Evaporation deposition turns a condensed source into vapor, transports that vapor through molecular-flow vacuum, and condenses it on surfaces that can see the source. Its apparent simplicity hides a coupled chain: vapor pressure sets source flux, source shape sets emission, chamber pressure determines whether trajectories remain collisionless, fixture geometry maps those trajectories onto the wafer, and surface condition decides sticking and film growth. The method is therefore not merely “heat material until it coats”; it is a source-thermodynamics, line-of-sight transport, calibration, and integration problem.

The starting point is the emission pattern of the source itself. A small molten pool radiating into a hemisphere does not emit isotropically; it emits with an intensity proportional to the cosine of the angle from its surface normal, because a surface element seen obliquely presents a smaller projected area. Combine that with the inverse-square falloff of flight distance and you get the classical thickness distribution on a plane held parallel to the source at height $h$:

$d(r) \;=\; \frac{m}{\pi\rho}\,\frac{h^{2}}{\bigl(h^{2}+r^{2}\bigr)^{2}} \;=\; \frac{d_{0}}{\bigl[1+(r/h)^{2}\bigr]^{2}}$

The right-hand form is the one worth memorising, because it says thickness uniformity is not a function of throw distance or wafer size independently — only of their ratio. At $r/h = 0.1$ the edge is 2.0 percent thinner than the centre. At $r/h = 0.2$ it is 7.5 percent thinner. At $r/h = 0.3$ it is 15.8 percent thinner, and at $r/h = 0.5$ the edge has lost 36 percent. The fourth-power denominator means uniformity degrades much faster than intuition suggests, which is why evaporator chambers are so conspicuously tall compared with sputtering chambers of the same wafer capacity.

Run the arithmetic on a real part and the design pressure becomes obvious. A 300 mm wafer has a 150 mm radius. Holding it flat and stationary 500 mm above the source puts the edge at $r/h = 0.3$, so the wafer comes out with roughly a 16 percent centre-to-edge thickness gradient — unusable for almost any purpose. Pushing the source down to 1500 mm brings the edge to $r/h = 0.1$ and the gradient to 2 percent, which is acceptable, but the chamber is now taller than the technician operating it, the pumping volume has grown by more than an order of magnitude, and the fraction of evaporated material that actually lands on product has fallen roughly as the inverse square of the throw distance. Brute-force throw distance works, and it is expensive in every dimension at once.

The elegant escape is to stop holding the wafer flat. If the substrate is tilted so that its normal points back toward the source, the obliquity loss at the edge is partly cancelled, and there is one particular arrangement in which the cancellation is exact. Put the source and every substrate on the surface of a single sphere of radius $R$. Then for any substrate position, the angle from the source normal and the angle of incidence at the substrate are equal, and both are fixed by the chord geometry of the circle:

$\cos\theta \;=\; \cos\varphi \;=\; \frac{r_{0}}{2R} \qquad\Longrightarrow\qquad d \;=\; \frac{m}{\pi\rho}\,\frac{\cos\theta\,\cos\varphi}{r_{0}^{2}} \;=\; \frac{m}{4\pi\rho R^{2}}$

The chord length $r_{0}$ cancels completely. The deposited thickness is the same everywhere on the sphere, independent of where the substrate sits and independent of how far it is from the source. This is Knudsen's result, and it is the reason production evaporators do not use flat platens: they use a spherical calotte, a dome whose radius of curvature is matched to the source-to-dome distance, so that every wafer sits on the same imaginary sphere and receives identical thickness by construction rather than by tuning. Planetary fixtures extend the idea further by giving each substrate a second rotation about its own axis, which averages out the residual asymmetries a real source has — a molten pool is not a mathematical point, a crucible rim shadows the low-angle emission, and a swept electron beam does not heat the pool symmetrically.

