Stability and electronic properties of ${\mathrm{CsK}}_2\mathrm{Sb}$ surface facets

First-principles methods have recently established themselves in the field of photocathode research to provide a microscopic, quantum-mechanical characterization of relevant materials for electron sources. While most of the existing studies are focused on bulk crystals, knowledge of surface properties is essential to assess the photoemission performance of the samples. In the framework of density-functional theory, we investigate the stability and the electronic properties of surface slabs of ${\mathrm{CsK}}_2\mathrm{Sb}$, an emerging semiconducting photocathode material for particle accelerators. Considering surfaces with Miller indices 0 and 1, and accounting for all possible terminations, we find that, at the interface with vacuum, the atomic layers may rearrange considerably to minimize the electrostatic repulsion between neighboring alkali species. From the analysis of the surface energy as a function of the chemical potential, we find a striking preference for surfaces oriented along the (111) direction. Yet, at large and intermediate concentrations of Cs and K, respectively, (100) and (110) slabs are energetically most favorable. The considered surfaces exhibit either semiconducting or metallic character. Of the former kind is the most stable (111) slab, which has a band gap of about 1.3 eV, in excellent agreement with experimental values for ${\mathrm{CsK}}_2\mathrm{Sb}$ samples. Metallic surfaces have a lower work function, on the order of 2.5 eV, in line with the emission threshold measured for ${\mathrm{CsK}}_2\mathrm{Sb}$ photocathodes. All in all, these results contribute to the fundamental understanding of the microscopic properties of ${\mathrm{CsK}}_2\mathrm{Sb}$ in particular and of multi-alkali antimonides in general, and they represent a useful complement to the ongoing experimental efforts in the characterization of this emerging class of photocathode materials.

Figure 1

Schematic view of the outermost atomic layers of the relaxed surface slabs considered in this work (bright spheres) compared with their initial structures constructed from the bulk (faded spheres).

Figure 2

Surface energies of the considered ${\mathrm{CsK}}_2\mathrm{Sb}$ slabs as a function of the chemical potential of K (left) and of Cs (right) for fixed values of ${\mu }_{\text{Cs}}$ and ${\mu }_{\text{K}}$, respectively. The $x$-axes are offset to ${\mu }_{\text{K}}=-768.979\text{eV}$ (left) and ${\mu }_{\text{Cs}}=-548.002\text{eV}$ (right).

Figure 3

False color plot of the most stable surfaces as a function of ${\mu }_{\text{Cs}}$ and ${\mu }_{\text{K}}$. The $x$ and $y$ axes are offset to ${\mu }_{\text{Cs}}=-548.002\text{eV}$ and ${\mu }_{\text{K}}=-768.979\text{eV}$, respectively.

Figure 4

Band structures calculated with the SCAN functional of the seven ${\mathrm{CsK}}_2\mathrm{Sb}$ slabs considered in this work offset with respect to the Fermi energy at 0 eV. In the semiconducting surfaces, the Fermi energy is set in the midgap and an arrow marks the fundamental gap between the valence-band maximum and the conduction-band minimum highlighted by horizontal dashed lines. Bottom-left panel: Brillouin zones of the indicated surfaces including the paths connecting the high-symmetry points adopted in the band-structure plots.

Figure 5

Atom-resolved projected density of states (PDOS) of the considered slabs calculated with the SCAN functional. The energy axis is scaled with respect to the Fermi energy set at 0 eV, which is in the midgap of the semiconducting surfaces.