SiH4 o2 presentation

COLLEGE OF ENGINEERING
Division of Electronics and Electrical Engineering

DOCTOR OF PHILOSOPHY DISSERTATION PRESENTATION

The Electron Collision Cross Sections
and the Electron Transport Coefficients
in BF3 and C2F6 molecules

By: Pham Xuan Hien
Advisor: Professor Byung-Hoon Jeon

th
Korea, December 17 2015


Contents

1.

Introduction

2.

Electron swarm method

3.

Electron collision cross sections for BF3 molecule
3.1. Derived electron collision cross section set for BF3 molecule
3.2. Electron transport coefficients in BF3-Ar and BF3-SiH4 mixtures

4.

Electron collision cross sections for C2F6 molecule

5.

Conclusion


1. Introduction
Plasma processing

1. Depositing a film
2. Coating the surface with a photoresist.
3. Optically projecting a pattern onto the
photoresist.
4. Developing the resist, removing the exposed
resist regions and leaving behind a patterned
resist mask.
5. Etching the metal that is not protected by
the mask.
6. Removing the mask

Fig. 1. Subtractive processing scheme used in fabrication microelectronic integrated circuit


1. Introduction
Electron collision cross sections (1/2)

Electron collisions directly connect to entire
processing plasma chemistry

•

Electron Collision

•

•

Other Input Data

Cross Sections
The accurate and detailed of electron collision

•

•
•

cross sections are necessary

•
•

Transport and
Reaction Coefficients

•

•

Modeling and
Simulation of
Plasma Processing

Fig. 2. Sample basic procedure of
semiconductor fabrication

•

Semiconductor

•

Fabrication


1. Introduction
Electron collision cross sections (2/2)

Electron swarm
Electron beam method

method
Electron

Electron Collision

transport

Cross Sections

coefficient

Momentum
transfer

Vibrational
cross section

Excitation
cross section

Dissociation
cross section

cross section

Fig. 3. Electron collision cross sections

Attachment
cross section

Ionization
cross section


1. Introduction

General properties and application of BF3 molecule

- Boron trifluoride (BF3): hard acid, non-flammable, toxic, corrosive to the skin, halogen-containing gas.
- Application:
+ Plasma-assisted fabrication of microcircuits
+ Alternative agent for plasma doping and metal surface treatment
+ Suggested to replace di-borane (used as a p-type dopant of amorphous Si films in solar cells)
+ BF3 – SiH4 and BF3 – Ar mixtures are used in microwave plasma, glow-discharge process.


1. Introduction
General properties and application of C2F6 molecule

Perfluoroethane (C2F6) is a man-made gas widely used in:

- Etching plasma processing
- PECVD chamber cleaning
- Gaseous dielectrics (discharge switches, gas insulator in high voltage equipment...)


1. Introduction
Objectives

Because of their industrial importance, the reliable sets for BF3 and C2F6 molecules and electron transport coefficients in binary mixtures of the BF3 and C2F6 with buffer
gases are necessary for understanding discharges plasma

(2)
(1)
Determine the sets of electron collision cross sections for BF3 and C2F6
molecules for a quantitative numerical modeling of a plasma discharge for

processing procedures with materials containing these molecules by using
an electron swarm method.
* The accurate electron collision cross sections and electron transport
coefficients, not only in pure gaseous molecules but also in the binary gas
mixtures, are necessary to understand quantitatively plasma phenomena
and ionized gases.

Analyse electron transport coefficients in BF3 -Ar and BF3 –SiH4 mixtures by u
sing a two-term approximation of the Boltzmann equation analysis for quantitativ
ely modeling.


2. Electron swarm method

- The electron transport coefficients in given gases are functions only of the ratio E/N, the gas temperature T, and when a magneti
c field is present, of B/N. They are related to the electron collision cross sections by complex integral expressions involving the el
ectron energy distribution function (EEDF). The EEDF can be obtained theoretically by solving the Boltzmann equation.

- A two-term approximation of the Boltzmann equation for the energy given by Tagashira et al.[1] (used for BF3).
- A multi-term approximation of the Boltzmann equation for the energy was developed at James-Cook university [2]. (used for C
2F6).

[1] H. Tagashira, Y. Sakai and S. Sakamoto: J. Phys. D 10, 1051 (1977)
[2] R. E. Robson and K. F. Ness, Phys. Rev. A 33, 2068 (1986)


2. Electron swarm method
Procedures of determination of the electron collision cross section set

Step 1: Modification of the low energy inelastic cross sections in order until calculated and measured electron transport coefficients (W, ND L, NDT, DL/μ and DT/μ) in

the mixtures of object gas are in good agreement.

