# The Sub-band Structure of Atomically Sharp Dopant Profiles in Silicon

## TL;DR

This study uses high-resolution ARPES to reveal complex electronic band structures in silicon phosphorus delta-layers, showing significant deviations from previous theoretical models and impacting quantum device design.

## Contribution

The paper provides the first experimental observation of three distinct bands in SiP delta-layers and revises theoretical models to include dielectric effects, enhancing understanding of their electronic structure.

## Key findings

- Three distinct electronic bands observed in SiP delta-layers.
- Large anisotropy and non-parabolic behaviour of the most occupied band.
- Revised band structure models incorporating dielectric effects.

## Abstract

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 SiP delta-layer, consisting of an ultra dense and sharp layer of dopants within a semiconductor host. Whilst several alternatives exist, phosphorus dopants in silicon have drawn the most interest, and it is on this 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 SiP delta-layer platform. In this work, we use high resolution angle-resolved photoemission spectroscopy (ARPES) to reveal the structure of the electronic states which exist because of the high dopant density of the SiP delta-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 bandstructure has important implications for quantum proto-devices which are built on the SiP delta-layer platform.