Viz Glow Training Module Plasma Modeling With Viz

Viz. Glow Training Module Plasma Modeling With Viz. Glow: Low-Temperature Plasma Discharge Theory (Part 2) 1301 S. Capital of Texas Highway Suite B-122 Austin, Texas 78746 www. esgeetech. com September 2015

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3 Sheaths

4 Sheaths §

5 Collisionless Sheath (low pressure) Bulk Plasma wall Number density Presheath Sheath Potential wall Un-driven (floating) sheath: no applied potential at the wall § Bulk Plasma : Quasi-neutral, negligible potential drop § Pre-sheath : Quasi-neutral, small potential drop (thickness ~ ion Debye length) § Sheath : Non-neutral, larger potential drop (thickness ~ few electron Debye lengths

6 Analysis of collisionless sheath: approximations § Electrons are in Boltzmann equilibrium § Constant electron temperature § No ionization in the sheath, ion continuity equation § Ions travel ballistically in the sheath (no collisions), energy conservation

7 Bohm sheath criterion § Bohm velocity

8 Potential drop in the bulk plasma § Zero ion velocity at center of plasma (symmetry), zero potential at sheath edge (assumed boundary condition) Potential at the center of the plasma with respect to the sheath edge for a collisionless sheath

9 Sheath potential at a floating wall § The ion flux in the sheath is (constant) § The electron flux at the wall is § Assuming no net current is carried to the wall by the plasma Potential at the wall with respect to the sheath edge for a collisionless sheath

Sheaths with applied voltage at the wall: Matrix sheath model (1/2) § 10

11 Matrix sheath model (2/2) § Matrix sheath thickness

12 Child law sheath model - collisionless (1/3) § The Child law sheath model accounts for the decrease in ion density in the sheath § Assumptions: § The applied voltage is much greater than the ion energy at the sheath edge, and § Ions travel in the sheath without collisions § Negligible electron density in the sheath § Conservation of energy and mass for ions § The ion density in the sheath can be expressed as

13 Child law sheath model – collisionless (2/3) § Potential in the sheath for Child’s law model

14 Child law sheath model – collisionless (3/3) § Child’s law (or Child-Langmuir law) for collisionless sheaths Child law sheath thickness

15 DC and Capacitive Discharges

16 Direct Current Discharges (DCD) § Ions accelerated in the sheath region towards the cathode surface § Excited species also diffuse towards the cathode surface § On impact, secondary electrons generated at cathode (Auger process) § Electrons are accelerated by the sheath electric fields reach the sheath edge resulting in electron impact excitation/ionization § Secondary electron emission processes are necessary to sustain discharge § Low-density plasmas (109 -1010 cm-3) E Potential +

17 Direct Current Discharges (DCD) – Vacuum breakdown (1/3) Sheath edge cathode § Electric field accelerates electrons located near the cathode to the edge of the sheath § The energetic electrons collide with neutrals and produce ions Ionization mean free path 0 § Ions travel towards the cathode, and emit more electrons at the surface due to secondary electron emission z=d § To satisfy charge continuity, Self-sustaining z

18 Direct Current Discharges (DCD) – Vacuum breakdown (2/3) Sheath edge cathode § The breakdown Electric field is the minimum value of the electric field required to produce a self-sustained plasma Breakdown voltage 0 z=d z § Breakdown condition in vacuum d First Townsend coefficient VB

Direct Current Discharges (DCD) – Vacuum breakdown (3/3) § The breakdown voltage in vacuum (Paschen’s Law) Breakdown voltage d VB Breakdown voltage (Paschen’s Law) 19

20 Capacitively Coupled Plasmas (CCP) (1/3) § potential E

21 Capacitively Coupled Plasmas (CCP) (2/3) § CCP discharge parameters § § Plasma density: (1015 -1017 m-3) Electron temperature: 1 -5 e. V Ion (Gas) temperature: 300 -1000 K Ionization Fraction: 10 -6 -10 -4 § For 1 -D, total current density in the plasma is a constant in space 1 -D

22 Capacitively Coupled Plasmas (CCP) (3/3) § For 1 -D, total current density in the plasma is a constant in space Conduction Displacement current density Conduction current density § The current density in the bulk plasma is mainly conduction current § The current density in the sheath is mainly displacement current

