What can transient absorption spectroscopy reveal about the trap distribution in a semiconductor?

We use a master equation to model the electronic relaxation process following the absorption of a pump pulse. The relaxation process is assumed to be dominated by trapping of conduction band electrons in shallow trap levels. We solve the master equation and obtain an expression for the experimentally accessible kinetic trace of the conduction band electronic population in terms of the trap energies and the equilibrium Fermi level perturbed by the pump pulse. The expression reveals the small window of trap energies that actually contributes to the signal and, investigating different trap distributions, we argue that basically the kinetic trace will be very well fitted either by a single-exponential, when all traps lie below the Fermi level, or by a double-exponential (and, naturally, even better by a triple-exponential) when some of the traps are above the Fermi level. The rates obtained do not allow one to reconstruct the trap distribution, but the equilibrium Fermi level and, in the case of single-exponential decays, an upper limit for the capture cross-section may be found.