Rectifying behavior in twisted bilayer black phosphorus nanojunctions mediated through intrinsic anisotropy

Abstract

We explore the possibility of using van der Waals bonded heterostructures of stacked together 2D bilayer black phosphorus (BP) for nanoscale device applications.

Electronic and Transport Properties of Bilayer Phosphorene Nanojunction: Effect of Paired Substitution Doping

“…This reduction in the band gap originates due to extra lone pair electrons present in phosphorus (P) atoms, which is entitled to the hybridization in between the layers. This hybridization becomes weaker when the bilayer is twisted by 90°, which has already been discussed in our earlier report …”

“…This anisotropic behavior of phosphorene is intrinsic and results from the asymmetric band dispersion between G- X and G- Y directions, which results in highly anisotropic effective masses of electrons and holes and eventually carrier mobilities in the respective directions. The G- X band disperses rather strongly and corresponds to lower effective mass in compression to the G- Y band, which has lower dispersion . As we are interested in isoelectric doping to understand the behavior of dopant in electronic transport, we further extended our study to the doped system.…”

“…When a given voltage is applied, the current is allowed to flow across the system. The electric current ( I ) is further calculated using the Landauer approach, and this can be obtained from the integration of the transmission curve as where I ( V b ) represents the electric current under applied bias voltages, e is the electron charge, h is Planck’s constant, f ( E – μ L/R ) is the Fermi–Dirac distribution function of the L and R electrodes, μ L/R is the chemical potential, which can move up and down according to the Fermi energy E F , and T ( E , V b ) is the quantum transmission probability of the electrons, which can be given as follows where the coupling matrices are given as Γ L/R = i [∑ L/R – ∑ L/R † ] and the NEGFs for the scattering region given as G ( E , V b ) = [ E × S s – H s [ρ] – ∑ L ( E , V b ) – ∑ R ( E , V b )] −1 , where S s is the overlap matrix, H s is the Hamiltonian matrix, ∑ L/R = V s L/R g L/R V L/R s is the self-interaction energy, ∑ L/R is a molecule electrode that takes into account L/R electrodes in the central scattering region, g L/R is the surface L/R Green’s function, and V L/R s = V S L/R † is the coupling matrix between L/R electrodes and the scattering region. ,,, …”

“…Recently, significant effort has been made to making vertical and lateral heterojunctions of these 2D materials ,, that can behave like a fundamental component of the electronic devices like photodiode, field-effect transistor (FET), rectifier, etc. − Several vertical and lateral nanojunctions have already been reported both theoretically and experimentally, such as graphene, hexagonal boron nitride (h-BN), MoS 2 , and WS 2 . , , In addition to all of these, recently, a monolayer of black phosphorus (BP) known as phosphorene has been exfoliated from bulk, and it has shown promising applications in nanoscale electronic devices such as sensing, − energy storage, and photocatalysis . It is noted that BP has a direct band gap of 0.3 eV and mobility of ∼10 000 cm 2 /VS, whereas monolayer phosphorene also has a direct band gap of 0.9 eV calculated with generalized gradient approximation (GGA) functional. − ,− BP has a highly anisotropic electronic structure in the x – y plane that is dependent on the number of layers. A few layers of phosphorene are more interesting than their monolayer.…”

“…Therefore, significant effort has been made to study the electronic and transport properties of BP with layer dependence that has been reported elsewhere. ,,,,, There are also several reports showing the band gap tuning of this phosphorene with nanostructure width (nanoribbon). , Also, bilayer phosphorene (Bi-P) flakes have been extensively studied both experimentally and theoretically for electronic and transport properties. , These bilayer flakes show exciting features along with bilayer nanoribbon. The energy gap of the bilayer with respect to its width and length and the corresponding atomic termination have also been reported. ,, …”