The fixture geometry also fixes what the process cannot do, and this is where evaporation parts company decisively from every other deposition method in the fab. Because atoms arrive along straight lines from a source that subtends a very small solid angle, a vertical sidewall inside a feature sees almost nothing. The cosine of the incidence angle on a wall parallel to the flight direction is zero, so the sidewall coverage of an evaporated film is not merely poor — it is close to nil, with whatever small amount does appear coming from the finite angular width of the source and from adatom surface diffusion after landing. A trench receives a film on its floor and a film on the field above it, and the two are not connected. For anyone whose mental model of deposition was formed on conformal processes, the failure mode is startling the first time it is measured: continuity checks pass on blanket monitors and fail catastrophically on patterned product. The quantitative treatment of that behaviour belongs to the step coverage and conformality discussions rather than here, but the physical cause sits entirely in the transport geometry described above.

The same property that disqualifies evaporation from interconnect makes it the only sensible choice for lift-off, and lift-off is why evaporators are still bought. Pattern a resist with a deliberate re-entrant undercut, evaporate metal, and the directional flux deposits a clean film in the exposed openings and a separate film on the resist top surface, with a genuine physical discontinuity at the undercut because nothing reaches into the shadow. Dissolving the resist floats the unwanted metal away and leaves patterned features with edges defined by the lithography rather than by an etch. There is no plasma exposure, no halogen chemistry, and no etch selectivity requirement, which matters enormously for material systems that cannot be etched cleanly at all — gold, platinum, refractory contacts to III-V, and the superconducting aluminium and niobium layers used in quantum devices. Shadow evaporation takes the idea further still: by evaporating the same material twice at two different substrate tilt angles through a single suspended resist bridge, two overlapping films can be laid down with a controlled oxide grown between them, which is how Josephson junctions for superconducting qubits are actually fabricated. That process is not a niche curiosity; it is the manufacturing basis of an entire class of quantum computing hardware, and it exists only because evaporation refuses to go around corners.

Rate and purity round out the picture. Evaporation deposits fast — hundreds of nanometres per minute is routine, several micrometres per minute is achievable with electron-beam power on aluminium — because there is no rate-limiting surface reaction and no working-gas collision loss between source and wafer. Arriving atoms carry only their thermal energy, a few tenths of an electron volt, which is orders of magnitude below the tens of electron volts a sputtered atom brings. That gentleness is a genuine advantage on damage-sensitive substrates and organic layers, and simultaneously the reason evaporated films are less dense, more columnar, and more prone to tensile stress and porosity than sputtered films of the same material: there is no energetic bombardment available to knock adatoms into their lowest-energy sites. Raising substrate temperature or adding a separate ion source recovers density, at the cost of the low-damage advantage that motivated the choice.

The practical decision in a modern fab therefore comes down to a short list. If the film must cover topography, evaporation is disqualified before any other consideration is evaluated. If the film must be patterned in a material that has no clean etch, evaporation with lift-off is likely the only route. If the substrate cannot tolerate plasma or energetic ions, evaporation is the gentlest option available. If throughput on a thick, flat, unpatterned metal layer is what matters, evaporation is usually the cheapest way to move mass. Everything else — the vacuum requirement and chamber base pressure that make collisionless flight possible in the first place, the choice between resistive and electron-beam heating of the charge, the compositional consequences of evaporating an alloy, and the collimation tricks that give sputtering a partial imitation of directional flux — is treated in its own place, because each is a substantial subject and none of them changes the geometric core described here.

The Hertz-Knudsen relation connects source temperature to evaporation flux. For a surface with equilibrium vapor pressure $P_v(T)$, the molecular flux leaving toward a lower ambient partial pressure $P$ can be written $J=\alpha(P_v-P)/\sqrt{2\pi m k_BT}$, where $m$ is molecular mass and $\alpha$ is an evaporation coefficient. The exponential temperature dependence hidden in $P_v$ makes source temperature the dominant rate lever. A small thermal change can cause a large flux change, especially near practical operating temperatures. The equation describes the emitting surface, not the wafer rate: transport solid angle, source depletion, crucible geometry, fixture interception, sticking, and QCM location still intervene. Treating beam power as flux ignores all of these transfer functions.

