Charge distribution across dislocation networks induced by a strained top layer in hexagonal boron nitride substrates

Abstract

Hexagonal boron nitride (hBN) flakes are key building blocks for encapsulating two-dimensional (2D) materials, providing atomically flat surfaces and an excellent dielectric environment for high-mobility field-effect transistors and tunnelling devices. However, strain induced during mechanical exfoliation and assembly of van der Waals heterostructures may lead to plastic deformations of the hBN surface, injecting dislocation lines between the topmost layer and the underlying film. Since a monolayer of hBN is non-centrosymmetric and exhibits a piezoelectric response to deformation, individual dislocations and, in particular their networks, can generate electrostatic potential modulations in the encapsulated 2D material. Here, we examine scenarios in which the top hBN layer is uniaxially strained and/or twisted, and show how lattice reconstruction into dislocation networks leads to the formation of piezoelectric charge hotspots that effectively behave as charged defects.

Figures (7)

• Figure 1: Piezoelectric charge textures from strained and/or twisted monolayer on top of an hBN film with thickness $w_{\rm hBN}$. The presence of inhomogeneous strain on the top layer of hBN gives rise to multiple regions with highly anisotropic piezoelectric charge densities originated from lattice reconstruction effects. Four possible regions are illustrated: two corresponding to uniaxial strain on the top layer (green for strain along the zigzag axis and purple along armchair), one for a relative twist angle (red), and one corresponding to the combination of the two previous cases (blue).
• Figure 2: (a) Diagram illustrating a dislocation or strained/twisted interface between two hBN films with $N$ and $M$ layers, indicated by orange and blue colours, respectively. The labelling of monolayers according to their proximity to the interface and the adhesion between each pair of layers is shown. (b) Orientation dependence of the dislocation energy per unit of length (defined in Eq. \ref{['Eq:DislocationEnergyDensity']}), described in terms of the angle $\phi$ between the dislocation axis and the Burgers vector. Black dots indicate the case of a dislocation in a bilayer ($N=1$, $M=1$), and red dots a dislocation between a monolayer and a multilayer film. (c) Screw dislocation ($\phi=0^{\circ}$) energy per unit of length as a function of the total number of layers $N+M$. Blue dots correspond to structures with equal number of layers in each side of the dislocation plane, $N=M$, and red dots correspond to a dislocation between a monolayer ($N=1$) and an $M$ layer film. Curves represent the power law and logarithmic fittings defined in Eqs. \ref{['Eq:LogFit']} and \ref{['Eq:PowerFit']}, respectively. The total elastic energy $\mathcal{B}$ of the constituent films is indicated by triangles and stars.
• Figure 3: In-plane displacement field maps of reconstructed moiré superlattices. (a) Divergence and (b) curl maps for displacement fields in the top layer ($\mathbf{\boldsymbol{u}}^{(1)}$). The structure corresponds to a uniaxially strained monolayer along an axis with angle $\alpha$ with respect to the zigzag direction stacked on top of bulk hBN with a relative twist angle $\theta$. Each row in the top panel corresponds to a different configuration of strain $\epsilon$ and twist angle $\theta$, whereas columns are the different axes where uniaxial strain is applied, with $\alpha=0^{\circ}$ being the zigzag direction and $\alpha=30^{\circ}$ the armchair direction. The last row corresponds to a purely twisted (unstrained) top layer.
• Figure 4: Electrical properties of dislocations between a monolayer and bulk hBN. (a) Piezoelectric charge profiles in each layer across a screw ($\phi=0^{\circ}$, left panel) and an edge dislocation (($\phi=90^{\circ}$, right panel)) in hBN films with $N=1$ and $M=10$, indicated by orange and purple, respectively. (b) Piezoelectric potential maps as a function of the distance to the hBN surface, $\tilde{z}=z-w_{\rm hBN}$. We show maps for screw, edge, and two mixed ($\phi=30^{\circ},60^{\circ}$) dislocations.
• Figure 5: (a) Piezopotential maps 0.3nm above a strained and/or twisted monolayer stacked on bulk hBN. Upper panel corresponds to a $\epsilon=0.3\%$ uniaxially strained monolayer, where each column is a different direction for the applied strain ($\alpha=0^{\circ}$ for zigzag and $\alpha=30^{\circ}$ for armchair) and rows are different twist angles. Bottom panel is the twist angle dependence for an unstrained monolayer. (b) Form factor, defined as the angular average of the Fourier transform of the piezopotential peaks, for purely strained upper monolayer ($\theta=0^{\circ}$), and for (c) twisted upper monolayer without strain ($\epsilon=0\%$). (d) Potential produced by an arbitrary distribution of charged point-defects with density $n=0.15\times10^{16}$cm$^{-3}$ in a 50nm thick film.