A SHORT COURSE ON THE PRINCIPLES OF PLASMA DISCHARGES AND MATERIALS PROCESSING
|
|
- Anastasia Lawson
- 6 years ago
- Views:
Transcription
1 A SHORT COURSE ON THE PRINCIPLES OF DISCHARGES AND MATERIALS PROCESSING Michael A. Lieberman Department of Electrical Engineering and Computer Sciences, CA LiebermanShortCourse15
2 TABLE OF CONTENTS Introduction to Plasma Discharges and Processing (Ch. 1) Summary of Plasma Fundamentals (Ch. 2, Secs ) Summary of Discharge Fundamentals (Secs. 3.1, 3.5, , ) Analysis of Discharge Equilibrium (Secs ) Capacitive RF Discharges Symmetric Homogeneous Model (Sec. 11.1) Self Consistent Sheath Results (Sec. 11.2) Simulation and Experimental Results (Sec. 11.3) Example Equilibrium Calculations (Sec. 11.2) Asymmetric Systems (Sec. 11.4) Inductive RF Discharges Transformer Model and Matching (Secs ) Power Balance (Secs ) Capacitive RF Sheaths Transit Time Effects (Sec. 11.5) Ion Energy Distribution (IED) (Sec. 11.6) i LiebermanShortCourse15
3 TABLE OF CONTENTS (CONT D) Chemical Fundamentals Atoms and Molecules (Sec. 3.4, Ch. 8) Gas Phase Kinetics (Sec ) Adsorption and Desorption (Sec ) Chemistry in Discharges Neutral Free Radicals (Sec. 10.2) Negative Ions (Sec. 10.3) Example of Oxygen (Sec. 10.4) Time-Varying Global Models (Sec ) Etching Processes (Secs ) Plasma-Induced Charging Damage (Sec. 15.5) Pulsed Discharges (Sec. 10.6) Dual Frequency Capacitive Discharges High Pressure Discharges and Deposition Kinetics (Ch. 16) ERRATA for textbook About the Instructor Self-Study Problems ii LiebermanShortCourse15
4 THE NANOELECTRONICS REVOLUTION Transistors/chip doubling every years since 1959 Billion-fold increase in performance for the same cost over the last 40 years CMOS transistors with 4 nm (16 atoms) gate length EQUIVALENT AUTOMOTIVE ADVANCE 60 billion miles/hr (90 speed of light!) 20 billion miles/gal 1 cm long 3 mm wide iii LiebermanShortCourse15
5 DAY 1 (ETCHING EMPHASIS) 8:00 AM 8:30 AM: Registration 8:30 AM 10:00 AM Introduction to Plasma Discharges and Processing Summary of Plasma Fundamentals (Undriven) 10:00 AM 10:30 AM: Coffee Break 10:30 AM 12 Noon Summary of Plasma Fundamentals (Driven) Summary of Discharge Fundamentals Analysis of Discharge Equilibrium 12:00 Noon 1:30 PM: Lunch 1:30 PM 3:00 PM Capacitive RF Discharges: Symmetric Homogeneous Model Capacitive RF Discharges: Self-Consistent Sheath Results Capacitive RF Discharges: Simulation and Experimental Results Capacitive RF Discharges: Example Equilibrium Calculations 3:00 PM 3:30 PM: Coffee Break 3:30 AM 5:00 PM Capacitive RF Discharges: Asymmetric Systems Inductive RF Discharges: Transformer Model and Matching Inductive RF Discharges: Power Balance iv LiebermanShortCourse15
6 DAY 2 (ETCHING EMPHASIS) 8:30 AM 9:30 AM Capacitive RF Sheaths: Ion Transit Time Effects Capacitive RF Sheaths: Ion Energy Distribution (IED) 9:30 AM 10:00 AM: Coffee Break 10:00 AM 12 Noon Chemical Fundamentals: Atoms and Molecules Chemical Fundamentals: Gas Phase Kinetics Chemical Fundamentals: Adsorption and Desorption Chemistry in Discharges: Neutral Free Radicals 12:00 Noon 1:30 PM: Lunch 1:30 PM 3:00 PM Chemistry in Discharges: Negative Ions Chemistry in Discharges: Example of Oxygen Chemistry in Discharges: Time-Varying Global Models Chemistry in Discharges: Etching Processes 3:00 PM 3:30 PM: Coffee Break 3:30 AM 5:00 PM Plasma-Induced Charging Damage OR Pulsed Discharges Dual Frequency Capacitive Discharges v LiebermanShortCourse15
7 DAY 1 (DEPOSITION EMPHASIS) 8:00 AM 8:30 AM: Registration 8:30 AM 10:00 AM Introduction to Plasma Discharges and Processing Summary of Plasma Fundamentals (Undriven) 10:00 AM 10:30 AM: Coffee Break 10:30 AM 12 Noon Summary of Plasma Fundamentals (Driven) Summary of Discharge Fundamentals Analysis of Discharge Equilibrium 12:00 Noon 1:30 PM: Lunch 1:30 PM 3:00 PM Capacitive RF Discharges: Symmetric Homogeneous Model Capacitive RF Discharges: Self-Consistent Sheath Results Capacitive RF Discharges: Simulation and Experimental Results Capacitive RF Discharges: Example Equilibrium Calculations 3:00 PM 3:30 PM: Coffee Break 3:30 AM 5:00 PM Capacitive RF Discharges: Asymmetric Systems High Pressure Discharges High Pressure Capacitive Discharges vi LiebermanShortCourse15
8 DAY 2 (DEPOSITION EMPHASIS) 8:30 AM 9:30 AM Alpha-To-Gamma Transition 9:30 AM 10:00 AM: Coffee Break 10:00 AM 12 Noon Chemical Fundamentals: Atoms and Molecules Chemical Fundamentals: Gas Phase Kinetics Chemical Fundamentals: Adsorption and Desorption Chemistry in Discharges: Neutral Free Radicals 12:00 Noon 1:30 PM: Lunch 1:30 PM 3:00 PM Chemistry in Discharges: Negative Ions Chemistry in Discharges: Example of Oxygen Chemistry in Discharges: Time-Varying Global Models Chemistry in Discharges: Etching Processes Chemistry in Discharges: Deposition Kinetics 3:00 PM 3:30 PM: Coffee Break 3:30 AM 5:00 PM Pulsed Discharges Dual Frequency Capacitive Discharges vii LiebermanShortCourse15
9 INTRODUCTION TO DISCHARGES AND PROCESSING 1 LiebermanShortCourse15
10 S AND DISCHARGES Plasmas A collection of freely moving charged particles which is, on the average, electrically neutral Discharges Are driven by voltage or current sources Charged particle collisions with neutral particles are important There are boundaries at which surface losses are important The electrons are not in thermal equilibrium with the ions Device sizes 30 cm 1 m Frequencies from DC to rf (13.56 MHz) to microwaves (2.45 GHz) 2 LiebermanShortCourse15
11 EVOLUTION OF ETCHING DISCHARGES 3 LiebermanShortCourse15
12 ANISOTROPIC ETCHING {}}{{}}{ Wet Etching Ion Enhanced Plasma Etching Plasma Etching 4 LiebermanShortCourse15
13 ISOTROPIC ETCHING 1. Start with inert molecular gas CF 4 2. Make discharge to create reactive species CF 4 CF 3 + F 3. Species reacts with material, yielding volatile product Si + 4F SiF 4 4. Pump away product 5. CF 4 does not react with Si; SiF 4 is volatile ANISOTROPIC ETCHING 6. Energetic ions bombard trench bottom, but not sidewalls (a) Increase etching reaction rate at trench bottom (b) Clear passivating films from trench bottom Mask Plasma Ions 5 LiebermanShortCourse15
14 UNITS AND CONSTANTS SI units: meters (m), kilograms (kg), seconds (s), coulombs (C) e = C, electron charge = e Energy unit is joule (J) Often use electron-volt 1 ev = J Temperature unit is kelvin (K) Often use equivalent voltage of the temperature T e (volts) = kt e(kelvins) e where k = Boltzmann s constant = J/K 1 V 11, 600 K Pressure unit is pascal (Pa); 1 Pa = 1 N/m 2 Atmospheric pressure 1 bar 10 5 Pa 760 Torr 1 Pa 7.5 mtorr 6 LiebermanShortCourse15
15 DENSITY VERSUS TEMPERATURE 7 LiebermanShortCourse15
16 RELATIVE DENSITIES AND ENERGIES 8 LiebermanShortCourse15
17 NON-EQUILIBRIUM Energy coupling between electrons and heavy particles is weak Input power Electrons weak Ions strong Walls Walls weak weak strong Neutrals strong Walls Electrons are not in thermal equilibrium with ions or neutrals T e T i Bombarding ion E i T e in plasma bulk at wafer surface High temperature processing at low temperatures 1. Wafer can be near room temperature 2. Electrons produce free radicals = chemistry 3. Electrons produce electron-ion pairs = ion bombardment 9 LiebermanShortCourse15
18 ELEMENTARY DISCHARGE BEHAVIOR Uniform density of electrons and ions n e and n i at time t = 0 Low mass warm electrons quickly drain to the wall, forming sheaths Bulk plasma is quasi-neutral = n e n i Ions accelerated to walls; ion bombarding energy E i = plasma-wall potential V p 10 LiebermanShortCourse15
19 SUMMARY OF FUNDAMENTALS 11 LiebermanShortCourse15
20 POISSON S EQUATION An electric field can be generated by charges E = ρ or ǫ Ē da = Q encl 0 S ǫ 0 For slow time variations (dc, rf, but not microwaves) E Φ E = electric field (V/m), ρ = charge density (C/m 3 ), Φ = potential (V), ǫ 0 = F/m In 1D planar geometry de x dx = ρ ǫ 0, dφ dx = E x Combining these yields Poisson s equation d 2 Φ dx 2 = ρ ǫ 0 This field powers a capacitive discharge or the wafer bias power of an inductive or ECR discharge V rf E Q encl S ~ E 12 LiebermanShortCourse15
21 FARADAY S LAW An electric field can be generated by a time-varying magnetic field E = B or E dl = B da t C t A I rf A C B B = magnetic induction vector This field powers the coil of an inductive discharge (top power) E I rf ~ E E 13 LiebermanShortCourse15
22 AMPERE S LAW Both conduction currents and displacement currents generate magnetic fields H H = J c + ǫ 0 E t = J [A/m2 ] J c = conduction current density (physical motion of charges) ǫ 0 E/ t = displacement current density (flows in vacuum) J = total current density Note the vector identity ( H) = 0 J = 0 In 1D J(x, t) x = 0 Total current J is independent of x 14 LiebermanShortCourse15
