Layer‐Number Dependent Optical Properties of 2D Materials and Their Application for Thickness Determination

The quantum confinement in atomic scale and the presence of interlayer coupling in multilayer make the electronic and optical properties of 2D materials (2DMs) be dependent on the layer number (N) from monolayer to multilayer. Optical properties of 2DMs have been widely probed by several optical techniques, such as optical contrast, Rayleigh scattering, Raman spectroscopy, optical absorption, photoluminescence, and second harmonic generation. Here, it is reviewed how optical properties of several typical 2DMs (e.g., monolayer and multilayer graphenes, transition metal dichalcogenides) probed by these optical techniques significantly depend on N. Further, it has been demonstrated how these optical techniques service as fast and nondestructive approaches for N counting or thickness determination of these typical 2DM flakes. The corresponding approaches can be extended to the whole 2DM family produced by micromechanical exfoliations, chemical-vapor-deposition growth, or transfer processes on various substrates, which bridges the gap between the characterization and international standardization for thickness determination of 2DM flakes.

[1]  Q. Gibson,et al.  Large, non-saturating magnetoresistance in WTe2 , 2014, Nature.

[2]  Jun Zhang,et al.  Interlayer breathing and shear modes in few-trilayer MoS2 and WSe2. , 2013, Nano letters.

[3]  S. Pantelides,et al.  Rapid and Nondestructive Identification of Polytypism and Stacking Sequences in Few‐Layer Molybdenum Diselenide by Raman Spectroscopy , 2015, Advanced materials.

[4]  Ting Yu,et al.  Raman characterization of ABA- and ABC-stacked trilayer graphene. , 2011, ACS nano.

[5]  Martina Hausner,et al.  Simple Approach for High-Contrast Optical Imaging and Characterization of Graphene-Based Sheets , 2007, 0706.0029.

[6]  K. Mak,et al.  Observation of intense second harmonic generation from MoS 2 atomic crystals , 2013, 1304.4289.

[7]  Wei Zhou,et al.  Raman vibrational spectra of bulk to monolayer ReS2 with lower symmetry , 2015, 1502.02835.

[8]  Xiaoli Li,et al.  Optical contrast determination of the thickness of SiO2 film on Si substrate partially covered by two-dimensional crystal flakes , 2015 .

[9]  A. Ramasubramaniam Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides , 2012 .

[10]  B. Sumpter,et al.  Low-Frequency Raman Fingerprints of Two-Dimensional Metal Dichalcogenide Layer Stacking Configurations. , 2015, ACS nano.

[11]  Anomalous frequency trends in MoS 2 thin films attributed to surface effects , 2013, 1308.6393.

[12]  Hua Zhang,et al.  Rapid and reliable thickness identification of two-dimensional nanosheets using optical microscopy. , 2013, ACS nano.

[13]  F. Xia,et al.  Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics. , 2014, Nature communications.

[14]  J. Hone,et al.  Linearly Polarized Excitons in Single- and Few-Layer ReS2 Crystals , 2016 .

[15]  Joerg Appenzeller,et al.  Screening and interlayer coupling in multilayer graphene field-effect transistors. , 2009, Nano letters.

[16]  D. Late,et al.  Rapid Characterization of Ultrathin Layers of Chalcogenides on SiO2/Si Substrates , 2012 .

[17]  A. Geim,et al.  Two-dimensional gas of massless Dirac fermions in graphene , 2005, Nature.

[18]  T. Pedersen,et al.  Observation of excitonic resonances in the second harmonic spectrum of MoS2 , 2015, 1506.08653.

[19]  Eli Yablonovitch,et al.  Strong interlayer coupling in van der Waals heterostructures built from single-layer chalcogenides , 2014, Proceedings of the National Academy of Sciences.

[20]  S. Louie,et al.  Optical spectrum of MoS2: many-body effects and diversity of exciton states. , 2013, Physical review letters.

[21]  Wang Yao,et al.  Optical signature of symmetry variations and spin-valley coupling in atomically thin tungsten dichalcogenides , 2012, Scientific Reports.

[22]  T. Wieting,et al.  Infrared and Raman Studies of Long-Wavelength Optical Phonons in Hexagonal Mo S 2 , 1971 .

