DS1100 Plasma and Dry Nano/Microtechnologies 3. Evaporation 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 vaporation • 3.1 Introduction to Evaporation • 3.2 Thermodynamics of Vaporization • 3.3 Evaporation Rate • 3.4 Alloys & Compounds • 3.4 Compounds o 3.5 Sources for Thermal Evaporation • 3.6 Sources using Energetic Beams • 3.7 Transport o 3.8 Monitoring of Deposition Process DS110 1 Introduction to Evaporation ka Zajíčková 3/31 3.1 Introduction to Evaporation Vacuum (high temperature) evaporation as the method of thin film deposition is purely physical process (belongs to physical vapor deposition methods - PVD). It is composed of three subsequent steps: 1. Obtaining the vapors of solid materials that do not have high enough vapor pressure (vaporization) materials are heated to so high temperatures that they melt and evaporate at sufficiently high vapor pressure. 2. Transport of vapors from the source to the substrate. 3. Condensation of vapors in the form of thin film on much colder substrate. Some historical facts: ► In 1857, Faraday created thin metallic films by exploding metal wires in a vacuum. ► Although sputtering and sputter-deposition were reported in the mid-1800s using oil seed piston pumps, vacuum evaporation had to await better vacuum provided by the Springer mercury-column vacuum pumps. In 1879, Edison used this type of pump to evacuate the first carbon-filament incandescent lamp (and observed deposition of carbon thin film). ► In 1887, Nahrwold performed the first thermal vacuum evaporation (from crucible). ► Vacuum evaporation of metallic thin films was not common until 1920s. https: //www. svc. org/Historyof VacuumCoating/History- of -Vacuum- Coating, cf m DS110 1 Introduction to Evaporation ka Zajíčková 4/31 3.1 Introduction to Evaporation Substrate Substrate Substrate Substrate Filament Target Arc cathode Filament (e) (f) (g) (h) - Ion plating - ,BAD Figure 1.1: PVD Processing Techniques: (a) Vacuum Evaporation, (b) and (c) Sputter Deposition in a Plasma Environment, (d) Sputter Deposition in a Vacuum, (e) Ion Plating in a Plasma Environment with a Thermal Evaporation Source, (f) Ion Plating with a Sputtering Source, (g) Ion Plating with an Arc Vaporization Source, and (h) Ion Beam-Assisted Deposition (IBAD) with a Thermal Evaporation Source and Ion Bombardment from an Ion Gun taken from Donald Mattox, 11ntroduction in Handbook of Physical Vapor Deposition Processing, 2010 (2nd ed.) DS110 3.2 Thermodynamics of Vaporization Lenka Zajíčková 5/31 3.2 Thermodynamics of Vaporization Objective of this section is to predict the dependence of vapor pressure on temperature. In the next section, the evaporation rate of a material will be determined from available data such as the boiling point and heat of evaporation. t pv - (saturation) vapor pressure, q - heat w - mechanical work F - force Qc - molar condensation rate Qv - molar evaporation rate (c) Different evaporation situations: ► (a) vapor-liquid (or solid) equilibrium situation in a closed isothermal container ► (b) Knudsen-cell effusion ► (c) vacuum evaporation DS110 3.2 Thermodynamics of Vaporization Lenka Zajíčková 6/31 Closed isothermal container - determination of pv(7~) Consider either a single element or a pure compound that does not dissociate upon evaporation. Vapor-liquid (or solid) equilibrium situation in a closed isothermal container: the pressure is pv, molar condensation rate Qc and molar evaporation rate Qv are balanced. The system is closed (no mass crossing) but ► energy in a form of heat q can be added causing evaporation ► energy in the form of mechanical work w = pvAV is removed from the resulting vapor as it pushes back the surrounding atmosphere (the piston) Not all of the heat input can be transformed into the work, most is consumed in increasing the internal energy U (1st law of thermodynamics) ail + Sw = 5q (1) Parts of U ► kinetic internal energy (discussed in chapter 2 