VUV PHOTON SOURCE OF A MICROWAVE EXCITED MICROPLASMAS AT LOW PRESSURE*

Slides:



Advertisements
Similar presentations
REACTION MECHANISM AND PROFILE EVOLUTION FOR CLEANING AND SEALING POROUS LOW-k DIELECTRICS USING He/H 2 AND Ar/NH 3 PLASMAS Juline Shoeb a) and Mark J.
Advertisements

PROPERTIES OF NONTHERMAL CAPACITIVELY COUPLED PLASMAS GENERATED IN NARROW QUARTZ TUBES FOR SYNTHESIS OF SILICON NANOPARTICLES* Sang-Heon Song a), Romain.
ION ENERGY DISTRIBUTIONS IN INDUCTIVELY COUPLED PLASMAS HAVING A BIASED BOUNDARY ELECTRODE* Michael D. Logue and Mark J. Kushner Dept. of Electrical Engineering.
CONTROL OF ELECTRON ENERGY DISTRIBUTIONS AND FLUX RATIOS IN PULSED CAPACITIVELY COUPLED PLASMAS* Sang-Heon Song a) and Mark J. Kushner b) a) Department.
CONTROL OF ELECTRON ENERGY DISTRIBUTIONS IN INDUCTIVELY COUPLED PLASMAS USING TANDEM SOURCES* Michael D. Logue (a), Mark J. Kushner (a), Weiye Zhu (b),
MODELING OF H 2 PRODUCTION IN Ar/NH 3 MICRODISCHARGES Ramesh A. Arakoni a), Ananth N. Bhoj b), and Mark J. Kushner c) a) Dept. Aerospace Engr, University.
OPTIMIZING THE PERFORMANCE OF PLASMA BASED MICROTHRUSTERS* Ramesh A. Arakoni, a) J. J. Ewing b) and Mark J. Kushner c) a) Dept. Aerospace Engineering University.
NUMERICAL INVESTIGATION OF WAVE EFFECTS IN HIGH-FREQUENCY CAPACITIVELY COUPLED PLASMAS* Yang Yang and Mark J. Kushner Department of Electrical and Computer.
EFFECT OF PRESSURE AND ELECTRODE SEPARATION ON PLASMA UNIFORMITY IN DUAL FREQUENCY CAPACITIVELY COUPLED PLASMA TOOLS * Yang Yang a) and Mark J. Kushner.
SiO 2 ETCH PROPERTY CONTROL USING PULSE POWER IN CAPACITIVELY COUPLED PLASMAS* Sang-Heon Song a) and Mark J. Kushner b) a) Department of Nuclear Engineering.
ISPC 2003 June , 2003 Consequences of Long Term Transients in Large Area High Density Plasma Processing: A 3-Dimensional Computational Investigation*
1 Particle-In-Cell Monte Carlo simulations of a radiation driven plasma Marc van der Velden, Wouter Brok, Vadim Banine, Joost van der Mullen, Gerrit Kroesen.
WAVE AND ELECTROSTATIC COUPLING IN 2-FREQUENCY CAPACITIVELY COUPLED PLASMAS UTILIZING A FULL MAXWELL SOLVER* Yang Yang a) and Mark J. Kushner b) a) Department.
FLUORINATION WITH REMOTE INDUCTIVELY COUPLED PLASMAS SUSTAINED IN Ar/F 2 AND Ar/NF 3 GAS MIXTURES* Sang-Heon Song a) and Mark J. Kushner b) a) Department.
SiO 2 ETCH RATE AND PROFILE CONTROL USING PULSE POWER IN CAPACITIVELY COUPLED PLASMAS* Sang-Heon Song a) and Mark J. Kushner b) a) Department of Nuclear.
THE WAFER- FOCUS RING GAP*
PLASMA DISCHARGE SIMULATIONS IN WATER WITH PRE-EXISTING BUBBLES AND ELECTRIC FIELD RAREFACTION Wei Tian and Mark J. Kushner University of Michigan, Ann.
WAFER EDGE EFFECTS CONSIDERING ION INERTIA IN CAPACITIVELY COUPLED DISCHARGES* Natalia Yu. Babaeva and Mark J. Kushner Iowa State University Department.
