Two-Dimensional Transition-Metal Dichalcogenides E-Book
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Two-Dimensional Transition-Metal Dichalcogenides
Comprehensive resource covering rapid scientific and technological development of polymorphic two-dimensional transition-metal dichalcogenides (2D-TMDs) over a range of disciplines and applications
Two-Dimensional Transition-Metal Dichalcogenides: Phase Engineering and Applications in Electronics and Optoelectronics provides a discussion on the history of phase engineering in 2D-TMDs as well as an in-depth treatment on the structural and electronic properties of 2D-TMDs in their respective polymorphic structures. The text addresses different forms of in-situ synthesis, phase transformation, and characterization methods for 2D-TMD materials and provides a comprehensive treatment of both the theoretical and experimental studies that have been conducted on 2D-TMDs in their respective phases.
Two-Dimensional Transition-Metal Dichalcogenides includes further information on:
- Thermoelectric, fundamental spin-orbit structures, Weyl semi-metallic, and superconductive and related ferromagnetic properties that 2D-TMD materials possess
- Existing and prospective applications of 2D-TMDs in the field of electronics and optoelectronics as well as clean energy, catalysis, and memristors
- Magnetism and spin structures of polymorphic 2D-TMDs and further considerations on the challenges confronting the utilization of TMD-based systems
- Recent progress of mechanical exfoliation and the application in the study of 2D materials and other modern opportunities for progress in the field
Two-Dimensional Transition-Metal Dichalcogenides provides in-depth review introducing the electronic properties of two-dimensional transition-metal dichalcogenides with updates to the phase engineering transition strategies and a diverse range of arising applications, making it an essential resource for scientists, chemists, physicists, and engineers across a wide range of disciplines.
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Table of Contents
Cover
Table of Contents
Title Page
Copyright
Preface
1 Two‐dimensional Transition Metal Dichalcogenides: A General Overview
1.1 Introduction to 2D‐TMDs
1.2 Crystal Structures of 2D‐TMDs in Different Phases
1.3 Electronic Band Structures of 2D‐TMDs
1.4 Excitons (Coulomb‐Bound Electron‐Hole Pairs)
1.5 Experimental Studies and Characterization of 2D‐TMDs
References
2 Synthesis and Phase Engineering of Low‐Dimensional TMDs and Related Material Structures
2.1 Introduction
2.2 Structure of 2D TMDs
2.3 Synthesis of 2D TMDs
2.4 Phase Engineering of 2D TMDs
2.5 Conclusion
References
3 Thermoelectric Properties of Polymorphic 2D‐TMDs
3.1 Introduction to 2D Thermoelectrics
3.2 Thermoelectric Transport
3.3 Experimental Characterization TE in 2D
3.4 Manipulation of TE Properties in 2D
3.5 Future Outlook and Perspective
References
4 Emerging Electronic Properties of Polymorphic 2D‐TMDs
4.1 Electronic Structure and Optical Properties of 2D‐TMDs
4.2 Polaron States of 2D‐TMDs
4.3 Valley Properties of 2D‐TMDs
4.4 Charge Density Waves of 2D‐TMDs
4.5 Janus Structures of 2D‐TMDs
4.6 Moiré Superlattices of 2D‐TMDs
References
5 Magnetism and Spin Structures of Polymorphic 2D TMDs
5.1 Two‐dimensional Ferromagnetism
5.2 Cr‐based Magnetic Materials and Device Applications
5.3 Polymorphic 2D Cr‐based Magnetic TMDs
5.4 Magnetism in 2D Vanadium, Ion, Manganese Chalcogenides
5.5 Conclusions and Outlook
Acknowledgements
References
6 Recent Progress of Mechanical Exfoliation and the Application in the Study of 2D Materials
6.1 Introduction
6.2 Different Ways for Preparing 2D Materials
6.3 New Mechanical Exfoliation Methods
6.4 Application of Mechanical Exfoliation Method
6.5 Summary and Outlook
Acknowledgments
References
7 Applications of Polymorphic Two‐Dimensional Transition Metal Dichalcogenides in Electronics and Optoelectronics
7.1 Field‐Effect Transistors (FETs)
7.2 Memory and Neuromorphic Computing
7.3 Energy Harvesting
7.4 Photodetectors
7.5 Solar Cells
7.6 Perspectives
References
8 Polymorphic Two‐dimensional Transition Metal Dichalcogenides: Modern Challenges and Opportunities
8.1 Summing up the Chapters
8.2 Projecting the Future: Challenges and Opportunities
8.3 Global Challenges and Threats
8.4 Exponential Growth in Demands for Modern Computation
8.5 Conclusion
References
Index
End User License Agreement
List of Tables
Chapter 2
Table 2.1 Electronic properties of different TMDs.
Chapter 4
Table 4.1 Parameters of the selected polar substrates and the surface optica...
Table 4.2 Band gap modulation of TMD monolayers in the presence of the SiO
2
...
Table 4.3 Band gap modulation of TMD monolayers due to the intrinsic longitu...
Table 4.4 Diverse CDWs in the 2D TMDs. In some materials, different CDWs hav...
Table 4.5 A summary of CDW formation mechanisms for the different groups of ...
List of Illustrations
Chapter 1
Figure 1.1 Lattice structures of 2D‐TMDs in the (a) trigonal prismatic (1H),...
Figure 1.2 Atomic structures of the 1T″‐phase 2D‐TMD with the atomic planes ...
Figure 1.3 Relative stability of various phases of TMDs in the H, T, and T
d
...
Figure 1.4 The structural stability and the electronic properties single pha...
Figure 1.5 Phase boundary under constant charge in MoTe
2
and MoS
2
monolayers...
Figure 1.6 Comparing the band structures of the respective TMD materials in ...
Figure 1.7 Spin‐splitting in the valence and conduction bands as functions o...
Figure 1.8 Theoretically and experimentally determined band structures of 2D...
Figure 1.9 Thickness‐dependent bandgap properties of semiconducting phase Mo...
Figure 1.10 Band structures of (a) quadrilayer, bilayer and monolayer MoS
2
w...
Figure 1.11 Band structure calculations of WSe
2
and MoS
2
monolayers with and...
Figure 1.12 Schematic of the optical absorption of an ideal 2D semiconductor...
Figure 1.13 (a) Real‐space representation of excitons in three‐dimensional a...
Figure 1.14 Schematic representation of quasiparticles. (a) Neutral exciton,...
Figure 1.15 (a) The typical lattice structure of 1H‐phase 2D‐TMDs. Despite s...
Figure 1.16 Schematics of CVD and MOCVD synthesis methods of TMD thin‐films....
Figure 1.17 MBE involves high‐purity elemental source materials that are co‐...
Figure 1.18 Different excitons in low‐dimensional layers and heterostructure...
Figure 1.19 (a) Schematic of spectroscopic ellipsometry with the rotating‐an...
Figure 1.20 (a)
ε
1
and (b)
ε
2
dielectric functions of monolayer‐Mo...
Figure 1.21 Dielectric functions (a)
ε
1
and, (b)
ε
2
of monolayer M...
Figure 1.22 (a) Refractive index,
n
(
ω
), and (b) extinction coefficient,...
Figure 1.23Figure 1.23 Comparing the symmetry operations between a monolayer...
Figure 1.24 Raman profiles of MoS
2
of different thicknesses. (a) Raman spect...
