Theoretical study on electron collisions with SiF and SiF
2
radicals
in the low- and intermediate-energy range
G. L. C. de Souza,
1
E. A. y Castro,
2
L. E. Machado,
2
L. M. Brescansin,
3
I. Iga,
1
and M.-T. Lee
1
1
Departamento de Química, UFSCar, 13565-905 São Carlos, SP, Brazil
2
Departamento de Física, UFSCar, 13565-905 São Carlos, SP, Brazil
3
Instituto de Física “Gleb Wataghin,” UNICAMP, 13083-970 Campinas, SP, Brazil
Received 29 May 2007; published 8 October 2007
A theoretical study on electron collisions with SiF and SiF
2
radicals in the low- and intermediate-energy
range is reported. More specifically, calculated elastic differential, integral, and momentum transfer cross
sections as well as total and total absorption cross sections are presented in the 1 – 1000-eV energy range. A
complex optical potential is used to represent the electron-radical interaction dynamics, whereas the iterative
Schwinger variational method combined with the distorted-wave approximation is used to solve the scattering
equations. Comparison of the present results with the available theoretical and experimental results in the
literature is made.
DOI: 10.1103/PhysRevA.76.042706 PACS numbers: 34.80.Bm
I. INTRODUCTION
Interest in electron interactions with highly reactive radi-
cals, such as CF
x
, SiF
x
x =1,2,3, etc., has grown recently
in view of their importance in developing plasma devices. It
is well known that a plasma environment is composed of
many species such as electrons, molecules in their ground
and excited states, neutral radicals, ionic fragments, etc.
Knowledge of the cross sections for electron interactions
with these constituents is important in determining plasma
properties and therefore is useful for plasma modeling. In
this sense, cross sections for e
-
-SiF
x
x =1,2,3 collisions
are particularly relevant. The SiF
x
radicals can be produced
during plasma etching of silicon when gaseous fluorine or
perfluorocarbons are used as reactant gases. Since plasma
etching is one of the most fundamental processes for the
manufacture of wafers in the semiconductor industry, knowl-
edge of several cross sections for e
-
-SiF
x
collisions is cer-
tainly relevant in order to optimize the process. The presence
of such species in the reactant environment can certainly
influence plasma properties. In particular, the interaction of
these radicals with electrons is not very well known. Also,
experimental determination of the cross sections of e
-
-SiF
x
collisions is difficult. Only a few experimental cross sections
for electron-impact ionization of these reactive radicals have
been reported in the literature so far 1–3. Theoretical inves-
tigations on electron collisions with the SiF
x
radicals re-
ported in the literature have been equally scarce. Electron-
impact total ionization cross sections TICSs for SiF
x
x
=1,2,3 were calculated and reported by Hwang et al. 4
using the semiempirical binary-encounter Bethe BEB ap-
proximation, by Deutsch et al. 5 using the Deutsch-Märk
DM model, and by Joshipura et al. 6 using the additivity
rule AR. A rather complete theoretical investigation on
electron interaction with the SiF radical was reported by Lee
et al. 7 in 2002. In that study, differential DCS, integral
ICS, and momentum-transfer MTCS cross sections, as
well as grand-total TCS and total absorption TACS cross
sections in the 1–500-eV range were reported. To our
knowledge, no similar studies have ever been reported for
other SiF
x
radicals. Therefore, additional theoretical calcula-
tions of various cross sections for e
-
-SiF
x
x =1,2,3 colli-
sions would certainly be interesting and could contribute to
fulfill this lack.
In the study of e
-
-SiF scattering reported by Lee et al. 7,
a complex optical potential composed of static-exchange,
correlation-polarization, and absorption contributions was
used to represent the interaction dynamics. The iterative
Schwinger variational method ISVM8 combined with the
distorted-wave approximation DWA9,10 was used to
solve the scattering equations. The static-exchange part of
the interaction potential was derived exactly from the target
wave function. A parameter-free model suggested by Padial
and Norcross 11 was used to generate the correlation-
polarization potential, whereas version 3 of the quasifree
scattering model QFSM3 proposed by Staszewska et al.
12, and lately modified by Jain and Baluja 13, was used
to account for the absorption contributions. During the last
five years, our group has applied this model to account for
the absorption component of the electron-molecule interac-
tion potential. We have found that for most of the targets
studied 7,14 –17, the use of that optical potential can pro-
vide quite accurate DCSs, ICSs, and MTCSs for elastic
electron-molecule collisions in the 10– 500-eV energy range.
On the other hand, such calculations have systematically un-
derestimated the magnitudes of TCSs and TACSs, particu-
larly at higher incident energies. The observed disagreement
with experiments is probably caused by some physical origin
inherently omitted in the QFSM3 formalism. In our concep-
tion, this problem could be due to the use of the free-electron
gas approximation. However, in an actual scattering prob-
lem, the target electronic density is not uniform. It is ex-
pected that many-body interactions would be relevant in the
region of high electronic densities and less important else-
where. The lack of such effects could lead to distortions of
the absorption potential generated by the QFSM3. In order to
incorporate many-body effects, in two recent studies 18,19
we have proposed a dimensionless scaling factor, which is a
function of both the incident energy and the local target den-
sity distribution, to be applied to the QFSM3 potential. It
contains two parameters that were obtained through the ad-
justment of the calculated TACSs for N
2
at 500 eV to better
PHYSICAL REVIEW A 76, 042706 2007
1050-2947/2007/764/0427069 ©2007 The American Physical Society 042706-1