The electron transport coefficients in not only pure atoms and molecules but also in the binary gas mixtures are necessary, especially on understanding quantitatively plasma phenomena and ionized gases. Electron transport coefficients (electron drift velocity, densitynormalized longitudinal diffusion coefficient, and densitynormalized effective ionization coefficient) in binary mixtures of TEOS gas with buffer gases such as Kr, Xe, He, and Ne gases, therefore, was analyzed and calculated by a twoterm approximation of the Boltzmann equation in the E/N range (ratio of the electric field E to the neutral number density N) of 0.1  1000 Td (1 Td = 10
^{−17}
V.cm
^{2}
). These binary gas mixtures can be considered to use as the silicon sources in many industrial applications depending on mixture ratio and particular application of gas, especially on plasma assisted thinfilm deposition.
1. Introduction
Tetraethoxysilane (TEOS), Si(OC
_{2}
H
_{5}
)
_{4}
, which is a gas with nontoxic and nonexplosive characteristics; and is mainly used as the silicon source to deposite SiO
_{2}
like films by plasmaenhanced chemical vapor deposition (PECVD) in remote microwave oxygen plasma reactors because the deposited films show good step coverage compared with films deposited from SiH
_{4}
[1]
. A simple model for the oxygen rich O
_{2}
and TEOS gas discharge plasmas was constructed
[2
,
3]
. The electron transport coefficients in TEOSO
_{2}
and TEOSAr mixture gases were calculated and measured
[4]
. The binary mixtures of TEOSN
_{2}
have been also used to instead of SiH
_{4}
based gas mixtures to reduce the dangers of explosion and toxicity while improving quality of the deposition of SiO
_{2}
by PECVD. Recently, the electron transport coefficients in TEOSN
_{2}
mixture gases were also calculated
[5]
. On the other hand, electron transport coefficients in the mixture gases are necessary data to obtain the plasma models.
For all of above reasons along with the lack of measured electron transport coefficients in the binary mixtures of TEOS gas with buffer gases such as Kr, Xe, He and Ne gases, in this study, we have calculated and analysed electron drift velocity, densitynormalized longitudinal diffusion coefficient, ratio of longitudinal diffusion coefficient to electron mobility, Townsend first ionization coefficient using a twoterm approximation of the Boltzmann equation over the wide E/N range (ratio of the electric field E to the number density of neutral atoms or molecules N) and the reliable electron collision cross sections of the TEOS, Kr, Xe, He and Ne gases. These results are the first calculations and the best available so far for the quantitative modeling of plasma discharge for processing procedures using these binary mixture gases.
2. Analysis
We used the electron swarm method to determine a set of accurate electron collision cross sections for TEOS, TMS, and BF
_{3}
molecules
[4
,
6
,
7]
. The twoterm approximation of the Boltzmann equation for the energy has been applied to calculate the electron transport coefficients in pure gases and binary mixture gases such as electron drift velocity, densitynormalized longitudinal diffusion coefficient, ratio of longitudinal diffusion coefficient to electron mobility, Townsend first ionization coefficient over the wide E/N range. The electron transport coefficients calculated from the present set of TEOS gas and binary mixtures of TEOS gas with Ar and O
_{2}
gases are agreement with those in experiments
[4]
. The sets of electron collision cross sections for Kr, Xe, He and Ne gases were slightly modified to obtain the accurate sets of electron collision cross sections. The electron transport coefficients calculated by using the present sets of these gases are also compared and good agreement with those in experiments.
In the present study, the electron collision cross sections for TEOS molecule determined by Tuan and Jeon
[4]
. This set includes one momentum transfer, one attachment, two vibrational excitation cross sections (threshold energies of 0.16 and 0.37 eV), one dissociation excitation (threshold energy of 3.6 eV), one electronic excitation (threshold energy of 1.7 eV), and one total ionization (threshold energy of 10.6 eV). The set of electron collision cross sections for Kr atom determined by Hayashi
[10]
includes one momentum transfer, fourteen electronic excitation cross sections (threshold energies of 9.915 to 13.437 eV), and one total ionization (threshold energy of 14.0 eV) cross section. The set of electron collision cross sections for Xe atom determined by Hashimoto and Nakamura
[11]
includes one momentum transfer, fourteen electronic excitation cross sections (threshold energies of 8.315 to 11.58 eV), and one total ionization (threshold energy of 12.13 eV) cross section. The set of electron collision cross sections for He atom determined by Hayashi
[10]
have been used as initial sets. This set includes one momentum transfer, twenty five electronic excitation cross sections (threshold energies of 19.82 to 24.19 eV), and one total ionization (threshold energy of 24.59 eV) cross section. The set of electron collision cross sections for Ne atom determined by Hayashi
[10]
have been used as initial sets. This set includes one momentum transfer, seven electronic excitation cross sections (threshold energies of 16.62 to 19.66 eV), and one total ionization (threshold energy of 21.56 eV) cross section. A brief summary of several reaction processes of TEOS molecule and other gases for plasma modeling is listed in
Table 1
.