Figure 1.25 Raman profiles of WSe
2
of different thicknesses. (a) Raman spect...
Figure 1.26 (a) Raman spectra of MoS
2
/Au at the respective annealing tempera...
Figure 1.27 Comparing the ARPES‐characterized band structures of monolayer a...
Figure 1.28 STM and STS characterization of mono‐, bi‐ and trilayer MoSe
2
sy...
Figure 1.29 STM and STS characterization of WSe
2
. (a) Schematic of the syste...
Chapter 2
Figure 2.1 Five reported structure prototype of TMDs. Yellow, chalcogen atom...
Figure 2.2 The atomic arrangement and corresponding d‐orbital splitting of t...
Figure 2.3 Commonly used top‐down methods for preparing 2D TMDs. (a) Mechani...
Figure 2.4 The CVD synthesis of 2D TMDs. (a) A collection of 2D TMDs produce...
Figure 2.5 Phase‐selective growth of MoS
2
. (a) Schematic for the phase‐selec...
Figure 2.6 Phase‐selective growth of MoTe
2
. (a) Phase diagram of the CVD‐gro...
Figure 2.7 (a) Schematic illustration of the CVD setup for synthesizing 3R M...
Figure 2.8 (a) A diagram demonstrating the proposed KCl‐enhanced deposition ...
Figure 2.9 (a) Schematic illustration of the CVD growth of 1T WS
2
with Fe
3
O
4
Figure 2.10 (a) Scheme of the sequential growth for coplanar heteroepitaxy o...
Figure 2.11 (a) Effect of cooling rate on the phase formation of CVD‐grown M...
Figure 2.12 (a) Surface area ratio between the 2H and 1T domains, with respe...
Figure 2.13 Bandgap engineering and carrier type modulation achieved in 2D T...
Figure 2.14 (a) Photographs of the CVT‐grown WSe
2(1−
x
)
Te
2
x
single crys...
Figure 2.15 (a) Schematic representation of the experimental setup for synth...
Figure 2.16 (a) Isosurface (0.003 e/Å3) of the charge distributions of 2H (l...
Figure 2.17 (a, b) Raman and PL spectra of 1T′ MoS
2
and 2H MoS
2
obtained by ...
Figure 2.18 (a) Optical images of the mechanically exfoliated few‐layer 2H M...
Chapter 3
Figure 3.1 Discretization of density of states from 3D to 2D and 1D due to q...
Figure 3.2 Interdependence between Seebeck coefficient (
S
), electrical condu...
Figure 3.3 (a) Carrier concentration (
n
) and (b) Seebeck coefficient (
S
) as ...
Figure 3.4 Schematic diagram of (a) four‐probe technique for electrical tran...
Figure 3.5 (a) Schematic diagram of temperature gradient (
Δ
T
) measureme...
Figure 3.6 Open‐circuit voltage (
V
TEP
) of a n‐type sample as a function of h...
Figure 3.7 (a) Sketch of Raman laser heating a suspended monolayer graphene ...
Figure 3.8 (a) Optical image of monolayer MoS
2
on h‐BN. Source: Liu et al. [...
Figure 3.9 (a) Schematic of TDTR setup. (b)Thin films and bulk materials mea...
Figure 3.10 (a) Temperature dependent in‐plane and out‐of‐plane thermal cond...
Figure 3.11 Schematic diagram of experimental setup for (a) thermal bridge m...
Figure 3.12 (a) Length dependent cumulative thermal resistance of few layer ...
Figure 3.13 (a) Schematic of H‐type measurement for a suspended 2D flake. So...
Figure 3.14 Typical thermoelectric devices employing the field‐effect modula...
Figure 3.15 (a) Illustration of rippled‐MoS
2
on a bulged substrate with a ro...
Figure 3.16 Band structures and density of states of bulk, four‐layer, bilay...
Figure 3.17 (a) Schematic of device structure for thermoelectric measurement...
Figure 3.18 (a) Electronic band structure of monolayer PdSe
2
. (b) Illustrati...
Figure 3.19 Different polymorphs or phases of single‐layer and multi‐layer T...
Figure 3.20 Relationship between the energy of carriers (electrons in this c...
Figure 3.21 Carrier filtering by (left) randomly distributed dopants or nano...
Figure 3.22 Experimental study on the thermoelectric properties of metallic ...
Chapter 4
Figure 4.1 Structure and electronic band structure of monolayer TMDs. (a) At...
Figure 4.2 Excitons in monolayer TMDs. Source: Wang et al. [4]/With permissi...
Figure 4.3 Structural and electronic properties of T‐TMDs. (a) Atomic struct...
Figure 4.4 (a) The 3D ARPES spectra taken for the Rb‐deposited MoS
2
at
ρ
...
Figure 4.5 (a) Schematic illustration of the spin‐resolved conduction band e...
Figure 4.6 (a) Schematic illustration of the Landau levels in the
K
and
K′
...
Figure 4.7 (a) Spin polarization band of monolayer MoS
2
, Red (blue) color re...
Figure 4.8 The Berry curvatures of monolayer MoS
2
along the high‐symmetry li...
Figure 4.9 (a) Schematic diagram of valley optical selection rule. (b) Polar...
Figure 4.10 (a) and (b) Schematic diagram of TMD doping sites. (c) Brillouin...
Figure 4.11 (a) side view of the WS
2
/MnO heterostructure. (b) Band structure...
Figure 4.12 (a) Atomic structure and, (b) the band structure of WSSe on MnO ...
Figure 4.13 Peierls model of a 1D half‐filled atomic chain with lattice cons...
Figure 4.14 STM images reveal (a)
3 × 3
CDW in 1H‐NbSe
2
, (b...
Figure 4.15 (a) Band structure of monolayer 1H‐NbSe
2
. The blue, red, and gre...
Figure 4.16 (a) The second derivative of ARPES dispersions along
ΓM
and...
Figure 4.17 Mechanisms for CDW formation in TMDs. (a) Fermi surface nesting....
Figure 4.18 (a) The phase diagram of 1T‐TaS
2
under pressure. Various CDW pat...
Figure 4.19 (a and b) The Moiré superlattice is formed by twisting bilayer M...
Figure 4.20 (a and b) Charge density of the VBM wave function of (a) M
3.5
an...
Chapter 5
Figure 5.1 (a) Schematic diagram of the exchange interaction between spins d...
Figure 5.2 (a) Atomic structure of CrI
3
. Source: Huang et al. [3]/with permi...
Figure 5.3 (a) Schematic of a dual‐gate field‐effect device based on bilayer...
Figure 5.4 (a) Spin‐polarized tunneling spectra of monolayer CrBr
3
under out...
Figure 5.5 (a) Crystal structure of CrCl
3
. Source: Cai et al. [13], (2019) ©...
Figure 5.6 (a) Crystal structure of Cr
2
Ge
2
Te
6
. Source: Hao et al. [62]/with ...
Figure 5.7 (a) Crystal structure of CrPS
4
. Source: Son et al. [14] Reproduce...
Figure 5.8 (a) Atomic model of CrSe crystal. Source: Zhang et al. [21]/with ...
Figure 5.9 (a) Schematic of MBE growth of CrTe
2
films on graphene. Source: Z...
Figure 5.10 Atomic structures (side views) of CrTe
2
(a), Cr
2
Te
3
(e), Cr
3
Te
4
...
Figure 5.11 (a) DFT calculated and experimental electronic structures of mon...
