light manipulation in micro and nano photonic materials ...525286/fulltext01.pdf · to design...

Light manipulation in micro and nanophotonic materials and structures

Zhihui Chen

KTH Royal Institute of TechnologySchool of Biotechnology

Division of Theoretical Chemistry and BiologyStockholm, Sweden 2012

c© Zhihui Chen, 2012TRITA-BIO Report 2012:13ISBN: 978-91-7501-353-4ISSN: 1654-2312Printed by Universitetsservice US AB,Stockholm, Sweden, 2012

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Abstract

Light manipulation is an important method to enhance the light-matter inter-actions in micro and nano photonic materials and structures by generating usefulelectric field components and increasing time and pathways of light propagationthrough the micro and nano materials and structures. For example, quantum wellinfrared photodetector (QWIP) cannot absorb normal incident radiation so thatthe generation of an electric field component which is parallel to the original inci-dent direction is a necessity for the function of QWIP. Furthermore, the increaseof time and pathways of light propagation in the light-absorbing quantum wellregion will increase the chance of absorbing the photons.

The thesis presents the theoretical studies of light manipulation and light-matter interaction in micro and nano photonic materials and structures, aiming atimproving the performance of optical communication devices, photonic integrateddevices and photovoltaic devices.

To design efficient micro and nano photonic devices, it is essential to knowthe time evolution of the electromagnetic (EM) field. Two-dimensional and three-dimensional finite-difference time-domain (FDTD) methods have been adopted inthe thesis to numerically solve the Maxwell equations in micro and nano photonicmaterials and structures.

Light manipulation in micro and nano material and structures studied in thisthesis includes: (1) light transport in the photonic crystal (PhC) waveguide, (2)light diffraction by the micro-scale dielectric PhC and metallic PhC structures(gratings); and (3) exciton-polaritons of semiconductor quantum dots, (4) surfaceplasmon polaritons at semiconductor-metallic material interface for subwavelengthlight control. All these aspects are found to be useful in optical devices of multiplebeam splitter, quantum well/dot infrared photodetectors, and solar cells.

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Preface

The work presented in this thesis has been carried out at the Division of The-oretical Chemistry and Biology, School of Biotechnology, Royal Institute of Tech-nology (KTH), Stockholm, Sweden. This thesis is based on the following papers.

List of papers included in the thesis

Journal papers

Paper I S. Hellstrom, Z.-H. Chen, Y. Fu, M. Qiu, R. Soltanmoradi, Q. Wang,and J. Y. Andersson, Increased photocurrent in quantum dot infrared photodetectorby subwavelength hole array in metal thin film, Appl. Phys. Lett. 96, 231110(2010).

Paper II Z.-H. Chen, Z.-Y. Yu, Y.-M. Liu, P.-F. Lu, and Y. Fu, Multiple beamsplitting to free space from a V groove in a photonic crystal waveguide, Appl. Phys.B-Lasers and Optics 102, 857-861 (2011).

Paper III Z.-H. Chen, S. Hellstrom, Z.-J. Ning, Z.-Y. Yu, and Y. Fu, Excitonpolariton contribution to the Stokes shift in colloidal quantum dots, J. Phys. Chem.C 115, 5286-5293 (2011).

Paper IV Z.-H. Chen, S. Hellstrom, Z.-Y. Yu, M. Qiu, and Y. Fu, Time-resolvedphotocurrents in quantum well/dot infrared photodetectors with different opticalcoupling structures, Appl. Phys. Lett. 100, 043502 (2012).

Paper V Z.-H. Chen, S. Hellstrom, Z.-Y. Yu, and Y. Fu, Comb-shaped photoniccrystal structure for efficient broadband light diffraction and funnelling in solarcells, Sol. Energy Mater. Sol. Cells 99, 316-320 (2012).

Conference papers

Paper I Z.-H. Chen, Y. Fu and Z.-Y. Yu, Improving efficiency of quantum dotinfrared photodetector by using photonic crystal framework in the active layer,The European Conference on Lasers and Electro-Optics (CLEO Europe), Munich,Germany, May 22-26, 2011.

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My contributions to the papers

• I participated in discussions, numerical calculations and manuscript writingof journal paper I.

• I was responsible for the model design, numerical calculations and writingthe first drafts of journal papers II, III, IV, V.

• I was responsible for the model design, calculations and writing of the con-ference Paper I and also for presenting of it in the conference.

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List of papers that are not included in the thesis

Journal papers

Paper I Z.-H. Chen, Z.-Y. Yu, P.-F. Lu, and Y.-M. Liu, Surface diffusion ofSi, Ge and C adatoms on Si (001) substrate studied by the molecular dynamicssimulation, Chin. Phys. B 18, 4591-4597 (2009).

Paper II Z.-H. Chen, Z.-Y. Yu, P.-F. Lu, and Y.-M. Liu, Molecular dynamicssimulations of atomic assembly in the process of GaN film growth, Physica B 404,4211-4215 (2009).

Paper III Z.-H. Chen, Z.-Y. Yu, P.-F. Lu, and Y.-M. Liu, Point defects in re-laxed and strained Si studied by molecular dynamics method, Proc. SPIE 7631,76310T (2009).

Paper IV B.-Y. Jia, Z.-Y. Yu, Y.-M. Liu, Z.-H. Chen, W.-J. Yao, W. Zhao,H. Ye, H. Feng, Electronic structures of GaAs/AlGaAs concentric double rings inapplied electric and magnetic field, Physica E 42, 82-85 (2009).

