coupled electrostatics and solid mechanics model  (COMSOL Inc)

Journal: ACS Nano

Article Title: Synthetic Band Structure Engineering of Graphene Using Block Copolymer-Templated Dielectric Superlattices

doi: 10.1021/acsnano.4c14500

Figure Lengend Snippet: Effect of high- k nanopatterns on SL potential. Schematic illustrations of the fabrication process showing (a) the BGB stack transferred onto (b) the remote SL substrate consisting of high- k nanopatterns. (c) Band diagram along the z -axis showing the electronic system in the nonpatterned regions of the remote substrate under a positive V SL . V ox = e·n SL,ox / C ox from eq . (d) Band diagram of graphene along x -axis, illustrating an induced difference in the charge neutrality point (CNP) position due to local variations of the dielectric constant in the neighboring hole and solid regions of the high- k nanopattern. (e) A model of the electric displacement, D , under graphene for a remote substrate with AlO x nanopatterns ( k = 8) at V SL = 50 V. The spatial variations of the field lines represent the local variations of the capacitance. (f) Modeled Δ n SL under V SL = 50 V corresponding to SiO 2 , AlO x , and HfO x nanopatterned dielectrics. The data illustrate the beneficial effect of employing high- k nanopatterns in enhancing the electrostatic strength of SL potential.

Article Snippet: We performed numerical calculations in COMSOL using electrostatic models to illustrate how the permittivity of the nanopatterned dielectric affects the U SL strength in graphene at a fixed V SL .

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