Step 2: Modification of the momentum transfer cross section until the calculated and measured electron transport coefficients (ND L, NDT, DL/μ and DT/μ) in the pure
object gas are good in agreement when the inelastic cross sections determined in step 1 are not altered.

Step 3: Modification of high energy inelastic cross sections such as electronic excitation, dissociation, attachment and ionization cross sections... until calculated and
measured electron transport coefficients (mainly α/N, η/N, and (α-η)/N) not only in pure but also in mixtures of object gas are in good agreement when the electron
collision cross sections determined in step 1 and 2 are not altered.

-Where W is electron drift velocity, NDL is density-normalized longitudinal coefficient, NDT is density-normalized transverse diffusion coefficients, D L/μ is ratio of the longitudinal diffusion coefficient (DL) to the electron mobility (μ), DT/μ is ratio of the
transverse diffusion coefficient (DT) to the μ, α/N is Townsend first ionization coefficient, η/N is electron attachment coefficient, and (α - η)/N is density-normalized effective ionization coefficient.


2. Electron swarm method
The procedure of the calculated method

Fig. 4. The procedure of calculated method


3. Electron collision cross sections for BF3 molecule
3.1. Derived electron collision cross section set for BF 3 molecule (1/5)
There were two published sets of electron collision cross section for the BF3 molecule:

-Stefanov and Pirgove [3]:
+ Includes momentum transfer cross section and two vibrational excitation cross sections.
+ Only electron drift velocity was calculated and compared with the experimental values.

-Nikitovic et al [4].
+ Includes momentum transfer cross section, five vibrational cross sections, one dissociation cross section.
+ Using Monte Carlo codes for electron transport involving null collision.

+ The differences between calculated and measured electron transport coefficients were significant.

[3] B. Stefanov and P. Pirgove: in Proc. ISPC-10, 1991, 2.1-6, p. 6.
[4] Ž. Nikitović, O. Šašić, Z. Raspopović, V. Stojanović, S. Radovanov, M. Mozetič
and U. Cvelbar: Acta Phys. Pol. 117, 748 (2010).


3. Electron collision cross sections for BF3
3.1. Derived electron collision cross section set for BF 3 molecule (2/5)
- Initial set:
Qm: from Nikitovic
Qvib1, 2,3 ,4 harm:from Nikitovic
Qdiss:from Nikitovic
Qa: from Kurepa (measurement)
Qi: from Kurepa (measurement)
- Use two-term approximation of Boltzmann equation.

- Present Qm has a peak at 3.85 eV. The minimum broad peak strongly
effects W in the E/N range of <100 Td, was change from about 0.63 eV
to 1.3 eV.

- Qvib.harm decreased from about 0.9*10-16 to 0.37*10-16 cm2.
- One dissociative excitation cross section with a threshold energy of
6.48 eV was suggested

strongly effected to electron attachment and

electron ionization coefficients in the range of E/N<200Td

Fig. 5. Set of electron collision cross sections for the BF molecule. The broken and solid curves

3
show the initial and present cross sections, respectively.


3. Electron collision cross sections for BF3
3.1. Derived electron collision cross section set for BF 3 molecule (3/5)

Differences between calculated and measured electron drift
velocity in the E/N range of 20-100 Td.
Negative differential conductivity (NDC) phenomenon is not
indicated.

Present: indicated a light NDC in the E/N range of 30-70 Td

Fig. 6. Electron drift velocity W as a function of E/N for a pure
BF3 molecule


3. Electron collision cross sections for BF3
3.1. Derived electron collision cross section set for BF 3 molecule (4/5)

Fig. 7. Townsend first ionization coefficient α/N as a function of E/N for the pure

Fig. 8. Electron attachment coefficient η/N as a function of E/N for the

BF molecule.
3

pure BF molecule.
3

3. Electron collision cross sections for BF3
3.1. Derived electron collision cross section set for BF 3 molecule (5/5)

- Differences between calculated and measured densitynormalized effective ionization coefficient in the E/N
range of > 40 Td.

Fig. 9. Density-normalized effective ionization coefficient (α-η)/N as a function of E/N for the pure BF molecule.
3


3. Electron collision cross sections for BF3
3.2. Electron transport coefficients in BF3-Ar and BF3-SiH4 mixtures (1/9)
The electron drift velocity W r in the BF3 -Ar mixtures are very sensitive to the
mixture ratio of the BF3 molecule, especially in the low energy.

