F4280 Technology of Thin Film Deposition & Surface Treatments 7. Plasma Fundamentals Lenka Zajíčková Faculty of Science, Masaryk University, Brno & Central European Institute of Technology - CEITEC lenkaz@physics.muni.cz spring semester 2024 E3RMO UNIUER5ITV OF" TECHNOLOGV UNI F4280 Outline Lenka Zajíčková 2/24 • Plasma Fundamentals 7.1 Conditions for Plasma as Ionized Gas 7.2 Plasma in Thermal Equilibrium 7.3 Non-equilibrium Plasmas 7.4 Fundamental Plasma Parameters 7.5 Plasma Sheath 7.6 Why Plasma Is Used in Material Processing? 7.7 Overview of Plasma Processing Methods 7.8 Reactions/Interactions in Plasma F4280 Plasma Fundamentals Lenka Zajíčková 3/24 .1 Conditions for Plasma as Ionized Gas Plasma is created from gas by adding sufficient energy (4th state of matter). Added energy leads to ionization of neutral gas, i. e. generation of electron-ion pairs: energy Natural length scale in plasma is Debye length Natural frequency (time) scale in plasma is plasma frequency V nee2 J 1/2 rie€r_ me£o 1/2 ► ► ► Ionized gas is the plasma namely if ne = n{ on the scales of L > AD. Plasma contains many interacting charged particles, condition: neX^ > 1 Plasma exhibits collective behavior of electrons that is not much disturbed by electron-neutral collisions (collision frequency ven), conditions: ujpe/{27r) > vy en F4280 Plasma Fundamentals Lenka Zajíčková 4/24 • Plasma contains many interacting charged particles. Condition: neXD » 1. Plasma exhibits collective behavior of electrons (plasma frequency) mt,e0 1/2 that is not much disturbed by electron-neutral collisions: A plasma oscillation: displaced electrons oscillate around fixed ions. The wave does not necessarily propagate. podle Chen & Chang 2003 7.2 Plasma in Thermal Equilibrium Plasma can be created by adding sufficient thermal energy the system is in thermodynamic equilibrium, characterized by one T - fusion plasma, Sun's plasma, not in laboratory ► Considering the system of N weakly interacting particles that is closed (does not exchange energy with its surroundings), the average number of particles in the states with energy E, is given by Boltzmann factor where C is constant determined by N = C^,exP(-£//^0 We assumed above that the number of states is the same for each group of states with energy E,. If we have to take into account the statistical weight of the states g-, ► Temperature T and degree of ionization a-, = n-J^rii + ns) are binded by Saha equation where n = r?i + n, F4280 Plasma Fundamentals Lenka Zajíčková 6/24 7.3 Non-equilibrium Plasmas Many plasmas are created out of thermodynamic equilibrium by increasing the ionization degree a above the equilibrium value with an additional ionization source photoionization - ionization potential of e.g. oxygen atom is 13.6eV photon with 91 nm (vacuum UV) photon OJliCtůíJ ---I:-■ = I -i>ľ resulting Jon example: Earth ionosphere - natural photoionized plasma ionization by electron impact in gaseous electrical discharges - el. field accelerates free electrons to ionization energies example: d.c. glow discharge Anode Positive column with sliiations Negative glow Cathode glow Faraday dark space Cathode layer Switching off the ionization source leads to plasma extinction due to the recombination. F4280 Plasma Fundamentals Lenka Zajíčková 7/24 Where to find plasma? glow discharge for etching & thin film deposition (CCP) ne=1014-1016 nr3 T=l-2 eV plasma torch for waste treatment ne=1021-1024 nr3 Te=0.5-2 eV (LTE) F4280 Plasma Fundamentals Lenka Zajíčková 8/24 4 Fundamental Plasma Parameters ne5 7e5 B -2-10 1 2 3 k*gioTe (V) Outside thermodynamic equilibrium other T appear (71, Ts, "Trot, Tvib)! 