Thermal Evaporator

1. Theory

• Definition: A thermal evaporator heats a source in high vacuum until its vapour pressure is high enough for atoms to travel line-of-sight and condense on the substrate (Darling; TU Wien).
• Evaporation rate: The Hertz-Knudsen relation ties the flux to the gap between equilibrium vapour pressure and ambient pressure; most elements give about $10^{-4}$ g cm${}^{-2}$ s${}^{-1}$ at $10^{-2}$ Torr (Darling; TU Wien).
• Vapour pressure: Vapour pressure rises exponentially with temperature and differs between elements by up to 14 orders of magnitude at 2000 K, which complicates alloys (TU Wien).
• Cosine emission: A surface source emits with a cosine distribution, so a flat wafer coats thinner at the edge as ${\cos }^4\theta$ (Darling; TU Wien).
• Vacuum: The mean free path, $\lambda p\approx 5$ mm Pa, must exceed the throw distance, and residual gas must arrive much more slowly than the evaporant (TU Wien).

2. Working Principle

• Resistive sources: W, Ta or Mo hairpins, helices, baskets, dimple boats or troughs, or alumina crucibles, carry 200 to 300 A and reach about 1800 ${}^{\circ }$C (Darling).
• Direct and indirect heating: Wires of Cr, Ti, Al and similar metals can be heated directly; other evaporants sit in W, Mo, Ta, C, BN or TiB${}_2$ holders (TU Wien).
• Rate and thickness: Typical rates are 1 to 20 angstrom/s, monitored by a crystal monitor (Darling; Quartz Crystal Microbalance (QCM) page).
• Pumping: About $10^{-6}$ Torr for medium-quality films, down to $10^{-9}$ Torr in UHV systems (Darling; Vacuum Gauges page).

3. Applications

• Metal contacts and films: Al and other low-melting metals from resistive boats (TU Wien; Darling).
• Flash evaporation of alloys: Small portions evaporated completely so vapour-pressure differences do not matter (TU Wien).
• Reactive evaporation: Evaporation in 10${}^{-4}$ to 10${}^{-3}$ mbar of reactive gas (TU Wien).

Evaporation Rate and Sources

Name	Formula	Related Formulae	Variables/Constants
Hertz-Knudsen evaporation	$\Gamma ={\alpha }_v{\left(\frac{m}{2\pi k_{B}T}\right)}^{1/2}\left(P^{\ast }-P\right)$	$M_e=\Gamma A_{e}t$	$\Gamma :massevaporationrateperarea$ $\begin{array}{r}{\alpha }_v:evaporation(sticking)coefficient,1\\ foraKnudsencell\end{array}$ $P^{\ast }:equilibriumvapourpressure$ $\begin{array}{r}P:ambientpressure;Darling:\Gamma about10^{-4}\\ \mathrm{g}\mathrm{c}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}at{P}^{\ast }=10^{-2}\mathrm{Torr};TUWien:same\\ formpermolecule\end{array}$ $\begin{array}{r}(computed:Alatanassumed1500Kgives\\ 7.8\times 10^{-5}\mathrm{g}\mathrm{c}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}at10^{-2}\mathrm{Torr})\end{array}$
Vapour pressure	$p^{\ast }=p_0\exp \left(-\frac{E}{k_{B}T}\right)$	$\frac{p_{In}^{\ast }}{p_W^{\ast }}\approx 10^{14}(2000\mathrm{K})$	$\begin{array}{r}TUWien:Arrheniusform,10^{-11}\mathrm{mbar}forW\\ and10^3\mathrm{mbar}forInat2000K;Darling:W\\ reaches10^{-2}\mathrm{Torr}onlyat3230{}^{\circ }C\end{array}$ $\begin{array}{r}(myreading:the10^{-2}\mathrm{Torr}vapourpressure\\ isthepracticalworkingpointforan\\ evaporant)\end{array}$
Resistive source limits	$T_{max}\approx 1800{}^{\circ }C,I=200\text{to}300\mathrm{A}$	$R_{dep}=1\text{to}20\mathring{\mathrm{A}}/s$	$\begin{array}{r}Darling:W,TaandMoboats,basketsand\\ helices;e-beamrates10to100\mathring{\mathrm{A}}/sfor\\ comparison;TUWien:directheatingofCr,\\ Ti,Alandothers,indirectheatingwith\\ W,Mo,Ta,BNorTi{B}_2\end{array}$ $\begin{array}{r}(myreading:the1800{}^{\circ }Climitexcludes\\ refractoryevaporants,whichgotothe\\ electron-beamevaporator)\end{array}$