Vapor pressure determines whether a material is practical to evaporate. A useful source must reach enough vapor pressure to deliver the desired mass flux without melting, decomposing, reacting with its container, or overwhelming the chamber. Elements span many orders of magnitude in vapor pressure at the same temperature. Refractory metals demand electron-beam heating or specialized sources, while zinc, magnesium, and other volatile species can escape readily and contaminate shields. Compounds may dissociate rather than evaporate congruently. Published vapor-pressure curves are starting points; actual charge form, oxide skin, alloy state, source geometry, and temperature measurement decide the operating point.

Source temperature is often inferred indirectly and can be spatially nonuniform. A resistive boat has hot spots set by current density, contact, fill, and radiative loss. An electron beam creates a localized molten pool whose temperature varies with beam sweep and skull geometry. Optical pyrometry requires emissivity and line of sight and may see the crucible rather than the charge. Electrical power includes conduction and radiation losses that change as the source wets or depletes. Rate feedback from a QCM is therefore usually more actionable than a nominal temperature, but QCM latency and geometry mean it cannot diagnose every local source instability.

The source state evolves throughout a run. Fresh pellets can outgas, crack oxide skins, rearrange, or suddenly wet the liner. A molten pool changes depth and emitting area; a resistive charge creeps along a boat; an e-beam hearth forms a skull and exposes new facets. Depletion changes the view factor and can uncover the crucible, adding contamination or changing emission. Ramp, soak, shuttered preconditioning, stable-rate qualification, and remaining-charge limits are part of the recipe. Matching only the initial rate does not guarantee identical late-run flux or particle behavior.

Substrate incidence adds a second cosine that creates feature shadowing. A surface tilted from the arriving ray sees reduced projected flux proportional to $\cos\theta_w$. A vertical sidewall parallel to a narrow beam ideally receives none. Pattern edges, resist overhangs, trench mouths, and particles cast geometric shadows whose length scales with height and tangent of incidence angle. Surface diffusion can soften the boundary, and source size supplies a penumbra, but neither creates conformality. Blanket thickness cannot establish continuity over a step because the local incidence distribution is entirely different.

Rotation averages azimuthal asymmetry but not every radial error. Single-axis rotation removes dependence on wafer azimuth when source and fixture remain stable, yet a point at fixed radius continues to sample the same family of distances and polar angles. Planetary motion adds rotation about a second axis, allowing each substrate to sample more of the source lobe. Speed matters mainly through averaging over source fluctuation and shutter transients; once many cycles occur, geometry dominates. Rotation cannot illuminate a permanently hidden surface or correct a source-centered radial gradient by itself.

A spherical calotte converts geometry into uniformity by construction. When source and receiving elements share the appropriate sphere, source and substrate cosines can cancel the chord-length dependence for ideal cosine emission. Real fixtures depart because wafers are finite flat surfaces, the source is extended, pocket depth varies, and the emission lobe changes with charge. Dome radius and source position should therefore be verified by maps rather than trusted from mechanical drawings. Fixture sag, deposition buildup, pocket replacement, and source-height changes can produce repeatable map drift.

Planetary fixtures introduce mechanical variables into a vacuum process. Gear backlash, bearing wear, missed rotation, thermal expansion, particle generation, and synchronization determine whether geometric averaging occurs. A stopped planet can leave a distinct one-sided gradient even when chamber-center monitors look normal. Rotation telemetry, witness placement, and map harmonics can diagnose the failure. Coating buildup changes balance and clearances; cleaning can change pocket seating. Preventive maintenance should track motion quality and geometry, not merely hours of operation.

Uniformity should be decomposed into source, fixture, and wafer-incidence contributions. A chamber-wide polar trend points to emission or source location; repeated pocket offsets point to fixture geometry; within-wafer dipoles suggest tilt or stopped rotation; local shadows indicate clips or contamination. Normalizing maps to mean thickness reveals shape but removes utilization information, so absolute rate and total captured mass should be retained. Comparing multiple materials can separate geometric signatures from material-specific sticking or re-evaporation. A tooling factor that repairs the center value does not repair a changed map shape.