7"e units are rather [eV], 1 eV = 11 600 K Other quantities are derived from the fundamental plasma parameters Debye length AD=r^y/2 V nee2 J plasma frequency / 2\1/2 / nee* \ ^pe = - \me£0 J cyclotron frequency uoc = qB/m Larmor radius rc = v±/ujc thermal velocity ^/kTj/nij lasma Shea Quasineutrality ne « n{ is fulfilled on the scale L > AD, i. e. on the dimensions larger than Debye length but this is violated in regions adjacent to walls and other solid objects in contact with plasma - plasma sheath. Plasma sheath regions are very important for plasma processing. Plasma potential is always the most positive potential electrons are repelled by a Coulomb barrier, ions accelerated towards solid surfaces. 1/2 -d t) d F4280 'lasma Fundamentals ka Zajíčková 10/24 age Charge densities and potential in bulk plasma, presheath and sheath adjacent to the wall or electrode sheath Relations valid for ► low sheath voltage (at floating or grounded walls) ► weakly ionized plasmas 7"e ~ feweV, 71 ^ 0 Densities of electrons and positive ions are expressed as eV nP = n*ekTe a?i = ns 1 - 2eV 1/2 where vs is ion velocity at the sheath edge, approximated by so called Bohm velocity uB vs> uB = kTe M Charge density at the sheath edge is ns « 0.5n0. Electron and ion fluxes toward surface l~i nsuB have to equal at the floating wall (surface dielectrically disconnected from ground or electrode) =>- For a typical low pressure discharge: ► Te = 2eV, ne = 108 cm-3 ► in argon floating potential is approx. 57"e = 10 V sheath thickness is approx. 5AD = 0.37 mm. F4280 'lasma Fundamentals ka Zajíčková 12/24 age High-voltage sheath (a voltage is applied) can be approximated by a model with Child-Langmuir sheath: Sheath is artificially divided into Debye sheath which contains electrons and high-voltage Child-Langmuir sheath which has ions only. Then, current density j, voltage drop V0 and sheath thickness d are related by the Child-Langmuir Law of Space-Charge-Limited Diodes 4 f2e y=9 1/2£0l/n3/2 o d2 d=2-3 2V( o 3/4 X D eV following previous example with assumption V0 = 400 V d = 30AD, total sheath thickness 35AD; i.e. about 1 cm i Chrid-Lan^nur PLASMA An exact calculation for a plane sheath shows that C-L scaling is not followed unless the sheath is very thick (notice log-log scale) F4280 Plasma Fundamentals Lenka Zajíčková 13/24 Table 4-2 Secondary Electron Coeficients 7j for Argon Ion Impact Ion Energy 10 eV 100 eV 1000eV Mo 0.122 0.115 C.118 W 0.096 0.095 0.099 Si (100) 0.024 0.027 0.039 Ni (111) 0.034 0.036 0.07 Ge (111) 0.032 0.037 0.047 high-energy ion bombardment at the cathode Plasma Quasi-Neutral Transition Region CATHODE PLASMA POTENTIAL ANODE A. LARGE ANODE T I APPLIED É POTENTIAL I 7 2.0 el. bombardment significant at the anode and walls Positive Self-limiting process Charge : 1) electron move away from the plasma Region —*■ 2) the plasma results in more positive —* 3) it hinders the escape of the negative electrons therefore, V(0) = miU(0)2/2e = (ny2e) (kTe/mi) 500 1000 1WX) 2000 Incident energy E. eV Secondary emission coefficient S of differcn I metals as a function of the energy of incident electrons (Hemenway et al. 1967) = kTe/2e F4280 Plasma Fundamentals Lenka Zajíčková 14/24 Low temperature plasma of gaseous discharges provides unique environment for material processing: ► hot electrons (7e few eV, leV = 11600 K) dissociation of molecules into reactive species + AB —► A + B + e" ► positive ions that can be accelerated by « 100 eV near solid surface sputtering of targets, implantation, modification of surfaces and growing films ► cold neutral gas =>- highly energetic process can be kept in a vessel, heat sensitive materials can be treated (e.g. polymers) F4280 lasma Fundamentals ka Zajíčková 15/24 7.7 Overview of Plasma Processing Methods I Plasma etching - irreplaceable etching method anisotropic dry