Figure 5.12 (a) Schematic view and crystal structures of tetragonal and hexa...
Chapter 6
Figure 6.1 (a and b) Ruoff et al. from the University of Washington in the U...
Figure 6.2 Illustration of the modified exfoliation process for layered crys...
Figure 6.3 Optical images of graphene flakes prepared by the standard exfoli...
Figure 6.4 Monolayer graphene and Bi2212 samples prepared by an oxygen plasm...
Figure 6.5 Mechanical exfoliation of different monolayer materials with macr...
Figure 6.6 Ag‐assisted exfoliation procedures and optical characterization o...
Figure 6.7 Fabrication process and characterization of suspended 2D material...
Figure 6.8 Variation of energy band structure of MoS
2
on SiO
2
/Si substrate, ...
Figure 6.9 Schematic of vdWs contact between bottom electrodes and TDACs. (a...
Figure 6.10 (a) Illustration of a typical absorption spectrum of doped graph...
Figure 6.11 Photograph of a ‐based saturable absorber modulated by visible f...
Figure 6.12 The correlated electronic states in a twisted WSe
2
device
.
Schem...
Figure 6.13 Schematic diagram of five basic magnetic states in a 3D crystal ...
Figure 6.14 The scheme of the reported different magnetic states in a 2D cry...
Figure 6.15 Layer‐dependent magnetic ordering in atomically‐thin CrI
3
. (a) M...
Figure 6.16 Ferromagnetism in an atomically thin Fe
3
GeTe
2
flake modulated by...
Figure 6.17 The tunnel transport in Atomically Thin MnPS3 crystals. (a) Colo...
Figure 6.18 Experimental observation of quasi‐ballistic phonon transport in ...
Figure 6.19 (a) Experimental observation of thickness‐dependent thermal cond...
Figure 6.20 (a) d
I
/d
V
spectra measured on a bias voltage scale from −10 to +...
Figure 6.21 (a) A schematic view of the (Li,Fe)OHFeSe based SIC‐FET device. ...
Figure 6.22 (a) Schematical illustration of fabrication processes of spin‐co...
Chapter 7
Figure 7.1 (a) Schematic illustration of the laser‐irradiation‐induced phase...
Figure 7.2 (a) Schematic illustration of the Pd/WS
2
/Pt memristor. (b)
I
–
V
ch...
Figure 7.3 (a) Schematic illustration of the fabrication process of the wear...
Figure 7.4 (a) Optical image of the 1T′‐MoTe
2
‐based photodetector. Inset: AF...
Figure 7.5 (a) Optical image of the Mo
x
Re
1–
x
S
2
‐based device. (b, c) Hi...
Figure 7.6 (a, b) SPCM maps of MoS
2
‐based photodetectors with metal/1T‐/2H‐M...
Figure 7.7 (a) Schematic illustration of single‐layer 1T‐MoS
2
x
Se
2(1−
x
)
Chapter 8
Figure 8.1 A list of schematics and charts displaying van der Waals junction...
Figure 8.2 Schematic diagram of a photocatalyst comprising monolayer‐MoS
2
on...
Figure 8.3 The optoelectronic properties of monolayer‐MoS
2
in its respective...
Figure 8.4 Schematic depicting the synthetic procedures of MoS
2
‐integrated c...
Figure 8.5 Different ways of manipulating 2D‐TMDs to be utilized for memrist...
Figure 8.6 Schematic of the MoS
2
memristor device encapsulated by the amorph...
Guide
Cover Page
Title Page
Copyright
Preface
Table of Contents
Begin Reading
Index
Wiley End User License Agreement
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Two-Dimensional Transition-Metal Dichalcogenides
Phase Engineering and Applications in Electronics and Optoelectronics
Edited by Chi Sin Tang, Xinmao Yin, and Andrew T. S. Wee
Editors
Dr. Chi Sin Tang
National University of Singapore
Singapore Synchrotron Light Source
5 Research Link
117603 Singapore
Singapore
Prof. Xinmao Yin
Shanghai University
Physics Department
200444 Shanghai
China
Prof. Andrew T. S. Wee
National University of Singapore
Department of Physics
2 Science Drive 3
Department of Physics
117551 Singapore
Cover Image: © oxygen/Getty Images
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Preface
Two‐dimensional transition‐metal dichalcogenides (2D‐TMDs) have undergone intense research and detailed scrutiny over the past decade. The years of intensive research yielded profound insights into their optical, electronic, mechanical, and magnetic properties and capabilities. The agglomeration of extensive scientific knowledge towards 2D‐TMDs has in turn opened new frontiers and created greater potential for applications in a diverse range of disciplines and over multiple domains, such as light emitters, photo‐sensors, catalysts, and clean‐energy media, and the list could possibly grow longer with time.
Unlike previous publications related to 2D‐TMDs, this new publication provides an in‐depth yet comprehensive review concerning the polymorphic phases of 2D‐TMDs, with emphasis on the phase engineering strategies and a diverse range of arising applications. We gathered experimental and theoretical experts of the respective sub‐domains in the multifaceted discipline of 2D‐TMDs who share valuable insights in areas including thermoelectricity, theoretical modeling, magnetic 2D‐TMDs, material preparation, and the extent to which 2D‐TMDs have been utilized in multiple areas of application. The book concludes by giving readers an idea how the rapid research and development of 2D‐TMDs could possibly address the major issues facing humanity today.
By elegantly piecing together various aspects of 2D‐TMD research and development in this publication, this reference text covers a broad range of topics that encompass the rapid scientific and technological development of polymorphic 2D‐TMDs. It serves as an ideal reference for physicists, chemists, materials engineers, and technologists to better comprehend the challenges, motivate them to address the utilization of TMD‐based applications, and propel this exciting field forward.
9 December 2022
Chi Sin TangSingapore Synchrotron Light SourceNational University of Singapore5 Research Link117603 Singapore
Xinmao YinShanghai Key Laboratory of HighTemperature SuperconductorsPhysics DepartmentShanghai UniversityShanghai, 200444, China
Andrew T. S. WeeDepartment of PhysicsNational University of Singapore2 Science Drive 3, 117551, Singapore
1Two‐dimensional Transition Metal Dichalcogenides: A General Overview
Chi Sin Tang1,2 and Xinmao Yin2
1National University of Singapore, Singapore Synchrotron Light Source (SSLS), 5 Research Link, Singapore, 117603, Singapore
2Shanghai University, Shanghai Key Laboratory of High Temperature Superconductors, Shanghai Frontiers Science Center of Quantum and Superconducting Matter States, Physics Department, 99 Shangda Road, Shanghai, 200444, China
1.1 Introduction to 2D‐TMDs
Since graphene was first exfoliated from graphite using the mechanical cleavage method [1], 2D materials have garnered widespread interest. Atomically thin 2D‐TMDs, with a formula of MX2 (M: transition metal atom; X: chalcogen atom), form a diverse class of 2D materials with about 60 members. While one can trace back the extensive studies on bulk and multilayer TMD materials to more than half a century ago [2], it was only the groundbreaking emergence of graphene of single‐atom thickness [1, 3] that led to the tremendous progress of monolayer van der Waals systems within the last two decades. With unique optoelectronic properties and robust mechanical features, 2D‐TMD is a class of low‐dimensional materials ideal for multiple applications in areas such as electronics, optoelectronics, and valleytronics [4–6]. They surpass graphene in terms of their functionality due to the combination of their non‐zero bandgap electronic structures and their pristine yet robust layered surface properties. 2D‐TMD is also a favorable class of materials in practical applications related to field‐effect‐transistor (FET) based systems. Hence, extensive research studies have taken center stage over the past decade to uncover both the fundamental physical properties and to unleash new frontiers for possible 2D‐TMD‐based device applications.
