300mm 웨이퍼 습식 챔버 시뮬레이터 | 반도체 세정 액막 두께 & 마랑고니 비젖음 해석기

Q: What is a 300mm wet chamber simulator?

A 300mm wet chamber simulator is an engineering software tool that models liquid chemical dispensing, rotational fluid dynamics, centrifugal radial transport, and thin-film flow behavior on a rotating 300 mm silicon semiconductor wafer during wet cleaning, etching, stripping, and rinsing processes.

Q: How does wafer spin affect liquid film transport?

Wafer spin imparts a centrifugal body force proportional to mass density, angular velocity squared (omega^2), and radius. This centrifugal acceleration drives liquid radially outward across the wafer surface against viscous shear resistance at the substrate boundary.

Q: How does nozzle position affect film thickness?

Nozzle position determines the local chemical source radius. Dispensing near the wafer center allows centrifugal force to spread liquid across the entire radius, whereas outer nozzle positions reinforce edge film thickness but do not supply chemical inward.

Q: How does nozzle flow rate affect uniformity?

Higher volumetric flow rates increase convective film thickness according to lubrication theory (h ~ Q^(1/3)). Balanced flow rates across center and intermediate nozzle arms minimize radial thickness variance and improve film uniformity.

Q: What is Marangoni-driven dewetting?

Marangoni-driven dewetting occurs when gradients in chemical concentration or temperature create surface tension gradients (grad sigma). Liquid flows from regions of low surface tension toward high surface tension, potentially causing local film thinning and dry patch formation.

Q: Why can a rotating wafer develop non-wetting regions?

Non-wetting regions (dry spots or dewetting) develop when centrifugal thinning reduces film thickness below a critical stability threshold, or when surface tension gradients and high evaporation rates overcome fluid replenishment.

Q: How does the simulator estimate film thickness?

The simulator uses a 2D depth-integrated lubrication approximation (LUB-2D) coupled with steady-state continuous spin-coating theory (Emslie-Bonner-Peck model), temperature-dependent Andrade viscosity, and radial superposition of multi-nozzle chemical sources.

Q: What is the Flow Balance Optimizer?

The Flow Balance Optimizer is an automated engineering tool that sweeps candidate flow rate allocations across active nozzles to find flow ratios that maximize wafer-wide film thickness uniformity and minimize dewetting risk.

Q: Is this simulator a CFD simulation?

No. This simulator is a reduced-order engineering analysis and visualization tool based on lubrication theory and analytical fluid dynamics approximations, rather than a 3D full Navier-Stokes CFD solver.

Q: Can the simulator be used for process engineering studies?

Yes. It serves as an effective engineering pre-screening and qualitative sensitivity analysis tool for evaluating nozzle configurations, spin recipes, temperature effects, and chemical combinations prior to physical chamber testing.

300mm Wet Chamber Simulator: Wafer Film Thickness, Marangoni & Dewetting Analysis

Welcome to the 300mm Single-Wafer Wet Chamber Simulator, an advanced reduced-order engineering analysis tool designed for semiconductor process engineers, equipment designers, and thin-film researchers. In modern semiconductor fabrication (sub-3nm logic and 3D NAND/DRAM), single-wafer wet processing—including cleaning (SC1, SC2, DHF), etching (BHF, DSP+), photoresist stripping (SPM), and solvent rinsing (DIW, IPA)—demands rigorous control over liquid chemical dispensing, rotational fluid dynamics, and thin-film stability. This interactive simulation models the dynamic interplay between rotating substrate centrifugal acceleration ($F_{\text{cent}} = \rho \omega^2 r$), viscous boundary layer shear resistance ($\tau = \mu \frac{\partial u}{\partial z}$), multi-arm nozzle continuous chemical dispensing, solutocapillary/thermocapillary Marangoni stresses ($\nabla \sigma$), local film thinning, and wafer-scale dewetting phenomena.

300mm Silicon Substrate 100 - 3000 RPM Dynamic Spin Multi-Nozzle Radial Positioning 8 Semiconductor Chemical Species LUB-2D Lubrication Model Marangoni Velocity Vectors Dewetting & Dry-Patch Screening Automated Flow Balance Optimizer

🖥️ DISPLAY VIEW:

1. WAFER PLAN VIEW (300mm Top-View) Coordinate System: WAFER RELATIVE ℹ️

2. NOZZLE TRACE & FOOTPRINT Chamber Fixed Position | Wafer Trace: Circular

N1 Trace N2 Trace N3 Trace N4 Trace Impact Area

3. RADIAL FILM THICKNESS PROFILE

Cursor r: r: 75 mm | h: 182.6 µm

RADIAL CURSOR INSPECTOR (r = 75 mm) [Drag cursor on graph to inspect]

Radius 75 mm

Film Thickness 182.6 µm

Chemical Blend DIW 60 / IPA 40

Viscosity (μ) 1.15 cP

Surface Tension (σ) 58.2 mN/m

Flow Velocity (u) 84.5 mm/s

Reynolds No. (Re) 1.21 × 10⁶

Flow Regime Turbulent

Dewetting Status Stable

Marangoni Effect 0.042 mm/s

Center (0mm)

742.1 µm

25mm

512.4 µm

50mm

298.7 µm

75mm

182.6 µm

100mm

112.3 µm

125mm

61.8 µm

Edge (150mm)

24.7 µm

4. RADIAL FILM TRANSPORT / SIDE VIEW

Reduced-Order Engineering Visualization Wave represents transient redistribution (not CFD free-surface)

Speed

                    
                        Radial Transport (→)
                    
                        Film Profile (h)
                    
                        Wave Motion (Transient)
                    
