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In-depth overview of two-dimensional semiconductors from theoretical studies, properties to emerging applications!
Two-dimensional (2D) materials have attracted enormous attention due to their exotic properties deriving from their ultrathin dimensions. 2D materials, such as graphene, transition metal dichalcogenides, transition metal oxides, black phosphorus and boron nitride, exhibit versatile optical, electronic, catalytic and mechanical properties, thus can be used in a wide range of applications, including electronics, optoelectronics and optical applications.
Two-Dimensional Semiconductors: Synthesis, Physical Properties and Applications provides an in-depth view of 2D semiconductors from theoretical studies, properties to applications, taking into account the current state of research and development. It introduces various preparation methods and describes in detail the physical properties of 2D semiconductors including 2D alloys and heterostructures. The covered applications include, but are not limited to, field-effect transistors, spintronics, solar cells, photodetectors, light-emitting diode, sensors and bioelectronics.
* Highly topical: 2D materials are a rapidly advancing field that attracts increasing attention
* Concise overview: covers theoretical studies, preparation methods, physical properties, potential applications, the challenges and opportunities
* Application oriented: focuses on 2D semiconductors that can be used in various applications such as field-effect transistors, solar cells, sensors and bioelectronics
* Highly relevant: newcomers as well as experienced researchers in the field of 2D materials will benefit from this book
Two-Dimensional Semiconductors: Synthesis, Physical Properties and Applications is written for materials scientists, semiconductor and solid state physicists, electrical engineers, and readers working in the semiconductor industry.
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Seitenzahl: 343
Veröffentlichungsjahr: 2020
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Table of Contents
Cover
Preface
About the Authors
Acknowledgments
1 Introduction
1.1 Background
1.2 Types of 2D Materials
1.3 Perspective of 2D Materials
References
2 Electronic Structure of 2D Semiconducting Atomic Crystals
2.1 Theoretical Methods for Study of 2D Semiconductors
2.2 Electronic Structure of 2D Semiconductors
2.3 Prediction of Novel Properties in 2D Moiré Heterostructures
References
3 Tuning the Electronic Properties of 2D Materials by Size Control, Strain Engineering, and Electric Field Modulation
3.1 Size Control
3.2 Strain Engineering
3.3 Electric Field Modulation
References
4 Transport Properties of Two-Dimensional Materials: Theoretical Studies
4.1 Symmetry-Dependent Spin Transport Properties of Graphene-like Nanoribbons
4.2 Charge Transport Properties of Two-Dimensional Materials
4.3 Contacts Between 2D Semiconductors and Metal Electrodes
References
5 Preparation and Properties of 2D Semiconductors
5.1 Preparation Methods
5.2 Characterizations of 2D Semiconductors
5.3 Electrochemical Properties of 2D Semiconductors
References
6 Properties of 2D Alloying and Doping
6.1 Introduction
6.2 Advantages of 2D Alloys
6.3 Preparation Methods for 2D Alloys
6.4 Characterizations of 2D Alloys
6.5 Doping of 2D Semiconductors
References
7 Properties of 2D Heterostructures
7.1 Conception and Categories of 2D Heterostructures
7.2 Advantages and Application of 2D Heterostructures
7.3 Preparation Methods for 2D Heterostructures
7.4 Characterizations of 2D Heterostructures
References
8 Application in (Opto) Electronics
8.1 Field-Effect Transistors
8.2 Infrared Photodetectors
8.3 2D Photodetectors with Sensitizers
8.4 New Infrared Photodetectors with Narrow Bandgap 2D Semiconductors
8.5 Future Outlook
References
9 Perspective and Outlook
Index
End User License Agreement
List of Tables
Chapter 2
Table 2.1 The bandgap and effective masses for graphyne.
Table 2.2 Calculated properties of MX
2
monolayers: lattice constant
a
, M—X bo...
Table 2.3 Layer distance
d
and adsorption energy
E
ad
per formula unit (each M...
Table 2.4 The parameters used when calculating the different
V
ppπ
and
V
p
...
List of Illustrations
Chapter 1
Figure 1.1 Graphene films. (a) Photograph (in normal white light) of a relativ...
Figure 1.2 (a) Room temperature quantum Hall effect in graphene.
σ
xy
(red...
Figure 1.3 Classification of 2D materials. (a) About 40 different layered TMDC...
Figure 1.4 Atomic structure of (a) 2D single materials, (b) 2D doped materials...
Figure 1.5 Wafer-scale growth and integrated circuit of 2D materials. (a) Thre...
