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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 - PowerPoint PPT Presentation
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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
b)Department of Electrical Engineering and Computer ScienceUniversity of Michigan, Ann Arbor, MI 48109, USA
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.
SHS_MJK_GEC2012
ELECTRON BEAM CONTROL OF f()
University of MichiganInstitute for Plasma Science & Engr.
Ref: S.-H. Seo, J. Appl. Phys. 98, 043301 (2005)
Ar, 3 mTorr Unipolar dc pulse, -350 V PRF = 20 kHz, Duty cycle = 50%
SHS_MJK_GEC2012
In pulsed dc magnetron, the electron energy distribution has a raised tail portion due to beam-like secondary electrons
ELECTRON BEAM-BULK INTERACTION
University of MichiganInstitute for Plasma Science & Engr.
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.
SHS_MJK_GEC2012
Ref: I. Silin, Phys. Plasmas 14, 012106 (2007)
Vlasov-Poisson Simulation nb/ne = 3 x 10-3, vDe/vTe = 8.0
ne
nb
University of MichiganInstitute 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
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
University of MichiganInstitute for Plasma Science & Engr.
SHS_MJK_GEC2012
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.
University of MichiganInstitute for Plasma Science & Engr.
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.
SHS_MJK_GEC2012
Injection of Beam Electron
SHS_MJK_GEC2012
REACTOR GEOMETRY: E-BEAM CCP
University of MichiganInstitute for Plasma Science & Engr.
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
ELECTRON DENSITY & TEMPERATURE
Without beam-bulk interaction With beam-bulk interaction
University of MichiganInstitute for Plasma Science & Engr.
Electron density is larger with beam-bulk interaction due to the increase of bulk electron temperature through the interaction.
MIN MAX
SHS_MJK_GEC2012
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.
University of MichiganInstitute for Plasma Science & Engr.
MIN MAX[3 dec]
Ar/N2 = 80/20, 40 mTorr, 100 eV Beam = 0.05 mA/cm2, Vrf = 50 V (10 MHz)
SHS_MJK_GEC2012
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.
University of MichiganInstitute for Plasma Science & Engr.
Ar/N2 = 80/20, 40 mTorr Beam = 0.05 mA/cm2, Vrf = 50 V (10 MHz)
SHS_MJK_GEC2012
Axial Heating Profile Average Heating Power Density
EED: BEAM ELECTRON ENERGY
100 eV 400 eV
University of MichiganInstitute for Plasma Science & Engr.
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
SHS_MJK_GEC2012
REACTOR GEOMETRY: E-BEAM CCP
University of MichiganInstitute for Plasma Science & Engr.
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
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
University of MichiganInstitute for Plasma Science & Engr.
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
SHS_MJK_GEC2012
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.
University of MichiganInstitute for Plasma Science & Engr.
Ar/N2 = 80/20, 40 mTorr Vdc = – 100 V, Vrf = 50 V (10 MHz)
Upper Center Secondary electron
emission coefficient ( = 0.15
SHS_MJK_GEC2012
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
University of MichiganInstitute for Plasma Science & Engr.
SHS_MJK_GEC2012
*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
University of MichiganInstitute for Plasma Science & Engr.
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
ELECTRON ENERGY DISTRIBUTION: e-SEE
University of MichiganInstitute for Plasma Science & Engr.
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
SHS_MJK_GEC2012
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