Paper V H. Ye, P.-F. Lu, Z.-Y. Yu, D.-L. Wang, Z.-H. Chen, Y.-M. Liu, S.-M.Wang, Dislocation-induced composition profile in alloy semiconductors, Solid StateCommun. 150, 1275-1278 (2010).

Paper VI H. Ye, P.-F. Lu, Z.-Y. Yu, Z.-H. Chen, B.-Y. Jia, H. Feng, Y.-M. Liu,Equilibrium critical thickness for a wurtzite InGaN/GaN heterostructure, Super-lattices Microstruct. 48, 58-65 (2010).

Paper VII H. Ye, P.-F. Lu, Z.-Y. Yu, W.-J. Yao, Z.-H. Chen, B.-Y. Jia, Y.-M. Liu, Electronic and optical properties of GaN/AlN quantum dots with adjacentthreading dislocations, Chin. Phys. B 19, 047302 (2010).

Conference papers

Paper I Z.-H. Chen, Z.-Y. Yu, P.-F. Lu, and Y.-M. Liu, Point defects in relaxedand strained Si studied by molecular dynamics method, Asia Communications andPhotonics Conference and Exhibition, Shanghai, China, Nov. 2009.

Paper II Z.-H. Chen, Z.-Y. Yu, P.-F. Lu, and Y.-M. Liu, Directional emissionfrom photonic crystal waveguide with different kinds of the nano-defects, Inter-national Conference on Nanoscience and Technology, (Chinanano 2009), Beijing,China, Sept. 2009.

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Acknowledgments

Firstly, I would like to give my sincere thanks to my supervisor Prof. YingFu who gave me the opportunity to work in these exciting projects in Division ofTheoretical Chemistry and Biology. He led me into the interesting research fieldof nano-photonics and helped me a lot in both my PhD study and life in Sweden.I am really impressed by his wide knowledge and enthusiasm.

I wish to thank Prof. Hans Agren for his co-supervising and creating suchwonderful working environment for us in Division of Theoretical Chemistry andBiology.

Special thanks to Prof. Zhongyuan Yu, Prof. Yumin Liu and Prof. Pengfei Lufor their valuable supervising on my research in Beijing University of Posts andTelecommunications, Beijing, China.

I would also like to thank Prof. Yi Luo, Prof. Faris Gel’mukhanov and Prof.Yaoquan Tu for their valuable suggestions to my research and warm-hearted helpin my life in Sweden.

I would thank Prof. Min Qiu and Prof. Min Yan of School of Information andCommunication Technology in KTH for their valuable help on my computing andsimulating in my research.

I would like to thank Dr. Staffan Hellstrom and Xiangjun Shang who helpedme a lot in the project in Division of Theoretical Chemistry and Biology.

I further like to thank Dr. Zhijun Ning and Chunze Yuan who introduced theprinciple and experiment on quantum dots solar cells to me.

Thanks to all colleagues in Division of Theoretical Chemistry and Biology inKTH and Beijing University of Posts and Telecommunications in China.

Finally, last but not least, I am infinitely grateful to my parents and YangWang, for their self-giving love and support.

Stockholm, April 2012,Zhihui Chen

Contents

1 Introduction 111.1 Optical diffraction and interference . . . . . . . . . . . . . . . . . . 111.2 Dielectric photonic crystals . . . . . . . . . . . . . . . . . . . . . . . 131.3 Metallic PhC structures . . . . . . . . . . . . . . . . . . . . . . . . 151.4 Quantum dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.5 QDs based infrared photodetectors and solar cells . . . . . . . . . . 17

2 Computational approaches and details 212.1 Time-dependant Maxwell equations and boundary conditions . . . . 212.2 Finite-difference time-domain method . . . . . . . . . . . . . . . . . 22

2.2.1 Incident wave sources . . . . . . . . . . . . . . . . . . . . . . 252.2.2 Boundary conditions in FDTD method . . . . . . . . . . . . 262.2.3 Dielectric constant of medium . . . . . . . . . . . . . . . . . 28

2.3 Computational skills in our FDTD simulation . . . . . . . . . . . . 292.4 Discrete Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . 302.5 Finite element method . . . . . . . . . . . . . . . . . . . . . . . . . 31

3 Light-matter interaction in nano photonic structures 333.1 Electron in electromagnetic field . . . . . . . . . . . . . . . . . . . . 333.2 Photons in semiconductors . . . . . . . . . . . . . . . . . . . . . . . 353.3 Wave functions of electrons in nano structures . . . . . . . . . . . . 353.4 Photocurrent in solid-state based QWs/QDs . . . . . . . . . . . . . 383.5 Exciton-polaritons in solution-based colloidal QDs . . . . . . . . . . 41

4 Light manipulation in micro photonic structures 474.1 Dielectric PhC structures . . . . . . . . . . . . . . . . . . . . . . . . 47

4.1.1 Photonic band structure . . . . . . . . . . . . . . . . . . . . 474.1.2 Multiple beam splitting from PhC waveguide . . . . . . . . . 484.1.3 Light diffraction and funneling in solar cell and QDIP . . . . 49

4.2 Metallic PhC structures . . . . . . . . . . . . . . . . . . . . . . . . 534.2.1 Reflective metallic gratings . . . . . . . . . . . . . . . . . . . 544.2.2 Surface plasmon polaritons in metallic gratings . . . . . . . 58

5 Summary of papers 61

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10 CONTENTS

Chapter 1

Introduction

Light is important for our understanding of the universe because light interactswith matter so that the light-matter interaction can tell us a great deal about thenature of the matter. Light-matter interaction can be regarded as the interactionbetween photons and electrons in matter. Large light-matter interaction and in-creased time/pathways of photons propagating in the light-absorbing regions areneeded in photovoltaic devices and light-absorbing devices, such as solar cells andphotodetectors. So, how to manipulate and control light to couple the light to thelight-absorbing materials, e.g., quantum wells (QWs) and quantum dots (QDs), isvery important.