                        Marangoni Effect (⇄)
                    
                        Dewetting Risk
                    
                        Transport Front

Wafer RPM

1000 RPM

Sim Time

0.0 s

Center Film h(0)

742.1 µm

Edge Film h(150)

24.7 µm

Avg Thickness

184.3 µm

Transport State

Centrifugal ➔

Marangoni Influence

Low (Outward)

Dewetting Risk

WET (Stable)

💡 Interactive Nozzle Adjust: 노즐 헤드를 마우스/터치로 좌우 드래그하면 토출 위치(X)가 실시간 이동합니다. Center (0 mm) ➔ Wafer Edge (150 mm) Radial Flow

                        🔬 [동적 액막 수송 및 파동 해석 - Radial Film Transport & Wave Dynamics]

Uniformity--%

Avg Film-- µm

DewettingStable

RPM1000

Temp25°C

MIXED PROPERTIES (Flow-Weighted)

ρ_mix: 0.91 g/cc
μ_mix: 1.47 cP
σ_mix: 55.3 mN/m

Local Equilibrium Properties

EDGE FORCE DOMINANCE

Centrifugal >> Viscous > Marangoni

Engineering Screening Indicator

EDGE EVAPORATION

LOW

Temp & RPM Screening Indicator

MARANGONI EFFECT

MEDIUM

u_M Screening: 0.042 mm/s

MODEL CONFIDENCE

MEDIUM

Reduced-Order LUB-2D Model

📊 V13.4-3 고급 300 mm 웨이퍼 액막 균일도 분석 (Advanced Film Uniformity Analysis)

SEMI / ASTM F81 Half-Range & 1-Sigma Metrics Continuous Source LUB-2D

[1. 전체 웨이퍼 글로벌 통계 지표 (Global 300 mm Statistical Metrics)] Sample Density: 0–150 mm Spatial Array

Mean (평균 h̄)
184.3 µm
Median (중앙값)
182.6 µm
Minimum (h_min)
24.7 µm
r = 150 mm
Maximum (h_max)
742.1 µm
r = 0 mm
Range (Δh)
717.4 µm
h_max - h_min
Std Dev (표준편차 σ)
88.4 µm
Coeff. of Variation (CV)
47.9 %
(σ / h̄) × 100%
Uniformity (균일도)

                            82.5% (SEMI)
                        
1-σ: 52.1%

                        [중심부 (Center Region)]
                        r: 0~50 mm
                    
• Avg Thickness: 517.7 µm
• Min / Max: 298.7 / 742.1 µm
• Std Dev (σ): 181.2 µm
• Uniformity: 72.3 %

                        [중간부 (Mid Region)]
                        r: 50~100 mm
                    
• Avg Thickness: 197.9 µm
• Min / Max: 112.3 / 298.7 µm
• Std Dev (σ): 76.1 µm
• Uniformity: 81.5 %

                        [외곽부 (Edge Region)]
                        r: 100~150 mm
                    
• Avg Thickness: 66.3 µm
• Min / Max: 24.7 / 112.3 µm
• Std Dev (σ): 35.8 µm
• Uniformity: 86.7 %

                            [웨이퍼 Edge 특화 평가]
                            THINNER THAN AVERAGE
                        

                            Edge(100~150mm) Avg: 66.3 µm

                            vs Wafer Avg(184.3 µm): -118.0 µm (-64.0%)
                        

                        Classification: Edge < 95% h̄ (Centrifugal / Evaporative Thinning)
                    

                    [3. 반경별 정밀 균일도 분포 (6-Zone Radial Uniformity Profile: 0–150 mm, 25mm Bins)]
                    Area Weight: A_i = (r2² - r1²)/R²
                
                                Radial Zone
                                Area Weight
                                Mean Thickness (h̄_i)
                                Zone Min / Max
                                Range (Δh)
                                Dev vs Wafer Avg (h̄_i - h̄)
                                Zone Uniformity
                                Relative Bar

                    [4. 노즐 배치-두께 편차 상관 분석 (Nozzle Spatial Correlation Analysis)]
                    Objective Statistical Association & Continuous Source Footprints

📋 [300mm Wafer 액막 균일도 종합 공정 엔지니어링 해석 결론] SEMI E10 & Advanced Process Control (APC) Screening

🌀 무차원 수 유동 영역 해석 (Hydrodynamic Regime Map) Reduced-Order Engineering Regime Screening

Reynolds Number (Re)
1.45 × 10⁵
Re = ρVL / μ (Laminar)
Weber Number (Engineering Screening)
128.4
We = ρV²L / σ
Characteristic Scales (L, V)

                        Veff: 15.7 m/s | Lfilm: 24.7 µm
                    
L = Local Film Thickness (h)
Dominant Regime Classification
INERTIA DOMINATED
High Re / Moderate We

                        [Hydrodynamic Regime Map (Re vs We)]
                        Log-Log Screening
                    

🔵 Viscous 🟢 Surface-Tension 🟡 Transition 🟠 Inertia 🟣 High-We

                        [반경별 무차원수 분포 (Radial Re & We Breakdown)]
                        r = 0 ~ 150 mm
                    
                                    Radius (r)
                                    Film h (µm)
                                    Vel V (m/s)
                                    Re (Reynolds)
                                    We (Weber)
                                    Local Flow Regime

[무차원수 (Re & We) 공정 영향 한국어 해석 (Korean Engineering Interpretation)]

* Re and We are used as reduced-order engineering screening parameters and do not represent a full CFD solution.

