Plasma and Dry Micro/Nanotechnologies 3. Chemical and Plasma Kinetics Lenka Zajíčková Faculty of Science, Masaryk University, Brno & Central European Institute of Technology - CEITEC lenkaz@physics.muni.cz spring semester 2023 Central European Institute of Technology BRNO I CZECH REPUBLIC Plasma & Dry Technologies 3. Chemical and Plasma Kinetics ka Zajíčková 2/20 • 3. Chemical and Plasma Kinetics 3.1 Chemical Kinetics 3.2 Plasma Kinetics 3.3 Elementary Processes in Plasma Involving Atoms 3.4 Elementary Processes in Plasma Involving Molecules Chemical vapor deposition (CVD): based on chemical reactions. Plasmachemical processing of materials (plasma treatment in reactive gases, plasma etching, plasma enhanced CVD - PECVD): chemical reactions with reactive species activated by hot electrons. ► homogeneous - if reactants are of the same phase (e.g. reactions in gas phase) ► heterogenous - if reactants are of two or more different phases (e.g. reaction between gas and solid - deposition, etching) Related terms: ► reaction rate, reaction order, rate constant, Arrhenius plot ► ellastic collisions (Coulomb, polarization scattering with permanent or induced dipole, hard sphere scattering) ► inellastic collisions (ionization, recombination, excitation, dissociation ...) ► collisional cross-section and its relation to the reaction constant Plasma & Dry Technologies 3. Chemical and Plasma Kinetics Lenka Zajíčková 3/20 .1 Chemical Kinetics Consider the reaction aA + bB---- The reactants A and B react with the rate dt ■> qQ + sS ra = - r'B = - dNB dt The products Q and S are created with the rate dNs d/V rs = dt i _ ^' VQ Q~~ďF' where A/y is molar amount (usually in kmol) and t is time. 1 dNA 1 d/Vß 1 d/VQ 1 d/Vs a dt b dt q dt s dt (1) (2) (3) (4) The reaction rate is generally expressed on an intensive basis, e.g. reaction volume V. -id^ = zld -i aV 6t aVóŕ A 1 aV vd-^ + cAdV 6t 6t (5) where Ca is the molar concentration of A (kmol/m3). When the volume is constant -1 dC^ r = a 6t (6) The reaction rate can be expressed also as (7) where kAB is the rate constant of the reaction aA + bB ->> products. ► The powers a, b are called partial orders of the reactions. ► The sum a + b is (global) order. The partial orders should be in fact replaced by a', b' determined experimentally because they coincide with the stoichiometric coefficients only for elementary processes. Arrhenius concluded from thermodynamics (T is temperature, R and kB gas and Boltzmann constants): In/c = - + lnA) + In A) RT ea and Ea activation energies in J/mol and J, A0 constant frequency factor. For non-reversible f irts order reaction A —> Q, we have at constant volume If we know the rate constant k (hr_1), we can calculated the reaction rate r for any concentration of the reactant. The rate constant k can be calculated from Eq. (8) if we know the time change of the concentration differential method. Integral method uses integrated Eq. (8): The semilog plot of Cao/Ca 'n dependence on time gives k. Now, think about the expressions for ► reversible 1st order reaction A ^\ Q ► irreversible 2nd order reaction 2A —>> Q + S ► irreversible 2nd order reaction A + B —>> Q + S We can encounter also with complex reactions: parallel, consequtive, free