[23]  A. Neto,et al.  Two-dimensional crystals-based heterostructures: materials with tailored properties , 2012 .

[24]  Hugen Yan,et al.  Anomalous lattice vibrations of single- and few-layer MoS2. , 2010, ACS nano.

[25]  Peng Yu,et al.  Extraordinarily Strong Interlayer Interaction in 2D Layered PtS2 , 2016, Advanced materials.

[26]  Andre K. Geim,et al.  Raman spectrum of graphene and graphene layers. , 2006, Physical review letters.

[27]  Yihong Wu,et al.  Interference enhancement of Raman signal of graphene , 2008, 0801.4595.

[28]  Dominique Baillargeat,et al.  From Bulk to Monolayer MoS2: Evolution of Raman Scattering , 2012 .

[29]  D. Ohlberg,et al.  Monolayer Molybdenum Disulfide Nanoribbons with High Optical Anisotropy , 2015, 1512.08338.

[30]  X. Qiao,et al.  Ultralow-frequency Raman system down to 10 cm(-1) with longpass edge filters and its application to the interface coupling in t(2+2)LGs. , 2016, The Review of scientific instruments.

[31]  Hongzheng Chen,et al.  Graphene-like two-dimensional materials. , 2013, Chemical reviews.

[32]  Andre K. Geim,et al.  Electric Field Effect in Atomically Thin Carbon Films , 2004, Science.

[33]  A. Ferrari,et al.  Intercalation of few-layer graphite flakes with FeCl3: Raman determination of Fermi level, layer by layer decoupling, and stability. , 2011, Journal of the American Chemical Society.

[34]  SUPARNA DUTTASINHA,et al.  Van der Waals heterostructures , 2013, Nature.

[35]  A. Krasheninnikov,et al.  Effects of confinement and environment on the electronic structure and exciton binding energy of MoS2 from first principles , 2012 .

[36]  M. Dresselhaus,et al.  Low-Frequency Interlayer Breathing Modes in Few-Layer Black Phosphorus. , 2015, Nano letters.

[37]  Yilei Li,et al.  Probing symmetry properties of few-layer MoS2 and h-BN by optical second-harmonic generation. , 2013, Nano letters.

[38]  T. Ren,et al.  Fabrication techniques and applications of flexible graphene-based electronic devices , 2016 .

[39]  J. Coleman,et al.  Two-Dimensional Nanosheets Produced by Liquid Exfoliation of Layered Materials , 2011, Science.

[40]  K. Novoselov,et al.  Rayleigh imaging of graphene and graphene layers. , 2007, Nano letters.

[41]  Soon Cheol Hong,et al.  High‐Detectivity Multilayer MoS2 Phototransistors with Spectral Response from Ultraviolet to Infrared , 2012, Advanced materials.

[42]  Andrea C. Ferrari,et al.  Resonant Raman spectroscopy of twisted multilayer graphene , 2014, Nature Communications.

[43]  Wei Shi,et al.  Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material. , 2015, Chemical Society reviews.

[44]  H. Peng,et al.  Raman spectroscopic characterization of stacking configuration and interlayer coupling of twisted multilayer graphene grown by chemical vapor deposition , 2016, 1609.00923.

[45]  F. Xia,et al.  Van der Waals heterostructures: Stacked 2D materials shed light. , 2015, Nature materials.

[46]  A Gholinia,et al.  Light-emitting diodes by band-structure engineering in van der Waals heterostructures. , 2014, Nature materials.

[47]  Louis E Brus,et al.  Imaging stacking order in few-layer graphene. , 2011, Nano letters.

[48]  Xia Congxin,et al.  Recent advances in optoelectronic properties and applications of two-dimensional metal chalcogenides , 2016 .

[49]  A. Splendiani,et al.  Emerging photoluminescence in monolayer MoS2. , 2010, Nano letters.

[50]  R. Piner,et al.  Transfer of large-area graphene films for high-performance transparent conductive electrodes. , 2009, Nano letters.

[51]  L. Wirtz,et al.  Phonons in single-layer and few-layer MoS2 , 2011 .

[52]  F. Xia,et al.  Interlayer interactions in anisotropic atomically thin rhenium diselenide , 2015, Nano Research.

[53]  Y. Wang,et al.  The shear mode of multilayer graphene. , 2011, Nature materials.