Material utilization is a system metric, not merely source efficiency. Useful mass is the amount landing on accepted product. The remainder coats shields, fixtures, chamber walls, shutters, QCM heads, or pump-facing surfaces. Long throw, small wafers, wide emission, and large edge exclusion reduce utilization. Thick shield deposition increases clean frequency and flake risk. A geometry that improves uniformity by discarding most material may still be correct for precious thin films but expensive for thick coatings. Cost, uptime, source refill, waste handling, and shield lifetime belong in the process trade.

Elemental evaporation is easiest because the vapor and solid share one composition. Even then, oxide skin, source-container reaction, and volatile impurities can create transients. High-purity charge does not guarantee a high-purity film if the hearth, liner, filament, clips, shields, and residual gas contribute material. Each source configuration has compatible and incompatible materials. A crucible that is inert for Au may alloy with Al or be attacked by Ti. Source qualification should include blank runs, film chemistry, and inspection of the spent charge and liner.

Alloys can fractionate because components have different vapor pressures. The vapor composition above a molten alloy depends on activities and component vapor pressures, and the more volatile species can be enriched early while the remaining charge evolves. A single premixed pellet therefore may not produce constant film composition through the run. Pool mixing, source temperature, charge depth, evaporation fraction, and refill practice matter. Multiple independent sources with calibrated flux can control composition more directly, but line-of-sight differences create spatial gradients. Composition should be mapped versus wafer position and run time, not inferred from starting charge.

Compounds may dissociate or evaporate incongruently. Oxides, nitrides, chalcogenides, and organics can release different molecular species, lose a volatile component, or change oxidation state. Reactive evaporation introduces oxygen or nitrogen to restore stoichiometry, but added gas shortens mean free path and changes source chemistry. Co-evaporation can compensate volatility but requires independent rate and composition control. A stable total QCM rate cannot reveal a drifting stoichiometric ratio. Optical emission, mass spectrometry, separate QCMs, in-situ spectroscopy, and ex-situ compositional measurements constrain different parts of the problem.

Co-evaporation makes composition a ratio of spatially varying fluxes. If sources A and B occupy different chamber locations, each produces its own wafer map $F_A(x,y)$ and $F_B(x,y)$; local composition follows their ratio, not their mean rates. Rotation can average azimuthal variation but may leave radial composition. Separate tooling factors are required. Source cross-talk, mutual heating, and shutter sequencing create additional transients. Calibrating each source alone is necessary but not sufficient because simultaneous operation can change pressure and thermal state.

Reactive evaporation balances incorporation against gas exposure. Introducing oxygen can convert evaporated metal into an oxide at the substrate, within the vapor, or on the source. Too little produces oxygen deficiency; too much oxidizes the source, changes its rate, and increases scattering. Plasma assistance can activate reactants at lower pressure but introduces ion damage and shifts the method toward ion-assisted deposition. Partial pressure, activation, substrate temperature, and metal flux should be mapped against phase, stoichiometry, optical properties, and stress rather than tuned to one refractive index.

Isotope and molecular form can affect the vapor species without changing QCM mass logic. Some materials leave as atoms; others form dimers or molecular fragments. Gas-phase association, dissociation, and source reaction affect sticking and composition, while the QCM ultimately senses coupled deposited mass. Residual-gas mass spectra must distinguish evaporant fragments from chamber background and ionizer fragmentation. This is especially important when a source produces a volatile suboxide or chalcogen molecule rather than the nominal bulk formula.

Substrate heating has several sources beyond an intentional heater. Radiant energy from a hot source, electron and X-ray emission from an e-beam gun, condensation energy, fixture conduction, and long deposition time raise wafer temperature. Resist softening can collapse lift-off profiles; polymers outgas; interdiffusion and stress change. A backside thermocouple may not represent the wafer surface or small chips. Temperature-sensitive labels, calibrated witness structures, pyrometry, or embedded sensors can bound the real excursion. Rate increases may shorten exposure even while raising instantaneous radiation.