Thickness Distribution

Name	Formula	Related Formulae	Variables/Constants
Cosine law	$\frac{d{M}_c}{d{A}_c}=\frac{M_e\cos \varphi \cos \psi }{\pi r^2}$	$\frac{d{M}_c}{d{A}_c}=\frac{M_e\cos \psi }{4\pi r^2}\text{(point source)}$	$\varphi :emissionangle$ $\psi :arrivalangle$ $\begin{array}{r}r:source-substratedistance;Darling:\\ Knudsenandpointsources;TUWien:\\ Lambertemission,e-gunlobes{\cos }^{n}withn\\ about3.5to4\end{array}$ $\begin{array}{r}(myreading:asurfacesourceputstwice\\ thepoint-sourcefluxonaxis)\end{array}$
Flat-wafer uniformity	$\frac{d_{edge}}{d_{center}}={\left(\frac{r_0^2}{r_0^2+r_w^2}\right)}^2$	$R(\theta )=\frac{m_1}{\pi }\frac{{\cos }^4\theta }{R^2}$	$r_0:sourceheight$ $\begin{array}{r}{r}_w:waferradius;Darling:3inchwaferat\\ 18inchesgives0.986(1.4percent);TU\\ Wien:plane-substrate{\cos }^4\theta form\end{array}$ $\begin{array}{r}(computed:a300\mathrm{mm}waferatthesame457\\ \mathrm{mm}gives0.815,18.5percent\\ non-uniformity)\end{array}$
Uniform sphere	$\frac{d{M}_c}{d{A}_c}=\frac{M_e}{4\pi r_0^2}$	$R=\frac{m_1}{4\pi R^2}=\text{const}$	$\begin{array}{r}Darling:substratesonaspherethrough\\ thesource;TUWien:Knudsenspheregiving\\ uniformthickness\end{array}$ $\begin{array}{r}(myreading:thisisthegeometrythat\\ dome-shapedwaferholdersapproximate)\end{array}$

Vacuum and Film Purity

Name	Formula	Related Formulae	Variables/Constants
Mean free path	$\lambda p\approx 5\mathrm{mm}\mathrm{Pa}$	$N=N_0\exp \left(-\frac{x}{\lambda }\right)$	$\begin{array}{r}TUWien:500\mathrm{mm}at10^{-4}\mathrm{mbar},74percent\\ ofparticlescrossing150\mathrm{mm}unscattered,\\ 97percentat10^{-5}\mathrm{mbar}\end{array}$ $\begin{array}{r}(computed:\exp (-0.3)=0.74and\exp (-0.03)=\\ 0.97;\lambda about38\mathrm{m}at10^{-6}\mathrm{Torr})\end{array}$
Contamination ratio	$\frac{{\Gamma }_g}{{\Gamma }_d}=\frac{p{m}_d}{a_w\rho \sqrt{2\pi m{k}_{B}T}}$	$\frac{{\Gamma }_g}{{\Gamma }_d}=0.5\text{to}0.005(10^{-3}\mathrm{Pa},1\text{to}100nm/s)$	${\Gamma }_g:residual-gasimpingement$ ${\Gamma }_d:evaporantarrival$ $a_w:growthrate$ $\begin{array}{r}\rho :filmdensity;TUWien:N_{2}andAr\\ toleratearationear1,O_2,H_{2}Oandoil\\ vapourneedmuchless\end{array}$ $\begin{array}{r}(computed:aironAlat293Kwithan\\ assumed2700kg/{\mathrm{m}}^{3}gives0.47at1nm/s)\end{array}$
Required vacuum	$P\le 10^{-6}\mathrm{Torr}\text{(medium-quality films)}$	$p<10^{-5}\mathrm{mbar}\text{(high vacuum)}$	$\begin{array}{r}Darling:UHVto10^{-9}\mathrm{Torr}possible;TU\\ Wien:themean-free-pathargumentalone\\ givesbelow10^{-3}\mathrm{mbar};VacuumGaugespage\end{array}$ $(computed:10^{-5}\mathrm{mbar}=7.5\times 10^{-6}\mathrm{Torr})$