in relation with heat capacity) molecular potential energy Ep - accompanies removal of molecules from condensed phase into vapor phase DS110 3.2 Thermodynamics of Vaporization Lenka Zajíčková 7/31 Closed isothermal container - determination of pv(7~) Consider either a single element or a pure compound that does not dissociate upon evaporation. Vapor-liquid (or solid) equilibrium situation in a closed isothermal container: the pressure is pv, molar condensation rate Qc and molar evaporation rate Qv are balanced. vapor phase -^ __-— z W^~~ condensed phase M- bond length The system is closed (no mass crossing) but ► energy in a form of heat q can be added causing evaporation ► energy in the form of mechanical work w = pvAV is removed from the resulting vapor as it pushes back the surrounding atmosphere (the piston) Not all of the heat input can be transformed into the work, most is consumed in increasing the internal energy U (1st law of thermodynamics) ail + Sw = 5q (1) Parts of U ► kinetic internal energy (discussed in chapter 2 in relation with heat capacity) molecular potential energy Ep - accompanies removal of molecules from condensed phase into vapor phase DS110 5.2 Thermodynamics of Vaporization ka Zajíčková 8/31 To further discuss equilibrium, we need to invoke the more subtle concept of entropy S. Consider a process involving slow changes in T and p, i.e. carried out close to equilibrium and let the system be brought back to its original state - reversible process dg T = & dS = 0 (2) obeying 2nd law of thermodynamics - S does not increase because it is already as high as it can be given the amount of energy available irreversible mixing: increase of S is a measure of the degree of randomization of the energy =>- increase of entropy from 0 to 1.79/cB S = /cBlnZ (3) where Z is the number of quantum states. Reason for In Z - S appears in energy terms and energy is additive (whereas probability terms are multiplicative). Gibbs Free Energy ► At fixed energy, entropy tends towards a maximum as the system approaches equilibrium. ► At fixed entropy, energy tends towards a minimum as the system approaches equilibrium. In evaporation, and many other processes, both energy and entropy are varying: ► Removal of the molecule from the potential well into the vapor phase increases its potential and kinetic energy. ► It increases also entropy because the molecule in vapor phase has more quantum states available to it, both in position ("configurational" entropy - because it is in free space) and in energy levels ("thermal" entropy - because the translational-energy quantum states are so closely spaced). The equilibrium relationship between the competing factors of energy and entropy is given by Eq. (1) in which 5w = pdV and 5q = TdS dU + pdV - TdS = dG = 0 (4) where Gibbs free energy G is introduced as G=(U + pV)-TS = H- TS. (5) Here, H is enthalpy that appeared earlier in connection to heat capacity at constant p. DS110 3.2 Thermodynamics of Vaporization Lenka Zajíčková 10/31 Thermodynamic Quantities - Energy Terms ► The enthalpy H is the energy term used for processes at constant p, where pdV work is being done on the surroundings. ► The internal energy U would be used for processes at constant V. Recall ÔT Cp = V ÔT Differentiating Eq. (5), we have dG = dil + pdV + dpV- TdS-dTS (6) that reduces to Eq. (4) at constant T and p, such as evaporation and many other processes in thin-film work: dU + pdV - TdS = dG = 0, (7) Gibbs free energy G provides a concise definition of equilibrium, i. e. System held at constant p and T is at equilibrium when dG = 0 (G is at minimum). Before we came to the definition of Gibbs free energy G as G = U - TS + pV. In this relation, TS represents a "thermal" energy, pV a "mechanical" energy, and G is a "chemical" energy G = /i/Vm (where A/m is number of moles). =>- Now, we have a complete expression for the internal energy U = TS — pV + fiN, Generalizing