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ICOPS Minicourse on Plasma Processing Technology

ICOPS Minicourse on Plasma Processing Technology. Part 1: Vacuum Basics Jeff Hopwood Northeastern University. Goals. To review basic vacuum technology Pressure, pumps, gauges To review gas flow and conductance To understand the flux of vapor phase material to a substrate

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ICOPS Minicourse on Plasma Processing Technology

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  1. ICOPS Minicourseon Plasma Processing Technology Part 1: Vacuum Basics Jeff Hopwood Northeastern University

  2. Goals • To review basic vacuum technology • Pressure, pumps, gauges • To review gas flow and conductance • To understand the flux of vapor phase material to a substrate • To understand mean free path, l

  3. Typical High Pressure Plasma 1.3x10-9 1.3x10-3 1.3x10-6 1 atm. 1 Torr = 1 mm-Hg 1 Torr 1x10-6 Torr 1 mTorr 760 Torr 1 Pascal = 1 N/m2 0.133x10-3 Pa 0.133 Pa 133 Pa 101,333 Pa Typical Low Pressure Plasma Processing Ultrahigh Vacuum Rough Vacuum High Vacuum Vacuum (units)

  4. Rough Vacuum • “Mechanical Pumps” typically create a base pressure of 1-10 mTorr or 0.13-1.3 Pa Warning: Certain process gases are incompatible with pump fluids and pose severe safety risks! Rotary Vane Pump (Campbell)

  5. High Vacuum Pumping • Cryopumps condense gases on cold surfaces to produce vacuum • Typically there are three cold surfaces: • Inlet array condenses water and hydrocarbons (60-100 Kelvin) • Condensing array pumps argon, nitrogen and most other gases (10-20 K) • Adsorption is needed to trap helium, hydrogen and neon in activated carbon at 10-12 K. These gases are pumped very slowly! (Campbell) Warning: all pumped gases are trapped inside the pump, so explosive, toxic and corrosive gases are not recommended. No mech. pump is needed until regen. adapted from www.helixtechnology.com

  6. High Vacuum Pumping Process chamber Turbomolecular Pump High rotation speed turbine imparts momentum to gas atoms Inlet pressures: <10 mTorr Foreline pressure: < 1 Torr Requires a rough pump Good choice for toxic and explosive gases – -gases are not trapped in pump All gases are pumped at approx. the same rate Pumping Speeds: 20 – 2000 liters per sec foreline adapted from Lesker.com

  7. High Vacuum Pumping Diffusion Pump The process gas is entrained by the downward flow of vaporized pumping fluid. Benefits: Low cost, reliable, and rugged. High pumping speed: ~ 2000 l/s Caution: The process chamber will be contaminated by pumping fluid. A cold trap must be used between the diffusion pump and the process chamber. Not recommended for “clean” processes. Process chamber Water- cooled walls Foreline -to mech pump Heater/Pumping Fluid adapted from Lesker.com

  8. Flow Rate Typically gas flows are cited in units of standard cubic centimeters per minute (sccm) or standard liters per minute (slm) “Standard” refers to T=273K, P = 1 atm. Example: Process gas flow of 50 sccm at 5 mTorr (@300k) requires 50 cm-3min-1(760Torr/5x10-3Torr)(300/273)(1min/60sec)(1/103) = 140 liters/sec of pumping speed at the chamber pump port

  9. Conductance Limitation 50 sccm Conductance depends on geometry and pressure (use tabulated data) 5 mTorr 140 l/s = Q/(P1 – P2) Fixed Throughput, Q: Q = 0.005 Torr x 140 l/s = 0.7 Torr-l/s > 140 l/s …since P2<P1 Corifice = ¼ (pa2)<v>l/s Ctube = pa3 (2<v>/3L) …if mean free path >> a, L (see Mahan, 2000)

  10. Convectron Gauge: Initial pumpdown from 1 atm, and as a foreline monitor Thermal Conductivity of Gas Baratron: Insensitive to gas composition, Good choice for process pressures True Pressure (diaphragm displacement) Ionization of Gas Ion Gauge: Sensitive to gas composition, but a good choice for base pressures Pressure Measurement RGA: A simple mass spectrometer Vacuum Gauge Selection adapted from Lesker.com