23 REVIEW OF PHASORS Physical voltage (or current), a real sinusoidal function of time V (t) V 0 V (t) = V 0 cos(ωt + φ) 0 2π ωt Phasor voltage (or current), a complex number, independent of time V I Ṽ = V 0 e jφ = V R + jv I V 0 φ V R Note that V (t) = Re (Ṽ ) e jωt Hence V (t) Ṽ (given ω) 15 LiebermanShortCourse15
24 THERMAL EQUILIBRIUM PROPERTIES Electrons generally near thermal equilibrium Ions generally not in thermal equilibrium Maxwellian distribution of electrons ( ) 3/2 m f e (v) = n e exp( mv2 2πkT e 2kT e where v 2 = vx 2 + vy 2 + vz 2 f e (v x ) ) v Te = (kt e /m) 1/2 v x Pressure p = nkt For neutral gas at room temperature (300 K) n g (cm 3 ) p(torr) 16 LiebermanShortCourse15
25 AVERAGES OVER MAXWELLIAN DISTRIBUTION Average energy 1 2 mv2 = 1 n e d 3 v 1 2 mv2 f e (v) = 3 2 kt e Average speed ( ) 1/2 8kTe v e = (= 1ne πm Average electron flux lost to a wall z Γ e [m 2 s 1 ] y ) d 3 v vf e (v) Γ e = 1 4 n e v e (= x ) dv x dv y dv z v z f e (v) Average kinetic energy lost per electron lost to a wall E e = 2 T e 0 17 LiebermanShortCourse15
26 FORCES ON PARTICLES For a unit volume of electrons (or ions) du e mn e = qn e E p e mn e ν m u e dt mass acceleration = electric field force + + pressure gradient force + friction (gas drag) force m = electron mass n e = electron density u e = electron flow velocity q = e for electrons (+e for ions) E = electric field p e = n e kt e = electron pressure ν m = collision frequency of electrons with neutrals [p. 36] p e p e p e (x) p e (x + dx) Drag force u e Neutrals x x + dx x 18 LiebermanShortCourse15
27 BOLTZMANN FACTOR FOR ELECTRONS If electric field and pressure gradient forces almost balance 0 en e E p e Let E = Φ and p e = n e kt e Φ = kt e n e e n e Put kt e /e = T e (volts) and integrate to obtain Φ n e (r) = n e0 e Φ(r)/T e n e x n e0 x 19 LiebermanShortCourse15
28 UNDERSTANDING BEHAVIOR The field equations and the force equations are coupled Fields, Potentials Maxwell's Equations Newton's Laws Charges, Currents 20 LiebermanShortCourse15
29 DEBYE LENGTH λ De The characteristic length scale of a plasma Low voltage sheaths few Debye lengths thick Let s consider how a sheath forms near a wall Electrons leave plasma before ions and charge wall negative n n e = n i = n 0 n + + Φ n i = n 0 + n e Electrons Sheath region ~ few λ De Quasi-neutral bulk plasma x x x Φ 0 Assume electrons in thermal equilibrium and stationary ions 21 LiebermanShortCourse15
30 DEBYE LENGTH λ De (CONT D) Newton s laws [p. 18] n e (x) = n 0 e Φ/T e, n i = n 0 Use in Poisson s equation [p. 12] d 2 Φ ( ) dx 2 = en 0 1 e Φ/T e ǫ 0 Linearize e Φ/T e 1 + Φ/T e d 2 Φ dx 2 = en 0 Φ ǫ 0 T e Solution is ( ) 1/2 ǫ0 T Φ(x) = Φ 0 e x/λ e De, λ De = en 0 In practical units λ De (cm) = 740 T e /n 0, T e in volts, n 0 in cm 3 Example At T e = 1 V and n 0 = cm 3, λ De = cm = Sheath is 0.15 mm thick (Very thin!) 22 LiebermanShortCourse15
31 ELECTRON FREQUENCY ω pe The fundamental timescale for a plasma Consider a plasma slab (no walls). Displace all electrons to the right a small distance x e0, and release them Charge/area + en 0 x e Ions + Electrons E(x) x e E Charge/area en 0 x e Maxwell s equations (parallel plate capacitor) [p. 12] E = en 0x e (t) ǫ 0 x 23 LiebermanShortCourse15
32 ELECTRON FREQUENCY ω pe (CONT D) Newton s laws (electron motion) [p. 18] m d2 x e (t) dt 2 = ee = e2 n 0 x e (t) ǫ 0 Solution is electron plasma oscillations x e (t) = x e0 cosω pe t, ω pe = Practical formula is f pe (Hz) = 9000 n 0, ( e 2 ) 1/2 n 0 ǫ 0 m n 0 in cm 3 = microwave frequencies (> 1 GHz) for typical plasmas 24 LiebermanShortCourse15
33 1D SIMULATION OF SHEATH FORMATION Particle-in-cell (PIC) simulations with uniform fixed ion density; 4000 electron sheets; solve Newton s laws + Maxwell s equations T e = 1 V (random), n e = n i = m 3 (low), l = 0.1 m Electron v x x phase space at t = 0.77 µs Note absence of electron sheets near the walls 25 LiebermanShortCourse15
34 1D SIMULATION OF SHEATH FORMATION (CONT D) Electron number N versus t Note 340 electron sheets lost to walls to form sheaths 26 LiebermanShortCourse15
35 1D SIMULATION OF SHEATH FORMATION (CONT D) Electron density n e (x) at t = 0.77 µs Note sheath width is a few Debye lengths 27 LiebermanShortCourse15
36 1D SIMULATION OF SHEATH FORMATION (CONT D) Electric field E(x) at t = 0.77 µs Note electric field retards electrons, accelerates ion into walls 28 LiebermanShortCourse15
37 1D SIMULATION OF SHEATH FORMATION (CONT D) Potential Φ(x) at t = 0.77 µs Note plasma potential builds up to a few T e with respect to wall 29 LiebermanShortCourse15
38 1D SIMULATION OF SHEATH FORMATION (CONT D) Right hand potential Φ(x = l) versus t Due to asymmetric electron initial conditions, a small oscillation of the right hand potential is excited at the plasma frequency 30 LiebermanShortCourse15
39 DIELECTRIC CONSTANT ǫ p RF discharges are driven at a frequency ω E(t) = Re (Ẽ ejωt ), etc. [p. 15] Define ǫ p from the total current in Maxwell s equations [p. 14] H = J c + jωǫ 0 Ẽ }{{} jωǫ pẽ Total current J Conduction current J c = en e ũ e is due to electrons Newton s law (electric field and neutral drag) is [p. 18] jωmũ e = eẽ mν mũ e Solve for ũ e and evaluate J c to obtain ǫ p ǫ 0 κ p = ǫ 0 [1 ω 2 pe ω(ω jν m ) with ω pe = (e 2 n e /ǫ 0 m) 1/2 the electron plasma frequency [p. 23] For ω ν m, ǫ p is mainly real (nearly lossless dielectric) For ν m ω, ǫ p is mainly imaginary (very lossy dielectric) ] 31 LiebermanShortCourse15
40 RF FIELDS IN LOW PRESSURE DISCHARGES Consider mainly lossless plasma (ω ν m ) ( ) ǫ p = ǫ 0 1 ω2 pe ω 2 For rf discharges, ω pe ω = ǫ p is negative (ǫ p = 1000 ǫ 0 ) RF current density J is continuous across the discharge [p. 14] Sheath ǫ 0 J Plasma ǫ p (continuous) Sheath ǫ 0 E= ~ J ~ E= ~ ~ J ~ E= jωεp J ~ jωε 0 jωε 0 Electric field in plasma is 1000 smaller than in sheaths! Although field in plasma is small, it sustains the plasma! 32 LiebermanShortCourse15
41 CONDUCTIVITY σ p It is useful to introduce rf plasma conductivity J c σ p Ẽ Find J c to be a linear function of Ẽ [p. 31] σ p = e 2 n e m(ν m + jω) DC plasma conductivity (ω ν m ) σ dc = e2 n e mν m The plasma dielectric constant and conductivity are related by jωǫ p = σ p + jωǫ 0 RF current flowing through the plasma heats electrons (just like a resistor) 33 LiebermanShortCourse15
42 OHMIC HEATING POWER Time average power absorbed/volume p d = J(t) E(t) = 1 2 Re( J Ẽ ) [W/m 3 ] Here Ẽ = complex conjugate of Ẽ Since J is the same everywhere in the discharge [p. 32], put Ẽ = J/jωǫ p to find p d in terms of J alone For discharges with ω ω pe (all rf discharges) p d = 1 2 J 2 1 σ dc [W/m 3 ] 34 LiebermanShortCourse15
43 SUMMARY OF DISCHARGE FUNDAMENTALS 35 LiebermanShortCourse15
44 ELECTRON COLLISIONS WITH ARGON Maxwellian electrons collide with Ar atoms (density n g ) # collisions of a particular kind s-m 3 = νn e = Kn g n e ν = collision frequency [s 1 ], K(T e ) = rate coefficient [m 3 /s] Electron-Ar collision processes e + Ar Ar + + 2e (ionization) e + Ar e + Ar e + Ar + photon (excitation) e e + Ar e + Ar (elastic scattering) e Rate coefficient K(T e ) is average of cross section σ(v R ) [m 2 ] for process, over Maxwellian distribution K(T e ) = σ v R Maxwellian v R = relative velocity of colliding particles Ar Ar 36 LiebermanShortCourse15
45 ELECTRON-ARGON RATE COEFFICIENTS 37 LiebermanShortCourse15
46 ION COLLISIONS WITH ARGON Argon ions collide with Ar atoms Ar + + Ar Ar + + Ar (elastic scattering) Ar + + Ar Ar + Ar + (charge transfer) Total cross section for room temperature ions σ i cm 2 Ion-neutral mean free path (distance ion travels before colliding) λ i = 1 n g σ i Practical formula Ion-neutral collision frequency λ i (cm) = 1, p in Torr 330 p ν i = v i λ i with v i = (8kT i /πm) 1/2 38 LiebermanShortCourse15 Ar + Ar + Ar Ar Ar + Ar Ar Ar +
47 THREE ENERGY LOSS PROCESSES 1. Collisional energy E c lost per electron-ion pair created K iz E c = K iz E iz + K ex E ex + K el (2m/M)(3T e /2) = E c (T e ) (voltage units) E iz, E ex, and (3m/M)T e are energies lost by an electron due to an ionization, excitation, and elastic scattering collision 2. Electron kinetic energy lost to walls [p. 17] E e = 2 T e 3. Ion kinetic energy lost to walls is mainly due to the dc potential V s across the sheath E i V s Total energy lost per electron-ion pair lost to walls E T = E c + E e + E i 39 LiebermanShortCourse15
48 COLLISIONAL ENERGY LOSSES 40 LiebermanShortCourse15
