Extended Data Fig. 8: Calculated dielectric spectra using the point-charge analytical model.
From: In-plane dielectric constant and conductivity of confined water
a, Its schematic. A point charge is used to approximate the AFM tip. The device is modelled as a water layer of infinite lateral size (red), which is encapsulated between top and bottom hBN layers (blue). For simplicity, the dielectric constant of hBN is assumed to be isotropic and equal to 4. b, Calculated |dC/dz| as a function of frequency for h = 30, 5 and 1.5 nm (colour-coded) and bulk water (ε// = ε⊥ = εbulk = 80, σ// = σ⊥ = σbulk = 2 × 10−4 S m−1). c, Same as in b for h = 5 nm but using various thicknesses of bottom hBN. d, The dotted curves are the same as in b but normalized with respect to the height of the low-f plateau. Dashed curves, corresponding analysis using the full-3D numerical simulations. e, Same as in b for h = 1.5 nm and different σ// (red curves, keeping σ⊥ = 0) and σ⊥ (grey, σ// = 0). f, Same as in b for h = 1.5 nm and various ε// (red solid curves, keeping ε⊥ = 2) and various ε⊥ (grey curves, ε// = 2). The red dotted curve is for the same channel filled with bulk water (also shown in b). Other parameters used in b–f (unless stated otherwise in the legends) are zscan = 20 nm, Htop = 50 nm and H = 100 nm. All of the plotted |dC/dz| curves are after subtracting the |dC/dz| values found for the same geometry but with hBN instead of the water layer.