  11. Residual Gas Analysis Low pressure systems are dominated by water vapor as seen in this RGA of a chamber backfilled with 4x10-5 torr of argon Why? H2O is a polar molecule that is difficult to pump from the walls --> bake-out the chamber Leak? Source: Pfeiffer vacuum products

  12. Gas Density (n) Ideal Gas Law PV = NkT Gas density at 1 Pascal at room temp. N/V = n = P/kT = (1 N/m2)/(1.3807x10-23J/K)(300 K) = [1 (kg-m/s2)/m2]/[4.1x10-21 kg-m2/s2] = 2.4x1020 atoms per m3 = 2.4x1014 cm-3 …at 1Pa Rule of Thumb n(T) = 3.2x1013 cm-3 x (300/T) …at a pressure of 1 mTorr

  13. Gas Kinetics Maxwellian Distribution Average speed of an atom: Flux of atoms to the x-y plane surface: Very important! (Campbell)

  14. Example A vacuum chamber has a base pressure of 10-6 Torr. Assuming that this is dominated by water vapor, what is the flux of H2O to a substrate placed in this chamber? n = 3.2x1013 cm-3/mTorr * 10-3 mTorr = 3.2x1010 cm-3 <v> = (8kT/pM)1/2 = 59200 cm/s Gz = (¼)n<v>= 4.74x1014 molecules per cm2 per sec! This is approximately one monolayer of H2O every second at 10-6 Torr base pressure.

  15. Rigorous Hard Sphere Collisions: l = kT / 2pd2P  lAr(cm) ~ 8 / P (mTorr) Collisions and Mean Free Path Gas Density n = P/ kT Cross-section s ~ pd2 l = 1/sn d Ar

  16. ICOPS Minicourseon Plasma Processing Technology Part 2: Plasma Basics Jeff Hopwood Northeastern University

  17. Plasma: an ionized gas consisting of atoms, electrons, ions, molecules, molecular fragments, and electronically excited species (informal definition) www.geo.mtu.edu/weather/aurora/

  18. plasma (electrons+ions) energy gas (steam) energy energy liquid (water) Plasma: the “fourth state of matter” solid (ice)

  19. ”sputtering” + + + + - - - - - + - - - - - - + - - Argon Electron Argon ion - + DC Plasma (or AC Fluorescent Lamp…why AC?) Argon + Mercury @ 0.05 atm. - + + lamp endcap

  20. VDC Too many collisions Electron energy<ionization energy d Too few ionizing collisions: l>d Paschen Curve F. Paschen, Ann. Phys. Chem., Ser. 3 37, 69 (1889). http://www.duniway.com/images/pdf/pg/Paschen-Curve.pdf

  21. light Power Gas flow gas (ng) excited atoms and molecules electrons ne, Te ions radicals, molecular fragments reaction products secondary electrons pumping pumping What do we need to know about plasma? Wall Wall PLASMA substrate

  22. light Gas flow gas (ng) excited atoms and molecules ions radicals, molecular fragments reaction products secondary electrons pumping pumping Power Absorbed Power Wall Wall PLASMA electrons ne, Te substrate

  23. Power Absorbed: DC • DC power • General electrical mobility and conductivity • Mobility: me = q<t>/m = q/nmme Where <t> is the average time between collisions and nm is the collision frequency (collisions per second) • Electron Conductivity: sDC= qneme = q2ne/nmme • DC power absorbed:

  24. VRF Power Absorbed: RF • RF/microwave power • Ohmic Heating • Generic electron-neutral collision frequency nm ~ 5x10-8 ngasTe1/2 (s-1) … ngas (cm-3), Te(eV). • Example: Find the pressure at which rf ohmic heating becomes ineffective: nm = 0.1w, Te = 2eV w = 13.56 MHz * 2p = 85.2Mrad/s ngas = 0.1*85.2x106/5x10-8(2)1/2 = 1.2x1014 cm-3 = 3.7 mTorr f=13.56 MHz An electron oscillates in a rf electric field without gaining energy unless electron collisions occur Hopwood and Mantei, JVST A21, S139 (2003)

  25. Stochastic Heatingan electron enters and exits a region of high field for a fraction of an rf cyclet0 << 2p/w Reflecting Boundary (plasma sheath) Emax ERF z x - E ~ 0 vx(t0) > vx(0) The usual mechanism for heating electrons using RF electric fields at low pressures

