# Recent Advances in Ultrafast Structural Techniques
## 3 Structural Techniques Involving Ultrashort Electron Pulses
### Bright Compact Direct Current (DC) FED Setups
Surface structures are sketched below, with In and Si atoms depicted as filled blue circles and open circles, respectively; In–In bonds are shaded grey. (**a**) In the insulating phase, the In atoms form distorted hexagons in an (8 \(\times\) 2) reconstructed unit cell. (**c**) In the metallic phase, the In atoms rearrange to form zigzag chains with (4 \(\times\) 1) structure. (**b**) Normalized difference between RHEED patterns (**c**) and (**a**). All of the (8 \(\times\) 2) ground-state features disappear (blue), while most (4 \(\times\) 1) spots gain intensity (red). (**d–e**) Time evolution of the diffraction intensities following photoexcitation with F = 6.7 mJ cm\({}^{-2}\). (**d**) Transient intensity of the (00) spot and an (8 \(\times\) 2) spot (rescaled) as a function of \(t\). The solid line is an exponential fit to the data for the (00) spot, from which a time constant of \(\tau_{\text{trans}}\) = 350 fs, reflecting the structural change, is extracted. The (8 \(\times\) 2) spot vanishes completely to the background level (dashed grey line). (**e**) Intensity of a fourth-order spot and the thermal diffuse background. The transient dip in the intensity of the fourth-order spot (yellow shaded area) at \(t\) = +6 ps indicates surface heating by \(\Delta\)T = 80 K (Debye–Waller effect), which coincides with the increase in background intensity. The fourth-order spot intensity is described (solid red curve) by the superposition of the two dashed lines, representing incoherent thermal motion (heating and subsequent cooling with time constants of 2.2 ps and 30 ps, respectively) and the structural transition with \(\tau_{\text{trans}}\) = 350 fs. Figure adapted from Reference [178] with permission from Springer Nature. geometrical electric field at the surface, i.e., in the area from which electrons are photoemitted. The main challenge is then to avoid vacuum breakdown (i.e., electrical discharges). The critical surface vacuum breakdown is given by, Equation (18):  
\[\left|\mathrm{E_{s,c}}\right|=\ \beta_{m}\beta_{g}\frac{\left|\mathrm{V_{c}} \right|}{\mathrm{d_{a}}} \tag{18}\]  
where \(\left|\mathrm{E_{s,c}}\right|\) is the magnitude of the critical surface vacuum breakdown field, \(\beta_{m}\) and \(\beta_{g}\) are microscopic and geometrical field enhancement factors, respectively, and \(\mathrm{V_{c}}\) is the critical applied potential drop over the cathode-anode separation distance, \(\mathrm{d_{a}}\).] Note that \(\left|\mathrm{V_{c}}\right|\mathrm{d_{a}}^{-1}=\ \left|\mathrm{\left<E_{c} \right>}\right|\), where \(\left|\mathrm{\left<E_{c}\right>}\right|\) is the magnitude of the average critical applied field and \(\beta_{g}\mathrm{|\left<E_{c}\right>}\) equals what we refer to as the geometrical critical surface electric field, \(\left|\mathrm{E_{g,c}}\right|\). Thus, Equation (19):  
\[\left|\mathrm{E_{s,c}}\right|=\ \beta_{m}\big{|}\mathrm{E_{g,c}}\big{|} \tag{19}\]  
Values of \(\left|\mathrm{E_{s,c}}\right|\) have been found to be 6.5-10 GV m\({}^{-1}\) for refractory metals [227; 228; 229] while \(\beta_{m}\) is governed by the surface roughness with \(\beta_{m}\approx 100\) for mirror-like finished and \(\beta_{m}=\ 1\) for a roughness free surface. Note that field emitters approach the limit \(\beta_{m}\approx\ 1\), and thus \(\left|\mathrm{E_{s,c}}\right|\ \approx\ \left|\mathrm{E_{g,c}}\right|\). For a bulky  
Figure 17: **Ultrafast electron source concept for the generation of <15-fs (rms) multi-electron bursts. ** (**a**) Schematic of the electron source concept. Equipotential and magnetic field lines calculated using Poisson Superfish, [226] are shown in red and green, respectively with a value of \(\left|\mathrm{E_{g}}\right|=50\) MV m\({}^{-1}\). (**b**,**c**) Results from ASTRA simulations. (b) Electron pulse duration (\(\sigma_{v}\) in fs) as a function of the number of electrons per bunch (#e-). Black trace corresponds to our 300-kV DC FED design with \(\mathrm{d_{a}}=5\) cm and a total cathode-sample distance \(\mathrm{d_{T}}=10\) cm.