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1.
Nature ; 633(8028): 83-89, 2024 Sep.
Artigo em Inglês | MEDLINE | ID: mdl-39198653

RESUMO

Crystallographic phase engineering plays an important part in the precise control of the physical and electronic properties of materials. In two-dimensional transition metal dichalcogenides (2D TMDs), phase engineering using chemical lithiation with the organometallization agent n-butyllithium (n-BuLi), to convert the semiconducting 2H (trigonal) to the metallic 1T (octahedral) phase, has been widely explored for applications in areas such as transistors, catalysis and batteries1-15. Although this chemical phase engineering can be performed at ambient temperatures and pressures, the underlying mechanisms are poorly understood, and the use of n-BuLi raises notable safety concerns. Here we optically visualize the archetypical phase transition from the 2H to the 1T phase in mono- and bilayer 2D TMDs and discover that this reaction can be accelerated by up to six orders of magnitude using low-power illumination at 455 nm. We identify that the above-gap illumination improves the rate-limiting charge-transfer kinetics through a photoredox process. We use this method to achieve rapid and high-quality phase engineering of TMDs and demonstrate that this methodology can be harnessed to inscribe arbitrary phase patterns with diffraction-limited edge resolution into few-layer TMDs. Finally, we replace pyrophoric n-BuLi with safer polycyclic aromatic organolithiation agents and show that their performance exceeds that of n-BuLi as a phase transition agent. Our work opens opportunities for exploring the in situ characterization of electrochemical processes and paves the way for sustainably scaling up materials and devices by photoredox phase engineering.

2.
Nature ; 610(7930): 61-66, 2022 10.
Artigo em Inglês | MEDLINE | ID: mdl-35914677

RESUMO

Digital logic circuits are based on complementary pairs of n- and p-type field effect transistors (FETs) via complementary metal oxide semiconductor technology. In three-dimensional (3D) or bulk semiconductors, substitutional doping of acceptor or donor impurities is used to achieve p- and n-type FETs. However, the controllable p-type doping of low-dimensional semiconductors such as two-dimensional (2D) transition-metal dichalcogenides (TMDs) has proved to be challenging. Although it is possible to achieve high-quality, low-resistance n-type van der Waals (vdW) contacts on 2D TMDs1-5, obtaining p-type devices by evaporating high-work-function metals onto 2D TMDs has not been realized so far. Here we report high-performance p-type devices on single- and few-layered molybdenum disulfide and tungsten diselenide based on industry-compatible electron beam evaporation of high-work-function metals such as palladium and platinum. Using atomic resolution imaging and spectroscopy, we demonstrate near-ideal vdW interfaces without chemical interactions between the 2D TMDs and 3D metals. Electronic transport measurements reveal that the Fermi level is unpinned and p-type FETs based on vdW contacts exhibit low contact resistance of 3.3 kΩ µm, high mobility values of approximately 190 cm2 V-1 s-1 at room temperature, saturation currents in excess of 10-5 A µm-1 and an on/off ratio of 107. We also demonstrate an ultra-thin photovoltaic cell based on n- and p-type vdW contacts with an open circuit voltage of 0.6 V and a power conversion efficiency of 0.82%.

3.
Nature ; 606(7912): 88-93, 2022 06.
Artigo em Inglês | MEDLINE | ID: mdl-35650356

RESUMO

Large-area single-crystal monolayers of two-dimensional (2D) materials such as graphene1-3, hexagonal boron nitride (hBN)4-6 and transition metal dichalcogenides7,8 have been grown. hBN is considered to be the 'ideal' dielectric for 2D-materials-based field-effect transistors (FETs), offering the potential for extending Moore's law9,10. Although hBN thicker than a monolayer is more desirable as substrate for 2D semiconductors11,12, highly uniform and single-crystal multilayer hBN growth has yet to be demonstrated. Here we report the epitaxial growth of wafer-scale single-crystal trilayer hBN by a chemical vapour deposition (CVD) method. Uniformly aligned hBN islands are found to grow on single-crystal Ni (111) at early stage and finally to coalesce into a single-crystal film. Cross-sectional transmission electron microscopy (TEM) results show that a Ni23B6 interlayer is formed (during cooling) between the single-crystal hBN film and Ni substrate by boron dissolution in Ni. There are epitaxial relationships between hBN and Ni23B6 and between Ni23B6 and Ni. We also find that the hBN film acts as a protective layer that remains intact during catalytic evolution of hydrogen, suggesting continuous single-crystal hBN. This hBN transferred onto the SiO2 (300 nm)/Si wafer acts as a dielectric layer to reduce electron doping from the SiO2 substrate in MoS2 FETs. Our results demonstrate high-quality single-crystal  multilayered hBN over large areas, which should open up new pathways for making it a ubiquitous substrate for 2D semiconductors.