Chapter 2
Figure 2.1 Illustration of the graphyne-
n
structures.
Figure 2.2 (a) Band structure of graphyne. Solid lines and open circles are GG...
Figure 2.3 (a) Top view of the atomic structure of a single-layer holey graphe...
Figure 2.4 (a) Structure of 1H-MX
2
. Yellow indicates X atoms and purple indica...
Figure 2.5 (a) Calculated band alignment for MX
2
monolayers. Solid lines are o...
Figure 2.6 Charge densities of VBM (a) and CBM (b) states for monolayer WX
2
–Mo...
Figure 2.7 (a) Moiré patterns A and B with 4.4% lattice mismatch corresponding...
Figure 2.8 (a) Band structures of the I
A
and III
A
bilayers. Blue and red denot...
Figure 2.9 Top view and side view of the spatial distribution of the VBM, VBM-...
Figure 2.10 Distribution of the energy of the V2 state based on the calculatio...
Figure 2.11 Illustration of the G/NHG heterostructures with AA, AB, and (7,3)–...
Figure 2.12 Band structure of the G/NHG heterostructures with (a) AA and (b) A...
Figure 2.13 (A) In the left panel (a), the solid lines indicate band structure...
Figure 2.14 (a) Band dispersion of (7,3)–(1,2) G/NHG and graphene near the Fer...
Chapter 3
Figure 3.1 Atomic structures of (a) zigzag and (b) armchair graphene nanoribbo...
Figure 3.2 Bandgaps of armchair graphene nanoribbons as a function of width ca...
Figure 3.3 (a) Schematic (1) and (4) indicates sp
2
hybridized C atoms, while (...
Figure 3.4 Top and side views of atomic structures of (a) zigzag and (b) armch...
Figure 3.5 Schematics of (a) z-PNR, (b) a-PNR, and (c) d-PNR. (d) Variation of...
Figure 3.6 Evolutions of the spectra of (a) 2D and (b) G bands of graphene und...
Figure 3.7 (a) Projected band structures of two carbon atoms with sp
2
(C1) and...
Figure 3.8 (A) Schematic of MoS
2
monolayer. Evolutions of (B) bandgap and stra...
Figure 3.9 (a) Band structures of armchair MoS
2
at three different bending cur...
Figure 3.10 Magnetic moment of (a) V atom and (b) X atom as a function of stra...
Figure 3.11 (a) Photoluminescence spectra of flat (black) and wrinkle (red) re...
Figure 3.12 (a) Out-of-plane dielectric constant of graphene of different laye...
Figure 3.13 (A) Atomic structure of bulk GaS. The rhombic shadow presents the ...
Figure 3.14 Dielectric constant of GaS multilayers as a function of the number...
Figure 3.15 Charge density distribution of the VBM and CBM of GaS under extern...
Chapter 4
Figure 4.1 (a, b) Band structures around the Fermi level for 7-ZGNR and 8-ZGNR...
Figure 4.2 Schematic band structures of the left lead and two-gate regions.
Figure 4.3 Geometric structures of (a) symmetric 4-ZαGNR and (b) asymmetric 5-...
Figure 4.4 (a) Band structure of 4-ZαGNR. (b) Γ-point wave functions of
π
Figure 4.5 (a) Band structure of FM 6-ZSiNR. The spin-up and spin-down compone...
Figure 4.6 Phonon (a) emission and (b) absorption scattering rates at
T
= 300 ...
Figure 4.7 Intrinsic resistivity as a function of temperature. At
T
< 200 K, t...
Figure 4.8 Phononic dispersion of monolayer WS
2
in the first Brillouin zone.
Figure 4.9 Intrinsic scattering rates of (a), (b) K-valley electrons, and (c, ...
Figure 4.10 (a) Electron and (b) hole drift velocity versus electric field in ...
Figure 4.11 (a) Effective mass of electrons and holes according to spatial dir...
Figure 4.12 A schematic of the metal/semiconductor interface according to inte...
Figure 4.13 Binding energy
E
b
as a function of the separation
d
between MoSe
2
...
Figure 4.14 (a) Projected band structures of single-layer MoSe
2
contacting wit...
Figure 4.15 Band structures of (a) perfect-MoSe
2
, (b) As
Se
–MoSe
2
, (c) Br
Se
–MoS...
Figure 4.16 Projected band structures of (a) perfect-MoSe
2
/Au, As
Se
–MoSe
2
/Au, ...
Chapter 5
Figure 5.1 (a) OM image and (b) AFM image of a typical monolayer MoS
2
. (c)...