At the molecular level, diverse variations to the chemical bonding and crystal configurations of the transition metal atom component in 2D‐TMDs have led to multiple structural phases that possess unique electronic properties. The semiconducting 1H phase is a quintessential example. Structural changes to one of the chalcogen planes will result in the metallic 1T phase. In addition, a unique quasi‐metallic 1T'phase arises due to its distorted sandwich structure, where an array of one‐dimensional zigzag transition metal chains are formed [7, 8].
1.2 Crystal Structures of 2D‐TMDs in Different Phases
TMDs present various structural polymorphs which have attracted huge interest in the last decade, both as an ideal platform for the fundamental study of layered quantum systems and their potential for multiple applications. Structurally, a unit layer is made up of a transition metal layer sandwiched between two chalcogen layers. Interestingly, TMDs, whether in the mono or multi‐layer form, manifest themselves in different structural phases arising due to different configurations of the transition metal atom component. The common polymorphs of 2D‐TMDs are the trigonal prismatic 1H phase and the octahedral 1T phase. In the case of the octahedral 1T phase structure, it has been experimentally and theoretically shown that it is dynamically unstable under free‐standing conditions [7–9]. Consequently, similar to the Peierls distortion, the 1T phase will relax and buckle spontaneously into a thermodynamically more stable distorted structure known as the 1T′ phase [7–9]. Hence, 1T phase 2D‐TMDs can further stabilize under favorable chemical, thermal and mechanical conditions [10], particularly into the 1T′phase.
To better understand the diverse structural properties of 2D‐TMDs, the respective structural phases can be visualized by the stacking configurations of the three atomic planes (i.e. the X‐M‐X structure). The 1H phase corresponds to an ABA stacking configuration where the chalcogen atoms at the top and bottom atomic planes are in the same vertical position and are located on top of each other in a direction perpendicular to the layer (Figure 1.1a). In contrast, the 1T structural phase has an ABC stacking configuration displayed in Figure 1.1b. Since the 1T phase structure is unstable under freestanding conditions, it will buckle and distort into the 1T′ structure where the transition metal atoms sandwiched between the upper and lower atomic layers distort. Consequently, it forms a period doubling 2 × 1 structure. As viewed from the top, this structural phase consists of an array of 1D zigzag transition metal chains (Figure 1.1c). Indeed, recent investigations related to symmetry‐reducing CDW properties [12] in metallic 1T phase 2D‐TMDs have created new opportunities for integrated low‐dimensional material‐based applications, including transistor systems, nanoscale charge channels and gate switching devices [13–15]. Besides, 1T′ phase 2D‐TMDs are known to possess anisotropic electronic and optical features. An in‐depth understanding of its unique structure can bring new insights to its characteristics, which can then be exploited for directionally regulated charge or photon channel applications in optoelectronics and electronics.
As discussed thereafter, electronic structure calculations have indicated that while the 1T phase 2D‐TMD is metallic [10, 16], the 1T′ phase counterpart possesses a unique quasi‐metallic electronic structure that will be discussed later. To clearly distinguish between these two structural phases, note that while low‐temperature charge density wave (CDW) phases are typically observed in 1T phase TMD systems (e.g. TCDW ∼120 K for TaSe2 and TCDW∼35 K for NbSe2 [17, 18]), a CDW‐like lattice distortion in the form of periodic 1D zigzag chain structure unique to the 1T′phase 2D‐TMD can be observed even at room temperature [7, 8]. Morphologically, while the low‐temperature commensurates CDW in 1T phase, TMDs can be distinguished by a unique star‐of‐David superlattice [19–21] typically characterized using scanning tunneling microscopy. Conversely, the 1D zigzag chains in the 1T′ phase are clearly distinguished via high‐resolution transmission electron microscopy.
Figure 1.1 Lattice structures of 2D‐TMDs in the (a) trigonal prismatic (1H), (b) octahedral (1T), and (c) distorted (1T′) phases. Stacking configuration of the atomic planes have been indicated. (d) The stacking orders that distinguish between the 1T′ and the 1Td phases. The red dashed boxes serve as visual guides. Source: Tang et al. [11]/With permission of AIP Publishing.
1.2.1 Other Structural Phases
Apart from the three common structural phases, TMDs are also present in other structural phases each with their unique optical and electronic properties. For example, MoTe2 and WTe2 would undergo a first‐order phase transition from the monoclinic 1T′ phase to form the orthogonal 1Td phase as temperature decreases. While the structures of both the 1T′ and 1Td phase are rather similar, their key differences lie with the dislocations between the stacking layers depicted in the layer distortion in Figure 1.1d. These seemingly trivial dislocations can lead to a significant symmetry change between the two structural phases [22, 23]. Nevertheless, with a similar structure present in the respective layer, 1Td phase TMDs still possess similar quasi‐metallic electronic properties as that of its 1T′ phase counterparts [9, 22, 23].
Figure 1.2 Atomic structures of the 1T″‐phase 2D‐TMD with the atomic planes indicated. Source: Reproduced with permission from Ma et al. [24]. Copyright 2016, The Royal Society of Chemistry.
In the monolayer regime, apart from the formation of the 1T′ structural phase due to distortion from its 1T phase counterpart, other stable polymorphs have also been reported. This includes another octahedrally coordinated 1T″ phase (Figure 1.2) [25]. While there is an association between the transition metal atoms in the M–M configuration in the 1T′ and 1T″ distorted phases, the transition metal atoms are dimerized in the 1T′ phase while trimerization takes place in the 1T″ phase [26]. Besides, while the 1T′ phase possesses quasi‐metallic electronic properties, computational studies have suggested that the 1T″ phase is a wide bandgap semiconductor where 1T″ phase monolayer‐MoS2 possesses an indirect bandgap of ∼0.27 eV [24]. Nevertheless, no consensus has been reached in terms of the relative stability between the octahedral phases, particularly for monolayer‐MoS2, where different studies have reported different stability levels between the structural phases [24, 27, 28].
1.2.2 Phase Stability
Theoretical studies have shown that the 1H‐1T′ energy differences vary between different Mo‐ and W‐based 2D‐TMD species, especially with the inclusion of spin‐orbit coupling [29, 30]. Figure 1.3 displays the phase energetics of the respective monolayers in their respective phases as extracted from Ref. [30, 31], with U = 0 as the reference energy for the respective 2D‐TMD in their 1H phase and 1T phase, which are the most unstable of the polymorph. A smaller energy difference between the 1T′ and the 1H phase would mean a correspondingly smaller amount of external energy required to induce the 1H‐1T′ phase transition. In the case of monolayer‐WTe2, the U < 0 registered for the 1T′ phase suggests that the compound is more stable in its 1T′ phase — i.e. 1H‐1T′ phase transition takes place spontaneously without any external influence.
Figure 1.3 Relative stability of various phases of TMDs in the H, T, and Td structural phases. The zero energy is the most stable phase for the TMDs. Source: Reproduced with permission from Santhosh et al. [31] © 2015 IOP Publishing Ltd.
