Prospects for Direct Electron Detectors in Ultrafast Electron Scattering Experiments

Abstract

Ultrafast electron diffraction and phonon-diffuse scattering (UED(S)) experiments make use of photo-induced changes to electron scattering intensity across 2D detectors to report on a very wide range of dynamic structural phenomena in molecules and materials. Compared to ultrafast spectroscopies, these techniques have very high structural-information content and competitive time-resolution, but sensitivity to relative changes in electron scattering intensity is orders of magnitude lower. Hybrid pixel counting detectors (HPCDs) are a promising technology for improved sensitivity and signal-to-noise in UED(S) experiments, as they offer near-zero readout noise and dark counts with the possibility of new acquisition modalities (e.g. shot-to-shot normalization) due to their high frame rates. However, it is well known that HPCDs suffer from count losses at high electron fluxes even in CW beam applications. How this translates to ultrashort electron pulse exposures has yet to be determined and is critical to understanding the application of this technology to ultrafast electron scattering experiments. Here we show that count losses are exacerbated significantly in ultrafast (pulsed) experiments and that HPCDs require count rates to be kept below $\approx 2$ electrons per pixel per pulse. This count-rate limitation presents a severe constraint on electron bunch charge when interrogating single crystal samples. A model for the electron counting uncertainties in HPCDs across the entire relevant range of average count rates is proposed, from which we derive experimental strategies to optimize data quality in UEDS using direct electron detectors. Finally, we suggest ways HPCDs could be better adapted to ultrashort pulsed beam experiments.

Figures (6)

• Figure 1: Schematic illustration of the experimental setup. Electron bunches (blue particle clouds) are compressed and focused onto the sample in normal incidence and produce a diffraction pattern on the detector, represented by a plane behind the sample. Simultaneously, the sample can be illuminated with a short optical laser pulse (red discs) with an adjustable time-delay. The temporal distance between electron bunches and optical pulses is dictated by the laser amplifier, in our case $\Gamma^{-1}=1$ ms. The four screens on the far right side illustrate how difference images are calculated for different delay times. Red (blue) regions increase (decrease) in diffracted intensity. Projected onto the screen are simulated diffraction patterns of graphite.
• Figure 2: Histograms of single-pixel count distributions $P_\mathrm{normal}(k)$ in normal (a--c) and $P_\mathrm{retrigger}(k)$ in retrigger (d--f) counting modes under low (a,d), intermediate (b,e), and high (c,f) electron doses. The incident electron count rates extracted with $P_0$ counting are 0.16, 1.04 and 7.6 EPP, respectively. $P_\mathrm{normal}(k)$ denotes the normalized probability distribution such that $\sum_k P_\mathrm{normal}(k) = 1$. The black points show the expected Poisson distribution for a mean value $\lambda$ extracted with the $P_0$ method from the normal-mode data; black circles in (a--c) truncate counts $\geq1$ as equivalent to $1$. Note that in panels (c) and (f), the horizontal axis is linear for $k \leq 3$ and logarithmic for larger values.
• Figure 3: a Detected per-pixel electron count rate in EPP using simple summation (black) and from $P_0$ counting (red) against the rate estimated by $P_0$ counting $\bar{\lambda}$. b Relative uncertainty in the per-pixel electron count rate versus $\bar{\lambda}$ for $P_0$ counting. The background heatmap shows the experimentally measured uncertainties from the data-set described in the text, with the corresponding colour bar at the top. A moving average of the experimental data is shown as a black solid line. The theoretical prediction from Eq. \ref{['eq:unc_in_px']} is shown in red. The theoretical optimum (minimum uncertainty) electron count rate is marked with a vertical dashed line. The contribution from the fundamental shot-noise limit decreases with increasing beam current and is plotted as a dotted black line. c Diffraction pattern of polycrystalline monoclinic VO$_2$. The left image half was processed by simple summation and subject to lost counts. The right half was processed by analyzing the ratio of zero events $\hat{P}_0$ and extracting $\bar{\lambda}$.
• Figure 4: a PSD of the fundamental 780 nm output from the laser amplifier (red) and the total scattered electron count (black). The black dashed line marks the shot-noise floor of the electron-count signal. The blue dashed line shows the fit to an $1/f^\alpha$ noise model. b Transient diffraction signal for the (220) Debye-Scherrer ring from $-30$ to $60$ ps. For the SNR analysis we use the time ranges outside the two black vertical lines. The data has been normalized with a shot-to-shot scheme. The grey points in the background show the same transient signal without using any normalization. c Change in SNR versus simulated exposure time for four different Debye-Scherrer rings.
• Figure 5: a Absolute azimuthally averaged diffraction pattern of VO$_2$ in equilibrium. Selected diffraction rings are labelled with their respective Miller indices. b Photoinduced signal change in diffracted intensity between 11 and 86 ps after photoexcitation (black) and rms noise (red). c Absolute uncertainty in the detected signal change as measured (black) and predicted (red).