FC250 Nano- and microtechnologies 3.2 Plasma Kinetics and Elementary Processes Lenka Zajíčková Přírodovědecká fakulta & CEITEC, Masarykova univerzita, Brno lenkaz@physics.muni.cz jarní semestr 2017 Central European Institute of Technology BRNO I CZECH REPUBLIC Electrons in plasma gain high energies (in the order of 1-10 eV) due to acceleration by electric field. Since electrons collide with heavy particles (atoms, molecules) they change direction of their velocity or even loose the energy. Collisions between electrons and heavy particles (according to the electron energy Ee): ► Ee < 2eV (depending on the atom/molecule): elastic collisions with very small fractional energy transfer. ► 2eV < Ee < 15eV (approx.): variety of inelastic collisions =^ Ee is partially converted into internal energy of the target molecule (atom) ► Ee > 15eV (approx.): ionization (sustains the discharge) Rate constant k for reaction of two particles with velocities v<\, v2 can be calculated from cross section a where vK = \ v<\ - v2\ and f-i(vi), h(yz) are velocity distribution functions. FC250 Nano- and microtechnologies: 3.2 Plasma Kinetics and Elementary Processes Lenka Zajíčková 3/17 Plasma Kinetics The velocity distributions are taken isotropic Maxwellian. f(v) = m 3/2 2tt/cb T exp - mv* 2k^Ť where m and T are particle mass and temperature. If the characteristics velocities of target particles are much less than those of incident particles (e.g. electron collision with heavy particle) vK « |v<\ | = v. k(T) = {a(v)v)v = m 2tt/c B If we consider collision of two different heavy particles — j J a(,R)vRexp l-^L 4ttv^6vr where mR is reduce mass. FC250 Nano- and microtechnologies: 3.2 Plasma Kinetics and Elementary Processes Lenka Zajíčková 4/17 Plasma Kinetics 7"e is generally less than the threshold energies for dissociation and ionization of gas molecules but the electrons from tail of the EEDF can do it! FC250 Nano- and microtechnologies: 3.2 Plasma Kinetics and Elementary Processes nka Zajíčková 5/17 mam ► Coulomb collisions - between two charged particles (e-e, e-ion, ion-ion) ► polarization scattering with permanent dipole (for molecules with permanent dipole) ► polarization scattering with induced dipole (e-neutral for electrons with low energies, ion-neutral) ► hard sphere - for neutrals, approx. for e-neutral for very low electron energies weakly ionized plasmas = collisions between charged and neutrals particles for e~ at low energy and ions scattering against neutrals: short-range polarization scattering {vR < vat where vat is char, electron velocity in atom) TABLE 3.1. Scaling of Cross Section a. Interaction Frequency *% and Rate Constant X, With Relative Velocity rK* for Various Scattering Potentials V Process U{r) (7 v or K Coulomb l/r \/vi \/v> Permanent dipole \/r2 \/vi Induced dipole \/r l/t* COtM Hard sphere const after Lieberman & Lichtenberg 1994 FC250 Nano- and microtechnologies: 3.2 Plasma Kinetics and Elementary Processes Lenka Zajíčková 6/17 Atomic Collisions ^7T HI:; vr X- ! b \ ' í(t) y / S / ' Fixed center ft) Scattering in (a) laboratory system, (b) the center of mass (CM) system (after Lieberman & Lichtenberg 1994). Electron - atom elastic collision: ► momentum and energy are conserved, ► treated as hard-sphere scattering Fraction of energy lost by the projectile in the laboratory system 7 Et 4/77-I /T?2 Ei (AT?! + A772)2 and in the CM system cos 02 2/77-I /T?2 Ei (AT?! + A7?2)2 (1 -COS0) Average loss obtained by averaging over all angles 0 using differential cross section a(vK, 0) as distribution function (7)0 2A7?! A772 fo^ - COS0)cr(l/R)27TSÍn0d0 for A7?