Even in the case of phase stability between the 1H and 1T phases, multiple studies have already been conducted specifically for MoTe2[32]. Under more general circumstances, simulations that involve the stability of different 2D‐TMD species have also been extensively studied with a summary comprising 44 species displayed in Figure 1.4[33]. When in their respective ground state polymorph, their different 2D‐TMD species can possess semiconducting (T**/H**), metallic (T*/H*), or half‐metallic (T+) behaviors.
Based on the energy differences between the semiconducting 1H and quasi‐metallic 1T′ phase of the respective Mo and W‐based 2D‐TMDs, the application of different electrostatic gating configurations can drive their 1H‐1T′ phase transition. This is carried out by changing the carrier density or electron‐chemical potential in the monolayer‐TMD via a capacitor structure displayed in Figure 1.5[29]. Specifically, in the case of undoped monolayer‐MoTe2 with a very small energy difference between the 1H and 1T′ phases, a mere surface charge density below −0.04e or above +0.09e per unit cell is required to drive the 1H‐1T′ structural phase transition under pristine conditions. Whereas a significantly higher surface charge density of about −0.29e or above +0.35e per unit cell is required to drive the same structural transition for monolayer‐MoS2.
The control of pressure is a thermodynamic parameter that affects the phase stability of 2D‐TMDs and induces a structural phase transition. As mentioned earlier, the highly symmetric 1T phase structure for Mo and W‐based 2D‐TMDs is unstable under free‐standing conditions and ambient pressure. They will therefore buckle and convert readily to the octahedral‐like 1T′ phase structure. Density functional theory (DFT)‐ based studies to determine the phase diagrams of 2D‐TMD with respect to tensile strain have shown that to maintain the stability of the metallic 1T phase structure, an equi‐biaxial tensile strain of 10–15% is required for most 2D‐TMDs (e.g. 13% for monolayer‐MoS2) except for MoTe2. For the latter, a considerably smaller tensile strain <1.5% is required under appropriate constraints [30]. Given the small energy differences between the 1H and 1T′ phases for MoTe2, minimal temperature changes also have profound effects on the transition dynamics due to the introduction of vibration effects to the system. Hence, the strain required to induce the structural phase transition is reduced at elevated temperatures [30]. Even monolayer‐WTe2, which is energetically more stable in the 1T′ phase under pristine conditions, will transform into semiconducting 1H phase when lattice compression is applied.
Figure 1.4 The structural stability and the electronic properties single phase and mixed phase of TMDs summarized in the table. The transition‐metal atomic components are classified into the 3d, 4d, and 5d groups. With the gray colour boxes indicating phase separation. The resulting structural phases (T or H) could be metallic (*) or semiconducting (**). Source: Reproduced with permission.
Figure 1.5 Phase boundary under constant charge in MoTe2 and MoS2 monolayers. (a) Schematic of a monolayer TMD lattice and an electron reservoir such as a metallic surface that is separated by a vacuum layer. Evolution in the energy difference of the respective 2D‐TMDs between their 1H and 1T′ phases changes with respect to charge density, σ. The blue line represents situations where both the 1H and 1T′‐phase lattices are in relaxed state while the red line represents the constant‐area case where monolayer is kept to the area when under 1H‐phase lattice constants. (b) 1H‐phase MoTe2 is a stable phase while 1T′‐phase MoTe2 is metastable when the monolayer is charge neutral. However, 1T′‐phase MoTe2 becomes increasingly stable when charged beyond the positive or negative threshold values. (c) 1H‐phase monolayer‐MoS2 is stable when charge neutral. Nevertheless, the magnitude of charge required to induce 1H‐1T′ transition is larger than its MoTe2 counterpart. In both cases, transition at constant stress is more easily induced than the transition under constant area. Source: Li et al. [29]/Springer Nature/Licensed under CC BY 4.0.
It is further discovered that the coexistence of multiple phases within a system –easily achievable under laboratory settings – is thermodynamically stable under reasonable thermodynamic conditions. Experimentally, such studies are achievable with a certain degree of restrictions. While tensile strain can easily be applied to 2D‐TMDs by attaching it to a large elastic substrate where its deformations can be regulated [34, 35], the spontaneous formation of ripple patterns complicates the strain process and characterization [35–37]. As for bulk or multi‐layer materials, deformations that are sufficiently significant can only be achieved via compression processes.
1.3 Electronic Band Structures of 2D‐TMDs
Given the number of members in the 2D‐TMD family, they exhibit a diverse range of macro properties related to their mechanical and electronic features. Their properties also differ between the monolayer, multilayer, and bulk counterparts. For example, in their bulk form, niobium, tantalum‐based sulfides, and selenides as well as β‐MoTe2, and 1Td phase WTe2 possess metallic properties [38–41]. Conversely, TMD species such as the commonly studied MoS2, WS2, MoSe2, WSe2, α‐MoTe2, ReS2, and ZrS2 are semiconducting in nature [38, 39, 42–44]. At the molecular level, the interlayer van der Waals forces of interaction play a pivotal role in dictating their properties at both the macro and micro‐electronic level. Even at the intralayer level, the intrinsic interactions taking place between the constituent atoms play a critical role in dictating the properties of the TMD species. Therefore, even though the lattice structures of the respective phases may be similar for different 2D‐TMDs, the extensive interplay of the spin, charge, and orbital degrees of freedom result in very distinct electronic and optoelectronic properties.
In addition, apart from the chemical compositions of different 2D‐TMDs, the diversity of structural phases and their respective stabilities brings about unique optoelectronic properties because of their unique electronic band structure, and the emergence of novel correlated and topological phases. These polymorphic electronic features are intimately related to the coupling between their charge, spin, orbital, and lattice degrees of freedom. A distinct example to be further elaborated on would be the presence of strong spin‐orbit coupling that leads to the opening of the fundamental gap in 1T′ phase 2D‐TMDs [8, 9].
1.3.1 Electronic Band Structures of the 1H, 1T, and 1T′ Phase
The electronic band structures of 2D‐TMDs are dictated by multiple effects including strong Coulomb interaction between the constituent atoms and the effects of crystal symmetry. Meanwhile, spin‐orbital coupling also has their distinct roles in determining the unique orbital characters, spin‐valley properties, and unique optical selection rules. As discussed in the following section, the electronic band structures of multilayer TMD systems in the 2H‐phase are a result of the weak interlayer van der Waals interactions. Structurally, 2H phase layered TMDs are characterized by the D6h point symmetry group [45, 46]. Unlike their monolayer (1H) counterparts (Figure 1.6a), 2H phase multilayer and bulk TMDs are indirect bandgap semiconductors where the valence band maximum (VBM) is situated at the Γ‐point of the hexagonal Brillouin zone, while the conduction band minimum (CBM) is approximately halfway between the Γ‐ and K‐points (Figure 1.6b) [48, 49].
When examined in greater detail, by taking the example of monolayer‐WSe2 with spin‐orbit coupling accounted for, the electronic bands at the Γ‐point consist of contributions from both the Se (chalcogen) pz‐orbitals and the (transition mtal) ‐orbitals in both the valence and conduction bands (Figures 1.7a,b, respectively). The energy bands of both the conduction and valence bands at the K/K′‐points have a majority in‐plane contribution from the localized transition metal orbitals. They include the and idxy‐states (VB) and a mixture of both the mtal and chalcogen px∓ipy orbitals at the conduction band [50–52]. The spatial overlap between adjacent layers and their corresponding effects on the band structure has long‐standing effects with variable layer thickness down to the monolayer limit [53, 54].