🧪 Marangoni Flow & Dewetting Risk Physical Screening (V13.3-4) Physical Risk Screening Chain | Reduced-Order Model

Max Surface-Tension Gradient (∇σ)
0.0 mN/m/mm
Chemical Boundary Gradient
Max Marangoni Velocity (u_M)
0.00 mm/s
Direction: Outward
Min Local Thinning Ratio (h/h_ref)
1.00
h_local vs Reference Film
Screening Risk Classification
WET (Stable)
Risk Index: 0.05

                    🔗 DEWETTING RISK CAUSALITY CHAIN (인과관계 체인 분석)
                    7-Stage Physical Sequence
                

STEP 1
🧪 Chem Mixing
IPA + DIW
STEP 2
⚡ Surf-Tension Grad
∇σ: 0.0 mN/m/mm
STEP 3
🌊 Marangoni Flow
u_M: 0.00 mm/s
STEP 4
🔄 Redistribution
Active Flow
STEP 5
📉 Film Thinning
h/h_ref: 1.00
STEP 6
⚠️ Stability Loss
Stable
STEP 7
🚨 Dewetting Risk
WET

                    📊 Radial Profile: Film Thickness, Marangoni Velocity & Dewetting Risk Index
                    Radius: 0 mm (Center) ─── 150 mm (Wafer Edge)
                

                    🎯 NOZZLE CAUSE ANALYSIS (노즐별 비젖음 위험 기여도 원인 분석)
                    Inspected Radius: 75 mm
                

Nozzle	Nozzle Pos (x, y)	Chemical	Flow Rate	Physical Weight	Contribution (%)	Primary Physical Function / Risk Role

                    [반경 위치별 Marangoni & Dewetting Screening Breakdown Table]
                

Radius (mm)	Film h (µm)	Surface Tension σ (mN/m)	Gradient \|∇σ\| (mN/m/mm)	u_M (mm/s)	Ratio (h/h_ref)	Risk Index (I_dewet)	Risk State

[Marangoni 재분포 및 비젖음 위험(Dewetting Risk) 한국어 해석 (Korean Engineering Conclusion)]

⚠️ Scientific Model & Engineering Limitation:
Marangoni-induced dewetting is represented as a reduced-order stability screening model. Actual dewetting depends on wettability, contact angle, surface condition, chemical composition, film thickness, evaporation, temperature, surface-tension gradients and transient flow.

⚖️ V13.4-4 다목적 공정 최적화기 (Multi-Objective Process Optimizer)

Pareto Frontier & MCDM Engine 4-Objective Simultaneous Scoring

                        ⚙️ [1. 다목적 가중치 제어 (User-Adjustable Objective Weights)]
                    
                        Presets:

                            1. Film Uniformity
                            35%
                        
Maximize Wafer-wide h̄ uniformity

                            2. Thickness Range
                            20%
                        
Minimize peak-to-valley Δh

                            3. Dewetting Risk
                            25%
                        
Minimize dry hole instability I_dewet

                            4. Marangoni Risk
                            20%
                        
Minimize |u_M| & ∇σ tension shock

                        Auto-Normalized Weight Composition (Total = 100%):
                        U: 35.0% | Range: 20.0% | Dewet: 25.0% | Marangoni: 20.0%
                    

                        Total Flow Constraint (mL/min)
                        
                        Target Nozzle Group
                        
                        Search Resolution
                        
                        Min Flow per Nozzle

                        
                            📈
                            Pareto Optimization Plot (X: Film Uniformity vs. Y: Dewetting Risk)
                        
                        Evaluated: 0 | Pareto Optimal: 0

                        • Legend: 💎 Pareto Front (Non-dominated) | ⭐ Best Balanced | ⭕ Current Baseline | 🔹 Candidates
                        Click any point to select
                    

                            ★ BEST BALANCED CONDITION
                            Rank 1
                        
Candidate Flow Distribution:
N1: 1500 / N2: 1000 mL/min (60:40)
1. Uniformity
82.5%
2. Thickness Range
717.4 µm
3. Dewetting Risk
0.24
4. Marangoni Risk
3.12 mm/s
Engineering Optimization Score (Higher = Better)
84.6 / 100 pts

                            *Only modifies chamber settings upon clicking this button.
                        

                    [4. 주요 공정 조건 후보군 비교 (Key Candidate Solutions Comparison Deck)]
                    *Do not call "Absolute Optimal" because result depends on weights & model
                

                    [5. 상위 후보군 종합 평가표 (Top Ranked Multi-Objective Candidates Table)]
                    Click row to inspect or apply
                

Rank	Candidate Type	Flow Distribution (mL/min)	Uniformity (%)	Range Δh (µm)	Dewetting Risk	Marangoni Risk	Total Score	Pareto Status	Action
Press "Run Multi-Objective Optimizer" to evaluate candidate flow distributions across the 4 engineering objectives.

📋 [다목적 공정 최적화 종합 엔지니어링 해석 결론 (Korean Engineering Conclusion)]

다목적 최적화 탐색을 실행하여 4가지 공정 지표(Film Uniformity, Thickness Range, Dewetting Risk, Marangoni Risk)의 종합 가중치 평가 및 Pareto Front 해를 도출하십시오.

⚠️ Scientific Model & Engineering Limitation:
The optimization result is dependent on objective weights and the current reduced-order engineering model.
Multi-objective trade-off frontiers are computed based on 2D depth-integrated lubrication approximations (LUB-2D) and simplified Marangoni instability screening. Final recipe deployment should be validated with chamber metrology.

