Ionized PVD Physics
I-PVD combines conventional sputtering with high-density inductively coupled plasma (ICP) to ionize sputtered metal atoms. Ionized metal flux enables directional deposition into high aspect ratio features with improved bottom coverage.
Metal Ionization Fraction
α = N_M⁺ / (N_M + N_M⁺)
α: ionization fraction
N_M⁺: ionized metal density
N_M: neutral metal density
Ionization requires:
1. High electron density (n_e > 10¹² cm⁻³)
2. High electron temperature (T_e > 3-5 eV)
3. Sufficient residence time in plasma
Typical α values:
Cu at 5 kW RF: α ≈ 30-50%
Al at 5 kW RF: α ≈ 20-40%
Ta at 5 kW RF: α ≈ 40-60%
Higher ionization → better bottom fill
Ionization Rate Coefficient
Metal ionization:
e⁻ + M → M⁺ + 2e⁻
Rate coefficient:
k_ion = <σv> ≈ 10⁻⁷ - 10⁻⁸ cm³/s
(for T_e = 3-5 eV)
Ionization rate:
R_ion = k_ion × n_e × N_M
Ionization time:
τ_ion = 1 / (k_ion × n_e)
For n_e = 5×10¹² cm⁻³:
τ_ion ≈ 2-20 μs
Require transit time > τ_ion
→ Need high pressure, tall plasma zone
ICP Discharge Physics
Inductively Coupled Plasma:
RF coil → time-varying magnetic field
∇ × E = -∂B/∂t (Faraday's law)
→ Azimuthal electric field
→ Electron heating
Skin depth:
δ = c / ω_pe ≈ 1-3 cm
(for n_e = 10¹² cm⁻³)
Power absorption:
P_abs ∝ n_e × ν_m × E_RF²
ν_m: collision frequency
Plasma density scaling:
n_e ∝ P_RF^α × P_Ar^β
α ≈ 0.5-0.7
β ≈ 0.3-0.5
Higher RF power → higher n_e → more ionization
Metal Transport and Ionization Path
Sputtered metal path:
1. Ejection from target (E ≈ 5-10 eV)
2. Thermalization in Ar (if P > 5 mTorr)
3. Diffusion through plasma zone
4. Ionization by electron impact
5. Ion acceleration in sheath
6. Deposition on substrate
Mean free path:
λ_M-Ar ≈ 0.5 cm at 10 mTorr
Diffusion length:
L_diff = √(D × τ_res)
D = kT / (m × ν_M-Ar)
Require L_diff > plasma zone height
for efficient ionization
Substrate Bias and Ion Energy
DC bias develops at substrate:
V_bias ∝ P_bias / A_substrate
Ion energy at substrate:
E_M⁺ = e × (V_plasma - V_bias)
E_M⁺ ≈ 10-100 eV (typical)
Directionality:
Ions accelerated normal to substrate
→ Bottom-up fill of vias/trenches
Neutral metals:
E_M ≈ 0.1-1 eV (thermal)
→ Isotropic deposition
→ Pinch-off at feature opening
High α (ionization) essential
for void-free fill
Bottom Coverage in High-AR Features
Step coverage:
S = d_bottom / d_top
For neutrals (cosine law):
S_neutral ≈ 1 / (AR + 1)
Poor for AR > 3
For ionized flux:
S_ion ≈ α + (1-α) / (AR + 1)
Example AR = 5:
α = 0%: S = 17% (pinch-off)
α = 50%: S = 58% (partial fill)
α = 80%: S = 83% (good fill)
Require α > 60-70%
for AR > 5 features
Collisional Effects on Directionality
Ion scattering in sheath:
λ_i-Ar = 1 / (n_Ar × σ_i-Ar)