Figure 5.2 (a) Substrate and prepared crystals on tapes. (b–e) Huang's modifie...
Figure 5.3 Schematic illustration of the
Desai's
Au assisted exfoliation p...
Figure 5.4 (a–d) Schematic demonstration of the gentle water freezing–thawing ...
Figure 5.5 (a–d) Schematic illustration of the electrochemical intercalation o...
Figure 5.6 (a, b) The schematic illustration of the synthesis process. (c) Opt...
Figure 5.7 (a) Schematic illustration of the two-step thermolysis process for ...
Figure 5.8 (a) The prepared large-area MoS
2
films. (b) SEM image of a typical ...
Figure 5.9 (a) Schematic illustration of the MOCVD growth setup. (b) Photograp...
Figure 5.10 Flow chart of the general growth process for the production of TMC...
Figure 5.11 (a) Schematic illustration of the MoS
2
CVD system. (b, c) Schemati...
Figure 5.12 Color OMs of the MoS
2
nanosheets from 1L to 15L on 90 nm SiO
2
/Si s...
Figure 5.13 (a) Micro-Raman spectra of monolayer and multilayer (1L to bulk) b...
Figure 5.14 (a–c) HAADF STEM-EDX mappings of an individual nanowire reveal uni...
Chapter 6
Figure 6.1 Schematic of tuning 2D TMD properties by constructing heterostructu...
Figure 6.2 (a) Optical bandgap vs. sulfur ratio in WS
2
x
Se
2−2
x
nanosheets...
Figure 6.3 (a) Transfer curves (
V
ds
= 2 V) of FETs based on monolayer MoSe
2
(b...
Figure 6.4 (a) Atomic configuration and total density of states of the H phase...
Figure 6.5 Optical absorption coefficients along the (a)
xy
-plane and (b)
z
-di...
Figure 6.6 (a) Schematic diagram of the growth process of the CVT method. The ...
Figure 6.7 (a) Schematic diagram of a three-zone tube furnace for growing a Mo...
Figure 6.8 (a) Schematic diagram of CVD synthesis of ReS
2
x
Se
2(1−
x
)
alloy...
Figure 6.9 (a–e) STEM-ADF images and EDS analysis of Mo
1−
x
W
x
S
2
single-la...
Figure 6.10 (a) Raman spectra of Mo
1−
x
W
x
S
2
monolayer alloys with differe...
Figure 6.11 (a) The PL spectrum of 2H-phase WSe
2(1−
x
)
Te
2
x
(
x
= 0–0.6) mo...
Figure 6.12 (a, b, d, e) Comparison of the electrical transport properties of ...
Chapter 7
Figure 7.1 (a) Vertical and lateral heterostructures of 2D materials. (b) ...
Figure 7.2 (a) Schematic diagram and electrical characteristics of MoS
2
/WSe
2
h...
Figure 7.3 (a) WS
2
/MoS
2
heterojunction optical microscopy and photoelectric pe...
Figure 7.4 (A, B) Schematic diagrams of the steps of wet transfer and dry tran...
Figure 7.5 (a, b) Pictures of heterojunction under an optical microscope,(...
Figure 7.6 (a, b) Growth process, optical image, and AFM image of growing vert...
Figure 7.7 (a–c) Schematic illustration of graphene–MoS
2
, WS
2
–MoS
2
, and h-BN–M...
Figure 7.8 (a) Type I, (b) type IIA and type IIB, and (c) type III.
Chapter 8
Figure 8.1 (a) Schematics of bP-based transistors. (b) Transfer curves of bP t...
Figure 8.2 Schematic representation of the photothermoelectric (a) and bolomet...
Figure 8.3 (a) Schematic diagram of graphene photodetectors with asymmetric in...
Figure 8.4 (a) Schematic of graphene CQD hybrid photodetectors, where graphene...
Figure 8.5 (a) Schematic diagram of MoS
2
and HgTe QDs hybrid-based phototransi...
Figure 8.6 (a) Schematic of bP-based photodetectors. The right panel is the li...
Figure 8.7 Optoelectronic memory devices based on monolayer MoS
2
. (a) Schemati...
Figure 8.8 Persistent photoconductivity in graphene/MoS
2
heterostructure. (a) ...
Figure 8.9 Two-terminal multibit optical memory in van der Waals heterostructu...
Figure 8.10 Nonvolatile infrared memory in PbS/MoS
2
heterostructure. (a) Devic...
