📝 SummarXiv

Abstract

Silicon can be heavily doped with phosphorus in a single atomic layer (a $\delta$ layer), significantly altering the electronic structure of the conduction bands within the material. Recent progress has also made it possible to further dope silicon with acceptor-based $\delta$ layers using either boron or aluminum, making it feasible to create devices with interacting $\delta$ layers with opposite polarity. It is not known, however, how these $\delta$ layers will interact, particularly at small separation distances. Using Density Functional Theory, we calculate the electronic structure of a phosphorus-based $\delta$ layer interacting with a boron or aluminum $\delta$ layer, varying the distances between the $\delta$ layers. At separations 10 \AA\ and smaller, the dopant potentials overlap and largely cancel each other out, leading to an electronic structure closely mimicking bulk silicon. At separations greater than 10 \AA, the two layers behave independently of one another, forming a p-n diode with an intrinsic layer taking the place of the depletion region. One mechanism for charge transfer between $\delta$ layers at larger distances could be tunneling, where we see a greater than 3\% probability for tunneling between a phosphorus and boron layer at 20 \AA\ separation. This tunneling rate exceeds what would be seen for a standard silicon 1.1 eV triangular barrier, indicating that the interaction between delta layers creates enhanced tunneling at larger separation distances compared to a traditional junction. These calculations provide a foundation for the design of silicon-based electronics based on interacting $\delta$ layers.