MAGNETICALLY ENHANCED MULTIPLE FREQUENCY CAPACITIVELY COUPLED PLASMAS: DYNAMICS AND STRATEGIES Yang Yang and Mark J. Kushner Iowa State University Department.
EDGE EFFECTS IN REACTIVE ION ETCHING: THE WAFER- FOCUS RING GAP* Natalia Yu. Babaeva and Mark J. Kushner Iowa State University Department of Electrical.
 Poisson’s equation, continuity equations and surface charge are simultaneously solved using a Newton iteration technique.  Electron energy equation.
STREAMER DYNAMICS IN A MEDIA CONTAINING DUST PARTICLES* Natalia Yu. Babaeva and Mark J. Kushner Iowa State University Department of Electrical and Computer.
LOW-k DIELECTRIC WITH H2/He PLASMA CLEANING
INVESTIGATIONS OF MAGNETICALLY ENHANCED RIE REACTORS WITH ROTATING (NON-UNIFORM) MAGNETIC FIELDS Natalia Yu. Babaeva and Mark J. Kushner University of.
MODELING OF MICRODISCHARGES FOR USE AS MICROTHRUSTERS Ramesh A. Arakoni a), J. J. Ewing b) and Mark J. Kushner c) a) Dept. Aerospace Engineering University.
MODELING OF MICRODISCHARGES FOR USE AS MICROTHRUSTERS Ramesh A. Arakoni a), J. J. Ewing b) and Mark J. Kushner c) a) Dept. Aerospace Engineering University.
Aspect Ratio Dependent Twisting and Mask Effects During Plasma Etching of SiO2 in Fluorocarbon Gas Mixture* Mingmei Wang1 and Mark J. Kushner2 1Iowa State.
STREAMER INITIATION AND PROPAGATION IN WATER WITH THE ASSISTANCE OF BUBBLES AND ELECTRIC FIELD INITIATED RAREFACTION Wei Tian a) and Mark J. Kushner b)
OPTIMIZATION OF O 2 ( 1  ) YIELDS IN PULSED RF FLOWING PLASMAS FOR CHEMICAL OXYGEN IODINE LASERS* Natalia Y. Babaeva, Ramesh Arakoni and Mark J. Kushner.
SIMULATION OF POROUS LOW-k DIELECTRIC SEALING BY COMBINED He AND NH 3 PLASMA TREATMENT * Juline Shoeb a) and Mark J. Kushner b) a) Department of Electrical.
PLASMA DYNAMICS OF MICROWAVE EXCITED MICROPLASMAS IN A SUB-MILLIMETER CAVITY* Peng Tian a), Mark Denning b), Mehrnoosh Vahidpour, Randall Urdhal b) and.
TRIGGERING EXCIMER LASERS BY PHOTOIONIZATION FROM A CORONA DISCHARGE* Zhongmin Xiong and Mark J. Kushner University of Michigan Ann Arbor, MI USA.
Yiting Zhangb, Mark Denninga, Randall S. Urdahla and Mark J. Kushnerb
Photos placed in horizontal position with even amount of white space between photos and header Sandia National Laboratories is a multi-program laboratory.
Why plasma processing? (1) UCLA Accurate etching of fine features.
SPACE AND PHASE RESOLVED MODELING OF ION ENERGY ANGULAR DISTRIBUTIONS FROM THE BULK PLASMA TO THE WAFER IN DUAL FREQUENCY CAPACITIVELY COUPLED PLASMAS*
SiO2 ETCH PROPERTIES AND ION ENERGY DISTRIBUTION IN PULSED CAPACITIVELY COUPLED PLASMAS SUSTAINED IN Ar/CF4/O2* Sang-Heon Songa) and Mark J. Kushnerb)
ATMOSPHERIC PRESSURE PLASMA TRANSFER OF JETS AND BULLETS ACROSS DIELECTRIC TUBES AND CHANNELS* Zhongmin Xiong (a), Eric Robert (b), Vanessa Sarron (b)
