$\sim$2.4 ps. Since the capture times decrease inversely with the defect density $n_{d}$, the capture times shown in Fig.\[fig:capture1\] can be interpolated for different values of the defect density. For example, a defect density of $8\times 10^{11}$ cm$^{-2}$ would result in an electron capture time of 0.6 ps for the $E$ state of a sulfur vacancy (under the same assumptions as stated above).

Fig.\[fig:capture1\] shows that shallower traps have much shorter capture times than deeper traps. This can be understood as follows. Energy conservation requires that the scattered electron (hole), in a hole (electron) capture process, takes away most of the energy. The deeper the trap the more the final energy of the scattered particle. Also, momentum conservation requires that the momentum of the scattered particle be provided by the relevant Fourier component of the defect state wavefunction. Therefore, the deeper the trap the larger the momentum transfer. Since in Fourier space the defect state wavefunction is $\chi_{d}(\vec{q}) = \sqrt{2\pi a_{d}^{2}} e^{-q^{2}a_{d}^{2}/4}$, larger momentum transfers result in smaller capture rates. Note that this result is largely independent of the exact assumed form of the defect state wavefunction. In addition, the Coulomb potential $V(\vec{q})$ also decreases for larger momentum transfers. Although 