Guide
Cover
Table of Contents
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Two-Dimensional Semiconductors
Synthesis, Physical Properties and Applications
Jingbo Li
Zhongming Wei
Jun Kang
Authors
Prof. Jingbo Li
South China Normal University
Institute of Semiconductors
No.55, West of Zhongshan Avenue
510631 Guangzhou
China
Prof. Zhongming Wei
Institute of Semiconductors, CAS
State Key Laboratory of Superlattices and Microstructures
No.A35, QingHua East Road
Haidian District
100083 Beijing
China
Prof. Jun Kang
Beijing Computational Science Research Center
Materials and Energy Division
Building 9, No.10 Xibeiwang East Road
Haidian District
100193 Beijing
China
Cover
Cover Image: © Rost9/Shutterstock
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The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at <http://dnb.d-nb.de>.
© 2020 Wiley-VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany
All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.
Print ISBN: 978-3-527-34496-3
ePDF ISBN: 978-3-527-81593-7
ePub ISBN: 978-3-527-81595-1
oBook ISBN: 978-3-527-81596-8
This book is dedicated to Prof. Jian-Bai Xia for his 80th birthday.
Preface
Ultrathin two-dimensional (2D) materials, such as graphene and MoS2, have attracted broad interest because of their exotic condensed-matter phenomena that are absent in bulk counterparts. Graphene, which is composed of a single layer of carbon atoms arranged in honeycomb lattice, has a linear dispersion near the K point, and charge carriers can be described as massless Dirac fermions, providing abundant physical picture. In contrast, 2D transition metal dichalcogenides (TMDs), transition metal oxides, black phosphorus, and boron nitride (BN) exhibit versatile optical, electronic, catalytic, and mechanical properties. It was reported that the 2D materials, especially 2D semiconductors with the intrinsic nanometer-scale size, can help to extend Moore's law, which face the challenge of further scaling down the transistor channel.
In this book, we discuss the theoretical study, synthetic method, the unique properties, the potential application, the challenges, and opportunities of the 2D semiconductors. Firstly, a general introduction of 2D materials was given. Then, the theoretical study including electronic structures and predications, the reparation, properties and applications in (opto) electronics or other devices of 2D materials/semiconductors and their alloys, and heterostructures were discussed in detail. At last, a perspective and outlook of this fast developing field is summarized.
I became a PhD student under the supervision of Prof. Jian-Bai Xia from 1998 to 2001. He gave plenty of guidelines to my study, research, and my life. We acknowledge him by dedicating this book on his 80th birthday this year. In addition, we convey our best wishes to him and his family and also to his fruitful research and healthy and happy life.
We sincerely hope this book can help researchers to understand 2D materials.
Jingbo Li
Beijing
10 December 2019
About the Authors
Jingbo Li received his PhD degree from the Institute of Semiconductors, Chinese Academy of Sciences, in 2001 under the supervision of Prof. Jian-Bai Xia. Then, he spent six years at the Lawrence Berkeley National Laboratory and National Renewable Energy Laboratory in USA. From 2007 to 2019, he worked as a professor at the Institute of Semiconductors, Chinese Academy of Sciences. Since 2019, he became a full-time professor and the dean of Institute of Semiconductors, South China Normal University. His research interests include the design, fabrication, and application of novel nanostructured semiconductors. He has published more than 290 scientific publications with more than 15000 citations.
Zhongming Wei received his BS degree from Wuhan University (China) in 2005 and PhD degree from the Institute of Chemistry, Chinese Academy of Sciences, in 2010 under the supervision of Prof. Daoben Zhu and Prof. Wei Xu. From August 2010 to January 2015, he worked as a postdoctoral fellow and then as an Assistant Professor in Prof. Thomas Bjørnholm's group at the University of Copenhagen, Denmark. Currently, he is working as a professor at the Institute of Semiconductors, Chinese Academy of Sciences. His research interests include low-dimensional semiconductors and their (opto)electronic devices.
Jun Kang received his PhD degree from the Institute of Semiconductors, Chinese Academy of Sciences, in 2014. After that, he performed his postdoctoral research at the University of Antwerp in Belgium and Lawrence Berkeley National Laboratory in USA. In 2019, he joined Beijing Computational Science Research Center as an assistant professor. His research field is first-principles calculations on novel electronic properties of low-dimensional semiconductors. He has published over 60 peer-reviewed articles with more than 4000 citations.
