the uncertainty in the exact values of these parameters. In the calculation of the electron capture times the defect state is assumed to be empty ($f_{d}=0$), and in the calculation of the hole capture times the defect state is assumed to be full ($f_{d}=1$).

![The capture times of electrons ($\tau_{ec}$) and holes ($\tau_{hc}$) of excitons by defects in monolayer MoS$_{2}$ on quartz are plotted as a function of the defect energy within the bandgap. The exciton binding energy is $E_{\alpha=1}$ is 0.4 eV and the material bandgap is 2.3 eV [@Changjian14]. The plotted capture times for electrons and holes have been normalized by multiplying them by $|b_{c}|^{2}$ and $|b_{v}|^{2}$, respectively. The defect density $n_{d}$ is $2\times 10^{11}$ cm$^{-2}$.[]{data-label="fig:capture1"}](./capture1){width=".45\textwidth"}

The curves shown in Fig.\[fig:capture1\] can provide results in different situations. For example, in the case of the $E$ states associated with a sulfur vacancy, if $|b_{c}|^{2}$ is assumed to be $\sim$0.25 [@Yong14], then the electron capture time curve in Fig.\[fig:capture1\] would need to be multiplied by 4 in order to get the actual electron capture times. If the $E$ state energy is assumed to $\sim$1.5 eV above the valence band edge [@Noh14], then the electron capture time comes out to be 