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2pacz的禁带宽度English Answer：2pacz is a novel two-dimensional (2D) material with a unique bandgap that has attracted significant interest for its potential applications in optoelectronic devices. The bandgap of a semiconductor material is the energydifference between its valence band and conduction band, and it determines the material's optical and electrical properties.The bandgap of 2pacz has been extensively studied both experimentally and theoretically. Experimental measurements have shown that the bandgap of 2pacz can vary depending on the number of layers, strain, and other factors. For example, single-layer 2pacz has a bandgap of around 2.0 eV, while few-layer 2pacz has a bandgap of around 1.5 eV.Theoretical calculations have also provided insights into the bandgap of 2pacz. Density functional theory (DFT)calculations have shown that the bandgap of 2pacz is mainly due to the strong Coulomb interaction between the electrons in the valence band and the holes in the conduction band. The DFT calculations also predict that the bandgap of 2pacz can be tuned by changing the interlayer spacing or by applying an external electric field.The tunable bandgap of 2pacz makes it a promising material for a variety of optoelectronic applications. For example, 2pacz could be used to develop high-efficiencysolar cells, light-emitting diodes (LEDs), and photodetectors.Chinese Answer：2pacz是一种新型的二维（2D）材料，具有独特的带隙，因其在光电器件中的潜在应用而备受关注。
半导体分离芯材料英语Semiconductor Materials for Isolation Cores.Semiconductor materials play a crucial role in modern electronics, particularly in the fabrication of isolation cores. Isolation cores are essential components in integrated circuits, ensuring that different sections of the circuit operate independently without interference. This article delves into the world of semiconductor materials suitable for isolation cores, discussing their properties, applications, and challenges.1. Introduction to Semiconductor Materials.Semiconductors are materials that have an electrical conductivity falling between that of conductors and insulators. They exhibit unique electronic properties, making them ideal for use in electronic devices. Silicon (Si) and germanium (Ge) are the most commonly used semiconductors, but others such as gallium arsenide (GaAs)and silicon carbide (SiC) are also finding applications in specific areas.2. Properties of Semiconductor Materials.Bandgap Energy: The bandgap energy is a measure of the energy required to excite an electron from the valence band to the conduction band. Materials with larger bandgap energies are better suited for high-temperature applications.Doping: Semiconductors can be doped with impurities to alter their conductivity. Dopants such as boron (B) or phosphorus (P) are introduced to create p-type or n-type semiconductors, respectively.Lattice Structure: The atomic lattice structure of semiconductors determines their physical and electrical properties. Silicon and germanium have diamond-like lattice structures, which contribute to their widespread use.3. Isolation Cores and Their Importance.Isolation cores are critical in integrated circuits, where they prevent electrical signals from leaking between different circuit sections. This isolation ensures that signals are contained within their designated paths, preventing crosstalk and noise. Isolation cores are typically made from insulating materials, but semiconductor materials can also be used to achieve isolation.4. Semiconductor Materials for Isolation Cores.Silicon-on-Insulator (SOI): SOI technology involves a thin layer of silicon sandwiched between two layers of insulating material, such as silicon dioxide or sapphire. This structure provides excellent isolation between different circuit sections. SOI wafers are widely used in high-performance microelectronics, as they offer reduced parasitic capacitance and improved thermal performance.Silicon Carbide (SiC): SiC is a wide-bandgap semiconductor material with excellent thermal conductivity and chemical stability. It is suitable for high-temperatureand high-power applications. SiC-based isolation cores can withstand extreme operating conditions, making them idealfor use in power electronics and aerospace applications.Gallium Arsenide (GaAs): GaAs has a smaller bandgap than silicon but offers higher electron mobility and saturation velocity. GaAs-based isolation cores are commonly used in high-frequency applications such as microwave and millimeter-wave circuits. GaAs also finds applications in optoelectronics due to its ability to emit and detect light.5. Challenges and Future Outlook.Despite the many advantages of semiconductor materials for isolation cores, there are still challenges to overcome. One major challenge is the scalability of these materialsfor smaller and more complex integrated circuits. Another challenge lies in the fabrication process, which requires precise control over doping levels, lattice structures, and defect densities.Future research in this area will focus on developing new semiconductor materials with improved properties and on optimizing fabrication processes for better scalability and performance. Materials such as two-dimensional semiconductors and topological insulators are beingactively explored for their potential in next-generation electronics.Conclusion.Semiconductor materials play a pivotal role in the fabrication of isolation cores, enabling the reliable operation of integrated circuits. Silicon, silicon carbide, and gallium arsenide are among the most commonly used semiconductors for this purpose, each offering its unique advantages and applications. Future research in this field will focus on addressing challenges related to scalability and fabrication processes while exploring novel materials with improved properties.。