49 BOHM (ION LOSS) VELOCITY u B u B Plasma Sheath Wall Density n s Due to formation of a presheath, ions arrive at the plasma-sheath edge with directed energy kt e /2 1 2 Mu2 B = kt e 2 Electron-ion pairs are lost at the Bohm velocity at the plasma-sheath edge (density n s ) Γ wall = n s u B, u B = ( kte M ) 1/2 41 LiebermanShortCourse15
50 AMBIPOLAR DIFFUSION AT HIGH PRESSURES Plasma bulk is quasi-neutral (n e n i = n) and the electron and ion loss fluxes are equal (Γ e Γ i Γ) Fick s law Γ = D a n with ambipolar diffusion coefficient D a = kt e /Mν i Density profile is sinusoidal n 0 Γ wall Γ wall l/2 0 l/2 n s x Loss flux to the wall is Γ wall = n s u B h l n 0 u B From diffusion theory, edge-to-center density ratio is h l n s = π u B n 0 l ν i Applies for pressures > 100 mtorr in argon 42 LiebermanShortCourse15
51 AMBIPOLAR DIFFUSION AT LOW PRESSURES The diffusion coefficient is not constant Density profile is relatively flat in the center and falls sharply near the sheath edge n 0 Γ wall Γ wall l/2 0 l/2 n s x The edge-to-center density ratio is h l n s n (3 + l/2λ i ) 1/2 where λ i = ion-neutral mean free path [p. 38] Applies for pressures < 100 mtorr in argon 43 LiebermanShortCourse15
52 AMBIPOLAR DIFFUSION IN LOW PRESSURE CYLINDRICAL DISCHARGE n sr = h R n 0 R Plasma n e = n i = n 0 n sl = h l n 0 For a cylindrical plasma of length l and radius R, loss fluxes to axial and radial walls are Γ axial = h l n 0 u B, Γ radial = h R n 0 u B where the edge-to-center density ratios are 0.86 h l (3 + l/2λ i ) 1/2, h 0.8 R (4 + R/λ i ) 1/2 Applies for pressures < 100 mtorr in argon l 44 LiebermanShortCourse15
53 ANALYSIS OF DISCHARGE EQUILIBRIUM 45 LiebermanShortCourse15
54 PARTICLE BALANCE AND T e Assume uniform cylindrical plasma absorbing power P abs R P abs Plasma n e = n i = n 0 Particle balance l Production due to ionization = loss to the walls K iz n g n/ 0 πr 2 l = (2πR 2 h l n/ 0 + 2πRlh R n/ 0 )u B Solve to obtain K iz (T e ) u B (T e ) = 1 n g d eff where d eff = 1 Rl 2 Rh l + lh R is an effective plasma size Given n g and d eff = electron temperature T e T e varies over a narrow range of 2 5 volts 46 LiebermanShortCourse15
55 ELECTRON TEMPERATURE IN ARGON DISCHARGE 47 LiebermanShortCourse15
56 ION ENERGY FOR LOW VOLTAGE SHEATHS E i = energy entering sheath + energy gained traversing sheath Ion energy entering sheath = T e /2 (voltage units) [p. 41] Sheath voltage determined from particle conservation Γ i Density n s Plasma Sheath ~ 0.2 mm Insulating wall Γ i Γ e + V s [p. 41] [p. 17] [p. 19] Γ i = n s u B, Γ e = 1 4 n s v e }{{} e V s/t e with v e = (8eT e /πm) 1/2 Random flux at sheath edge The ion and electron fluxes at the wall must balance V s = T ( ) e M 2 ln 2πm or V s 4.7 T e for argon Accounting for the initial ion energy, E i 5.2 T e 48 LiebermanShortCourse15
57 ION ENERGY FOR HIGH VOLTAGE SHEATHS Large ion bombarding energies can be gained near rf-driven electrodes embedded in the plasma s V rf ~ C large Plasma V s ~ 0.4 V rf + + V s V s Low voltage sheath ~ 5.2 T e V rf ~ Plasma V s ~ 0.8 V rf V s + The sheath thickness s ( 0.5 cm) is given by the Child Law J i = en s u B = 4 ( ) 1/2 2e 9 ǫ V 3/2 s 0 M s 2 Estimating ion energy is not simple as it depends on the type of discharge and the application of bias voltages 49 LiebermanShortCourse15
58 POWER BALANCE AND n 0 Assume low voltage sheaths at all surfaces [p. 40] [p. 17] [p. 48] E T (T e ) = E c (T e ) }{{} + 2 T e }{{} T e }{{} Power balance Solve to obtain Collisional Electron Ion Power in = power out P abs = (h l n 0 2πR 2 + h R n 0 2πRl) u B ee T P abs n 0 = A eff u B ee T where A eff = 2πR 2 h l + 2πRlh R is an effective area for particle loss [V] [W] Density n 0 is proportional to the absorbed power P abs Density n 0 depends on pressure p through h l, h R, and T e 50 LiebermanShortCourse15
59 PARTICLE AND POWER BALANCE Particle balance = electron temperature T e (independent of plasma density) Power balance = plasma density n 0 (once electron temperature T e is known) 51 LiebermanShortCourse15
60 EXAMPLE 1 Let R = 0.15 m, l = 0.3 m, n g = m 3 (p = 1 mtorr at 300 K), and P abs = 800 W Assume low voltage sheaths at all surfaces Find λ i = 0.03 m [p. 38]. Then h l h R 0.3 [p. 44] and d eff 0.17 m [p. 46] T e versus n g d eff figure gives T e 3.5 V [p. 47] E c versus T e figure gives E c 42 V [p. 40]. Adding E e = 2T e 7 V and E i 5.2T e 18 V yields E T = 67 V [p. 39] Find u B m/s [p. 41] and find A eff 0.13 m 2 [p. 50] Power balance yields n m 3 [p. 50] Ion current density J il = eh l n 0 u B 2.9 ma/cm 2 [p. 46] Ion bombarding energy E i 18 V [p. 48] 52 LiebermanShortCourse15
61 EXAMPLE 2 Apply a strong dc magnetic field along the cylinder axis = particle loss to radial wall is inhibited Assume no radial losses, then d eff = l/2h l 0.5 m From the T e versus n g d eff figure, T e 3.3 V (was 3.5 V) From the E c versus T e figure, E c 46 V. Adding E e = 2T e 6.6 V and E i 5.2T e 17 V yields E T = 70 V Find u B m/s and find A eff = 2πR 2 h l m 2 Power balance yields n m 3 (was m 3 ) Ion current density J il = eh l n 0 u B 7.8 ma/cm 2 Ion bombarding energy E i 17 V = Slight decrease in electron temperature T e = Significant increase in plasma density n 0 EXPLAIN WHY! What happens to T e and n 0 if there is a sheath voltage V s = 500 V at each end plate? 53 LiebermanShortCourse15
62 CAPACITIVE RF DISCHARGES SYMMETRIC HOMOGENEOUS MODEL 54 LiebermanShortCourse15
63 BASIC PROPERTIES Simplicity of concept RF rather than microwave powered Inherent high sheath voltages No independent control of plasma density and ion energy Control parameters RF current Ĩrf (1 10 ma/cm 2 ) Driving frequency ω ( MHz) Neutral gas density n g ( cm 3 ) Electrode separation l (1 10 cm) Discharge parameters to find Plasma density n ( cm 3 ) Electron temperature T e (2 4 V) Discharge voltage V rf ( V) Discharge power P rf ( W) Ion bombarding energy E i ( V) 55 LiebermanShortCourse15
64 CONFIGURATIONS Multi-wafer parallel plate and hex configurations (1980 s) Modern configurations are single wafer parallel plate, sometimes driven at multiple rf frequencies 56 LiebermanShortCourse15
65 CURRENT-DRIVEN HOMOGENEOUS MODEL 57 LiebermanShortCourse15
66 HOMOGENEOUS MODEL ASSUMPTIONS No transverse variations (along the electrodes) Electrons respond to instantaneous electric fields Ions respond to only time-average electric fields Electron density is zero in the sheath regions Ion density is constant in the plasma and sheath regions n i (z) = n 0 (We will correct this later) 58 LiebermanShortCourse15
67 ELECTRON SHEATH EDGE MOTION n Electrode a I rf (t) I ap (t) n e n i =n Plasma p 0 s a (t) s m z The electric field is found by integrating the charge density in the sheath [p. 12] de dz = en, z < s a (t) ǫ 0 to obtain E(z, t) = en ǫ 0 ( z sa (t) ) E + V ap sa (t) E(z,t) z 59 LiebermanShortCourse15
68 ELECTRON SHEATH EDGE MOTION (CONT D) The displacement current in the sheath is [p. 14] I ap = ǫ 0 A E t = enads a dt Let I rf (t) = Ĩ0 cosωt and integrate to obtain s a (t) = s 0 s 0 sinωt s 0 = Ĩ0 enωa The oscillation amplitude of the sheath motion is s 0, but what is the constant of integration s 0? 60 LiebermanShortCourse15
69 CONDUCTION CURRENT Assume a steady loss of ions to electrode a I i = enu B A The time-average total conduction current to the electrode is zero Hence electrons must be lost to the electrode The sheath thickness s a (t) must then collapse to zero at some time during the rf cycle = s 0 = s 0 s a (t) = s 0 (1 sinωt) ~ s m =2s 0 s(t) I i I e (t) 0 0 I i I e 0 0 ωt 2π 61 LiebermanShortCourse15
70 VOLTAGE ACROSS THE SHEATH n Electrode a I rf (t) I ap (t) n e n i =n Plasma p 0 s a (t) s m z E + V ap sa (t) E(z,t) z V ap (t) V s a (t) V(z,t) The voltage is found by integrating the electric field in the sheath dv dz = E z 62 LiebermanShortCourse15
71 VOLTAGE ACROSS THE SHEATH (CONT D) Integrating the electric field in the sheath [p. 12] dv dz = E we obtain sa (t) V ap (t) = E(z, t) dz = en s 2 a(t) ǫ 0 2 Using s a (t) [p. 61] 0 V ap (t) = en s 2 ( ) sinωt 2ǫ 0 V ap (t) is a nonlinear function of I rf ; there are second harmonics 63 LiebermanShortCourse15
72 VOLTAGE ACROSS BOTH SHEATHS By symmetry s b (t) = s 0 (1 + sinωt); since s a (t) = s 0 (1 sinωt) s a (t) + s b (t) = 2 s 0 = const + V ab (t) I rf (t) s a (t) Rigid Electron Cloud s b (t) I rf (t) a p b There is a rigid bulk electron cloud oscillation 64 LiebermanShortCourse15
73 VOLTAGE ACROSS BOTH SHEATHS (CONT D) Voltage across sheath b is V bp (t) = en s 2 ( ) sinωt 2ǫ 0 Voltage across the plasma is small because I rf = jωǫ p EA and ǫ p is large = E across bulk plasma is small Discharge voltage is V rf = V ap + V pb V rf (t) = 2en s2 0 ǫ 0 sinωt Each sheath is nonlinear, but the combination of both sheaths is linear 65 LiebermanShortCourse15