for a multicomponent mixtures, G — flNm — \x\ A/mi + /i2A/m2 + M3^m3 • • • , an incremental change in G for addition of material to a phase at constant T and p is where /i, is chemical potential of component /, A/m/ is the number of moles of component /, A/my is the number of moles of other components. For a single-component system, such as evaporating pure condensate, li is just the free energy per mole of condensate, Gmc- (8) DS110 3.2 Thermodynamics of Vaporization Lenka Zajíčková 12/31 At vapor-liquid equilibrium of closed vapor + liquid system, G = const (as evaporation proceeds at constant T and p) =^ Mc = Mv (9) where c and v denote the condensed and vapor phases. This is another way of stating the equilibrium conditions - number of moles of each component is constant (no reaction). During evaporation, H t but it is compensated by S t- G= (U + pV) - TS = H - TS At higher 7~, the entropy term TS becomes more important (increasing thermal motion produces randomization) =^ more H can be compensated DS110 .2 Thermodynamics of Vaporization ka Zajíčková 13/31 Finding Dependence of Vapor Pressure pv on T p (atm) ý—Equilibrium ^—Equilibrium \ CRITICAL POINT solid vaporization deposition TRIPLE POINT T fC) ► At any point along vapor-liquid (or solid) equilibrium curve fic = Mv holds. ► As we move up the curve, \± values of both phases increases d/ic = d/iv or dGmc = dGmv for pure material Using Eq. (6) and equilibrium conditions Eq. (4) dG = Vdp — SdT or dGmi = V^dp — Smid7" (10) where / = c, v. Thus, at equilibrium between the two phases Wnc dpv Sme d T — Wnv dpv Smv d T dPv dT m c AS m Vmv V mc m (11) Since AGm = 0 for evaporation and G = H - TS =>- AVH = 7ASm where AVH is the "latent heat" (enthalpy change) of vaporization per mole. DS110 .2 Thermodynamics of Vaporization ka Zajíčková 14/31 Clausius-Clapeyron Equation, i.e. A(7") The heat of vaporization is an H term rather than a U term because it is measured at constant p, not constant V and, thus, it includes the pAV work of expansion. Substituing AVH/T for ASm = Smv - Smc in Eq. (11) leads to Clausius-Clapeyron equation: dpv dT TAVi m (12) The volume term AVm = \/mv - Vmc may be eliminated as follows: ► VmC is negligible - it is typically 1 /1000\/mv at 1 atmosphere ► for ideal gases \/mv = RT/p pv = Bexp(-AVH/RT) (14) This exponential expression is familiar from all thermally activated chemical processes, evaporation being an example. It is very useful for estimation of pv if Pv(7~) data are not available. .i 2.1 2 • g,g í O.J I '■■ - ii .■ I.<: i : i j.i ■3.1 dp^ Pv AyH RT2 dT Yapoi Pieiiun? Curve ai Liquid -or*] Solid BmiHW (13) Vapor Prewura ■\—+—i—4 MeHing Pon Extrapolated Liqgid Vapof Pressure iSctKj Banzwe) i.t in i Í.Í J.Ě }.í 1 S.3 1.4 JjÉ 4 4.2 ÁÁ 1t t.t Í 5J lAWT»mfrwr«tun |K) DS110 3.3 Evaporation Rate Lenka Zajíčková 15/31 3.3 Evaporation Rate - Expression of Effusion Rate Qe Closed system from previous discussion is modified by opening an orifice, which is small enough =^ Qe does not significantly reduce the pressure, i.e. p « Pv Pv ► For orifice with small diameter L, Kn = X/L > 1, i.e. molecular-flow regime. ► If the orifice length < orifice diameter (ideal orifice) the effusion rate Qe can be easily derived. The mass flow or throughput Q is usually expressed in Pa.l/s Q=C5p (15) where C is conductance, 5p is the pressure difference across the element. For molecular flow, the flux through the orifice in each direction is the flux at the plane of orifice (A is the area of orifice) p - ----- . .A V27t/cb Tm o = (r2-r1)/\ = (p2-p1) V27t/cb Tm = (02 -Pi)C (16) Close to vapor-liquid (or solid) equilibrium, the effusion rate Qe from the Knudsen cell (vapor source with small orifice, outside pressure negligible « 0) can be found just from the vapor pressure pv: Qe=pv^=^= (17) DS110 .3 Evaporation Rate Lenka Zajíčková 16/31 After determining Qe we want to express the evaporation rate from the surface of the