The propagation of a microwave in an atmospheric pressure plasma layer: 1 and 2 dimensional numerical solutions Conference on Computation Physics-2006.
FLCC March 28, 2005 FLCC - Plasma 1 Fluid Modeling of Capacitive Plasma Tools FLCC Presentation March 28, 2005 Berkeley, CA David B. Graves, Mark Nierode,
EXCITATION OF O 2 ( 1 Δ) IN PULSED RADIO FREQUENCY FLOWING PLASMAS FOR CHEMICAL IODINE LASERS Natalia Babaeva, Ramesh Arakoni and Mark J. Kushner Iowa.
DEVELOPMENT OF ION ENERGY ANGULAR DISTRIBUTION THROUGH THE PRE-SHEATH AND SHEATH IN DUAL-FREQUENCY CAPACITIVELY COUPLED PLASMAS* Yiting Zhanga, Nathaniel.
CONTROL OF ELECTRON ENERGY DISTRIBUTIONS THROUGH INTERACTION OF ELECTRON BEAMS AND THE BULK IN CAPACITIVELY COUPLED PLASMAS* Sang-Heon Song a) and Mark.
DRY ETCHING OF Si 3 N 4 USING REMOTE PLASMA SOURCES SUSTAINED IN NF 3 MIXTURES* Shuo Huang and Mark J. Kushner Department of Electrical Engineering and.
PROPERTIES OF UNIPOLAR DC-PULSED MICROPLASMA ARRAYS AT INTERMEDIATE PRESSURES* Peng Tian a), Chenhui Qu a) and Mark J. Kushner a) a) University of Michigan,
Consequences of Implanting and Surface Mixing During Si and SiO 2 Plasma Etching* Mingmei Wang 1 and Mark J. Kushner 2 1 Iowa State University, Ames, IA.
HIGH FREQUENCY CAPACITIVELY COUPLED PLASMAS: IMPLICIT ELECTRON MOMENTUM TRANSPORT WITH A FULL-WAVE MAXWELL SOLVER* Yang Yang a) and Mark J. Kushner b)
DBD ON LIQUID COVERED TISSUE: MODELING LONG-TIMESCALE CHEMISTRY*
Chenhui Qu, Peng Tian and Mark J. Kushner
PLASMA DYNAMICS AT THE IONIZATION FRONT OF HIGH
University of Michigan, Ann Arbor, MI, 48109, USA
Yiting Zhang and Mark J. Kushner
ENERGY LOADING AND DECAY OF N2 VIBRATION
Amanda M. Lietza and Mark J. Kushnerb
DEVELOPMENT OF ION ENERGY DISTRIBUTIONS THROUGH THE PRE-SHEATH AND SHEATH IN DUAL-FREQUENCY CAPACITIVELY COUPLED PLASMAS* Yiting Zhanga, Nathaniel Mooreb,
COMPLEX ELECTRON ENERGY DISTRIBUTIONS IN ASYMMETRIC RF-DC DISCHARGES
DEVELOPMENT OF ION ENERGY DISTRIBUTIONS THROUGH THE PRE-SHEATH AND SHEATH IN DUAL-FREQUENCY CAPACITIVELY COUPLED PLASMAS* Yiting Zhanga, Nathaniel Mooreb,
Sang-Heon Songa) and Mark J. Kushnerb)
ENGINEERING THE FOCUS RING*
PLASMA PROPAGATION THROUGH POROUS BONE SCAFFOLDING*
Amanda M. Lietz, Seth A. Norberg, and Mark J. Kushner
Flux and Energy of Reactive Species Arriving at the Etch Front in High Aspect Ratio Features During Plasma Etching of SiO2 in Ar/CF4/CHF3 Mixtures* Soheila.
Peng Tian, Sang-Heon Song and Mark J. Kushner
Chenhui Qua), Steven Lanhama), Peng Tiana),
SURFACE CORONA-BAR DISCHARGES
ELECTRON CURRENT EXTRACTION
CONTROL OF ION ACTIVATION ENERGY TO SURFACES IN ATMO-
ION ENERGY DISTRIBUTIONS TO PARTICLES IN CORONA DISCHARGES
BREAKDOWN CHARACTERISTICS
Presentation transcript:

VUV PHOTON SOURCE OF A MICROWAVE EXCITED MICROPLASMAS AT LOW PRESSURE* Peng Tiana), Mark Denningb) and Mark J. Kushnera) a)University of Michigan, Ann Arbor, MI 48109 USA tianpeng@umich.edu, mjkush@umich.edu b)Agilent Technologies, 5301 Stevens Creek Blvd, Santa Clara, CA mark.denning@agilent.com * Work supported by Agilent Technologies.

University of Michigan Institute for Plasma Science & Engr. AGENDA Microplasma UV/VUV photon sources Split Ring Microwave Micro-plasma Description of model Photon generation Pressure Pd Scaling Pulsing with Ar/He gas mixtures Concluding Remarks University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T.

UV/VUV PHOTON SOURCES BY MICROPLASMA Rare gas microplasmas are efficient and discretely tunable UV/VUV light sources. Compact, inexpensive microplasma light sources have many applications ranging from analytical chemistry, mass spectrometry and surface analysis. Controlling metastable fluxes, light wavelengths and ion, VUV photon fluxes are important to achieving chemical selectivity. Microwave excited microplasmas can provide lower excitation voltage, high power efficiency and longer life time of the devices compared with DC microplasmas. In this project, a microwave excited microplasma light source by a split-ring resonator (SRR) antenna will be studied as discretely tunable VUV source. University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T.

SPLIT-RING-RESONATOR (SRR) MICROPLASMA CAVITY A microstrip split-ring resonator was investigated to ignite and sustain a RF microplasma proposed by N. Miura and J. Hopwood. This concept was further developed as a SRR microplasma cavity as VUV light source. Recently, N. Miura and J. Hopwood in Tufts University proposed a microstrip split-ring resonator to ignite and sustain RF microplasma. This concept was then further developed as a SRR microplasma cavity as a VUV light source. University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T.

SRR-GEOMETRY BASE CASE Main focus: production of VUV photons and metastable states at the collection plane. Microwave capacitively coupled plasma excited by push-pull electrodes. Quartz coated electrodes. Base Condition: Ar, 4 Torr, 3 sccm 2.5 GHz CW power, 2 W. Cavity width: 2 mm The geometry of the light source is a micro-cavity, which is shown in this slide. The cavity is about 2 mm in width and 1.5 mm in height, with side wall formed by alumina. Two electrodes are sitting at the bottom driven by microwave, and operated in a push-pull mode. Quartz is used to coat the electrode. Two openings on the cavity, with gas flows in from the bottom, and plasma/photon come through from the top opening. In this setup, different species are collected on the top plane in the diffusion region, while the plane is considered metal and grounded. The base case, plasma is ingnited and sustained in pure Argon, 4 Torr and 3 sccm. Frequency is 2.5 GHz. University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T.

University of Michigan Institute for Plasma Science & Engr. ATOMIC MODEL FOR Ar Ar(4p) Ar(1s3) Ar+ Ar(1s2) Ar(1s5) Ar(1s4) Ar(3s)  = 105, 106 nm Ar(4d) Argon Species: Ar(3s), Ar(1s2,3,4,5), Ar(4p), Ar(4d), Ar+, Ar2+, e Electron impact excitation and super-elastic collisions between all levels. Radiation transport for Ar(1s2) (106 nm), Ar(1s4) (105 nm) and Ar2* (121 nm). This is the atomic model of Argon. Excited states are resolved, excimer ions are also resolved. University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T.

HYBRID PLASMA EQUIPMENT MODEL Surface Chemistry Module The Hybrid Plasma Equipment Model (HPEM) is a modular simulator that combines fluid and kinetic approaches. Radiation transport is addressed using a spectrally resolved Monte Carlo simulation. University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T.

RADIATION TRANSPORT MODEL IN HPEM Frequency resolved radiation transport in HPEM is modeled using a Monte Carlo simulation that accounts for radiation trapping MIPSE_2013 P.T.