74 DC VOLTAGE ACROSS ONE SHEATH n Electrode a I rf (t) I ap (t) n e n i =n Plasma p 0 s a (t) s m z V pa (t) = en s 2 ( sinωt + sin 2 ωt ) 2ǫ 0 Take time average V s = 3 en s 2 0 = E i 4 ǫ 0 Compare to rf voltage across discharge [p. 65] = V s = 3 8Ṽrf We can think of Ṽrf as divided equally across the two sheaths V s = 3 4Ṽs with Ṽ s = 1 2 V rf 66 LiebermanShortCourse15
75 SHEATH VOLTAGES VERSUS TIME Sheath voltages V ap (t), V pb (t), and their sum V ab (t) = V rf (t); the time average V s of V pb (t) is also shown 67 LiebermanShortCourse15
76 SHEATH POTENTIAL VERSUS POSITION AT VARIOUS TIMES V rf (t) = sin ωt Spatial variation of the total potential Φ (solid curves) for the homogeneous model at four different times during the rf cycle. The dashed curve shows the spatial variation of the timeaverage potential Φ V s Φ 1/4 0 Φ 1 3/8 I rf (t) Φ ω t = 0 π 2 Φ 1/4 π Φ 3π LiebermanShortCourse15
77 SHEATH CAPACITANCE Define total discharge capacitance by I rf (t) = Ĩ0 cosωt, V rf (t) = 2en s2 0 ǫ 0 sinωt [p. 65] which yields I rf = C s dv rf dt with C s = ǫ 0A 2 s 0 We can think of each sheath as having a capacitance C a = C b = ǫ 0A s 0 We now have a lossless discharge model a p b I rf (t) C a C b 69 LiebermanShortCourse15
78 OHMIC AND STOCHASTIC HEATING Ohmic heating in the bulk plasma [p. 34] P Ω = 1 2 J rf 2mν md e 2 n A Stochastic heating by oscillating sheaths with Electrode a n n i n e v v 0 s a (t) z v = v + 2 u s (t) [watts] u s (t) u s (t) = ds a dt = ũ 0 cosωt with ũ 0 = ω s 0 Average energy transferred [ is 1 E e = 2 m( v + 2 u s (t) ) ] mv2 = mũ 2 0 E e is positive, so the oscillating sheath heats electrons 70 LiebermanShortCourse15 v v
79 STOCHASTIC HEATING POWER For a Maxwellian distribution, the electron flux incident on a sheath is [p. 17] Γ e = 1 4 n v e with v e = (8eT e /πm) 1/2 the mean electron speed The time-average stochastic heating power is found to be P sa = Γ e A 2 E e = 1 2 mn v eω 2 s 2 0 A [watts] This is a powerful electron heating mechanism in a capacitive discharge 71 LiebermanShortCourse15
80 HEATING POWERS VERSUS DRIVING VOLTAGE For stochastic heating [p. 71] P sa = 1 2 mn v eω 2 s 2 0 A Using Ṽrf = 2en s 2 0/ǫ 0 [p. 65] we obtain for the two sheaths P s = P sa + P sb = m 2e ǫ 0 v e ω 2 Ṽ rf A For bulk ohmic heating [p. 70] P Ω = 1 2 J rf 2mν md e 2 n A Using J rf = enω s 0 and Ṽrf given above P Ω = m 4e ǫ 0ν m d ω 2 Ṽ rf A Ohmic and stochastic heating powers depend on Ṽrf 72 LiebermanShortCourse15
81 CAPACITIVE RF DISCHARGES SELF-CONSISTENT SHEATH RESULTS 73 LiebermanShortCourse15
82 HOMOGENEOUS AND CHILD LAW SHEATHS Electrode Electrode Homogeneous Model n n i n e s(t) s m Bulk plasma Self-Consistent Child Law n n ine s(t) n e s m z Bulk plasma Child law ion density decreases and sheath width increases compared to homogeneous model z 74 LiebermanShortCourse15
83 COLLISIONLESS CHILD LAW SHEATH + V s n i Plasma Sheath Wall J i = en s u B n e n i s m n e 0 Larger sheath width = larger sheath oscillation velocity u s ωs m Stochastic heating is larger than for homogeneous model Collisionless ion motion = Child law relating s m to n s and V s ( ) 1/2 2e V 3/2 s J i = en s u B = 0.82 ǫ 0 M s 2 m RF voltage Ṽs across sheath = dc voltage V s V s 0.83 Ṽs 75 LiebermanShortCourse15
84 SUMMARY SELF-CONSISTENT MODEL + ~ ~ V rf =2V s ~ I rf 0 J i n 0 n s Sheath Plasma Sheath V s + + V s s m ~ I rf E i = V s = 0.83 ( Ṽs ) 1/2 2e V 3/2 s J i = en s u B = 0.82 ǫ 0 M s 2 m Ĩ rf = 1.23 jω ǫ 0A Ṽ s s m P s = 1.12 m 2e ω2 ǫ 0 v e Ṽ s A P Ω = 1.73 n s n 0 m 2e ω2 ǫ 0 ν m d (T e Ṽ s ) 1/2 A 76 LiebermanShortCourse15
85 CAPACITIVE RF DISCHARGES SIMULATION AND EXPERIMENTAL RESULTS 77 LiebermanShortCourse15
86 PIC SIMULATION OF DENSITIES Symmetric rf discharge with right hand electrode grounded, V rf = 1 kv at 10 MHz, 20 mtorr hydrogen gas (Thesis of D. Vender, Australian National University, 1990) 78 LiebermanShortCourse15
87 PHASE SPACE AND POTENTIALS VERSUS POSITION Symmetric rf discharge with right hand electrode grounded, V rf = 1 kv at 10 MHz, 20 mtorr hydrogen gas; left panels show electron and ion phase space; right panels show potentials (see [p. 68] for comparison to theory) (Thesis of D. Vender, Australian National University, 1990) 79 LiebermanShortCourse15
88 TIME VARIATION OF VOLTAGES AND CURRENTS V (kv) J e 10 MHz V pb J(A/m 2 ) 0 0 V rf J i ( 10) 1.0 (Thesis of D. Vender, ANU, 1990) π 4π Phase ωt Note plasma always positive with respect to both electrodes Note steady ion current [p. 61] Note pulsed electron current when V pa = V pb V rf 0 [p. 61] 80 LiebermanShortCourse15
89 SPACE-TIME DISTRIBUTION OF IONIZING COLLISIONS The darkness of each square is proportional to the number of ionizing collisions within that square of time and position intervals; symmetric rf discharge with right hand electrode grounded, V rf = 1 kv at 10 MHz, 20 mtorr hydrogen gas (Thesis of D. Vender, Australian National University, 1990) 81 LiebermanShortCourse15
90 MEASUREMENTS OF STOCHASTIC HEATING Effective collision frequency ν eff versus pressure p, for a mercury discharge driven at 40.8 MHz; the solid line shows the collision frequency due to ohmic dissipation alone (Popov and Godyak, 1985) 82 LiebermanShortCourse15
91 CAPACITIVE RF DISCHARGES EXAMPLE EQUILIBRIUM CALCULATIONS 83 LiebermanShortCourse15
92 Electron power balance where Specify Ṽs = n s Total power balance POWER BALANCE El. col + kin {}}{ P Ω + 2P s = en s u B 2A (E c + 2T e ) P Ω = 1.73 h l m 2e ω2 ǫ 0 (ν m d)(t e Ṽ s ) 1/2 A P s = 0.56 m 2e ω2 ǫ 0 v e Ṽ s A El. { col.+kin. }}{{ Ion}} kin. { P abs = en s u B 2A (E c + 2T e Ṽs) Eliminate n s from electron and total power balance ( ) P abs (P Ω + 2P s ) Ṽs E c + 2T e Specify P abs = Ṽs In this case, electron or total power balance = n s 84 LiebermanShortCourse15
93 EXAMPLE 1 Let p = 3 mtorr argon at 300 K, l = 10 cm, A = 1000 cm 2, f = MHz (ω = s 1 ), and V rf = 500 V Start with estimate s m 1 cm Ion mean free path λ i = 1/n g σ i 1.0 cm [p. 38] With bulk plasma thickness d = l 2s m = 8 cm, λ i /d h l = n s /n [p. 43] and d eff = d/2h l = 12.3 cm [p. 46] With n g d eff m 2, the T e versus n g d eff figure [p. 47] yields T e 3.1 V Bohm velocity u B m/s [p. 41] E c versus T e figure [p. 40] yields E c 47 V and E c + 2T e 53 V. Use the K el versus T e figure [p. 37] to find ν m K el n g s 1 85 LiebermanShortCourse15
94 EXAMPLE 1 (CONT D) Evaluate ohmic and stochastic electron heating [p. 76 or 84] P Ω Ṽ s 1/2 [W] P s Ṽs [W] Use Ṽs V rf /2 = 250 V in above to find P Ω W and P s 3.03 W Electron power balance [p. 84] yields n s m 3 Since h l 0.325, n m 3 Using E i 0.83 Ṽs [p. 76] yields E i 208 V J i = en s u B 0.59 A/m 2 [p. 76] The Child law [p. 76] gives s m 0.90 cm J rf 1.23 ωǫ 0 Ṽ s /s m 25.8 A/m 2 [p. 76] Total power balance [p. 84] gives P abs 30.8 W s m reasonably close to the initial estimate = iteration over d is not useful 86 LiebermanShortCourse15
95 EXAMPLE 2 Let p = 3 mtorr argon at 300 K, l = 10 cm, A = 1000 cm 2, f = MHz and P abs = 200 W As before, h l 0.325, T e 3.1 V, u B m/s, and E c + 2T e 53 V. Because n g and T e are the same, P Ω and P s are the same functions of Ṽs as in EXAMPLE 1 Using P abs = 200 W, we obtain the equation for the rf sheath voltage Ṽs [p. 84] 200 = ( Ṽ 1/2 s Ṽs ) ( Ṽs 53 A numerical solution gives Ṽs = 687 V Then V rf 2Ṽs 1374 V and E i = 0.83 Ṽs 570 V Use this in total power balance [p. 84] to find n s m 3 and n m 3 We then find J i 1.6 A/m 2, s m 1.16 cm, and J rf 54.9 A/m 2 ) 87 LiebermanShortCourse15
96 CAPACITIVE RF DISCHARGES ASYMMETRIC SYSTEMS 88 LiebermanShortCourse15
97 ASYMMETRIC RF DISCHARGE Powered electrode area A a smaller than grounded area A b ~ V rf ~ C large Powered a Sheath a Plasma Sheath b Grounded b V a + + V b + V bias V a = dc sheath voltage from plasma to powered electrode a V b = dc sheath voltage from plasma to grounded electrode b Ṽ a = rf voltage amplitude across sheath a Ṽ b = rf voltage amplitude across sheath b V a = 0.83 Ṽa, V b = 0.83 Ṽb, Ṽ rf = Ṽa + Ṽb A negative DC bias voltage V bias = V b V a appears 89 LiebermanShortCourse15
98 DEPENDENCE OF VOLTAGES ON AREAS Given Ṽrf, A a and A b, what are V a, V b and V bias? Voltage ratio V a /V b depends on area ratio A b /A a V a V b = q = area ratio scaling exponent Experiments show q Collisionless Child law gives q = 4 ( ) q Ab A a 90 LiebermanShortCourse15
99 COLLISIONLESS CHILD LAW ANALYSIS I rf a +V b V a + Plasma (good conductor) s a n a Electrodes and plasma are good conductors, so V a is the same everywhere along electrode a Capacitive sheath [p. 76] Child law [p. 76] n b I rf V aa a s a n a V 3/2 a s 2 a s b b I rf Eliminating s a I rf V 1/4 a n 1/2 a A a 91 LiebermanShortCourse15