二维光子晶体完全光子带隙的优化设计刘茂军;周莹;王丽;马季【摘要】应用平面波展开法推导二维光子晶体横磁场模式和横电场模式主方程,得到两种模式下的二维光子晶体完全带隙,并研究二维光子晶体完全带隙宽度及中心频率位置随填充比和背景介质介电常数的变化规律,从而实现二维光子晶体完全光子带隙的优化.%We used the plane-wave expansion method to derive the master equation of two-dimensional photonic crystal for transverse magnetic mode and transverse electric mode,and obtained the complete photonic-band-gap of two-dimensional photonic crystal for two modes.We studied the change rule of filling ratio and dielectric constant of background medium with the complete photonic-band-gap width and center frequency location of two-dimensional photonic crystal.Thus,the optimal design of the complete photonic-band-gap was realized.【期刊名称】《吉林大学学报（理学版）》【年(卷),期】2017(055)005【总页数】5页(P1292-1296)【关键词】二维光子晶体;平面波展开法;完全光子带隙【作者】刘茂军;周莹;王丽;马季【作者单位】吉林师范大学物理学院,吉林四平136000;吉林师范大学物理学院,吉林四平136000;吉林师范大学物理学院,吉林四平136000;同济大学物理科学与工程学院,上海200092【正文语种】中文【中图分类】O436光子晶体是介电常数受空间位置周期性调制的光学微结构, 具有光子局域态和光子禁带, 在新型光电器件、光学传感、高效低损耗反射镜、光子晶体微谐振腔及高效率发光二极管等领域应用广泛[1-9]. 光子晶体的理论研究方法主要有传输矩阵法、时域有限差分法和平面波展开法等[10-12]. 其中, 平面波展开法是研究光子晶体带隙结构的主要方法. 本文将电磁场在倒格矢空间内展开为平面波叠加的形式, 进而将Maxwell方程组化为一个本征方程, 通过求解本征值得到相应的本征解, 即得到在光子晶体内存在的本征模式. 平面波展开法优点在于能快速得到本征模式的电磁场分布以及光子晶体的带隙结构, 计算各种理想结构光子晶体带隙所得结果准确且高效[13]. 根据平面波展开法得到的光子晶体带隙结构可考察能带结构、禁带宽度以及各光子态之间的关系等光学特性[14]. 对于某个偏振态, 若在一定频率范围内不存在对应的模式, 则称其为该偏振态的光子带隙. 对于两个偏振态, 若在一定频率范围内均不存在对应的模式, 则称其为完全光子带隙[15]. 完全光子带隙的宽度与位置均决定了该光子晶体的应用性能, 因此对于光子晶体完全带隙的优化设计研究有一定的意义. 本文用平面波展开法计算两种模式下二维光子晶体的完全带隙, 并讨论填充比及背景介质介电常数对二维光子晶体完全带隙的影响.光在电介质内的传播遵循Maxwell方程, 假设构成二维光子晶体介质为无源介质, 则Maxwell方程为：对于非磁性材料光子晶体, 有所以, Maxwell方程组可表示为：其中ε(r)为二维光子晶体的介电常数, 受空间位置的周期性调制, 二维情况下可记为ε(r∥).对于横磁场模式(TM模式), 电磁场为:其中r∥=xi+yj. 将式(11),(12)代入式(9),(10), 有将式(13)～(15)中的时间项、Hx和Hy消除后可得式(16)即为TM模式对应的主方程.对于横电场模式(TE模式), 电磁场为:将式(17),(18)代入式(9),(10), 有将式(19)～(21)中的时间项、Ex和Ey消除后可得式(22)即为TE模式对应的主方程.根据二维光子晶体介电常数的周期性分布, 有其中在求解主方程时, 可将1/ε(r∥)在倒易空间进行Fourier展开其中: G∥=l1b1+l2b2为倒易空间内的二维矢量; K(G∥)为1/ε(r∥)的Fourier系数, 为二维光子晶体的填充比, ac为二维光子晶体原包面积, J1为一阶Bessel函数.对二维光子晶体完全光子带隙进行数值分析, 通过参数调节得到二维光子晶体完全光子带隙宽度及其完全带隙中心频率位置的变化规律, 从而实现完全光子带隙的优化设计. 二维光子晶体的基本参数为：背景介质介电常数εb=11.56, 空气柱εa=1, 空气柱在空间为正方结构排列, 如图1所示. 空气柱半径ra=0.45a, a=10-6 m为晶格常数, 填充比k=0.636 2.二维光子晶体结构的完全光子带隙如图2所示. 由图2可见: 当f=0～0.8ω时, TM 模式比TE模式有更宽的带隙, 二者重合的部分称为完全光子带隙; 该结构具有宽为Δ ω=0.057ω的完全光子带隙, 中心频率ωmid=0.452ω, Δ ω/ωmid=12.61%.填充比对完全光子带隙结构的影响如图3所示. 由图3可见: 当f=0～0.8ω时, TM 模式比TE模式有更宽的带隙; 当k=0.536 2时, 该结构不存在完全光子带隙; 当k=0.636 2时, 该结构具有宽为Δ ω=0.057ω的完全光子带隙, 中心频率ωmid=0.452ω, Δ ω/ωmid=12.61%; 当k=0.736 2时, 该结构具有宽为Δω=0.089ω的完全光子带隙, 中心频率ωmid=0.475ω, Δ ω/ωmid=18.74%; 该结构二维光子晶体的完全光子带隙宽度随填充比的增大而增大, 且完全光子带隙中心频率的位置发生蓝移.背景介质介电常数对完全光子带隙结构的影响如图4所示. 由图4可见: 当f=0～0.8ω时, TM模式比TE模式有更宽的带隙; 当εb=10.24时, 该结构具有宽为Δω=0.036ω的完全光子带隙, 中心频率ωmid=0.467ω, Δ ω/ωmid=7.71%; 当εb=11.56时, 该结构具有宽为Δ ω=0.057ω的完全光子带隙, 中心频率ωmid=0.452ω, Δ ω/ωmid=12.61%; 当εb=12.89时, 该结构具有宽为Δω=0.071ω的完全光子带隙, 中心频率ωmid=0.438ω, Δ ω/ωmid=16.21%; 该结构二维光子晶体的完全光子带隙宽度随背景介质介电常数的增大而增大, 且完全光子带隙中心频率的位置发生红移.综上, 本文用平面波展开法推导了二维光子晶体的主方程, 并对二维光子晶体完全光子带隙进行了数值分析, 通过调节参数, 得到了正方晶格二维光子晶体完全光子带隙的宽度和位置的变化规律. 结果表明: 增大填充比可使完全光子带隙的宽度增加, 完全光子带隙的位置蓝移；增大背景介质介电常数可使完全光子带隙的宽度增加, 完全光子带隙的位置红移.【相关文献】[1] Yablonovitch E. 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硅光子晶体结构参数对其带隙宽度影响分析作者：王婷婷杨运兴李支新孙晶来源：《科技创新与应用》2020年第24期摘 ;要：借助光子晶体的理论知识和平面波展开法理论方法，依托Matlab、Comsol等计算分析软件，分析了二维三角晶格硅光子晶体结构参数对带隙宽度的影响。
就基元形状与旋转角度等结构参数调整对光子带隙宽度的影响进行模拟以及研究。
结果发现，在一种固定晶格的光子晶体中，其他条件为定量时，基元形状所占的空间比例越大，光子带隙显现出的结构越好;基元面积固定时，其旋转角度的改变只和带隙宽窄有关，而对带隙的中心频率无影响，或者影响不大。
关键词：硅光子晶体;二维三角晶格;结构参数;带隙宽度;平面波展开法中图分类号：O734 文献标志码：A ; ; ; ; 文章编号：2095-2945（2020）24-0020-03Abstract： Based on the theoretical knowledge of photonic crystals and the theoretical method of plane wave expansion method， the influence of the structural parameters of two-dimensional triangular lattice silicon photonic crystals on the band gap width is analyzed by using Matlab，Comsol and other kinds of calculation and analysis software. The influence of structural parameters such as element shape and rotation angle on photonic band gap width is simulated and studied. The results show that in a fixed lattice photonic crystal， when other conditions are quantitative， the larger the proportion of space occupied by the primitive shape， the better the structure of the photonic band gap appears; when the element area is fixed， the change of its rotation angle is only related to the width of the bandgap， but has no or little effect on the center frequency of the band gap.Keywords： silicon photonic crystal; two-dimensional triangular lattice; structural parameter; width of the bandgap; plane wave expansion method1 概述目前电子领域发展面临集成和微型化极限，颇难突破瓶颈，急需通过选择其他有良好性能且符合需求的器件材料实现性能提升[1-2]。
More informationFundamentals of Photonic Crystal GuidingIf you’re looking to understand photonic crystals,this systematic,rigorous,and peda-gogical introduction is a must.Here you’llfind intuitive analytical and semi-analyticalmodels applied to complex and practically relevant photonic crystal structures.Y ou willalso be shown how to use various analytical methods borrowed from quantum mechanics,such as perturbation theory,asymptotic analysis,and group theory,to investigate manyof the limiting properties of photonic crystals,which are otherwise difficult to rationalizeusing only numerical simulations.An introductory review of nonlinear guiding in photonic lattices is also presented,as are the fabrication and application of photonic crystals.In addition,end-of-chapterexercise problems with detailed analytical and numerical solutions allow you to monitoryour understanding of the material presented.This accessible text is ideal for researchersand graduate students studying photonic crystals in departments of electrical engineering,physics,applied physics,and mathematics.Maksim Skorobogatiy is Professor and Canada Research Chair in Photonic Crystals atthe Department of Engineering Physics in´Ecole Polytechnique de Montr´e al,Canada.In2005he was awarded a fellowship from the Japanese Society for Promotion of Science,and he is a member of the Optical Society of America.Jianke Yang is Professor of Applied Mathematics at the University of Vermont,USA.Heis a member of the Optical Society of America and the Society of Industrial and AppliedMathematics.Fundamentals of Photonic Crystal GuidingMAKSIM SKOROBOGATIY 1JIANKE YANG 2´Ecole Polytechnique de Montr ´e al,Canada 1University of Vermont,USA2More informationMore informationcambridge university pressCambridge,New Y ork,Melbourne,Madrid,Cape Town,Singapore,S˜a o Paulo,DelhiCambridge University PressThe Edinburgh Building,Cambridge CB28RU,UKPublished in the United States of America by Cambridge University Press,New Y orkInformation on this title:/9780521513289C Cambridge University Press2009This publication is in copyright.Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place withoutthe written permission of Cambridge University Press.First published2009Printed in the United Kingdom at the University Press,CambridgeA catalog record for this publication is available from the British LibraryLibrary of Congress Cataloging in Publication dataSkorobogatiy,Maksim,1974–Fundamentals of photonic crystal guiding/by Maksim Skorobogatiy and Jianke Y ang.p.cm.Includes index.ISBN978-0-521-51328-91.Photonic crystals.I.Y ang,Jianke.II.Title.QD924.S562008621.36–dc222008033576ISBN978-0-521-51328-9hardbackCambridge University Press has no responsibility for the persistence oraccuracy of URLs for external or third-party internet websites referred toin this publication,and does not guarantee that any content on suchwebsites is,or will remain,accurate or appropriate.More informationM.Skorobogatiy dedicates this book to his family.He thanks his parentsAlexander and Tetyana for never-ceasing support,encouragement,andparticipation in all his endeavors.He also thanks his wife Olga,his children,Alexander junior and Anastasia,andhis parents for their unconditional love.J.Yang dedicates this book to his family.More informationContentsPreface page xiAcknowledgements xii1Introduction11.1Fabrication of photonic crystals21.2Application of photonic crystals41.2.1Photonic crystals as low-loss mirrors:photonicbandgap effects41.2.2Photonic crystals for out-of-bandgap operation10References112Hamiltonian formulation of Maxwell’s equations(frequency consideration)142.1Plane-wave solution for uniform dielectrics162.2Methods of quantum mechanics in electromagnetism182.2.1Orthogonality of eigenstates192.2.2Variational principle202.2.3Equivalence between the eigenstates of twocommuting Hamiltonians222.2.4Eigenstates of the operators of continuous anddiscrete translations and rotations232.3Properties of the harmonic modes of Maxwell’s equations302.3.1Orthogonality of electromagnetic modes322.3.2Eigenvalues and the variational principle322.3.3Absence of the fundamental length scale in Maxwell’sequations342.4Symmetries of electromagnetic eigenmodes352.4.1Time-reversal symmetry352.4.2Definition of the operators of translation and rotation352.4.3Continuous translational and rotational symmetries382.4.4Band diagrams432.4.5Discrete translational and rotational symmetries44More informationviii Contents2.4.6Discrete translational symmetry and discreterotational symmetry522.4.7Inversion symmetry,mirror symmetry,and other symmetries532.5Problems553One-dimensional photonic crystals–multilayer stacks593.1Transfer matrix technique593.1.1Multilayer stack,TE polarization593.1.2Multilayer stack,TM polarization613.1.3Boundary conditions623.2Reflection from afinite multilayer(dielectric mirror)633.3Reflection from a semi-infinite multilayer(dielectricphotonic crystal mirror)643.3.1Omnidirectional reflectors I683.4Guiding in afinite multilayer(planar dielectric waveguide)693.5Guiding in the interior of an infinitely periodic multilayer703.5.1Omnidirectional reflectors II803.6Defect states in a perturbed periodic multilayer:planarphotonic crystal waveguides823.7Problems864Bandgap guidance in planar photonic crystal waveguides934.1Design considerations of waveguides with infinitelyperiodic reflectors934.2Fundamental TE mode of a waveguide with infinitelyperiodic reflector964.3Infinitely periodic reflectors,field distribution in TM modes984.3.1Case of the core dielectric constantεc<εhεl/(εh+εl)984.3.2Case of the core dielectric constantεl≥εc>εhεl/(εh+εl)1014.4Perturbation theory for Maxwell’s equations,frequencyformulation1034.4.1Accounting for the absorption losses of the waveguidematerials:calculation of the modal lifetime and decay length1044.5Perturbative calculation of the modal radiation loss in aphotonic bandgap waveguide with afinite reflector1064.5.1Physical approach1064.5.2Mathematical approach1085Hamiltonian formulation of Maxwell’s equations for waveguides(propagation-constant consideration)1105.1Eigenstates of a waveguide in Hamiltonian formulation1105.1.1Orthogonality relation between the modes of a waveguide madeof lossless dielectrics111More informationContents ix5.1.2Expressions for the modal phase velocity1145.1.3Expressions for the modal group velocity1145.1.4Orthogonality relation between the modes of a waveguide madeof lossy dielectrics1155.2Perturbation theory for uniform variations in a waveguide dielectric profile1165.2.1Perturbation theory for the nondegenerate modes:example ofmaterial absorption1185.2.2Perturbation theory for the degenerate modes coupled byperturbation:example of polarization-mode dispersion1205.2.3Perturbations that change the positions of dielectric interfaces1235.3Problems126References127 6Two-dimensional photonic crystals1296.1T wo-dimensional photonic crystals with diminishingly smallindex contrast1296.2Plane-wave expansion method1326.2.1Calculation of the modal group velocity1346.2.2Plane-wave method in2D1346.2.3Calculation of the group velocity in the case of2Dphotonic crystals1356.2.4Perturbative formulation for the photonic crystallattices with small refractive index contrast1386.2.5Photonic crystal lattices with high-refractive-index contrast1426.3Comparison between various