condensed phase, Qv. For the Knudsen cell (pressure should stay Pv) Qe < Q^ (18) How to determine Qv? We can reliably determine an upper limit of Qv. In steady state Qv = Qc + Qe (19) and Qe can be neglected, i. e., Qv ~ Qc and we can write the same balance in terms of fluxes per unit area l~v « rc (rv = Qv/A). Upon impingement, there is a range of interations with condensate surface (analyzed in chapter 4 - adsorption, deposition): ► everything is reflected - lower limit, ► everything impinging condenses l~c = l~i & consider vapor-liquid equilibrium l"i = Tv0 = ,Pl (20) V27r/cB 77?7 where rv0 denotes the upper limit. We expect that rv0 is unchanged if we remove the vapor phase and consider evaporation from an open crucible (justification: evaporation of individual molecule of condensate is not retarded by the impingement of vapor molecules). 3.3 Evaporation Rate ion and Condensation Coefficient Lenka Zajíčková 17/31 It has been verified experimentally that evaporation occurs at the upper limit rv0 (0 for upper limit) for those metals that have atomic vapors (most metals). For other materials rv < rv0 and emipirically v I v0 (21) where av is evaporation coefficient. There is a corresponding condensation coefficient a< At equilibrium l~c = n l~c = ac\~i ac = av. Otherwise they are different functions of p, T. (22) The coefficient av has been determined only for few materials, e.g. 10-4 for As. Generally, it is not known. Unless evaporation is being carried out from the Knudsen cell, effusion rate cannot be predicted accurately and must instead be measured directly in thin-film deposition process. DS110 3.4 Alloys & Compounds Lenka Zajíčková 18/31 3.4 Alloys -1 Partial Pressures Multicomponent materials bring additional complication - the composition of the vapor phase generally differs from that of the condensed phase. Different approach for ► alloys - a solid solution or a mixture of solid phases, its composition is variable over a wide range. Examples: solder alloy Pb^Sn^*, ► compounds - specific ratio of elements (stoichiometry), e.g. GaAs, Si02. Dissociatively evaporating compounds - discussed in next section. ► alloy of compounds, e.g. (AIAs)x(GaAs)1_x Consider a generalized binary metal alloy BxCi_x (well mixed liquid phase) whose component elements B and C are completely miscible at the evaporation T, i.e. atomic fraction x can vary from 0 to 1 without precipitating a second solid phase. Total equilibrium vapor pressure over the melt Pv = Pb + Pc Pb = aBxPvB Pc = ac(1 - *)pvc (23) where pVB, pvc are pv of pure elements and a^,c are the activity coefficients. For simplicity, "Raoult's law" behaviour is assumed, i.e. aB,c = 1, even though they generally deviate somewhat from unity due to differences between B-C versus B-B and C-C bond strengths. Flux Ratio If the evaporation coefficients aVB,c are unity (common for metals) the ratio of evaporation fluxes is The vapor flux will be richer that the melt in the more volatile element for any composition x. It leads to continuous changes of the melt composition until the equilibrium is reached (time consuming). The problem has two possible solutions: 1. use separate sources operating at different T levels 2. feed an alloy ByCi_y wire or rod steadily into the melt during evaporation (24) ,W cm3/s DS110 3.4 Compounds Lenka Zajíčková 20/31 Compounds behave very differently from alloys during evaporation: ► some compounds evaporate as molecules (ionically bonded compounds, e.g. MgF2 for antireflective coating) - similar as single-component material ► dissociative evaporation - oxides vary in behaviour, Si02 evaporates as SiO in the presence of reducing agent Si, C, H2 DS110 .5 Sources for Thermal Evaporation ka Zajíčková 21 /31 3.5 Sources for thermal evaporation - Resistive Heating Několik typů zdrojů pro naparování využívajících ohřevu průchodem elektrického proudu: Přímé odporové zahřívání - Tato metoda je založena na ohřívání