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Optical and Electrical Properties of Nanoscale MaterialsSuurem pilt

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This book covers the optical and electrical properties of nanoscale materials with an emphasis on how new and unique material properties result from the special nature of their electronic band structure. Beginning with a review of the optical and solid state physics needed for understanding optical and electrical properties, the book then introduces the electronic band structure of solids and discusses the effect of spin orbit coupling on the valence band, which is critical for understanding the optical properties of most nanoscale materials. Excitonic effects and excitons are also presented along with their effect on optical absorption.

2D materials, such as graphene and transition metal dichalcogenides, are host to unique electrical properties resulting from the electronic band structure. This book devotes significant attention to the optical and electrical properties of 2D and topological materials with an emphasis on optical measurements, electrical characterization of carrier transport, and a discussion of the electronic band structures using a tight binding approach. This book succinctly compiles useful fundamental and practical information from one of the fastest growing research topics in materials science and is thus an essential compendium for both students and researchers in this rapidly moving field.
1 The Interaction of Light with Solids: An Overview of Optical Characterization
1(60)
1.1 The Wave Nature of Light
2(5)
1.2 Dielectric Tensor of Bulk Crystals
7(3)
1.3 Spectroscopic Ellipsometry
10(2)
1.4 Fresnel Equations for the Reflection of Light
12(12)
1.4.1 Fresnel Description of the Reflection of Light from an Isotropic Material
12(2)
1.4.2 Isotropic Bulk Materials
14(1)
1.4.3 Isotropic Thin Film on Isotropic Bulk Substrate
15(1)
1.4.4 Ultra-Thin Dielectric Film Ellipsometry
15(1)
1.4.5 Thin 2D Film on Transparent Solid
16(1)
1.4.6 Effective Medium Approximation for Surface Roughness
17(1)
1.4.7 Anisotropic Uniaxial Solid with Uniaxial Optical Axis Normal to the Surface
17(2)
1.4.8 Anisotropic Uniaxial Solid with Uniaxial Optical Axis Parallel to the Surface
19(1)
1.4.9 Anisotropic Uniaxial Thin Film with the Optical Axis Normal to the Surface of an Isotropic Substrate (or Anisotropic Uniaxial Thin Film with the Optical Axis Normal to a Uniaxial Substrate with Optical Axis also Normal to the Surface)
20(2)
1.4.10 Anisotropic Biaxial Solid with One Optical Axis Normal to the Surface and the Second Normal to the Plane of Incidence
22(1)
1.4.11 Anisotropic Biaxial Film on an Isotropic Substrate with One Optical Axis Normal to the Surface and the Second Normal to the Plane of Incidence
23(1)
1.5 Examples of Reflectance and Ellipsometry of 2D Films
24(9)
1.5.1 Graphene
25(3)
1.5.2 Monolayer TMD's (Trilayers of Chalcogenide---Transition Metal---Chalcogenide)
28(2)
1.5.3 Topological Insulators
30(1)
1.5.4 2D Slab and Surface Current Models for the Optical Conductivity of 2D Films
31(2)
1.6 Generalized Ellipsometry: Optical Transition Matrix Approach for Crystals and Thin Films with Arbitrarily Oriented Optical Axes
33(3)
1.7 Optical Properties of Materials (Dielectric Function/Complex Refractive Index)
36(3)
1.8 The Particle Nature of Light
39(1)
1.9 Raman Spectroscopy
40(15)
1.9.1 Theory of Raman Scattering
42(4)
1.9.2 Diamond and Zinc Blende Crystals
46(1)
1.9.3 Wurtzite and other Uniaxial Crystals
47(2)
1.9.4 Van Der Waals (Layered) Materials
49(6)
1.10 Photoluminescence
55(2)
References
57(4)
2 Introduction to the Band Structure of Solids
61(44)
2.1 Band Structure and Optical Properties
62(1)
2.2 Block Theorem
63(1)
2.3 First Brillouin Zone
64(1)
2.4 Block Function Wave Vector k
65(3)
2.5 A Simple s Level Conduction Band for a Semiconductor Using a Tight Binding Approximation
