capture-cross-section-deep-centers

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 charge
• ε₀: vacuum permittivity
• εr: relative permittivity
• m*: effective mass
• ħ: reduced Planck constant
• Ec - 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 energy
• k: 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