In the middle of 1800’s, James Clerk Maxwell proposed the Maxwell equationsto describe the propagation of an electromagnetic (EM) wave. The concept ofphoton was introduced to interpret the blackbody radiation and photoelectric ef-fect at the beginning of 20th century by Max Planck and Albert Einstein. Lightis understood to have both particle and wave characters depending on differentsituations [1, 2]. The study of light, i.e., optics, has been an important researcharea in modern physics. The theories of optics developed roughly in the followingsequence: (1) ray optics, (2) wave optics, (3) EM optics, (4) quantum optics. Thequantum optics theory can explain most of the optical phenomena; The EM opticstheory always treat light in the classical optics region; Wave optics can be seenas a scalar approximation of EM optics. Ray optics can handle the light whenthe wavelength is much short [3]. Fig. 1.1 shows the relationship between thesetheories.

Fig. 1.2 shows the EM spectrum. In this thesis, we focus on the visible-lightand near/middle Infrared (NIR/MIR) wavelengths.

1.1 Optical diffraction and interference

Photonics mainly focuses on the function and application research of light, includ-ing novel micro and nano photonic materials and devices, and their applications inoptical communication, computing, display technology, energy, biology, and etc.

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12 CHAPTER 1. INTRODUCTION

Ray opticsWave optics

Electromagneticoptics

Quantum optics

Figure 1.1: The theories of optics.

γ rays X rays IRMircro

wave

Radio

waveUV

Visible (380-750nm)

Long radio

wave

10-11 10-8 10-6 10-3 100 103 λ (m)10-5

(a) EM wave spectrum

(c) QWIP(b) Solar cell

Figure 1.2: (a)Electromagnetic wave spectrum. The shaded region shows thewavelength region we have focused on in this thesis. (b) Solar cell (fromhttp://en.wikipedia.org/wiki) (c) quantum well infrared photodetector (QWIP)(from http://www.ir-nova.se/)

1.2. DIELECTRIC PHOTONIC CRYSTALS 13

With the rapid improvement of micro/nano fabrication techniques such aselectron-beam lithography, ion-beam milling, self-assembly techniques of molecu-lar beam epitaxy (MBE) and metal-organic chemical vapor deposition (MOCVD),micro and nano photonic structures, such as dielectric photonic crystals (PhCs),metallic PhC structures, surface plasmon polariton structures, and QWs/QDs havebeen developed extensively. They play key roles in both fundamental research andapplied research including quantum optics/electronics and optoelectronic devices.

Wave-optics based diffraction and interference are two important ways to ma-nipulate light in micro/nano photonic structures/devices. In the limit where thewavelength (λ) is small relative to the structure, “diffraction” refers to deviationsfrom geometric optics due to the fact that λ > 0. For the optical scattering fromperiodic structures such as PhCs, “diffraction” refers to the phenomenon of multi-ple reflected/refracted waves that arises because λ < ∞, and especially in the casewhere λ/2 is comparable to the periodicity of the structures [4]. In this thesis,we use “diffraction” in the latter sense for our PhC structures including reflection,refraction, diffraction and interference in our PhC structures [5, 6]. Diffractiongrating is an optical structure or component with periodic structure, which splitsand diffracts incident light into several beams traveling in different directions bymodifying the phase and amplitude of the incident wave. The directions of thesebeams depend on the geometry of the grating and the wavelength of the light [3].

Optical interference is a phenomenon in which two or more optical waves meet-ing in the same point of space and time can form a resultant wave of larger orsmaller amplitude (i.e. constructive interference and destructive interference). In-terference usually refers to the interaction of waves coming from the same sourceor having the same or similar frequency. The interference pattern that occursunder certain conditions provides a highly directional beam or split beam pattern[7, 8, 9], which is useful in the optical communications. See more details in chapter4.

1.2 Dielectric photonic crystals

The lattice constants of PhCs are usually in the same order as the visible-light andnear-infrared radiation wavelengths, so wave-optics based PhC structures havegood diffraction effects on the solar radiation and near infrared radiation. Forexample, in solar cells, PhCs can diffract incoming beams into highly obliqueangles, which increases the pathways of photons inside the absorbing material;and the light with frequencies outside the photonic bandgap can be refracted andscattered into photonic modes with a high photon density of states in the lattice,which increases the trapped photons and the time spent by photons propagatingin the solar cell. These effects can help to maximize the probability of absorptionand to exceed the ray-optics based (traditional) 4n2 limit for solar cells in a broadregion of wavelengths.

Since the pioneering works of E. Yablonovitch and S. John [10, 11] that pro-


(a) (b) (c)

Figure 1.3: Illustration of (a) 1D, (b) 2D, and (c) 3D photonic crystals.

posed the photonic bandgap in periodic dielectric structures, the term photoniccrystal (PhC) has been used to describe the structures with a periodic dielectricfunction (permittivity ε) in one or more dimensions, as shown in Fig. 1.3.

The materials of PhCs can be either dielectric or metallic materials. Similaras conventional crystals which can provide an energy bandgap for electrons in thecrystal, PhCs can provide energy bandgaps for the photons, thus can control andmanipulate the propagation of light by utilizing the dispersion relation, i.e. bandstructure of PhCs (a relation between the wave vector and the frequency).