Important Questions

Ques: How does a resistive thermal evaporator work?

By heating a source until it evaporates in vacuum. Darling lists the resistive sources: tungsten, tantalum or molybdenum hairpins, helices, wire baskets, dimple boats, troughs, and alumina crucibles in wire baskets. They carry 200 to 300 A and reach only about 1800 ${}^{\circ }\mathrm{C}$. Tungsten itself melts at 3380 ${}^{\circ }\mathrm{C}$ and reaches $10^{-2}$ $\mathrm{Torr}$ vapour pressure only at 3230 ${}^{\circ }\mathrm{C}$, which is why it serves as the boat. TU Wien adds that wires of Cr, Ti, Al and similar metals can be heated directly, while other evaporants sit in W, Mo, Ta, C, Pt, BN or TiB${}_2$ holders. Rates are typically 1 to 20 angstrom/s, against 10 to 100 angstrom/s for electron-beam evaporation (Darling), and a crystal monitor tracks thickness (Quartz Crystal Microbalance (QCM) page). Reference: R. B. Darling, ‘Physical Vapor Deposition’, EE-527 MicroFabrication lecture slides, University of Washington: Hertz-Knudsen mass evaporation rate Gamma = alpha_v (m/2 pi kB T)^(1/2) (P* - P) in g/cm2 s, alpha_v = 1 for a Knudsen cell, Gamma about 1e-4 g/cm2 s at P* = 1e-2 torr for most elements, M_e = Gamma A_e t, 1e-6 torr needed for medium quality films and UHV down to 1e-9 torr, Knudsen-cell deposit dM/dA = M_e cos(phi) cos(psi)/(pi r^2), point source M_e cos(psi)/(4 pi r^2), sphere M_e/(4 pi r0^2), edge-to-centre ratio (r0^2/(r0^2+rw^2))^2 with a 3 inch wafer 18 inches above the cell giving 0.986 or 1.4 per cent non-uniformity, W (MP 3380 C, P* 1e-2 torr at 3230 C), Ta and Mo supports, hairpins, helices, baskets, dimple boats, troughs and alumina crucibles, resistive heating only to about 1800 C, filament currents 200 to 300 A, rates 1 to 20 angstrom/s against 10 to 100 angstrom/s for electron-beam evaporation (fetch-tool summary); TU Wien Institute of Solid State Physics, ‘Physik und Technologie Duenner Schichten / Thin Film Technology’, chapter 2 (vacuum evaporation), pp. 9 to 53: mean free path lambda p about 5 mm Pa, 500 mm at 1e-4 mbar with about 74 per cent of particles crossing 150 mm without collision and 97 per cent at 1e-5 mbar, N = N0 exp(-x/lambda), impingement rate p/sqrt(2 pi m kB T), Hertz-Knudsen dN/dt = a (p* - p) A/sqrt(2 pi m kB T) with p* = p0 exp(-E/kB T), evaporation coefficient 1 for clean surfaces, Lambert cosine emission, plane-substrate rate (m1/pi) cos^4(theta)/R^2, Knudsen sphere uniform, electron-gun lobes cos^n with n about 3.5 to 4 for 5 kW, vapour pressures at 2000 K of 1e-11 mbar (W) and 1e3 mbar (In), 14 orders of magnitude, flash evaporation making vapour-pressure differences irrelevant, high vacuum below 1e-5 mbar while the mean-free-path argument gives base pressure below 1e-3 mbar, contamination ratio Gamma_g/Gamma_d = p m_d/(a_w rho sqrt(2 pi m kB T)) giving 0.5 to 0.005 at 1e-3 Pa for 1 to 100 nm/s, N2 and Ar with small sticking coefficients tolerating a ratio near 1, O2, H2O and oil vapours sticking near 1 requiring a ratio much below 1, direct heating of C, Cr, Fe, Mo, Ni, Pd, Rh, Ti, Al and indirect heating with W, Mo, Ta, C, Pt, BN, TiB2 (fetch-tool summary); Quartz Crystal Microbalance (QCM) page of this vault.