Radiation damage is source specific and must not be confused with particle energy. Evaporated atoms are gentle, but an electron-beam source can generate X-rays, secondary electrons, ions, and reflected electrons that charge or damage sensitive dielectrics. Resistive evaporation avoids the electron beam but may require contact with a hot boat and can introduce container impurities. Ion-assisted deposition intentionally adds energetic species. Device-threshold shifts, oxide leakage, charge monitors, and shield splits identify radiation mechanisms more directly than film morphology.

Spitting produces droplets rather than a smooth vapor flux. Trapped gas, moisture, oxide rupture, rapid heating, beam drilling, and unstable molten pools can eject liquid or solid fragments. Droplets form raised metal defects with composition matching the source and often appear during ramp or near charge edges. Slow degas, shuttered soak, appropriate pellet packing, beam sweep, clean charge, and avoiding pool-wall impact mitigate the mechanism. Raising filtration or cleaning frequency downstream does not prevent source spitting.

Particles can originate before, during, or after deposition. Pre-existing substrate particles create shadow cones and nodules; source droplets land during deposition; fixture flakes fall from accumulated coating; resist-top film fragments during lift-off; stressed shield films shed later. Defect height, shape, composition, film coverage, map, and lot timing distinguish them. A particle counter total without classification can mix unrelated populations. Shield mass and clean interval should be correlated with flake signatures, while source event logs should be correlated with droplets.

Shadow defects amplify the effect of tiny contaminants. A particle blocks the narrow incident cone and leaves an uncoated wake whose lateral size grows with particle height and source angle. Rotation can turn a single shadow into a halo or annulus. In multilayers, an early shadow propagates through later films and can cause opens or pinholes. Patterned functional tests are often more sensitive than optical counts because a small bare region can sever a line. Cleanliness requirements should therefore be derived from source directionality and critical feature size.

Chamber shields are consumables with mechanical memory. Each run adds film with its own stress, thermal expansion, adhesion, and composition. Multilayer stacks on shields can curl, crack, and delaminate even if each product film is sound on the wafer. Line-of-sight gaps expose chamber walls; poor shield overlap creates particle traps. Cleaning can roughen surfaces or leave chemistry that changes adhesion. Shield kits should have controlled material, texture, installation torque, accumulated thickness, and replacement history.

Cross-contamination follows both vapor trajectories and thermal history. A volatile residue on a shield may re-evaporate when heated by a later source. Uncovered crucible material, shared liners, shutter deposits, and source pockets contribute memory. Base-pressure RGA may miss contamination released only at process temperature. Blank witness wafers, source-only heating tests, and film-specific SIMS or XPS can localize memory. Dedicated hardware is justified when trace contaminants dominate contact, optical, magnetic, or superconducting performance.

Optical films require control of index, absorption, and thickness together. Porosity, stoichiometry, and microstructure change refractive index independently of physical thickness. Multilayer interference amplifies small layer errors, and angular distribution across curved optics creates both thickness and incidence effects. Broadband spectral fitting can separate some parameters but is model dependent. Calibrated witness optics, ellipsometry, XRR, and stress measurements should be tied to fixture location. A QCM endpoint alone cannot certify optical performance.

Electrical films require continuity and interface control before bulk resistivity models apply. Below percolation, sheet resistance reflects disconnected islands and tunneling; after closure, surface and grain-boundary scattering elevate resistivity above bulk. Contact resistance may be dominated by native oxide or pretreatment rather than metal thickness. Four-point sheet resistance, transfer-length structures, Kelvin contacts, and thickness series distinguish these regimes. Entering bulk density and bulk resistivity into a monitor does not make the deposited film bulk-like.

Magnetic and superconducting films are unusually sensitive to trace process history. Oxygen, hydrogen, magnetic contamination, grain boundaries, texture, stress, and interface roughness can change coercivity, critical temperature, loss, and junction behavior. A deposition that passes thickness and composition can still fail microwave loss or critical-current distribution. Dedicated source liners, vacuum transfer, controlled oxidation, magnetic cleanliness, and low-particle lift-off become part of the material specification. Functional cryogenic or magnetic testing must close the loop.