4.
Nature ; 582(7813): 511-514, 2020 06.
Artigo em Inglês | MEDLINE | ID: mdl-32581381

RESUMO

Decrease in processing speed due to increased resistance and capacitance delay is a major obstacle for the down-scaling of electronics1-3. Minimizing the dimensions of interconnects (metal wires that connect different electronic components on a chip) is crucial for the miniaturization of devices. Interconnects are isolated from each other by non-conducting (dielectric) layers. So far, research has mostly focused on decreasing the resistance of scaled interconnects because integration of dielectrics using low-temperature deposition processes compatible with complementary metal-oxide-semiconductors is technically challenging. Interconnect isolation materials must have low relative dielectric constants (κ values), serve as diffusion barriers against the migration of metal into semiconductors, and be thermally, chemically and mechanically stable. Specifically, the International Roadmap for Devices and Systems recommends4 the development of dielectrics with κ values of less than 2 by 2028. Existing low-κ materials (such as silicon oxide derivatives, organic compounds and aerogels) have κ values greater than 2 and poor thermo-mechanical properties5. Here we report three-nanometre-thick amorphous boron nitride films with ultralow κ values of 1.78 and 1.16 (close to that of air, κ = 1) at operation frequencies of 100 kilohertz and 1 megahertz, respectively. The films are mechanically and electrically robust, with a breakdown strength of 7.3 megavolts per centimetre, which exceeds requirements. Cross-sectional imaging reveals that amorphous boron nitride prevents the diffusion of cobalt atoms into silicon under very harsh conditions, in contrast to reference barriers. Our results demonstrate that amorphous boron nitride has excellent low-κ dielectric characteristics for high-performance electronics.

5.
Nature ; 568(7750): 70-74, 2019 04.
Artigo em Inglês | MEDLINE | ID: mdl-30918403

RESUMO

As the dimensions of the semiconducting channels in field-effect transistors decrease, the contact resistance of the metal-semiconductor interface at the source and drain electrodes increases, dominating the performance of devices1-3. Two-dimensional (2D) transition-metal dichalcogenides such as molybdenum disulfide (MoS2) have been demonstrated to be excellent semiconductors for ultrathin field-effect transistors4,5. However, unusually high contact resistance has been observed across the interface between the metal and the 2D transition-metal dichalcogenide3,5-9. Recent studies have shown that van der Waals contacts formed by transferred graphene10,11 and metals12 on few-layered transition-metal dichalcogenides produce good contact properties. However, van der Waals contacts between a three-dimensional metal and a monolayer 2D transition-metal dichalcogenide have yet to be demonstrated. Here we report the realization of ultraclean van der Waals contacts between 10-nanometre-thick indium metal capped with 100-nanometre-thick gold electrodes and monolayer MoS2. Using scanning transmission electron microscopy imaging, we show that the indium and gold layers form a solid solution after annealing at 200 degrees Celsius and that the interface between the gold-capped indium and the MoS2 is atomically sharp with no detectable chemical interaction between the metal and the 2D transition-metal dichalcogenide, suggesting van-der-Waals-type bonding between the gold-capped indium and monolayer MoS2. The contact resistance of the indium/gold electrodes is 3,000 ± 300 ohm micrometres for monolayer MoS2 and 800 ± 200 ohm micrometres for few-layered MoS2. These values are among the lowest observed for three-dimensional metal electrodes evaporated onto MoS2, enabling high-performance field-effect transistors with a mobility of 167 ± 20 square centimetres per volt per second. We also demonstrate a low contact resistance of 220 ± 50 ohm micrometres on ultrathin niobium disulfide (NbS2) and near-ideal band offsets, indicative of defect-free interfaces, in tungsten disulfide (WS2) and tungsten diselenide (WSe2) contacted with indium alloy. Our work provides a simple method of making ultraclean van der Waals contacts using standard laboratory technology on monolayer 2D semiconductors.