Ques: What sets the evaporation rate?

The source’s vapour pressure through the Hertz-Knudsen relation. Darling gives $\Gamma ={\alpha }_v(m/2\pi k_{B}T{)}^{1/2}(P^{\ast }-P)$ in mass per area per time, with ${\alpha }_v=1$ for a Knudsen cell, and states that most elements give about $10^{-4}$ $\mathrm{g}\mathrm{c}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$ at $P^{\ast }=10^{-2}$ $\mathrm{Torr}$. TU Wien writes the same law per molecule, with $p^{\ast }=p_0\exp (-E/k_{B}T)$, so the rate is strongly temperature dependent. As a check, aluminium at an assumed 1500 K and $10^{-2}$ $\mathrm{Torr}$ gives $7.8\times 10^{-5}$ $\mathrm{g}\mathrm{c}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$ (computed), in line with Darling’s figure. TU Wien notes an evaporation coefficient of 1 for very clean surfaces. Contaminated surfaces evaporate more slowly, so source cleanliness matters as much as temperature (my reading). Reference: R. B. Darling, ‘Physical Vapor Deposition’, EE-527 MicroFabrication lecture slides, University of Washington: Hertz-Knudsen mass evaporation rate Gamma = alpha_v (m/2 pi kB T)^(1/2) (P* - P) in g/cm2 s, alpha_v = 1 for a Knudsen cell, Gamma about 1e-4 g/cm2 s at P* = 1e-2 torr for most elements, M_e = Gamma A_e t, 1e-6 torr needed for medium quality films and UHV down to 1e-9 torr, Knudsen-cell deposit dM/dA = M_e cos(phi) cos(psi)/(pi r^2), point source M_e cos(psi)/(4 pi r^2), sphere M_e/(4 pi r0^2), edge-to-centre ratio (r0^2/(r0^2+rw^2))^2 with a 3 inch wafer 18 inches above the cell giving 0.986 or 1.4 per cent non-uniformity, W (MP 3380 C, P* 1e-2 torr at 3230 C), Ta and Mo supports, hairpins, helices, baskets, dimple boats, troughs and alumina crucibles, resistive heating only to about 1800 C, filament currents 200 to 300 A, rates 1 to 20 angstrom/s against 10 to 100 angstrom/s for electron-beam evaporation (fetch-tool summary); TU Wien Institute of Solid State Physics, ‘Physik und Technologie Duenner Schichten / Thin Film Technology’, chapter 2 (vacuum evaporation), pp. 9 to 53: mean free path lambda p about 5 mm Pa, 500 mm at 1e-4 mbar with about 74 per cent of particles crossing 150 mm without collision and 97 per cent at 1e-5 mbar, N = N0 exp(-x/lambda), impingement rate p/sqrt(2 pi m kB T), Hertz-Knudsen dN/dt = a (p* - p) A/sqrt(2 pi m kB T) with p* = p0 exp(-E/kB T), evaporation coefficient 1 for clean surfaces, Lambert cosine emission, plane-substrate rate (m1/pi) cos^4(theta)/R^2, Knudsen sphere uniform, electron-gun lobes cos^n with n about 3.5 to 4 for 5 kW, vapour pressures at 2000 K of 1e-11 mbar (W) and 1e3 mbar (In), 14 orders of magnitude, flash evaporation making vapour-pressure differences irrelevant, high vacuum below 1e-5 mbar while the mean-free-path argument gives base pressure below 1e-3 mbar, contamination ratio Gamma_g/Gamma_d = p m_d/(a_w rho sqrt(2 pi m kB T)) giving 0.5 to 0.005 at 1e-3 Pa for 1 to 100 nm/s, N2 and Ar with small sticking coefficients tolerating a ratio near 1, O2, H2O and oil vapours sticking near 1 requiring a ratio much below 1, direct heating of C, Cr, Fe, Mo, Ni, Pd, Rh, Ti, Al and indirect heating with W, Mo, Ta, C, Pt, BN, TiB2 (fetch-tool summary).

