Electron-electron interactions in highly degenerately doped embedded Si:P delta layers in silicon produced by variable PH₃ dosing

Key to producing quantum computing devices based on the atomistic placement of dopants in Si by STM lithography is the formation of embedded highly doped Si:P delta layers (δ-layers). This study investigates the transport behavior and the electron-electron interaction (EEI) physics in the highly doped regions of embedded Si:P-based devices by means of self-consistent magnetotransport (MT) measurements. In earlier work, we demonstrated that a careful MT study at low T, along with analysis of the weak localization (WL) signal, allows us to extract parameters associated with the electronic transport that offer a meaningful quantitative characterization of δ-layer quality and dopant diffusion. We build on this work by examining EEI behaviors in a set of samples with embedded Si:P delta layers produced with different PH₃ exposure procedures prior to Si encapsulation. We show that the charge carriers behave as 2DEGs in embedded Si:P δ-layers in samples grown with a locking layer (LL) to bolster confinement of the dopants, while samples grown without a LL demonstrate several signatures of transport and EEI in a 3D system. The impact between δ-layer confinement and EEI on screening lengths affects both electrostatic gating of and tunneling transport through Si:P single atom transistors.