-| = A77e, A772 = M and me e~ + e~ + A+ Since the metastable atom is already excited, less energy is required. Metastable-neutral ionization A* +B —> A + e" +B+ If the ionization energy of the neutral B is less than the excitation energy of the metastable A* =^ Penning ionization (He* 19.8, Ne* 16.7, Ar* 11.7eV) Electron impact ionization e~ + A —> e~ + e~ + A+ Electron impact excitation e~ + A —> e~ + A* A* can have quite different chemical reactivity towards the surface. Some excited atoms have very long lifetimes 1-1 Oms) =^ metastables FC250 Nano- and microtechnologies: .2 Plasma Kinetics and Elementary Processes ka Zajíčková 8/17 Relaxation and Recombination Processes De-excitation -» A + hzy In most cases, the relaxation of electronically excited states is practically instantaneous 10 ns). Electron-ion recombination e" +A+(+C) —► A*(+C) A third-body (neutrals, reactor walls) must be involved to conserve energy and momentum. Radiative recombination e~ + A+ (+C) —> A + hv (+C) Electron attachment e" + A(+C) —► A"(+C) Ion-ion recombination A+ + A" —y A + A FC250 Nano- and microtechnologies: .2 Plasma Kinetics and Elementary Processes Lenka Zajíčková 9/17 In molecules, excitation of vibrational and rotational states (besides electronic states) are possible: x FC250 Nano- and micro-technologies: 3.2 Plasma Kinetics and Elementary Processes Lenka Zajíčková 10/17 Electron collisions with molecules Time scales: ► interaction time of typical e~ (1-10 eV) with molecule fint « 10_1 ► electron motion in the molecule tat « 10_16-10_15s ► typical vibrational period of molecule řvib ~ 10_14-10_13s ► typical time for molecule dissociation řdiss « 10_14-10_13s ► typical transition time for electric dipole radiation řrad « 10_9-10-8 s ► typical time between e-molecule collisions in a low pressure plasma toi « 10-8-10-6s fat ~ ftnt 62 Dissociation key role for plasma chemistry of low pressure discharges: e~ + AB —> A + B + e" Collisions a and a'\ ground state v = 0 excited to repulsive state of AB, energy (ea - £diss,ea' - £diss) shared among the dissociation products A and B. Typically, ea — ediss ~ few eV hot neutral fragments (profound effect on plasma chemistry of growing films if hitting the substrate surface) Collisions band b'\ ground state excited to an attractive state of AB but energy exceeds ed[SS =>* dissociation of AB resulting in fragments having energies from thermal up to eh - ed[ss « few eV. Collision c: excitation to bound state AB* that radiates creating A + B or AB*(bound) —> AB*(unbound) —> A+B* FC250 Nano- and micro-technologies: 3.2 Plasma Kinetics and Elementary Processes nka Zajíčková 12/17 A + B' A + B* A + B Dissociative Ionization (in addition to normal ionization) e~ + AB —> A + B+ + e" is common for polyatomic molecules. Formation of molecular ion (collision a) for threshold energy eiz. Collisions b, c for higher threshold energies ^aiz => fast ion and neutral. Dissociative Recombination e" + AB+ —y A + B* collisions d, d' ^ fast excited neutral fragments. FC250 Nano- and micro-technologies: 3.2 Plasma Kinetics and Elementary Processes Lenka Zajíčková 13/17 Electron collisions with molecules IV A + B A + B- Dissociative Electron Attachment e"+AB —y A + B" important in discharges containing atoms with positive electron affinities because of production of negative ions ► threshold energy for dissociation is generally lower than for pure dissociation processes (a) e~ capture into repulsive state autodetachment or dissociation; autodetach. rate ^/MK/m « 100x dissoc. rate (MR reduced mass); hot fragments (b) AB- bound state a, a' dissociative attach, with low energy fragments; b collision AB-* —y e~ + AB (c) for few molecules (e.g. halogens) ea^B > £diSS => slow e~ produce hot A + B~; max. a as high as 10 16 cm2 Polar Dissociation (d) e~ + AB —y A+ + B~ + e" ► Maximum cross section and its dependence on electron impact energy are similar to pure dissociation. ► Threshold energy is generally large. FC250 Nano- and microtechnologies: 3.2 Plasma Kinetics and Elementary Processes Lenka Zajíčková 14/17 Electron collisions