Ques: Why is the film thinner at the wafer edge, and how much?

Because of cosine emission and the longer, oblique path to the edge. Darling gives the Knudsen-source deposit as $M_e\cos \varphi \cos \psi /\pi r^2$, and for a flat wafer of radius $r_w$ at height $r_0$ the edge-to-centre ratio $(r_0^2/(r_0^2+r_w^2){)}^2$. TU Wien writes the same as a ${\cos }^4\theta$ law. Darling’s example, a 3 inch wafer 18 inches above the cell, gives 0.986, or 1.4 per cent non-uniformity. The same throw over a 300 $\mathrm{mm}$ wafer gives 0.815, or 18.5 per cent (computed), so large wafers need longer throws or other geometry. Placing substrates on a sphere through the source makes the deposit $M_e/4\pi r_0^2$, uniform everywhere (Darling; TU Wien). Dome-shaped holders approximate this (my reading). Reference: R. B. Darling, ‘Physical Vapor Deposition’, EE-527 MicroFabrication lecture slides, University of Washington: Hertz-Knudsen mass evaporation rate Gamma = alpha_v (m/2 pi kB T)^(1/2) (P* - P) in g/cm2 s, alpha_v = 1 for a Knudsen cell, Gamma about 1e-4 g/cm2 s at P* = 1e-2 torr for most elements, M_e = Gamma A_e t, 1e-6 torr needed for medium quality films and UHV down to 1e-9 torr, Knudsen-cell deposit dM/dA = M_e cos(phi) cos(psi)/(pi r^2), point source M_e cos(psi)/(4 pi r^2), sphere M_e/(4 pi r0^2), edge-to-centre ratio (r0^2/(r0^2+rw^2))^2 with a 3 inch wafer 18 inches above the cell giving 0.986 or 1.4 per cent non-uniformity, W (MP 3380 C, P* 1e-2 torr at 3230 C), Ta and Mo supports, hairpins, helices, baskets, dimple boats, troughs and alumina crucibles, resistive heating only to about 1800 C, filament currents 200 to 300 A, rates 1 to 20 angstrom/s against 10 to 100 angstrom/s for electron-beam evaporation (fetch-tool summary); TU Wien Institute of Solid State Physics, ‘Physik und Technologie Duenner Schichten / Thin Film Technology’, chapter 2 (vacuum evaporation), pp. 9 to 53: mean free path lambda p about 5 mm Pa, 500 mm at 1e-4 mbar with about 74 per cent of particles crossing 150 mm without collision and 97 per cent at 1e-5 mbar, N = N0 exp(-x/lambda), impingement rate p/sqrt(2 pi m kB T), Hertz-Knudsen dN/dt = a (p* - p) A/sqrt(2 pi m kB T) with p* = p0 exp(-E/kB T), evaporation coefficient 1 for clean surfaces, Lambert cosine emission, plane-substrate rate (m1/pi) cos^4(theta)/R^2, Knudsen sphere uniform, electron-gun lobes cos^n with n about 3.5 to 4 for 5 kW, vapour pressures at 2000 K of 1e-11 mbar (W) and 1e3 mbar (In), 14 orders of magnitude, flash evaporation making vapour-pressure differences irrelevant, high vacuum below 1e-5 mbar while the mean-free-path argument gives base pressure below 1e-3 mbar, contamination ratio Gamma_g/Gamma_d = p m_d/(a_w rho sqrt(2 pi m kB T)) giving 0.5 to 0.005 at 1e-3 Pa for 1 to 100 nm/s, N2 and Ar with small sticking coefficients tolerating a ratio near 1, O2, H2O and oil vapours sticking near 1 requiring a ratio much below 1, direct heating of C, Cr, Fe, Mo, Ni, Pd, Rh, Ti, Al and indirect heating with W, Mo, Ta, C, Pt, BN, TiB2 (fetch-tool summary).

