DC Sputtering Physics
DC magnetron sputtering uses a DC electric field to accelerate Ar⁺ ions toward a target, physically ejecting atoms that deposit on a substrate. Magnetic fields confine plasma to increase efficiency.
Sputter Yield - Sigmund Theory
Y(E) = Y₀ × (E - E_th)^n / E^m
Y: sputter yield (atoms/ion)
E: ion energy (eV)
E_th: threshold energy (10-30 eV)
n ≈ 1-2, m ≈ 1 (material dependent)
For Cu + Ar⁺ at 500 eV: Y ≈ 1.5-2.0
For Ti + Ar⁺ at 500 eV: Y ≈ 0.5-0.8
For Al + Ar⁺ at 500 eV: Y ≈ 1.0-1.3
Ion Current Density
J_ion = e × n_i × v_Bohm
v_Bohm = √(kT_e / M_i) ≈ ion sound speed
n_i: ion density in sheath (cm⁻³)
J_ion ∝ P^α × B^β (magnetron effect)
α ≈ 0.5-0.7, β ≈ 0.3-0.5
Target Erosion - Racetrack Formation
Erosion profile:
E(r) = E_max × exp(-(r - r_peak)² / (2σ_race²))
r_peak: racetrack radius (typically 0.6-0.8 × R_target)
σ_race: racetrack width
Caused by E × B drift confining plasma
Limits target utilization to 20-40%
Magnetron Plasma Confinement
Electron gyroradius: r_ce = m_e × v_e / (e × B)
For B = 400 G, r_ce ≈ 0.1 mm
E × B drift: v_drift = E × B / B²
Electrons spiral in magnetic field
Ions unmagnetized (r_ci >> system size)
Plasma density increase: n_e ∝ B^0.5
Angular Distribution - Cosine Law
Flux(θ) = Φ₀ × cos^n(θ)
θ: angle from target normal
n ≈ 1 for sputtering (true cosine)
n > 1 for evaporation (over-cosine)
Affects step coverage and uniformity
Film Composition vs Pressure
Thermalization of sputtered atoms:
λ_mfp = kT / (√2 × π × d² × P)
Low P (< 5 mTorr): Ballistic transport
→ Energy retention, dense films
High P (> 20 mTorr): Diffusive transport
→ Thermalized, porous films
Deposition Rate
R_dep = (Y × J_ion × M_target × A_target) / (ρ × e × A_substrate × d²)
M_target: atomic mass
ρ: film density
d: target-substrate distance
Typical rates: 1-10 Å/s at 500 W
Film Properties
Resistivity: ρ(d) = ρ_bulk [1 + 3λ/(8d)]
λ: electron mean free path
d: film thickness
Grain size: D_grain ∝ T_substrate^α × R_dep^(-β)
α ≈ 0.3-0.5, β ≈ 0.2-0.3
Stress: σ ∝ E_ion / (M_target × v_thermal)