with molecules IV Electron Impact Detachment e~ + AB ■» AB + 2e similar to electron-neutral ionization with el. affinity eaff of AB playing the role of the ionization potential BUT the peak in cross section is shifted to energies of 10-20eaff due to repulsive Coulomb force between e~ and AB-. Vibrational and Rotational Excitations Typically it is a two step process: e~ + AB(v = 0) —> AB" Lifetime of AB~ is 10-15-10-10s, /. e. comparable or larger than its vibrational timescale 10~14 s AB- > AB(v > 0) + e~ FC250 Nano- and microtechnologies: 3.2 Plasma Kinetics and Elementary Processes ka Zajíčková 15/17 y-particle col hsions - cl large transfer ► In general, the energy level from which e~ is released is not equal to the energy level into which the electron is captured =^ energy defect A l/l/. ► For A l/l/ / 0, the kinetic energy of the colliding particles is not conserved in the collision. Resonant charge transfer If atom and ion are parent and child, the transfer occur with AW = 0 A+(fast) + A(slow) —y A(fast) + A+(slow) Cross section is larger for low energies, important process in weakly ionized plasmas. O* + N' N4 +0 0* ■»■ N Nonresonant charge transfer A+ + B —y A + B+ Illustrated for N+ + O and 0+ + N (ioniz. potential of N and O are 14.53 and 13.61 eV, respectively) Exothermic reaction a-x-b N+ + O —> N + 0+ does not have a threshold energy, products share an increased kinetic energy of 0.92 eV. The inverse endothermic reaction (ethr = 0.92 eV) has very small rate constant at thermal energies 0+ + N —y O + N+ but if 0+ or N are excited, the reaction a'-x'-a has no ethr and a can be large at thermal energies. FC250 Nano- and micro-technologies: 3.2 Plasma Kinetics and Elementary Processes Lenka Zajíčková 16/17 Complex reaction scl iemes for 02 plasma Number Reaction Rate Constant (cm Vs) Reactions among e, O;, O,*, and 0 1 e + 0; momentum transfer 4.7E-8T,?5 e + 02 — O" + 0 8.8E-)lexp(-4 4/Tt) J e + 0; — 20 + c 4.2£-9exp(-5.6/Tc) 1 e + 0: — Oj + 2e 9.0E-10Tf05exp(-12.6Ac) ŕ e + 0" — d+ 2e 2.0E-7exp(-5.3/T,) h e + o; — 20 5.2E-9/T, 7 O" +OJ -O + O; (0.96, 2)E-7(300/7)aí s 0" + 0 — 02 + e (1.4, 5)E-10 9 O" + Ot — 30 1E-7 Addition of O' 10 e + 02 —O" +0' +c 7.1E-HT°5cxp(-l7/Tc) II e + 02 -»0 + 0' + 2e 5.3E-IOTc^exp<-20/Tc> 9.0E-9T?7exp(-13.6/Tc) 12 e + 0 — 0+ + 2e 1 í O" + 0+ — 20 (2.7.2)E-7(300/7)úi 14 O* + Oj — 0 + O; 2.0E-1 l(300/T)(" Addition of metastable OJ('At); .w note f below 13 e + Oj — O: + c 1 7E-9exp(-3.l/Te) 16 e + O; — e + Oi 5.6E-9exp(-2.2Ař) 17 OJ + Oj — 20j 2.2E-18(77300)°" IS OJ +0 —O2 + 0 (1.0,7)E-I6 Addition of metastable 0(' D) 19 c + Oj-»0 + 0*+e S.OE-Sexpí-S^/t,.) :o e + O — 0' + c 4.2E-9exp(-2.25Ae) 21 c + 0* -»e +• O 8E-9 22 c + O" - 0* + 2e 9.0E-9T. Ol. and O e + e + —"e + Oz Rate Constant lcmA/s) 2 4 5 6 e + O; + 02 — 02 + 0> e + O + 02 —• O" + 02 o + o; + o2 — o + o2 + (h O + O + O;—O2+O2 O + O + O — On + 0 Addition of O"" 7 e + c + O'—c + 0 8 c + 0* +Oj — O + O2 9 O" + 0+ + O2 — 02 + 02 10 0"+O"+M —O + O + M 11 O^ + O + 0: — O, + 02 Addition of metastuhle Oi1D.l 12 O + O* +0> — 02 +0, Addition of selected reactions for mctastahle O- i • I? 16 17 t s 19 ?•:> 21 e + 02 + O2 — Of + Oj e + Oj + O — 02" + O O" + 024 + Ch — Oj + Oj O + O2 + Oj — O, + O2 0 + 02+0 — O> + 0 e + o; + 02 — O; + o> e + Oj + O — Oj+O O, + 0~ + M —♦ O3 + M Oj + 0^ + Oj — O, + 0> + 02 IE-19(0.026/T£)4:5 6E-27(0026/Te)1J> 1E-26 1E^31 2E-25(300/n" 145E-3ir_ws 1.3E-32(300/7\) expt -170/D 6.2E-32exp(-750/7') 1 E-19(0.026Ar )*■* 6E-27{0.026Ae)'5. 1E-26 2E-25ŕ300/D2 s. 2E-25 2E-25(300/D:5 1E-29 9.9E^33 O^andO) l.4E-29(0.026/Ttf) XexptlOO/r -0.061/TJ IE-31 2E-2ít3O0/rj2s 6.9E-34(300/r)' 6.4E-35exp(663/ľ) 2.15E-34ex|X345/ľ) 1.9E-30 1E-31 2E-25(300/r>?' 2E-25(300/7):5 Note. Tc in volts and T in kelvins; M denotes cither 02 or O. Two values t'rom different s sometimes given. The notation E-19 means 10"19.