Ques: What base pressure does an evaporator need, and which figure is more likely right?

About $10^{-6}$ $\mathrm{Torr}$ for good films; the $10^{-3}$ $\mathrm{mbar}$ figure is only a lower bound. Darling states that $10^{-6}$ $\mathrm{Torr}$ is needed for medium-quality films and that UHV systems reach $10^{-9}$ $\mathrm{Torr}$. TU Wien defines high vacuum as below $10^{-5}$ $\mathrm{mbar}$, which is $7.5\times 10^{-6}$ $\mathrm{Torr}$ (computed), but its mean-free-path argument alone gives below $10^{-3}$ $\mathrm{mbar}$. That argument ensures only that atoms cross the chamber unscattered, with 74 per cent crossing 150 $\mathrm{mm}$ at $10^{-4}$ $\mathrm{mbar}$. Film purity also requires residual gas to arrive much more slowly than the evaporant, which TU Wien’s contamination ratio makes clear. The $10^{-6}$ $\mathrm{Torr}$ value is therefore more likely right for practical films (my reading). Reference: R. B. Darling, ‘Physical Vapor Deposition’, EE-527 MicroFabrication lecture slides, University of Washington: Hertz-Knudsen mass evaporation rate Gamma = alpha_v (m/2 pi kB T)^(1/2) (P* - P) in g/cm2 s, alpha_v = 1 for a Knudsen cell, Gamma about 1e-4 g/cm2 s at P* = 1e-2 torr for most elements, M_e = Gamma A_e t, 1e-6 torr needed for medium quality films and UHV down to 1e-9 torr, Knudsen-cell deposit dM/dA = M_e cos(phi) cos(psi)/(pi r^2), point source M_e cos(psi)/(4 pi r^2), sphere M_e/(4 pi r0^2), edge-to-centre ratio (r0^2/(r0^2+rw^2))^2 with a 3 inch wafer 18 inches above the cell giving 0.986 or 1.4 per cent non-uniformity, W (MP 3380 C, P* 1e-2 torr at 3230 C), Ta and Mo supports, hairpins, helices, baskets, dimple boats, troughs and alumina crucibles, resistive heating only to about 1800 C, filament currents 200 to 300 A, rates 1 to 20 angstrom/s against 10 to 100 angstrom/s for electron-beam evaporation (fetch-tool summary); TU Wien Institute of Solid State Physics, ‘Physik und Technologie Duenner Schichten / Thin Film Technology’, chapter 2 (vacuum evaporation), pp. 9 to 53: mean free path lambda p about 5 mm Pa, 500 mm at 1e-4 mbar with about 74 per cent of particles crossing 150 mm without collision and 97 per cent at 1e-5 mbar, N = N0 exp(-x/lambda), impingement rate p/sqrt(2 pi m kB T), Hertz-Knudsen dN/dt = a (p* - p) A/sqrt(2 pi m kB T) with p* = p0 exp(-E/kB T), evaporation coefficient 1 for clean surfaces, Lambert cosine emission, plane-substrate rate (m1/pi) cos^4(theta)/R^2, Knudsen sphere uniform, electron-gun lobes cos^n with n about 3.5 to 4 for 5 kW, vapour pressures at 2000 K of 1e-11 mbar (W) and 1e3 mbar (In), 14 orders of magnitude, flash evaporation making vapour-pressure differences irrelevant, high vacuum below 1e-5 mbar while the mean-free-path argument gives base pressure below 1e-3 mbar, contamination ratio Gamma_g/Gamma_d = p m_d/(a_w rho sqrt(2 pi m kB T)) giving 0.5 to 0.005 at 1e-3 Pa for 1 to 100 nm/s, N2 and Ar with small sticking coefficients tolerating a ratio near 1, O2, H2O and oil vapours sticking near 1 requiring a ratio much below 1, direct heating of C, Cr, Fe, Mo, Ni, Pd, Rh, Ti, Al and indirect heating with W, Mo, Ta, C, Pt, BN, TiB2 (fetch-tool summary); Vacuum Gauges page of this vault.