23 Magnetron CCPs (1/2) § Electrons trapped along field lines; improved hot electron confinement; improved uniformity § Stable plasma at very low pressures § Collapse of positive sheath structure with decrease in cross field electron mobility; § Loss of self-shielding effect; inverted sheath structure § Bulk plasma E fields are stronger because of sheath collapse § Increased resistivity of discharge (ions are important current carriers) B E no B field potential with B field

24 Magnetron CCPs (2/2) § Increased sensitivity to secondary electron emission on powered electrode § Increased confinement of ionization/excitation sources near powered electrode § Decreased dc negative bias when powered electrode has a blocking capacitor § Decrease in ion impact energies when B field is included Effect of magnetic field on the IEDF E B

25 Magnetron CCPs § Electrons trapped along field lines; improved hot electron confinement; improved uniformity § Decrease in cross field electron mobility; § Increased resistivity of discharge (ions are important current carriers) With magnetic field No magnetic field Hall parameter no B field potential E with B field B

26 EM waves and plasmas – ICPs, Microwaves

27 Inductively Coupled Plasmas (ICP) § RF coils generate EM field § Induced E field deposits power to electrons through collisional/stochastic heating § Power deposition within skin depth § Induced B field has no significant consequence on charge particle dynamics § Relatively high-density plasmas (1010 -1012 cm-3) B E

28 Microwave Plasmas (Radial line source) § Microwaves create a standing wave pattern in a dielectric wave plate § Antenna transmits radiation to window § Standing wave pattern also established in window § Electric fields penetrate region at the window-plasma chamber interface and heat electrons, generates plasma discharge § Over dense discharge region produces ions and radicals § Ions and radicals diffuse to the surface § Typical plasma density ~ 1011 -1012 cm-3 Microwaves Wave plate Window Plasma Radial line source Antenna

29 Plasma Conductivity § Electron momentum equation § Homogeneous density (neglect density and pressure gradients) § Phasor form: § Current density Plasma conductivity

30 Plasma Dielectric Constant § Total current density § Plasma dielectric constant

31 Collisionless regime (real dielectric) § Wave propagation is unhindered § (speed lower; wavelength shortening) (cut-off density) § Collisionless regime: (negative refractive index) § Wave propagation is attenuated § (skin depth)

32 Collisional regime Highly collisional regime: § Lossy material, wave attenuated § DC plasma conductivity (skin depth)

A simple model to study plasma-EM wave interaction effects • Linearly increasing electron density in z • Cutoff location Zo is varied • Critical density for 2. 45 GHz = 7. 5 e 16 m-3 • Assume pressure = 50 m. Torr • Regime: Collision freq. = 3. 5 e 7 #/s Excitation freq = 1. 54 e 10 rad/s (Nearly collisionless) Ref: Yasaka and Hojo, Physics of Plasmas, 7 (2000), 1601. 33

34 Field variation in plasma (inlet Ay = 1 e-7 V/m-s) -0. 1 to 0 m = dielectric (eps = 1. 0) 0 to 0. 5 m = plasma with linearly varying density Ne= Ne_critical * (x/Zo) Zo = 0. 2 m Computation domain: underdense overdense Zo = 0. 08 m dielectric overdense Zo = 0. 015 m dielectric overdense Ref: Yasaka and Hojo, Physics of Plasmas, 7 (2000), 1601. 34

35 Power deposition in plasma Zo = 0. 015 m (pressure = 50 m. Torr in argon) dielectric overdense dielectric Zo = 0. 08 m overdense dielectric overdense Zo = 0. 2 m dielectric underdense overdense 35

36 Effect of collisions (varying pressure) Plasma conductivity: P (Torr) Coll. Freq. (#/s) Real conductivity at cutoff density (S/m) Imaginary conductivity at cutoff density (S/m) 0. 05 3. 5 e 7 3. 1 e-4 -1. 36 e-1 0. 5 3. 5 e 8 3. 1 e-3 -1. 36 e-1 5 3. 5 e 9 2. 95 e-2 -1. 3 e-1 50 3. 5 e 10 5. 02 e-2 2. 21 e-2 Note: Excitation frequency =

37 Effect of collisions (Zo = 0. 015 m case) Location of cutoff density 50 m. Torr 500 m. Torr 50 Torr

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