Ionized Physical Vapor Deposition (I-PVD) Simulation

Advanced PVD: High-density plasma ionization of sputtered metal flux for bottom-fill of trenches and vias with ionized metal species

10 kW
5 kW
10 mTorr
100 W
15 cm
1.0×
Cu
5:1

Metal Ion Fraction

0%

Plasma Density

0.0×10¹² cm⁻³

Bottom Coverage

0%

Sidewall Angle

0°

Deposition Rate

0.0Å/s

Ion Energy

0eV

3D I-PVD Chamber with ICP Ionization Zone

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

Plasma Density Profile

Via Fill Profile Evolution

Ion Energy Distribution

Bottom Coverage vs AR

Deposition Rate Trade-off

Process Window Map