TCAD Model Parameters are physical values used in device and process simulation — including diffusion coefficients, mobility models, recombination lifetimes, and material properties that determine simulation accuracy, requiring careful selection from literature, calibration to experiments, or ab-initio calculations for predictive modeling.
What Are TCAD Model Parameters?
- Definition: Physical constants and model coefficients used in TCAD simulations.
- Categories: Process parameters, device parameters, material properties.
- Sources: Literature, calibration, ab-initio calculations, vendor databases.
- Impact: Determine accuracy and predictive capability of simulations.
Why Parameters Matter
- Simulation Accuracy: Correct parameters essential for quantitative predictions.
- Process Optimization: Accurate parameters enable virtual process development.
- Technology Transfer: Parameter sets encode process knowledge.
- Uncertainty: Parameter uncertainty propagates to simulation results.
- Calibration: Starting point for calibration to experimental data.
Process Parameters
Diffusion:
- Diffusion Coefficient: D = D_0 · exp(-E_a / kT).
- D_0: Pre-exponential factor (cm²/s).
- E_a: Activation energy (eV).
- Species-Dependent: Different for each dopant (B, P, As, Sb).
- Concentration-Dependent: Enhanced diffusion at high concentrations.
Segregation:
- Segregation Coefficient: Ratio of dopant concentration across interface.
- Example: Si/SiO₂ interface segregation.
- Impact: Dopant redistribution during oxidation.
Oxidation:
- Deal-Grove Parameters: Linear and parabolic rate constants.
- Temperature-Dependent: Arrhenius behavior.
- Orientation-Dependent: Different rates for (100) vs. (111) silicon.
Implantation:
- Range Parameters: Projected range R_p, straggle ΔR_p.
- Channeling: Enhanced penetration along crystal axes.
- Damage: Lattice damage from ion bombardment.
Device Parameters
Mobility Models:
- Low-Field Mobility: μ_0 for electrons and holes.
- Field-Dependent: μ(E) models (Caughey-Thomas, etc.).
- Doping-Dependent: Mobility degradation at high doping.
- Temperature-Dependent: μ ∝ T^(-α).
Recombination:
- SRH Lifetime: τ_n, τ_p for Shockley-Read-Hall recombination.
- Auger Coefficients: C_n, C_p for Auger recombination.
- Surface Recombination: S_n, S_p at interfaces.
Bandgap:
- Intrinsic Bandgap: E_g(T) temperature dependence.
- Bandgap Narrowing: ΔE_g at high doping.
- Strain Effects: Bandgap modification under stress.
Tunneling:
- Effective Mass: m* for tunneling calculations.
- Barrier Height: Φ_B for metal-semiconductor, insulator barriers.
Material Properties
Thermal:
- Thermal Conductivity: κ(T) for heat transfer.
- Specific Heat: C_p for thermal capacity.
- Thermal Expansion: α for stress calculations.
Mechanical:
- Young's Modulus: E for elastic deformation.
- Poisson's Ratio: ν for stress-strain relationships.
- Yield Strength: For plastic deformation.
Electrical:
- Dielectric Constant: ε_r for insulators.
- Work Function: Φ_M for metals, Φ_S for semiconductors.
- Electron Affinity: χ for band alignment.
Parameter Sources
Literature Values:
- Textbooks: Sze, Streetman for standard parameters.
- Papers: Research papers for specific materials, conditions.
- Databases: NIST, semiconductor handbooks.
- Advantages: Readily available, peer-reviewed.
- Limitations: May not match specific process conditions.
Calibration to Experiments:
- Method: Fit parameters to match experimental measurements.
- Advantages: Accurate for specific process.
- Limitations: Time-consuming, requires experimental data.
- Use Case: Critical parameters, process-specific values.
Ab-Initio Calculations:
- Method: DFT (Density Functional Theory) calculations.
- Advantages: No experimental data needed, fundamental.
- Limitations: Computationally expensive, approximations.
- Use Case: New materials, defect properties, interfaces.
Vendor Databases:
- Source: TCAD tool vendors provide default parameter sets.
- Advantages: Integrated, tested, documented.
- Limitations: Generic, may need customization.
- Use Case: Starting point for simulations.
Parameter Sensitivity
High-Impact Parameters:
- Mobility: Strongly affects device current, speed.
- Diffusion Coefficient: Determines dopant profiles, junction depth.
- Recombination Lifetime: Affects leakage, minority carrier devices.
- Bandgap: Fundamental for all electrical properties.
Low-Impact Parameters:
- Some Material Properties: Thermal conductivity (unless thermal effects critical).
- Higher-Order Terms: Often negligible for first-order analysis.
Sensitivity Analysis:
- Method: Vary each parameter, measure impact on simulation output.
- Identify Critical: Focus calibration on high-sensitivity parameters.
- Uncertainty Propagation: Quantify how parameter uncertainty affects results.
Parameter Management
Version Control:
- Track Changes: Maintain history of parameter set modifications.
- Documentation: Record why parameters were changed.
- Branching: Different parameter sets for different processes.
Documentation:
- Source: Document where each parameter came from.
- Conditions: Record calibration conditions, temperature range, etc.
- Uncertainty: Quantify parameter uncertainties.
- Validation: Document validation against experimental data.
Database Management:
- Centralized: Maintain central parameter database.
- Access Control: Manage who can modify parameters.
- Backup: Regular backups of parameter sets.
Best Practices
Start with Literature:
- Baseline: Begin with well-established literature values.
- Validate: Check if literature values match your process.
- Calibrate: Adjust only parameters that need it.
Calibrate Systematically:
- Prioritize: Calibrate high-sensitivity parameters first.
- One at a Time: Avoid changing many parameters simultaneously.
- Validate: Test calibrated parameters on independent data.
Physical Reasonableness:
- Check Values: Ensure parameters are physically reasonable.
- Compare: Compare to literature, other processes.
- Expert Review: Have experts review parameter sets.
Uncertainty Quantification:
- Confidence Intervals: Quantify parameter uncertainties.
- Propagation: Understand how uncertainty affects predictions.
- Sensitivity: Know which parameters matter most.
Tools & Resources
- TCAD Software: Synopsys, Silvaco, Crosslight with parameter databases.
- Literature: Sze, Streetman, Grove textbooks.
- Databases: NIST, semiconductor material databases.
- Calibration Tools: Integrated parameter extraction tools.
TCAD Model Parameters are the foundation of simulation accuracy — careful selection, calibration, and management of parameters determines whether simulations provide quantitative predictions or just qualitative trends, making parameter management a critical aspect of successful TCAD-based process development and optimization.