| name | carrier-lifetime-calculation |
| description | Calculate minority carrier lifetimes using SRH recombination model and understand their spatial distribution in semiconductor devices with pn-junctions. Use when analyzing recombination rates, carrier lifetime in bulk materials, or lifetime variation across device junctions. |
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
-
Thermal equilibrium (U = 0): Carrier lifetime is infinity
-
Non-equilibrium: Lifetime is finite only when deviating from equilibrium
-
Bulk p/n materials: Lifetimes are nearly constant (τₙ₀, τₚ₀)
-
At pn-junction interface: Lifetime reaches maximum when Fermi level (E_F) coincides with intrinsic level (Eᵢ)
-
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.
