Method for Evaluating the Spatial Distribution of Dielectric Constants: Application to Hydrogenated C(111) and Si(111) Surfaces

Abstract

In this study, we developed a method to evaluate and visualize the three-dimensional (3D) spatial distribution of the local dielectric constant at the atomic scale. We applied this method to hydrogenated C(111) and Si(111) thin films (i.e., C(111)-H and Si(111)-H) using first-principles calculations to evaluate the relationship between their surface electronic states and local dielectric properties. While the Si(111)-H film exhibits a reduced dielectric constant near the surface, consistent with the depolarization field effect reported in previous studies, the C(111)-H film shows a significant dielectric enhancement in the surface region, reaching values exceeding that of the bulk. We demonstrate that this anomalous enhancement is attributed to the highly polarizable nearly free electron (NFE) state, which constitutes the conduction band minimum (CBM) of C(111)-H and distributes broadly into the vacuum. Our analysis also confirms that the NFE state persists as a robust surface feature regardless of film thickness. These findings provide evidence that surface-specific electronic states govern the near-surface dielectric response, offering new insights for the design of carbon-based nanoscale devices.