## 4 Results and Discussion
### Limit on the Time Resolution  
Equation (5) indicates that the SNR can be decreased via multiple routes. First, as shown in Section 3 by increasing the incoming current, the SNR is improved. However, it is not always possible to increase the current due to limits of the electron gun or the sample being radiation sensitive. Another method would be to acquire longer however this is sometimes not possible due to drift which leaves us with two other options: increasing the collection efficiency or improving the time resolution of the setup. From Figure 2a it is seen that the time coincidence interval has a width of approximately 400 ns which is disappointingly low in comparison to the \(<\)10 ns sampling capabilities of both EDX and EELS detector electronics. To improve the time resolution, the contributions from the different parts of the setup should be investigated. It is known that the relatively large size of the SDD detectors influences the TOA of the X-rays. This is of no surprise since the SDD was developed as a 2D position-sensitive detector for ionizing particles where the point of impact was derived using the travel time of the signal [38; 39]. If the limiting factor on the time resolution would be the area of the detectors then this would be visible in the shape of the time coincidence interval. The X-ray detectors used in the experiment have a circular shape, which should correspond to a sawtooth shape for the time resolution since the travel time depends linearly on the distance between X-ray impact point and detector center but the detection area scales as  
Figure 7: **(a)** A 300 \(\times\) 1024 \(\times\) 1024 STEM scan at 10 \(\upmu\)s on a diamond layer grown on top of a germanium substrate. The image shows the total number of electrons on the EELS detector at every probe position. The red window indicates the area from which the spectra are shown. **(b,c)** The conventional EDX and EELS signals. **(d)** Two-dimensional histogram, using a post selection on electron energy losses which are shown in **(c)**, between time difference and X-ray energy where the electron energies chosen are the ones within the red window. **(e)** Similar to **(d)** except that one axis is now electron energy loss and the post selection is performed on the X-ray energies shown in **(b)**. **(f)** The background-subtracted X-ray spectrum for the two electron energy windows indicated in **(c)**. The black ellipse indicates the region where an excess of counts is seen compared to the blue spectrum. **(g)** The background-subtracted EEL spectrum where an increase of signal is observed starting from the Ga L\({}_{2}\)s edge indicating the presence of core-loss events. The signal is binned to improve the SNR of the spectrum. Additionally, the conventional background-subtracted EEL spectrum is shown where the region for the power-law fit is indicated in **(c)**. meaning that on average more events will hit the outer region of the detector resulting in more weight for the longer time delays. This reasoning holds when the detector normal points exactly on the illuminated area on the sample. When this is not the case, the probability for an X-ray to land on the detector area is non-homogeneous modifying time coincidence histogram. However due to the configuration of the detector setup, this is expected to be a minor effect, but more research needs to be performed to understand this influence. In Figure 8a, the time coincidence histogram is shown from which an asymmetric shape is indeed visible (blue). The black dotted line is a sawtooth function convolved with an extra instrumental Gaussian function with a standard deviation of 30 ns. This model shows that the shape and size of the SDD plays a dominant role in limiting the time resolution to a value much lower than what we could handle with the electronics. The extra convolution with 30 ns could be related to the finite electronic bandwidth of the preamplifier stages which would then be estimated to be in the 10 MHz range.