Sputtering Deposition
DC magnetron sputtering of a metal target in argon: ion current, sputtered atom rate from measured yields, on-axis deposition rate, sputtered-atom energy, gas thermalisation distance and structure zone.
Al: Y(500 eV Ar⁺) = 1.05 atoms/ion, Us = 3.39 eV, ρ = 2.70 g/cm³, Tm = 933 K. The ions reach the target with ≈ the full discharge voltage.
Mostly diffusive: atoms ejected below E* = 19 eV, 72 % of the Thompson distribution, are thermalised before the substrate at 10.0 cm and reach it by diffusion through the argon. The rest arrive with part of their energy after about 2.8 collisions on average. So the deposition rate is below the collisionless value shown here, and the more so the larger the thermalised share.
On-axis deposition rate
1.866 nm/s
1120 Å/min; collisionless
Ion current to the target
0.561 A
I/(1+γ), I = P/V = 0.600 A
Sputtered atoms
3.67e+18 s⁻¹
(Iᵢ/e) Y, Y = 1.05 (500 eV table)
Thermalised before the substrate
72 %
ejected below E* = 19 eV; Thompson CDF (E/(E + U_s))²
Thermalisation distance D at the peak energy
6.3 cm
1.25 η′λ, E₀ = U_s/2 = 1.70 eV: η′ = 1.8, λ = 2.85 cm
Homologous temperature
0.51
zone 3: recrystallised grains
Model
Iᵢ = P / (V(1 + γ)); Φ = (Iᵢ/e)·Y; F = Φ / (π(a² + d²)); r = F·M / (ρ NA)
Thompson peak E₀ = Us/2; λ = kBT / (π((σs + σg)/2)² p √(1 + Ms/Mg)), σg = 0.29 nm, σs 0.30–0.45 nm
η′ = ln(vg/v₀) / ln(ν′/ν), vg/v₀ = √(kBT/E₀), ν′/ν Jeans' persistence for Mg/Ms; D = 1.25 η′λ (Westwood 1978)
E* = kBT (ν′/ν)−2d/1.25λ (D(E*) = d); thermalised share (E*/(E* + Us))²
A disk of radius a emitting uniformly with a cosine distribution, seen on axis from a parallel substrate; a real magnetron erodes a ring (racetrack), so take a as its mean radius. Every atom sticks and the film has bulk density. The rate ignores gas scattering. Westwood's D is the distance an atom ejected normal to the target travels before it slows to thermal speed (gas at 300 K); beyond it the atoms diffuse, the rate falls below this value and the profile flattens. D scales as 1/p and grows as ln E₀. Oblique ejection shortens the normal distance, and the gas-averaged persistence makes D about 25 % shorter than for a fast atom hitting gas at rest. Zones are Movchan–Demchishin by Ts/Tm; Thornton's sputtered-film zones also shift with the argon pressure. Reactive sputtering (oxides, nitrides) changes the yield and the film and isn't covered.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Measured 500 eV Ar⁺ yields, ion current P/(V(1+γ)), cosine disk on axis, sticking 1, bulk density. The rate ignores gas scattering; Westwood's thermalisation distance and the Thompson spectrum give the share that diffuses. Not reactive.
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