[54]  S. Novak,et al.  SiO2 thickness determination by x-ray photoelectron spectroscopy, Auger electron spectroscopy, secondary ion mass spectrometry, Rutherford backscattering, transmission electron microscopy, and ellipsometry , 2000 .

[55]  Zongfu Yu,et al.  Extraordinary photoluminescence and strong temperature/angle-dependent Raman responses in few-layer phosphorene. , 2014, ACS nano.

[56]  D. Basko,et al.  Raman spectroscopy as a versatile tool for studying the properties of graphene. , 2013, Nature nanotechnology.

[57]  Tao Chen,et al.  Determining layer number of two-dimensional flakes of transition-metal dichalcogenides by the Raman intensity from substrates , 2016, Nanotechnology.

[58]  Hua Xu,et al.  Optical Anisotropy of Black Phosphorus in the Visible Regime. , 2016, Journal of the American Chemical Society.

[59]  Kinam Kim,et al.  High-mobility and low-power thin-film transistors based on multilayer MoS2 crystals , 2012, Nature Communications.

[60]  Wei Zhou,et al.  Integrated digital inverters based on two-dimensional anisotropic ReS2 field-effect transistors , 2015, Nature Communications.

[61]  Alexey Chernikov,et al.  Measurement of the optical dielectric function of monolayer transition-metal dichalcogenides: MoS 2 , Mo S e 2 , WS 2 , and WS e 2 , 2014 .

[62]  Kai Xu,et al.  Ultrasensitive Phototransistors Based on Few‐Layered HfS2 , 2015, Advanced materials.

[63]  Aaron M. Jones,et al.  Highly anisotropic and robust excitons in monolayer black phosphorus. , 2014, Nature nanotechnology.

[64]  M. Dresselhaus,et al.  Raman spectroscopy in graphene , 2009 .

[65]  W. Cao,et al.  Ultrahigh photo-responsivity and detectivity in multilayer InSe nanosheets phototransistors with broadband response† , 2015 .

[66]  L. Wirtz,et al.  Unified Description of the Optical Phonon Modes in N-Layer MoTe2. , 2015, Nano letters.

[67]  Xiaodong Cui,et al.  Exciton Binding Energy of Monolayer WS2 , 2014, Scientific Reports.

[68]  Qing Wu,et al.  New method for thickness determination and microscopic imaging of graphene-like two-dimensional materials , 2016 .

[69]  C. N. Lau,et al.  Superior thermal conductivity of single-layer graphene. , 2008, Nano letters.

[70]  D. Lynch,et al.  Handbook of Optical Constants of Solids , 1985 .

[71]  F. Xia,et al.  Tunable optical properties of multilayer black phosphorus thin films , 2014, 1404.4030.

[72]  G. Steele,et al.  Isolation and characterization of few-layer black phosphorus , 2014, 1403.0499.

[73]  Walter R. L. Lambrecht,et al.  Quasiparticle band structure calculation of monolayer, bilayer, and bulk MoS 2 , 2012 .

[74]  P. Ajayan,et al.  Evolution of the electronic band structure and efficient photo-detection in atomic layers of InSe. , 2014, ACS nano.

[75]  Wenhui Wang,et al.  Strong photoluminescence enhancement of MoS(2) through defect engineering and oxygen bonding. , 2014, ACS nano.

[76]  N. Peres,et al.  Fine Structure Constant Defines Visual Transparency of Graphene , 2008, Science.

[77]  Christian Kloc,et al.  Lattice dynamics in mono- and few-layer sheets of WS2 and WSe2. , 2013, Nanoscale.

[78]  Zhongfan Liu,et al.  Interlayer vibrational modes in few-quintuple-layer Bi 2 Te 3 and Bi 2 Se 3 two-dimensional crystals: Raman spectroscopy and first-principles studies , 2014 .

[79]  Y. Hao,et al.  Experimental demonstration of a transparent graphene millimetre wave absorber with 28% fractional bandwidth at 140 GHz , 2014, Scientific Reports.

[80]  Lain-Jong Li,et al.  Second harmonic generation from artificially stacked transition metal dichalcogenide twisted bilayers. , 2014, ACS nano.