projected band diagrams1426.4Dispersion relation at a band edge,density of states andVan Hove singularities1446.5Refraction from photonic crystals1476.6Defects in a2D photonic crystal lattice1486.6.1Line defects1486.6.2Point defects1586.7Problems167References171 7Quasi-2D photonic crystals1727.1Photonic crystalfibers1727.1.1Plane-wave expansion method1727.1.2Band diagram of modes of a photonic crystalfiber1767.2Optically induced photonic lattices1777.2.1Light propagation in low-index-contrast periodicphotonic lattices1787.2.2Defect modes in2D photonic lattices with localized defects1817.2.3Bandgap structure and diffraction relation for the modes of auniform lattice182More informationx Contents7.2.4Bifurcations of the defect modes from Bloch band edges forlocalized weak defects1857.2.5Dependence of the defect modes on the strength oflocalized defects1887.2.6Defect modes in2D photonic lattices with nonlocalized defects1927.3Photonic-crystal slabs1957.3.1Geometry of a photonic-crystal slab1957.3.2Eigenmodes of a photonic-crystal slab1977.3.3Analogy between the modes of a photonic-crystal slab and themodes of a corresponding2D photonic crystal2007.3.4Modes of a photonic-crystal slab waveguide2047.4Problems207References208 8Nonlinear effects and gap–soliton formation in periodic media2108.1Solitons bifurcated from Bloch bands in1D periodic media2118.1.1Bloch bands and bandgaps2118.1.2Envelope equations of Bloch modes2128.1.3Locations of envelope solitons2158.1.4Soliton families bifurcated from band edges2168.2Solitons bifurcated from Bloch bands in2D periodic media2188.2.1T wo-dimensional Bloch bands and bandgaps of linearperiodic systems2198.2.2Envelope equations of2D Bloch modes2208.2.3Families of solitons bifurcated from2D band edges2238.3Soliton families not bifurcated from Bloch bands2268.4Problems227References228Problem solutions230Chapter2230Chapter3236Chapter5244Chapter6246Chapter7257Chapter8260 Index263More informationPrefaceThefield of photonic crystals(aka periodic photonic structures)is experiencing anunprecedented growth due to the dramatic ways in which such structures can control,modify,and harvest theflow of light.The idea of writing this book came to M.Skorobogatiy when he was developingan introductory course on photonic crystals at the Ecole Polytechnique de Montr´e al/University of Montr´e al.Thefield of photonic crystals,being heavily dependent onnumerical simulations,is somewhat challenging to introduce without sacrificing thequalitative understanding of the underlying physics.On the other hand,exactly solvablemodels,where the relation between physics and quantitative results is most transpar-ent,only exist for photonic crystals of trivial geometries.The challenge,therefore,wasto develop a presentational approach that would maximally use intuitive analytical andsemi-analytical models,while applying them to complex and practically relevant pho-tonic crystal structures.We would like to note that the main purpose of this book is not to present the latestadvancements in thefield of photonic crystals,but rather to give a systematic,logical,andpedagogical introduction to this vibrantfield.The text is largely aimed at students andresearchers who want to acquire a rigorous,while intuitive,mathematical introductioninto the subject of guided modes in photonic crystals and photonic crystal waveguides.The text,therefore,favors analysis of analytically or semi-analytically solvable problemsover pure numerical modeling.We believe that this is a more didactical approach whentrying to introduce a novice into a newfield.To further stimulate understanding of thebook content,we suggest many exercise problems of physical relevance that can besolved analytically.In the course of the book we extensively use the analogy between the Hamiltonian for-mulation of Maxwell’s equations and the Hamiltonian formulation of quantum mechan-ics.We present both frequency and propagation-constant based Hamiltonian formula-tions of Maxwell’s equations.The latter is particularly useful for analyzing photoniccrystal-based linear and nonlinear waveguides andfibers.This approach allows us touse a well-developed machinery of quantum mechanical semi-analytical methods,suchas perturbation theory,asymptotic analysis,and group theory,to investigate many ofthe limiting properties of photonic crystals,which are otherwise difficult to investigatebased only on numerical simulations.M.Skorobogatiy has contributed Chapters2,3,4,5,and6of this book,and J.Y anghas contributed Chapter8.Chapters1and7were co-authored by both authors.More informationAcknowledgementsM.Skorobogatiy would like to thank his graduate and postgraduate program mentors,Professor J.D.Joannopoulos and Professor Y.Fink from MIT,for introducing him intothefield of photonic crystals.He is grateful to Professor M.Koshiba and ProfessorK.Saitoh for hosting him at Hokkaido University in2005and for having many excitingdiscussions in the area of photonic crystalfibers.M.Skorobogatiy acknowledges theCanada Research Chair program for making this book possible by reducing his teachingload.J.Y ang thanks the funding support of the US Air Force Office of Scientific Research,which made many results of this book possible.He also thanks the Zhou Pei-Yuan Centerfor Applied Mathematics at Tsinghua University(China)for hospitality during his visit,where portions of this book were written.Both authors are grateful to their graduate andpostgraduate students for their comments and help,while this book was in preparation.Especially,J.Y ang likes to thank Dr.Jiandong Wang,whose help was essential for hisbook writing.。
二维材料英语Two-Dimensional Materials。
Introduction。
Two-dimensional (2D) materials have attracted significant attention in recent years due to their unique properties and potential applications in various fields. These materials, consisting of a single layer of atoms or molecules, exhibit extraordinary mechanical, electrical, optical, and thermal properties. In this article, we will explore the fascinating world of 2D materials and their promising future.Graphene。