Figure 1.6 Comparing the band structures of the respective TMD materials in their monolayer and bulk form with SOC accounted for. (a) Band structure of MoS2, MoSe2, WS2, and WSe2 monolayers obtained from DFT calculations. Dashed arrows suggest that these are direct bandgap semiconductors. (b) Band structure of bulk MoS2, MoSe2, WS2, and WSe2 obtained from DFT calculations. Dashed arrows suggest that these are indirect bandgap semiconductors in their bulk form. Source: Roldán et al. [47]/With permission of John Wiley & Sons.
Figure 1.7 Spin‐splitting in the valence and conduction bands as functions of k// along the Γ–K points in the Brillouin zone with the contributions of the W (d) and Se (p) orbitals. (a) Uppermost valence band, and (b) lowermost conduction band. Source: Zhu et al. [50]/With permission of American Physical Society.
As for the electronic band structures of the commonly observed 1H, 1T, and 1T′ polymorphs, examples of the respective polymorphs of monolayer‐MoS2 are displayed in Figures. 1.8a,b,c, respectively [8, 54, 55]. The 1H‐phase is a direct K–K bandgap semiconductor. The direct K–K transition has strong contributions from the transition metal d‐orbitals (i.e. the Mo‐atoms). With two contributing electrons from the transition metal d‐orbitals, they will be paired and fully occupied in its lowest ‐orbital state due to the hexagonal symmetry of the 1H phase structure. Hence, the 1H phase semiconducting structure is stabilized by the electron count of the transition metal d‐orbitals. As discussed later, high‐resolution scanning tunneling spectroscopy (STS) serves as an effective characterization technique that reveals a ∼2.4 eV bandgap for chemical vapor deposition (CVD) synthesized monolayer‐MoS2 where it has been demonstrated that this bandgap decreases significantly with increasing thickness [57]. The thickness‐dependent band structures have been further characterized using high‐resolution angle‐resolved photoemission spectroscopy (ARPES) as displayed in Figure 1.8d,g[56]. Note how the electronic structures of MoS2 near the Fermi level evolves between its mono‐, bi‐, trilayer and its bulk form [56].
In terms of the quasi‐stable metallic 1T‐phase, there is a degeneracy in the electronic structure (lowest dxy,yz,zx degenerate orbitals) that is attributed to the structure's tetragonal symmetry. This results in the partially occupied transition metal d‐orbitals that brings about the metallic character. In the regions near the Γ‐point, the Fermi‐level crosses both the Mo d‐ and S p‐orbitals (Figure 1.8b). While the 1H‐phase structure is stabilized by the electron count of the transition metal d‐orbitals, charge‐doping processes such as intercalation, alloying, gating, and defect engineering processes are expected to modify the transition metal d‐orbital electron population. Consequently, this de‐stabilizes the 1H‐phase structure and leads to a structural transition into the 1T or 1T′‐phase. Apart from modifying the electron count, external effects in the form of atomic distortion can also destabilize the electronic structure of the semiconducting 1H‐phase which in turn leads to the formation of the 1T/1T′‐phase.
Figure 1.8 Theoretically and experimentally determined band structures of 2D‐TMDs in their respective phases. (a) 1H, (b) 1T, and (c) 1T′‐phase monolayer‐MoS2. The green lines in (a) show the top (bottom) valence (conduction) bands in bulk MoS2. The lines marked by red and blue in (b) represent the bands, contributed mainly by the Mo 4d‐orbitals and S 3p‐orbitals, respectively. Band structure of 1T′‐phase monolayer‐MoS2 in (c) with the fundamental, Eg, and inverted gap, 2δ. Inset: comparison of band structures with (red dashed line) and without (black solid line) spin‐orbit coupling. ARPES band map of exfoliated (d) monolayer, (e) bilayer, (f) trilayer, and (g) bulk MoS2 along the M–Γ–K high symmetry lines. Source: (a) Kadantsev et al. [16]/Reproduced with permission from Elsevier. (b) Hu et al. [55]/Reproduced with permission from AIP Publishing. (c) Zhuang et al. [28]/Reproduced with permission of American Physical Society. (d)–(g) Reprinted with permission from Jin et al. [56], 2017 American Physical Society.
As for the 1T′‐phase 2D‐TMDs, the zigzag chain structure lowers the transition metal d‐orbitals below the chalcogen p‐orbitals. This leads to a band inversion which in turn, leads to the formation of an inverted gap, 2δ, at the Γ‐point in the Brillouin zone, along with two Dirac cones near the Γ‐point in the 2D Brillouin zone. Under the influence of spin‐orbit coupling, there is an opening of a fundamental gap, Eg, at the Dirac points (Figure 1.8(c)). ARPES study of 1T′‐phase monolayer‐WSe2 synthesized by molecular beam epitaxy (MBE)[[58]] has shown a ∼0.12 eV fundamental gap that is consistent with their band structure calculations. In this case the high‐symmetry Γ–Y and Γ–P directional contributions have been detected in a single ARPES measurement. The STS and ARPES results exhibit the direct observation of the ∼56 meV fundamental gap for the epitaxially grown 1T′‐phase monolayer‐WTe2[59]. Optical techniques have also been utilized to probe the optoelectronic properties of TMD materials. For instance, Fourier‐transform infrared spectroscopy (FTIR) investigations by Keum et al. revealed an absorption feature at ∼0.06 eV, which can be attributed to the fundamental gap of mechanically exfoliated 1T′‐phase monolayer‐MoTe2 samples [9]. As presented later in the subsequent sections, spectroscopic ellipsometry has been used to probe the 1T′‐phase MoS2 and WSe2 monolayers, where the emergence of the fundamental and inverted gaps has been observed [60, 61].
TMD systems in both their monolayer and multilayer forms exhibit myriads of rich physical phenomena, and they hold immense promise both in the realm of fundamental science and for future device and optoelectronic applications in their respective polymorphs. To effectively investigate and exploit the unique properties of each polymorph, efficient phase engineering strategies must be implemented to access the respective phases with minimal damage and interference to the system. The subsequent section will discuss the development of multiple phase transition strategies alongside the challenges and advantages each of them hold.
1.3.2 Indirect‐to‐Direct Bandgap Transition
In the natural state, TMD materials in their bulk and multilayer forms are indirect bandgap materials. Interestingly, as the sample thickness decreases gradually from a bulk system to one that is monolayer, not only does its bandgap increase in magnitude, but it also evolves into a direct bandgap semiconductor [38, 47, 51, 53, 54, 62, 63].
In the cases of TMD systems with constituent atoms from Group VI transition metals (Mo and W) and chalcogens such as S and Se, they are usually thermodynamically stable in the semiconducting 1H‐phase [64]. Both monolayer‐WSe2[65] and MoS2 [38, 51] were first computationally predicted to possess such direct bandgap electronic structures at the K/K′‐points of their hexagonal Brillouin zone. Figure 1.9 displays the calculated band structure of MoS2 as it reduces from a bulk and eventually into the monolayer structure where it shows the gradual transition from an indirect to a direct electronic bandgap [53, 54]. Besides, the computationally derived electronic bandgap for semiconducting phase MoS2 shows an increase in magnitude from 0.88 eV in its bulk form to 1.71 eV for monolayer‐MoS2[67]. The experimentally measured optical bandgap using photoluminescence measurements for monolayer‐MoS2 has been registered to be 2.16 eV where there is a distinct increase in the luminescence efficiency in the monolayer as compared to its bulk and multi‐layer forms [53, 54]. Nevertheless, the disparity between the experimentally measured and theoretical value in the monolayer direct bandgap can be attributed to the presence of actual charge interactions in the real monolayer system.