100 COLLISIONLESS CHILD LAW ANALYSIS (CONT D) Similarly I rf V 1/4 b n 1/2 b A b Set currents at sheaths a and b equal and solve for V a /V b ( ) 2 ( ) 4 V a nb Ab = V b n a A a Simplest assumption for plasma is equal densities at the sheath edges a and b V a V b = ( ) 4 Ab A a 92 LiebermanShortCourse15
101 COLLISIONAL CHILD LAW SHEATH SCALING For pressures above 3 10 mtorr, ions suffer collisions with neutrals in the sheaths The Child law is modified to the scaling n a V 3/2 a This leads to s 5/2 a V a V b = ( ) 2.5 Ab A a The weaker scaling q = 2.5 is more in agreement with experiments 93 LiebermanShortCourse15
102 VARIATION OF DENSITIES Low density High density b a ~ V rf ~ C large Plasma density near powered electrode is usually larger than near grounded electrode This leads to additional modifications in scaling 94 LiebermanShortCourse15
103 INDUCTIVE DISCHARGES TRANSFORMER MODEL AND MATCHING 95 LiebermanShortCourse15
104 MOTIVATION High density (compared to capacitive discharge) Independent control of plasma density and ion energy Simplicity of concept RF rather than microwave powered No source magnetic fields 96 LiebermanShortCourse15
105 CYLINDRICAL AND PLANAR CONFIGURATIONS Cylindrical coil Planar coil 97 LiebermanShortCourse15
106 EARLY HISTORY First inductive discharge by Hittorf (1884) Arrangement to test discharge mechanism by Lehmann (1892) 98 LiebermanShortCourse15
107 HIGH DENSITY REGIME Inductive coil launches decaying wave into plasma Decaying wave Ẽ H δ p Plasma z Coil Window Wave decays exponentially into plasma Ẽ = Ẽ0 e z/δ p, δ p = c ω 1 Im(κ 1/2 p ) where κ p = plasma dielectric constant [p. 31] ωpe 2 κ p = 1 ω(ω jν m ) For typical high density, low pressure (ν m ω) discharge δ p c ω pe = ( m e 2 µ 0 n e ) 1/2 1 2 cm 99 LiebermanShortCourse15
108 TRANSFORMER MODEL For simplicity consider a long cylindrical discharge N turn coil Ĩ rf b R δ p Ĩ p Plasma z l Current Ĩrf in N turn coil induces current Ĩp in 1-turn plasma skin = A transformer 100 LiebermanShortCourse15
109 RESISTANCE AND INDUCTANCE Plasma resistance R p R p = 1 circumference of plasma loop σ dc average cross sectional area of loop where σ dc = e2 n es mν m [p. 33] with n es = density at plasma-sheath edge = R p = πr σ dc lδ p Plasma inductance L p magnetic flux produced by plasma current L p = plasma current Using magnetic flux = πr 2 µ 0 Ĩ p /l = L p = µ 0πR 2 l 101 LiebermanShortCourse15
110 Model the source as a transformer COUPLING OF COIL TO Ṽ rf = jωl 11 Ĩ rf + jωl 12 Ĩ p Ṽ p = jωl 21 Ĩ rf + jωl 22 Ĩ p Transformer inductances magnetic flux linking coil L 11 = = µ 0πb 2 N 2 coil current l magnetic flux linking plasma L 12 = L 21 = = µ 0πR 2 N coil current l L 22 = L p = µ 0πR 2 l 102 LiebermanShortCourse15
111 SOURCE CURRENT AND VOLTAGE Put Ṽp = ĨpR p in transformer equations and solve for the impedance Z s = Ṽrf/Ĩrf seen at coil terminals Z s = jωl 11 + ω2 L 2 12 R p + jωl p R s + jωl s Equivalent circuit at coil terminals R s = N 2 πr σ dc lδ p L s = µ 0πR 2 N 2 ( ) b 2 l R 2 1 Power balance = Ĩrf P abs = 1 2Ĩ2 rf R s From source impedance = V rf Ṽ rf = ĨrfZ s 103 LiebermanShortCourse15
112 EXAMPLE Assume plasma radius R = 10 cm, coil radius b = 15 cm, length l = 20 cm, N = 3 turns, gas density n g = cm 3 (20 mtorr argon at 300 K), ω = s 1 (13.56 MHz), absorbed power P abs = 600 W, and low voltage sheaths At 20 mtorr, λ i 0.15 cm, h l h R 0.1, d eff 34 cm [p. 38, 44, 46] Particle balance (T e versus n g d eff figure [p. 47]) yields T e 2.1 V Collisional energy losses (E c versus T e figure [p. 40]) are E c 110 V. Adding E e + E i = 7.2T e yields total energy losses E T 126 V [p. 39] u B cm/s [p. 41] and A eff 185 cm 2 [p. 50] Power balance yields n e cm 3 and n se cm 3 [p. 50] Use n se to find skin depth δ p 2.0 cm [p. 99]; estimate ν m = K el n g (K el versus T e figure [p. 37]) to find ν m s 1 Use ν m and n se to find σ dc 61 Ω 1 -m 1 [p. 33] Evaluate impedance elements R s 23.5 Ω and L s 2.2 µh; Z s ωl s 190 Ω [p. 103] Power balance yields Ĩrf 7.1A; from source impedance Z s = 190 Ω, Ṽ rf 1360 V [p. 103] 104 LiebermanShortCourse15
113 MATCHING DISCHARGE TO POWER SOURCE Consider an rf power source connected to a discharge + Z T Ĩ + Ṽ T ~ Ṽ Z L Source Discharge Source impedance Z T = R T + jx T is given Discharge impedance Z L = R L + jx L Time-average power delivered to discharge P abs = 1 2 Re (Ṽ Ĩ ) For fixed source ṼT and Z T, maximize power delivered to discharge X L = X T R L = R T Maximum time-average power delivered to discharge P abs = 1 ṼT 2 8 R 105 T LiebermanShortCourse15
114 MATCHING NETWORK Insert lossless matching network between power source and coil Power source Matching network Discharge coil Continue EXAMPLE [p. 104] with R s = 23.5 Ω and ωl s = 190 Ω; assume R T = 50 Ω (corresponds to a conductance 1/R T = 1/50 S) Choose C 1 such that the conductance seen looking to the right at terminals AA is 1/50 S = C 1 = 71 pf Choose C 2 to cancel the reactive part of the impedance seen at AA = C 2 = 249 pf For P abs = 600 W, the 50 Ω source supplies Ĩrf = 4.9 A Voltage at source terminals (AA ) = ĨrfR T = 245 V 106 LiebermanShortCourse15
115 PLANAR COIL DISCHARGE Magnetic field produced by planar coil RF power is deposited in a ring-shaped plasma volume δ p Ĩ rf N turn coil Primary inductance Coupling inductance Ĩ p Plasma Plasma inductance z As for a cylindrical discharge, there is a primary (L 11 ), coupling (L 12 = L 21 ) and secondary (L p = L 22 ) inductance 107 LiebermanShortCourse15
116 PLANAR COIL FIELDS A ring-shaped plasma forms because { 0, on axis Induced electric field = max, at r 1 2 R wall 0, at r = R wall Measured radial variation of B r (and E θ ) at three distances below the window (5 mtorr argon, 500 W, Hopwood et al, 1993) 108 LiebermanShortCourse15
117 INDUCTIVE DISCHARGES POWER BALANCE 109 LiebermanShortCourse15
118 RESISTANCE AT HIGH AND LOW DENSITIES Plasma resistance seen by the coil [p. 103] ω 2 L 2 12 R s = R p Rp 2 + ω2 L 2 p High density (normal inductive operation) [p. 103] R s R p 1 1 σ dc δ p ne Low density (skin depth > plasma size) R s number of electrons in the heating volume n e R s n e Low density High density δ p ~ plasma size n e 1 n e 110 LiebermanShortCourse15
119 POWER BALANCE WITHOUT MATCHING Drive discharge with rf current Power absorbed by discharge is P abs = 1 2 Ĩrf 2 R s (n e ) [p. 110] Power lost by discharge P loss n e [p. 50] Intersection (red dot) gives operating point; let Ĩ1 < Ĩ2 < Ĩ3 P loss Power P abs = 1 2Ĩ2 3R s P abs = 1 2Ĩ2 2R s P abs = 1 2Ĩ2 1R s Inductive operation impossible for Ĩrf Ĩ2 111 LiebermanShortCourse15 n e
120 CAPACITIVE COUPLING OF COIL TO For Ĩrf below the minimum current Ĩ2, there is only a weak capacitive coupling of the coil to the plasma + Ṽ rf Capacitive coupling Ĩ p Plasma A small capacitive power is absorbed = low density capacitive discharge z P loss Power Cap Ind P abs = 1 2Ĩ2 3R s P abs = 1 2Ĩ2 1R s Cap Mode Ind Mode n e 112 LiebermanShortCourse15
121 MEASURMENTS OF ARGON ION DENSITY Above 100 W, discharge is inductive and n e P abs Below 100 W, a weak capacitive discharge is present 113 LiebermanShortCourse15
122 SOURCE EFFICIENCY The source coil has some winding resistance R coil R coil is in series with the plasma resistance R s Power transfer efficiency is η = High efficiency = maximum R s R s R s + R coil R s n e Low density n 1 e High density δ p ~ plasma size Power transfer efficiency decreases at low and high densities Poor power transfer at low or high densities is analogous to poor power transfer in an ordinary transformer with an open or shorted secondary winding n e 114 LiebermanShortCourse15
A MINI-COURSE ON THE PRINCIPLES OF LOW-PRESSURE DISCHARGES AND MATERIALS PROCESSING
A MINI-COURSE ON THE PRINCIPLES OF LOW-PRESSURE DISCHARGES AND MATERIALS PROCESSING Michael A. Lieberman Department of Electrical Engineering and Computer Science, CA 94720 LiebermanMinicourse10 1 OUTLINE
More informationA MINI-COURSE ON THE PRINCIPLES OF LOW-PRESSURE DISCHARGES AND MATERIALS PROCESSING
A MINI-COURSE ON THE PRINCIPLES OF LOW-PRESSURE DISCHARGES AND MATERIALS PROCESSING Michael A. Lieberman Department of Electrical Engineering and Computer Science, CA 94720 LiebermanMinicourse07 1 OUTLINE
More informationA MINI-COURSE ON THE PRINCIPLES OF PLASMA DISCHARGES
A MINI-COURSE ON THE PRINCIPLES OF DISCHARGES Michael A. Lieberman Department of Electrical Engineering and Computer Science, CA 94720 LiebermanShortCourse06 1 THE MICROELECTRONICS REVOLUTION Transistors/chip
More informationPhysique des plasmas radiofréquence Pascal Chabert