Acknowledgments
Finally, I would like to thank all my group members who spent a lot time for the writing and revising of this book: Dr. Bo Li, Dr. Mianzeng Zhong, Dr. Yan Li, Dr. Le Huang, Dr. Nengjie Huo, Dr. Xiaoting Wang, Ziqi Zhou, Jingzhi Fang, Kai Zhao, Yu Cui, and Longfei Pan. Without their hard work and contribution, we would not be able to finish this book on time. Thanks to Project Editor Ms. Shirly Samuel at Wiley-VCH for all her help in the publication of this book.
1Introduction
1.1 Background
In 2004, Ander Geim and Konstantin Novoselov from the University of Manchester, UK, first obtained graphene sheets by mechanical exfoliation method, successfully fabricated the first graphene field effect transistor (FET), and investigated its unique physical properties [1]. Before the discovery of graphene, according to the thermodynamic fluctuation law, the two-dimensional (2D) atomic thick layer under nonabsolute zero degrees is unlikely to exist stably [2]. Why is graphene stable at temperatures above absolute zero? Further theoretical studies have shown that this is because large-scale graphene is not distributed in a perfect 2D plane but in a wave-like shape. The experimental results support this view [3, 4]. Therefore, the discovery of graphene shocked the condensed matter physics community and also quickly ignited the enthusiasm of scientists to study 2D materials (a crystalline material composed of a single atomic layer or few atomic layers), indicating the arrival of the “two-dimensional material era.”
In 2010, Ander Geim and Konstantin Novoselov were awarded the Nobel Prize in Physics for their outstanding contribution to graphene (Figure 1.1) [1]. Graphene is a 2D material composed of carbon atoms and having a hexagonal lattice structure. Graphene has good toughness and its Young's modulus can theoretically reach as 1 TPa [5]. Therefore, graphene can form different structures through different curved stacks, such as zero-dimensional fullerenes, one-dimensional carbon nanotubes, and three-dimensional stacked graphite [6].
Graphene has shown many excellent physical properties resulting from the unique structure, and the disappearance of interlayer coupling makes the two carbon atoms in the cell completely equivalent, thus making the effective mass of electrons on the Fermi surface zero [7–11]. Because graphene has a unique Dirac band structure, carriers can completely tunnel in graphene, and electrons and holes in graphene have a very long free path. Therefore, the electronic transport of graphene is hardly affected by phonon collisions and temperature [8]. The mobility of electrons in monolayer graphene is much larger than that in its parent graphite (Figure 1.2c) [16]. In addition, graphene has shown good thermal conductivity (Figure 1.2d) [17], room temperature quantum Hall effect (Figure 1.2a) [12, 14], single-molecule detection (Figure 1.2b), and high light transmission [18]. Graphene is a semimetal material without band gap, it cannot form a good switching ratio in terms of regulation, thus greatly limiting the application of graphene in electronic devices. Although on the bilayer and multilayer graphene, the graphene can obtain a certain band gap by applying an electric field and stress [19]. However, this band gap is not only small but also has a low electrical on/off ratio and is difficult to apply to a controllable device. With the extensive research on two-dimensional materials, it is found that the disadvantages of graphene are compensated for in other families of 2D materials [20–26].
Figure 1.1 Graphene films. (a) Photograph (in normal white light) of a relatively large multilayer graphene flake with thickness ∼3 nm on top of an oxidized Si wafer. (b) Atomic force microscope (AFM) image of 2 μm by 2 μm area of this flake near its edge. Colors: dark brown, SiO2 surface; orange, 3 nm height above the SiO2 surface. (c) AFM image of single-layer graphene. Colors: dark brown, SiO2 surface; brown-red (central area), 0.8 nm height; yellow-brown (bottom left), 1.2 nm; orange (top left), 2.5 nm. Notice the folded part of the film near the bottom, which exhibits a differential height of ∼0.4 nm. (d) SEM micrograph of an experimental device prepared from few-layer graphene, and (e) its schematic view.
Source: Reproduced with permission from Novoselov et al. [1]. Copyright 2004, The American Association for the Advancement of Science.
Figure 1.2 (a) Room temperature quantum Hall effect in graphene. σxy (red) and ρxx (blue) as a function of gate voltages (Vg) in a magnetic field of 29 T. The need for high B is attributed to broadened Landau levels caused by disorder, which reduces the activation energy.
Source: Reproduced with permission from Novoselov et al. [12]. Copyright 2007, The American Association for the Advancement of Science.
(b) Single-molecule detection in graphene. Examples of changes in Hall resistivity observed near the neutrality point (|n| < 1011 cm−2) during adsorption of strongly diluted NO2 (blue curve) and its desorption in vacuum at 50 °C (red curve). The green curve is a reference – the same device thoroughly annealed and then exposed to pure He. The curves are for a three-layer device in B = 10 T. The adsorbed molecules change the local carrier concentration in graphene one by one electron, which leads to step-like changes in resistance. The achieved sensitivity is due to the fact that graphene is an exceptionally low-noise material electronically.