6.
Nano Lett ; 24(8): 2561-2566, 2024 Feb 28.
Artigo em Inglês | MEDLINE | ID: mdl-38363877

RESUMO

Two-dimensional transition metal dichalcogenide (2D TMD) semiconductors allow facile integration of p- and n-type materials without a lattice mismatch. Here, we demonstrate gate-tunable n- and p-type junctions based on vertical heterostructures of MoS2 and WSe2 using van der Waals (vdW) contacts. The p-n junction shows negative differential resistance (NDR) due to Fowler-Nordheim (F-N) tunneling through the triangular barrier formed by applying a global back-gate bias (VGS). We also show that the integration of hexagonal boron nitride (h-BN) as an insulating tunnel barrier between MoS2 and WSe2 leads to the formation of sharp band edges and unintentional inelastic tunnelling current. The devices based on vdW contacts, global VGS, and h-BN tunnel barriers exhibit NDR with a peak current (Ipeak) of 315 µA, suggesting that the approach may be useful for applications.

7.
Nano Lett ; 24(42): 13232-13237, 2024 Oct 23.
Artigo em Inglês | MEDLINE | ID: mdl-39382966

RESUMO

Some van der Waals (vdW) materials exhibit ferroelectricity, making them promising for novel nonvolatile memories (NVMs) such as ferroelectric diodes (FeDs). CuInP2S6 (CIPS) is a well-known vdW ferroelectric that has been integrated with graphene for memory devices. Here we demonstrate FeDs with self-rectifying, hysteretic current-voltage characteristics based on vertical heterostructures of 10 nm thick CIPS and graphene. By using vdW indium-cobalt top electrodes and graphene bottom electrodes, we achieve a high electroresistance (on- and off-state resistance ratios) of ∼106, an on-state rectification ratio of 2500 for read/write voltages of 2 V/0.5 V, and a maximum output current density of 100 A/cm2. These metrics compare favorably with state-of-the-art FeDs. Piezoresponse force microscopy measurements show that stabilization of intermediate net polarization states in CIPS leads to stable multibit data retention at room temperature. The combination of two-terminal design, multibit memory, and low-power operation in CIPS-based FeDs is potentially interesting for compute-in-memory and neuromorphic computing applications.

8.
Nano Lett ; 23(23): 10731-10738, 2023 Dec 13.
Artigo em Inglês | MEDLINE | ID: mdl-37970788

RESUMO

Fatigue-induced failure resulting from repetitive stress-strain cycles is a critical concern in the development of robust and durable nanoelectromechanical devices founded on 2D semiconductors. Defects, such as vacancies and grain boundaries, inherent in scalable materials can act as stress concentrators and accelerate fatigue fracture. Here, we investigate MoS2 with controlled atomic vacancies, to elucidate its mechanical reliability and fatigue response as a function of atomic defect density. High-quality MoS2 demonstrates an exceptional fatigue response, enduring 109 cycles at 80% of its breaking strength (13.5 GPa), surpassing the fatigue resistance of steel and approaching that of graphene. The introduction of atomic defect densities akin to those generated during scalable synthesis processes (∼1012 cm-2) reduces the fatigue strength to half the breaking strength. Our findings also point toward a sudden defect reconfiguration prior to global failure as the primary fatigue mechanism, offering valuable insights into structure-property relationships.

9.
Angew Chem Int Ed Engl ; 63(42): e202409719, 2024 Oct 14.
Artigo em Inglês | MEDLINE | ID: mdl-39052469

RESUMO

A stable solid-electrolyte interphase (SEI) is crucial for cycling reversibility of Na-ion batteries by mitigating continuous side reactions. So far, the severe SEI dissolution leads to low Coulombic efficiency (CE) and short cycle life. Meanwhile, the quantified relationship between SEI components and their solubility remains unclear. In this work, we establish the direct correlation between SEI components and SEI solubility, and quantify that the solubility of organic-rich SEI is 3.26 times of inorganic-rich SEI. We further propose a feasible strategy to preform inorganic-rich insoluble SEI and demonstrate a practical hard carbon (HC)||NaMn0.33Fe0.33Ni0.33O2 full cell in a commercial electrolyte of 1 M NaPF6 in propylene carbonate (PC) with 80.0 % capacity retention for 900 cycles, and achieve a record-high average CE of 99.95 % for a practical Na-ion full cell. This study provides an effective strategy of preforming insoluble SEI to suppress its dissolution towards highly reversible Na-ion batteries.