[81]  Likai Li,et al.  Black phosphorus field-effect transistors. , 2014, Nature nanotechnology.

[82]  D. Smirnov,et al.  New First Order Raman-active Modes in Few Layered Transition Metal Dichalcogenides , 2014, Scientific Reports.

[83]  Hua Zhang,et al.  The chemistry of two-dimensional layered transition metal dichalcogenide nanosheets. , 2013, Nature chemistry.

[84]  L. Dai,et al.  Physical origin of Davydov splitting and resonant Raman spectroscopy of Davydov components in multilayer MoTe 2 , 2016, 1602.05692.

[85]  Large Frequency Change with Thickness in Interlayer Breathing Mode--Significant Interlayer Interactions in Few Layer Black Phosphorus. , 2015, Nano letters.

[86]  Andre K. Geim,et al.  The rise of graphene. , 2007, Nature materials.

[87]  L. Chu,et al.  Evolution of electronic structure in atomically thin sheets of WS2 and WSe2. , 2012, ACS nano.

[88]  Yihong Wu,et al.  Graphene thickness determination using reflection and contrast spectroscopy. , 2007, Nano letters.

[89]  Ji Feng,et al.  Valley-selective circular dichroism of monolayer molybdenum disulphide , 2012, Nature Communications.

[90]  Andre K. Geim,et al.  Two-dimensional atomic crystals. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[91]  R. Ruoff,et al.  Carbon-Based Supercapacitors Produced by Activation of Graphene , 2011, Science.

[92]  Steven G. Louie,et al.  Probing excitonic dark states in single-layer tungsten disulphide , 2014, Nature.

[93]  François M. Peeters,et al.  From graphene to graphite : Electronic structure around the K point , 2006 .

[94]  T. Yu,et al.  Stacking sequence determines Raman intensities of observed interlayer shear modes in 2D layered materials – A general bond polarizability model , 2015, Scientific Reports.

[95]  Jun Zhang,et al.  Raman characterization of AB- and ABC-stacked few-layer graphene by interlayer shear modes , 2016 .

[96]  B. Park,et al.  Interference effect on Raman spectrum of graphene on SiO 2 / Si , 2009, 0908.4322.

[97]  Wenhui Dang,et al.  Few-layer nanoplates of Bi 2 Se 3 and Bi 2 Te 3 with highly tunable chemical potential. , 2010, Nano letters.

[98]  C. Felser,et al.  A combined experimental and theoretical study of the structural, electronic and vibrational properties of bulk and few-layer Td-WTe2 , 2015, Journal of physics. Condensed matter : an Institute of Physics journal.

[99]  Jorge Quereda,et al.  Spatially resolved optical absorption spectroscopy of single- and few-layer MoS₂ by hyperspectral imaging. , 2015, Nanotechnology.

[100]  J. Kysar,et al.  Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene , 2008, Science.

[101]  Jiangbin Wu,et al.  Review on the Raman spectroscopy of different types of layered materials. , 2016, Nanoscale.

[102]  Quantitative Raman spectrum and reliable thickness identification for atomic layers on insulating substrates. , 2012, ACS nano.

[103]  Madan Dubey,et al.  Two-dimensional material nanophotonics , 2014, 1410.3882.

[104]  Temperature-activated layer-breathing vibrations in few-layer graphene. , 2014, Nano letters.

[105]  Wei Ji,et al.  Interface Coupling in Twisted Multilayer Graphene by Resonant Raman Spectroscopy of Layer Breathing Modes. , 2015, ACS nano.

[106]  T. Wieting,et al.  Interlayer Bonding and the Lattice Vibrations ofβ-GaSe , 1972 .

[107]  Jun Zhang,et al.  Raman spectroscopy of few-quintuple layer topological insulator Bi2Se3 nanoplatelets. , 2011, Nano letters.

[108]  A. Ferrari,et al.  Raman spectroscopy of shear and layer breathing modes in multilayer MoS2 , 2012, 1212.6796.

[109]  Qing Hua Wang,et al.  Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. , 2012, Nature nanotechnology.

[110]  V. Kravets,et al.  Spectroscopic ellipsometry of graphene and an exciton-shifted van Hove peak in absorption , 2010, 1003.2618.

[111]  A. Radenović,et al.  Single-layer MoS2 transistors. , 2011, Nature nanotechnology.

