Strong Quantization of Current-carrying Electron States in $\delta$-layer Systems

TL;DR

This study uses an open-system quantum approach to analyze size quantization and conductive properties in phosphorus δ-layers, revealing strong quantization effects below 10 nm width and their impact on electron states and conductivity.

Contribution

It introduces an open-system quantum-mechanical real-space method to accurately predict conductive properties and size quantization in δ-layer systems, surpassing traditional boundary condition approaches.

Findings

Quantization effects are significant for widths less than 10 nm.

Number of propagating modes influences conductivity and current distribution.

Quantization effects diminish for widths greater than 10 nm, approaching bulk behavior.

Abstract

We present an open-system quantum-mechanical real-space study of the conductive properties and size quantization in phosphorus $\delta$-layers systems, interesting for their beyond-Moore and quantum computing applications. Recently it has been demonstrated that an open-system quantum mechanical treatment provides a much more accurate match to ARPES measurements in highly-conductive, highly-confined systems than the traditional approaches (i.e. periodic or Dirichlet boundary conditions) and, furthermore, it allows accurate predictions of conductive properties of such systems from the first principles. Here we reveal that quantization effects are strong for device widths $W<10$~nm, and we show, for the first time, that the number of propagating modes determines not only the conductivity, but the distinctive spatial distribution of the current-carrying electron states. For $W>10$~nm, the quantization effects practically vanish and the conductivity tends to the infinitely-wide device's values.