Physique des plasmas radiofréquence Pascal Chabert LPP, Ecole Polytechnique pascal.chabert@lpp.polytechnique.fr Planning trois cours : Lundi 30 Janvier: Rappels de physique des plasmas froids Lundi 6 Février:
More informationLecture 6 Plasmas. Chapters 10 &16 Wolf and Tauber. ECE611 / CHE611 Electronic Materials Processing Fall John Labram 1/68
Lecture 6 Plasmas Chapters 10 &16 Wolf and Tauber 1/68 Announcements Homework: Homework will be returned to you on Thursday (12 th October). Solutions will be also posted online on Thursday (12 th October)
More informationPRINCIPLES OF PLASMA DISCHARGES AND MATERIALS PROCESSING
PRINCIPLES OF PLASMA DISCHARGES AND MATERIALS PROCESSING Second Edition MICHAEL A. LIEBERMAN ALLAN J, LICHTENBERG WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC PUBLICATION CONTENTS PREFACE xrrii PREFACE
More informationMODELING AND SIMULATION OF LOW TEMPERATURE PLASMA DISCHARGES
MODELING AND SIMULATION OF LOW TEMPERATURE PLASMA DISCHARGES Michael A. Lieberman University of California, Berkeley lieber@eecs.berkeley.edu DOE Center on Annual Meeting May 2015 Download this talk: http://www.eecs.berkeley.edu/~lieber
More information4 Modeling of a capacitive RF discharge
4 Modeling of a capacitive discharge 4.1 PIC MCC model for capacitive discharge Capacitive radio frequency () discharges are very popular, both in laboratory research for the production of low-temperature
More informationDOE WEB SEMINAR,
DOE WEB SEMINAR, 2013.03.29 Electron energy distribution function of the plasma in the presence of both capacitive field and inductive field : from electron heating to plasma processing control 1 mm PR
More informationElectron Series Resonant Discharges: Part II: Simulations of Initiation
Electron Series Resonant Discharges: Part II: Simulations of Initiation K. J. Bowers 1 W. D. Qiu 2 C. K. Birdsall 3 Plasma Theory and Simulation Group Electrical Engineering and Computer Science Department
More informationChapter 7 Plasma Basic
Chapter 7 Plasma Basic Hong Xiao, Ph. D. hxiao89@hotmail.com www2.austin.cc.tx.us/hongxiao/book.htm Hong Xiao, Ph. D. www2.austin.cc.tx.us/hongxiao/book.htm 1 Objectives List at least three IC processes
More informationDiffusion during Plasma Formation
Chapter 6 Diffusion during Plasma Formation Interesting processes occur in the plasma formation stage of the Basil discharge. This early stage has particular interest because the highest plasma densities
More information2D Hybrid Fluid-Analytical Model of Inductive/Capacitive Plasma Discharges
63 rd GEC & 7 th ICRP, 2010 2D Hybrid Fluid-Analytical Model of Inductive/Capacitive Plasma Discharges E. Kawamura, M.A. Lieberman, and D.B. Graves University of California, Berkeley, CA 94720 This work
More informationHong Young Chang Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Republic of Korea
Hong Young Chang Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Republic of Korea Index 1. Introduction 2. Some plasma sources 3. Related issues 4. Summary -2 Why is
More informationMonte Carlo Collisions in Particle in Cell simulations
Monte Carlo Collisions in Particle in Cell simulations Konstantin Matyash, Ralf Schneider HGF-Junior research group COMAS : Study of effects on materials in contact with plasma, either with fusion or low-temperature
More informationNARROW GAP ELECTRONEGATIVE CAPACITIVE DISCHARGES AND STOCHASTIC HEATING
NARRW GAP ELECTRNEGATIVE CAPACITIVE DISCHARGES AND STCHASTIC HEATING M.A. Lieberman, E. Kawamura, and A.J. Lichtenberg Department of Electrical Engineering and Computer Sciences University of California
More informationLow Temperature Plasma Technology Laboratory
Low Temperature Plasma Technology Laboratory Equilibrium theory for plasma discharges of finite length Francis F. Chen and Davide Curreli LTP-6 June, Electrical Engineering Department Los Angeles, California
More informationETCHING Chapter 10. Mask. Photoresist
ETCHING Chapter 10 Mask Light Deposited Substrate Photoresist Etch mask deposition Photoresist application Exposure Development Etching Resist removal Etching of thin films and sometimes the silicon substrate
More informationPlasmas rf haute densité Pascal Chabert LPTP, Ecole Polytechnique
Plasmas rf haute densité Pascal Chabert LPTP, Ecole Polytechnique chabert@lptp.polytechnique.fr Pascal Chabert, 2006, All rights reserved Programme Introduction Généralité sur les plasmas Plasmas Capacitifs
More informationPlasma Astrophysics Chapter 1: Basic Concepts of Plasma. Yosuke Mizuno Institute of Astronomy National Tsing-Hua University
Plasma Astrophysics Chapter 1: Basic Concepts of Plasma Yosuke Mizuno Institute of Astronomy National Tsing-Hua University What is a Plasma? A plasma is a quasi-neutral gas consisting of positive and negative
More informationEtching Issues - Anisotropy. Dry Etching. Dry Etching Overview. Etching Issues - Selectivity
Etching Issues - Anisotropy Dry Etching Dr. Bruce K. Gale Fundamentals of Micromachining BIOEN 6421 EL EN 5221 and 6221 ME EN 5960 and 6960 Isotropic etchants etch at the same rate in every direction mask
More informationLow Temperature Plasma Technology Laboratory
Low Temperature Plasma Technology Laboratory CENTRAL PEAKING OF MAGNETIZED GAS DISCHARGES Francis F. Chen and Davide Curreli LTP-1210 Oct. 2012 Electrical Engineering Department Los Angeles, California
More informationFeature-level Compensation & Control
Feature-level Compensation & Control 2 Plasma Eray Aydil, UCSB, Mike Lieberman, UCB and David Graves UCB Workshop November 19, 2003 Berkeley, CA 3 Feature Profile Evolution Simulation Eray S. Aydil University
More informationCharacteristics and classification of plasmas
Characteristics and classification of plasmas PlasTEP trainings course and Summer school 2011 Warsaw/Szczecin Indrek Jõgi, University of Tartu Partfinanced by the European Union (European Regional Development
More informationFundamentals of Plasma Physics
Fundamentals of Plasma Physics Definition of Plasma: A gas with an ionized fraction (n i + + e ). Depending on density, E and B fields, there can be many regimes. Collisions and the Mean Free Path (mfp)
More informationDual-RadioFrequency Capacitively-Coupled Plasma Reactors. Tomás Oliveira Fartaria nº58595
Dual-RadioFrequency Capacitively-Coupled Plasma Reactors Tomás Oliveira Fartaria nº58595 Index Capacitive Reactors Dual Frequency Capacitively-Coupled reactors o Apparatus for improved etching uniformity
More informationElectromagnetic Waves
Electromagnetic Waves Maxwell s equations predict the propagation of electromagnetic energy away from time-varying sources (current and charge) in the form of waves. Consider a linear, homogeneous, isotropic
More informationP. Diomede, D. J. Economou and V. M. Donnelly Plasma Processing Laboratory, University of Houston
P. Diomede, D. J. Economou and V. M. Donnelly Plasma Processing Laboratory, University of Houston 1 Outline Introduction PIC-MCC simulation of tailored bias on boundary electrode Semi-analytic model Comparison
More informationInduction_P1. 1. [1 mark]
Induction_P1 1. [1 mark] Two identical circular coils are placed one below the other so that their planes are both horizontal. The top coil is connected to a cell and a switch. The switch is closed and
More information1P22/1P92 Exam Review Problems 2013 Friday, January 14, :03 AM. Chapter 20
Exam Review Problems 2011 Page 1 1P22/1P92 Exam Review Problems 2013 Friday, January 14, 2011 10:03 AM Chapter 20 True or false? 1 It's impossible to place a charge on an insulator, because no current
More informationLECTURE 5 SUMMARY OF KEY IDEAS
LECTURE 5 SUMMARY OF KEY IDEAS Etching is a processing step following lithography: it transfers a circuit image from the photoresist to materials form which devices are made or to hard masking or sacrificial
More informationChapter 7. Plasma Basics
Chapter 7 Plasma Basics 2006/4/12 1 Objectives List at least three IC processes using plasma Name three important collisions in plasma Describe mean free path Explain how plasma enhance etch and CVD processes
More informationChapter VI: Cold plasma generation
Introduction This photo shows the electrical discharge inside a highpressure mercury vapor lamp (Philips HO 50) just after ignition (Hg + Ar) Chapter VI: Cold plasma generation Anode Positive column Cathode
More informationPlasma Processing in the Microelectronics Industry. Bert Ellingboe Plasma Research Laboratory
Plasma Processing in the Microelectronics Industry Bert Ellingboe Plasma Research Laboratory Outline What has changed in the last 12 years? What is the relavant plasma physics? Sheath formation Sheath
More informationLouisiana State University Physics 2102, Exam 3 April 2nd, 2009.
