Brillouin zone selection effects in angle resolved photoemission spectroscopy for Silicon

The advancement of semiconductor-based atomic-scale quantum electronics hinges on a deep understanding of the electronic properties of subsurface δ-layers[1]. In this rapidly evolving field, soft X-ray angle-resolved photoemission spectroscopy (SX-ARPES) has emerged as a pivotal, non-destructive probing tool[2]. The large energy range of SX-ARPES allows for measurements across a broad momentum space, covering multiple Brillouin zones. During these measurements, interference effects from photoemission across different atoms in a unit cell can lead to pronounced intensity fluctuations between adjacent Brillouin zones, even causing some bands to vanish. In this study, we present the first detailed observations of such photoemission structure factor effects from a cubic semiconductor, revealing periodic fluctuations in both the valence and conduction band states of δ-doped silicon. By applying a simple tight binding calculation to Fermi's golden rule we are able to calculate the structure factor of Silicon and reproduce our experimental findings with a minimal number of approximations. Our findings pave the way for investigations at higher photon energies in the hard X-ray domain, crucial for exploring deeper δ-layers (~10 nm) typical in silicon quantum electronic devices.