One-dimensional (1D) PhCs including periodic stacks of parallel planar multi-layers film (such as Bragg mirror) had been studied before 1987. 1D photoniccrystal bandgap (stop-band) was found by L. Rayleigh in 1887 [12]. Now they areused in highly reflective mirrors/coatings in optical devices, for example, LEDsand VCSEL [13]. They have also been used in grating structures to diffract andreflect optical waves at certain angles [14]. V. P. Bykov speculated the situationsfor two dimensional (2D) and three dimensional (3D) PhCs [15]. The concept of3D photonic crystals was discussed by Ohtaka in 1979 [16]. By 1991, Yablonovitchhad demonstrated the first 3D photonic bandgap in the microwave regime byusing the famous Yablonovite structure [17]. In 1996, T. F. Krauss made thefirst demonstration of a 2D photonic crystal at optical wavelengths [18]. All theseopened the door for fabricating semiconductor material based PhCs. 2D PhCs havebeen used firstly in PhC fibres by Philip Russell to enhance the properties of opticalfibres [19]. Other 3D PhCs were also fabricated, like woodpile structures, inverseopals and stacked 2D PhCs [20, 21, 22]. 3D PhCs also comprise arrays of cubes,spheres, holes of various shapes and other active units such as QDs, organized inlattice structures like those found in natural crystals [23, 24, 25, 26, 27].

PhC cavities are introduced in perfect PhCs to create local modes (or group ofmodes) at a frequency (or some frequencies) within the photonic bandgap (PBG).PhC cavities usually have very high quality factors due to the light resonance,which can enhance the optical amplitude. High-Q PhC cavities can be used invery low-threshold lasers, resonators, antennas, high-sensitivity filters, sensors anddetectors [28, 29, 30, 31, 32], and the PhC cavities are also important for theapplication of cavity quantum electrodynamics and light diffraction and trapping.

1.3. METALLIC PHC STRUCTURES 15

See more details in chapter4.Light whose frequencies are within the PBG can be guided from one location

to another by PhC waveguides (line defects in perfect PhCs). The PhC waveguidecan be used in directional emitter, beam splitter and coupler in free-space opticsor photonic integrated circuits. Guided modes in 2D dielectric PBG crystals havebeen studied in many previous works [33, 34]. See more details in chapter4.

1.3 Metallic PhC structures

1D, 2D and 3D PhCs made of metallic elements have been proposed to create ar-tificial dielectrics with fully controllable dielectric permittivity from optical wave-lengths to the microwave domain. Metallic photonic crystals have properties dif-ferent from those of dielectric ones. Metallic PhC structures always refer to 1D/2Dmetallic gratings or 3D PhCs consisting of periodic metallic units (such as metallicspheres). Reflective metallic gratings based on geometry optics, i.e., conventionaloptical diffraction gratings lithographically patterned on the tops of photodetec-tors [35, 36] were proposed at the end of 20th century and used in the real devicesnow.

With the rapid improvement of nanofabrication techniques, wave-optics basedmetallic diffraction gratings and surface Plasmon polaritons (SPPs) structureshave been extensively investigated both theoretically and experimentally. Sur-face plasmon exists as electron oscillations at the interface between two materi-als whose signs of real part of dielectric constants are different. When it inter-acts (couples) strongly with the light (photon), SPP is created. Many nano-scale metallic structures such as nano-particle chains [37] and nano-wires [38]have been developed, which are able to be used in sub-wavelength optical de-vices, such as plasmonic lenses [39, 40, 41, 42], surface plasmonic waveguides[37, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55], plasmonic light sources[56, 57, 58, 59, 60], and active plasmonic devices [61, 62, 63, 64, 65, 66, 67, 68].

Nano-scale optical components for high-density photonic integrated circuits aremore and more important according to Moore’s law. From wave-optics point ofview, when the dimensions of an optical component are similar to or smaller thanthe wavelength of the light, the light propagation will be interfered by opticaldiffraction [2]. This effect limits the minimum size of optical devices as well as thedensity of photonic integrated circuits. These restrictions in the subwavelengthoptics regime are very critical to the conventional optical production (this is alsocalled as “diffraction limit”) [69, 70, 71, 72, 73, 74, 75]. The field of plasmonicsis becoming an exciting area for the application of surface/interface plasmons inmerging the fields of photonics and electronics in nanoscale[70, 76]. SPP canbe constructed into nanoscale photonic circuits to carry both optical signals andelectric currents [77, 78] and overcome the diffraction limit effectively. This canminimize the size of the optical components to the sub-100nm scale which benefitsthe integration of the optical components in micro or nano scale electronic systems


[70, 71, 72, 73]. Some practical applications like light guiding and manipulation inthe nanoscale, bio-detection at molecular level have been realized [79, 80, 81, 82,83].

The dispersion relationship of an SPP at a dielectric-metal interface is

ksp =ω

c

[εdεmetal

εd + εmetal

]1/2

(1.1)

where ω is the frequency of the EM wave, and c is the speed of light in vacuum. εd

is the positive permittivity of dielectric material, and εmetal is a complex dielectricfunction of metal. To excite a SPP, momentum conservation must be satisfied sothat the wave vector of the incident light paralleling to the surface k|| should equalto the SPP wave vector ksp. However, for ordinary light shining on the smoothsemiconductor-metal interface,

ksp > k|| (1.2)

Kretschmann [84] and Otto [85] configurations are normally used to provide thenecessary momentum conservation. Another method is to use periodic corruga-tions in the metal surface, where the periodicity of the structure leads to thephase matching. The diffraction gratings made of metallic film with hole arrays[77, 86, 87] have been used in QW and QD infrared photodetectors (QWIP andQDIP) to diffract the normal-incident infrared radiation and create strong EMfield enhancement in the near field region due to the subwavelength mode confine-ment. Plasmonic excitation using metallic nanoparticles has also been extensivelystudied to harvest light for solar cell applications [88, 89, 90]. See more in Chapter4.