-Small regions of the NDC in these mixtures in the E/N range of 0.35-70 Td.
- The electron drift velocity in the BF3 -Ar mixtures was enhanced by adding
a small fraction of BF3 molecules.

- At a higher E/N, the electron drift velocities in 1, 5 and 10% BF3 -Ar
mixtures are close to that in pure Ar.

- This due to dominant inelastic collision processes in the swarm shifting from
those caused by the vibrational excitation of the BF3 molecule to those caused
by electronic excitations of the majority Ar atom because the mean energy of
the electrons is enhanced at a higher E/N

Fig. 10. Electron drift velocity W as functions of

E/N for the BF3 -Ar mixtures with 1, 5, 10, 30, 50, 70, and 90% BF3 molecule.


3. Electron collision cross sections for BF3
3.2. Electron transport coefficients in BF3-Ar and BF3-SiH4 mixtures (2/9)

Fig. 11. Density-normalized longitudinal diffusion coefficient NDL as

Fig. 12. Density-normalized longitudinal diffusion coefficient ND L as

functions of E/N for the BF3-Ar mixtures with 1, 5, 10, 30, 50, 70, and 90%

functions of E/N for the BF3-SiH4 mixtures with 10, 30, 50, 70, and 90%

BF3 molecule.

BF3 molecule.


3. Electron collision cross sections for BF3
3.2. Electron transport coefficients in BF3-Ar and BF3-SiH4 mixtures (3/9)

Fig. 13. Ratio of the longitudinal diffusion coefficient to the electron mobility D L/µ as functions
of E/N for the BF3-Ar mixtures with 1, 5, 10, 30, 50, 70, and 90% BF3 molecule.

Fig. 14. Ratio of the longitudinal diffusion coefficient to the electron mobility D L/µ as
functions of E/N for the BF3-SiH4 mixtures with 10, 30, 50, 70, and 90% BF3
molecule.

3. Electron collision cross sections for BF3
3.2. Electron transport coefficients in BF3-Ar and BF3-SiH4 mixtures (4/9)

Fig. 15. Townsend first ionization coefficient α/N as functions of E/N for the
BF3 -Ar mixtures with 1, 5, 10, 30, 50, 70, and 90% BF3 molecule.


3. Electron collision cross sections for BF3
3.2. Electron transport coefficients in BF3-Ar and BF3-SiH4 mixtures (5/9)

Remarkable synergism: Electron ionization coefficients in the BF3 –
SiH4 mixtures are greater than those in pure BF3 and SiH4 molecules.

Fig. 16. Townsend first ionization coefficient α/N as functions of E/N for the BF3-SiH4 mixtures with 10, 30, 50, 70,
and 90% BF3 molecule.


3. Electron collision cross sections for BF3
3.2. Electron transport coefficients in BF3-Ar and BF3-SiH4 mixtures (6/9)

Fig. 17. Electron attachment coefficient η/N as functions of E/N for the
BF3 -Ar mixtures with 1, 5, 10, 30, 50, 70, and 90% BF3 molecule.

Fig. 18. Electron attachment coefficient η/N as functions of E/N for the BF3 –SiH4
mixtures with 10, 30, 50, 70, and 90% SiH4.


3. Electron collision cross sections for BF3
3.2. Electron transport coefficients in BF3-Ar and BF3-SiH4 mixtures (7/9)

Fig. 19. Variation in α/N in BF3 –SiH4 mixtures at E/N = 200 Td with the mixture ratio of BF3.


3. Electron collision cross sections for BF3
3.2. Electron transport coefficients in BF3-Ar and BF3-SiH4 mixtures (8/9)

The electron energy distribution in the 90% BF3-SiH4
mixture relatively significantly differs from that in the pure
BF3 while there are no significant differences between the
pure SiH4 molecule and the 10% BF3-SiH4 mixture.

Fig. 20. Electron energy distribution functions for pure BF3 , pure SiH4, a 10% BF3 -90% SiH4 mixture, and a 90% BF3-10% SiH4 mixture at
E/N = 200 Td.


3. Electron collision cross sections for BF3
3.2. Electron transport coefficients in BF3-Ar and BF3-SiH4 mixtures (9/9)

The momentum transfer cross section for the BF3
molecule is much larger than that for pure SiH4.
The mean electron energy in the pure BF3 therefore, is
dramatically lower than that in the pure SiH4

Fig. 21. Mean electron energy as a function of E/N for pure BF3, pure SiH4, and BF3 –SiH4 mixtures.