PRINT Your Name: Instructor: Louisiana State University Physics 2102, Exam 3 April 2nd, 2009. Please be sure to PRINT your name and class instructor above. The test consists of 4 questions (multiple choice),
More informationPhysics 240 Fall 2005: Exam #3 Solutions. Please print your name: Please list your discussion section number: Please list your discussion instructor:
Physics 4 Fall 5: Exam #3 Solutions Please print your name: Please list your discussion section number: Please list your discussion instructor: Form #1 Instructions 1. Fill in your name above. This will
More informationNONLINEAR ELECTROMAGNETICS MODEL OF AN ASYMMETRICALLY DRIVEN CAPACITIVE DISCHARGE
NONLINEAR ELECTROMAGNETICS MODEL OF AN ASYMMETRICALLY DRIVEN CAPACITIVE DISCHARGE M.A. Lieberman Department of Electrical Engineering and Computer Sciences University of California Berkeley, CA 94720 Collaborators:
More informationPart 4: Electromagnetism. 4.1: Induction. A. Faraday's Law. The magnetic flux through a loop of wire is
1 Part 4: Electromagnetism 4.1: Induction A. Faraday's Law The magnetic flux through a loop of wire is Φ = BA cos θ B A B = magnetic field penetrating loop [T] A = area of loop [m 2 ] = angle between field
More informationRLC Circuit (3) We can then write the differential equation for charge on the capacitor. The solution of this differential equation is
RLC Circuit (3) We can then write the differential equation for charge on the capacitor The solution of this differential equation is (damped harmonic oscillation!), where 25 RLC Circuit (4) If we charge
More informationADVENTURES IN TWO-DIMENSIONAL PARTICLE-IN-CELL SIMULATIONS OF ELECTRONEGATIVE DISCHARGES
ADVENTURES IN TWO-DIMENSIONAL PARTICLE-IN-CELL SIMULATIONS OF ELECTRONEGATIVE DISCHARGES PART 1: DOUBLE LAYERS IN A TWO REGION DISCHARGE E. Kawamura, A.J. Lichtenberg, M.A. Lieberman and J.P. Verboncoeur
More informationYell if you have any questions
Class 36: Outline Hour 1: Concept Review / Overview PRS Questions Possible Exam Questions Hour : Sample Exam Yell if you have any questions P36-1 Before Starting All of your grades should now be posted
More informationSinusoidal Steady State Power Calculations
10 Sinusoidal Steady State Power Calculations Assessment Problems AP 10.1 [a] V = 100/ 45 V, Therefore I = 20/15 A P = 1 (100)(20)cos[ 45 (15)] = 500W, 2 A B Q = 1000sin 60 = 866.03 VAR, B A [b] V = 100/
More informationOne dimensional hybrid Maxwell-Boltzmann model of shearth evolution
Technical collection One dimensional hybrid Maxwell-Boltzmann model of shearth evolution 27 - Conferences publications P. Sarrailh L. Garrigues G. J. M. Hagelaar J. P. Boeuf G. Sandolache S. Rowe B. Jusselin
More informationLecture 11 - AC Power
- AC Power 11/17/2015 Reading: Chapter 11 1 Outline Instantaneous power Complex power Average (real) power Reactive power Apparent power Maximum power transfer Power factor correction 2 Power in AC Circuits
More informationFINAL REPORT. DOE Grant DE-FG03-87ER13727
FINAL REPORT DOE Grant DE-FG03-87ER13727 Dynamics of Electronegative Plasmas for Materials Processing Allan J. Lichtenberg and Michael A. Lieberman Department of Electrical Engineering and Computer Sciences
More informationCHAPTER 6: Etching. Chapter 6 1
Chapter 6 1 CHAPTER 6: Etching Different etching processes are selected depending upon the particular material to be removed. As shown in Figure 6.1, wet chemical processes result in isotropic etching
More informationBasic Electronics. Introductory Lecture Course for. Technology and Instrumentation in Particle Physics Chicago, Illinois June 9-14, 2011
Basic Electronics Introductory Lecture Course for Technology and Instrumentation in Particle Physics 2011 Chicago, Illinois June 9-14, 2011 Presented By Gary Drake Argonne National Laboratory drake@anl.gov
More informationYell if you have any questions
Class 36: Outline Hour 1: Concept Review / Overview PRS Questions Possible Exam Questions Hour : Sample Exam Yell if you have any questions P36-1 efore Starting All of your grades should now be posted
More informationMWP MODELING AND SIMULATION OF ELECTROMAGNETIC EFFECTS IN CAPACITIVE DISCHARGES
MWP 1.9 MODELING AND SIMULATION OF ELECTROMAGNETIC EFFECTS IN CAPACITIVE DISCHARGES Insook Lee, D.B. Graves, and M.A. Lieberman University of California Berkeley, CA 9472 LiebermanGEC7 1 STANDING WAVES
More informationSUMMARY Phys 2523 (University Physics II) Compiled by Prof. Erickson. F e (r )=q E(r ) dq r 2 ˆr = k e E = V. V (r )=k e r = k q i. r i r.
SUMMARY Phys 53 (University Physics II) Compiled by Prof. Erickson q 1 q Coulomb s Law: F 1 = k e r ˆr where k e = 1 4π =8.9875 10 9 N m /C, and =8.85 10 1 C /(N m )isthepermittivity of free space. Generally,
More informationarxiv: v1 [physics.plasm-ph] 10 Nov 2014
arxiv:1411.2464v1 [physics.plasm-ph] 10 Nov 2014 Effects of fast atoms and energy-dependent secondary electron emission yields in PIC/MCC simulations of capacitively coupled plasmas A. Derzsi 1, I. Korolov
More information2. The following diagram illustrates that voltage represents what physical dimension?
BioE 1310 - Exam 1 2/20/2018 Answer Sheet - Correct answer is A for all questions 1. A particular voltage divider with 10 V across it consists of two resistors in series. One resistor is 7 KΩ and the other
More informationMODELING PLASMA PROCESSING DISCHARGES
MODELING PROCESSING DISCHARGES M.A. Lieberman Department of Electrical Engineering and Computer Sciences University of California Berkeley, CA 94720 Collaborators: E. Kawamura, D.B. Graves, and A.J. Lichtenberg,
More informationBasics of Electromagnetics Maxwell s Equations (Part - I)
Basics of Electromagnetics Maxwell s Equations (Part - I) Soln. 1. C A. dl = C. d S [GATE 1994: 1 Mark] A. dl = A. da using Stoke s Theorem = S A. ds 2. The electric field strength at distant point, P,
More informationPIC-MCC/Fluid Hybrid Model for Low Pressure Capacitively Coupled O 2 Plasma
PIC-MCC/Fluid Hybrid Model for Low Pressure Capacitively Coupled O 2 Plasma Kallol Bera a, Shahid Rauf a and Ken Collins a a Applied Materials, Inc. 974 E. Arques Ave., M/S 81517, Sunnyvale, CA 9485, USA
More informationPIC-MCC/Fluid Hybrid Model for Low Pressure Capacitively Coupled O 2 Plasma
PIC-MCC/Fluid Hybrid Model for Low Pressure Capacitively Coupled O 2 Plasma Kallol Bera a, Shahid Rauf a and Ken Collins a a Applied Materials, Inc. 974 E. Arques Ave., M/S 81517, Sunnyvale, CA 9485, USA
More informationarxiv: v1 [physics.plasm-ph] 16 Apr 2018
Consistent simulation of capacitive radio-frequency discharges and external matching networks Frederik Schmidt Institute of Theoretical Electrical Engineering, arxiv:1804.05638v1 [physics.plasm-ph] 16
More informationModule 4. Single-phase AC Circuits
Module 4 Single-phase AC Circuits Lesson 14 Solution of Current in R-L-C Series Circuits In the last lesson, two points were described: 1. How to represent a sinusoidal (ac) quantity, i.e. voltage/current
More informationPhysics 142 Steady Currents Page 1. Steady Currents
Physics 142 Steady Currents Page 1 Steady Currents If at first you don t succeed, try, try again. Then quit. No sense being a damn fool about it. W.C. Fields Electric current: the slow average drift of
More informationPlasmas as fluids. S.M.Lea. January 2007
Plasmas as fluids S.M.Lea January 2007 So far we have considered a plasma as a set of non intereacting particles, each following its own path in the electric and magnetic fields. Now we want to consider
More informationSinusoidal Steady State Analysis (AC Analysis) Part II
Sinusoidal Steady State Analysis (AC Analysis) Part II Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/
More informationLangmuir Probes as a Diagnostic to Study Plasma Parameter Dependancies, and Ion Acoustic Wave Propogation
Langmuir Probes as a Diagnostic to Study Plasma Parameter Dependancies, and Ion Acoustic Wave Propogation Kent Lee, Dean Henze, Patrick Smith, and Janet Chao University of San Diego (Dated: May 1, 2013)
More informationElectromagnetic Field Theory Chapter 9: Time-varying EM Fields
Electromagnetic Field Theory Chapter 9: Time-varying EM Fields Faraday s law of induction We have learned that a constant current induces magnetic field and a constant charge (or a voltage) makes an electric
More informationMODELING OF AN ECR SOURCE FOR MATERIALS PROCESSING USING A TWO DIMENSIONAL HYBRID PLASMA EQUIPMENT MODEL. Ron L. Kinder and Mark J.