Graphene, the first discovered 2D material, is a single layer of carbon atoms arranged in a hexagonal lattice. It possesses exceptional electrical conductivity, mechanical strength, and thermal conductivity. Graphene's unique properties make it an ideal candidate for applications in electronics, energy storage, and composites. Researchers are actively exploring ways to scale up the production of graphene and integrate it into practical devices.Transition Metal Dichalcogenides (TMDs)。
一维光子晶体表面模的特性罗砚浓;吴美燕;蒙成举;黄照峰;卢强华;韦以明;高英俊【摘要】[目的]研究一维光子晶体表面模的特性,探究使用衰减全反射(ATR)技术激发光子晶体表面模的可行性.[方法]采用超元胞法和迭代菲涅尔方程计算一维光子晶体表面模的色散曲线及其ATR反射谱(利用棱镜装置).[结果]当一维光子晶体最外层是高折射率层时,改变其厚度可以灵活控制表面模,相同带隙内不同位置的表面模其电场局域性不同;能带图中同一带隙内远离真空光线且居于带隙中部的表面模其电场局域性更强.[结论]利用棱镜装置能激发一维光子晶体的表面波;通过反射谱的形状和极小值点的位置可以判断透射介质的光学性质.【期刊名称】《广西科学》【年(卷),期】2015(022)001【总页数】5页(P104-108)【关键词】一维光子晶体;表面模;超元胞法;衰减全反射【作者】罗砚浓;吴美燕;蒙成举;黄照峰;卢强华;韦以明;高英俊【作者单位】广西大学物理科学与工程技术学院,广西南宁 530004;广西大学物理科学与工程技术学院,广西南宁 530004;广西大学物理科学与工程技术学院,广西南宁 530004;广西大学物理科学与工程技术学院,广西南宁 530004;广西大学物理科学与工程技术学院,广西南宁 530004;广西大学物理科学与工程技术学院,广西南宁530004;广西大学物理科学与工程技术学院,广西南宁 530004;广西大学广西有色金属及特色材料加工重点实验室,广西南宁 530004【正文语种】中文【中图分类】TG111.2【研究意义】表面电磁波是一种沿界面传播且其振幅在界面两侧介质的指数衰减的非辐射电磁模。
某频率下当界面两侧介质的介电常数异号时，表面波可以在界面存在[1～3]。
电磁波在光子晶体中传输时由于散射和干涉的共同作用，其在禁带处的等效介电函数为负，因此可以在光子晶体的表面激发表面模[4～6]。
相比表面等离子体波，光子晶体表面波的优势在于：(1)可以支持TE和TM两种偏振类型的入射光；(2)低介电损耗可以获得更高的表面电场和更敏感的传感特性；(3)不受材料的特性限制，可以灵活地设计出任意频率段的表面波。
2020年24期创新前沿科技创新与应用Technology Innovation and Application硅光子晶体结构参数对其带隙宽度影响分析*王婷婷，杨运兴，李支新，孙晶*（吉首大学物理与机电工程学院，湖南吉首416000）1概述目前电子领域发展面临集成和微型化极限，颇难突破瓶颈，急需通过选择其他有良好性能且符合需求的器件材料实现性能提升[1-2]。
在经过大量的尝试和探索后发现，硅基光子晶体有以下几点特性：一是损耗低；二是成本少；三是能效高；四是易制备。
因此，这类晶体凭借其多种优良的特性得以发展[3]。
光子晶体内部光子受到周期性的约束和影响，且其具有光子带隙[4-6]（photonic band gap ，PBG ）。
PBG 中是禁止任何光入射并传播的，其对于光子晶体掌控光的能力起决定性作用，它的宽度越宽，表明光子晶体掌控光的频域范围越大。
针对此，结构参数是PBG 的一个重大影响因素，通过对预先设计好的光子晶体结构改变参数变量并不断优化，得到更为理想的PBG ，从而达到满足高集成、小尺寸的工艺目标。
但面对硅光子晶体器件结构的设计和应用以及实现部分功能的问题上，由于缺乏相关结构参数的理论研究分析，研究过程显得尤为缓慢[7-8]。
本文首先通过光子晶体的理论基础和平面波展开法，建立了二维三角晶格硅光子晶体模型；定量分析了三角晶格内基元形状以及旋转角度等结构参数因素对其带宽的影响；最后总结了模拟计算得出的结果分析并对今后实验研究提供一定的参考依据。
2理论方法在模拟计算光子晶体内光子带隙时，平面波展开法[9]将电磁场量与介电常数以傅里叶级数展开，并用平面波形式表达，再利用一个特征方程代替转化的Maxwell 方程组，求解该特征方程的特征值得到其带隙特征，有如下形式：光子晶体对应于一些倒格子矢量的周期介电函数（对于所有二维的晶体周期而言，i=1，2）。
在这种情况下，周期特征问题的布洛赫-弗洛凯定理表明方程的解：（1）可以被表达为包含有特征值（2）在每个布洛赫波矢k ⭢处的倒格子上产生一个不同的埃尔米特本征问题。
二维MoS2薄膜的可控制备及其电子输运特性研究【摘要】二维MoS2作为一种新型半导体材料，在电子学和光电子学领域具有广泛的应用前景。
在本文研究中，我们采用化学气相沉积（CVD）技术在氧化硅基底上制备了高质量的二维MoS2薄膜，并通过压电传感器进行了表征。
通过在不同条件下控制CVD过程中的温度、气体流量和反应时间等参数，成功地实现了对MoS2薄膜的可控制备。
同时，利用离子束雕刻技术对MoS2薄膜进行了纳米加工，使其形成了具有排列有序的长条纹的结构，可作为电极进行电子输运特性研究。
进一步的电子输运实验表明，MoS2薄膜具有半导体特性，并在室温下呈现出n型导电性。
在不同温度和电场的情况下，MoS2薄膜的电子输运性质表现出明显的变化。
通过调控材料的缺陷和掺杂，成功地实现了对MoS2薄膜电子输运特性的调控。
结果表明，MoS2薄膜在电子学和光电子学器件中具有广泛的应用前途。
【关键词】二维MoS2；CVD；可控制备；纳米加工；电子输运特性【Abstract】Two-dimensional (2D) MoS2 as a novel semiconductor material has great potential applications in thefields of electronics and optoelectronics. In this study, high-quality 2D MoS2 film was prepared on aSiO2 substrate by chemical vapor deposition (CVD) technique and characterized by piezoelectric sensors. The controllable preparation of MoS2 film was achieved by controlling the temperature, gas flow rate, and reaction time in the CVD process under different conditions. Meanwhile, the MoS2 film was patterned by ion beam etching, forming a structure with a longitudinally aligned stripe that was used as an electrode for the study of electronic transport characteristics.Further electronic transport experiments demonstrated that the MoS2 film exhibited semiconductor properties and showed an n-type conductivity at room temperature. The electronic transport properties of MoS2 film showed significant changes under different temperatures and electric fields. By controlling the material defects and doping, the electronic transport characteristics of MoS2 film were successfully regulated. The results indicated that MoS2 film had great potential applications in electronics and optoelectronics devices.【Keywords】Two-dimensional MoS2; CVD; Controllable preparation; Nanofabrication; Electronic transport characteristicTwo-dimensional MoS2 has attracted increasingattention in recent years due to its unique properties and potential applications in electronics and optoelectronics devices. In order to fully utilize its potential, the controllable preparation of high-quality MoS2 film is crucial.One of the most commonly used methods for preparing MoS2 film is chemical vapor deposition (CVD). By controlling the growth conditions, such as temperature, pressure, and precursor concentration, high-quality MoS2 film with uniform thickness and large area can be obtained.The electronic transport properties of MoS2 film are strongly dependent on its crystal quality, defect density, and doping level. It has been found that the electronic transport properties of MoS2 film can be significantly improved by reducing the defect density and doping with certain impurities.Under different temperatures and electric fields, the electronic transport properties of MoS2 film exhibitsignificant changes. For instance, the electrical conductivity of MoS2 film can increase with increasing temperature or electric field due to the enhanced carrier mobility. Furthermore, the conductivity can also be tuned by controlling the doping level, as certain dopants can either enhance or suppress the carrier concentration.In summary, the controllable preparation andregulation of electronic transport characteristics of MoS2 film provide opportunities for its potential applications in future electronic and optoelectronics devices. The nanofabrication of MoS2-based devices with high performance and reliability can be achieved with the advancement of the synthesis and characterization techniquesApart from electronic and optoelectronic applications, MoS2 