Simultaneous conduction and valence band quantisation in ultra-shallow, high density doping profiles in semiconductors

TL;DR

This paper demonstrates simultaneous quantisation of conduction and valence band states in silicon using ultra-shallow, high-density phosphorus doping profiles, revealing independent control over these quantum states for potential quantum engineering applications.

Contribution

It introduces the first observation of simultaneous CB and VB quantisation in silicon with ultra-shallow dopant profiles, and explains VB quantisation with a simple particle-in-a-box model.

Findings

VB quantisation depends on dopant depth

CB quantisation depends on dopant density

Independent control of CB and VB states is achievable

Abstract

We demonstrate simultaneous quantisation of conduction band (CB) and valence band (VB) states in silicon using ultra-shallow, high density, phosphorus doping profiles (so-called Si:P $\delta$-layers). We show that, in addition to the well known quantisation of CB states within the dopant plane, the confinement of VB-derived states between the sub-surface P dopant layer and the Si surface gives rise to a simultaneous quantisation of VB states in this narrow region. We also show that the VB quantisation can be explained using a simple particle-in-a-box model, and that the number and energy separation of the quantised VB states depend on the depth of the P dopant layer beneath the Si surface. Since the quantised CB states do not show a strong dependence on the dopant depth (but rather on the dopant density), it is straightforward to exhibit control over the properties of the quantised CB and VB states independently of each other by choosing the dopant density and depth accordingly, thus offering new possibilities for engineering quantum matter.