materiálu držáku z odporového, těžko tavitelného materiálu, jako je W, Mo, Ta, Nb. Někdy se používá i keramické úpravy povrchu těchto držáků. Tyto zdroje můžeme dále dělit podle tvaru držáku, a tedy způsobu uchycení taveného materiálu. ► Drátěný držák má formu spirály. Odpařovaný materiál ve tvaru svorky U je na spirále zavěšen. Odpařovaný materiál musí smáčet spirálu, aby se na něj po roztavení nalepil. ► Drátěný držák má tvar košíku. Naparovaný materiál nesmí košík smáčet, aby po roztavení vytvořil kapku, která nevyteče. ► Držák má tvar plechové lodičky, v níž je odpařovaný materiál vložen. Lodička je přibližně 0,3 cm hluboká, 10 cm dlouhá a 1 až 2 cm široká. Výkon potřebný pro tyto zdroje je podstatně větší, než v případě drátového uchycení, ale lze deponovat tlustší vrstvy. ► Zdroj je realizován jako uzavřená pec s jedním nebo více malými otvory, kterými proudí naparovaný materiál. Kelímek z křemene, grafitu nebo keramiky (např. heat shielding heating coil support roď thermocouple leads ► Nepřímé odporové zahřívání korundu) je obtočen drátěnou odporovou spirálou. Pokud má materiál dostatečně vysokou tenzi par před tavením, začne sublimovat a následné kondenzát vytváří tenkou vrstvu. Nevýhodou je nízká depoziční rychlost. DS110 3.6 Sources using Energetic Beams ka Zajíčková 22/31 ources using Energetic Beams ► Jiskrové naparování Rychlé naparování slitin, či několikasložkových sloučenin, které se normálně mají tendenci rozpadat na složky, lze dosáhnout kapáním malinkých kapek na horký povrch. Dojde tak k separátnímu odpařování na mnoha místech kdy se ale v každém místě odpaří všechny složky. ► Obloukové naparování. Zapálením elektrického oblouku mezi dvěma vodivými elektrodami dochází v místě dopadu oblouku k velkému ohřevu materiálu. Teplota je dostatečná i k odpařování Nb a Ta. Tato metoda je také často používá k naparování uhlíku na vzorky pro elektronový mikroskop. ► Exploding wire method. This technique is based on the explosion of the wire caused by rapid heating due to the passage of a large current density 104—106 A/mm2. This effect is achieved by an array of capacitors 10 to 100 /iF) charged to a voltage of ~ 1 to 10 kV. The energy consumption is about 25 kWh/kg. The wire is typically gold, aluminum, iron or platinum, and is usually less than 0.5 mm in diameter. ► Laserové naparování nebo spíše Pulsed Laser Deposition - PLD. Obrovská intenzita laserového svazku může být použita k ohřevu a odpařování materiálu. Laserový zdroj může být mimo vakuový systém a svazek bývá zaostřen na povrch naparovaného materiálu. ► RF ohřev. Pro ohřev materiálu lze použít elektromagnetickou indukci. Ohřev lze aplikovat buď přímo na naparovaný materiál, nebo nepřímo na kelímek v němž je naparovaný materiál uložen. DS110 3.6 Sources using Energetic Beams Lenka Zajíčková 23/31 3.6 Sources using Energetic Beams - Electron Beam Evaporation Evaporation using resistance heating has a major disadvantage that the material being evaporated tends to be contaminated by the holder material. Also, the evaporation is limited by the input power (melting of the holder would occur), which makes evaporation of high melting temperature materials very difficult. This can be circumvented by electron beam evaporation. The simplest arrangement consists of a tungsten filament that is heated and emits electrons. These are then accelerated by applying a positive voltage to the material being evaporated. The electrons heat the material because they lose their energy there, causing it to evaporate. For more details see scanned copy of Smith's book. DS110 3.7 Transport ka Zajickova 24/31 ranspor Transport = 2. step in the deposition process. Main issues: ► contamination - reason for high-vacuum operation ► arrival rate uniformity - analyzed with molecular flow Kn = X/L > 1 where L is the distance from the source to substrate solely geometrical factors Different models of the source: ► circular disc - emitting material