CONTROL OF ELECTRON ENERGY DISTRIBUTIONS THROUGH INTERACTION OF ELECTRON BEAMS AND THE BULK IN CAPACITIVELY COUPLED PLASMAS* Sang-Heon Song a) and Mark.

CONTROL OF ELECTRON ENERGY DISTRIBUTIONS THROUGH INTERACTION OF

ELECTRON BEAMS AND THE BULK IN CAPACITIVELY COUPLED PLASMAS*

Sang-Heon Songa) and Mark J. Kushnerb)

a)Department of Nuclear Engineering and Radiological Sciences University of Michigan, Ann Arbor, MI 48109, USA

[email protected]

b)Department of Electrical Engineering and Computer ScienceUniversity of Michigan, Ann Arbor, MI 48109, USA

[email protected]

http://uigelz.eecs.umich.edu

Gaseous Electronics Conference October 24th, 2012

* Work supported by DOE Plasma Science Center, Semiconductor Research Corp. and National Science Foundation

AGENDA

Interaction of beams with plasmas

Description of the model

Electron energy distribution (EED) control

Electron beam injection

Negative dc bias

Electron induced secondary electron emission

Concluding remarks

University of MichiganInstitute for Plasma Science & Engr.

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ELECTRON BEAM CONTROL OF f()


Ref: S.-H. Seo, J. Appl. Phys. 98, 043301 (2005)

Ar, 3 mTorr Unipolar dc pulse, -350 V PRF = 20 kHz, Duty cycle = 50%

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In pulsed dc magnetron, the electron energy distribution has a raised tail portion due to beam-like secondary electrons

ELECTRON BEAM-BULK INTERACTION


The coherent Langmuir wave is generated with nb/ne of 3 x 10-3, and the bulk electron is heated as the wave is damped out.

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Ref: I. Silin, Phys. Plasmas 14, 012106 (2007)

Vlasov-Poisson Simulation nb/ne = 3 x 10-3, vDe/vTe = 8.0

ne

nb


COULOMB COLLISION BETWEEN BEAM-BULK

However, with much smaller beam electron density the stream instability is not important, thus rather purely kinetic approach is presented in this investigation.

Beam electron transfers energy to bulk electron through electron-electron Coulomb collision.

The electron beam heating power density (Peb)

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2 2

3

1 1

2new

eb e e b bi

WP n m v v

tcm

HYBRID PLASMA EQUIPMENT MODEL (HPEM)

Fluid Kinetics Module: Heavy particle continuity, momentum, energy Poisson’s equation

Electron Monte Carlo Simulation: Includes secondary electron transport Captures anomalous electron heating Includes electron-electron collisions

E, Ni, ne

Fluid Kinetics ModuleFluid equations

(continuity, momentum, energy)Poisson’s equation

Te, Sb, Ss, kElectron Monte Carlo Simulation


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FLOW CHART: E-BEAM BULK INTERACTION

Electron Monte Carlo Simulation

MCS

MCSEB

Update f()

Collision between beam electron (vb) and bulk electron (vth) occurs.

Record energy loss of beam electron.

Energy loss is transferred to bulk electron energy distribution.


Bulk electron transport calculation

Beam electron transport calculation

...

...

2 21

2loss newij e b bE m v v

Bulk electron at ,lossi jE( , )i j gains energy by

in random direction.

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Injection of Beam Electron

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REACTOR GEOMETRY: E-BEAM CCP


2D, cylindrically symmetric

Ar/N2 = 80/20, 40 mTorr, 200 sccm

Base case conditions

Lower electrode: 50 V, 10 MHz

Upper electrode: e-Beam injection with 0.05 mA/cm2

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ELECTRON DENSITY & TEMPERATURE

Without beam-bulk interaction With beam-bulk interaction


Electron density is larger with beam-bulk interaction due to the increase of bulk electron temperature through the interaction.

MIN MAX

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Ar/N2 = 80/20, 40 mTorr, 100 eV Beam = 0.05 mA/cm2, Vrf = 50 V (10 MHz)

E-BEAM HEATING POWER DENSITY

The beam electrons deliver their kinetic energy to the bulk electrons through the Coulomb collisions.

The heating power density is maximum adjacent to the electrodes due to lower beam energy accelerating out of and into sheaths.