radical chain reaction (initiation, propagation, termination), free radical addition Plasma & Dry Technologies 3. Chemical and Plasma Kinetics Lenka Zajíčková 6/20 3.2 Plasma Kinetics Elastic collisions (momentum and energy are conserved): ► 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 collisions) hard sphere - between neutrals, e-neutral for very low electron energies (approx.) TABLE 3.1. Scaling of Cross Section a. Interaction Frequency i>, and Rate Constant %. With Relative Velocity rR, for Various Scattering Potentials V Process U(r) /' or K Coulomb i/r iM Permanent dipole \/r2 t/už I Ar Induced dipole i/t* Hard sphere const t* after Lieberman & Lichtenberg 1994 Inelastic collisions: ionization, recombination, excitation, dissociation 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 slide in Atomic Collisions). ► 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. Plasma & Dry Technologies 3. Chemical and Plasma Kinetics Lenka Zajíčková 8/20 Plasma Kinetics The velocity distributions are taken isotropic Maxwellian. f(v) = m 3/2 2irkBT exp mv* 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) vR ^ \ 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{vR)vR)Vuv2 = 3/2 2tt/cb7" roc I cK^FÜ^Rexp ^0 mv\ R 2kBT 47tvr6vr where mR is reduce mass. Plasma & Dry Technologies 3. Chemical and Plasma Kinetics Lenka Zajíčková 9/20 3.3 Atomic Collisions / Elastic scattering _____J____ 'K; X— t 6 1 / / / ' Fixed center AJ 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 4/77-I /T?2 Ei (AT?! + A772)2 and in the CM system cos 62 2/77-I /T?2 Ei (AT?! + A772)2 (1 - COS0) Average loss obtained by averaging over all angles 0 using differential cross section a(vK, 0) as distribution function (7)0 2a771A772 fo(1 — cos0)cr(vR)27rsin 0d0 for A77-| = me, m2 = M and me - metastables y > 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) Plasma & Dry Technologies Chemical and Plasma Kinetics ka Zajíčková 11/20 Atomic Processes - Relaxation an ecombination De-excitation -» A + hu 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 Plasma & Dry Technologies 5. Chemical and Plasma Kinetics ka Zajíčková 12/20 arge 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. 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. O* + N' N4 +0 £2 ^ ^ (47reoei) 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, £a — £diSs ~ few eV =^ hot neutral fragments (profound effect on plasma chemistry of growing films if hitting the substrate surface) Collisions b and b'\ ground state excited to an attractive state of AB but energy exceeds £d-lss dissociation of AB resulting in fragments having energies from thermal up to £h - £d[SS « few eV. Collision c: excitation to bound state AB* that radiates creating A + B or AB* (bound) —> AB* (unbound) —> 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 eiz. Collisions b, cfor higher threshold energies eaiz => fast ion and neutral. Dissociative Recombination e" + AB+ —y A + B* collisions d, d' =>* fast excited neutral fragments. Plasma & Dry Technologies 3. Chemical and Plasma Kinetics Lenka Zajíčková 17/20 Electron Collisions with Molecules - contin. £thr ' 0--- (a) (b) A + B A + 8~ 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-* —> 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 —> A+ + B~ + e" ► Maximum cross section and its dependence on electron impact energy are similar to pure dissociation. ► Threshold energy is generally large. 