Reaction processes with threshold energy for plasma modeling in atoms and molecules
Reaction processes with threshold energy for plasma modeling in atoms and molecules
The present twoterm approximation of the Boltzmann equation for the energy given by Tagashira
et al
.
[12]
was also previously used for the pure gases and binary mixture gases
[4

9]
. The centreofmass drift velocity of an electron swarm (W
_{r}
) and the longitudinal diffusion coefficient (D
_{L}
) are calculated in the timeofflight (TOF) parameters. The diffusioncorrected ionization and attachment coefficients are also calculated in the steady state Townsend (SST) parameters. A description of the Boltzmann equation analysis in the previous publications
[4

9
,
12

16]
is also briefly following represented.
The electron transport coefficients in given gases are functions only of the ratio E/N, the gas temperature T, and when a magnetic field is present, of B/N. They are related to the electron collision cross sections by complex integral expressions involving the electron energy distribution function (EEDF)
[13]
. The electron energy distribution function (EEDF), f(ε, E/N), is normalized by
where ε is the electron energy. Electron transport properties directly depend on EEDF
[13]
. The EEDF is normally nonMaxwellian in the nonequilibrium plasma used for applications. The EEDF can be obtained theoretically by solving the Boltzmann Eq.
[13]
where
is the distribution function of the positions r and velocities of electrons v,
is the acceleration due to external forces, and (∂f/∂t)
_{coll}
is the collision induced rate of change of the number of electrons per unit volume of phase space. The solution normally involves the assumptions that the fields are time independent, that spatial gradient terms can be omitted, and that the distribution in velocity space is only slightly disturbed from spherical.
The electron drift velocity calculated from the solution of electron energy distribution function, f(ε, E/N), of the Boltzmann equation is defined as
where m is the electron mass, e is the elementary charge and q
_{m}
(ε) is the momentumtransfer cross section.
The densitynormalized longitudinal diffusion coefficient is defined as
where V
_{1}
is the speed of electron, q
_{T}
is the total cross section, here F
_{n}
and
are respectively the electron energy distributions of various orders and their eigen values. V
_{1}
,
,
, and A
_{n}
are given by
where q
_{i}
is the ionization cross section.
The Townsend first ionization coefficient is defined as
where I is the ionization onset energy and q
_{i}
(ε) is the ionization cross section.
3. Electron transport coefficients
The electron drift velocities, W, the densitynormalized longitudinal diffusion coefficients, ND
_{L}
, the ratio of the longitudinal diffusion coefficients to the electron mobility, D
_{L}
/µ, the Townsend first ionization coefficients, α/N, as functions of E/N for the binary mixtures of TEOS gas with other gases such as Kr, Xe, He and Ne have been calculated in the E/N range 0.1 < E/N < 1000 Td by a twoterm approximation of the Boltzmann equation for energies.
The calculated electron drift velocities in TEOSKr, TEOSXe, TEOSHe, and TEOSNe mixture gases are shown in
Figs. 1

4
. In
Figs. 1
and
2
, the W values in TEOSKr and TEOSXe mixture gases are suggested to be between those of the pure gases over the range of E/N > 100 Td. In the range of E/N < 100 Td, the W values in these binary mixtures are higher than those of Kr, Xe, and TEOS gases, especially on E/N = 10 Td corresponding to electron energy of about 0.202 eV. To the best of our knowledge, the electron drift velocity strongly depends onmomentum transfer cross sections and vibrational excitation cross sections. In these cases, the reasons could be suggested that at this energy the vibrational excitations in TEOS gas occured, the momentum transfer cross section of TEOS gas is higher than that of Kr and Xe gases and the momentum transfer cross sections of Kr and Xe gases are deeply decreasing to the minimum points. Therefore, these curves have the same tendency as that of pure TEOS gas. For TEOSHe and TEOSNe mixture gases in
Figs. 2
and
4
, the W values are suggested to be between those of the pure gases over the all range of E/N. However, the W values of 10% TEOSHe and 10% TEOSNe mixtures are higher than those of pure TEOS, He, and Ne gases in the range of E/N < 20 Td (corresponding to electron energy of about 0.202 eV of about 0.15 eV). In these cases, the reasons could be suggested that at this energy the momentum transfer cross section of TEOS gas is higher than that of He and Ne gases and the momentum transfer cross sections of He and Ne gases are slightly increasing.
