Advanced Model Links Material Properties to Efficient Electron Source Performance

Scientists are increasingly focused on accurately predicting the performance of semiconducting photocathodes for advanced electron sources. Richard Schier from Carl von Ossietzky Universit at Oldenburg and Friedrich-Schiller Universit at Jena, Chen Wang working with colleagues at Helmholtz-Zentrum Berlin and Universit at Siegen, and Jonas Dube from Helmholtz-Zentrum Berlin and Humboldt-Universit at zu Berlin, alongside Julius Kühn, Alice Galdi, Thorsten Kamps, and Caterina Cocchi, present a novel many-body extension to the three-step photoemission model. This research integrates the Bethe-Salpeter equation with density functional theory, overcoming limitations of standard approaches by explicitly accounting for quasiparticle and excitonic effects. The team’s collaborative effort, spanning Helmholtz-Zentrum Berlin, Carl von Ossietzky Universit at Oldenburg, Friedrich-Schiller Universit at Jena, Universit at Siegen, Humboldt-Universit at zu Berlin, and Universit a degli Studi di Salerno, delivers a parameter-free, ab initio tool achieving quantitative agreement with experimental quantum efficiency values and offering a critical pathway towards the rational design of next-generation electron sources.

Scientists have developed a new computational tool to accurately predict photoemission from semiconducting materials, a crucial step in designing next-generation electron sources for applications like free-electron lasers and particle accelerators. This work addresses a long-standing challenge: linking the microscopic electronic properties of materials to their macroscopic behaviour during photoemission, the release of electrons when light strikes a surface.

To overcome limitations in conventional density functional theory (DFT) calculations, researchers integrated the GW approximation and the Bethe-Salpeter equation, advanced techniques from many-body perturbation theory, directly on top of DFT calculations. This allows for a more realistic depiction of quasiparticle and excitonic effects, which significantly influence the photoexcitation process.

The resulting model calculates the quantum efficiency (QE), a measure of how effectively a material emits electrons when illuminated, by combining calculated light absorption with an emission probability weighted by exciton contributions. Validation focused on representative alkali antimonides, demonstrating the ability to capture intricate spectral features that simpler models cannot reproduce.

Crucially, the team incorporated macroscopic optical effects, such as thin-film interference and polarization, using Fresnel post-processing, enabling quantitative agreement with experimental QE values without adjustable parameters. Minor discrepancies near the photoemission threshold are attributed to the simplified surface barrier used in the model and the presence of impurities, providing clear directions for future improvements.

This work establishes a robust, parameter-free method for predicting photoemission characteristics from first principles, bridging the gap between microscopic electronic correlations and macroscopic observables. The tool promises to accelerate the rational design of advanced photocathode materials, paving the way for more efficient and powerful electron sources.

The ability to accurately simulate photoemission without empirical adjustments represents a significant advancement, offering a pathway to tailor materials for specific applications and optimise performance. Density functional theory (DFT) calculations underpin the theoretical framework used to model photoemission from semiconducting photocathodes, establishing the initial electronic structure upon which many-body perturbations are applied.

Specifically, the Kohn-Sham equations were solved self-consistently to determine the ground state electronic configuration of the alkali antimonide materials, utilising plane-wave basis sets and a carefully converged k-point mesh to ensure accurate representation of the Brillouin zone. To move beyond the limitations of standard DFT, the GW approximation was implemented to calculate quasiparticle energies, addressing the many-body effects neglected in conventional DFT.

The GW self-energy accounts for the screening of the electron-electron interaction, providing a more accurate description of the electronic structure and optical properties. Following the GW calculation, the Bethe-Salpeter equation (BSE) was solved to determine the excitation energies and wavefunctions of excitons, bound electron-hole pairs that significantly influence the optical response of semiconductors.

The resulting quasiparticle energies and excitonic wavefunctions were then integrated into a modified three-step photoemission model. This model calculates the QE by combining the ab initio absorption spectrum, derived from the BSE, with an emission probability weighted by the exciton contributions. Macroscopic effects, such as thin-film interference and polarization, were incorporated via Fresnel post-processing, employing the sample thickness and incidence angle of the incoming radiation as input parameters.

Calculations reveal an excitation probability for hexagonal potassium antimonide, K3Sb, derived from the macroscopic dielectric function, averaging both in-plane and out-of-plane contributions. The research team modelled electron transport, adopting an elastic process approximation justified by the negligible electron-electron scattering in semiconducting photocathodes and minimal impact on the predicted spectral dependence of the photoemission yield.

Crucially, the emission probability was determined by employing a transmission function, T(E), adjusted to match the experimentally measured work function of 2.9 electron volts, exhibiting no transmission below 2.9 eV and asymptotically approaching unity at higher energies. The energy distribution of excited electrons, Dλ(E), was calculated by summing k-resolved electron weights obtained from the Bethe-Salpeter equation, effectively mapping the probability of finding photogenerated electrons at specific energies above the band gap.

By combining these elements, the work establishes a parameter-free ab initio tool capable of quantitatively matching experimental photoemission yields without adjustment. Discrepancies observed near the photoemission threshold are attributed to the idealized surface barrier adopted in the model and potential impurity effects within the samples, providing clear targets for future refinement.

Scientists have long sought a reliable, predictive link between the materials science of electron sources and their actual performance, a connection often obscured by complex quantum mechanical effects. This work represents a step towards that goal, moving beyond empirical models to a genuinely first-principles approach for understanding photocathode materials.

For decades, the design of these components, used in particle accelerators and advanced imaging technologies, has relied heavily on trial and error, a slow and expensive process. What distinguishes this research is the explicit inclusion of many-body effects, specifically how electrons interact with each other and with the material’s excited states. By integrating the Bethe-Salpeter equation with density functional theory, the researchers have created a framework that captures these subtleties, successfully reproducing complex spectral features previously inaccessible to simulation.

The validation against experimental data for alkali antimonides is compelling, demonstrating the model’s predictive power without needing to fine-tune parameters. However, the model still relies on an idealised surface barrier, and the impact of real-world imperfections, impurities and surface roughness, remains an area for further investigation. Extending this approach to a wider range of cathode materials and operating conditions will be crucial. Future work might explore the influence of surface reconstruction and chemical doping, and the development of even more efficient algorithms to handle the computational demands of these complex calculations.