1.4 Quantum dots

Besides SPP, when a strong coupling between EM waves and excitons in low-dimensional semiconductor structures (such as QDs) occurs [91, 92, 93], the exciton-polaritons created in the QDs can also have the characteristics of both photonicsand electronics. This exciton-polariton effect offers another solution to overcomethe diffraction limit.

QD is an artificial creation of quantum confinement of a few electrons, holes orexcitons in three spatial directions. Based on the advanced semiconductor mate-rials grown techniques such as MBE and MOCVD, III-V semiconductor (galliumarsenide (GaAs)/indium arsenide (InAs)) QDs can be fabricated [94]; II-VI semi-conductor (CdS/CdSe) QDs for solar cells can be produced by chemical synthesis[95]. Fig. 1.4 (a) and (b) shows these two types of QDs.

Generally speaking, the typical size of a QD is about 2 to 18 nm in radius. Bycontrolling the geometrical size and shape, the properties of QDs are relatively easyto be engineered. The emission peak (resonance) frequency of a QD is sensitive toboth its size and composition. While reducing the size of a semiconductor material

1.5. QDS BASED INFRARED PHOTODETECTORS AND SOLAR CELLS 17

(a)xz

Solid-state based QDs

(b)

Solution-based QDs

electrolyteITO

ITO

cathode

e-

anodeTiO2 Quantum dot

PtQWs/QDs

UnderfillSubstrate

Thinned substrate

PassivationIn bumpROIC

(c) (d)(c) (d)Figure 1.4: (a) Solid-state based QDs, (b) chemically synthesized solution-basedQDs, (c) QW/QDIPs, (d) QDs solar cell.

to a small size approaching its exciton Bohr radius, the exciton will not be ableto move freely due to the quantum confinement, resulting in quantized energyspectra, sharp density of states, and spatially localized wave functions. Becauseof these electronic and optical properties, QDs have many important applications:diode lasers, light emitting devices (LED), optical amplifiers, photovoltaic devices(solar cells and photodetectors in Fig. 1.4 (c) and (d)), quantum calculations andcomputers, and biological sensors [96, 97, 98, 99, 100, 101, 102]. In this thesis, wefocus on light-matter interaction in the QDs infrared photodetectors (QDIPs) andQDs solar cells.

1.5 QDs based infrared photodetectors and solar

cells

Infrared photodetectors made of semiconductor materials generally contain solid-state-based QWs or QDs which are fabricated by MBE and MOCVD methods.The first clear demonstration of QWIPs was made in 1987 [103]. Since then,tremendous progress was made by the Bell Laboratories’ group (see [104] and ref-erences therein). Now, large focal plane arrays (FPAs) with excellent performancehave been fabricated [35, 105, 106, 107, 108, 109, 110, 111, 112]. The detection


mechanism in both QWIPs and QDIPs relies on the intraband photoexcitation ofelectrons from confined states in the conduction band wells to the extended statesin continuous band.

There are two types of the photocarrier extraction methods: photoexcited car-riers are swept out of the light absorbing region by (1) an externally applied electricfield (photoconductive), and (2) built-in internal field due to inversion asymmetry(photovoltaic). QWIP and QDIP adopt the photoconductive detection mecha-nism, where photoexcited carriers are moved out of the QW/QD region by anexternally applied electric field [113]. QDIPs are similar to GaAs/AlGaAs QWIP,with the QWs replaced by the self-assembled InAs QDs in GaAs matrix. An idealQDIP is expected to be substantially superior to a QWIP because of the advantageof the normal incidence response for QDIPs.

In common infrared focal plane arrays (FPAs), a near-transparent epoxy un-derfill is used between pixels for mechanic support as shown in Fig. 1.4(c) [114].(The refractive index of epoxy is about 1.5). SiO2 or Si3N4 thin films are alsoused to cover on the pixels as passivation-materials whose optical absorptions arealso very small [112, 115]. Indium bumps serve as the electrical interconnectionbetween detector pixels and readout integrated circuits (ROIC) unit cells, and thedetector substrate is thinned to reduce the crosstalk from substrate.

Solar cells are devices converting solar energy into electricity. It has been de-veloped from the first generation solar cells, i.e., p-n junction silicon cells, then thethin-film solar cells, to the third generation solar cells, which include nanocrys-tal solar cells, QD/dye-sensitized hybrid solar cells, as well as polymer solar cells[95, 116, 117, 118, 119, 120].

QDs solar cells can be made of either solid-state-based QDs (Fig. 1.4 (a)) orchemically synthesized solution-based QDs as shown in Fig. 1.4 (b,d). Differentfrom the QDIPs, interband photoexcitation of electrons from valence band to theconduction band corresponding to solar radiation wavelength is used in solar cells.The solid-state QDs can be embedded in p-n junction made of semiconductor ma-terials to form a p-i-n solar cell, the photoexcited electrons can be moved by thebuilt-in internal field. However, for a solution-based QDs solar cell, it is an n-typesolar cell and the efficiency depends on the electrons’ diffusion from conductionband of QDs to those of other materials such as TiO2 and ITO glass-electrodes. Aliquid redox electrolyte is filled between the two electrodes, creating an environ-ment for the electrons re-generation [121].