Electron drift velocity, W, as functions of E/N for the TEOSKr mixtures with 10%, 30%, 50%, 70%, and 90% TEOS. The solid curves show present W values calculated for the pure Kr atom and TEOS molecule.
Electron drift velocity, W, as functions of E/N for the TEOSXe mixtures with 10%, 30%, 50%, 70%, and 90% TEOS. The solid curves show present W values calculated for the pure Xe atom and TEOS molecule.
Electron drift velocity, W, as functions of E/N for the TEOSHe mixtures with 10%, 30%, 50%, 70%, and 90% TEOS. The solid curves show present W values calculated for the pure He atom and TEOS molecule.
Electron drift velocity, W, as functions of E/N for the TEOSNe mixtures with 10%, 30%, 50%, 70%, and 90% TEOS. The solid curves show present W values calculated for the pure Ne atom and TEOS molecule.
The calculated densitynormalized longitudinal diffusion coefficients and calculated ratio of the longitudinal diffusion coefficients to the electron mobility in TEOSKr, TEOSXe, TEOSHe, and TEOSNe mixture gases are shown in
Figs. 5

8
and
Figs. 9

12
, respectively. The calculated values of these coefficients in the binary mixtures of TEOS with Kr, Xe, He, and Ne gases are suggested to be between those of the pure gases over the all range of E/N.
Densitynormalized longitudinal diffusion coefficient, ND_{L}, as functions of E/N for the TEOSKr mixtures with 10%, 30%, 50%, 70%, and 90% TEOS. The solid curves show present ND_{L} values calculated for the pure TEOS molecule and Kr atom.
Densitynormalized longitudinal diffusion coefficient, ND_{L}, as functions of E/N for the TEOSXe mixtures with 10%, 30%, 50%, 70%, and 90% TEOS. The solid curves show present ND_{L} values calculated for the pure TEOS molecule and Xe atom.
Densitynormalized longitudinal diffusion coefficient, ND_{L}, as functions of E/N for the TEOSHe mixtures with 10%, 30%, 50%, 70%, and 90% TEOS. The solid curves show present ND_{L} values calculated for the pure TEOS molecule and He atom.
Densitynormalized longitudinal diffusion coefficient, ND_{L}, as functions of E/N for the TEOSNe mixtures with 10%, 30%, 50%, 70%, and 90% TEOS. The solid curves show present ND_{L} values calculated for the pure TEOS molecule and Ne atom.
Ratios of longitudinal diffusion coefficient to the electron mobility, D_{L}/μ, as functions of E/N for the TEOSKr mixtures with 10%, 30%, 50%, 70%, and 90% TEOS. The solid curves show present D_{L}/μ values calculated for the pure TEOS molecule and Kr atom.
Ratios of longitudinal diffusion coefficient to the electron mobility, D_{L}/μ, as functions of E/N for the TEOSXe mixtures with 10%, 30%, 50%, 70%, and 90% TEOS. The solid curves show present D_{L}/μ values calculated for the pure TEOS molecule and Xe atom.
Ratios of longitudinal diffusion coefficient to the electron mobility, D_{L}/μ, as functions of E/N for the TEOSHe mixtures with 10%, 30%, 50%, 70%, and 90% TEOS The solid curves show present D_{L}/μ values calculated for the pure TEOS molecule and He atom.
Ratios of longitudinal diffusion coefficient to the electron mobility, D_{L}/μ, as functions of E/N for the TEOSNe mixtures with 10%, 30%, 50%, 70%, and 90% TEOS The solid curves show present D_{L}/μ values calculated for the pure TEOS molecule and Ne atom.