films also have potential in other fields such as energy storage and catalysis. One of the most promising applications is in supercapacitors, which are energy storage devices with high power density and fast charging and discharging capabilities. MoS2 has been explored as an electrode material for supercapacitors due to its large surface area, high electrical conductivity, and good stability. Researchers have reported that MoS2-basedsupercapacitors exhibit excellent electrochemical performance, which can be further improved by tuning the morphology and structure of the material.MoS2-based catalysts have also attracted muchattention in recent years due to their high catalytic activity and selectivity in various chemical reactions. For instance, MoS2 has been reported to be anefficient catalyst for the hydrogen evolution reaction (HER), which is a key step in water-splitting technologies for the production of hydrogen fuel. The high catalytic activity of MoS2 for HER can be attributed to its unique electronic and geometric structures, as well as the synergistic effect between the active sites and the support material.In addition, MoS2 can also be used as a catalyst for other reactions such as hydrodesulfurization (HDS) and oxygen reduction reaction (ORR), which are important processes in the petrochemical industry and fuel cells, respectively. The catalytic performance of MoS2 can be further enhanced by modifying its surface chemistry, morphology, and structure through various methods such as doping, surface functionalization, and nanostructuring.Overall, the controllable preparation and regulationof MoS2 films offer great opportunities for their applications in various fields. With the continuous development of synthesis and characterization techniques, as well as the increasing understanding of the fundamental properties and behaviors of MoS2, we can expect more breakthroughs in the design and fabrication of advanced MoS2-based materials and devices in the futureOne promising application of MoS2 is in optoelectronics. Due to its direct bandgap nature and strong light-matter interaction, MoS2 has been demonstrated to have excellent performance as a photoelectric material, making it an ideal candidatefor solar cells and photodetectors. Additionally,MoS2-based light-emitting diodes (LEDs) have shown promising performance in terms of brightness and efficiency, and could potentially be integrated with electronic devices for optoelectronic applications.Another potential application of MoS2 is in energy storage devices, such as batteries and supercapacitors. MoS2 has been shown to have a high specific capacitance and excellent cycling stability, making it an attractive electrode material for supercapacitors. In addition, MoS2 has been used as a cathode material in lithium-ion batteries, with promising results interms of both capacity and cycle life. Further research is needed to fully realize the potential of MoS2 in energy storage applications, but thematerial's unique properties make it a promising candidate for future developments.In the field of catalysis, MoS2 has shown great potential due to its high surface area, abundance, and unique electronic and chemical properties. MoS2-based catalysts have been used in various applications, such as electrocatalysis, photocatalysis, and hydrogen evolution reactions. Additionally, MoS2-basedcatalysts have shown promising activity for conversion of greenhouse gases, such as carbon dioxide, into valuable chemicals, making them a potentially important tool for addressing climate change.Overall, the unique properties and versatile applications of MoS2 make it an exciting material for research and development in various fields. As the understanding of MoS2 continues to grow, we can expect to see more advances in the design and fabrication of advanced materials and devices. The development of new synthesis and characterization techniques will also play a critical role in unlocking the full potential of MoS2-based materials. Ultimately, these advancements have the potential to revolutionize anumber of industries and make a significant impact on our daily livesIn conclusion, MoS2 is a promising material that has garnered significant attention due to its unique properties and potential applications in various fields. The research and development in this area are expected to lead to significant advancements in the design and fabrication of advanced materials and devices, which could revolutionize numerous industries and make a significant impact on our daily lives. Continued efforts in the development of new synthesis and characterization techniques are critical to unlocking the full potential of MoS2-based materials。
a r X i v :p h y s i c s /0501072v 1 [p h y s i c s .o p t i c s ] 14 J a n 2005Applied Physics B.manuscript No.(will be inserted by the editor)Bandgap properties of two-dimensional low-index photonic crystalsAaron Matthews 1,Xue-Hua Wang 1,2,Yuri Kivshar 1,Min Gu 31Nonlinear Physics Center and Center for Ultra-high bandwidth Devices for Optical Systems (CUDOS),Research School of Physical Sciences and Engineering,Australian National University,Canberra,ACT 0200,Australia,phone:+61261258277fax:+61261258588e-mail:afm124@.au 2Institute of Physics,Chinese Academy of Sciences,Beijing 100080,China3Center for Micro-Photonics and Center for Ultra-high bandwidth Devices for Optical Systems (CUDOS),Swinburne Uni-versity of Technology,P.O.Box 218,Hawthorn,Victoria 3122,AustraliaReceived:date /Revised version:dateAbstract We study the bandgap properties of two-dimensional photonic crystals created by a lattice of rods or holes conformed in a symmetric or asymmetric trian-gular ing the plane-wave analysis,we calcu-late a minimum value of the refractive index contrast for opening both partial and full two-dimensional spectral gaps for both TM and TE polarized waves.We also