📁 V13.4-5 공정 조건 비교 분석기 (Process Case Comparison & Radial Overlay)

Snapshot & LocalStorage Persistence Up to 4-Case Radial Overlay

                        📸 [1. 현재 챔버 상태 스냅샷 저장 (Save Case Snapshot)]
                    
                        Saved: 0 Cases

                    
                        📋 [2. 저장된 공정 케이스 목록 (Case List & Compare Selection)]
                        (Select up to 4 cases to compare)
                    
                    Selected: 0 / 4

Compare	Tag	Case Name & Time	RPM / Temp	Nozzle / Chem / Flow	Uniformity	Avg h̄ (µm)	Dewet Risk	Re / We	Actions
No saved cases found. Click "Save Current State as Case" or "Reset Benchmark Presets".

                    
                        📈
                        [3. 반경별 액막 두께 중첩 비교 곡선 (Radial Film Thickness Overlay: h(r) Curve Comparison)]
                    
                    Hover to inspect exact thickness at radius r

                            Radius r = 0 mm (Center)
                            r = 75 mm (Mid)
                            r = 150 mm (Edge / Bevel)
                        

                                📍 Radial Probe Cursor
                            
Radius: r = 75.0 mm

Active Compared Cases:

                    
                        [4. 공정 조건 및 지표 다중 비교 분석표 (Side-by-Side Comprehensive Comparison)]
                    
                    Compared parameters & physics metrics (Up to 4 Cases)

📋 [공정 조건 비교 종합 엔지니어링 결론 (Korean Comparison Conclusion)]

비교할 케이스를 2개 이상 선택(체크)하면 각 조건 간 액막 균일도, Dewetting Risk, Marangoni 속도, Re/We 무차원 수의 정량적 비교 결론이 자동 산출됩니다.

ℹ️ Process Case Storage & Metrology Notice:
Cases are saved directly into browser LocalStorage. Loading a case restores the complete chamber state (RPM, Temperature, Nozzle geometry, and flow rates). All comparative values are calculated dynamically using the unified physical solver.

📑

300mm SEMICONDUCTOR PROCESS ENGINEERING ANALYSIS REPORT

                        Simulation Type: Reduced-Order Engineering Model
                        Purpose: Relative Process Screening
                        Target Wafer: 300 mm Silicon Wafer (R=150 mm)
                        Doc ID: RPT-2026-0813-01
                    

Data Classification Guide:
                    [CALCULATED VALUES] 수치 계산값
                    [ENGINEERING SCREENING] 스크리닝 지표
                    [INTERPRETATION] 공정 해석 및 가이드
                

                        
                            1. Process Conditions (공정 운전 조건)
                        
                        
                            CALCULATED VALUES
                        
                    
Wafer Rotation
1200 RPM
ω = 125.7 rad/s
Chamber Temp
25.0 °C
298.15 K
Active Nozzles
2 Arms
Multi-Arm Dispense
Total Chemical Flow
25.0 mL/s
1.50 L/min

                        
                                Arm #
                                Status
                                Position (X, Y)
                                Radius $r_N$ (mm)
                                Chemical Species
                                Flow Rate $\dot{Q}$
                                Dispense Ratio
                            

                        
                            
                        
                    

                        
                            2. Film Thickness & Uniformity (반경별 액막 두께 및 균일도)
                        
                        
                            CALCULATED VALUES
                        
                    
Center h(0 mm)
642.0 µm
Stagnation core
Average Thickness h̄
510.4 µm
Radial mean
Minimum $h_{min}$
380.2 µm
at r = 150 mm
Maximum $h_{max}$
680.5 µm
at r = 10 mm
Edge h(150 mm)
380.2 µm
Bevel boundary
Film Uniformity (U)
89.4%
Δh = 300.3 µm

                        
                            3. Hydrodynamics & Flow Regime (수력학적 무차원수 및 유동 영역)
                        
                        
                            CALCULATED VALUES
                        
                    
Reynolds Number ($Re$)
2.83 × 10⁵
$Re = \rho \omega R^2 / \mu$ (Rotational)
Weber Number ($We$)
142.6
$We = \rho v^2 h / \sigma$ (Inertia / Capillary)
Ekman Boundary Layer Depth
89.2 µm
$\delta_E = \sqrt{\nu / \omega}$
Hydrodynamic Flow Regime
Laminar Ekman / Thin-Film
Centrifugal-dominated flow

                        
                            4. Chemical & Surface Effects (화학종 혼합 및 계면 특성)
                        
                        
                            ENGINEERING SCREENING
                        
                    
Chemical Blend / Species
DIW (60%) + IPA (40%)
μ: 1.00 mPa·s | ρ: 1000 kg/m³
Effective Surface Tension ($\sigma$)
42.5 mN/m
Max ∇σ: 1.25 mN/(m·mm)
Marangoni Peak Velocity ($u_M$)
3.42 mm/s
Outward surface shear
Solvent Evaporation Flux
0.082 g/(m²·s)
Thermal activation: 1.00×

                        
                            5. Film Stability & Wetting Integrity (액막 안정성 및 젖음성 스크리닝)
                        
                        
                            ENGINEERING SCREENING
                        
                    
Dewetting Risk Index ($I_{dewet}$)
0.24 (LOW RISK)
Threshold: < 0.35 (Safe)
Local Thinning Risk Level
STABLE (Δh < 350µm)
Dry spot vulnerability: Minimal
Non-Wetting / Edge Pinning
FULL COVERAGE (100%)
Wafer edge bevel wetness: Secured
Centrifugal Shear Margin
ADEQUATE
Radial drainage balanced with supply

                        
                            📋
                            6. Engineering Conclusion & Actionable Recommendations (종합 엔지니어링 결론)
                        
                        
                            INTERPRETATION
                        
                    

                        
                    

                        ⚠️
                        Scientific Metrology Disclaimer & Verification Boundary Notice:
                    