68(7)
2.6 A Simple p Level Valence Band Using a Tight Binding Approximation
75(8)
2.7 Hybrid sp3 Bonding in Semiconductors Versus the Band Picture
83(1)
2.8 Spin-Orbit Coupling (A Semiclassical Approach)
83(7)
2.9 K-p Theory
90(2)
2.10 Effective Mass
92(3)
2.11 Tight Binding Model in the Second Quantization Formalism
95(3)
2.12 Crystal Structure Symmetry - Definitions of Point Groups and Space Groups
98(4)
References
102(3)
3 Instrumentation
105(10)
3.1 Spectroscopic Ellipsometry
105(4)
3.2 Raman Spectroscopy
109(1)
3.3 Photoluminescence Spectroscopy
110(2)
References
112(3)
4 Microscopic Theory of the Dielectric Function
115(34)
4.1 Relationship Between Dielectric Function and Optical Absorption
117(1)
4.2 Semiclassical Derivation of the Dielectric Function
118(5)
4.3 The Energy Dependence of the Dielectric Function for Parabolic Bands
123(2)
4.4 Joint Density of States, Critical Points, and Van Hove Singularities
125(1)
4.5 The Naming and Energy Dependence of the Critical Points
126(2)
4.6 Determining the Critical Point Energy Using Experimental Data
128(2)
4.7 Critical Points in Semiconductors (E1, E2, etc.) Review of Si, Ge, GaAs and Other Group IV and III-V Materials
130(13)
4.7.1 Brillouin Zone of Silicon, Germanium, Tin, and Diamond
130(1)
4.7.2 Critical Points of Silicon
131(2)
4.7.3 Critical Points of Germanium and Diamond
133(2)
4.7.4 Comments on Spin Orbit Splitting and CP Energies for Ge
135(1)
4.7.5 Critical Points of Sn
135(1)
4.7.6 Critical Points of GaAs and GaSb
136(2)
4.7.7 Critical Points of GaN
138(1)
4.7.8 Critical Points of CdSe
139(2)
4.7.9 Critical Points of Si1-xGex Alloys
141(1)
4.7.10 Critical Points of Ge1-xSnx Alloys
142(1)
4.8 The Effect of Doping on the Dielectric Function
143(2)
References
145(4)
5 Excitons and Excitonic Effects During Optical Transitions
149(30)
5.1 Description of Excitons in 3D, 2D, and 1D
150(2)
5.2 Energy of Excitons in 3D, 2D, and 1D
152(4)
5.2.1 3D (Bulk Materials)
152(1)
5.2.2 2D (Nanofilms)
152(1)
5.2.3 1D (Nanowire)
153(1)
5.2.4 OD (Nanodots)
153(3)
5.3 Exciton Binding Energy in Semiconductor Dielectric Quantum Wells
156(1)
5.4 The Impact of Nanolayer Thickness on Band Gap and Photoluminescence Determination of Exciton Binding Energy
157(3)
5.5 Derivation of Dielectric Function Including Excitons and Excitonic Effects
160(8)
5.5.1 Quantum Mechanical Derivation of Excitonic Effects for a Direct Gap Transition
161(4)
5.5.2 Elliott Description of Absorption for 3D, 2D, and 1D and the Sommerfeld Factor for Coulomb Enhancement
165(3)
5.6 The Effect of Nanoscale Dimensions on the Band Gap, Band Structure and Exciton Energies of Semiconductors
168(6)
5.6.1 The Bandgap of Semiconductor Nanodots
170(1)
5.6.2 Thickness Dependence of Exciton Binding Energies in I-V Quantum Wells
171(1)
5.6.3 Electron-Phonon Interactions in Nanoscale SiO2-Si-SiO2 Quantum Wells
172(2)
5.7 Comments on Photoluminescence Lineshape
174(1)
References
175(4)
6 Hall Effect Characterization of the Electrical Properties of 2D and Topologically Protected Materials
179(50)
6.1 Classical Hall Effect (HE)
181(5)
6.1.1 Classical Picture of Edge States
184(1)
6.1.2 Classical Picture of Magneto-Conductivity Tensor
185(1)
6.2 Integer Quantum Hall Effect (IQHE)
186(12)
6.2.1 Landau Levels---The Quantization of 3D and 2D Carrier Motion in a Magnetic Field
188(3)
6.2.2 Integer Quantized Transport
191(4)
6.2.3 Experimental Microscopic Observation of Carrier Transport and Chemical Potential for the IQHE
195(2)
6.2.4 Summary for experimental imaging of IQHE
197(1)
6.3 Topological Explanation of the Integer Quantum Hall Effect (IQHE)
198(12)
6.3.1 Berry Phase, Berry Curvature, and Berry Potential
199(3)
6.3.2 The Kubo Formula for the Conductivity and the TKNN Theory of the IQHE
202(2)
6.3.3 Why Topological
204(2)
6.3.4 Quantization of the Hall Conductance and the TKNN (Chern) Number
206(2)
6.3.5 Winding Number and Edge State Quantization in IQHE