Figure 1.9 Thickness‐dependent bandgap properties of semiconducting phase MoS2 in its bulk, trilayer, bilayer, and monolayer form. With the arrows indicating the lowest energy transitions from the valence to the conduction band, one can see a gradual transition from an indirect (1.29 eV) to a direct bandgap (1.8 eV) with decreasing layer number. This accounts for the significant increase in photoluminescence efficiency of monolayer‐MoS2. Source: Reproduced with permission © 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim Bonaccorso et al. [66].
The gradual transition of TMD systems from an indirect bandgap material in its multi‐layer form to a direct bandgap system in its monolayer form can be attributed to the presence of interlayer hopping in their multilayer form. Figure 1.10 compares the band structures of WS2 of different layer numbers with and without the effects of spin‐orbit coupling (spin‐orbit coupling effects to be discussed in the next section), the band edges at the respective high symmetry points Kv, Γv and Qc (where subscripts C: conduction band; V: valence band) are shown to split with increasing layer number – these are direct evidence of interlayer hopping and the important role that Van der Waals interaction plays in such multilayer systems in dictating the system's electronic structures. The quantity of band splitting at each symmetry point also corresponds to the interlayer hopping strength. One should also note that contributions by the respective transition metal d‐ or chalcogen p‐orbitals also vary at different regions of the electronic band structure. They result in different splitting magnitudes at different points in momentum space.
Figure 1.10 Band structures of (a) quadrilayer, bilayer and monolayer MoS2 without the SOC effects, and (b) that with SOC in consideration. Source: (a) Reproduced with permission from Kuc et al. [62]. Copyright (2011) by the American Physical Society. (b) Reproduced with permission from Wickramaratne et al. [68]. AIP Publishing.
Notably, the Γv and Qc‐points display considerably more pronounced band splitting than Kv. This is because orbital contributions at the Kv‐point are attributed mainly to the metal d‐orbitals. Conversely, the chalcogen pz‐orbitals dominate the Γv and Qc‐points (c.f., Figure 1.7). With this in consideration, it is noted that interlayer charge hopping between the chalcogen pz‐orbitals plays a more significant role in comparison with other orbital interactions. Conversely, such interlayer hopping processes at the Kv‐point is comparatively much weaker due to the large spatial separation between the transition metal planes. With increasing layer number, the energy level of the Γv‐point registers a significant increase while that of Qc is reduced. Meanwhile, the positions of both the KC and Kv‐points remain largely unchanged in the Brillouin zone. These relative evolution of the energy bands with contributions from both the metal and chalcogen orbitals results in the transformation of band structure from one that comprises an indirect band gap in the multilayer form to a direct bandgap system in the monolayer form.
1.3.3 Spin‐Orbit Coupling and Its Effects and Optical Selection Rules
Readers who would like a very comprehensive treatment on this subject can also refer to the review [69]. Without the effects of interlayer van der Waals interaction, the effects of spin‐orbit coupling (SOC) will become very prominent on the electronic properties of 2D‐TMDs as compared to single‐layer graphene. This is attributed to the heavy elemental components in the TMD systems where the SOC strength is directly proportional to the fourth power of the atomic number, Z[70]. Specifically, effects of the transition metal component outweighs that of the chalcogen atoms, particularly with the d‐orbitals of the former [70]. For instance, there is a ∼0.4 eV band splitting at the K‐point in the valence band for W‐based (WSe2 displayed in Figure 1.11a,b) and ∼0.2 eV for Mo‐based 2D‐TMDs (MoS2 displayed in Figure 1.11c,d) as a result of SOC effects [50,71–75]. This spin‐split ultimately gives rise to the two valence sub‐bands which in turn result in the appearance of the notable excitons A and B due to the band transitions at the K/K′‐point.
Likewise, a significantly smaller spin‐orbit split is also present at the CBM due contributions from the p‐ and d‐orbitals [52,76–78]. The polarity of the conduction band spin split may also differ depending on the transition metal atomic component. This leads to the lifting of the spin degeneracy of both the conduction and valence bands at the K/K′‐point. Moreover, spin‐splitting at the conduction band results in an energy separation between the spin‐allowed and optically active (bright) transitions and the spin‐forbidden and optically inactive transitions (dark).
Figure 1.11 Band structure calculations of WSe2 and MoS2 monolayers with and without the effects of spin–orbit coupling. (a) Electronic band structure of monolayer‐WSe2 without, and (b) with the effects of spin–orbit coupling. (c) Electronic band structure of monolayer‐MoS2 without, and (d) with the effects of spin–orbit coupling. The valence band splits at the K(‐K)‐points are indicated by the red circles. Source: Tang et al. [71]/Reproduced with permission from American Chemical Society.
Contributions from the electron‐hole Coulomb exchange energy also affect the amplitude of the excitonic state splittings [79–81]. In the case of Mo‐based 2D‐TMDs, the lowest‐energy transition will be the bright exciton [76, 77] as experimentally confirmed [82, 83]. Conversely, dark excitons in W‐based 2D‐TMDs are located at lower energy positions than their bright counterparts [82,84–86].
With the spin‐splitting effects, chiral optical selection rules apply for interband transitions at the K/K′‐points. While the orbital Bloch functions at the conduction band transform with the angular momentum components of ±1, those at the valence band remain invariant. This renders the optical selection rules for the interband transitions at the K/K′ valley to be chiral. In other words, circularly polarized light of orientation σ± can only couple with interband transitions at the K± band, respectively [73,87–90]. This unique optical selection behavior of 2D‐TMDs makes them ideal for the investigation of valleytronic properties and applications [91–93].
While it is possible for the electrons to switch their valley, a spin‐flip or a very energetically unfavorable transition is required. Hence, optically‐generated electron‐hole pairs are generally spin‐valley polarized (locked). Hence, by conducting a spin‐polarized excitation, exciton emission of 2D‐TMDs can be co‐polarized with the laser if the valley polarization lifetime is of similar order or longer than the exciton recombination time.
1.4 Excitons (Coulomb‐Bound Electron‐Hole Pairs)
An exciton is a quasiparticle bound state formed by an excited electron and hole due to their Coulomb interaction [94]. With the onset of photoexcitation, an electron will be excited from the filled valence band into the empty conduction band, and it will leave a hole in the valence band. With the electron and the hole possessing opposite polarity, they can attract each other via Coulomb interaction and such a many‐body system involving a negatively charged conduction electron and a positively charged hole in the valence band can now be simplified. The formation of a bound state form between the electron‐hole pair corresponds to a neutral Exciton which possesses a strongly‐correlated relative spatial displacement between the constituents.
Based on the exciton radius and the Coulomb interactions within the electron‐hole pair, two main classes of excitons can arise as a result of long‐range and short‐range coupling. With the large dielectric function within the crystal lattice, electric field screening reduces the Coulomb interaction between the electron‐hole pairs. Hence, the exciton radii are significantly larger (long‐range) in the scale of interparticle distances than the interatomic bond lengths. These are generally known as the Wannier‐Mott or large‐radius‐type excitons commonly found in semiconducting systems such as GaAs [95] and Cu2O [96]. With the smaller masses and screened Coulomb interaction, the binding energies of Wannier excitons are generally in the order of ∼0.01 eV [97, 98].