[112]  A. Neto,et al.  Making graphene visible , 2007, Applied Physics Letters.

[113]  Sefaattin Tongay,et al.  Monolayer behaviour in bulk ReS2 due to electronic and vibrational decoupling , 2014, Nature Communications.

[114]  A. Klein,et al.  Density-functional-theory calculations of electronic band structure of single-crystal and single-layer WS 2 , 2002 .

[115]  E. Pop,et al.  Reliably counting atomic planes of few-layer graphene (n > 4). , 2010, ACS nano.

[116]  J. Shan,et al.  Tightly bound excitons in monolayer WSe(2). , 2014, Physical review letters.

[117]  Jun Zhang,et al.  Charge transfer and optical phonon mixing in few-layer graphene chemically doped with sulfuric acid , 2010 .

[118]  Yubing Zhou,et al.  Strong Second-Harmonic Generation in Atomic Layered GaSe. , 2015, Journal of the American Chemical Society.

[119]  Y. Wang,et al.  The shear mode of multi-layer graphene , 2011 .

[120]  Tao Chen,et al.  Polytypism and unexpected strong interlayer coupling in two-dimensional layered ReS2. , 2015, Nanoscale.

[121]  Yi Wan,et al.  The In-Plane Anisotropy of WTe2 Investigated by Angle-Dependent and Polarized Raman Spectroscopy , 2016, Scientific Reports.

[122]  Wang Yao,et al.  Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides. , 2011, Physical review letters.

[123]  Lifeng Wang,et al.  Synthesis of few-layer GaSe nanosheets for high performance photodetectors. , 2012, ACS nano.

[124]  Sung Kim,et al.  Optical properties of large-area ultrathin MoS2 films: Evolution from a single layer to multilayers , 2014 .

[125]  S. Banerjee,et al.  Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils , 2009, Science.

[126]  Tao Chen,et al.  Substrate-free layer-number identification of two-dimensional materials: A case of Mo0.5W0.5S2 alloy , 2015, 1505.04236.

[127]  Ping-Heng Tan,et al.  Layer number identification of intrinsic and defective multilayered graphenes up to 100 layers by the Raman mode intensity from substrates. , 2015, Nanoscale.

[128]  Wei Shi,et al.  Raman and photoluminescence spectra of two-dimensional nanocrystallites of monolayer WS2 and WSe2 , 2016 .

[129]  J. Knights,et al.  Transmission spectra of some transition metal dichalcogenides. II. Group VIA: trigonal prismatic coordination , 1972 .

[130]  Wang Yao,et al.  Valley polarization in MoS2 monolayers by optical pumping. , 2012, Nature nanotechnology.

[131]  Davydov Splitting and Excitonic Resonance Effects in Raman Spectra of Few-Layer MoSe2. , 2016, ACS nano.

[132]  J. Wilson,et al.  The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical and structural properties , 1969 .

[133]  G. Shen,et al.  Photodetectors based on two dimensional materials , 2016 .

[134]  P. Avouris,et al.  Electroluminescence in single layer MoS2. , 2012, Nano letters.

[135]  S. Lau,et al.  Layer-dependent nonlinear optical properties and stability of non-centrosymmetric modification in few-layer GaSe sheets. , 2015, Angewandte Chemie.

[136]  C. Dimitrakopoulos,et al.  100-GHz Transistors from Wafer-Scale Epitaxial Graphene , 2010, Science.

[137]  Robert L. Johnson,et al.  Electronic band structure of GaSe(0001): Angle-resolved photoemission and ab initio theory , 2003 .

[138]  Keliang He,et al.  Control of valley polarization in monolayer MoS2 by optical helicity. , 2012, Nature nanotechnology.

[139]  J. Shan,et al.  Atomically thin MoS₂: a new direct-gap semiconductor. , 2010, Physical review letters.

[140]  J. Grossman,et al.  Defects activated photoluminescence in two-dimensional semiconductors: interplay between bound, charged, and free excitons , 2013, Scientific Reports.

[141]  Takashi Taniguchi,et al.  Hunting for monolayer boron nitride: optical and Raman signatures. , 2011, Small.

[142]  Stefano Borini,et al.  Optical constants of graphene layers in the visible range , 2009 .