Effects of physical and chemical surface roughness on the brightness of electron beams from photocathodes

The performance of free electron laser x-ray light sources, and systems for ultrafast electron diffraction and ultrafast electron microscopy, is limited by the brightness of the electron sources used. The intrinsic emittance, or equivalently, the mean transverse energy (MTE) of electrons emitted from the photocathode determines the maximum possible brightness in such systems. With ongoing improvements in photocathode design and synthesis, we are now at a point where the physical and chemical surface roughness of the cathode can become a limiting factor. Here we show how measurements of the spatially dependent variations in height and surface potential can be used to compute the electron beam mean transverse energy (MTE), one of the key determining factors in evaluation of brightness.

Figure 1

Parallel-plate model to simulate equipotential lines produced by surface and chemical roughness. The gray arrows represent electrons emitted from the cathode. The blue regions show areas with positive surface potential, the beige regions show areas with zero surface potential and the red regions show areas with negative surface potentials. This image is only meant to describe the model used to solve the problem and a rough depiction of the equipotential lines close to a surface with physical and chemical roughness and does not depict a real cathode surface used for simulations in this paper.

Figure 2

Comparison of electric fields in $x$ direction (a) and in $z$ direction (b) 100 nm away from a 1-D sinusoidal surface as calculated using Bradleys equations (orange dashes) and using the formalism presented here (blue dashes). The z-direction is plotted with the constant electric fields removed. The two match to within three significant digits.

Figure 3

Comparison of the electric potential computed 10 nm above a uniform cathode surface with 2D sinusoidally varying surface potential using (a) Eq. (12) as obtained from [21] and (b) using the formalism presented in this paper. The offset term of the electric potential is subtracted to show the variation. The two match to within 1.6%.

Figure 4

(a) Surface physical and chemical roughness of ${\mathrm{Cs}}_3\mathrm{Sb}$ as measured by AFM and KPFM. (b) Surface potential as calculated by our formalism on the rough surface. The color coding denotes the potential variation on the surface.

Figure 5

Surface nonuniformities contribution to the MTE from the ${\mathrm{Cs}}_3\mathrm{Sb}$ photocathode surface shown in Fig. 4 (solid black line). At lower electric fields the MTE is dominated by the variations in surface potential, whereas, at higher electric fields it is dominated by the physical surface roughness. The figure also shows the MTE obtained from the surface assuming only potential variations and no height variations (red dotted line), assuming only height variations and a constant potential (blue dotted line) and the sum of the two (gray dotted line). Despite the same surface potential on the surfaces corresponding to the solid black line and the dashed gray/red line, the 3 meV difference in MTE at zero electric field arises due to the fact that these surfaces have a different physical roughness and hence different surface electric fields despite the same surface potential.