F4280 Technologie depozice tenkých vrstev a
povrchových úprav 3. Evaporation
Lenka Zajíčková
Přírodovědecká fakulta & CEITEC, Masarykova univerzita, Brno
lenkaz@physics.muni.cz
jarní semestr 2020
Central European Institute of Technology ^ U*U i
BRNO | CZECH REPUBLIC ^*$L*^
• 3.1 Introduction to Evaporation
• 3.2 Thermodynamics of Vaporization
• 3.3 Evaporation Rate
• 3.3 Alloys
• 3.4 Compounds
• 3.5 Sources for Thermal Evaporation
• 3.6 Sources using Energetic Beams
• 3.7 Transport
• 3.8 Monitoring of Deposition Process
F4280 Technologie depozice a povrchových úprav:
3.1 Introduction to Evaporation
ka Zajíčková
3/25
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). It is composed of three subsequent steps:
1. Obtaining the vapors of solid materials (vaporization) that do not have high enough vapor pressure =^ material have to be 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.
► 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 vacuum evaporation.
► Vacuum evaporation of metallic thin films was not common until 1920s.
F4280 Technologie depozice a povrchovych uprav:    3.2 Thermodynamics of Vaporization
nka Zajíčková
4/25
ermo
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.
.:y::i:y. pv - (saturation) vapor
pressure, q - heat
w - mechanical work F - force
Qc - molar condensation rate
Qv - molar evaporation rate
••t • • . . • •
(c)
Different evaporation situations:
► (a) vapor-liquid (or solid) equilibrium situation in a closed isothermal container
► (b) Knudsen-cell effusion
► (c) vacuum evaporation
F4280 Technologie depozice a povrchových úprav:    3.2 Thermodynamics of Vaporization Lenka Zajíčková 5/25
Closed isothermal container - determination of pv("0
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 O, 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)
díl + dw = dg
(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
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
dQ
T
= &dS = 0
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
S = /cBlnZ
•	•
•	•
o	o
o	o
(a)
(3)
o
(6)
increase of entropy from 0 to 1 J9kB
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).
► 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 dw = pdV and dq = TdS
Here, H is enthalpy that appeared earlier in connection to heat capacity at constant p.
dU + pdV- TdS = dG = 0
(4)
where Gibbs free energy G is introduced as
G=(U + pV)-TS= H- TS.
(5)
F4280 Technologie depozice a povrchových úprav:    3.2 Thermodynamics of Vaporization Lenka Zajíčková 8/25
Thermodynamic Quantities - Chemical Potential
► 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. Diiferentiating 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 - 7"dS = dG = 0, (7)
—■ System held at constant p and T is at equilibrium when dG = 0 (G is at minimum) for any disturbance such as evaporation of d/Vm moles of condensate.
Incremental change in G for addition of material to a phase at constant T and p (applied to multicomponent mixtures)
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, H is just the free energy per mole of condensate, Gmc-
We have shown that at vapor-liquid equilibrium of closed vapor + liquid system,
G =const (as evaporation proceeds at constant T and p)
He — /iv (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).
(8)
F4280 Technologie depozice a povrchových úprav: 1	3.2 Thermodynamics of Vaporization	Lenka Zajíčková	10/25
			
Dependence ot vapor	pressure pv on /		
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 & we know pv increases with T
Evaporation can proceed by absorption of heat from surroundings (evaporative cooling), which creats a T difference. Then, it is driven by S t accompanying the evaporation =^ example of endothermic (heat absorbing) reaction.
F4280 Technologie depozice a povrchových úprav: 1	3.2 Thermodynamics of Vaporization	Lenka Zajíčková	11/25
			
Dependence ot vapor	pressure pv on /		
P
(atm)
ý— Equ
ilibrium
^—Equilibrium
\
CRITICAL POINT
solid
vaporization
► At any point along vapor-liquid (or solid) equilibrium curve /ic = Mv holds.
► As we move up the curve, /i values of both phases increases
deposition
TRIPLE POINT
or dGmc = dGmv for pure material
T fC)
Using Eq. (6) and equilibrium conditions Eq. (4)
dG Vdp -SdT or dGmi Vmidp - Smid7" where / = c, v.
Thus, at equilibrium between the two phases
VmcdPv — SmcdT = \/mvdPv —SmvdT
dpv d7"
Smv 5
m c
A Si
m
Vmv - V,
mc
AVr
m
(10)
(11)
Since AGm = 0 for evaporation and G = H — TS ^> AVH = TASm where AVW is the "latent heat" (enthalpy change) of vaporization per mole.
F4280 Technologie depozice a povrchových úprav:
3.2 Thermodynamics of Vaporization
ka Zajíčková
12/25
Clausius-Clapeyron Equation, i.e. pv("0
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/7~for ASm = Smv - Smc in Eq. (11) leads to Clausius-Clapeyron equation:
The volume term AVU] = Vmv - Vmc may be eliminated as follows:
► VmC is negligible - it is typically 1 /1000\/mv at 1 atmosphere
► for ideal gases Vmv = RT/p
pv = B exp(-Av H/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(T) data are not available.
■i
M n.; i.í
2
W 14
S."
1
* »
T-0-* - -d.j
1J
l.i: 1 .■ I
).t
U
dpv d7"
dpv
Pv
A v H
m
AyH RT2
(12)
d7" (13)
Vkp« Pnuurí Cur*» oí Liquid and Solid B*niDnir
1.1 1.1  S  I.í ľ.l J.Ě JJ  3  J.S 3 1 U1J i 4.Í AA *6 U 5 5J lÚMVTtmfiHAhn [K|
F4280 Technologie depozice a povrchových úprav:    3.3 Evaporation Rate Lenka Zajíčková 13/25
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
► 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)
r, =
P
V27r/cb 7/77
Q = (r2-r1)/\ = (p2-p1)
A
= (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 p<\ « 0) can be found just from the vapor pressure pv:
A
F4280 Technologie depozice a povrchových úprav:    3.3 Evaporation Rate		Lenka Zajíčková	14/25
			
