Fig. 7: Tuning the bandgap by an applied electric field.
From: Bandgap engineering of two-dimensional semiconductor materials
a Sketch of the quantum-confined Franz–Keldysh effect (top): in the presence of an applied field (blue, F ≠ 0), the otherwise constant bands (black, F = 0) are tilted, which pushes electrons and holes toward opposite sides of the system. Electron and hole wave functions are given by Airy functions (red) with tails that slightly overlap, thus allowing for a light absorption-induced transition with energy EFK lower than the original quasi-particle gap Eg of the system. Bottom panels show an experimental observation of the Franz–Keldysh effect in light absorption for few-layer (9-nm-thick) BP, with several values of applied bias Vg (in volts) and light polarized along the armchair (AC) and zigzag (ZZ) directions of the material145. b Experimental observation of Franz–Keldysh effect as a subgap shoulder (FK) in the absorption spectrum, which emerges among A exciton peaks as the gate voltage VB increases in monolayer WSe2 at temperature T = 30 K151. c Band structure of 2-BP, as obtained with tight-binding (red dashed) and continuum (blue solid) models, in the presence of 1.5-eV (top) and 2-eV (bottom) bias158. d Experimental verification of the bandgap closing and consequent formation of a Dirac cone in few-layer BP due to an effective bias across the sample155. Experimental data and theoretical simulations are shown together, for comparison. e Stark shift of the PL peak (at T = 4.2 K) due to IL excitons in a MoSe2/WSe2 vdWH, as a function of bias induced by top and bottom gates, set at potentials VTG and VBG, respectively. Two energy peaks, labeled as IX1 and IX2 are consistently observed76. Panel a reprinted with permission from145 Nano Lett. 2017, 17, 10, 6315–6320 Publication Date: September 27, 2017 https://doi.org/10.1021/acs.nanolett.7b03050, Copyright (2017) American Chemical Society; panel b reused from Springer Nature/Massicotte et al.151, permissible under a CC-BY [4.0/3.0] license; panel d used with permission from AAAS/Kim et al.155; panel e reprinted by permission from Springer Nature Nature Photonics76, Ciarrocchi, A., Unuchek, D., Avsar, A. et al. Polarization switching and electrical control of interlayer excitons in two-dimensional van der Waals heterostructures. Nature Photon. 13, 131–136 (2019), Copyright (2019) advance online publication, 31st December 2018 (https://doi.org/10.1038/s41566-018-0325-y Nature Photon.).