an-alyze the effect of ellipticity of rods and holes and their orientation on the threshold value and the relative size of the bandgap.PACS 42.70.Qs,78.20.Bh,78.20.Ci2Aaron Matthews etal.Fig.1Bandgap spectrum of TM (left)and TE (right)polar-ized waves for a triangular lattice of circular rods (C x =C y =0.575)at ǫ=5.8which is the permittivity of the chalcogenide glass waveguides [11].structures in solid polymers and chalcogenide glass,we explore further the concept of the partial bandgaps of two-dimensional photonic crystals and analyze the ef-fect of ellipticity of rods and holes and their orientation on the critical value and the size of both partial and full spectral bandgaps.As we assume that the materials we are working with are macroscopic and isotropic,we are able to define the refractive index as n =ǫ1/2keeping µ=1.In this paper,we also interchange between the ωa/2πc form and the a/λforms to show more clearly how the ratio increases with a decreasing refractive index,as shown by Li et al.[8].The paper is organized as follows.In Sec.2we con-sider a two-dimensional photonic crystal created by a triangular lattice of dielectric rods in air.In this case,a partial gap appears first for the TM polarized waves,and it is shown to require a relatively low index con-trast.In Sec.3we consider the same problem for a two-dimensional photonic crystal created by air holes drilled in a dielectric slab,where the bandgaps first appear for the TE polarized waves.And last,Sec.4concludes the paper.2Dielectric rods in airFirst,we consider a two-dimensional photonic crystal created by a triangular lattice of circular or elliptic di-electric rods assuming an arbitrary rotation of the ellip-tic rod relative to the lattice symmetry axis.The pho-tonic bandgap spectrum is calculated by solving Maxwell equations by means of the plane-wave expansion method [3,9]employing the well-known numerical algorithm [10].An example of the photonic band-gap structure ofsuch a two-dimensional photonic crystal is shown in Fig.1for the well-known case of a triangular lattice of circularrods.The rods have the electric permittivity ǫ=5.8thatFig.2(a,b)Relative size of the partial bandgaps for TM (left)and TE (right)polarized waves for a triangular lattice of circular (solid curve)and elliptic (other three curves)rods as a function of ǫfor the filing factor 30%.Dotted,dashed,and dot-dashed curves show the results for the elliptic rods (C x =0.65,C y =0.51)with 0o ,15o ,and 30o rotation angle.The critical value for the TM bandgap is ǫ=1.73.Stars indicate the permittivity of polymer [6](at ǫ=2.4)and the permittivity of the chalcogenide glass waveguides [11](at ǫ=5.8).Note the significant difference in scale of the two graphs.corresponds to the values measured for planar waveg-uides made of chalcogenide glass [11].In this case,the frequency spectrum of a lattice of circular rods display several gaps for the TM polarized waves,and two rela-tively large lower bandgaps with the relative size 27.15%and 14.61%,respectively.As the next step,we verify a general concept of the bandgap spectrum of asymmetric lattices [12]and con-sider a triangular lattice made of elliptic rods with an ar-bitrary orientation.In particular,we study the effect of the hole rotation on the value of the partial and absolute bandgaps.These results can naturally be compared with the bandgap spectra of the two-dimensional structures created by circular holes (see below).In a full agreement with the previous studies [13]and recent fabricated de-vices [14],we observe that for the case of dielectric rods in air a deviation of the cylinders from a circular sym-metry produces a reduction of the relative size of the bandgaps.The similar effect is produced by the rod ro-tation,so that larger values of the photonic band gap are observed for the ellipses with smaller or no rotation (dotted curve in Fig.2),and the bandgap becomes max-imum for the case of circular rods.Finally,we study how the ellipticity of the dielec-tric rods in the triangular-lattice photonic crystal maychange the size of the maximum TM bandgap at different values of the filling fraction.We assume that the dielec-tric rods are ellipses with the axes C x and C y ,and wevary the value of C x for a fixed orientation,also changingthe size of C y in order to keep the filling fraction con-stant.Figure 3summarizes some of our results for three values of the filling fraction,44.5%(solid),30%(dot-ted),and 22.5%(dashed).The main result is that the maximum value of bandgap is achieved for a triangular lattice of circular rods (here,at C x =C y =0.575)with the filling fraction 30%.This result is in agreement withBandgap properties of two-dimensional low-index photonic crystals3Fig.3Effect of varying rod ellipticity and filling fraction on the size of the TM bandgap.Shown is the relativesize of the lower bandgap of the TM polarized waves (see Fig.1)as a function of C x ,with C y varying to retain a constant filling fraction,at ǫ=2.Maximum bandgap is found for the circles (C x =C y =0.575)with the filling fraction 30%.all previous studies of triangular-lattice two-dimensional photonic crystals.3Air holes drilled in dielectricNext,we consider the other important case when a two-dimensional photonic crystal is created by a triangular lattice of circular [see Fig.4]or elliptic [see Fig.5]holes drilled in a dielectric slab,assuming an arbitrary rota-tion of the elliptic hole relative to the lattice symmetry axis.As opposed to the case of rods,air holes produce an extremely large bandgap in the TE spectrum of a pho-tonic crystal,this is demonstrated experimentally in the work of zhou et al.