## 4 Results and Discussion
### EELS Background Subtraction  
Contrary to conventional EELS, no prior knowledge of the background signal is needed since the RUP events contain all the information of the background. Indeed the \(N_{RUP}\) signal is independent of the time difference between the X-rays and electrons and hence the background signal is approximated very well using all events outside the time coincidence interval [8,11]. In previous works, a proof of principle was shown but a clear experimental validation with respect to conventional background subtraction was lacking. Therefore, in the present work, eight coincidence datasets were recorded where for each set we shift the energy range of the EELS detector by 200 eV. This provides eight experimental EELS spectra with consecutive energy windows. The incoming current and acquisition time was kept constant over all measurements. The core-loss edge measured is the K-edge from Si on a crystalline Si reference sample. In Figure 3a, the combined EEL spectrum is given, where each color indicates a different acquisition and energy window. The black line indicates the fitted background signal which is obtained via power-law fitting where the grey area indicates the fitting region [19]. The background fitting was performed using the Hyperspy open-source software [27]. Figure 3b shows the coincidence EEL spectrum with considerably more noise due to the fact that only a small subset of the EELS events is retained as coincident events (\(\sim\)0.1%). This can be explained by comparing Equations (1) and (3) where the number of coincident events is a factor of \(\epsilon_{x}\cdot\omega\) smaller than \(N_{EEL}\) where \(\epsilon_{x}\approx 3\%\) and \(\omega\approx 5\%\)[28]. The background signal (black) is obtained by taking only electrons which do not have an X-ray within the time coincidence interval region ranging from 2200-2600 ns which is chosen to include all the coincidence events inside the interval. Please note that the background signal also includes some edge signal since there are uncorrelated events arising from the inelastic scattering on the Si K-edge (see Equation (4)). In Figure 3c, the conventional and coincidence background-subtracted EEL spectra are scaled and shown together for comparison. The coincidence method reproduces the result obtained from the standard power-law subtraction method where no significant discrepancy between the two signals is observed. The noise on the coincidence EEL spectrum is considerably larger as the number of detected coincidence events is only 0.1% compared to the number of detected EEL electrons. At first sight it therefore seems that coincidence background subtraction only leads to the same result with higher noise. The advantage of the coincidence EEL spectra, however, is that no pre-edge region was needed to subtract the background. This is of fundamental importance when, e.g., core-loss energies of two elements are close to each other preventing a good background fitting region in conventional EELS [29]. This situation also occurs often in the low loss regime, but in this case correlation with cathodoluminescence photons would be required as opposed to the X-rays used here, which would form a highly attractive area for future research as well [30]. Even when X-ray lines are overlapping due to the limited energy resolution of the detectors, the EEL background signal can be correctly subtracted which is shown in Figure 4. In Figure 4a the X-ray spectrum of GaAs semiconductor reference sample is shown, the red and blue line indicate the extent of respectively the Ga L\({}_{\alpha}\) line and As L\({}_{\alpha}\) line. It is clear that by selecting _regions 1+2_ in Figure 4a X-rays arising from both the As and Ga atoms are included when creating the background-subtracted EEL signal, which is shown in Figure 4b. An additional shoulder in the EEL spectrum is visible coming from electrons that scattered inelastically with the As L\({}_{23}\) edge. To remove the electron from the As signal only X-rays with energy in _region 1_ are chosen.