Sheath thickness:
s ≈ 1-3 mm (typical)
At 10 mTorr:
λ_i-Ar ≈ 1-2 cm
If s < λ_i-Ar:
Ions cross sheath without collision
→ Highly directional
If s > λ_i-Ar:
Scattering → angular spread
→ Reduced directionality
Optimal: 5-15 mTorr
Balance ionization vs scattering
Re-sputtering and Re-emission
Metal ion bombardment:
E_M⁺ = 10-100 eV
Sputter yield:
Y(Cu⁺ → Cu) ≈ 0.1-0.5
(self-sputtering)
Re-emission coefficient:
β = atoms re-emitted / atoms arriving
β ≈ Y × (1 - s)
s: sticking probability
For Cu at 50 eV:
Y ≈ 0.2, s ≈ 0.9
β ≈ 0.02 (low)
Sidewall cleaning:
High E_M⁺ removes overhang
→ Improved profile control
Plasma Potential and Sheath Structure
ICP plasma potential:
V_plasma = V_float + kT_e / e × ln(√(M_i / m_e))
For Ar, T_e = 4 eV:
V_plasma ≈ V_float + 17 V
Sheath voltage:
V_sheath = V_plasma - V_substrate
With RF bias:
V_sheath(t) = V_DC + V_RF sin(ωt)
Ion energy distribution:
Bimodal IEDF for RF bias
Monoenergetic for DC bias
Pulsed bias:
Separate ionization & deposition
→ Better control
Metal-to-Argon Ratio Optimization
Metal flux density:
Γ_M = sputter rate × area / volume
Ar density:
n_Ar = P / kT ≈ 10¹⁴ cm⁻³ at 10 mTorr
Metal density (steady-state):
n_M ≈ Γ_M × τ_res / L
τ_res: residence time
L: chamber height
Typical n_M / n_Ar ≈ 10⁻⁴ - 10⁻³
Too low n_M: wasted Ar ionization
Too high n_M: insufficient ionization
Optimal M/Ar loading factor
depends on τ_ion and pump speed
Magnetic Field Enhancement
External magnetic field:
B = 10-100 Gauss (axial)
Electron confinement:
r_ce = m_e v_e / (e B)
For B = 50 G, T_e = 4 eV:
r_ce ≈ 2 mm
Effects:
• Increased n_e near axis
• Reduced wall losses
• Enhanced ionization efficiency
BUT:
• Non-uniform plasma
• E×B drifts
• Increased complexity
Often not used in production
Deposition Rate vs Ionization Trade-off
Total flux:
Γ_total = Γ_neutral + Γ_ion
Higher RF power:
+ Increases α (ionization)
+ Improves bottom fill
- Reduces Γ_neutral (re-sputtering)
- Lower total rate
Optimization:
Maximize α × Γ_total
Typical trade-off:
Standard PVD: α=0%, R=100 Å/s
I-PVD low: α=30%, R=70 Å/s
I-PVD high: α=70%, R=40 Å/s
Choose based on AR requirement
Process Window for Via Fill
Requirements for AR=5 via:
1. Ionization: α > 60%
→ P_RF > 3-5 kW
2. Ion energy: 20 < E_M⁺ < 80 eV
→ V_bias = -20 to -80 V
3. Directionality: λ_i > s
→ 5 < P < 15 mTorr
4. Rate: R > 20 Å/s
→ P_DC > 5-10 kW
5. Uniformity: σ/μ < 5%
→ Substrate rotation
Narrow process window!
Requires precise control
ICP Source Design and Optimization
Inductively coupled plasma sources require careful coil design, impedance matching, and power coupling optimization to achieve high plasma density with good uniformity.