ELECTRON DENSITY & TEMPERATURE First, here is the basic plasma properties for a CW base case. The plasma has a diffusive profile, with an electron density close to 1014 cm-3, that is an ionization fraction of 1%. The electron temperature in the cavity is distributed quite uniform, with a relative high te even in the diffusion region, that is because of high energy electron can scatter through the opening, since they have smaller collision cross section. Electron Density Electron Temperature Electron density reaches nearly 1014 cm-3, or an ionization fraction of 1%. High energy electrons scatter through nozzle due to smaller collision cross section. Ar, 4 Torr, 3 sccm, 2 W University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T.

University of Michigan Institute for Plasma Science & Engr. ION DENSITIES Also, the ions consists of two portion, Ar+ and Ar2+ . The have the same order of magnitude, with Ar+ a little more. We believe the Ar2+ are mainly formed by 2 body associative ionization. The ion will then be driven to the collection plane on top by the ambipolar electric field. Ar2+ Density Ar+ Density Substantial amount of Ar2+ are created by 2 body associative ionization. Ions driven through nozzle by positive plasma potential. Ar, 4 Torr, 3 sccm, 2 W University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T.

Total Ion and Photon flux FLUX TO TOP PLANES The fluxes collected on the top plane are shown here. The left shows flux of different ions and photons. Photons most from Ar*, Ar dimer radiation is not important. But for ion, Ar excimer ions are important. Ion and Photon fluxes Total Ion and Photon flux Resonant radiation from Ar excited states is the main photon source, far exceeding the excimer radiation from Ar2*. Ar+ and Ar2+ fluxes are comparable at the collection plane. Ar, 4 Torr, 3 sccm, 2 W Fluxes University of Michigan Institute for Plasma Science & Engr.

POWER/PRESSURE=0.5 W/Torr: ELECTRON DENSITY Bulk electron densities maintain a diffusive profile due to highly conductive plasma. Peak electron densities are 1013 cm-3 with power/pressure=0.5 W/Torr We then trying to gain some control on the photon generation in CW plasma. We change different parameters along the way, but always keeping power/atom constant for all the different conditions. First, change pressure. Increase power correspondingly, such that power/pressure, i.e. power/atom is constant. The plasma maintain a diffusive profile, because of its large density and high conductivity. The peak electron density is also maintained fairly steady between 6-10 x 10^13 cm^-3. We do observe a localization of plasma at higher pressure, a more flat shape of the electron density profile. Electron Density (cm-3) University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T.

POWER/PRESSURE=0.5 W/Torr: Ar(1s2)+Ar(1s4) As Pressure increases, mean free path decreases. The source of photons (Ar(1s2, 1s4)) is localized above electrodes. Power efficiency of photon generation decreases. Meanwhile, photon generation changed. Due to smaller MFP at high pressure, source of photons, the radiative states of Ar, is localized above the electrodes. With the peak excited states density unchanged, this profile shows a decreasing photon generation efficiency as pressure increases. Ar Radiative States (cm-3) University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T.

University of Michigan Institute for Plasma Science & Engr. PD (PRESSURE x SIZE) SCALING 1 1/2 1/4 Varying the size of cavity, while keeping pd (pressure x size) constant. The input power is also varied to keep (power/Ngas Volume) constant. Flow rate adjusted to maintain constant gas residence time. Having a split photon source could be a problem at certain cases, so we tried to push it at the center again by shrinking the size of the cavity. In order to maintain a similar operation condition for the microwave source, the pd scaling is kept constant by increasing the pressure at smaller cavity size, such that according to the paschen’s law, breakdown voltage is kept the same. The flow rate of the gas was also adjusted to maintain constant gas residence time. Also, as stated earlier, power/atom is kept constant. University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T.

University of Michigan Institute for Plasma Science & Engr. PD SCALING : LIGHT SOURCE SIZE Photon sources are confined at center of the cavity. Relative source size (Source/Cavity) decreases at higher pressure (i.e., smaller cavity). 4 Torr Relative Source Size Here are the results. The photon sources (Ar radiative states) have a similar diffusive profile with bulk plasma, even at high pressure due to the confinement of smaller cavity size. These sources are characterized by their sizes, at 50% and 20% of its center value. The size is then compared with its corresponding cavity size, to see how large the source is compared with the cavity. The trend is shown in the 1-d plot. The source is more condensed when the cavity is small. 8 Torr 16 Torr Ar(1S2)+Ar(1S4), Max=8.7 x 1013 cm-3 [2 dec] University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T.

