ShaneLogic/auger-recombination-analysis

Auger Recombination Analysis

When to Use This Skill

Apply Auger recombination analysis when:

• Working with narrow gap semiconductors (Eg < 0.35 eV) at room temperature
• Analyzing high carrier density conditions (>10¹⁷ cm⁻³)
• Evaluating recombination in heavily doped materials
• Determining carrier lifetime limiting mechanisms
• Designing optoelectronic devices where Auger losses are critical

Core Workflow

Step 1: Assess Auger Relevance

Check if Auger recombination is significant:

• Band gap criterion: Auger dominates for Eg < 0.35 eV at room temperature
• Carrier density criterion: Auger becomes dominant at high injection levels
• Material type: Critical for InSb, HgCdTe, and similar narrow gap materials

Step 2: Calculate Basic Recombination Rate

Use the fundamental Auger recombination formula:

R_Auger = B × n² × p

Where:

• B = Auger coefficient (typically 10⁻³⁰ to 10⁻²² cm⁶s⁻¹)
• n = electron density (cm⁻³)
• p = hole density (cm⁻³)

Step 3: Calculate Carrier Lifetime

For electron lifetime limited by Auger:

τ_A = 1/(B × n²)

Lifetime scaling with density:

• Low densities: τ independent of n
• Medium densities: τ ∝ 1/n
• High densities: τ ∝ 1/n² (Auger-dominated regime)

Step 4: Detailed Quantum-Mechanical Calculation

For precise calculations, use Haug's formula (see references/haug-formula.md):

τ_A = [2.4 × 10⁻³¹ × (εr/m*)² × (1 + m*/m₀) × exp(ΔE/kT)] / (n² × I₁² × I₂²)

Where ΔE = [(2m* + mp)/(m* + mp)] × Eg

Step 5: Interpret Results

Band gap dependence:

• τ_A increases rapidly with increasing Eg
• For Eg > 0.35 eV: τ_A typically reaches 10⁻⁶ s (Auger negligible)
• Narrow gap materials: Auger is intrinsic and unavoidable at room temperature

High doping effects:

• Heavy doping creates sufficient carrier densities for Auger activation
• Auger can dominate even in wider gap semiconductors under high doping

Quick Reference Values

| Material Type | Typical B (cm⁶s⁻¹) | Critical Density | |---------------|---------------------|------------------| | Narrow gap (InSb) | 10⁻²⁶ to 10⁻²² | >10¹⁶ cm⁻³ | | Medium gap (Si) | 10⁻³¹ to 10⁻³⁰ | >10¹⁸ cm⁻³ | | Wide gap (GaAs) | 10⁻³⁰ to 10⁻²⁹ | >10¹⁸ cm⁻³ |

Output Format

Provide results as:

• Recombination rate in cm⁻³s⁻¹
• Carrier lifetime in seconds
• Dominant recombination regime identification
• Comparison with other recombination mechanisms if data available