Calculation of polarization and bound charge density inside a dielectric material in triboelectric nanogenerators: Analytical and numerical study

Abstract

We analytically calculated polarization and bound charge density inside the dielectric material in metal-to-dielectric-mode triboelectric nanogenerators (TENG) where the transferred charges are collected on the bottom metal via electrostatic induction from the triboelectric charges that are generated by frictional contact. This bound charge density is associated with the surface density of states (DOS), $\overline{N_{s}(E)}$ . Two cases are considered here: i) for $\overline{N_{s}(E)} \gg 1$ , it is calculated that the bound charge density is proportional to the dielectric constant and the work function difference between the two materials, but inversely proportional to the thickness of the dielectric material ( $\frac{\varepsilon_{0}(\varepsilon_{2}-1) (E_{0}-W)}{e \cdot d_{2}}$ ); ii) for $\overline{N_{s}(E)} \ll 1$ with constant $\overline{N_{s}(E)}$ , the bound charge density is mostly proportional to the work function difference between the materials, and inversely proportional to the thickness of the dielectric material ( $\frac{(\varepsilon_{2}-1)x}{d_{2}+\varepsilon_{2}\cdot x} \cdot N_{s}(E)\cdot e\cdot (E_{0}-W)$ ).