F4280 Technologie depozice tenkých vrstev a povrchových úprav 7.2 Plasma Kinetics and Plasma Chemistry Lenka Zajíčková Faculty of Science, Masaryk University, Brno & Central European Institute of Technology - CEITEC lenkaz@physics.muni.cz spring semester 2021 ^CEITEC Central European Institute of Technology BRNO I CZECH REPUBLIC 3. 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 (see next slide). ► 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. F4280 Technologie depozice a povrchovych uprav: 7.2 Plasma Kinetics and Elementary Processes ka Zajíčková 3/16 Plasma Kinetics The velocity distributions are taken isotropic Maxwellian. f(v) = m 3/2 2irkBT exp 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 7)3/2^00a(v)vexp(-^ÍjWdv If we consider collision of two different heavy particles k(T) = {a{vK)vK)Vuv2 = 3/2 2tt/cb7" roc i rnv where mR is reduce mass. F4280 Technologie depozice a povrchových úprav: 7.2 Plasma Kinetics and Elementary Processes Lenka Zajíčková 4/16 astic Coulomb collisions - between two charged particles (e-e, e-ion, ion-ion) hard sphere - for neutrals, approx. for e-neutral for very low electron energies ► polarization scattering with induced dipole (e-neutral for electrons with low energies, ion-neutral) ► polarization scattering with permanent dipole (for molecules with permanent dipole) TABLE 3.1. Scaling of Cross Section a* Interaction Frequency »>, and Rate Constant If, With Relative Velocity rRt for Various Scattering Potentials V Process U(r) (ľ /' or K Coulomb \/r i/4 Permanent dipole \hl Induced dipole «Kl M Hard sphere l/r',i—« const after Lieberman & Lichtenberg 1994 F4280 Technologie depozice a povrchovych uprav: 7.2 Plasma Kinetics and Elementary Processes Lenka Zajíčková 5/16 Atomic Collisions vr ! b \ ' ta) y / S / ' Fixed center f b. 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 4/7?-i m2 Ei (AT?! + A7?2)2 and in the CM system cos #2 2/77-i /7?2 Ei (/T?! + m2)2 (1 - COS0) Average loss obtained by averaging over all angles 0 using differential cross section a(vK, 0) as distribution function (7)0 2/7?1A7?2 Jo^O -COS0)cr(l/R)27TSin0d0 for /7?-| = me, m2 = M and me e~ + e~ + A+ Since the metastable atom is already excited, less energy is required. Metastable-neutral ionization A* +B —y 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 F4280 Technologie depozice a povrchovych uprav: 7.2 Plasma Kinetics and Elementary Processes Lenka Zajíčková 7/16 Relaxation and Recombination Processes De-excitation 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 F4280 Technologie depozice a povrchovych uprav: 7.2 Plasma Kinetics and Elementary Processes ka Zajíčková 8/16 In molecules, excitation of vibrational and rotational states (besides electronic states) are possible: F4280 Technologie depozice a povrchových úprav: 7.2 Plasma Kinetics and Elementary Processes Lenka Zajíčková 9/16 Electron collisions with molecules Interaction times: ► electron motion in the molecule fat ~ 10_16-10_15s ► interaction time of e~ with molecule tint « 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 řcoi « 10-8-10-6 s tat ~ fint <^ Uib ~ tdiss £2 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 (e& - £diss,ea' - £diss) shared among the dissociation products A and B. Typically, £a — ~ 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 eaiss =>* dissociation of AB resulting in fragments having energies from thermal up to £^ - eaiss ~ few eV. Collision c: excitation to bound state AB* that radiates creating A + B or AB*(bound) —> AB*(unbound) —> A+B* F4280 Technologie depozice a povrchových úprav: 7.2 Plasma Kinetics and Elementary Processes Lenka Zajíčková 11/16 A + B' A + B* A + B Dissociative Ionization (in addition to normal ionization) e~ + AB —y A + B+ + e" is common for polyatomic molecules. Formation