Influence of sample momentum space features on scanning tunnelling microscope measurements

TL;DR

This paper demonstrates that the electronic structure of the STM tip, especially in materials with indirect band gaps like silicon, critically influences STM measurements due to complex momentum space features, challenging the traditional s orbital approximation.

Contribution

It reveals the importance of detailed tip electronic state modeling in STM measurements of indirect band-gap materials, highlighting the role of momentum space features.

Findings

STM tip orbital choice has minor effect in direct band-gap GaAs

Momentum space features significantly alter STM images in silicon

Accurate tip modeling is essential for interpreting STM data in indirect band-gap semiconductors

Abstract

Theoretical understanding of scanning tunnelling microscope (STM) measurements involve electronic structure details of the STM tip and the sample being measured. Conventionally, the focus has been on the accuracy of the electronic state simulations of the sample, whereas the STM tip electronic state is typically approximated as a simple spherically symmetric $ s $ orbital. This widely used $ s $ orbital approximation has failed in recent STM studies where the measured STM images of subsurface impurity wave functions in silicon required a detailed description of the STM tip electronic state. In this work, we show that the failure of the $ s $ orbital approximation is due to the indirect band-gap of the sample material silicon (Si), which gives rise to complex valley interferences in the momentum space of impurity wave functions. Based on direct comparison of STM images computed from multi-million-atom electronic structure calculations of impurity wave functions in direct (GaAs) and indirect (Si) band-gap materials, our results establish that whilst the selection of STM tip orbital only plays a minor qualitative role for the direct band gap GaAs material, the STM measurements are dramatically modified by the momentum space features of the indirect band gap Si material, thereby requiring a quantitative representation of the STM tip orbital configuration. Our work provides new insights to understand future STM studies of semiconductor materials based on their momentum space features, which will be important for the design and implementation of emerging technologies in the areas of quantum computing, photonics, spintronics and valleytronics.