Ques: How do residual gases contaminate an evaporated film?

By striking the growing surface alongside the evaporant. TU Wien defines the contamination ratio ${\Gamma }_g/{\Gamma }_d=p{m}_d/(a_w\rho \sqrt{2\pi m{k}_{B}T})$, the residual-gas impingement over the evaporant arrival rate. At $10^{-3}$ $\mathrm{Pa}$ and growth rates of 1 to 100 $nm/s$ it is 0.5 to 0.005. As a check, air on aluminium at 293 K with an assumed density of 2700 $kg/{\mathrm{m}}^3$ gives 0.47 at 1 $nm/s$ (computed). Whether this matters depends on sticking: N${}_2$ and Ar stick so weakly that a ratio near 1 is acceptable, but O${}_2$, H${}_2$O and oil vapours stick with probability near 1, so their ratio must be far below 1 (TU Wien). Lower pressure or faster deposition both reduce incorporation (my reading). Reference: TU Wien Institute of Solid State Physics, ‘Physik und Technologie Duenner Schichten / Thin Film Technology’, chapter 2 (vacuum evaporation), pp. 9 to 53: mean free path lambda p about 5 mm Pa, 500 mm at 1e-4 mbar with about 74 per cent of particles crossing 150 mm without collision and 97 per cent at 1e-5 mbar, N = N0 exp(-x/lambda), impingement rate p/sqrt(2 pi m kB T), Hertz-Knudsen dN/dt = a (p* - p) A/sqrt(2 pi m kB T) with p* = p0 exp(-E/kB T), evaporation coefficient 1 for clean surfaces, Lambert cosine emission, plane-substrate rate (m1/pi) cos^4(theta)/R^2, Knudsen sphere uniform, electron-gun lobes cos^n with n about 3.5 to 4 for 5 kW, vapour pressures at 2000 K of 1e-11 mbar (W) and 1e3 mbar (In), 14 orders of magnitude, flash evaporation making vapour-pressure differences irrelevant, high vacuum below 1e-5 mbar while the mean-free-path argument gives base pressure below 1e-3 mbar, contamination ratio Gamma_g/Gamma_d = p m_d/(a_w rho sqrt(2 pi m kB T)) giving 0.5 to 0.005 at 1e-3 Pa for 1 to 100 nm/s, N2 and Ar with small sticking coefficients tolerating a ratio near 1, O2, H2O and oil vapours sticking near 1 requiring a ratio much below 1, direct heating of C, Cr, Fe, Mo, Ni, Pd, Rh, Ti, Al and indirect heating with W, Mo, Ta, C, Pt, BN, TiB2 (fetch-tool summary).

Ques: Why are alloys hard to evaporate from one boat?