Conversely, the short‐range counterpart arises due to the overlapping wave functions of the constituent electron‐hole pair at the scales in the order of the crystal lattice constant (e.g. a0 ∼ 3 Å for 2D‐TMDs) and typically within the range of up to a few unit cells. This class of excitons correspond to the charge‐transfer between nearest lattice sites. Besides, typically found in ionic crystals and organic molecular crystals, such electron‐hole bound states are known as Frenkel Excitons which have binding energies in the order of ∼0.1—1 eV [99–102].
Another important consideration regarding exciton formation due to Coulomb interaction is the self‐energy of the electron‐hole quasiparticle. This concept of self‐energy is related to the repulsion between identical charges which results in an overall increase in the exciton bandgap of the system. It is the energy required to break the interaction between the electron‐hole pair in the continuum similar to that of the Rydberg series of the hydrogen atom to create a free particle. Therefore, it is considered an excitonic Rydberg series (excited state of the electron‐hole pairs) where the excitonic properties can be experimentally derived with the schematic of the optical absorption in the ideal 2D semiconductor displayed in Figure 1.12.
The presence of many‐body interactions in the form of Coulomb interactions leads to the formation of the exciton resonances below the bandgap. Known as the optical bandgap, this energy gap is taken with reference to the lowest‐energy excitonic feature in absorption at the exciton ground state (n = 1). As seen in Figure 1.12, the optical bandgap is distinct from the so‐called free‐particle band gap – corresponding to the continuum of free electrons and holes (where n = ∞). As a result of varying dielectric environments of different 2D systems, it plays a crucial role in tuning both the exciton binding energy and the free‐particle bandgap of the system. Interestingly, this results in different systems possessing relatively similar optical bandgaps [103–105].
Figure 1.12 Schematic of the optical absorption of an ideal 2D semiconductor. It comprises a series of bright exciton transitions below the renormalized quasiparticle bandgap. Strong Coulomb interaction also enhances the continuum absorption in the energy range beyond the exciton binding energy, EB. The inset shows the hydrogen atom‐like energy level scheme of the exciton states, designated by the principal quantum number n, with EB of the exciton ground state (n = 1) below the free‐particle (FP) bandgap. Source: Wang et al. [69]/Reproduced with permission from American Physical Society.
1.4.1 Exciton Binding Energy
Apart from the dielectric properties of the material in consideration, another key factor dictating the exciton binding energy would be the material's dimensionality. The exciton binding energy can thus be expressed based on the equation [106]:
where α denotes the material dimensionality, n the principal quantum number, and E0 is the Rydberg constant.
As a result of this relation, the excitonic properties of 2D systems differ significantly from their 3D counterparts even of the same material. Strong electron‐hole interaction results in a significantly different optical spectrum as compared to the 3D counterpart with the formation of a series of new excitonic levels below the quasiparticle bandgap as seen in Figure 1.12. A distinct feature of excitons in 2D systems is that they are strongly confined within the in‐plane system where the electronic excitations are restricted within the 2D structure. Unlike excitons found in typical bulk three‐dimensional systems, the large spatial overlap between the electron‐hole orbitals can be attributed to the effects of quantum confinement. In addition, the electric field between the electron‐hole pair can penetrate the 2D‐plane where charge screening is absent. These features unique to 2D systems lead to the significant enhancement in the Coulomb attraction which in turn results in a larger excitonic binding energy as compared to the 3D counterpart (Figure 1.13a). For instance, while excitons in bulk WS2 have binding energy of ∼ 50 meV, excitons in monolayer‐WS2 have binding energies of ∼ 320 meV [107].
Figure 1.13 (a) Real‐space representation of excitons in three‐dimensional and two‐dimensional systems. The changes in the dielectric environment are schematically represented by the respective dielectric constants ε3D and ε2D and the permittivity of free space ε0. (b) The effects of dimensionality on the electronic and excitonic properties schematically represented by the optical absorption spectra. Change in dimensionality from 3D to 2D leads to an increase in the band gap and exciton binding energy represented by red dashed line. Source: Reproduced with permission Chernikov et al. [107]/Reproduced with permission from American Physical Society.
As a result of the dimensionality, 2D excitons have unique properties with a combination of both Wannier‐Mott and Frenkel features – they have both large Bohr radii and are strongly bound, respectively. In general, the exciton Bohr radii are in the order of ∼1 nm [108–110]. Based on quasiparticle GW band structure calculations, the effective Bohr radius for MoS2 is 9.3 and 13.0 Å in its monolayer and bilayer form, respectively, at the low‐dimension limit [72]. While these may not appear to a significant magnitude, they are sufficiently large relative to the in‐plane lattice constant of 2D‐TMDs in general (∼3 Å). Hence, the Wannier‐Mott exciton theory is still applicable in such 2D systems. Correspondingly, the effective exciton binding energies stood at 0.224 and 0.106 eV in its monolayer and bilayer form, respectively. Interestingly, an alternative study has even reported an exciton spread over 65 Å [111]. Further unique excitonic effects attributed to the two‐dimensional features come in the form of a step‐function for gapped systems with dipole‐allowed interband transitions (Figure 1.13b) [107].
Figure 1.14 Schematic representation of quasiparticles. (a) Neutral exciton, (b) positive trion, (c) negative trion, and (d) neutral biexciton.
1.4.2 Excitons and Other Complex Quasiparticles
With increasing exciton (Figure 1.14a) and other charged‐particle concentrations, complexes including the three‐particle charged excitons known trions (Figure 1.14b,c) [71, 112, 113], and four‐particle bi‐excitons (Figure 1.14d) can also be formed [114, 115]. In the case of bi‐excitons, their binding energies (∼52 meV for monolayer‐WSe2) is more than an order of magnitude greater than those in conventional quantum‐well systems [116]. This is attributed to the effects of both strong carrier confinement and reduced and non‐local dielectric screening [108, 117].
While excitons and biexcitons are of neutral polarity due to their two‐particle or four‐particle composition, charged excitons known as a trion have odd‐numbered (3) particles. Depending on its polarity, it can either comprise two holes and an electron (positive trion – Figure 1.14b) or two electrons and a hole (negative trion – Figure 1.14c) [112]. These charged quasiparticles are only formed in systems where excess charges are present and implies that the trion emission intensity serves to quantify the excess charge concentration.
While excitons in 2D‐TMDs have binding energies in the order of ∼102 meV, the binding energy of trions are usually an order of magnitude smaller but are still considerably larger than excitons in conventional semiconducting systems [116]. In many cases, both the exciton and trion peaks can be observed in photoluminescence experiments particularly at low temperatures. There are also instances where trions are observed in gated samples at an additional line 20–35 meV below the main exciton emission line and these can be attributed to the emission from charged excitons of both polarity [112, 118].
While exciton energy can vary as a result of varying Fermi energy induced by electronic gating process, the trion energy usually remained largely unchanged [112]. Besides, the energy split between the exciton and trion energy is expected to be linearly‐dependent on the Fermi energy [119]. Hence, the trion binding energy can be estimated via the differences between the respective trion position and the associated exciton peak position based on the following expression [71, 112]:
where EX and EX′ denote the peak positions of the exciton and the associated trion, respectively; Ebin
