Electronic structure of black phosphorus: Tight binding approach

Takao, Yukihiro; Morita, Akira

doi:10.1016/0378-4363(81)90222-9

Cited by 208 publications

(192 citation statements)

References 6 publications

Supporting

Mentioning

163

Contrasting

Order By: Relevance

“…Early attempts to provide a real-space model to the electronic structure of BP were based on molecular orbital theory [18], whose simplified nature and complex orbital character of BP prevent a quantitatively accurate description [19]. Recently, two of us have proposed a more rigorous real-space model for single-and doublelayer BP, which was constructed by downfolding the full G 0 W 0 Hamiltonian to the minimal (one interaction site per phosphorus atom) low-energy effective Hamiltonian [20].…”

Section: Introductionmentioning

confidence: 99%

Toward a realistic description of multilayer black phosphorus: FromGWapproximation to large-scale tight-binding simulations

Руденко¹,

Yuan²,

Katsnelson³

2015

Phys. Rev. B

209

147

View full text Add to dashboard Cite

We provide a tight-binding model parametrization for black phosphorus (BP) with an arbitrary number of layers. The model is derived from partially self-consistent GW0 approach, where the screened Coulomb interaction W0 is calculated within the random phase approximation on the basis of density functional theory. We thoroughly validate the model by performing a series of benchmark calculations, and determine the limits of its applicability. The application of the model to the calculations of electronic and optical properties of multilayer BP demonstrates good quantitative agreement with ab initio results in a wide energy range. We also show that the proposed model can be easily extended for the case of external fields, yielding the results consistent with those obtained from first principles. The model is expected to be suitable for a variety of realistic problems related to the electronic properties of multilayer BP including different kinds of disorder, external fields, and many-body effects.

show abstract

Section: Introductionmentioning

confidence: 99%

Toward a realistic description of multilayer black phosphorus: FromGWapproximation to large-scale tight-binding simulations

Руденко¹,

Yuan²,

Katsnelson³

2015

Phys. Rev. B

209

147

View full text Add to dashboard Cite

show abstract

“…For few-layer phosphorene, interlayer interactions reduce the band gap for each layer 3 added, and eventually reach ~ 0.3 eV (refs 8-11) for bulk black phosphorus. The direct gap also moves to the Z point as a consequence 7,12 . Such a band structure provides a much needed gap for the field-effect transistor (FET) application of two dimensional (2D) materials such as graphene, and the thickness-dependent direct band gap may lead to potential applications in optoelectronics, especially in the infrared regime.…”

mentioning

confidence: 98%

“…1a). The three bonds take up all three valence electrons of phosphorus, so unlike graphene 5,6 a monolayer black phosphorus (termed "phosphorene") is a semiconductor with a predicted direct band gap of ~ 2 eV at the Γ point of the first Brillouin zone 7 . For few-layer phosphorene, interlayer interactions reduce the band gap for each layer 3 added, and eventually reach ~ 0.3 eV (refs 8-11) for bulk black phosphorus.…”

mentioning

confidence: 99%

Black phosphorus field-effect transistors

et al. 2014

View full text Add to dashboard Cite

Black phosphorus is a layered material in which individual atomic layers are stacked together by Van der Waals interactions, much like bulk graphite 1 . Inside a single layer, each phosphorus atom is covalently bonded with three adjacent phosphorus atoms to form a puckered honeycomb structure [2][3][4] (Fig. 1a). The three bonds take up all three valence electrons of phosphorus, so unlike graphene 5,6 a monolayer black phosphorus (termed "phosphorene") is a semiconductor with a predicted direct band gap of ~ 2 eV at the Γ point of the first Brillouin zone 7 . For few-layer phosphorene, interlayer interactions reduce the band gap for each layer 3 added, and eventually reach ~ 0.3 eV (refs 8-11) for bulk black phosphorus. The direct gap also moves to the Z point as a consequence 7,12 . Such a band structure provides a much needed gap for the field-effect transistor (FET) application of two dimensional (2D) materials such as graphene, and the thickness-dependent direct band gap may lead to potential applications in optoelectronics, especially in the infrared regime. In addition, observations of phase transition from semiconductor to metal 13,14 and superconductor under high pressure 15,16 We next fabricate few-layer phosphorene FETs with a back-gate electrode (see Fig. 2a). A scotch tape based mechanical exfoliation method is employed to peel thin flakes from bulk crystal onto degenerately doped silicon wafer covered with a layer of thermally grown silicon dioxide. Optical microscopy and atomic force microscopy (AFM) are used to hunt thin flake samples and determine their thickness (Fig. 2a). The switching behaviour of our few-layer phosphorene transistor at room temperature is characterized in vacuum (~ 10 -6 mBar), in a configuration depicted in -30 V to 0 V, the channel switches from "on" state to "off" state, and a drop in drain current by a factor of ~ 10 5 is observed. The measured drain current modulation is 4 orders of magnitude larger than that in graphene (due to its lack of bandgap), and 5 approaches the value recently reported in MoS2 devices 17 . Such a high drain current modulation makes black phosphorus thin film a promising material for applications in digital electronics 22 . Similar switching behaviour (with varying drain current modulation) is observed on all black phosphorous thin film transistors with thicknesses up to 50 nm. We note that the "on" state current of our devices has not yet reached saturation, due to the fact that the doping level is limited by the break-down electric field of the SiO2 back-gate dielectric. It is therefore possible to achieve even higher drain current modulation by using high-k materials as gate dielectrics for higher doping. Meanwhile, a subthreshold swing (SS) of ~ 5 V/decade is observed, which is much larger than the SS in commercial Si-based devices (~ 70 mV/decade).We note that the SS in our devices varies from sample to sample (from ~ 3.7 V/decade to ~ 13.3 V/decade), and is on the same order of magnitude as reported in multilayerMoS2 devices with a simila...

show abstract

“…The energy band gap close to 2 eV has been measured by scanning tunneling spectroscopy (STS) from monolayer BP 2 . With the increasing number of layers, the band gap decreases and finally reaches 0.3 eV for bulk BP 3 . This tunable band gap enables BP to be a promising candidate for applications in field effect transistors 4,5,6,7,8 .…”

Section: Introductionmentioning

confidence: 99%

Thermal sublimation: a scalable and controllable thinning method for the fabrication of few-layer black phosphorus

et al. 2017

View full text Add to dashboard Cite

In this work, we reported uniform layer-by-layer sublimation of black phosphorus under heating below 600 K. The uniformity and crystallinity of BP samples after thermal thinning were confirmed by Raman spectra and 2D Raman imaging. A uniform and crystalline bilayer black phosphorus flake with an area of 180 µm 2 was prepared with this method. No micron scale defects were observed. The sublimation rate of BP was around 0.18 nm / min at 500 K and 1.5 nm / min at 550 K. Both room and high temperature Raman peak intensity ratio Si A 2 g as functions of BP thickness were established for in-situ thickness determination.The sublimation thinning method was shown to be a controllable and scalable approach to prepare few-layer black phosphorus.

show abstract

Electronic structure of black phosphorus: Tight binding approach

Cited by 208 publications

References 6 publications

Toward a realistic description of multilayer black phosphorus: FromGWapproximation to large-scale tight-binding simulations

Toward a realistic description of multilayer black phosphorus: FromGWapproximation to large-scale tight-binding simulations

Black phosphorus field-effect transistors

Thermal sublimation: a scalable and controllable thinning method for the fabrication of few-layer black phosphorus

Contact Info

Product

Resources

About