ShaneLogic/carrier-lifetime-calculation

Carrier Lifetime Calculation (SRH Model)

When to Use

• Calculating electron or hole lifetimes in semiconductors
• Analyzing recombination center effects on carrier lifetime
• Understanding lifetime spatial variation in pn-junction devices
• Computing recombination rate U from carrier concentrations

Prerequisites

• Capture coefficients (cₙ for electrons, cₚ for holes)
• Density of recombination centers (Nᵣ)
• Carrier densities (n, p, n₀, p₀)
• Intrinsic carrier concentration (nᵢ)
• Trap energy level (Eₜ) relative to intrinsic level (Eᵢ)

Simplified Minority Carrier Lifetimes (Bulk Regions)

For p-type bulk material:

τₙ₀ = 1 / (cₙ × Nᵣ)

For n-type bulk material:

τₚ₀ = 1 / (cₚ × Nᵣ)

These assume p >> n (for electron lifetime) or n >> p (for hole lifetime).

General Lifetime Expressions

Polynomial Form for Electrons:

τₙ = τₙ₀ × (p + p₁) / (n + p + 2nᵢ × cosh((Eₜ - Eᵢ)/kT))

General Two-Carrier Semiconductor Lifetime:

τₙ = (p - p₀) / U
τₚ = (n - n₀) / U

Recombination Rate Relation:

U = Δp / τₚ = Δn / τₙ

Spatial Distribution Rules

1. Thermal equilibrium (U = 0): Carrier lifetime is infinity

2. Non-equilibrium: Lifetime is finite only when deviating from equilibrium

3. Bulk p/n materials: Lifetimes are nearly constant (τₙ₀, τₚ₀)

4. At pn-junction interface: Lifetime reaches maximum when Fermi level (E_F) coincides with intrinsic level (Eᵢ)

5. Key principle: Carrier lifetimes are never the same throughout a semiconducting device including a junction

Variables

| Symbol | Description | Type | |--------|-------------|------| | τₙ₀ | Electron lifetime in p-type bulk | Time | | τₚ₀ | Hole lifetime in n-type bulk | Time | | cₙ | Electron capture coefficient | Coefficient | | cₚ | Hole capture coefficient | Coefficient | | Nᵣ | Density of recombination centers | Density |

See references/lifetime-spatial-distribution.md for detailed derivation and edge cases.