Because their components have very different vapour pressures. TU Wien gives $10^{-11}$ $\mathrm{mbar}$ for tungsten and $10^3$ $\mathrm{mbar}$ for indium at 2000 K, a spread of 14 orders of magnitude, extending to 17 orders with selenium, potassium and zinc. A heated alloy therefore loses its volatile component first, and the film composition drifts during the run (my reading). TU Wien describes flash evaporation, where small portions are evaporated completely so vapour-pressure differences become irrelevant, and contrasts sputtering, where the target surface enriches in the lower-yield component until the deposit matches the target. Refractory components are a further problem, since resistive sources reach only about 1800 ${}^{\circ }\mathrm{C}$ (Darling); these go to an electron-beam evaporator. Reference: TU Wien Institute of Solid State Physics, ‘Physik und Technologie Duenner Schichten / Thin Film Technology’, chapter 2 (vacuum evaporation), pp. 9 to 53: mean free path lambda p about 5 mm Pa, 500 mm at 1e-4 mbar with about 74 per cent of particles crossing 150 mm without collision and 97 per cent at 1e-5 mbar, N = N0 exp(-x/lambda), impingement rate p/sqrt(2 pi m kB T), Hertz-Knudsen dN/dt = a (p* - p) A/sqrt(2 pi m kB T) with p* = p0 exp(-E/kB T), evaporation coefficient 1 for clean surfaces, Lambert cosine emission, plane-substrate rate (m1/pi) cos^4(theta)/R^2, Knudsen sphere uniform, electron-gun lobes cos^n with n about 3.5 to 4 for 5 kW, vapour pressures at 2000 K of 1e-11 mbar (W) and 1e3 mbar (In), 14 orders of magnitude, flash evaporation making vapour-pressure differences irrelevant, high vacuum below 1e-5 mbar while the mean-free-path argument gives base pressure below 1e-3 mbar, contamination ratio Gamma_g/Gamma_d = p m_d/(a_w rho sqrt(2 pi m kB T)) giving 0.5 to 0.005 at 1e-3 Pa for 1 to 100 nm/s, N2 and Ar with small sticking coefficients tolerating a ratio near 1, O2, H2O and oil vapours sticking near 1 requiring a ratio much below 1, direct heating of C, Cr, Fe, Mo, Ni, Pd, Rh, Ti, Al and indirect heating with W, Mo, Ta, C, Pt, BN, TiB2 (fetch-tool summary); R. B. Darling, ‘Physical Vapor Deposition’, EE-527 MicroFabrication lecture slides, University of Washington: Hertz-Knudsen mass evaporation rate Gamma = alpha_v (m/2 pi kB T)^(1/2) (P* - P) in g/cm2 s, alpha_v = 1 for a Knudsen cell, Gamma about 1e-4 g/cm2 s at P* = 1e-2 torr for most elements, M_e = Gamma A_e t, 1e-6 torr needed for medium quality films and UHV down to 1e-9 torr, Knudsen-cell deposit dM/dA = M_e cos(phi) cos(psi)/(pi r^2), point source M_e cos(psi)/(4 pi r^2), sphere M_e/(4 pi r0^2), edge-to-centre ratio (r0^2/(r0^2+rw^2))^2 with a 3 inch wafer 18 inches above the cell giving 0.986 or 1.4 per cent non-uniformity, W (MP 3380 C, P* 1e-2 torr at 3230 C), Ta and Mo supports, hairpins, helices, baskets, dimple boats, troughs and alumina crucibles, resistive heating only to about 1800 C, filament currents 200 to 300 A, rates 1 to 20 angstrom/s against 10 to 100 angstrom/s for electron-beam evaporation (fetch-tool summary).

References

1. R. B. Darling, “Physical vapor deposition,” EE-527 MicroFabrication lecture notes, University of Washington. Available: https://WeCanFigureThisOut.org/NANO/lecture_notes/Microfabrication_Supporting_materials_files/R_B_Darling - Washington U - PhysicalVaporDeposition.pdf
2. TU Wien Institute of Solid State Physics, “Physik und Technologie duenner Schichten (Thin film technology),” chapter 2, vacuum evaporation. Available: https://static.ifp.tuwien.ac.at/homepages/Personen/duenne_schichten/pdf/t_p_tf_chapter2.pdf
3. Quartz Crystal Microbalance (QCM) page of this vault.
4. Vacuum Gauges page of this vault.

Related pages in this vault: Quartz Crystal Microbalance (QCM), Vacuum Gauges, Residual Gas Analyzer (RGA), Electron-Beam Evaporator, DC and RF Magnetron Sputter System, Molecular Beam Epitaxy (MBE) System.