ICP coil configurations:
Planar coil (spiral):
• Simple design
• Good for small areas
• Axial non-uniformity
Cylindrical coil (solenoid):
• Better uniformity
• Requires taller chamber
• Complex field pattern
Multi-turn coil:
N = 3-10 turns typical
Inductance: L ∝ N²
Resistance: R ∝ N
Coil-plasma coupling:
M = k × √(L_coil × L_plasma)
k: coupling coefficient (0.1-0.5)
Plasma inductance:
L_plasma ∝ 1 / n_e
Decreases with density
Power transfer efficiency:
η = R_plasma / (R_coil + R_plasma)
R_plasma >> R_coil desired
η ≈ 0.6-0.8 (typical)
Coil cooling:
Water-cooled copper tubing
Flow: 2-5 L/min
ΔT < 30°C
Dielectric window:
Material: quartz, Al₂O₃, AlN
Thickness: 10-25 mm
Coating resistance needed
Faraday shield (optional):
Reduces capacitive coupling
Slotted metal screen
Complicates inductive coupling
Metal Vapor Transport and Ionization
Understanding the transport and ionization of sputtered metal atoms is crucial for optimizing I-PVD. The residence time in the high-density plasma region determines ionization probability.
Metal atom trajectory:
Initial velocity (thermal):
v₀ = √(2 × E_sputter / M_metal)
E_sputter ≈ 5-10 eV
For Cu (M = 64 amu):
v₀ ≈ 10⁴ m/s
Thermalization distance:
λ_th = v₀ / ν_M-Ar
ν_M-Ar: collision frequency
At 10 mTorr:
λ_th ≈ 1-5 cm
Diffusion after thermalization:
D = kT / (M × ν_M-Ar)
Diffusion length:
L_diff = √(D × τ_res)
τ_res: residence time
For optimal ionization:
L_diff > L_plasma
Metal must traverse plasma zone
Ionization probability:
P_ion = 1 - exp(-k_ion × n_e × τ_res)
For n_e = 5×10¹² cm⁻³:
k_ion ≈ 10⁻⁷ cm³/s
τ_res ≈ 10-50 μs
P_ion ≈ 0.3-0.7 (30-70%)
Metal density in plasma:
n_M = Γ_sputter × τ_res / V_plasma
n_M / n_Ar ≈ 10⁻⁴ - 10⁻³
Via Fill Metallization Mechanisms
Bottom-up fill of high aspect ratio features requires understanding the balance between neutral and ionized flux, sidewall scattering, and re-sputtering effects.
Via fill mechanisms:
1. Direct ion bombardment (bottom):
Γ_ion,bottom = Γ_ion,total × cos(θ)
θ ≈ 0° for ions (directional)
2. Neutral deposition (isotropic):
Γ_neutral = Γ₀ × cos^n(θ) / d²
n ≈ 1 (cosine law)
Hits sidewalls → pinch-off risk
3. Re-sputtering from bottom:
Y_re × Γ_ion,bottom
Y_re ≈ 0.1-0.3 (self-sputter)
Cleans overhang
4. Sidewall scattering:
Reduces directionality
Depends on P × L_sheath
Net bottom fill rate:
R_bottom = (1 - Y_re) × Γ_ion,bottom + Γ_neutral,bottom
Pinch-off condition:
R_sidewall / R_bottom > AR / 2
Void-free fill requires:
• High ionization (α > 60%)
• Moderate bias (E_ion = 20-80 eV)
• Optimal pressure (5-15 mTorr)
• Re-sputtering to clear overhang
Advanced techniques:
• Pulsed bias (separate fill/clean)
• Temperature ramping
• Multi-step deposition
• Liner + seed + fill
Plasma Modeling and Simulation
Computational modeling of I-PVD systems employs fluid, kinetic, and hybrid approaches to predict plasma parameters and optimize reactor design.
