CONTROL OF ELECTRON ENERGY DISTRIBUTIONS THROUGH INTERACTION OF ELECTRON BEAMS AND THE BULK IN CAPACITIVELY COUPLED PLASMAS*

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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 ssongs_at_umich.edu b)Department of Electrical
Engineering and Computer Science University of
Michigan, Ann Arbor, MI 48109, USA
mjkush_at_umich.edu http//uigelz.eecs.umich.edu Gas
eous Electronics Conference October 24th, 2012
Work supported by DOE Plasma Science Center,
Semiconductor Research Corp. and National Science
Foundation
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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

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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)
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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)
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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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HYBRID PLASMA EQUIPMENT MODEL (HPEM)
Te, Sb, Ss, k
Fluid Kinetics Module Fluid equations (continuity,
momentum, energy) Poissons equation
Electron Monte Carlo Simulation
E, Ni, ne

• Fluid Kinetics Module
• Heavy particle continuity, momentum, energy
• Poissons equation
• Electron Monte Carlo Simulation
• Includes secondary electron transport
• Captures anomalous electron heating
• Includes electron-electron collisions

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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.
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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

• 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.

MIN
MAX

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

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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)

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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)

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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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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)

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ELECTRON ENERGY DISTRIBUTION

• Upper

• Center

• 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)

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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.

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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)
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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

• 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

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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.

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