Band Bending and Beyond

Christopher C Leon,Olle Gunnarsson,Klaus Kuhnke

doi:10.1021/acs.jpcc.0c10247

Christopher C Leon, Olle Gunnarsson + Show 1 more

Open Access

https://doi.org/10.1021/acs.jpcc.0c10247

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Abstract

In the band bending (BB) picture, electric potentials assumed to be constant parallel to a surface rigidly shift the pristine electronic structure of semiconductors. This approximation is often applied in scanning tunneling microscopy (STM) to describe effects of the spatially localized potential of the tip. Here, we derive the BB approximation for STM using the Dyson equation. This requires the tip’s externally driven locally induced potential to be small compared to the surface’s electronic band width and the tip’s radius to be large compared to the surface’s lattice constant. Violating these conditions leads to outright failure of BB, for example, the formation of bound states in band gaps. We use thin films of C60 as a pedagogical example of this breakdown by comparing accurate calculations with approximations and connecting experimental data to four distinct regimes of BB validity derived through theory. This framework helps to identify and systematize effects beyond BB.

Highlights

How layered semiconductor-based devices work in response to an external electric field is due in large part to band bending (BB).1 “Standard” BB treats this electric field like that of an ideal plate capacitor
The theory reported in this paper provides access to a broader picture of electronic structure that is difficult to achieve in experiments
While we have examined how a tip perturbs the electronic structure of a thick molecular film of C60 at applied bias voltages of several volts, analogous effects will occur whenever applying mild voltages (≲ 0.1 V) leads to high fields (≫1 GV/m), such as in semiconductor samples

Summary

■ INTRODUCTION

How layered semiconductor-based devices work in response to an external electric field is due in large part to band bending (BB).1 “Standard” BB treats this electric field like that of an ideal plate capacitor. These differences were not minor perturbations to some quantitative features of the unperturbed electronic structure but were direct observations of major failures of BB, for example, the appearance of sharp localized states[12] when none were predicted This motivated our reevaluation of BB itself to elucidate effects “beyond BB” that may occur when common experimental tunneling parameters such as tip-surface distance, tip radius, and applied voltage are varied. For a narrow band molecular solid (whose narrowness of the band is due to weakly coupled intermolecular interactions), we find that the BB picture does not resemble accurate calculations and is qualitatively wrong in all details To understand these results, we find that one important ratio is the substrate band width (W) compared to the tipinduced potential differences in the substrate (ΔV), that perpendicular to the tip axis.

Im π n

■ DISCUSSION AND CONCLUSIONS

Findings

■ REFERENCES