[Calculated Values (수치 계산값)]: 챔버 작동 파라미터(RPM, 온도, 노즐 좌표, 토출 유량) 및 1D/2D 정상상태 연속방정식·무차원수($Re, We$) 기반 결정론적 물리 수치입니다.
[Engineering Screening (엔지니어링 스크리닝)]: 삭감 차원 모델(Reduced-Order Engineering Model)에 기반하여 비젖음(Dewetting), 마랑고니 대류, 국소 박막화 위험도를 신속 스크리닝하기 위한 상대 비교 지표입니다.
[Interpretation (공정 해석)]: 공정 엔지니어의 레시피 튜닝을 보조하기 위한 모델 기반 추론 가이드입니다.
중요 고지: 본 보고서에 제시된 스크리닝 결과는 실험적으로 최종 검증된 양산 장비 실측 예측값이 아니며, 공정 레시피 후보군 탐색 및 상대적 거동 비교(Relative Screening) 목적으로만 활용되어야 합니다.

🎯 Nozzle Position Optimizer (V13.3-5) Engineering Screening | Lightweight Reduced-Order Sweep

                    Target Nozzle
                    
                    Objective Function
                    
X Range (Start → End mm)
                        
                        →
                        
Y Range (Start → End mm)
                        
                        →
                        
                    Position Step (mm)

                    🗺️ Candidate Position Score Map & Top Ranking Comparison
                    Candidates evaluated: 0
                

                    [Top 5 Candidate Position Sweep Results Table]
                    
                

Rank	X (mm)	Y (mm)	Uniformity (%)	Thickness Range (µm)	Dewetting Risk	Score	Action
Press "Run Nozzle Sweep" to evaluate candidate nozzle positions.

[노즐 위치 최적화 결과 및 공정 제언 (Korean Optimization Conclusion)]

탐색 버튼을 클릭하여 선택한 노즐 위치 범위에 대한 최적 배치 및 액막 품질 평가를 수행하십시오.

⚠️ Model Limitation: Optimization is based on the current reduced-order model and should be interpreted as engineering screening.

💧 Nozzle Flow Balance Optimizer (V13.3-6) Flow Ratio Distribution Sweep | Constant Total Flow

                    Total Flow Rate (mL/min)
                    
                    Target Pair / Group
                    
                    Min Flow per Nozzle
                    
                    Max Flow per Nozzle
                    
                    Ratio Step (mL/min)
                    
                    Objective Function

                    📊 Flow Rate Ratio vs. Film Uniformity & Optimization Score Chart
                    Distributions tested: 0
                

                    [Top Candidate Flow Distribution Results Table]
                    
                

Rank	Flow Rates (mL/min)	Flow Ratio (%)	Uniformity (%)	Thickness Range (µm)	Dewetting Risk	Score	Action
Press "Run Flow Ratio Sweep" to evaluate candidate flow distributions.

[노즐 유량 분배 최적화 결과 및 공정 제언 (Korean Flow Optimization Conclusion)]

탐색 버튼을 클릭하여 총 유량 조건에 대한 노즐 간 최적 유량 분배 비율을 평가하십시오.

⚠️ Model Limitation: Flow distribution optimization is based on the current reduced-order film thickness and Marangoni stability screening model.

🔬 SCIENTIFIC MODEL & ENGINEERING LIMITATIONS (CLICK TO TOGGLE)

⚠️ Model Scope & Limitations

• Reduced-Order Model: Uses 2D depth-integrated lubrication approximation (LUB-2D).
• Not 3D CFD / VOF: Does not resolve 3D navier-stokes or explicit phase-volume tracking.
• Representative Properties: Chemical physical constants are reference baseline values.
• Reaction Kinetics: Multi-chemical reaction enthalpy or complex phase changes are not explicitly modeled.
• Equipment Calibration: Actual chamber matching requires empirical process calibration constants.

① Continuous Spin Film Equation

h(r) = [ 3μQ / (2πρω²) ]^1/3 · r^-2/3

Balance between centrifugal force and viscous shear stress in steady-state spin coating (Emslie, Bonner, Peck 1958).

② Viscosity Temperature Dependency

μ(T) = μ₂₅ · exp( -B · (T - 25) )

Andrade viscosity fitting model for thermal processing effects.

③ Marangoni Screening Velocity

u_M ≈ (h / 2μ) · ∇σ

Effective surface tension gradient flow screening model.

📐 Engineering Methodology & Reduced-Order Model

The 300mm Wet Chamber Simulator employs a depth-integrated, reduced-order physical framework designed to provide rapid, interactive insights into single-wafer semiconductor wet processing. Rather than solving transient, multi-phase 3D Navier-Stokes equations with Volume-of-Fluid (VOF) surface capturing—which typically requires hours of high-performance computing (HPC) time per process second—this tool uses an analytical and numerical Lubrication Approximation (LUB-2D) framework tailored for thin-film rotational flows.