208(1)
6.3.6 Brief Introduction to the Topological Description of Electronic Band Structure
209(1)
6.4 Integer Quantum Hall Effect for Graphene
210(2)
6.5 Fractional Quantum Hall Effect (FQHE): Many Body Physics in Action
212(3)
6.6 Anomalous Hall Effect (AHE)
215(4)
6.7 Quantum Anomalous Hall Effect (QAHE)
219(1)
6.8 Spin Hall Effect (SHE) and Quantum Spin Hall Effect (QSHE)
220(1)
6.9 Optical Measurement of Spin and Pseudospin Conductance
221(1)
6.10 Thermal (Nernst) Spin Hall Effect
222(1)
6.11 Skyrmion Hall Effect
222(1)
6.12 Summary
223(2)
References
225(4)
7 Optical and Electrical Properties of Graphene, Few Layer Graphene, and Boron Nitride
229(66)
7.1 Hexagonal Graphene
231(3)
7.1.1 Bravais Lattice of Graphene
232(2)
7.2 Tight Binding Approximation for the π Bands of Graphene
234(12)
7.2.1 Another Look at the Reciprocal Lattice of Graphene
239(1)
7.2.2 Graphene's n Electronic Band Structure
240(2)
7.2.3 Comparing Nearest Neighbor Graphene Energy Bands to Ab Initio Results
242(1)
7.2.4 Sub-lattice PseudoSpin (Valley) and the Graphene Band Structure
242(2)
7.2.5 Dirac Points and Dirac Cones
244(1)
7.2.6 Dirac Cone Shape for Graphene with NNN (Next Nearest Neighbor) Hopping
244(1)
7.2.7 Hexagonal 2D Lattices with Different Atoms at A and B Positions (E.G., Hexagonal Boron Nitride, h-BN)
244(2)
7.3 The Importance of Understanding the Optical and Electrical Properties of Graphene: Proof of Dirac Carriers
246(5)
7.3.1 Electrical Test Structures for Graphene and Graphene Multilayers
250(1)
7.4 Introduction to Relativistic Quantum Mechanics for 2D Materials
251(7)
7.4.1 Sub-lattice Pseudospin, Valley Pseudospin, and Chirality for Dirac Fermions in Graphene
255(2)
7.4.2 Berry Phase of an Electron in the π Bands of Graphene
257(1)
7.5 The Berry Phase Correction for the Quantum Hall Effect and Shubnikov De Hass Oscillations in Graphene
258(7)
7.6 Electronic Structure of Bilayer Graphene
265(6)
7.6.1 Massive Dirac Fermions in Bilayer Graphene
269(1)
7.6.2 The Berry Phase Correction for the Quantum Hall Effect and Shubnikov De Hass Oscillations in Bilayer Graphene
270(1)
7.7 The Electronic Structure of TriLayer and TetraLayer Graphene
271(3)
7.7.1 The Berry Phase Correction for the Quantum Hall Effect and Shubnikov De Hass Oscillations in Trilayer Graphene
273(1)
7.8 Optical Characterization of Graphene and Multilayer Graphene
274(2)
7.9 Effect of Rotational Orietation Between Layers on Bilayer Graphene (Twisted Bilayer Graphene), Monolayer---Bilayer Graphene, and Bilayer-Bilayer Graphene Properties
276(10)
7.9.1 Twisted Bilayer Graphene
277(6)
7.9.2 Monolayer---Bilayer Graphene, Middle Layer---Twist Angle Trilayer Graphene, and Bilayer-Bilayer Graphene
283(3)
7.10 The Electronic Band Structure and Optical Properties of Hexagonal Boron Nitride (h-BN) and Graphene---h-BN
286(5)
7.10.1 Graphene---BN Heterostructures
288(3)
References
291(4)
8 Optical and Electrical Properties of Transition Metal Dichalcogenides (Monolayer and Bulk)
295(68)
8.1 Structure and Bonding for TMD Materials
298(3)
8.2 Tight Binding Model for Highest Energy Valence Band and Lowest Energy Conduction Bands of Trigonal Prismatic Monolayer TMD
301(20)
8.2.1 Band Splitting Due to Spin Orbit Coupling
317(4)
8.3 Direct Observation of Monolayer TMD Valley Pseudospin and Valence Band Spin Splitting
321(3)
8.4 Massive Dirac Fermions: Physics and Optical Transitions at the K and K' Points in the Brillouin Zone
324(3)
8.5 Band Gap Renormalization and Photoluminescence Lineshape
327(1)
8.6 The Complex Refractive Index (Dielectric Function) and Optical Conductivity of Monolayer TMD
328(4)
8.6.1 Optical Conductivity of Monolayer TMD
330(2)
8.7 Structure, Electronic Band Structure, and Optical Properties of Bilayer Trigonal Prismatic TMD
332(4)
8.8 Twisted Bilayer TMD
336(3)
8.9 The Complex Refractive Index (Dielectric Function) of Multilayer and Bulk TMD
339(1)