A robust qualification matrix separates transport, source, surface, and metrology axes. Throw, fixture orientation, and rotation test geometry; source power, charge state, and rate test emission; base and deposition pressure plus RGA test gas environment; pretreatment and queue test nucleation; QCM position, density, and tooling factor test measurement. Change one physical axis at a time while holding deposited mass and thermal exposure as consistently as possible. Correlated maps and thickness series reveal mechanism more reliably than a large recipe-screen with coupled changes.

A practical diagnostic begins by deciding whether the failure is mass, geometry, composition, interface, or defect tail. Mean-thickness error with stable map points toward QCM calibration or endpoint; map-shape change points toward source and fixture; composition drift points toward fractionation or reaction; opens on pattern but not blanket point toward shadowing and continuity; particles demand morphology and timing. Every proposed mechanism should predict at least two independent signatures. Recipe changes should follow the evidence branch rather than precede it.

problem=>start: Evaporated-film result is out of specification
qcm=>condition: Did raw QCM frequency and actuator traces behave normally?
sensor=>operation: Check crystal health, cooling, density, tooling factor and shutter timing
mean=>condition: Is wafer areal mass or mean physical thickness wrong?
source=>operation: Inspect charge state, vapor flux, pressure burst, source depletion and emission lobe
map=>condition: Did the spatial map shape change?
fixture=>operation: Check source position, dome geometry, rotation, pocket seating, clips and shields
chem=>condition: Are composition, phase or interface wrong?
material=>operation: Test fractionation, dissociation, residual gas, crucible reaction and pretreatment queue
pattern=>condition: Does blanket pass while patterned product fails?
shadow=>operation: Inspect incidence, undercut, sidewall continuity, particles and feature orientation
tail=>operation: Classify droplets, flakes, nodules and adhesion failures by SEM/EDS and timing
close=>end: Change one physical lever and repeat matched witnesses
problem->qcm
qcm(no)->sensor->mean
qcm(yes)->mean
mean(yes)->source->map
mean(no)->map
map(yes)->fixture->chem
map(no)->chem
chem(yes)->material->pattern
chem(no)->pattern
pattern(yes)->shadow->tail
pattern(no)->tail->close

Evaporation should be chosen for the integration advantage it uniquely provides. Directionality enables lift-off and shadow-defined overlap; low arriving-particle energy protects delicate surfaces; high material flux makes thick blanket coatings efficient; absence of working gas preserves ballistic transport. Those advantages are inseparable from poor sidewall coverage, low utilization at long throw, source and composition complexity, and sensitivity to fixture geometry. Comparing evaporation with sputtering, CVD, and ALD should begin with required topology and damage budget, not with nominal rate.

The handoff must preserve geometry and calibration as controlled process state. Record source pocket and charge lot, liner or boat, source height and remaining mass, shutter and QCM geometry, dome and planetary configuration, wafer pocket, rotation telemetry, base and deposition pressure, RGA state, pretreatment queue, rate trace, tooling factor provenance, and shield age. Archive wafer thickness, composition, stress, resistance, and defect maps in the same coordinates. Without that record, a recipe file cannot reproduce the actual view factor or source condition.

The central physical chain is testable from source to function. Hertz and Knudsen connect vapor pressure and molecular emission; the cosine law and view factors connect source to wafer; Sauerbrey connects resonator shift to local areal mass; film-growth physics connects arrivals to continuity, density, stress, and properties; Dolan-style shadow geometry converts directionality into patterned overlap. Each link has a measurable state and known limits. A strong process model exposes those links rather than hiding them behind source power and nominal thickness.

Read evaporation deposition through a vapor-pressure, molecular-flow, emission-view-factor, fixture-motion, mass-calibration, composition-evolution, interface-growth, and defect-signature lens rather than a heat-source-and-thickness lens.