1. Coordinate Systems: Chamber-Fixed vs. Wafer-Relative Rotating Frame

In an industrial 300mm single-wafer wet spin chamber, chemical dispensing nozzles are mounted on rigid swing arms positioned above the substrate at fixed Cartesian coordinates $(x_{\text{nozzle}}, y_{\text{nozzle}})$ relative to the stationary chamber bowl. As the wafer rotates at angular speed $\omega = \frac{2\pi \cdot \text{RPM}}{60}$, points on the substrate surface sweep beneath the dispense stream in a circular trajectory. The simulation transforms stationary nozzle discharge fluxes into rotating wafer-relative polar coordinates $(\tilde{r}, \tilde{\theta})$ through continuous azimuthal averaging and transient Lagrangian trace integration:

Radial Coordinate: $r = \sqrt{x_{\text{nozzle}}^2 + y_{\text{nozzle}}^2} \in [0, 150\,\text{mm}]$
Azimuthal Inflow Rate: Continuous volumetric source term $S(r, \theta, t) = \sum_{i=1}^{N} \frac{Q_i}{\pi w_{\text{footprint}}^2} \exp\left(-\frac{|\mathbf{r} - \mathbf{r}_{n,i}|^2}{2 \sigma_{\text{nozzle}}^2}\right)$

2. LUB-2D Thin Liquid Film Formulation & Radial Transport

Assuming the liquid film thickness $h(r) \ll R_{\text{wafer}}$ (typically $10\,\mu\text{m} \le h \le 800\,\mu\text{m}$ compared to wafer radius $R=150\,\text{mm}$), the Navier-Stokes equations simplify under boundary-layer lubrication scaling. The momentum balance in the radial direction equates centrifugal body force to viscous shear stresses:

$\rho \omega^2 r + \mu \frac{\partial^2 u_r}{\partial z^2} = 0 \quad \implies \quad u_r(z) = \frac{\rho \omega^2 r}{\mu} \left( h z - \frac{1}{2} z^2 \right)$

Integrating the parabolic velocity profile across the depth $z \in [0, h]$ yields the radial volumetric flux $q_r(r) = \int_0^h u_r(z) dz = \frac{\rho \omega^2 r h^3}{3 \mu}$. In steady state with a continuous volumetric inflow $Q$, mass continuity $2\pi r q_r(r) = Q$ leads to the classical Emslie-Bonner-Peck relationship:

$h(r) = \left[ \frac{3 \mu Q}{2 \pi \rho \omega^2} \right]^{1/3} r^{-2/3}$

3. Thermal Viscosity & Multi-Species Mixture Laws

Chemical viscosity varies strongly with process temperature $T$ (°C). The simulator applies an Andrade exponential fitting equation $\mu(T) = \mu_{25} \exp(-B \cdot (T - 25))$ where $B$ is the empirical thermal sensitivity constant. For multi-chemical dispense scenarios (e.g. simultaneous DHF and DIW or SC1 and SC2 mixtures), effective mixture density ($\rho_{\text{mix}}$), viscosity ($\mu_{\text{mix}}$), and surface tension ($\sigma_{\text{mix}}$) are evaluated via volume-weighted mixing rules.

4. Solutocapillary & Thermocapillary Marangoni Stress Modeling

Gradients in chemical species concentration ($C$) and liquid surface temperature ($T$) create spatial surface tension gradients ($\nabla \sigma = \frac{\partial \sigma}{\partial T} \nabla T + \sum \frac{\partial \sigma}{\partial C_i} \nabla C_i$). These gradients exert a tangential shear stress $\tau_{\text{surf}} = \nabla \sigma$ on the free liquid surface, inducing a Marangoni screening velocity:

$u_M(r) \approx \frac{h(r)}{2 \mu} \nabla \sigma(r)$

When volatile solvents like IPA (low surface tension $\approx 21.7\,\text{mN/m}$) are dispensed adjacent to aqueous solutions (high surface tension $\approx 72.8\,\text{mN/m}$), intense solutocapillary Marangoni forces pull liquid toward the higher surface tension zone, creating rapid localized thinning or film retraction.

5. Dewetting Risk Screening Index ($i_{\text{Dewet}}$)

Dewetting occurs when the liquid film thickness falls below a critical stabilization margin ($h_{\text{crit}} \approx 10\,\mu\text{m}$) or when outward Marangoni stresses exceed the viscous replenishment capacity. The simulator calculates a composite dimensionless Dewetting Risk Index $i_{\text{Dewet}} \in [0, 1]$ based on local thinning ratio ($h/h_{\text{center}}$), surface tension gradient magnitude ($|\nabla \sigma|$), and local Weber number ($We = \frac{\rho u^2 h}{\sigma}$).

⚠️ Scientific Scope & Model Limitation Notice:

This simulator is a reduced-order engineering visualization and analysis tool and is not a full CFD solver. It is developed to support preliminary recipe formulation, qualitative parameter sensitivity studies, and engineering education. Industrial process qualification requires empirical chamber matching and hardware-in-the-loop experimental verification.

📖 How to Use the 300mm Wet Chamber Simulator

Follow this comprehensive step-by-step user guide to configure recipes, evaluate thin-film hydrodynamics, optimize nozzle flow distribution, and interpret process results:

STEP 1

Set Wafer Spin Speed (RPM)

Adjust wafer rotation between 100 and 3000 RPM using the slider or numeric input. Observe how centrifugal acceleration changes radial liquid transport velocity and film thickness.

STEP 2

Set Process Temperature (°C)

Configure process discharge temperature from 10°C to 180°C. Temperature directly modifies fluid dynamic viscosity via the Andrade thermal model and changes evaporation kinetics.

STEP 3

Configure Chemical Species

Select from 8 semiconductor chemicals: DIW, SC1 (NH₄OH/H₂O₂), SC2 (HCl/H₂O₂), DHF, SPM (Piranha), IPA, BHF, or DSP+. Physical properties (density, viscosity, surface tension) update automatically.

STEP 4

Configure Nozzle Position (mm)

Adjust nozzle discharge radius from -140 mm to +140 mm relative to wafer center. You can also drag nozzle icons directly inside the interactive Wafer Side View canvas.

STEP 5

Configure Nozzle Flow Rate

Set volumetric flow rate ($0.1 - 25.0\,\text{mL/s}$ or equivalent $\text{mL/min}$) for each active nozzle arm. Toggle unused nozzle arms ON/OFF to simulate single-arm or multi-arm recipes.