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 Life time of AB~ is 10-15-10-10 s, /. e. comparable or larger than its vibrational timescale 10-14 s AB > AB(v > 0) + e Plasma & Dry Technologies 3. Chemical and Plasma Kinetics Lenka Zajíčková 19/20 Complex reaction schemes for 02 plasma - 2nd order reactions Number Reaction Rate Constant (cm3/s) Reactions among e, 02, 02, O, and O 1 e + 02 momentum transfer 4.7E-8T0/5 2 e + 02 -» O +0 1.07E-9T,:1 391 exp(-6.26/Te) 3 e + Oz ->• 20 + e 6.86E-9exp(-6.29/Te) 4 6 + 02^-0^ + 26 2.34E-9T^03exp(- 12.29/Te) 5 e + 0~^0 + 2e 5.47E-8T°-324exp(-2.98/Te) 6 e +0^-^20 2.2E-8/Te/2 7 0~ + 0j-» 0 + 0, 2.6E-8(300/7)()44 8 0" + 0^02 + e (1.9,3,5)E-10 9 0~ + Ot -» 30 2.6E-8(300/7)044 Addition ofO+ 10 e + 02^0~+0+ + e 7.1E-1 lT°'5exp(- 17/Te) 11 e + 02^ 0 + 0+ + 2e 1.88E-10T,I'699exp(-16.81/Te) 12 e + O 0+ + 2e 9.0E-9T0 7exp(- 13.6/Te) 13 O" + 0+ -> 20 4.0E-8(300/7)0'44 14 0+ + 02^ O + Oj 2.0E-11(300/7)° 5 Addition of metastable 02('Ag); see notef below 15 e + 02^Oj + e 1.37E-9 exp(-2.14/Te) 16 e + 02^e + 02 2.06E-9 exp(- 1.163/Te) 17 e + Oj^O + O" 4.19E-9T~1 376 exp(-5.19/Te) 18 02 + 02 ^ 202 2.2E-18(7//300)°'8 19 0| + 0^02 + 0 (1.0,7)E-16 20 0~ + 02 -» 03 + e 2.2E-11 21 0" +02*^02+0 LIE-11 Addition of metastable O('D) 22 e + 02^ 0 + 0*+e 3.49E-8 exp(-5.92/Te) 23 e + O -> O* + e 4.54E-9 exp(-2.36/Te) 24 e + 0*^e + 0 8.17E-9 exp(-0.4/Te) 25 e + O* -> 0+ + 2e 9.0E-9T" 7 exp(- 11.6/Te) 26 0*+0^ 20 8.0E-12 27 O* + 02 -> O + Oz (6.4, 7.0)E-12 exp(67/7) 28 0*+02 ^0 + Oj 1.0E-12 Addition of selected reactions for 02 and 03 29 0~ + 02->03 + e 5E-15 30 e + 03^-OJ+0 1E-9 31 e + 03->-0_+02 2.12E-9T71()58exp(-0.93/Te) 32 OJ + Ot -*■ 202 2E-7(300/7)a5 33 Oi" + 0+ -+ 02 + 0 (1, 2)E-7(300/7)°'5 34 0, + 02 -* 02 + 0 + 02 7.3E-10exp(-11400/7) 35 03 + O 202 1.8E-1 lexp( - 2300/7) Plasma & Dry Technologies 3. Chemical and Plasma Kinetics Lenka Zajíčková 20/20 Complex reaction schemes for 02 plasma - 3rd order reactions Number Reaction Rate Constant (cm6/s) Reactions among e, 02, Oj, and O 1 e + e + Oj^e + 02 IE - 19(0.026/Te)4 5 2 e + + 02 02 + 02 6E-27(0.026/Te)' 5, 1E-26 3 e + 0 + 02^0~ + 02 1E-31 4 0~ + Oj + 02 0 + 02 + 02 2E-25(300/r>25 5 O + O + 02 02 + 02 2.45E-31 T~° 63 1.3E-32(300/7)exp(- 170/r) 6 0 + 0 + 0^02 + 0 6.2E-32exp(-750/7) Addition ofO+ 7 e + e + O+^e + O 1E-19(0.026/Te)45 8 e + 0+ + 02 O + 02 6E-27(0.026/Te)' 5, 1E-26 9 O" + 0+ + 02 -> 02 + 02 2E-25(300/7f-5, 2E-25 10 CT + 0+ + M^O + 0 + M 2E-25(300/7)2-5 11 0+ + 0 + 02^ Ot + 02 1E-29 Addition of metastable O('D) 12 O + O* +02 -> 02 + 02 9.9E-33 Addition of selected reactions for metastable 02('Ag), O^, and 03 13 e + 02 + 02 -► O2 + 02 1.4E-29(0.026/Te) x exp(100/r- 0.061/Te) 14 e + 02 + 0^02+0 1E-31 15 0~ + + 02 -> 03 + 02 2E-25(300/7)2 5 16 O + 02 + 02 03 + 02 6.9E-34(300/7)125, 6.4E-35 exp(663/7) 17 O + 02 + O 03 + O 2.15E-34 exp(345/7) 18 e + 02 + 02 -+ O2 +02 1.9E-30 19 e + 02 + 0^02+0 1E-31 20 02 + 0+ + M -> 03 + M 2E-25(300/7)2'5 21 O2" + Ot + 02 -> 02 - 02 + 02 2E-25(300/D2 5