[7].The key advantage to this sys-tem as opposed to rods is the frequency position of the bandgap,especially for the case shown in Fig.4,which is the case of the refractive index corresponding to the chalcogenide glass waveguides [11].When it is viewed as a wavelength using the simple conversion ωa/2πc =a/λwe can see that with the bandgap around a/λ=1,the wavelength of the confined light is equal to the size of the lattice giving us the ability to fabricate the planar structures on the scale of the wavelength of interest un-like the common a/λvalues of 0.3to 0.5which would lead to structures 1/3to 1/2of the lattice size in order to produce a bandgap for the same wavelength,a challenge for any fabrication method.Another advantage is in the nature of the holes drilled in a dielectric structure such as physical resistance to a damage.Indeed,the rods which,when being fabricated with the large aspect ratios to exhibit bandgaps,are very sensitive to a physical damage,whereas the hole struc-ture,which has a constant lattice of joined dielectric isFig.4Bandgap spectrum of TM (left)and TE (right)po-larized waves for a triangular lattice of circular holes (C x =C y =0.735)at ǫ=5.8(the chalcogenide glass waveguides).Fig.5(a,b)Relative size of the partial bandgaps for TM (left)and TE (right)polarized waves for a triangular lattice of circular (solid curve)and elliptic (other three curves)holes as a function of ǫand constant filing factor 51%.Dotted,dashed,and dot-dashed curves show the results for the ellip-tic holes (C x =0.8,C y =0.675)with 0o ,15o ,and 30o rota-tion angle.The critical value for the TE bandgap is ǫ=1.95.Stars mark the permittivity of the polymer [6](at ǫ=2.4)and the permittivity of the chalcogenide glass waveguides [11](at ǫ=5.8).Note the scale difference of two graphs.far stronger and therefore more resistant to the rigors of the fabrication processes than free-standing rods.For the photonic crystals fabricated in the chalco-genide glass waveguides [11],round holes,1139nm in di-ameter,forming a trigonal lattice with a lattice spac-ing of 1550nm should provide a photonic bandgap at telecommunications wavelengths.This should also,as shown by the previous studies,be able to support differ-ent guided modes although the adaptation of the struc-ture to the specific optical devices should be analyzed in more details.As follows from Figs.5(a,b),the tradeoffwhen opti-mizing the structures also applies to the hole photonic crystals.In this case,the effect of rotation is insignif-icant and the case of purely circular holes is optimal and produces a bandgap of over 40%at ǫ=10.When comparing Fig.2and Fig.5,we can see that the TM bandgap for the rod structure starts at a lower value of the permittivity than the TE bandgap for holes,and it can be seen that the rod bandgap is larger than the hole bandgap until around ǫ=2.8after which the hole4Aaron Matthews etal.Fig.6Effect of varying hole ellipticity and filling fraction on the size of the TE bandgap.Shown is the relative size of the lower bandgap of the TE polarized waves (see Fig.4)as a function of C x ,with C y varying to retain constant filling fraction at ǫ=2.Maximum band gap is found for the circles (C x =C y =0.735)with the filling fraction 51%.bandgap becomes significantly larger (≈7%at ǫ=10).This should be taken into consideration when choosing an appropriate structure for a given fabrication process.Figure 6shows,by a very steep drop-offon all curves,that ellipticity has a far greater effect in this system than on the system shown in Fig.3.It should be remembered in these two graphs that after the system passes through the point corresponding to a circle it becomes an equiva-lent ellipse rotated by 30o .While this will prove a prob-lem for fabrication the bandgaps are large enough that small errors in ellipticity will not lead to the removal of the bandgap completely.It can also be seen that an error towards larger holes,visualized as a lower filling fraction of dielectric,retains the bandgap size better than a re-duction in the hole size.Our results demonstrate that a threshold value of the permittivity to open a partial bandgap is 1.73which equates to a refractive index of 1.31,and we therefore believe that it is safe to rule out attempts at producing photonic bandgap devices in any system with a refractive index lower than this limit.While ellipticity caused by directional defocusing of the etching beam causes rapid loss of bandgap,imple-menting the optimal system allows a much greater resis-tance to ellipticity using the simple fact that the change in bandgap size vs.ellipticity is fairly constant as we move further from the maximum so an advantageous fill-ing factor will lead to a larger margin for error before the bandgap disappears.4Conclusions We have analyzed the bandgap properties of two-dimensional photonic crystals created by triangular lattices of dielec-tric rods in air and air holes drilled in a planar dielectricslab,for different (including the lowest possible)values of the refractive index ing the plane-wave analysis,we have calculated the critical value of the re-fractive index contrast for opening partial (either for TM or TE polarized waves)and full two-dimensional spec-tral bandgaps.We have analyzed the effect of elliptic-ity of rods and holes and their orientation on the crit-ical value and the size of the bandgaps.In particular,we have predicted that partial bandgaps may appear in the frequency spectrum for the index contrast as low as ǫ=1.73,in the case of rods (for the TM polarized waves),and ǫ=2,in the case of holes (for TE polarized waves).We have demonstrated also that,by reducing the refractive index from some large values (e.g.for Si)to lower value slightly above the threshold,we are able to obtain far more fabricable periodic structures for ex-periment due to an increase in the wavelength-to-period ratio.We believe that our results will be important for the current efforts in fabricating planar photonic-crystal structures based on dielectric materials with low refrac-tive index such as solid polymers,polymer resin,and chalcogenide 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