RIE LAG & ARDE Simulator

Watch multiple trenches etch at different rates based on aspect ratio. Observe Knudsen transport, neutral shadowing, and microloading effects in real-time 3D animation.

Auto-Running Multi-Trench Simulation

The simulation starts automatically, showing trenches with AR from 1:1 to 50:1 etching simultaneously. Particle system shows radical diffusion into high aspect ratio features.

Process Parameters

Elapsed Time

0
seconds

Shallow Depth (AR=1)

0.0
μm

Deep Depth (AR=50)

0.0
μm

Lag Factor

1.00
(deep/shallow)

Knudsen Number

0.0
(deep trench)

Neutral Flux Ratio

100
% (deep/shallow)

Microloading Effect

0
% reduction

Transport Regime

Continuum

3D Multi-Trench Array with Particle Transport

RIE LAG & ARDE Physics

Knudsen Number and Transport Regimes

The Knudsen number determines transport mechanisms:

Knudsen number: Kn = λ_mfp / D_trench λ_mfp: Mean free path ≈ 5×10⁻³ cm / P(mTorr) at 300K D_trench: Trench diameter/width Transport regimes: Kn < 0.01: Continuum (viscous flow) - Collisions dominate - Bulk gas transport - Pressure-driven flow 0.01 < Kn < 10: Transition - Mixed regime - Both mechanisms Kn > 10: Molecular (Knudsen diffusion) - Collision-free - Ballistic transport - Geometric shadowing dominates

Gotoh ARDE Model

Empirical model for aspect ratio dependent etching:

R(AR) = R₀ / (1 + K × AR^n) Where: R(AR): Etch rate at aspect ratio AR R₀: Etch rate for shallow/open areas AR: Aspect ratio = depth / width K: ARDE coefficient (0.1-0.3 typical) n: Exponent (1-2, typically 1.5) Physical interpretation: K and n depend on: - Pressure (lower P → higher K) - Sticking coefficient - Neutral/ion ratio - Reaction probability At high AR: R(AR) → R₀/(K × AR^n) ~ 1/AR^n Etch slows dramatically

Neutral Transport Limitation

Radical flux decreases with depth:

Concentration at depth z: C(z) = C₀ × exp(-z / λ_diff) λ_diff: Diffusion length λ_diff = D_trench × √(D / k_rxn) D: Diffusion coefficient k_rxn: Surface reaction rate For molecular regime (high Kn): Flux ~ solid angle = Ω / 4π Ω decreases with depth Angular distribution: F(θ) = F₀ × cos(θ) Trenches see reduced effective flux Neutral shadowing: Fraction reaching bottom ~ (D/depth)² Strong AR dependence

Ion Shadowing and Beam Divergence

Ion angular distribution limits deep etch:

Ion angular distribution: f(θ) ~ exp(-θ² / 2σ²) σ: Angular spread ≈ 2-5° typical Maximum etchable AR: AR_max ≈ 1 / (2 × tan(σ)) For σ = 3°: AR_max ≈ 10 Beyond AR_max: Ions hit sidewalls, not bottom Sidewall damage, no bottom etch Sheath collisions increase σ: High pressure → more collisions → larger σ Lower AR_max at high P

Microloading Effect

Local pattern density affects etch rate:

Microloading: R_local = R_global × (1 - β × ρ_local) ρ_local: Local open area fraction (0-1) β: Microloading coefficient (0.2-0.5) Physical mechanism: Dense patterns → more trenches competing Local reactant depletion Byproduct accumulation Scale lengths: Local: < 100 μm (diffusion) Global: Wafer-scale (mm-cm) Mitigation: - Higher pressure (shorter λ_mfp) - Dummy fills - Local gas injection - Temperature control

Reaction-Diffusion Competition

Balance between transport and reaction:

Damköhler number: Da = k_rxn × L / D Da << 1: Reaction-limited - Slow surface reaction - Good transport - Uniform profiles Da >> 1: Diffusion-limited - Fast reaction - Poor transport into trenches - Strong ARDE Optimization: Want Da ≈ 1 for balance Adjust T, P, chemistry Trade rate vs uniformity

Pressure Dependence

Pressure dramatically affects LAG:

Low pressure (2-5 mTorr): - Long λ_mfp (> 1 cm) - Kn > 10 (molecular) - Severe neutral shadowing - Strong ARDE (K large) - Better anisotropy High pressure (50-100 mTorr): - Short λ_mfp (< 1 mm) - Kn < 0.1 (continuum) - Better neutral transport - Weaker ARDE (K small) - More isotropic Optimal pressure: Balance ARDE vs anisotropy Typically 10-30 mTorr Depends on AR requirements

Sticking Coefficient Effects

Surface reaction probability affects depth penetration:

Sticking coefficient s: Probability that incident species reacts Low s (0.01-0.1): - Multiple bounces possible - Better depth penetration - Reduced ARDE - Example: F radicals on Si High s (0.5-1.0): - First surface reaction - Poor depth penetration - Strong ARDE - Example: Cl on Al Effective sticking in trenches: s_eff increases with AR Multiple wall collisions Each has probability s

Mitigation Strategies

Techniques to reduce RIE LAG:

1. Higher pressure: - Reduce Kn → continuum regime - Better neutral transport - Trade-off: Less anisotropic 2. Pulsed plasma: - ON: Generate radicals - OFF: Allow diffusion - Separates generation and transport 3. Neutral-rich chemistry: - Higher F/ion ratio - Chemical component stronger - Less AR dependence 4. Multi-step process: - Fast initial etch - Slow deep etch (higher P) - Adaptive conditions 5. Overetch compensation: - Small features: Shorter time - Large features: Longer time - CD-based recipes