Source: Reproduced with permission from Schedin et al. [13]. Copyright 2007, Nature Publishing Group.
(c) Mobility of graphene. Maximum values of resistivity ρ = 1/σ (circles) exhibited by devices with different mobilities μ (left y axis). The histogram (orange background) shows the number P of devices exhibiting ρmax within 10% intervals around the average value of ∼h/4e2. Several of the devices shown were made from two or three layers of graphene, indicating that the quantized minimum conductivity is a robust effect and does not require “ideal” graphene.
Source: Reproduced with permission from Novoselov et al. [14]. Copyright 2005, Nature Publishing Group.
(d) Schematic of the experiment showing the excitation laser light focused on a graphene layer suspended across a trench. The focused laser light creates a local hot spot and generates a heat wave inside single-layer graphene propagating toward heat sinks.
Source: Reproduced with permission from Balandin et al. [15]. Copyright 2008, American Chemical Society.
1.2 Types of 2D Materials
The rapid pace of progress in graphene and the methodology developed in synthesizing ultrathin layers have led to exploration of other 2D materials, such as monolayer of group IVA elements (silicon, germanium, and tin) [27, 28] and their adjacent group elements (such as boron and phosphorus) monolayers; 2D layered metal oxides or metal hydroxides (octahedral or orthogonal tetrahedral structure in the layer) [29]; transition metal dichalcogenides (TMDCs) [21]; and graphene analogs such as boron nitride (BN) [30]. These 2D materials ranging from insulators (e.g. BN), semiconductors (e.g. TMDCs, tellurene, PtSe2, and BP) to semimetals (e.g. MoTe2), topological insulators (e.g. Bi2Se3), superconductors (NbSe2), and metals (1T-VS2) exhibit diverse property.
There are many 2D materials, and some literature studies have classified the 2D materials based on their positions in periodic table of elements (Figure 1.3a) [22], stoichiometric ratios [31], space groups, and structural similarities [32]. The advantage of classifying 2D materials by periodic table of elements is that 2D materials with the same group of elements often have similar properties, which has a good guiding significance for finding novel 2D materials. In 2017, Michael Ashton et al. have found that 826 2D materials can be grouped according to their stoichiometric ratios and 50% of the layered materials are represented by just five stoichiometries (Figure 1.3b) [31]. The advantage of classifying two-dimensional materials by stoichiometric ratios is to distinguish 2D materials with different stoichiometric ratios but the same elements. At the same time, when synthesizing 2D materials, the vapor pressure of growth can be adjusted according to the stoichiometric ratios, which is conductive to synthetic materials. Recently, Nicolas Mounet et al. developed a system based on high-throughput computational exfoliation of 2D materials (Figure 1.3c) [32]. They searched for materials with layered structure from more than 100 000 kinds of three-dimensional compounds in the existing database, and the 1036 kinds of easily exfoliable cases provide novel structural prototypes and simple ternary compounds by high-throughput calculations. They classify the 2D materials of the easily exfoliated group into different prototypes, according to their space groups and their structural similarities. The structure of 2D materials can be useful to search for more suitable substrates. 2D materials with a similar structure can often form stable 2D alloys. In this book, we will focus on the electronic structure, synthesis, and applications of 2D materials. We will classify 2D materials into three types based on the synthesis, structure, and application: 2D single, doped components, and van der Waals heterostructures.
2D single materials, such as graphene and MoS2, generally refer to materials that can be exfoliated from corresponding van der Waal layered three-dimensional materials. 2D doped materials include adsorption, intercalation, substitution doping, and so on. In this book, we focus on the substitution doping: transition metal element or chalcogen element is substituted by other element, such as MoS2(1−x)Se2x [33] and Fe-doped SnS2 [34]. 2D heterostructures contain vertical and lateral types (Figure 1.4).
Figure 1.3 Classification of 2D materials. (a) About 40 different layered TMDCs compounds exist. The transition metals and the three chalcogen elements that predominantly crystallize in those layered structure are highlighted in the periodic table.
Source: Reproduced with permission from Chhowalla et al. [22]. Copyright 2013, Nature Publishing Group.
(b) Distribution of stoichiometries of the 826 layered compounds.
Source: Reproduced with permission from Ashton et al. [31]. Copyright 2017, American Physical Society.
