ShaneLogic/auger-recombination-via-centers

Auger Recombination via Recombination Centers

When to Use

• High excitation conditions with sufficient carrier density
• Materials with significant recombination center density (Nr)
• Analyzing carrier lifetime dependence on majority carrier density
• Distinguishing intrinsic Auger recombination from other mechanisms

Prerequisites

• Recombination center density (Nr)
• Carrier density (n)
• Energy of recombination center (Er) and conduction band edge (Ec)
• Effective mass (m*) of carriers

Procedure

1. Calculate Auger Lifetime

Use the center-specific formula:

τ_A = [Q × exp(ΔE/kT)] / (R × Nr × n²)

Where:

• Q = 0.5 × (m₀/m*)³/² × (1 + m*/m₀)² (mass-dependent factor)
• R = 2.6 (enhancement factor)
• ΔE = Ec - Er (energy difference from conduction band to center)
• k = Boltzmann constant
• T = temperature

2. Estimate Auger Coefficient for Specific Materials

For GaAs and similar materials:

B ∝ (Ec - Er)⁻³.⁵

This power law describes the energy dependence.

3. Calculate Capture Cross-Section

σ_Auger = B / (v_th × n)

Where v_th is the thermal velocity of carriers.

4. Verify Intrinsic Auger Behavior

Check if the process is intrinsic by examining the dependence:

• τ_minority ∝ 1/(majority_density)²
• This quadratic dependence confirms intrinsic Auger recombination

Typical Values

• For Ec - Er = 0.5 eV and m* = 0.1m₀: B ≈ 10⁻²⁶ cm⁶s⁻¹
• For Nr = 10¹⁷ cm⁻³ and n = 10¹⁴ cm⁻³: τ_A ≈ 10⁻⁵ s
• Shallow trap capture cross-section: ~10⁻¹¹ cm²
• Deep trap capture cross-section: ~10⁻¹⁸ cm²

Key Insight

The exponential term exp(ΔE/kT) accounts for the energy barrier between the band and the recombination center, making deep centers less effective for Auger recombination.