STEP 6

Run / Pause / Reset Simulation

Click "시뮬레이션 일시정지" (Toggle Play/Pause) or "초기화" (Reset). On mobile devices, use the floating sticky bottom control bar for quick single-tap execution.

STEP 7

Observe 2D Film Thickness Distribution

Examine Card 1 (2D Plan View) with 11 distinct visualization modes including Thickness Deviation, Marangoni Velocity Vectors, Chemical Concentration, and 2D Dewetting Risk Maps.

STEP 8

Evaluate Uniformity (%) & Profile

Check Card 3 (Radial Film Thickness Profile) and the Live KPI summary to evaluate center thickness ($h_0$), edge thickness ($h_{150}$), radial thickness range ($\Delta h$), and wafer uniformity.

STEP 9

Inspect Marangoni & Dewetting Behavior

Review the Marangoni vector overlay and Dewetting Warning Shader in Card 4 (Wafer Side View & Radial Film Transport) to check for edge dry patches or local liquid starvation.

STEP 10

Use Flow Balance Optimizer

Expand the Nozzle Flow Balance Optimizer panel to automatically sweep candidate flow ratios, ranking configurations by wafer uniformity (%) and minimum dewetting risk score.

STEP 11

Review Conclusion & Export Report

Read the real-time dynamic Korean engineering conclusion and export a complete PDF/Print-ready Engineering Analysis Report containing full process metrics and charts.

📊 Engineering Interpretation & Physical Concepts

What does film thickness uniformity mean?

In semiconductor single-wafer wet processing, film thickness uniformity represents the spatial consistency of the liquid boundary layer covering the 300mm silicon surface. Uniformity is quantified using the standard half-range metric:

$\text{Uniformity} = \left( 1 - \frac{h_{\max} - h_{\min}}{2 \cdot h_{\text{avg}}} \right) \times 100\%$

A high uniformity value (typically $> 85\%$) indicates consistent chemical replenishment across all wafer dies from center to bevel. Poor uniformity leads to radial etch rate gradients, non-uniform particle removal efficiency, and localized chemical under-etch or over-etch defects.

What is radial liquid transport?

Radial liquid transport is the outward convective displacement of liquid chemical driven by centrifugal acceleration ($a_r = \omega^2 r$) on the rotating wafer surface. Because centrifugal acceleration increases linearly with radius $r$, liquid accelerates toward the wafer edge, driving a continuous outward thinning profile. Understanding radial transport velocity ($u_r \propto \omega^2 r h^2$) is essential for optimizing chemical residence time, boundary layer thickness, and chemical consumption efficiency.

What is the Marangoni effect (Solutocapillary & Thermocapillary)?

The Marangoni effect is mass transfer along an interface between two fluids driven by a surface tension gradient ($\nabla \sigma$). In wet processing, surface tension variations arise from:

Solutocapillary Marangoni Flow: Concentration gradients caused by dispensing chemicals with different surface tensions (e.g. IPA vs. DIW or concentrated acid vs. rinse water). Liquid is drawn from lower surface tension regions toward higher surface tension zones.
Thermocapillary Marangoni Flow: Temperature gradients across the wafer surface caused by hot chemical dispense, heated chucks, or evaporative cooling ($\frac{d\sigma}{dT} < 0$ for most liquids).

What is dewetting and why do dry spots form on rotating wafers?

Dewetting refers to the rupture and retraction of a liquid film from a solid wafer surface, resulting in dry patches or droplets. Dewetting occurs when:

Centrifugal thinning reduces the liquid film thickness below the critical stabilization threshold ($h < h_{\text{crit}} \approx 10\,\mu\text{m}$).
Marangoni shear stresses pull liquid away from local hot spots or solvent-rich regions faster than outward bulk flow can replenish it.
Evaporative loss at elevated temperatures and high spin speeds depletes the thin liquid boundary layer near the wafer bevel.

What does nozzle flow balance mean in multi-arm single-wafer chambers?

In advanced multi-nozzle wet chambers, dispensing chemical from a single central nozzle often results in excessive center film thickness ($h_{\text{center}} > 600\,\mu\text{m}$) and inadequate edge coverage ($h_{\text{edge}} < 30\,\mu\text{m}$). Nozzle flow balance is the strategic division of total volumetric flow ($Q_{\text{total}}$) among center, mid-radius, and outer-radius nozzle arms. Allocating a fraction of the chemical flux to mid-radius nozzles compensates for centrifugal thinning, significantly improving wafer-wide thickness uniformity and mitigating edge dewetting risks.

What is the physical relationship between wafer RPM and radial liquid transport?

Wafer spin speed (RPM) exerts a quadratic influence on centrifugal body forces ($F_{\text{cent}} \propto \omega^2$). Under steady-state lubrication theory, liquid film thickness scales inversely with angular velocity:

$h(r) \propto \omega^{-2/3} \quad \text{and} \quad u_r(r) \propto \omega^{2/3}$

Doubling spin speed from 500 RPM to 1000 RPM increases outward radial velocity by approximately $58.7\%$ and decreases film thickness by approximately $37.0\%$, reducing chemical residence time on the substrate surface.

❓ Frequently Asked Questions (FAQ)

Q1. What is a 300mm wet chamber simulator?

A 300mm wet chamber simulator is an engineering software tool that models liquid chemical dispensing, rotational fluid dynamics, centrifugal radial transport, and thin-film flow behavior on a rotating 300 mm silicon semiconductor wafer during wet cleaning, etching, stripping, and rinsing processes.

Q2. How does wafer spin affect liquid film transport?