10.
Nature ; 549(7672): 370-373, 2017 09 21.
Artigo em Inglês | MEDLINE | ID: mdl-28854166

RESUMO

Actuators that convert electrical energy to mechanical energy are useful in a wide variety of electromechanical systems and in robotics, with applications such as steerable catheters, adaptive wings for aircraft and drag-reducing wind turbines. Actuation systems can be based on various stimuli, such as heat, solvent adsorption/desorption, or electrochemical action (in systems such as carbon nanotube electrodes, graphite electrodes, polymer electrodes and metals). Here we demonstrate that the dynamic expansion and contraction of electrode films formed by restacking chemically exfoliated nanosheets of two-dimensional metallic molybdenum disulfide (MoS2) on thin plastic substrates can generate substantial mechanical forces. These films are capable of lifting masses that are more than 150 times that of the electrode over several millimetres and for hundreds of cycles. Specifically, the MoS2 films are able to generate mechanical stresses of about 17 megapascals-higher than mammalian muscle (about 0.3 megapascals) and comparable to ceramic piezoelectric actuators (about 40 megapascals)-and strains of about 0.6 per cent, operating at frequencies up to 1 hertz. The actuation performance is attributed to the high electrical conductivity of the metallic 1T phase of MoS2 nanosheets, the elastic modulus of restacked MoS2 layers (2 to 4 gigapascals) and fast proton diffusion between the nanosheets. These results could lead to new electrochemical actuators for high-strain and high-frequency applications.

12.
Chem Soc Rev ; 50(18): 10087-10115, 2021 Sep 20.
Artigo em Inglês | MEDLINE | ID: mdl-34396377

RESUMO

The advent of two-dimensional transition metal dichalcogenides (2D-TMDs) has led to an extensive amount of interest amongst scientists and engineers alike and an intensive amount of research has brought about major breakthroughs in the electronic and optical properties of 2D materials. This in turn has generated considerable interest in novel device applications. With the polymorphic structural features of 2D-TMDs, this class of materials can exhibit both semiconducting and metallic (quasi-metallic) properties in their respective phases. This polymorphic property further increases the interest in 2D-TMDs both in fundamental research and for their potential utilization in novel high-performance device applications. In this review, we highlight the unique structural properties of few-layer and monolayer TMDs in the metallic 1T- and quasi-metallic 1T'-phases, and how these phases dictate their electronic and optical properties. An overview of the semiconducting-to-(quasi)-metallic phase transition of 2D-TMD systems will be covered along with a discussion on the phase transition mechanisms. The current development in the applications of (quasi)-metallic 2D-TMDs will be presented ranging from high-performance electronic and optoelectronic devices to energy storage, catalysis, piezoelectric and thermoelectric devices, and topological insulator and neuromorphic computing applications. We conclude our review by highlighting the challenges confronting the utilization of TMD-based systems and projecting the future developmental trends with an outlook of the progress needed to propel this exciting field forward.

13.
Int J Mol Sci ; 23(24)2022 Dec 09.
Artigo em Inglês | MEDLINE | ID: mdl-36555250

RESUMO

The main challenge in lithium sulphur (Li-S) batteries is the shuttling of lithium polysulphides (LiPSs) caused by the rapid LiPSs migration to the anode and the slow reaction kinetics in the chain of LiPSs conversion. In this study, we explore 1T-MoS2 as a cathode host for Li-S batteries by examining the affinity of 1T-MoS2 substrates (pristine 1T-MoS2, defected 1T-MoS2 with one and two S vacancies) toward LiPSs and their electrocatalytic effects. Density functional theory (DFT) simulations are used to determine the adsorption energy of LiPSs to these substrates, the Gibbs free energy profiles for the reaction chain, and the preferred pathways and activation energies for the slow reaction stage from Li2S4 to Li2S. The obtained information highlights the potential benefit of a combination of 1T-MoS2 regions, without or with one and two sulphur vacancies, for an improved Li-S battery performance. The recommendation is implemented in a Li-S battery with areas of pristine 1T-MoS2 and some proportion of one and two S vacancies, exhibiting a capacity of 1190 mAh/g at 0.1C, with 97% capacity retention after 60 cycles in a schedule of different C-rates from 0.1C to 2C and back to 0.1C.