University of Michigan Institute for Plasma Science & Engr. PD SCALING: EFFICIENCY As pressure increases (cavity size decreases): The photon source is more focused at center of the cavity, providing larger viewing angle to top plane. Power efficiency of photon source increases. Photon Flux vs. Power The efficiency is then characterized by the center photon flux on the top plane vs. input power. At smaller size and higher pressure, the efficiency increases. This could be explained by a larger viewing of the source to the plane, due to a more focused source at higher pressure. Photon Flux University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T.

University of Michigan Institute for Plasma Science & Engr. PULSING - GAS MIXTURES: Ar We then do an investigation on pulsing. The RF pulse is implemented using a 200 kHz PRF rectangular pulse, with a 10% duty cycle. This time, the voltage is kept constant at 160 V. Electron temperature and plasma potential overshoots during pulse, and fall back. Electron temperature is maintained by superelastic collisions. Bulk Ion Density and Photon Flux Te and Plasma Potential Electron temperature over-shoots at the beginning of pulse. Bulk averaged photon flux and ion density peaked during pulse-on time. 200 kHz PRF, 10% DC, 160 V. University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T.

University of Michigan Institute for Plasma Science & Engr. PULSING - GAS MIXTURES: He/Ar He/Ar=90/10 He/Ar=70/30 He/Ar=10/90 Then, Helium is added to the gas mixture. We can observe an increase of peak electron temperature with higher helium fraction during pulse, and similar after-glow temperature. As a result, a larger photon flux over-shoot is generated. With more He, larger over-shoot of Te enhanced photon generation during pulse-on period. University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T.

University of Michigan Institute for Plasma Science & Engr. PULSING - GAS MIXTURES: He/Ar He/Ar=90/10 He/Ar=70/30 He/Ar=10/90 And it can be seen that Ar+ is always the dominant ion in the plasma even with 90% of He, due to charge exchange and penning ionization. Penning ionization also accounts for the fast drop of high energy photon flux in afterglow. Pening ionization is depleting He radiative states during afterglow. Ar+ is always the dominant ion in plasma. University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T.

University of Michigan Institute for Plasma Science & Engr. CONCLUDING REMARKS Modeling of a microwave excited SRR microplasmas as sources of VUV light. Pure Ar plasma at 4 Torr, 2 W produces peak electron density close to 1014 cm-3, a fractional ionization of 1%. Shape and position of light source in plasma can be controlled by pressure. The relative size of light source in plasma and power efficiency of photon flux generation is related to the size of the cavity, with p*d scale kept unchanged. Pulsing with He addition could increase Te and thus enhanced pulsing effect. University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T. 20 20

BACKUP SLIDES

APPLICATION OF MICROWAVE LIGHT SOURCES Microplasmas as VUV light source for resonance absorption spectroscopy University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T.

HPEM-EQUATIONS SOLVED - Electron Energy Distributions – Electron Monte Carlo Simulation Phase dependent electrostatic fields Phase dependent electromagnetic fields Electron-electron collisions using particle-mesh algorithm Phase resolved electron currents computed for wave equation solution. Captures long-mean-free path and anomalous behavior. Separate calculations for bulk and beam (secondary electrons)

HPEM-EQUATIONS SOLVED -

VARYING PRESSURE AND POWER: CONDITION Pressure (Torr) Power (W) 4 2 6 3 8 10 5 12 16 20 Based on base case condition, change pressure and power. Power deposited per particle is kept constant by keeping Power/Pressure = 0.5 W/Torr MIPSE_2013 P.T.

University of Michigan Institute for Plasma Science & Engr. PULSED PLASMAS Carrier frequency is modulated by a pulse, a fixed pulsing voltage and duty cycle. The fast rising edge can “over-shoot” the self sustaining E/N, raising the “hot tail” in EEDF f(). Time  = 1/ Duty Cycle Power(t) Pmax Pmin University of Michigan Institute for Plasma Science & Engr. MIPSE_2013 P.T.