of molecular ion (collision a) for threshold energy s-lz. Collisions b, c for higher threshold energies £diz => fast ion and neutral. Dissociative Recombination e" + AB+ —y A + B* collisions d, d' ^ fast excited neutral fragments. F4280 Technologie depozice a povrchových úprav: 7.2 Plasma Kinetics and Elementary Processes Lenka Zajíčková 12/16 Electron collisions with molecules IV A + B A + B •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 ^/Mr/iw « 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) eafm > £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. F4280 Technologie depozice a povrchových úprav: 7.2 Plasma Kinetics and Elementary Processes Lenka Zajíčková 13/16 Electron collisions with molecules IV Electron Impact Detachment e~ + AB ■> AB + 2e similar to electron-neutral ionization with el. affinity 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" F4280 Technologie depozice a povrchových úprav: 7.2 Plasma Kinetics and Elementary Processes ka Zajíčková 14/16 y-particle col Iisions - et 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) —> A(fast) + A+(slow) Cross section is larger for low energies, important process in weakly ionized plasmas. O* + N' N"1 -i- 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+ + 0 —^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 ethi and a can be large at thermal energies. F4280 Technologie depozice a povrchových úprav: 7.2 Plasma Kinetics and Elementary Processes Lenka Zajíčková 15/16 Complex reaction schemes for 02 plasma Number Reaction Rate Constant (cm Vs) Reactions among e, O;, 02, andO~ 1 e + 0; momentum transfer 4.7E-8T°5 : e + 0: — 0" + 0 8.8E-llexpM-4 4/Tt) 3 e + 0: — 20 + e 4.2E-9exp(-5.6/T<) 1 e + 0: — 0> + 2e 9.0E-10Tf0?exp(-12.6Ao) e + 0" — O + 2e 2.0E-7exp(-5.3/Tj 6 e + O; — 20 5.2E-9/T, 7 O" + 02" -O + O; (0.96, 2)F^7(300/7-)o; 0" + 0 — 02 + e (l.4,5)E-10 cr + oí — 30 1E-7 Addition ofO~ 10 I i 12 I \ 14 Addition of metastahle Oj('At); see note}below 15 e + Oj — 0: + e e + 0: —O' +0' +e e + 02 — O + O' + 2e e + O — CT + 2c O" + 0+ — 20 O* + Oi — O + 02 16 e + O'j —e + Oj 17 0;+02 — 20j 18 o\ + O — 02 + O Addition of metastahle 0('d) 19 c + Oi-«0 + 0-+e 20 e + O — O* + c 21 e + 0*-»e + 0 22 c + O" - Ov f 2e 23 O' + O — 20 24 O* + 02 — O + 02 25 O* + 02 — O + Oi Addition of selected reactions for 0:~ and O3 26 O + O^ — O, + c 27 e + 0,-»0-rO 2« O" + OJ — Oj + c 29 O + o; — OJ + O 30 O" + OJ — 20, 31 Of + 0~ — 02 + O 32 Oj + 02 — Oi + 0 + O2 33 O3+O —202 7.1E-llTe05cxp(-l7/Tc) 5.3E-IOT«,'exp(-20Ac> 9.0E-9T?7exp(-13.6/T.} (2.7.2)E-7(300/7)(,S 2.0E-11(300/77" 1 7E-9cxp(-3.lAe) 5.6E-9exp(-2.2Ař) 2.2E-18(7/300)"H (1.0.7)E-I6 S.0E-8exp(-8.4/Tr> 4.2E-9. CK . and O e + e + Ot —"e + 02 e + OÍ + 02 —• O2 + 0> e + O + 02 —» 0~ +0; O +0^ + O; — O + 02 + Oj O + O + O: — 0> + 02 2 3 6 O + O + O^ 0: + 0 Addition of O" 7 e + e + C— c + 0 8 c + O^+Oi-'O + Cb 9 O" + O* + O2 — 02 + Oj 10 0"+0A+M —O + O + M 11 O* + O + O; — Of + 02 Addition of metmtabie Oi1D.) 12 O + O* + 0> — 02 + 02 Addition of selected reactions for melastahle O] 13 e + Oj + — O," + Oj 14 e + Oj + O — 02 + O 15 O" + 01 +■ Oj — 03 + Oj 16 O + 02 + Oj -» Oj + 0i 17 O + 02+0 —O> + 0 18 e + 0;+0:^0j- +02 19 e + Oj + O —02"+0 20 O, + O" + M —» 03 + M 21 Of + 0; + (h — O2 + O2 + Q2 IE-19(0.026A,)4' 6E-27(0.026/Tc)'-5,1E-26 IE-31 2E-25<300/7*y23 2.45E-3ir-a*J 1.3E-32(30O/7\) exp( -170/7) 6.2E-32exp(-750/7) IE-19(0.026A,)4 5 6E-27{0.026Ae)'5. 1E-26 2E-25Í300/7Í2 s. 2E-25 2E-25(300/7)2i 1E-29 9.9E-33 ťAs).02 ,andO} l.4E-29(0.026/Te) x expt 100/7/ -0.061 /Tc) 1E-31 2E-25(300/7)2S 6.9E-34(300/7)'-2\ 6.4E-35exp{663/7) 2.l5E-34ex|X345/7) 1.9E-30 1E-3I 2E-25(300/7)25 2E-25(3O0/7)25 Note- Tc in volts and T in kclvins; M denotes cither 02 or O. Two values from different s sometimes given. The notation E-19 means 10"19.