Assuntos
Lítio , Molibdênio , Adsorção , Eletrodos , Enxofre
14.
Faraday Discuss ; 227: 332-340, 2021 Apr 01.
Artigo em Inglês | MEDLINE | ID: mdl-33523053

RESUMO

In this work, we report the synthesis and characterization of mixed phase Nb1+xS2 nanoflakes prepared by chemical vapor deposition. The as-grown samples show a high density of flakes (thickness ∼50 nm) that form a continuous film. Raman and X-ray diffraction data show that the samples consist of both 2H and 3R phases, with the 2H phase containing a high concentration of Nb interstitials. These Nb interstitials sit in between the NbS2 layers to form Nb1+xS2. Cross-sectional Energy Dispersive Spectroscopy analysis with transmission electron microscopy suggests that the 2H Nb1+xS2 region is found in thinner flakes, while 3R NbS2 is observed in thicker regions of the films. The evolution of the phase from 2H Nb1+xS2 to 3R NbS2 may be attributed to the change of the growth environment from Nb-rich at the start of the growth to sulfur-rich at the latter stage. It was also found that the incorporation of Nb interstitials is highly dependent on the temperature of the NbCl5 precursor and the position of the substrate in the furnace. Samples grown at high NbCl5 temperature and with substrate located closer to the NbCl5 source show higher incorporation of Nb interstitials. Electrical measurements show linear I-V characteristics, indicating the metallic nature of the Nb1+xS2 film with relatively low resistivity of 4.1 × 10-3Ω cm.

15.
Nano Lett ; 20(2): 841-851, 2020 Feb 12.
Artigo em Inglês | MEDLINE | ID: mdl-31888332

RESUMO

The dielectric constant, which defines the polarization of the media, is a key quantity in condensed matter. It determines several electronic and optoelectronic properties important for a plethora of modern technologies from computer memory to field effect transistors and communication circuits. Moreover, the importance of the dielectric constant in describing electromagnetic interactions through screening plays a critical role in understanding fundamental molecular interactions. Here, we show that despite its fundamental transcendence, the dielectric constant does not define unequivocally the dielectric properties of two-dimensional (2D) materials due to the locality of their electrostatic screening. Instead, the electronic polarizability correctly captures the dielectric nature of a 2D material which is united to other physical quantities in an atomically thin layer. We reveal a long-sought universal formalism where electronic, geometrical, and dielectric properties are intrinsically correlated through the polarizability, opening the door to probe quantities yet not directly measurable including the real covalent thickness of a layer. We unify the concept of dielectric properties in any material dimension finding a global dielectric anisotropy index defining their controllability through dimensionality.

16.
Nat Mater ; 18(12): 1309-1314, 2019 12.
Artigo em Inglês | MEDLINE | ID: mdl-31451781

RESUMO

Metallic transition metal dichalcogenides (TMDs)1-8 are good catalysts for the hydrogen evolution reaction (HER). The overpotential and Tafel slope values of metallic phases and edges9 of two-dimensional (2D) TMDs approach those of Pt. However, the overall current density of 2D TMD catalysts remains orders of magnitude lower (~10-100 mA cm-2) than industrial Pt and Ir electrolysers (>1,000 mA cm-2)10,11. Here, we report the synthesis of the metallic 2H phase of niobium disulfide with additional niobium (2H Nb1+xS2, where x is ~0.35)12 as a HER catalyst with current densities of >5,000 mA cm-2 at ~420 mV versus a reversible hydrogen electrode. We find the exchange current density at 0 V for 2H Nb1.35S2 to be ~0.8 mA cm-2, corresponding to a turnover frequency of ~0.2 s-1. We demonstrate an electrolyser based on a 2H Nb1+xS2 cathode that can generate current densities of 1,000 mA cm-2. Our theoretical results reveal that 2H Nb1+xS2 with Nb-terminated surface has free energy for hydrogen adsorption that is close to thermoneutral, facilitating HER. Therefore, 2H Nb1+xS2 could be a viable catalyst for practical electrolysers.