MIN MAX[3 dec]

Ar/N2 = 80/20, 40 mTorr, 100 eV Beam = 0.05 mA/cm2, Vrf = 50 V (10 MHz)

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HEATING: BEAM ELECTRON ENERGY

As the beam electron energy increases, the heating power density decreases due to the energy dependency of the e-e Coulomb collision cross section.


Ar/N2 = 80/20, 40 mTorr Beam = 0.05 mA/cm2, Vrf = 50 V (10 MHz)

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Axial Heating Profile Average Heating Power Density

EED: BEAM ELECTRON ENERGY

100 eV 400 eV


The bulk electron energy distribution is altered more significantly with the intermediate energy range of beam electron where the Coulomb collision cross section is larger.

Ar/N2 = 80/20, 40 mTorr Beam = 0.05 mA/cm2, Vrf = 50 V (10 MHz)

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Negative dc Bias

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REACTOR GEOMETRY: E-BEAM CCP


2D, cylindrically symmetric

Ar/N2 = 80/20, 40 mTorr, 200 sccm

Base case conditions

Lower electrode: 10 MHz

Upper electrode: Negative dc bias

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Secondary electrons emitted from the biased electrode heat up the bulk electrons through Coulomb interaction.

Since the beam electron density is much smaller than bulk electron density, the beam instability is not considered.

E-BEAM HEATING POWER DENSITY


MIN MAX[3 dec]

Ar/N2 = 80/20, 40 mTorr Vdc = – 100 V, Vrf = 50 V (10 MHz)

Sec. coefficient () = 0.15

Ion flux = 2 x 1015 cm-2s-1

e-beam current = 0.05 mA/cm2

e-beam density = 4 x 105 cm-3

Plasma density = 2 x 1010 cm-3

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ELECTRON ENERGY DISTRIBUTION

The cross section of Coulomb collision between beam and bulk electrons increases as the beam electron energy decreases.

Adjacent to the upper electrode, the tail part of EED is more enhanced due to the moderated electrons in the sheath region.


Ar/N2 = 80/20, 40 mTorr Vdc = – 100 V, Vrf = 50 V (10 MHz)

Upper Center Secondary electron

emission coefficient ( = 0.15

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SECONDARY ELECTRON EMISSION

Beam electrons are generated by ion induced secondary electron emission (i-SEE) on the upper electrode.

Beam electrons emitted from upper electrode produce electron induced secondary electron emission (e-SEE) on the lower electrode.

University of MichiganInstitute for Plasma Science & Engr.SHS_MJK_GEC2012

SECONDARY EMISSION YIELD


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*Ref: C. K. Purvis, NASA Technical Memorandum, 79299 (1979)

If the dc bias is large enough for beam electrons to penetrate RF potential, those are more likely to be collected on the RF electrode producing more e-SEE.

HEATING: MAGNITUDE OF NEGATIVE BIAS


The electron beam heating power increases due to additional heating from e-SEE, when the beam electrons have enough energy to penetrate the RF sheath potential and to reach the surface producing e-SEE.

Ar/N2 = 80/20, 40 mTorr Vrf = 100 V

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ELECTRON ENERGY DISTRIBUTION: e-SEE


As a result of additional heating from e-SEE, the tail portion of the EED is raised, when the dc bias is large enough to generate high energy beam electrons.

Ar/N2 = 80/20, 40 mTorr Vrf = 100 V

Vdc = – 80 V Vdc = – 140 V

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CONCLUDING REMARKS

The EED can be manipulated by beam electron injection in CCP.

Beam electron heating power is strong adjacent to the electrodes due to large decelerating sheath potential.

Beam electron heating power is dependent on the beam electron energy due to the energy dependency of Coulomb collision between beam and bulk electrons.

Negative bias on the electrode plays a same role to produce electron beam injected into the bulk plasma altering the bulk EED.

The beam heating effect is more prominent when the amplitude of dc bias is larger than rf voltage, since the beam electrons produce secondary electron emission when hitting the other electrode.

University of MichiganInstitute for Plasma Science & Engr.22/22SHS_MJK_GEC2012

CONTROL OF ELECTRON ENERGY DISTRIBUTIONS THROUGH INTERACTION OF ELECTRON BEAMS AND THE BULK IN CAPACITIVELY COUPLED PLASMAS* Sang-Heon Song a) and Mark.

Documents

beam electron vb

beam electron transfers

bulk electron vth

smaller beam electron

interaction of electron

bulk electrons

ebeam ccp2d

ebeam injection