First-Principles Nanocapacitor Simulations of the Optical Dielectric Constant in Water Ice

Abstract

We introduce a combined density functional theory (DFT) and non-equilibrium Green's function (NEGF) framework to compute the capacitance of nanocapacitors and directly extract the dielectric response of a sub-nanometer dielectric under bias. We identify that at the nanoscale conventional capacitance evaluations based on stored charge per unit voltage suffer from an ill-posed partitioning of electrode and dielectric charge. This partitioning directly impacts the geometric definition of capacitance through the capacitor width, which in turn makes the evaluation of dielectric response uncertain. This ambiguous separation further induces spurious interfacial polarizability when analyzed via maximally localized Wannier functions. Focusing on crystalline ice, we develop a robust charge-separation protocol that yields unique capacitance-derived polarizability and dielectric constants, unequivocally demonstrating that confinement neither alters ice's intrinsic electronic response nor its insensitivity to proton order. Our results lay the groundwork for rigorous interpretation of capacitor measurements in low-dimensional dielectric materials.

Figures (14)

• Figure 1: Illustrations of the $\mathbf{(a, c)}$ ice $\it{Ih}$ - Au[111] capacitor and $\mathbf{(b, d)}$ ice $\it{XI}$ - Au[111] capacitor. $\mathbf{(a, b)}$ are side views and $\mathbf{(c, d)}$ are top views. The left and right electrodes (LE and RE, respectively) and the scattering region (SR) are shown.
• Figure 2: Optical dielectric constant $\varepsilon_{\perp}$ in (a) half-full capacitor and (b) standalone slab geometries calculated using two methods. (a,b) The Wannier charge center (WCC) method described by Eqs. \ref{['eq:eps']} and \ref{['eq:alpha_Wannier']}. (c) The electron density method described by Eqs. \ref{['eq:Gauss']}-\ref{['eq:ep_from P']}. Surface Au electrode planes are at $z = 0$ and $z = 40$ Å . In both cases finite differences are computed with $\Delta V=1V$.
• Figure 3: Illustrations of (a) the empty capacitor and (b) the half-full capacitor geometries. (c) Electrode charge density difference for the empty capacitor (solid blue) and the half-full capacitor (solid red) geometries. The total charge density difference for the half-full capacitor geometry is also shown (dotted red). Surface Au electrode planes are at $z = 0$ and $z = 40$ Å. The vertical dashed lines give the boundaries of the dielectric region, and the capacitor widths, $w$ and $w_0$, for each system are labeled.
• Figure 4: Optical dielectric constant $\varepsilon_{\perp}$ in full (a) ice Ih and (b) ice XI capacitor geometries calculated using two methods. (a,b) The Wannier charge center (WCC) method described by Eqs. \ref{['eq:eps']} and \ref{['eq:alpha_Wannier']}. (c) The electron density method described by Eqs. \ref{['eq:Gauss']}-\ref{['eq:ep_from P']}. Surface Au electrode planes are at $z = 0$ and $z = 40$ Å . In both cases finite differences are computed with $\Delta V=1V$.
• Figure 5: Illustrations of the ferroelectric unit cell used to generate all ice structures used in this work: a)xz-plane and b)xy-plane.