  26. Ex t1 t3 t2 - - - x Electron cyclotron frequency: wce = qB/me = 1.76x107 B(gauss) If w = wce and ERF is perpendicular to BDC, then the electron gains energy from Ex in the absence of collisions. Ex. f=2.45 GHz --> B=875 G k ERF W/cm3 Wave/Resonant Heating BDC E=0 v y F = q(vxB) x Hopwood and Mantei, JVST A21, S139 (2003)

  27. light Gas flow gas (ng) excited atoms and molecules ions radicals, molecular fragments reaction products secondary electrons pumping pumping Electron Collisions Power Wall Wall PLASMA electrons ne, Te substrate

  28. Electron Collisions • Elastic Collisions: • Ar + e  Ar + e • Gas heating: energy is coupled from e to the gas • Excitation Collisions • Ar + ehot Ar* + ecold, Ar* Ar + hn • Responsible for the characteristic plasma “glow” • Eelectron>Eexc (~11.55 eV for argon) • Ionization Collisions: • Ar + ehot Ar+ + 2ecold • Couples electrical energy into producing more e_ • Eelectron > Eiz (15.76 eV for argon) • Dissociation: • O2 + ehot 2O + ecold or O2 + ehot O + O+ + ecold • Creates reactive chemical species within the plasma • Eelectron > Ediss(5.12 eV for oxygen)

  29. Collision Cross Sections • Unlike the hard sphere model, real collision cross sections are a function of electron kinetic energy s(E), or electron velocity s(v). • We must find the expected collision frequency by averaging over all E or v. becomes (cm3s-1)

  30. Graphically f(E) f(E) or s(E) sAr+(E) Note: the exponential tail of energetic electrons is responsible for ionization Te Eiz Electron energy, E The RATE CONSTANT: Kiz(Te) Kizoexp(-Eizo/Te) curve fitting

  31. Graphically Hot electrons – more ionization f(E) f(E) or s(E) sAr+(E) Note: the exponential tail of energetic electrons is responsible for ionization Te Eiz Electron energy, E The RATE CONSTANT: Kiz(Te) Kizoexp(-Eizo/Te) curve fitting

  32. Examples of Numerically Determined Rate Constants (Lieberman, 2005)

  33. Generation Rate of Plasma Species by Electron Collisions y + e  x + e dnx/dt = Kxneny For example, Ar + e  Ar+ + e + e dne/dt = Kiznengas is the number of electrons (and ions) generated per cm3 per second

  34. Electron-Ion Recombination Three-Body Problem: e + Ar+ + M  Ar + M the third body is needed to conserve energy and momentum in the recombination process volume recombination wall recombination - M - M M + + wall recombination dominates at low pressure because three body collisions are rare

  35. light Gas flow gas (ng) excited atoms and molecules ions Gn = ¼ n<v> radicals, molecular fragments reaction products secondary electrons pumping pumping Transport to Surfaces Power Wall Wall PLASMA electrons ne, Te substrate

  36. - - - neni r  0 - neni r  0 - - - - - - - Electron and Ion Loss to the Substrate and Walls- the plasma sheath - neni r  0 chamber electrons are much more mobile than ions me = q<t>/me >> q<ti>/mi = mi

  37. s ne = ni ne<<ni (sheath) -1kV 0 v r(x) + + V x x e V(x) x (after Mahan, 2000) Electron and Ion Loss to the Substrate and Walls- the plasma sheath - + low energy electrons are trapped within the plasma, but ions are accelerated by the sheath potential to the chamber walls and substrate

  38. Ion Flux The ion flux to a solid object is determined by the Bohm velocity (or sound speed) of the ion: uB = (kTe/mi)1/2= 9.8x105 (Te/M)1/2cm/s =9.8x105 (3 eV/40 amu)1/2 ~ 2.5x105 cm/s …and the ion flux is given byGi = uBni (cm-2s-1) (this is the ion speed at the edge of the sheath)

  39. Electron Flux • Only the most energetic electrons can overcome the sheath potential, Vs. • Ge = ¼ ne<ve> exp (qVs/kTe) flux to surface Boltzmann factor f(E) Te qVs Electron energy, E

  40. Sheath Potential, Vs In the steady state, the electron and ion fluxes to the chamber/substrate must be equal, if there is no external current path Ge = Gi ¼ ne<ve> exp (qVs/kTe) = uBni = (kTe/mi)1/2 ne giving Vs = -Teln(mi/2pme) ~ -5Te This is often called the floating potential: Isolated surfaces have a negative potential relative to the plasma.

