The sub-band structure of atomically sharp dopant profiles in silicon

The downscaling of silicon-based structures and proto-devices has now reached the single-atom scale, representing an important milestone for the development of a silicon-based quantum computer. One especially notable platform for atomic-scale device fabrication is the so-called Si:P δ-layer, consisting of an ultra-dense and sharp layer of dopants within a semiconductor host. Whilst several alternatives exist, it is on the Si:P platform that many quantum proto-devices have been successfully demonstrated. Motivated by this, both calculations and experiments have been dedicated to understanding the electronic structure of the Si:P δ-layer platform. In this work, we use high-resolution angle-resolved photoemission spectroscopy to reveal the structure of the electronic states which exist because of the high dopant density of the Si:P δ-layer. In contrast to published theoretical work, we resolve three distinct bands, the most occupied of which shows a large anisotropy and significant deviation from simple parabolic behaviour. We investigate the possible origins of this fine structure, and conclude that it is primarily a consequence of the dielectric constant being large (ca. double that of bulk Si). Incorporating this factor into tight-binding calculations leads to a major revision of band structure; specifically, the existence of a third band, the separation of the bands, and the departure from purely parabolic behaviour. This new understanding of the band structure has important implications for quantum proto-devices which are built on the Si:P δ-layer platform.