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Calculate carrier capture cross-sections using gas-kinetic models and Coulomb-attractive center theory. Use this for determining recombination rates, carrier lifetimes, and analyzing temperature-dependent capture at defect centers.
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| name | carrier-capture-cross-section-models |
| description | Calculate carrier capture cross-sections using gas-kinetic models and Coulomb-attractive center theory. Use this for determining recombination rates, carrier lifetimes, and analyzing temperature-dependent capture at defect centers. |
s = π × r₀²
Where r₀ is the radius of the electron eigenstate at kT below the band edge.
Carrier capture requires:
λ = 1 / [(N_r - n_r) × s]
Where (N_r - n_r) is the density of free recombination centers.
τ_r = λ / v_th
Where v_th is the thermal velocity.
E_n = E_c - E_Ry / n_q²
Where:
Find n_kT: the smallest integer where E_n > kT relative to continuum.
r₀ = 2 × n_kT² × a_B
Where a_B is the quasi-Bohr radius.
Since ground state is often slightly below kT:
r₀ ≈ 2 × a_B
s ≈ 4 × a_B² × (E_Ry / kT)²
| Model | Temperature Dependence | Physical Origin |
|---|---|---|
| Gas-kinetic (neutral) | Weak (thermal velocity) | Geometric capture |
| Coulomb-attractive | s ∝ 1/T² | Coulomb focusing decreases with T |