation. The finite element
method is used for the calculation of the global
electric field E via wave propagation, which is given
by

(1)
   E   2 0 0  E  i0 J ext ,

where ω, 0, 0,  , and Jext are the frequency of the
wave, permeability, permittivity in vacuum,
dielectric tensor, and the external RF current (power
source), respectively. The power absorption Pabs of
electrons from the wave field is calculated using
 *T 
1
(2)
pabs  i 0 E       E 
4
where * is the complex conjugate, and T is the
transposition. The time development of the density ne
and the electron temperature Te of Maxwellian
plasma is calculated by mass and energy conservation
equations represented by
ne
(3)
   ne v   n j   i j v  ne 
t
and

  3
5

ne k BTe      k BTe ne v  q   pabs



t  2
2


(4)


 3m

    m j k BTe   n j   i j v  Vi j  ne 


j  M
i



where v is the electron velocity,  i j is the cross
section of the electron impact collision of kind i to
species j, q is the thermal flux, kB is the Boltzmann
constant, vmj is the elastic collision frequency with the
species j, and Vi j is the threshold potential for the
related i, j collision, respectively. We use the plasma
approximation that the ion density is equal to ne and
nev is represented by the ambipolar diffusion:
ne v   Dne with D being the ambipolar diffusion
coefficient. Furthermore, the density nk of k-th neutral
particle in gas phase is calculated by rate equation
represented by
nk
  ne  i j ,k v n j   Rk j l n j nl
t
j
j l
(5)







n
e
j



jkl l 


 i k , j v   R n nk    Γ k
j l
where ns is the density of species s  k  j , or l ,  i j ,k
is the cross section of the i-th kinnd electron impact
collision to species j with the product of species k, R
is the rate coefficients for neutral–neutral and ion–
neutral reactions, and Γ k is the particle flux of species
k. The Euler method is applied to Eq. (5) because the
Courant condition is not stringent due to small values
of the diffusion coefficient of neutral species. It is
assumed in solving Eq. (5) that the densities of
unsaturated species are zero on the wall and that the
density gradient of saturated species is zero at the
wall along the normal vector. We use the latter
boundary condition for some of the unsaturated
species which have a small sticking coefficient.
2.2 Electron impact collision
In order to calculate Eq.(3)-(5), we need to know the
values of  i j for i-type collisions of electrons with
species j. We determine the values of cross section of
c-C5F8 that was not reported in literature by using
Gaussian03. The density functional theory (DFT)
method is used for structural optimization with 6311G+ basis set, and excitation energies are obtained
by using configuration interactions of singles (CIS)
method. For example, the ionization cross section is
obtained as follows; using DFT, structural
optimizations are performed for c-C5F8 and c-C5F8+
to find the difference in potentials, Ui, of the two
states. The cross section is given by the Thompson
formula;
2
 ion
 e2  1  1 1 

   , W  U i ,
  
 4 0  W  U i W 
(6)
where W is the kinetic energy of electrons. The
values of   ion v  is then calculated by, using the
velocity distribution function of electrons F̂e ,

  ionv    ion (W )v(W )Fˆe (W )dW
(7)
The same procedure is repeated for fragment species
of c-C5F8 such as C5F7, C4F6, and so on.
0
3. Simulation results
The bottom half of the sketch in Fig. 1 shows
configuration of a model device, which consists of a
glass tube of 100  with a helicon RF antenna at a
frequency of 13.56 MHz, three solenoid coils
producing the axial magnetic field, and a metal
chamber of 350 . He gas is injected from the left
end of the device as a buffer gas and c-C5F8 at the
metal chamber as a material gas. The total gas
pressure is 14.0 mTorr and RF power is 500W. The
top half in Fig. 1 depicts the distribution of ne, which
indicates that the plasma is mainly produced under
the RF antenna and diffuses axially along magnetic
field lines. The distribution of Te is much more
uniform along the axis, but radially inhomogeneous
with peak values of 9.6 eV under the RF antenna and
2~1.5 eV in the metal chamber.
in (b) and (c). They are much less dense in the glass
tube where further dissociation of radicals would
occur due to higher electron temperatures.
4. Experimental results
A quadrupole mass analyzer (QMS) is attached at the
center of the right-end of the device shown in Fig. 1.
In Fig. 3, ion species from the plasma is measured by
applying a small negative voltage to an extractor and
without using electron beam in an ionization chamber
of QMS. Many species produced by ionization and
dissociative ionization of c-C5F8 in the plasma are
observed. Ions of lower mass number such as C3F3,
CF3, CF2, and CF are also found.
Figure 1. Simplified sketch of the simulation device
(bottom half) and the calculated distribution of electron
density [cm] (top half).
1000
C5F8
SIMS mode
C4F5+
We have included ionization, dissociation, and
dissociative ionization of c-C5F8 in the simulation and
resultant products are C5F7, C4F6, C5F7, C4F5, C3F7,
C2F4, C3F3, CF3, CF2, CF, and their ions. Calculated
distributions of some radical species are given in Fig.
2. The density of c-C5F8 is concentrated at the inlet
and very low in other regions as seen in (a) because
of immediate dissociation or dissociative ionization.
Products by electron impacts to c-C5F8, C5F7 or CF3,
are widely distributed in the metal chamber as shown
(a) C5F8 [cm]
(b) C5F7 [cm]
(c) CF3 [cm]
Figure. 2 Calculated distribution of species of c-C5F8, C5F7,
and CF3 in unit of cm.
count/s
C4F6+
C5F7+
100
C5F8+
10
120
140
160 180 200
mass (amu)
220
240
Figure 3. Mass spectrum of ions in He/c-C5F8 plasma as
measured by QMS without ionizing electron beams.
We also measure radical species by setting the
extractor at a positive potential and using the electron
beam with energies of 15 eV. This electron energy is
small enough to prevent c-C5F8 from being
dissociated into fragments inside QMS and to
measure species only from the plasma. The
exception is C5F7 that can be produced from c-C5F8
at electron energies of less than 12 eV.
Figure 4 shows the plot of QMS counts at the mass
number of 50 (CF2+) versus the voltage on the
extractor. The black line is the case without the
ionizing electron beam in QMS, and the red line
with the electron beam. In the latter case, the counts
without the beam are subtracted to reduce the effects
of noise. Form these curves we can obtain the values
of counts for CF2+ from the plasma at negative
voltages of the extractor and counts for CF2 radicals
from the plasma at positive voltages. Detected
radical species include C4F6, C3F4, C3F3, CF3, CF2,
and CF with a small amount of C5F7. We can
calculate absolute densities of radicals by using a
procedure in Ref.4 and compare them with the
simulation results. Preliminary comparison suggests
that the radical species and their relative amounts are
in overall agreement between the experiment and the
modeling.
Figure 4. Counts of CF2+ versus the voltage on the
extractor of QMS without (black line) and with (red line)
ionizing electron beams.
5. Summary
We use quantum chemistry calculations by
Gaussian03 to obtain approximate values of the
cross sections of ionization, dissociation, and
dissociative ionization. The total modeling of RF
discharges (2D fluid model), which includes RF
wave propagation, plasma transport, and gas phase
chemical reaction, is performed and 2D profiles of
radicals as well as plasmas are obtained for He/cC5F8 discharges. We also measure densities of
radicals by QMS and compare them with the
modeling results. It is found that the radical species
and their relative amounts are in overall agreement
between the modeling and the experiment.
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