17.
Nat Mater ; 18(2): 156-162, 2019 02.
Artigo em Inglês | MEDLINE | ID: mdl-30531848

RESUMO

Bulk and two-dimensional black phosphorus are considered to be promising battery materials due to their high theoretical capacities of 2,600 mAh g-1. However, their rate and cycling capabilities are limited by the intrinsic (de-)alloying mechanism. Here, we demonstrate a unique surface redox molecular-level mechanism of P sites on oxidized black phosphorus nanosheets that are strongly coupled with graphene via strong interlayer bonding. These redox-active sites of the oxidized black phosphorus are confined at the amorphorized heterointerface, revealing truly reversible pseudocapacitance (99% of total stored charge at 2,000 mV s-1). Moreover, oxidized black-phosphorus-based electrodes exhibit a capacitance of 478 F g-1 (four times greater than black phosphorus) with a rate capability of ~72% (compared to 21.2% for black phosphorus) and retention of ~91% over 50,000 cycles. In situ spectroelectrochemical and theoretical analyses reveal a reversible change in the surface electronic structure and chemical environment of the surface-exposed P redox sites.

18.
Phys Rev Lett ; 125(24): 246102, 2020 Dec 11.
Artigo em Inglês | MEDLINE | ID: mdl-33412019

RESUMO

The formation, propagation, and structure of nanoscale cracks determine the failure mechanics of engineered materials. Herein, we have captured, with atomic resolution and in real time, unit cell-by-unit cell lattice-trapped cracking in two-dimensional (2D) rhenium disulfide (ReS_{2}) using in situ aberration corrected scanning transmission electron microscopy (STEM). Our real time observations of atomic configurations and corresponding strain fields in propagating cracks directly reveal the atomistic fracture mechanisms. The entirely brittle fracture with non-blunted crack tips as well as perfect healing of cracks have been observed. The mode I fracture toughness of 2D ReS_{2} is measured. Our experiments have bridged the linear elastic deformation zone and the ultimate nm-sized nonlinear deformation zone inside the crack tip. The dynamics of fracture has been explained by the atomic lattice trapping model. The direct visualization on the strain field in the ongoing crack tips and the gained insights of discrete bond breaking or healing in cracks will facilitate deeper insights into how atoms are able to withstand exceptionally large strains at the crack tips.

19.
Phys Rev Lett ; 125(8): 086803, 2020 Aug 21.
Artigo em Inglês | MEDLINE | ID: mdl-32909796

RESUMO

Electrons commonly couple through Fröhlich interactions with longitudinal optical phonons to form polarons. However, trions possess a finite angular momentum and should therefore couple instead to rotational optical phonons. This creates a polaronic trion whose binding energy is determined by the crystallographic orientation of the lattice. Here, we demonstrate theoretically within the Fröhlich approach and experimentally by photoluminescence emission that the bare trion binding energy (20 meV) is significantly enhanced by the phonons at the interface between the two-dimensional semiconductor MoS_{2} and the bulk transition metal oxide SrTiO_{3}. The low-temperature binding energy changes from 60 meV in [001]-oriented substrates to 90 meV for [111] orientation, as a result of the counterintuitive interplay between the rotational axis of the MoS_{2} trion and that of the SrTiO_{3} phonon mode.

20.
Nat Mater ; 17(10): 908-914, 2018 10.
Artigo em Inglês | MEDLINE | ID: mdl-30202109

RESUMO

Due to their layered structure, two-dimensional Ruddlesden-Popper perovskites (RPPs), composed of multiple organic/inorganic quantum wells, can in principle be exfoliated down to few and single layers. These molecularly thin layers are expected to present unique properties with respect to the bulk counterpart, due to increased lattice deformations caused by interface strain. Here, we have synthesized centimetre-sized, pure-phase single-crystal RPP perovskites (CH3(CH2)3NH3)2(CH3NH3)n-1PbnI3n+1 (n = 1-4) from which single quantum well layers have been exfoliated. We observed a reversible shift in excitonic energies induced by laser annealing on exfoliated layers encapsulated by hexagonal boron nitride. Moreover, a highly efficient photodetector was fabricated using a molecularly thin n = 4 RPP crystal, showing a photogain of 105 and an internal quantum efficiency of ~34%. Our results suggest that, thanks to their dynamic structure, atomically thin perovskites enable an additional degree of control for the bandgap engineering of these materials.

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