from the top surface only, represents the boat, Knudsen-cell orifice, filled crucible ► sphere - approximates wire-coil source ► collimated source - partly filled crucible or non-ideal orifice (orifice whose length > its diameter) DS110 3.7 Transport Lenka Zajíčková 25/31 3.7 Transport - Evaporant Flux r How to calculate evaporant flux at r0? As projected area of the source in direction 0. For sphere it is equal to perpendicular evaporation flux r0: :sphere m A :collimated Q = Ve = l~n = Q o 47rr02 (25) where Q = rvA is total evap. rate from the source - emitting flux, A - area). For disc: r0 =? = l~n cos 9 0 '2.71 nu 0 ^0 f0 cosOTq sin 0á0á (r- 1/r2) ► flux that determines dep. rate is the flux perpendicular to the substrate (I\l) at point S r i = r.c cos o Finally, = l~n cos 6 = Q cos4 0 o (28) o DS110 3.8 Monitoring of Deposition Process Lenka Zajíčková 27/31 3.8 Monitoring of Deposition Process Calculation of the vapor flux is complicated by uncertainity in the evaporation rates of the various species or due to the presence of the lobed flux distribution. The vapor flux is related to ► concentration of source vapor (ion-gauge flux monitor, mass spectrometer, electron-impact emission spectrometer) ► mass deposition - quartz crystal microbalance (QCM) ► thickness by optical methods - reflectance, ellipsometry DS110 3.8 Monitoring of Deposition Process Lenka Zajíčková 28/31 3.8 Monitoring of Deposition Process Calculation of the vapor flux is complicated by uncertainity in the evaporation rates of the various species or due to the presence of the lobed flux distribution. The vapor flux is related to ► concentration of source vapor (ion-gauge flux monitor, mass spectrometer, electron-impact emission spectrometer) ► mass deposition - quartz crystal microbalance (QCM) ► thickness by optical methods - reflectance, ellipsometry quadrupole mass spectrometer electron-impact emission spectrometer ö-Efeirn DS110 Monitoring of Deposition Process ka Zajíčková 29/31 Quartz Crystal Microbalance (QCM) QCM sensor is based on the piezoelectric effect: A crystal under strain becomes electrically polarized. When deformed, the atoms are displaced, producing electrical dipoles in the material. In noninversion symmetry crystals, the summation of these dipoles generates dipole moments. The effect can be reversed by applying an electrical field to the crystal, and the internal mechanical strain is generated. Piezoelectric Effect in Quartz Q°M structure: a pair of electrodes coupled with piezoelectric crystal, typically No Stress Tension Compression AT-cut quartz (Si02). Side view If an alternating electric field with a frequency close to the resonant frequency of the crystal plate is applied to the electrode, the crystal vibrates intensely and stably (high Q factor). DS110 Monitoring of Deposition Process ka Zajíčková 30/31 Quartz Crystal Microbalance (QCM) The AT-cut quartz crystal operates at thickness-shear mode. The fundamental frequency of this crystal cut is typically 1-30 MHz. No Stress Piezoelectric Effect in Quartz T Tension Compression + + + + + + + + + + o Silicon Atom 0 Oxygen Atom Mass loading \ Electric field Quartz plate Displacement QCM is extremely sensitive to mass changes Am in the nano-scale regime per unit area A 2ß Am Af =--- where f0 is the fundamental frequency, g and E are the crystal mass density and Young's modulus. For quartz: g = 2.647 g/cm3 and E = 2.947 x 1011 dyn/cm2 DS110 3.8 Monitoring of Deposition Process Lenka Zajíčková 31 /31 uartz Crystal Microbalance (QCM) Sensing can be active or passive. The active or "oscillating" method requires connecting the sensor to an oscillator amplifier circuit providing a positive feedback. The piezoelectric crystal's oscilations can be measured using a frequency counter. T ~ 1 The change of frequency Af gives the mass change Am 2ß Am Af =--- The film thickness can be determined from the film density and the gold electrode area.