TECHCON 98 Las Vegas, Nevada September 9-11, 1998 MODELING OF AN ECR SOURCE FOR MATERIALS PROCESSING USING A TWO DIMENSIONAL HYBRID PLASMA EQUIPMENT MODEL Ron L. Kinder and Mark J. Kushner Department of
More informationOscillations and Electromagnetic Waves. March 30, 2014 Chapter 31 1
Oscillations and Electromagnetic Waves March 30, 2014 Chapter 31 1 Three Polarizers! Consider the case of unpolarized light with intensity I 0 incident on three polarizers! The first polarizer has a polarizing
More informationPlasma Deposition (Overview) Lecture 1
Plasma Deposition (Overview) Lecture 1 Material Processes Plasma Processing Plasma-assisted Deposition Implantation Surface Modification Development of Plasma-based processing Microelectronics needs (fabrication
More informationECE 6340 Intermediate EM Waves. Fall Prof. David R. Jackson Dept. of ECE. Notes 1
EE 6340 Intermediate EM Waves Fall 2016 Prof. David R. Jackson Dept. of EE Notes 1 1 Maxwell s Equations E D rt 2, V/m, rt, Wb/m T ( ) [ ] ( ) ( ) 2 rt, /m, H ( rt, ) [ A/m] B E = t (Faraday's Law) D H
More informationOn my honor, I have neither given nor received unauthorized aid on this examination.
Instructor: Profs. Andrew Rinzler, Paul Avery, Selman Hershfield PHYSICS DEPARTMENT PHY 049 Exam 3 April 7, 00 Name (print, last first): Signature: On my honor, I have neither given nor received unauthorized
More informationFigure 1.1: Ionization and Recombination
Chapter 1 Introduction 1.1 What is a Plasma? 1.1.1 An ionized gas A plasma is a gas in which an important fraction of the atoms is ionized, so that the electrons and ions are separately free. When does
More informationPIC-MCC simulations for complex plasmas
GRADUATE SUMMER INSTITUTE "Complex Plasmas August 4, 008 PIC-MCC simulations for complex plasmas Irina Schweigert Institute of Theoretical and Applied Mechanics, SB RAS, Novosibirsk Outline GRADUATE SUMMER
More informationChap. 1 Fundamental Concepts
NE 2 Chap. 1 Fundamental Concepts Important Laws in Electromagnetics Coulomb s Law (1785) Gauss s Law (1839) Ampere s Law (1827) Ohm s Law (1827) Kirchhoff s Law (1845) Biot-Savart Law (1820) Faradays
More informationThe low-field density peak in helicon discharges
PHYSICS OF PLASMAS VOLUME 10, NUMBER 6 JUNE 2003 Francis F. Chen a) Electrical Engineering Department, University of California, Los Angeles, Los Angeles, California 90095-1597 Received 10 December 2002;
More informationremain essentially unchanged for the case of time-varying fields, the remaining two
Unit 2 Maxwell s Equations Time-Varying Form While the Gauss law forms for the static electric and steady magnetic field equations remain essentially unchanged for the case of time-varying fields, the
More informationElectromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance
Lesson 7 Electromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance Oscillations in an LC Circuit The RLC Circuit Alternating Current Electromagnetic
More informationPIC/MCC Simulation of Radio Frequency Hollow Cathode Discharge in Nitrogen
PIC/MCC Simulation of Radio Frequency Hollow Cathode Discharge in Nitrogen HAN Qing ( ), WANG Jing ( ), ZHANG Lianzhu ( ) College of Physics Science and Information Engineering, Hebei Normal University,
More informationYell if you have any questions
Class 31: Outline Hour 1: Concept Review / Overview PRS Questions possible exam questions Hour : Sample Exam Yell if you have any questions P31 1 Exam 3 Topics Faraday s Law Self Inductance Energy Stored
More informationChapter 31 Electromagnetic Oscillations and Alternating Current LC Oscillations, Qualitatively
Chapter 3 Electromagnetic Oscillations and Alternating Current LC Oscillations, Qualitatively In the LC circuit the charge, current, and potential difference vary sinusoidally (with period T and angular
More informationEXPERIMENTAL STUDIES ON ELECTRO- POSITIVE/NEGATIVE PLASMAS PRODUCED BY RF DISCHARGES WITH EXTERNAL ANTENNA IN LOW-PRESSURE GASES
EXPERIMENTAL STUDIES ON ELECTRO- POSITIVE/NEGATIVE PLASMAS PRODUCED BY RF DISCHARGES WITH EXTERNAL ANTENNA IN LOW-PRESSURE GASES SEPTEMBER 2004 DEPARTMENT OF ENERGY AND MATERIALS SCIENCE GRADUATE SCHOOL
More informationSinusoidal Response of RLC Circuits
Sinusoidal Response of RLC Circuits Series RL circuit Series RC circuit Series RLC circuit Parallel RL circuit Parallel RC circuit R-L Series Circuit R-L Series Circuit R-L Series Circuit Instantaneous
More informationLecture 6: High Voltage Gas Switches
Lecture 6: High Voltage Gas Switches Switching is a central problem in high voltage pulse generation. We need fast switches to generate pulses, but in our case, they must also hold off high voltages before
More informationREACTANCE. By: Enzo Paterno Date: 03/2013
REACTANCE REACTANCE By: Enzo Paterno Date: 03/2013 5/2007 Enzo Paterno 1 RESISTANCE - R i R (t R A resistor for all practical purposes is unaffected by the frequency of the applied sinusoidal voltage or
More informationMagnetostatic fields! steady magnetic fields produced by steady (DC) currents or stationary magnetic materials.
ECE 3313 Electromagnetics I! Static (time-invariant) fields Electrostatic or magnetostatic fields are not coupled together. (one can exist without the other.) Electrostatic fields! steady electric fields
More informationChapter 1 The Electric Force
Chapter 1 The Electric Force 1. Properties of the Electric Charges 1- There are two kinds of the electric charges in the nature, which are positive and negative charges. - The charges of opposite sign
More informationField and Wave Electromagnetic
Field and Wave Electromagnetic Chapter7 The time varying fields and Maxwell s equation Introduction () Time static fields ) Electrostatic E =, id= ρ, D= εe ) Magnetostatic ib=, H = J, H = B μ note) E and
More informationTHE TOROIDAL HELICON EXPERIMENT AT IPR
THE TOROIDAL HELICON EXPERIMENT AT IPR Manash Kumar Paul Supervisor Prof. Dhiraj Bora D.D.G, ITER Acknowledgement Dr. S.K.P.Tripathi UCLA Institute for Plasma Research Gandhinagar, Gujarat (India) MOTIVATION
More informationUHV - Technology. Oswald Gröbner
School on Synchrotron Radiation UHV - Technology Trieste, 20-21 April 2004 1) Introduction and some basics 2) Building blocks of a vacuum system 3) How to get clean ultra high vacuum 4) Desorption phenomena
More informationEELE 3332 Electromagnetic II Chapter 9. Maxwell s Equations. Islamic University of Gaza Electrical Engineering Department Dr.
EELE 3332 Electromagnetic II Chapter 9 Maxwell s Equations Islamic University of Gaza Electrical Engineering Department Dr. Talal Skaik 2013 1 Review Electrostatics and Magnetostatics Electrostatic Fields
More informationAlternating Current. Symbol for A.C. source. A.C.
Alternating Current Kirchoff s rules for loops and junctions may be used to analyze complicated circuits such as the one below, powered by an alternating current (A.C.) source. But the analysis can quickly
More informationWhere k = 1. The electric field produced by a point charge is given by
Ch 21 review: 1. Electric charge: Electric charge is a property of a matter. There are two kinds of charges, positive and negative. Charges of the same sign repel each other. Charges of opposite sign attract.
More informationIII. Electromagnetic uniformity: finite RF wavelength in large area, VHF reactors: standing waves, and telegraph effect
III. Electromagnetic uniformity: finite RF wavelength in large area, VHF reactors: standing waves, and telegraph effect IV. Uniformity in time: minimize transients, rapid equilibration to steady-state
More informationELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT
Chapter 31: ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT 1 A charged capacitor and an inductor are connected in series At time t = 0 the current is zero, but the capacitor is charged If T is the
More informationElectron heating in capacitively coupled radio frequency discharges
Electron heating in capacitively coupled radio frequency discharges Dissertation zur Erlangung des Grades eines Doktors der Naturwissenschaften in der Fakultät für Physik und Astronomie der Ruhr-Universität
More informationIntroduction. Chapter Plasma: definitions
Chapter 1 Introduction 1.1 Plasma: definitions A plasma is a quasi-neutral gas of charged and neutral particles which exhibits collective behaviour. An equivalent, alternative definition: A plasma is a
More informationSupplemental Notes on Complex Numbers, Complex Impedance, RLC Circuits, and Resonance
Supplemental Notes on Complex Numbers, Complex Impedance, RLC Circuits, and Resonance Complex numbers Complex numbers are expressions of the form z = a + ib, where both a and b are real numbers, and i
More informationPlasma Modeling with COMSOL Multiphysics
Plasma Modeling with COMSOL Multiphysics Copyright 2014 COMSOL. Any of the images, text, and equations here may be copied and modified for your own internal use. All trademarks are the property of their
More informationSinusoidal Steady State Analysis
Sinusoidal Steady State Analysis 9 Assessment Problems AP 9. [a] V = 70/ 40 V [b] 0 sin(000t +20 ) = 0 cos(000t 70 ).. I = 0/ 70 A [c] I =5/36.87 + 0/ 53.3 =4+j3+6 j8 =0 j5 =.8/ 26.57 A [d] sin(20,000πt
More informationDriven RLC Circuits Challenge Problem Solutions
Driven LC Circuits Challenge Problem Solutions Problem : Using the same circuit as in problem 6, only this time leaving the function generator on and driving below resonance, which in the following pairs
More informationElectromagnetism. 1 ENGN6521 / ENGN4521: Embedded Wireless
Electromagnetism 1 ENGN6521 / ENGN4521: Embedded Wireless Radio Spectrum use for Communications 2 ENGN6521 / ENGN4521: Embedded Wireless 3 ENGN6521 / ENGN4521: Embedded Wireless Electromagnetism I Gauss
More informationIntroduction to Plasma
What is a plasma? The fourth state of matter A partially ionized gas How is a plasma created? Energy must be added to a gas in the form of: Heat: Temperatures must be in excess of 4000 O C Radiation Electric
More informationExam 3 Topics. Displacement Current Poynting Vector. Faraday s Law Self Inductance. Circuits. Energy Stored in Inductor/Magnetic Field
Exam 3 Topics Faraday s Law Self Inductance Energy Stored in Inductor/Magnetic Field Circuits LR Circuits Undriven (R)LC Circuits Driven RLC Circuits Displacement Current Poynting Vector NO: B Materials,
More information