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.

我们使用主方程来模拟吸收泵浦脉冲后的电子弛豫过程。假定弛豫过程主要是通过将导电带电子捕获在浅陷阱能级中。我们求解主方程，并根据陷阱能和泵浦脉冲扰动的平衡费米能级，获得了导带电子族的实验可及动力学轨迹的表达式。该表达式揭示了实际上对信号有贡献的陷阱能量的小窗口，并且通过研究不同的陷阱分布，我们认为，当所有陷阱都位于费米能级以下时，基本上无论是单指数还是动力学曲线都将很好地拟合，或采用双指数（当然，当某些陷阱在费米能级以上时，甚至可以提高三倍。所获得的速率不允许人们重建阱的分布，但是可以找到费米能级，并且在单指数衰减的情况下，可以找到捕获截面的上限。