etching: combination of chemistry and effect of ions (reactive ion etching) ttfcm O Miteriiil MttHn 9 Activated i ■ i.i:-_■ 11.11 alum VuLutiLe product Plasma treatment dry modification of the top surface layer (no material added, modification of existing material by oxidation, nitridation etc.) in Ar, 02, NH3 ... discharges for ► change of roughness ► change of surface chemistry ► creation of dangling bonds Plasma synthesis - high purity plasma in liquids ► plasma synthesis of nanoparticles (dry or in liquid) e. g. iron oxide superparamagnetic NPs -(minimum toxic effects for cells) F4280 Plasma Fundamentals Lenka Zajíčková 16/24 7 Overview of Plasma Processing Methods II plasma enhanced chemical vapor deposition (PECVD) ► from gases and vapors ► very easy for organic materials and Si compounds (SiH4, variety of volatile organosilicon compounds) ► for metals - necessary to find sufficiently volatile compounds (organometallic) Si(OC2Hs)4+e- -> Si(OC2H5)3(OH) + C2H4 + e 02 + e -> 20 + e~ O + Si(OC2H5)3(OH) Si(OC2H5)2(OH)2 + C2H40 © 4 © e" e' 0 © e" r 0 0 e- o O e" © O © x sheath IT feature plasma sputter-deposition - physical vapor deposition (PVD) ► gasification of solid targets by ion sputtering deposition ► simple method for metals ► a bit more complex for oxides, nitrides, carbides (reactive sputtering) Ground shield " Anode Substrate Plasma Cathode (target) OOOOOOOOOOOOO wafer coohng I Si Silicon (dc diode sputtering, magnetron sputtering) (in various low or atm. pressure discharges) 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 Plasma Fundamentals ka Zajíčková 18/24 Elastic and Inelastic Collisions Elastic scattering (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 o\ Interaction Frequency and Rate Constant %. With Relative Velocity rR, for Various Scattering Potentials V Process U(r) /' or K Coulomb i/r iM Permanent dipole \/r2 I/už I Ar Induced dipole l/r' i/t* Hard sphere l/r',/-« const t* after Lieberman & Lichtenberg 1994 Inelastic scattering: ionization, recombination, excitation, dissociation ... F4280 Plasma Fundamentals Lenka Zajíčková 19/24 Electron-metastable ionization 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 + A: -» 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) F4280 lasma Fundamentals ka Zajíčková 20/24 Atomic Processes - Relaxation an ecombination 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 F4280 Plasma Fundamentals Lenka Zajíčková 21 / 24 Processes Involving Molecules In molecules, excitation of vibrational and rotational states (besides electronic are possible: E X F4280 Plasma Fundamentals Lenka Zajíčková 22/24 Electron Collisions with Molecules - Dissociation A + B* A + B* A + B Dissociation cross section rises linearly from threshold ethr « ^ to a max. value (typically 10_15cm2) at e2 and then falls off as 1 /e: cdiss = 0 e < £ — £-| ^diss = O-Q- 6-\ < £ < £2 ^1 £2 - e^ ^diss — O-Q £ > £2 a° ^ (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* F4280 Plasma Fundamentals Lenka Zajíčková 23/24 Complex reaction schemes for 02 plasma - 2nd order reactions Number Reaction Rate Constant (cm3/s) Reactions among e, 02, Oj, 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 + 02 ->• 20 + e 6.86E-9exp(-6.29/Te) 4 6 + 02^-0^ + 26 2.34E-9Tl03exp(- 12.29/Te) 5 e + 0~^0 + 2e 5.47E-8T°-324exp(-2.98/Te) 6 e + Oj-^O 2.2E-8/Te/2 7 CT + Oj-*- 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" + 0| 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) F4280 Plasma Fundamentals Lenka Zajíčková 24/24 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(300/7)25, 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 -► Os" + 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 C-3 + 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