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CONTROL OF ELECTRON ENERGY DISTRIBUTIONS THROUGH INTERACTION OF ELECTRON BEAMS AND THE BULK IN CAPACITIVELY COUPLED PLASMAS * Sang-Heon Song a) and Mark J. Kushner b) a) Department of Nuclear Engineering and Radiological Sciences University of Michigan, Ann Arbor, MI 48109, USA

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slide1
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 Science

University 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

slide2
University of Michigan

Institute for Plasma Science & Engr.

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

SHS_MJK_GEC2012

slide3
University of Michigan

Institute for Plasma Science & Engr.

ELECTRON BEAM CONTROL OF f()

  • In pulsed dc magnetron, the electron energy distribution has a raised tail portion due to beam-like secondary electrons
  • Ar, 3 mTorr
  • Unipolar dc pulse, -350 V
  • PRF = 20 kHz, Duty cycle = 50%

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

SHS_MJK_GEC2012

slide4
University of Michigan

Institute for Plasma Science & Engr.

ELECTRON BEAM-BULK INTERACTION

ne

nb

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

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

SHS_MJK_GEC2012

slide5
University of Michigan

Institute for Plasma Science & Engr.

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)

SHS_MJK_GEC2012

slide6
University of Michigan

Institute for Plasma Science & Engr.

HYBRID PLASMA EQUIPMENT MODEL (HPEM)

Te,Sb, Ss, k

Fluid Kinetics Module

Fluid equations

(continuity, momentum, energy)

Poisson’s equation

Electron

Monte Carlo Simulation

E,Ni, ne

  • 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

SHS_MJK_GEC2012

slide7
University of Michigan

Institute for Plasma Science & Engr.

FLOW CHART: E-BEAM BULK INTERACTION

Electron Monte Carlo Simulation

Bulk electron transport calculation

MCS

...

gains energy by

Bulk electron at

Update f(e)

...

in random direction.

MCSEB

Beam electron transport calculation

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.

SHS_MJK_GEC2012

slide9
University of Michigan

Institute for Plasma Science & Engr.

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

SHS_MJK_GEC2012

slide10
University of Michigan

Institute for Plasma Science & Engr.

ELECTRON DENSITY & TEMPERATURE

  • With beam-bulk interaction
  • Without beam-bulk interaction
  • Electron density is larger with beam-bulk interaction due to the increase of bulk electron temperature through the interaction.

MAX

MIN

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

SHS_MJK_GEC2012

slide11
University of Michigan

Institute for Plasma Science & Engr.

E-BEAM HEATING POWER DENSITY

[3 dec]

MAX

MIN

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

SHS_MJK_GEC2012

slide12
University of Michigan

Institute for Plasma Science & Engr.

HEATING: BEAM ELECTRON ENERGY

  • Axial Heating Profile
  • Average Heating Power Density
  • 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)

SHS_MJK_GEC2012

slide13
University of Michigan

Institute for Plasma Science & Engr.

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)

SHS_MJK_GEC2012

negative dc bias

Negative dc Bias

SHS_MJK_GEC2012

slide15
University of Michigan

Institute for Plasma Science & Engr.

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

SHS_MJK_GEC2012

slide16
University of Michigan

Institute for Plasma Science & Engr.

E-BEAM HEATING POWER DENSITY

  • Sec. coefficient (g) = 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

MAX

MIN

[3 dec]

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

SHS_MJK_GEC2012

slide17
University of Michigan

Institute for Plasma Science & Engr.

ELECTRON ENERGY DISTRIBUTION

  • Center
  • Upper
  • Secondary electron emission coefficient (g) = 0.15
  • 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)

SHS_MJK_GEC2012

slide18
University of Michigan

Institute for Plasma Science & Engr.

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.

SHS_MJK_GEC2012

slide19
University of Michigan

Institute for Plasma Science & Engr.

SECONDARY EMISSION YIELD

  • 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.

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

SHS_MJK_GEC2012

slide20
University of Michigan

Institute for Plasma Science & Engr.

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

SHS_MJK_GEC2012

slide21
University of Michigan

Institute for Plasma Science & Engr.

ELECTRON ENERGY DISTRIBUTION: e-SEE

  • Vdc = – 80 V
  • Vdc = – 140 V
  • 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

SHS_MJK_GEC2012

slide22
University of Michigan

Institute for Plasma Science & Engr.

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.

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SHS_MJK_GEC2012

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