the case of uncorrelated electrons and holes, the rate for this process is proportional to the product of the hole density $p$ and the probability of finding an electron near the hole, which is proportional to the electron density $n$. But in the case of tightly bound excitons, an electron is present near the hole with a very high probability proportional to $|\phi(\vec{r}=0)|^{2}$, where $\phi(\vec{r})$ is related to the exciton wavefunction (see the discussion below). Therefore, the rate for a hole (or an electron) in a tightly bound exciton to get captured by a defect is proportional to the exciton density times $|\phi(\vec{r}=0)|^{2}$. Generally speaking, Auger rates in semiconductors are considered to be important only at large carrier densities [@Landsberg92]. But given the small exciton radii in 2D-TMDs (in the 7-10$\AA$ range), $|\phi(\vec{r}=0)|^{2}$, which is inversely proportional to the square of the exciton radius, can be extremely large and, consequently, Auger capture rates in 2D-TMDs can be very fast. Compared to the rates for direct electron-hole recombination via interband Auger scattering (exciton-exciton annihilation), which can be limited by the orthogonality of the conduction and valence band Bloch states, the rates for the capture of electrons and holes of excitons by 