Conductivity and size quantization effects in semiconductor $\delta$-layer systems

TL;DR

This study uses 3D quantum-mechanical simulations to analyze how size quantization affects conductivity in semiconductor delta-layer systems, revealing strong effects at nanoscale widths and their impact on device properties.

Contribution

It provides the first detailed 3D real-space analysis of size quantization effects on conductivity in delta-layer systems, including finite and infinite widths, relevant for quantum devices.

Findings

Quantization effects are significant for widths less than 10 nm.

Number of propagating modes influences conductivity and current distribution.

Conductivity approaches infinite-width values for widths greater than 10 nm.

Abstract

We present an open-system quantum-mechanical 3D real-space study of the conduction band structure and conductive properties of two semiconductor systems, interesting for their beyond-Moore and quantum computing applications: phosphorus $\delta$-layers in silicon and the corresponding $\delta$-layer tunnel junctions. In order to evaluate size quantization effects on the conductivity, we consider two principal cases: nanoscale finite-width structures, used in transistors, and infinitely-wide structures, electrical properties of which are typically known experimentally. For devices widths $W<10$~nm, quantization effects are strong and it is shown 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 values. For tunnel junctions, two distinct conductivity regimes are predicted due to the strong conduction band quantization.