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 b) Department of Electrical Engineering and Computer Science University of Michigan, Ann Arbor, MI 48109, USA Gaseous Electronics Conference October 24 th, 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 Michigan Institute for Plasma Science & Engr. SHS_MJK_GEC2012

ELECTRON BEAM CONTROL OF f(  ) University of Michigan Institute for Plasma Science & Engr. Ref: S.-H. Seo, J. Appl. Phys. 98, (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 Michigan Institute for Plasma Science & Engr.  The coherent Langmuir wave is generated with n b /n e 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, (2007)  Vlasov-Poisson Simulation  n b /n e = 3 x 10 -3, v De /v Te = 8.0 nene nbnb

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 (P eb ) SHS_MJK_GEC2012

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, N i, n e Fluid Kinetics Module Fluid equations (continuity, momentum, energy) Poisson’s equation T e, S b, S s, k Electron Monte Carlo Simulation University of Michigan Institute 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 (v b ) and bulk electron (v th ) occurs. Record energy loss of beam electron. Energy loss is transferred to bulk electron energy distribution. University of Michigan Institute for Plasma Science & Engr. Bulk electron transport calculation Beam electron transport calculation... Bulk electron at gains energy by in random direction. SHS_MJK_GEC2012

Injection of Beam Electron SHS_MJK_GEC2012

REACTOR GEOMETRY: E-BEAM CCP University of Michigan Institute for Plasma Science & Engr.  2D, cylindrically symmetric  Ar/N 2 = 80/20, 40 mTorr, 200 sccm  Base case conditions  Lower electrode: 50 V, 10 MHz  Upper electrode: e-Beam injection with 0.05 mA/cm 2 SHS_MJK_GEC2012

ELECTRON DENSITY & TEMPERATURE  Without beam-bulk interaction  With beam-bulk interaction University of Michigan Institute 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/N 2 = 80/20, 40 mTorr, 100 eV  Beam = 0.05 mA/cm 2, V rf = 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 Michigan Institute for Plasma Science & Engr. MIN MAX [3 dec]  Ar/N 2 = 80/20, 40 mTorr, 100 eV  Beam = 0.05 mA/cm 2, V rf = 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 Michigan Institute for Plasma Science & Engr.  Ar/N 2 = 80/20, 40 mTorr  Beam = 0.05 mA/cm 2, V rf = 50 V (10 MHz) SHS_MJK_GEC2012  Axial Heating Profile  Average Heating Power Density

EED: BEAM ELECTRON ENERGY  100 eV  400 eV University of Michigan Institute 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/N 2 = 80/20, 40 mTorr  Beam = 0.05 mA/cm 2, V rf = 50 V (10 MHz) SHS_MJK_GEC2012

Negative dc Bias SHS_MJK_GEC2012

REACTOR GEOMETRY: E-BEAM CCP University of Michigan Institute for Plasma Science & Engr.  2D, cylindrically symmetric  Ar/N 2 = 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 Michigan Institute for Plasma Science & Engr. MIN MAX [3 dec]  Ar/N 2 = 80/20, 40 mTorr  V dc = – 100 V, V rf = 50 V (10 MHz)  Sec. coefficient (  ) = 0.15  Ion flux = 2 x cm -2 s -1  e-beam current = 0.05 mA/cm 2  e-beam density = 4 x 10 5 cm -3  Plasma density = 2 x 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 Michigan Institute for Plasma Science & Engr.  Ar/N 2 = 80/20, 40 mTorr  V dc = – 100 V, V rf = 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 Michigan Institute for Plasma Science & Engr. SHS_MJK_GEC2012

SECONDARY EMISSION YIELD University of Michigan Institute for Plasma Science & Engr. SHS_MJK_GEC2012 *Ref: C. K. Purvis, NASA Technical Memorandum, (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 Michigan Institute 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/N 2 = 80/20, 40 mTorr  V rf = 100 V SHS_MJK_GEC2012

ELECTRON ENERGY DISTRIBUTION: e-SEE University of Michigan Institute 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/N 2 = 80/20, 40 mTorr  V rf = 100 V  V dc = – 80 V  V dc = – 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 Michigan Institute for Plasma Science & Engr. 22/22 SHS_MJK_GEC2012