8.10 The Layer Number Dependence of Raman Scattering from Trigonal Prismatic TMD
339(6)
8.11 Transition-Metal Dichalcogenide Haeckelites (A Theoretical Material)
345(6)
8.12 Twisted and Hetero-Bilayers of Transition Metal Dichalcogenides with graphene and h-BN
351(1)
8.13 ReS2 and ReSe2 with the 1T' Structure
352(1)
8.14 Practical Aspects of Characterization of TMD Materials Using Spectroscopic Ellipsometry
353(1)
8.15 Symmetry and Space Group Summary for Transition Metal Dichalcogenides
354(4)
References
358(5)
9 Optical and Electrical Properties Topological Materials
363(100)
9.1 Overview of Topological (Dirac) Materials
366(12)
9.1.1 Topological Surface States on 3D Topological Insulators
371(2)
9.1.2 Weyl Semimetals and Dirac Semimetals
373(3)
9.1.3 Large Gap Quantum Spin Hall Insulator
376(1)
9.1.4 Axion and Axion Insulator
377(1)
9.1.5 Mott Insulator
377(1)
9.1.6 Chern Insulator
377(1)
9.1.7 Topological Superconductors
378(1)
9.2 Tight Binding Hamiltonian with Spin-Orbit and On-Site Coulomb (Hubbard) Interactions and a 3D Dirac Equation
378(3)
9.3 Optical and Electronic Properties of Topological Materials
381(4)
9.4 3D Topological Insulators
385(22)
9.4.1 Crystal and Electronic Band Structure of 3D Topological Insulators and Large Gap Quantum Spin Hall Insulators
385(8)
9.4.2 Optical Properties of 3D Topological Insulators and Large Gap Quantum Spin Hall Insulators
393(9)
9.4.3 Electrical Properties of 3D Topological Insulators and Large Gap Quantum Spin Hall Insulators
402(5)
9.5 Weyl, Dirac Semimetals, and Related Materials
407(47)
9.5.1 Structure, Bonding, and Electronic Band Structure of Weyl, Dirac Semimetals, and Related Materials
409(21)
9.5.2 Optical Properties of Weyl, Dirac Semimetals, and Related Materials
430(13)
9.5.3 Electrical Properties of Weyl, Dirac Semimetals, and Related Materials
443(11)
References
454(9)
Appendix A Mueller Matrix Spectroscopic Ellipsometry 463(4)
Appendix B Kramers--Kronig Relationships for the Complex Refractive Index and Dielectric Function 467(2)
Appendix C Topological Periodic Tables 469(10)
Index 479
Alain Diebold is Professor Emeritus and an Empire Innovation Professor of Nanoscale Science in the College of Nanoscale Science and Engineering at the State University of New Yorks Polytechnic Institute.  His primary research areas include nanoscale characterization and metrology as well as materials science at the nanoscale using optical and X-Ray measurements, electron microscopy, and semiconductor metrology. One part of this research involves extending these concepts to new materials and structures. 

Dr. Diebold earned his BS in Chemistry from Indiana University-Purdue University, and holds a PhD in Chemistry from Purdue University where his thesis topic was Statistical Mechanics of Gas-Solid Surface Scattering.  He is Associate Editor of the IEEE Transactions on Semiconductor Manufacturing.  A frequent presenter at international conferences, Dr. Diebold has been named a Fellow of both the International Society for Optics and Photonics (SPIE) and the American Vacuum Society (AVS).

Tino Hofmann is an assistant professor at the University of North Carolina at Charlotte. His expertise is in the area of complex materials characterization. His research work covers a broad range of experimental condensed matter physics and photonics with a strong emphasis on characterizing the anisotropic optical response of spatially-coherent nanostructured materials in the visible and THz spectral range. A part of his research involves the design and construction of optical instruments for the characterization of metamaterials and metasurfaces.  Dr. Hofmann received both his Dr. rer. nat. in Physics and his Diploma in Physics, from the University Leipzig, Germany. Dr. Hofmann is the recipient of a 2014 EU Marie Curie Fellowship and A VINNMER Fellow (Fellowship of the Swedish innovation agency VINNOVA).   
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