Evaporation I	Rate uv		
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 ~ l~c (l~v = 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 rc = l~i + vapor-liquid equilibrium
Pv
I~v0 = l~i =
V27r/cb 7/77
where rv0 denotes the upper limit.
(20)
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).
F4280 Technologie depozice a povrchových úprav:    3.3 Evaporation Rate
Lenka Zajíčková
15/25
Evaporation and Condensation Coefficient
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 l~v < rv0 and emipirically
l~v = avrvo where av is evaporation coefficient.
(21)
There is a corresponding condensation coefficient ac
rc=acri (22) At equilibrium l~c = l~v   =^   ac = av. Otherwise they are different functions of p, T.
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.
F4280 Technologie depozice a povrchových úprav:    3.3 Alloys
Lenka Zajíčková
16/25
3.3 Alloys - Partial Pressures
Multicomponent materials bring additional complication - the composition of the vapor phase generally differs from that of the condenced 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 aB,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.
If the evaporation coefficients are unity (common for metals) the ratio of evaporation fluxes is
rvb       x   pvB frn^
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 ByO^_y wire or rod steadily into the melt during evaporation
(24)
,W cm3/s
F4280 Technologie depozice a povrchovych üprav:    3.4 Compounds
3.4 Compounds
Lenka Zajíčková
18/25
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
F4280 Technologie depozice a povrchových úprav:
3.5 Sources for Thermal Evaporation
ka Zajíčková
19/25
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.
heat shielding
heating
coil
thermocouple leads
► Nepřímé odporové zahřívání - Kelímek z křemene, grafitu nebo keramiky (např. 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.
F4280 Technologie depozice a povrchových úprav:			3.6 Sources using Energetic Beams				ka Zajíčková                                20 / 25
							
	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.
► Technika explodujícího drátu. Tato technika je založení na explozi drátku způsobené prudkým ohřevem díky průchodu velkého proudu, řádově 106 A/cm2. Takovéhoto efektu je dosaženo polem kondenzátoru    10 to 100 /iF) nabitým na napětí ~ 1 to 10 k V.
► Laserové naparování. 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.
F4280 Technologie depozice a povrchových úprav:			3.6 Sources using Energetic Beams				ka Zajíčková 21/25
							
	ources using	Energetic		Beams			
► Naparování elektronovým svazkem Naparování použitím odporového zahřívání má velkou nevýhodu v tom, že naparovaný materiál bývá kontaminován materiálem držáku. Také je naparování limotováno vstupním výkonem (došlo by k tavení držáku), což značně ztěžuje naparování materiálů s vysokou teplotou tání. =^ lze to obejít pomocí elektronového bombardu materiálu.
Nejjednodušší uspořádání sestává z wolframového vlákna, které je žhaveno a emituje elektrony. Ty jsou následně urychlovány díky přivedení kladného napětí na naparovaný materiál. Elektrony v něm ztrácejí svou energii, čímž materiál ohřívají a dochází k jeho vypařování.
For more details see scanned copy of Smith's book.
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 ffrom the source to substrate solely geometrical factors
/     Xre = ro/cos0
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)
xollimated
F4280 Technologie depozice a povrchových úprav:
3.7 Transport
Lenka Zajíčková
23/25
How to calculate evaporant flux Ve at r0? As projected area of the source in direction 0.
substrate	j-p- x	J±	V'-
		J	
r sinö
r0 ~ r0/cos8
xollimated
For sphere it is equal to perpendicular evaporatn flux r0:
ľ e = l~n =
Q
o
47rr02
(25)
where Q = VVA is total evap. rate from the source (Vv - emitting flux, A - area).
For disc:
Y q = V q cos 9
r0 =?
'2.71     r TT
Q= I     /   r0cos6>r,f sin6>dŕ9d0 = 7rr|r0 fo Jo
(26)
r0 =
Q
(27)
o
For colimated source: more complicated - lobe distribution. Although there is some angle 0C above which the evaporant source is not visible at all, there will be some flux at high angles because of evaporant scattering from the collimating sidewals.
F4280 Technologie depozice a povrchových úprav:
3.7 Transport
ka Zajíčková
24/25
3.7 Transport - Uniformity
y<\re = ro/cose
sourceidisc
:s
phere -^:-:/é::\\
xolliraated
For disc (simple cosine distribution)
Two factors have to be taken into account:
► substrate at point S is at radius
re = r0/s\nO
Ts = l~0 cos2 0
► 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 0 =
Q cos4 0
o
(28)
o
F4280 Technologie depozice a povrchových úprav:		3.8 Monitoring of Deposition Process				ka Zajíčková                                 25 / 25
						
	onitoring of Deposition		Process			
► vapor flux monitoring (ion-gauge flux monitor, mass spectrometer, electron-impact emission spectrometer)
► mass deposition - quartz crystal microbalance (QCM)
► thickness by optical methods - reflectance, ellipsometry
For more details see scanned copy of Smith's book.