| name | capture-cross-section-deep-centers |
| description | Calculate capture cross-section pre-exponential factors for deep centers in semiconductors, including thermal activation corrections. Use when analyzing carrier capture by deep traps where thermal energy effects are significant. |
Capture Cross-Section for Deep Centers
When to Use
- Calculating capture cross-sections for deep trap centers in semiconductors
- Analyzing carrier recombination at deep levels with thermal activation
- Estimating capture rates for defects requiring substantial thermal energy
Core Procedure
1. Calculate Pre-exponential Factor s∞
Use Eq. (22.14):
s∞ = (e²/4πε₀εr)² × (m*/ħ²) × (1/Ec - Et)
Where:
e: elementary chargeε₀: vacuum permittivityεr: relative permittivitym*: effective massħ: reduced Planck constantEc - Et: energy difference between conduction band and trap level
2. Apply Thermal Correction Factor
Calculate correction factor η using Eq. (22.15):
η = (1 + 2m*Ea/ħ²k²)⁻¹
Where:
Ea: activation energyk: wave vector
Apply correction: modified s∞ = η × s∞
3. Calculate Material Parameter
Use Eq. (22.16):
Parameter = √(2m*/ħ²) × (Ec - Et)
4. Interpret Results
- Typical s∞ for deep centers: ~10⁻¹⁵ cm
- Thermal activation energies range from few meV to 0.6 eV
- Larger energies indicate significant thermal activation requirements
Output
Modified capture cross-section pre-exponential factor (ηs∞) in cm