The calculated Townsend first ionization coefficients in TEOSKr, TEOSXe, TEOSHe, and TEOSNe mixture gases are shown in
Figs. 13

16
. In
Figs. 13
and
14
, the α/N values in TEOSKr and TEOSXe mixture gases are suggested to be between those of the pure gases over the ranges of E/N < 200 Td and E/N < 700 Td, respectively. The α/N values in 10% TEOSKr and 10% TEOSXe gas mixtures are closed to those of pure Kr and Xe gases. These values could be greater than those of pure Kr and Xe gases over the ranges of E/N > 200 Td and E/N > 700 Td, respectively.
The Townsend first ionization coefficients, α/N, as functions of E/N for the TEOSKr mixtures with 10%, 30%, 50%, 70%, and 90% TEOS. The solid curves show present α/N values calculated for the pure TEOS and Kr molecules.
The Townsend first ionization coefficients, α/N, as functions of E/N for the TEOSXe mixtures with 10%, 30%, 50%, 70%, and 90% TEOS. The solid curves show present α/N values calculated for the pure TEOS and Xe molecules.
The Townsend first ionization coefficients, α/N, as functions of E/N for the TEOSHe mixtures with 10%, 30%, 50%, 70%, and 90% TEOS The solid curves show present α/N values calculated for the pure TEOS and He molecules.
The Townsend first ionization coefficients, α/N, as functions of E/N for the TEOSNe mixtures with 10%, 30%, 50%, 70%, and 90% TEOS The solid curves show present α/N values calculated for the pure TEOS and Ne molecules.
To the best of our knowledge, the Townsend first ionization coefficient strongly depends on ionization cross sections and dissociation excitation cross sections. The reasons could be suggested that the ionization and dissociation excitation cross sections of TEOS gas are much higher than those of Kr and Xe gases. For TEOSHe and TEOSNe mixture gases in
Figs. 15
and
16
, the α/N values are suggested to be between those of the pure gases over the all range of E/N. However, the α/N values of 10% TEOSHe and 10% TEOSNe mixtures are higher than those of pure TEOS, He, and Ne gases over the all range of E/N. In these cases, the reasons could be suggested that ionization cross sections of He and Ne gases are much lower than that of TEOS gas.
The present results, that have been also calculated for the first time, are reliable over the E/N range of 0.1 to 1000 Td because of the accuracy of the electron collision cross sections for the present gases and the validity of the Boltzmann equation. More experiments of the electron transport coefficients for these binary mixtures need to be performed over the wide range of E/N in the future. From ionization coefficients of these binary mixtures, we could make the source of plasma corresponding equivalent industrial applications in manufacturing nanomaterial, depending on mixture ratio and particular application of gas, especially on plasma assisted thinfilm deposition. Especially on models for the binary mixture gases of TEOS gas with high concentration of buffer gases such as Kr, Xe, He, and Ne should be experimented in gas discharge plasma conditions in order to reduce the dangers of explosion and toxicity while improving quality of the deposition of SiO
_{2}
.
4. Conclusions
The electron transport coefficients (electron drift velocity, densitynormalized longitudinal diffusion coefficient, and densitynormalized effective ionization coefficient) in binary mixtures of TEOS gas with buffer gases such as Kr, Xe, He, and Ne gases was calculated for the first time and analyzed by a twoterm approximation of the Boltzmann equation in the E/N range of 0.1  1000 Td. Models of gas discharge plasmas could be constructed using the binary mixture gases of TEOS gas with high concentration of buffer gases such as Kr, Xe, He, and Ne. These binary gas mixtures can be considered to use as the silicon sources in many industrial applications depending on mixture ratio and particular application of gas, especially on plasma assisted thinfilm deposition.
BIO
Do Anh Tuan He received the B.S and M.Sc. degrees in electrical engineering from Hanoi University of Science and Technology, Vietnam in 2004 and 2008, respectively. He received the Ph.D. degree in electrical engineering from Dongguk University, Korea in 2012. He is the Lecturer at the Faculty of Electronics and Electrical Engineering of Hung Yen University of Technology and Education, Vietnam from 2008. His research interests include electron swarm study, discharges and high voltage, and plasma applications.
Tochitani G.
,
Shimozuma M.
,
Tagashira H.
(1993)
“Deposition of Silicon Oxide Films from TEOS by Low Frequency Plasma Chemical Vapor Deposition”
J. Vac. Sci. Technol. A
11
400 
Sano K.