The quantum confinement effect and multiple exciton generation (one photoncreates two or more excitons) [122] in QDs can enhance the light-matter interactionin QDs and enlarge photocurrents in QDIPs and solar cells. The continuous energybands in bulk semiconductor materials will split into quantized energy levels in theQDs and the band gap of QD will increase with the reducing of size. Therefore,the absorption wavelength of QDs can be tuned by the size. So the solar cell madeof different size of QDs can absorb light efficiently in a broader wavelength region.

The difference between photovoltaic QD solar cell and QDIP is the operating

1.5. QDS BASED INFRARED PHOTODETECTORS AND SOLAR CELLS 19

wavelength that depends on whether the intraband or interband transition willhappen in QDs.

Chapter 2

Computational approaches anddetails

2.1 Time-dependant Maxwell equations and bound-

ary conditions

Firstly, we study the wave propagation of the electromagnetic (EM) wave in thephotonic structures by solving the Maxwell equations, which are a group of fourequations for the electric filed and magnetic field intensities E and H , the electricand magnetic flux densities D and B. Let ρ be the volume charge density, j theconduction current density [123], the differential forms of the Maxwell equationsare:

(1) Gauss’ law for electricity

∇ ·D = ρ (2.1)

(2) Gauss’ law for magnetism

∇ ·B = 0 (2.2)

(3) Faraday’s law of induction

∇×E = −∂B

∂t(2.3)

(4) Ampere’s law

∇×H =∂D

∂t+ j (2.4)

Other relations are:

B = µH , D = εE , j = σE (2.5)

Here µ is the magnetic permeability, ε is the electric permittivity, σ is theelectric conductivity. At a surface of discontinuity, the boundary conditions are asfollows:

21

22 CHAPTER 2. COMPUTATIONAL APPROACHES AND DETAILS

(1) For the vector DDn,1 −Dn,2 = ρ (2.6)

where ρ is the surface charge density, and “n” means the normal direction. Thenormal component of D changes across the surface if the surface charge densityρ 6= 0.

(2) For the vector BBn,1 = Bn,2 (2.7)

the normal component of B is continuous across the surface of discontinuity.(3) For the vector E

Et,1 = Et,2 (2.8)

the tangential component of E is continuous across the surface. “t” means thetangential direction.

(4) For the vector HHt,1 −Ht,2 = j (2.9)

where j is the surface current density. The tangential component of the vector Hchanges if the surface current density j 6= 0.

Several powerful numerical methods have been developed to solve the Maxwell’sequations: (1) Finite element method (FEM) is often used to solve Maxwell differ-ential equations in the frequency domain [124]; (2) Plane wave method is employedto simulate periodic structures [24, 26, 27, 99, 125, 126]; (3) Finite-difference time-domain (FDTD) method is a direct time-domain solution of the Maxwell’s dif-ferential equations on spatial grids [123, 127, 128, 129, 130, 131, 132, 133]. Thesimulation in this thesis is based on the FDTD technique.

2.2 Finite-difference time-domain method

The FDTD method is a time-domain EM analysis method. It can solve rigor-ously the Maxwell’s equations without any approximations or theoretical restric-tions. FDTD therefore can provide more accurate information about the EM fieldthan other approximate methods. The FDTD method solves the time-dependentMaxwell’s equations by first discretizing the equations via central differences ap-proximations in time and space, then numerically solving these partial differentialequations [123, 127]. It can find the time-dependent solutions in a long time rangewith a single simulation. Furthermore, a fast Fourier transform (FFT) or dis-crete Fourier transform (DFT) of the time-dependent solutions will result in thefrequency-dependent solutions. Light propagation in many micro/nano structuresmade of either active or passive materials, such as PhCs and QDs, can be simu-lated by FDTD method. In the following, basic equations for 2D and 3D FDTDmethods will be introduced.

Yee lattice was first proposed in 1966 [127] to store different field componentsat different spatial grid locations. The forms of the Yee lattice in 3D cubic and2D square are shown in Fig. 2.1 and Fig. 2.2.

2.2. FINITE-DIFFERENCE TIME-DOMAIN METHOD 23

(i,j,k+1)

(i+1,j+1,k+1)

(i+1,j+1,k)

(i,j,k) (i+1,j,k)

(i,j+1,k+1)

Ez

Ex

Ey

Hy

Hz

Hx

Figure 2.1: Illustration of a 3D Yee lattice used for 3D FDTD, different field com-ponents are located at different locations in a grid. The electric field componentsare at the edges of the cube, and the magnetic field components are at the centersof faces.

Ez

Ex(i,j)

Hy

(i+1,j)

(i,j+1) (i+1,j+1)

Figure 2.2: Illustration of a 2D Yee lattice used for TE-polarization, differentfield components are located at different locations in a grid. The electric fieldcomponents are at the edges of the square, and the magnetic field components areat the center.


In 3D case, we denote a space domain (x, y, z) = (i : i + 1, j : j + 1, k : k + 1),and a space point as (i, j, k) = (iδx, jδy, kδz), where, δx, δy, and δz are spaceincrements in the x, y, and z directions, respectively, i, j, and k are integers. Thetime dimension is discretized as t = nδt (n is an integer). A function u of spaceand time at a point in the spatial grid:

u(iδx, jδy, kδz, nδt) = uni,j,k (2.10)

Yee used the central-difference expressions for the space and time derivatives.Considering the first partial space derivative of u in x direction, at the time nδt,we get:

∂u(iδx, jδy, kδz, nδt)

∂x=

uni+1/2,j,k − un

i−1/2,j,k

δx+ O[(δx)2] (2.11)

The ±1/2 increment of the i subscript denotes the space finite-difference over±1/2δx. Similarly, while the ±1/2 increment is used in the n subscript (time-coordinate), we get:

∂u(iδx, jδy, kδz, nδt)

∂t=

un+1/2i,j,k − u

n−1/2i,j,k

δt+ O[(δt)2] (2.12)

Using the above expressions, the Maxwell’s equations in 3D can be expressedas

Ex|n+1i,j,k =

1− σ′i,j,kδt

2εi,j,k

1 +σ′i,j,kδt

2εi,j,k

Ex|ni,j,k +

δtεi,j,k

1 +σ′i,j,kδt

2εi,j,k

Hz |n+1/2i,j+1/2,k

−Hz |n+1/2i,j−1/2,k

δy

−Hy |n+1/2i,j,k+1/2

−Hy |n+1/2i,j,k−1/2

δz

(2.13)

Ey|n+1i,j,k =

1− σ′i,j,kδt

2εi,j,k

1 +σ′i,j,kδt

2εi,j,k

Ey|ni,j,k +

δtεi,j,k

1 +σ′i,j,kδt

2εi,j,k

Hx|n+1/2i,j,k+1/2

−Hx|n+1/2i,j,k−1/2

δz

−Hz |n+1/2i+1/2,j,k

−Hz |n+1/2i−1/2,j,k

δx

(2.14)

Ez|n+1i,j,k =

1− σ′i,j,kδt

2εi,j,k

1 +σ′i,j,kδt

2εi,j,k

Ez|ni,j,k +

δtεi,j,k

1 +σ′i,j,kδt

2εi,j,k

Hy |n+1/2i+1/2,j,k

−Hy |n+1/2i−1/2,j,k

δx

−Hx|n+1/2i,j+1/2,k

−Hx|n+1/2i,j−1/2,k

δy

(2.15)

Hx|n+1/2i,j,k =

1− ρ′i,j,kδt

2µi,j,k

1 +ρ′i,j,kδt

2µi,j,k

Hx|n−1/2i,j,k +

δtµi,j,k

1 +ρ′i,j,kδt

2µi,j,k

(Ey |ni,j,k+1/2

−Ey |ni,j,k−1/2

δz

−Ez |ni,j+1/2,k−Ez |ni,j−1/2,k

δy

)(2.16)

Hy|n+1/2i,j,k =

1− ρ′i,j,kδt

2µi,j,k

1 +ρ′i,j,kδt

2µi,j,k

Hy|n−1/2i,j,k +

δtµi,j,k

1 +ρ′i,j,kδt

2µi,j,k

(Ez |ni+1/2,j,k

−Ez |ni−1/2,j,k

δx

−Ex|ni,j,k+1/2−Ex|ni,j,k−1/2

δz

)(2.17)

Hz|n+1/2i,j,k =

1− ρ′i,j,kδt

2µi,j,k

1 +ρ′i,j,kδt

2µi,j,k

Hz|n−1/2i,j,k +

δtµi,j,k

1 +ρ′i,j,kδt

2µi,j,k

(Ex|ni,j+1/2,k

−Ex|ni,j−1/2,k

δy

−Ey |ni+1/2,j,k−Ey |ni−1/2,j,k

δx

)(2.18)


where ε, σ′, µ, and ρ′ are material parameters mean electric permittivity, electricconductivity, magnetic permeability, equivalent magnetic resistivity, respectively.Based on the above equations, the present value of a field component at one latticepoint depends on its previous value and the previous values of the other fieldcomponents at adjacent spatial points.

For 2D simulations, the EM wave propagation can be studied separately in twodifferent polarizations: transversal magnetic (TM) and transversal electric (TE),depending on if the electric filed or the magnetic field is perpendicular to the planewhere the structure is defined. Usually for 2D photonic crystal structures, if EMwaves are propagating in the plane-of-periodicity, in which the structural period-icity can be observed (also referred to as the transverse plane), TE means thatall (two) E field components are in the transverse plane, while a third magneticfield component is along the longitudinal direction. TM is defined similarly [4].According to this definition, for our 2D cases in this thesis, a TE mode has Ex,Hy, Ez components; a TM mode has Hx, Ey, Hz components (Note that EM wavepropagates in z direction, x− z plane is used for 2D domain definition from hereto the following). Take the TE situation shown in Fig. 2.2 as an example, theequations can be reduced as follows:

Ex|n+1i,j =

1− σ′i,jδt

2εi,j

1 +σ′i,jδt

2εi,j

Ex|ni,j +

δtεi,j

1 +σ′i,jδt

2εi,j

Hy|n+1/2i,j+1/2 −Hy|n+1/2

i,j−1/2

δz(2.19)

Ez|n+1i,j =

1− σ′i,jδt

2εi,j

1 +σ′i,jδt

2εi,j

Ez|ni,j +

δtεi,j

1 +σ′i,jδt

2εi,j

Hy|n+1/2i−1/2,j −Hy|n+1/2

i+1/2,j

δx(2.20)

Hy|n+1/2i,j =

1− ρ′i,jδt

2µi,j

1 +ρ′i,jδt

2µi,j

Hy|n−1/2i,j +

δtµi,j

1 +ρ′i,jδt

2µi,j

(Ex|ni,j+1/2 − Ex|ni,j−1/2

δz−

Ez|ni+1/2,j − Ez|ni−1/2,j

δx)

(2.21)

2.2.1 Incident wave sources

There are many excitation sources for different practical situations, such as (1) fieldsource and current source; (2) impulse with very broad wavelength region, pulsewith finite wavelength region and continue wave (CW) with only one wavelength;(3) point source, line source and plane wave source; (4) Gaussian, rectangle andmultimode profiles. The excitation is composed of both spatial and temporalcomponents. E-field sources in 1D-line and 2D-plane are used for 2D and 3DFDTD simulations in this thesis. If the periodic boundary is used and the line orplane source covers the whole width of the computational domain, then the planewave is simulated. The pulse source having the following Gaussian time envelopeis:

sin(ω0t)e−((t−t0)∆ω)2/2 (2.22)


where the source center frequency ω0 and the pulse bandwidth ∆ω are included.Some PhC structures are usually very dispersive, if the pulse source covers toomany wavelengths (with very large bandwidth), the pulse will be broadened quicklyduring the simulation. This will lead to an unstable result in the FDTD simulations[130, 131]. If the ∆ω is zero, the source becomes a CW source. CW simulation isvery useful when we want to study the wave propagation in the photonic materialsand structures at some specific wavelengths or when the pulse study is too coarsefor some situations.

