Analyze carrier kinetics in semiconductors with continuous trap distributions using quasi-stationary approximation. Use when modeling decay transients, calculating effective carrier lifetimes, or extracting trap density profiles from kinetic measurements in materials with distributed defect levels rather than discrete traps.
Apply this skill when:
Verify these conditions before applying:
Confirm that temperature and light intensity are high enough to justify:
Integrate the trap distribution from the conduction band edge to the quasi-Fermi level:
nt = ∫[0 to EF] Nt(E) dE
Where:
Calculate dn_t/dn as a function of electron density using the integral of the trap distribution.
Substitute the distribution-based dn_t/dn into the decay relation:
τ / τn = 1 + (1/n) × ∫[0 to EF] Nt(E) dE
Where:
For n distinct groups of trap levels, expect (n-1) relaxation times corresponding to:
| Variable | Type | Description |
|---|---|---|
| Nt(E) | Distribution | Trap density distribution function [cm⁻³(eV)⁻¹] |
| EF | Energy | Quasi-Fermi level position [eV] |
| nt | Density | Total trapped electron density [cm⁻³] |
| τ₀ | Time | Inverse generation rate constant (n/g₀) [s] |
| τ | Time | Measured decay time [s] |
| τn | Time | Intrinsic carrier lifetime [s] |