Recent breakthroughs in single-atom fabrication in silicon have brought the exciting prospect of monolayer-based nanoelectronics and theoretical understanding of such systems into sharp focus. Of particular interest is the effect of such sharp two-dimensional Coulomb array confinement on electronic properties of these donor-based semiconducting systems such as valley splitting, which is critical to quantum electronic applications. In this paper we apply ab initio techniques to these high-density donor systems specifically in order to investigate the approach to monolayer confinement. An optimized basis set is developed for Si:P and validated against our previous work on single $\delta$-doped layers. A systematic study is then conducted wherein the effect of multiple adjacent phosphorus $\delta$ layers on the electronic properties of the material is explored. We find nonmonotonic electronic behavior as we approach the monolayer confinement limit, with potentially far-reaching implications for large-scale fabrication techniques.

• Received 22 April 2012

DOI:https://doi.org/10.1103/PhysRevB.86.165123