Transcript Document

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
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 electronelectron Coulomb collision.
 The electron beam heating power density (Peb)
1  new 2
2
 W  1
Peb  3    ne 
me  vb
 vb 


 cm  t
i 2

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Institute for Plasma Science & Engr.
HYBRID PLASMA EQUIPMENT MODEL (HPEM)
Electron
Monte Carlo
Simulation
Te, Sb, Ss, k
E, Ni, ne
Fluid Kinetics Module
Fluid equations
(continuity, momentum, energy)
Poisson’s equation
 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
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Institute for Plasma Science & Engr.
FLOW CHART: E-BEAM BULK INTERACTION
Electron Monte Carlo Simulation
MCS
Bulk electron transport calculation
...
Update f()
...
MCSEB
Bulk electron at
(i, j )
gains energy by
Eiloss
,j
in random direction.
Beam electron transport calculation
Collision between beam electron (vb) and bulk electron (vth) occurs.
Record energy loss of beam electron.
Eijloss
1  new 2
2
 me  vb
 vb 
2 

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
 Ar/N2 = 80/20, 40 mTorr, 100 eV
 Beam = 0.05 mA/cm2, Vrf = 50 V (10 MHz)
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MAX
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Institute for Plasma Science & Engr.
E-BEAM HEATING POWER DENSITY
[3 dec]
MIN
MAX
 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.
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 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.
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 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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