  41. s -1kV 0 v V x (after Mahan, 2000) Ion Energy Ex: Assuming argon with Te = 3 eV, the ion energy at the cathode is Ei = q(1 kV + 4.7Te) = 1014 eV ignoring ion-neutral collision within s, and the ion energy at the anode is Ei = 4.7 Te = 14 eV Ion mean free path: li = 1/ngassi ~ 3/p (cm) for Ar+ …where p is the pressure in mTorr Here li = 3/100 cm or 0.3 mm @ 0.1 torr NOTE: s>>li Ei << 1014 eV!

  42. ne=ni Particle Conservationand Electron Temperature A simple model for electron temperature can be found for a steady state plasma: # of ions created/sec = # of ions lost/sec KizngasneV = uBniAeff Kiz/uB = Kizoe-Eiz/kTe /(kTe/mi)1/2 = Aeff/(V ngas) =1/deffngas (V=plasma volume, Aeff = effective chamber area, deff = V/Aeff)

  43. Ar + e  Ar+ + 2e Ar+eAr*+e Ar* + e  Ar+ + 2e • The electron temperature (Te) is a unique function of • gas density, ngas (pressure) • chamber size, deff = V/Aeff • gas type: Kiz, Eiz Example: Two large parallel plates separated by 2 cm are used to sustain an argon plasma at 25 mTorr. Find Te. deff = V/Aeff ~ pR2d / (pR2 +pR2)= d/2 ngasdeff ~ (25*3.2x1019m-3)(0.01m) =0.8e+19 m-2 Te = 3 eV (Note: we have assume that the plasma density is uniform)

  44. Power Conservation and Electron Density, ne Power Absorbed by the Plasma = Power Lost from the Plasma Pabs = [qniuBEion+q(¼ne<ve>eVs/kTe )Eelec]Aeff +(Pheat+Plight+Pdiss) ≡ qneuBAeff(Eion + Eelec + Ec) where EC is the collisional energy lost in creating an electron-ion pair due to ionization, light, dissociative collisions, and heat: EC = [nizEiz + nexEex + ndissEdiss + nm(3me/mi)Te]/niz Pion Pelectron 2Te qVs

  45. C Collisional Energy Loss

  46. Electron Density Example Continuing with the previous example A plasma is sustained in argon at 25 mTorr between to parallel plates separated by 2 cm. The radius of the plates is 20 cm and the power absorbed by the plasma is 100 watts. Find ne. 100 W = qneuBAeff(Eion + Eelec + Ec) = (1.6x10-19C)ne(2.5x105cm/s)(2px202 cm2) x (5Te + 2Te + 55 eV) ne = 1.3x1010 cm-3 Find ne if the gas is N2, assuming that Te ~ 3 eV 100 W = (1.6x10-19C)ne(2.5x105cm/s)(2px202 cm2)(5Te + 2Te + 400 eV)  ne = 2.3 x 109 cm-3

  47. Example (cont’d) Repeat the previous example using argon, BUT include an electrode voltage of 1000v that is applied to one plate to sustain the plasma. 100 W = qneuBAeff(Eion + Eelec + Ec) = (1.6x10-19C)ne(2.5x105cm/s)(px202 cm2) x {(5Te + 2Te + 55 eV)+[(1000 eV+5Te)+ 2Te + 55 eV]}  ne = 1.7x109 cm-3 anode cathode

  48. Secondary ElectronsGe = gsec Gi ,where gsec~0.1-10 and Ee ~ qVs light Gas flow gas (ng) excited atoms and molecules ions radicals, molecular fragments reaction products pumping pumping Power Wall Wall PLASMA electrons ne, Te secondary electrons secondary electrons substrate

  49. light Power Gas flow gas (ng) excited atoms and molecules electrons ne, Te ions radicals, molecular fragments reaction products secondary electrons pumping pumping Summary Wall Wall PLASMA substrate

  50. Basic Plasma Technology

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