Quantum efficiency and thermal emittance of metal photocathodes

Modern electron beams have demonstrated the brilliance needed to drive free electron lasers at x-ray wavelengths with major advances occurring since the invention of the photocathode gun and the realization of emittance compensation. These state-of-the-art electron beams are now becoming limited by the intrinsic thermal emittance of the cathode. In both dc and rf photocathode guns details of the cathode emission physics strongly influence the quantum efficiency and the thermal emittance. Therefore improving cathode performance is essential to increasing the brightness of beams. It is especially important to understand the fundamentals of cathode quantum efficiency and thermal emittance. This paper investigates the relationship between the quantum efficiency and the thermal emittance for metal cathodes using the Fermi-Dirac model for the electron distribution. We use a consistent theory to derive the quantum efficiency and thermal emittance, and compare our results to those of others.

Figure 1

Three-step model of photoemission.

Figure 2

The energy distribution of occupied states for a metal (left) and the electric potentials next to the cathode surface (right). The Schottky potential (green curve) is the sum of the applied field potential (blue) and the image charge potential (red). The Schottky work function is the amount the material work function is reduced at the peak of the Schottky potential. The Schottky potential is shown for an applied field of $100\mathrm{MV}/\mathrm{m}$ where the peak of the photoemission barrier is 1.9 nm from the surface. The effective work function is the height of this barrier above the Fermi level and is the material work function reduced by the Schottky work function.

Figure 3

Diagram showing the conservation of transverse momentum at the metal-vacuum interface. Outside the surface the maximum angle is $\pi /2$ when the electrons are refracted with the largest internal angle of incidence ${\theta }_{\max }^{\mathrm{in}}$. Electrons with angles greater than ${\theta }_{\max }^{\mathrm{in}}$ are reflected back into the metal.

Figure 4

Graphical representation of the electron momentum inside the cathode and the maximum angle of escape.

Figure 5

Definition of the coordinate system and components of the momentum just inside the cathode surface used to derive the photoelectric emittance.

Figure 6

The normalized emittance per rms beam size for Cu as a function of photon energy for the typical operating electric fields of metal cathodes in rf guns due to the Schottky reduction of the barrier as described in the text. The work function is assumed to be 4.31 eV.

Figure 7

The quantum efficiency and the normalized emittance per rms beam size plotted as functions of the effective work function, ${\varphi }_{\mathrm{eff}}$, for a photon energy of 4.90 eV (${\lambda }_{\mathrm{laser}}=253\mathrm{nm}$).