Thickness and electric field dependent polarizability and dielectric constant in phosphorene

TL;DR

This study uses first-principles calculations to analyze how the dielectric constant and polarizability of phosphorene vary with thickness and electric field, providing insights for device design.

Contribution

It reveals the thickness-dependent dielectric properties of phosphorene and how they can be tuned by an external electric field, advancing understanding of 2D material electrostatics.

Findings

Dielectric constant decreases with fewer layers.

Dielectric constant can be tuned by out-of-plane electric field.

Polarizability scales linearly with layer number.

Abstract

Based on extensive first principle calculations, we explore the thickness dependent effective di- electric constant and slab polarizability of few layer black phosphorene. We find that the dielectric constant in ultra-thin phosphorene is thickness dependent and it can be further tuned by applying an out of plane electric field. The decreasing dielectric constant with reducing number of layers of phosphorene, is a direct consequence of the lower permittivity of the surface layers and the in- creasing surface to volume ratio. We also show that the slab polarizability depends linearly on the number of layers, implying a nearly constant polarizability per phosphorus atom. Our calculation of the thickness and electric field dependent dielectric properties will be useful for designing and interpreting transport experiments in gated phosphorene devices, wherever electrostatic effects such as capacitance, charge screening etc. are important.