Wafer spin imparts a centrifugal body force proportional to mass density, angular velocity squared (omega^2), and radius. This centrifugal acceleration drives liquid radially outward across the wafer surface against viscous shear resistance at the substrate boundary.

Q3. How does nozzle position affect film thickness?

Nozzle position determines the local chemical source radius. Dispensing near the wafer center allows centrifugal force to spread liquid across the entire radius, whereas outer nozzle positions reinforce edge film thickness but do not supply chemical inward.

Q4. How does nozzle flow rate affect uniformity?

Higher volumetric flow rates increase convective film thickness according to lubrication theory (h ~ Q^(1/3)). Balanced flow rates across center and intermediate nozzle arms minimize radial thickness variance and improve film uniformity.

Q5. What is Marangoni-driven dewetting?

Marangoni-driven dewetting occurs when gradients in chemical concentration or temperature create surface tension gradients (grad sigma). Liquid flows from regions of low surface tension toward high surface tension, potentially causing local film thinning and dry patch formation.

Q6. Why can a rotating wafer develop non-wetting regions?

Non-wetting regions (dry spots or dewetting) develop when centrifugal thinning reduces film thickness below a critical stability threshold, or when surface tension gradients and high evaporation rates overcome fluid replenishment.

Q7. How does the simulator estimate film thickness?

The simulator uses a 2D depth-integrated lubrication approximation (LUB-2D) coupled with steady-state continuous spin-coating theory (Emslie-Bonner-Peck model), temperature-dependent Andrade viscosity, and radial superposition of multi-nozzle chemical sources.

Q8. What is the Flow Balance Optimizer?

The Flow Balance Optimizer is an automated engineering tool that sweeps candidate flow rate allocations across active nozzles to find flow ratios that maximize wafer-wide film thickness uniformity and minimize dewetting risk.

Q9. Is this simulator a CFD simulation?

No. This simulator is a reduced-order engineering analysis and visualization tool based on lubrication theory and analytical fluid dynamics approximations, rather than a 3D full Navier-Stokes CFD solver.

Q10. Can the simulator be used for process engineering studies?

Yes. It serves as an effective engineering pre-screening and qualitative sensitivity analysis tool for evaluating nozzle configurations, spin recipes, temperature effects, and chemical combinations prior to physical chamber testing.

ℹ️ About This Simulator

The 300mm Wet Chamber Simulator was created to bridge the gap between high-overhead 3D CFD simulations and empirical fab trial-and-error in semiconductor wet processing. In advanced nodes (GAA FETs, EUV patterning cleans, high-aspect-ratio 3D NAND contact etching), wet chemical delivery requires fine-grained balance between spin recipe, nozzle positioning, and multi-chemical interactions.

What the model represents: Reduced-order depth-integrated lubrication theory, continuous rotating wafer source transformations, thermal viscosity scaling, solutocapillary/thermocapillary Marangoni screening, and multi-objective flow balancing.

What the model does not represent: Turbulent gas-liquid droplet atomization, full 3D Volume-of-Fluid (VOF) free-surface splashing, reactive chemical kinetics (e.g. exothermic reaction heat generation), or chamber bowl exhaust aerodynamics.

🔒 Privacy Policy & Consent Preferences

We value your privacy and transparency. This Privacy Policy details our data processing practices for this engineering simulation platform:

1. Local Browser Storage: This application utilizes window.localStorage exclusively on your client device to preserve customized process recipes, nozzle spatial coordinates, and selected UI view preferences. This data remains on your local machine and is never transmitted to or stored on external servers.

2. Google AdSense & Advertising Cookies: We use Google AdSense to serve non-intrusive advertisements. Google and its certified third-party advertising partners utilize cookies (including the DoubleClick cookie) to serve ads based on user visits to this website and other websites across the Internet. You can learn more, opt out of personalized advertising, or customize your ad settings at Google Ads Settings.

3. European Economic Area (EEA), UK & Switzerland Consent: For users in the EEA, United Kingdom, and Switzerland, advertising consent is managed via Google-certified Consent Management (Privacy & Messaging CMP). Where applicable, the Google consent dialogue allows users to grant, deny, or customize consent for advertising cookies and personalized data processing.

4. Analytics & Personal Data: No personally identifiable information (PII) is collected, gathered, sold, or shared by this simulator. Standard anonymous web server HTTP request logs may be maintained solely for cybersecurity and infrastructure reliability.

5. Managing Consent & Browser Cookies: You may adjust your browser cookie preferences, block third-party trackers, or clear stored local cache at any time via your browser settings.

📜 Terms of Use

1. Purpose of Service: The 300mm Wet Chamber Simulator is provided solely for engineering analysis, preliminary screening, research, and educational purposes.

2. Model-Based Estimates: All numerical values, film thickness estimates, Marangoni vectors, dewetting risk indices, and flow balance optimizations generated by this software are simplified model-based calculations. They do not constitute guaranteed equipment performance or physical wafer yields.

3. Independent Validation: Users must independently evaluate and validate all process parameters, chemical compatibility, safety hazards, and recipe formulations on certified semiconductor equipment before physical wafer fabrication.

4. Limitation of Liability: Under no circumstances shall the developers, contributors, or publishers be liable for any direct, indirect, incidental, or consequential damages resulting from the use or inability to use this simulation tool.

✉️ Contact & Engineering Feedback

We welcome inquiries, feedback, and technical discussions regarding single-wafer wet processing simulation, thin-film hydrodynamics, or tool enhancements.

Engineering Contact: CONTACT_EMAIL

Project Repository / Web: CANONICAL_SITE_URL/

When submitting recipe questions, please provide your wafer RPM, process temperature, nozzle coordinates, and chemical species.