Thickness and Stacking Dependent Polarizability and Dielectric Constant of Graphene–Hexagonal Boron Nitride Composite Stacks

Abstract

The giant carrier mobility of graphene is significantly reduced due to external perturbations, such as substrate based charge impurities, and their impact can be minimized by encapsulating graphene between hexagonal boron nitride (hBN) layers. Using density functional theory (DFT) based ab initio calculations, we study the static response of such a composite by placing it in a vertical electric field. We find that at relatively low electric field (∼0.1 V/Å), although the relative permittivity (εr) of a composite stack increases with the number of layers, εr for a fixed stack thickness is independent of the field strength. However, at higher electric field strength, εr increases monotonically with the applied field strength even for a fixed stack thickness, signifying nonlinear response. The relative permittivity changes more readily for graphene rich stacks as compared to hBN rich stacks, which is consistent with the property of the pristine phases. We also present an empirical formulation to calculate the thickness and stacking dependent effective dielectric constant of any arbitrary stack of graphene–hBN layers, which fits very well with the ab initio calculations. Our empirical formulation will also be applicable for van der Waals stacks of other two-dimensional materials and will be useful for designing and interpreting transport experiments, where electrostatic effects such as capacitance and charge screening are important.

Dielectric properties of hexagonal boron nitride and transition metal dichalcogenides: from monolayer to bulk

“…Our findings are in contrast with the findings in ref. 26 , which found a strong layerdependence for h-BN, and ref. 20 , where a dielectric constant of unity was obtained.…”

“…The definition of thickness employed in ref. 26 is the total extent of the polarization, where the cutoff is made at the points where the polarization reaches <1% of its peak value. However, this choice is arbitrary and different results would be obtained if a 0.5% or a 5% cutoff would have been used, or, if the extent of the charge density would have been used rather than the extent of the polarization.…”

“…A few of the studies related to the dielectric constant include a first principles calculation of the outof-plane dielectric constant of MoS 2 and h-BN. 26,27 However, an exhaustive study of both the in-plane and out-of-plane dielectric properties of the other 2D materials is missing.…”

An atom-to-circuit modeling approach to all-2D metal–insulator–semiconductor field-effect transistors

“…Dielectric constant values and carrier mobilities of the materials have been acquired from reported first principle-based calculations. 35,36 The material level attributes thus obtained are then used to develop physics-based compact device model to understand the properties of MIS capacitor and FET. Limited by the computational budget, we consider only two layers of hBN for developing the atomistic model, although experiments 12,17 were conducted using several layers of it.…”

“…ε to be 1.9. 35 The variation of C gg as a function of V GS has been plotted in Fig. 4(c) keeping V DS = 0 V. It reveals that saturated C gg increases with increasing bandgap of graphene and the crossing between individual graphs is a direct consequence of threshold voltage increment of the device.…”