(c) Polar histogram showing the number of structures belonging to the 10 most common 2D structural prototypes in the set of 1036 easily exfoliable 2D materials. A graphical representation of each prototype is shown, together with the structure-type formula and the space group of the 2D systems. The room temperature values of the thermal conductivity in the range ∼(4.84 ± 0.44) × 103 to (5.30 ± 0.48) × 103 W/mK were extracted for a single-layer graphene from the dependence of the Raman G peak frequency on the excitation laser power and independently measured G peak temperature coefficient.
Source: Reproduced with permission from Mounet et al. [32]. Copyright 2018, Springer Nature.
Figure 1.4
Atomic structure of (a) 2D single materials, (b) 2D doped materials, and (c) 2D heterostructures. Red and blue balls stand for transition metal element (M), yellow and green balls represent chalcogen element (X).
1.3 Perspective of 2D Materials
2D materials have been attracting wide interest because of their peculiar structural properties and fascinating applications in the areas of electronics, optics, magnetism, biology, and catalysis. Overall, the current research on 2D materials is mainly in two aspects: (i) Wafer-scale growth of 2D materials and their industrial applications. (ii) Synthesis of novel 2D materials and study their physicochemical properties.
The ability to grow large, high-quality single crystals for 2D components is essential for the industrial application of 2D devices. Until now, some 2D materials, such as MoS2 (Figure 1.5a), WS2 (Figure 1.5b), InSe (Figure 1.5c), and BN (Figure 1.5d), have been synthesized as wafer scale by vapor-phase deposition or pulsed laser deposition method. Thus, developing a simple and low-cost method to synthesize wafer-scale 2D materials is a current research focus. On the other hand, taking advantage of unique characteristics of 2D materials, direct integration based on 2D heterostructures is an ingenious method (Figure 1.5e) [39].
Although some 2D materials have been synthesized and investigated now, there are more than 1000 2D materials in theory and many of them still have a lot to discover, which are suggested to have peculiar property and need further study. The efforts on exploiting the application of 2D materials in optoelectronic and electronic area, such as FET and photodetector, have been intensified in recent years. Multifunctional thermoelectric, superconducting, and magnetic devices need further investigation. For example, thermoelectric applications of 2D p–n junctions have not been thoroughly investigated yet. Giant magnetoresistance effect has been realized in CrI3, while spin–orbit torque switching, spin Hall effect in antiferromagnets, and memory transistor based on 2D materials are rarely reported.
Figure 1.5 Wafer-scale growth and integrated circuit of 2D materials. (a) Three wafer-scale MoS2 films transferred and stacked on a 4 in. SiO2/Si wafer.
Source: Reproduced with permission from Yu et al. [35]. Copyright 2017, American Chemical Society.
(b) Raman spectra of WS2 at different positions marked in the wafer-scale monolayer image.
Source: Reproduced with permission from Chen et al. [36]. Copyright 2019, American Chemical Society.
(c) Photograph of 1 × 1 cm SiO2/Si covered with InSe film.
Source: Reproduced with permission from Yang et al. [37]. Copyright 2017, American Chemical Society.
(d) Schematic diagrams highlighting the unidirectional growth of h-BN domains and the anisotropic growth speed on a Cu surface with steps. This method obtained 100-cm2 single-crystal hexagonal boron nitride monolayer on copper.
Source: Reproduced with permission from Wang et al. [38]. Copyright 2019, Springer Nature.
(e) Illustration of a chemically synthesized inverter based on MoTe2.
Source: Reproduced with permission from Zhang et al. [39]. Copyright 2019, Springer Nature.
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2Electronic Structure of 2D Semiconducting Atomic Crystals
With recent developments in theoretical and numerical methods, as well as the growing power of supercomputers, theoretical modeling has become a more and more important tool in the research of 2D semiconductors. On the one hand, theoretical modeling can help people to understand the experimental results in a more systematic and fundamental way, thus giving insight into processes that are hidden behind the experiment. On the other hand, it can also be employed to predict new properties or design new materials, thus providing guidance to experiment and accelerate material development. For example, based on theoretical calculations, type-II band alignment between 2D semiconductors is proposed [1], and such a model is widely used to understand the optoelectronic properties in 2D heterostructures. Localized band edge states are predicted in 2D heterostructures from computation first [2] and later observed in experiments [3]. In the following three chapters, we will discuss topics related to theoretical modeling of 2D semiconductors. In this chapter, we will focus on the fundamental electronic structures of several typical 2D semiconductors and their heterostructures. In Chapter 3, we will focus on band structure modulations of 2D semiconductors. In Chapter 4, we will focus on quantum transport properties of 2D semiconductors.