Modeling approaches:
1. Global (0D) models:
• Particle/power balance
• No spatial resolution
• Fast, approximate
• Parameter scaling laws
2. Fluid (2D/3D) models:
• Continuity equations
• Momentum balance
• Energy balance
• Spatial profiles
• Assumes Maxwellian EEDF
3. Kinetic (PIC/MCC):
• Particle-in-cell
• Monte Carlo collisions
• Non-Maxwellian EEDF
• Computationally expensive
• High accuracy
4. Hybrid models:
• Fluid for bulk plasma
• Kinetic for sheaths
• Balance accuracy vs speed
Key outputs:
• n_e(r, z): density profile
• T_e(r, z): temperature profile
• V_plasma(r, z): potential
• IEDF: ion energy distribution
• Power absorption
Validation:
• Langmuir probe data
• OES measurements
• Deposition profiles
• Compare multiple diagnostics
Design optimization:
• Coil geometry
• Gas injection
• Magnetic field
• Bias frequency
Advanced I-PVD Configurations
Modern I-PVD systems employ sophisticated configurations including pulsed power, dual-frequency operation, and hybrid approaches to expand process capabilities.
Pulsed I-PVD:
DC power pulsing:
f_pulse = 10-100 kHz
Duty cycle: 50-90%
Peak power: 2-3× average
Benefits:
• Reduced arcing on insulators
• Better target utilization
• Cooler substrate
• Improved film quality
RF power pulsing:
Sync with DC or independent
Control ion/electron ratio
Optimize ionization efficiency
Bias pulsing:
Separate deposition/etch cycles
Clear overhang periodically
Improve bottom fill
Dual-freq RF (LF + HF):
LF (400 kHz): ion energy control
HF (13.56 MHz): density control
Independent knobs for process
Hollow cathode magnetron (HCM):
Enhanced ionization near target
Higher plasma density
Better target utilization
Hybrid I-PVD + CVD:
I-PVD seed layer
CVD fill
Best of both worlds
Self-ionized PVD (Si-PVD):
No external ICP
High-power magnetron
Self-sustaining ionization
α ≈ 20-40% (lower than I-PVD)
Metrology and Process Qualification
Comprehensive metrology is essential for qualifying I-PVD processes and ensuring production-worthy performance across all metrics.
Thickness measurements:
• 4-point probe (sheet resistance)
• XRF (X-ray fluorescence)
• Ellipsometry (optical)
• Cross-section SEM/TEM
Sheet resistance:
R_s = ρ / d
For Cu film:
ρ_bulk = 1.7 μΩ·cm
d = 100 nm
R_s ≈ 0.17 Ω/sq
Grain size analysis:
• Plan-view TEM
• EBSD (orientation)
• AFM (surface topology)
Via fill qualification:
• Cross-section SEM
• FIB (focused ion beam) prep
• Look for voids, seams
Acceptance criteria:
• No voids > 5% of via area
• Continuous bottom coverage
• Smooth sidewall profile
Electrical testing:
• Via chain resistance
• Electromigration lifetime
• Time-dependent dielectric breakdown
Reliability metrics:
MTTF > 10 years at use conditions
σ_stress < 200 MPa (compressive)
Hillock density < 0.01 cm⁻²
Process window:
Map all critical parameters
Define center point + tolerance
Cpk > 1.67 for production
Yield learning:
• Defect pareto analysis
• SPC (statistical process control)
• DOE (design of experiments)
• Continuous improvement
Process Integration and Future Trends
Advanced process integration combines multiple deposition techniques for optimal device performance.
Integration strategies:
• Multi-chamber cluster tools
• Sequential processing without vacuum break
• In-situ surface preparation
• Real-time endpoint detection
Future directions:
• Atomic layer control (ALD-like precision)
• Machine learning process optimization
• Digital twin modeling
• Autonomous process control
Equipment trends:
• Larger substrate sizes (450 mm)
• Higher throughput (> 100 WPH)
• Lower cost of ownership
• Improved particle performance
• Extended mean time between cleans
• Predictive maintenance algorithms
Application expansion:
• Advanced packaging (TSV, RDL)
• 3D NAND metallization
• MRAM and emerging memories
• Power devices (GaN, SiC)
Ionization Fraction vs RF Power
Via Fill Profile Evolution
Deposition Rate Trade-off