## 4 Results and Discussion
### Low Concentration Detection
In practice, beam damage and limitations on total exposure time due to drift will limit the maximum dose. To demonstrate the above prediction, a coincidence mapping on a 100 nm layer of diamond, grown on top of a germanium substrate, was performed using a 300 \(\times\) 1024 \(\times\) 1024 scan with a dwell time of 10 \(\upmu\)s. The sample drift per frame was calculated using the individual EELS frames since they have sufficient signal per frame to align them. The drift-corrected and summed EELS signal is shown in Figure 7a where the distortions on the left are flyback distortions since there was no flyback time in the experimental setup. For this sample, the main inquiry was to measure if there was any Ge incorporated in the diamond layer. The first step is to create an average EEL and EDX spectrum in a region of the diamond layer where the region of interest is shown in Figure 7a. The conventional EDX and EELS spectra are shown in Figure 7b,c. The conventional EDX spectrum shows an X-ray peak at the energy of Ge where the overlap of another X-ray peak, originating from the Cu L\({}_{\text{a}}\) X-ray line, of the experimental sample grid [21]. Furthermore, due to the FIB sample preparation method Ga is likely incorporated into the sample which has a similar core-loss energy making it hard to distinguish between the Ge and Ga for EDX. The conventional EELS spectrum does not show any features around the Ge L\({}_{\text{23}}\)-edge, or Ga L\({}_{\text{23}}\)-edge. However, when fitting a power law to the background region indicated in Figure 7g, a small gradual increase is seen starting from the Ga L\({}_{\text{23}}\)-edge which does not correspond to a sharp core-loss edge. The gradual increase of the background-subtracted signal gives no clear  
Figure 6: (**a**,**b**) The SNR of the coincidence and conventional EELS while varying the \(SBR\) and \(I\) and keeping the exposure time constant. Please note that both axes are logarithmic. The other parameters used to determine the SNR are indicated in Table A1. (**c**) The ratio between the SNR of coincidence and conventional EELS where a value larger than one indicates the region where coincidence outperforms conventional EELS (red colored areas). indication on the presence of Ga or Ge. The residual spectrum seen from the background fit comes from the incapacity of the power law to reproduce the background signal when the abundance of the element is very low. Next, the two-dimensional histogram using time difference and X-ray energy is shown in Figure 7d where the post selection electron energy-loss window is shown in Figure 7c (red window). An increase in signal is observed inside the time coincidence interval at a particular X-ray energy. From the two-dimensional histogram, the coincidence and background signal is calculated as discussed in Section 4.3. From this two background-free EDX spectra are calculated where the colors correspond to the EELS energy windows shown in Figure 7c (blue and red). The blue window only corresponds to electrons undergoing the core-loss events with Ga. The red window has both Ga and Ge electrons in the coincidence signal hence both X-ray lines are excited which is similar to Figure 5. This is seen in Figure 7f where for the red spectrum, a small increase in signal is seen at higher energies indicating the presence of X-rays with a larger energy (see black ellipse) than the one arising from the Ga L\({}_{a}\) line. The same method can be applied for EELS where in Figure 7e the 2D histogram between time difference and EEL energy is shown. An increase in signal at higher electron energy loss is seen inside the time coincidence window indicating the presence of an element with a core-loss edge at these energy ranges. The background-subtracted coincidence EEL signal is shown in Figure 7g where an onset is seen at an energy around 1100 eV which is before the Ge L\({}_{23}\)-edge but could correspond to the Ga L\({}_{23}\)-edge (1115 eV).