2.1 Theoretical Methods for Study of 2D Semiconductors
Before discussing the detailed electronic properties of 2D semiconductors, here, we briefly introduce several methods that are commonly used in theoretical modeling.
2.1.1 Density Functional Theory
Density functional theory (DFT) reveals that the electron density of a many-electron system can solely determine the properties of this system, and the total energy is minimized by the correct ground-state electron density [4]. In DFT, the many-body problem is transformed into a single-particle Kohn–Sham equation, by attributing all the contributions of many-body effects to the exchange–correlation energy term Exc [5]. DFT is exact in principle, but the actual form of Exc is unknown; hence, approximate functionals for Exc are usually used. It is assumed by the local density approximation (LDA) that the Exc functional depends only on the value of local electronic density [5, 6]. The generalized gradient approximation (GGA) takes both the electron density and its gradient into account [7]. LDA and GGA are employed extensively to investigate the structural, mechanical, electronic, and magnetic properties of materials. Usually, they give acceptable results. However, one of the major problems of LDA and GGA is that both of them severely underestimate the bandgap resulted from the missing of derivative discontinuity of total energy at integer particle numbers. The hybrid functionals such as HSE [8] improve the total energy estimation by mixing nonlocal Hartree–Fock exchange with LDA or GGA energy. They usually give much better bandgaps than LDA or GGA does, but computational cost is significantly larger.
2.1.2 Linear Scaling Three-Dimensional Fragment (LS3DF) Method
The computational scaling of direct DFT calculations is O(N3), where N is the number of atoms in the supercell. Thus, its application to systems with over 1000 atoms is limited because of huge computational cost, and linear scaling O(N) electronic structure algorithms are in high demand. The linear scaling three-dimensional fragment (LS3DF) method [9] is one of such O(N) methods. It divides the system into fragments and then calculates each fragment and patches them into the original system with novel boundary cancellation techniques. The Coulomb potential, based on the global charge density, is solved on the whole system, and it thus includes all the self-consistent effects. It yields almost the same results as do direct DFT calculations and allows simulations of systems with over 10 000 atoms at a moderate computational cost.
2.1.3 GW Approximation
To date, the most suitable approach to study electronic quasiparticle excitations is the many-body perturbation theory based on the one-body Green's function [10]. In this approach, the energy-dependent and nonlocal self-energy term Σxc includes all nonclassical many-body effects. The GW method approximates the Σxc using its first-order expansion with respect to the dynamically screened Coulomb interaction W and the Green's function G [10, 11]. W and G are often calculated on the basis of the eigen states of a reference single-particle Hamiltonian, and the quasiparticle energies are calculated as a first-order correction to the single-particle eigen energies. So far, the GW method has been successfully applied to the calculation of quasiparticle band structure properties for a wide class of materials. However, it also suffers from convergence issues and unfavorable scaling of the computational cost regarding the system size.
2.1.4 Semiempirical Tight-Binding Method
Tight-binding (TB) method is primarily used for band structure calculation of a material. It uses atomic orbitals as a basis to expand the single-electron wave functions of the system. The Hamiltonian matrix elements between these atomic orbitals are treated as adjustable parameters [12] and fitted to the results of experiments or first-principles calculations, and the eigen values and eigen states are then calculated by diagonalizing the Hamiltonian matrix. Despite its simplicity, tight-binding model can give good qualitative results with much low computational cost compared to DFT calculations. A major problem of the tight-binding method is that the fitted parameters are highly system dependent; thus, the transferability is poor.
2.1.5 Nonequilibrium Green's Function Method
The nonequilibrium Green's function (NEGF) formalism is a popular method to calculate the electron or phonon transport properties of extended systems [13, 14]. In this approach, the simulated system is constructed by three parts. Two semi-infinite leads serve as the electron or heat baths, and they are connected by a central conductor region. The transmission of electron or phonon is calculated based on the Green's function for the center region, and the self-energy of the leads which describes the lead–center interaction. The main advantage of NEGF is that the quantum mechanical effects such as tunneling and diffraction are preserved, which allows a highly accurate description of nanoscale devices. However, for large devices, the NEGF method can be computationally expensive.
2.2 Electronic Structure of 2D Semiconductors
There are various types of 2D semiconductors. One class of the representatives is graphene derivative. Examples of graphene derivatives include the graphyne family members (GFM, such as graphyne and graphdiyne) and nitrogenated holey graphene (NHG) C2
