Numerical Simulations of the Band Bending Profile of an Adatom-covered

Abstract

Accurately characterizing the properties of semiconductors at atomic resolution is crucial for advancing semiconductor technology. One of the key challenges in quantitatively interpreting Scanning Tunneling Spectroscopy (STS) is the influence of tipinduced band bending (TIBB) during semiconductor measurements. This thesis presents a numerical method that self-consistently solves the one-dimensional Poisson equation to correct for TIBB in adatom-covered semiconductors. The model uses the Block-SOR-Newton method to solve the nonlinear system of equations that arises from the discretization of the Poisson equation. Simulations demonstrate that the model can accurately describe the effect of the STM tip voltage on band bending. However, numerical instabilities were observed for high doping concentrations and surface state energies close to the Fermi level, attributed to overshooting of the Newton method. Potential solutions, such as using a Newton-Krylov method and adaptive grid refinement, were proposed to address these instabilities. Future work includes extending the model to non-equilibrium situations by introducing the full set of semiconductor equations and expanding to three dimensions to account for the STM tip geometry. These advancements would provide a useful tool for correcting STS data, ultimately deepening our understanding of semiconductor physics at the atomic scale.