,
Tamamaki H.
,
Nomura M.
,
Wickramanayaka S.
,
Nakanishi Y.
,
Hatanaka Y.
1995
“Deposition of High Quality SiO2 Films Using Teos by ECR Plasma”
MRS Proceedings
396
Janča J.
,
Tálský A.
,
Zvoníček V.
1996
“Kinetics of O2 + TEOS GasPhase Chemical Reactions in a Remote RF Plasma Reactor with Electron Spin Resonance”
Plasma Chemistry and Plasma Processing
16
(2)
187 
194
DOI : 10.1007/BF01570177
Tuan D. A.
,
Jeon B. H.
2012
“Electron Collision Cross Sections for the Tetraethoxysilane Molecule and Electron Transport Coefficients in TetraethoxysilaneO2 and TetraethoxysilaneAr Mixtures”
Journal of the Physical Society of Japan
81
(6)
0643011 
8
Tuan D. A.
,
Thang P. N.
“Electron Transport Coefficients in TEOSN2 Mixture for using in Plasma Assisted Thinfilm Deposition”
Journal of Science and Technology (in Thai Nguyen University)
137
(07)
121 
125
Hien P. X.
,
Jeon B. H.
,
Tuan D. A.
2013
“Electron Collision Cross Sections for the BF3 Molecule and Electron Transport Coefficients in BF3Ar and BF3SiH4 Mixtures“
Journal of the Physical Society of Japan
82
(3)
0343011 
8
Hien P. X.
,
Tuan D. A.
,
Jeon B. H.
2012
“Electron Collision Cross Sections for the TMS Molecule and Electron Transport Coefficients in TMSAr andTMSO2 Mixtures,”
Journal of the Korean Physical Society
61
(1)
62 
72
DOI : 10.3938/jkps.61.62
Tuan D. A.
2014
“Calculations of Electron Transport Coefficients in Cl2Ar, Cl2Xe, and Cl2O2 Mixtures”
Journal of the Korean Physical Society
64
(1)
23 
29
DOI : 10.3938/jkps.64.23
Tuan D. A.
2015
“Analysis of Insulating Characteristics of Cl2He Mixture Gases in Gas Discharges”
J. Electr. Eng. Technol.
10
(4)
1735 
1738
Hashimoto 11T.
,
Nakamura Y.
“Momentum Transfer Cross Section of Xenon Deducted from Electron Drift Velocity Data,”
IEE
Japan
as quoted in M. Suzuki, T. Taniguchi, N. Yoshimura, and H. Tagashira, “Momentum Transfer Cross Section of Xenon Deducted from Electron Drift Velocity Data,” , vol. 25, no. 1, pp. 5056 (Jan. 1992)
ED9061
(1)
Tagashira H.
,
Sakai Y.
,
Sakamoto S.
(1977)
“The Development of Electron Avalanches in Argon at High E/N Values. II. Boltzmann Equation Analysis”
J. Phys. D
10
1051 
DOI : 10.1088/00223727/10/7/011
Tuan D. A.
2012
“Determination of Electron Collision Cross Sections for F2, Cl2 Molecules, and Electron Transport Coefficients in Mixture Gases as Prospective Substitutes for the SF6 Gas in Industrial Applications”, PhD Dissertation
Dongguk Univ.
Korea
Huxley L. G. H.
,
Crompton R. W.
(1974)
“The Diffusion and Drift of Electrons in Gases”
John Wiley & Sons
New York
Chaps. 6 and 13
Jeon B. H.
(2006)
“Determination of Electron Collision Crosssections for the C3F8 Molecule by Using an Electron Swarm Study”
J. Korean Phys. Soc.
49
2321 
Christophorou L. G.
,
Hunter S. R.
,
Christophorou L G
(1984)
ElectronMolecule Interations and Their Applications
Academic Press
Florida
318 
412
Morgan W. L.
,
Winstead C.
,
McKoy V.
2002
“Electron Collision Cross Sections for Tetraethoxysilane”
Journal of Applied Physics
92
(3)
1663 
1667
DOI : 10.1063/1.1491024
Holtgrave J.
,
Riehl K.
,
Abner D.
,
Haaland P. D.
1993
“Ion Chemistry in Tetraethylorthosilicate (C2H5O)4Si”
Chemical Physics Letters
215
(6)
548 
553
DOI : 10.1016/00092614(93)89353J