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 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.
Highlights
Si:P δ-doping offers potential for the realisation of true atomicscale components for quantum computer applications[1,2,3,4,5,6,7,8], whilst retaining compatibility with the simple processing, stability, and technological relevance of silicon
Density functional theory (DFT) calculations and angle-resolved photoemission spectroscopy (ARPES) recently shed new light on these systems, giving the first glimpse of their electronic structure[9,10,11,12,13,14,15,16,17,18]: the metallic nature of Si:P δ-layers was believed to originate from two nearly-parabolic states, called 1Γ and 2Γ, dispersing across the Fermi level (EF) as a consequence of the strong electronic confinement created by the P dopants in the semiconducting Si bulk
We reveal the presence of additional anisotropic electronic states crossing EF, resolved only for specific directions in the BZ
Summary
Si:P δ-doping offers potential for the realisation of true atomicscale components for quantum computer applications[1,2,3,4,5,6,7,8], whilst retaining compatibility with the simple processing, stability, and technological relevance of silicon. The presence of three states across EF cannot be reconciled with published DFT9,11,12 and tightbinding (TB) calculations[10] This discrepancy is seen in our TB calculations (Fig. 1d and see Supplementary Information), where only two bands, instead of three, are responsible for the metallic properties of the system. [Note: reports of SOC in Si:P δ-layers are generally absent, studies of SOC in Si:P derived structures do exist19.] We show that ε is expected to be dramatically increased in the vicinity of the high-density dopant layer, thereby causing a large increase in the efficiency of the screening This causes the confinement to be stronger than previously expected, and for additional states originally predicted to be well above EF (as in Fig. 1d) to become occupied
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