Band Bending and Beyond

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 C-6(0) 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.

Automated summary

In the band bending (BB) approximation, electric potentials are assumed to rigidly shift the pristine electronic structure of semiconductors parallel to a surface, with certain conditions needing to be met for its validity. Through studying thin films of C-60, the accuracy of approximate calculations and the four distinct regimes of BB validity derived through theory can be confirmed.