2.2.2 Boundary conditions in FDTD method

Proper boundaries are necessary for minimizing the computational domain andgetting accurate results during the FDTD simulations. There are several boundaryconditions (BCs) in common FDTD simulation:

(1) Periodic BCs are generally used when both the structures and EM fieldsare periodic and injected radiation is in the normal direction to the surface of thestructure. It can be chosen in one or more directions so that the simulation isequivalent to be performed on an infinite structure composed of the basic compu-tational domain repeated endlessly in one or more dimensions.

E(r + a) = E(r) (2.23)

where a is the period.(2) Metal BCs are used to specify boundaries which are perfectly reflective in

the optical wavelength, it allows no energy to escape the simulation volume alongthat boundary.

(3) Symmetric BCs are used when both the structure and source are symmetricin one plane or more planes. It creates mirrors for the electric field, and anti-mirrorsfor the magnetic field. The opposite situation is the asymmetric BCs.

(4) Bloch BCs should be used when the structures and the EM fields are peri-odic, but a phase shift exists between each period. For example, when launchinga plane wave at an angle to a periodic structure, the EM field propagating in thestructure can be expressed by:

E(r + a) = eik·aE(r) (2.24)

where k is the corresponding Bloch wave vector (phase shift), and a is the periodiclattice constant (period).

(5) Perfectly matched layer (PML) absorbing BCs perform total absorption ofthe waves touching them and avoid the interference between the reflected fieldsand forward fields inside the computational domain. PML is the most effectiveabsorbing BC in the simulation of photonic structures. It splits electric or mag-netic field components in the absorbing boundary region and assigns losses to theindividual split field components [134, 135].


In 2D situation, considering TE polarization case, where the relevant fieldcomponents are Ex, Hy, Ez (assume light is injected in +z direction), Maxwell’sequations reduce to:

ε0∂Ex

∂t+ σEx =

∂Hy

∂z

ε0∂Ez

∂t+ σEz = −∂Hy

∂x

µ0∂Hy

∂t+ σ∗Hy =

∂Ex

∂z− ∂Ez

∂x(2.25)

where ε0 and µ0 are free space permittivity and permeability, and σ, σ∗ are pos-sible electric conductivity and magnetic loss assigned to free space. The PMLmodification of Maxwell equations are as follows:

ε0∂Ex

∂t+ σzEx =

∂(Hyx + Hyz)

∂z

ε0∂Ez

∂t+ σxEz = −∂(Hyx + Hyz)

∂x

µ0∂Hyx

∂t+ σ∗xHyx = −∂Ez

∂x

µ0∂Hyz

∂t+ σ∗zHyz =

∂Ex

∂z(2.26)

where σx, σz denote electric conductivities and σ∗x, σ∗z denote magnetic losses.In 3D situation, all six Cartesian field components are split, and the PML

modification of Maxwell equations yields 12 equations, as follows:

µ0∂Hxy

∂t+ σ∗yHxy = −∂(Ezx + Ezy)

∂y(2.27)

µ0∂Hxz

∂t+ σ∗zHxz =

∂(Eyx + Eyz)

∂z(2.28)

µ0∂Hyz

∂t+ σ∗zHyz = −∂(Exy + Exz)

∂z(2.29)

µ0∂Hyx

∂t+ σ∗xHyx =

∂(Ezx + Ezy)

∂x(2.30)

µ0∂Hzx

∂t+ σ∗xHzx = −∂(Eyx + Eyz)

∂x(2.31)

µ0∂Hzy

∂t+ σ∗yHzy =

∂(Exy + Exz)

∂y(2.32)

ε0∂Exy

∂t+ σyExy =

∂(Hzx + Hzy)

∂y(2.33)

ε0∂Exz

∂t+ σzExz = −∂(Hyx + Hyz)

∂z(2.34)


ε0∂Eyz

∂t+ σzEyz =

∂(Hxy + Hxz)

∂z(2.35)

ε0∂Eyx

∂t+ σxEyx = −∂(Hzx + Hzy)

∂x(2.36)

ε0∂Ezx

∂t+ σxEzx =

∂(Hyx + Hyz)

∂x(2.37)

ε0∂Ezy

∂t+ σyEzy = −∂(Hxy + Hxz)

∂y(2.38)

where σ and σ∗ are variables describing the absorption of PML.

2.2.3 Dielectric constant of medium

From the Ref. [115], we can find many optical constants of common materials insolid-state, including the n and k values at different wavelengths. For example, thek values for silicon (Si) and GaAs bulk are very small in the NIR wavelength region,and the optical loss of the electromagnetic field due to the optical absorption is thussmall, so we can neglect the optical absorption while calculating the propagationof the incident radiation in Si or III-V materials, ε ≈ n2.

However, for metals, they are very dispersive materials which can be describedby the Lorentz model or Drude model of the dielectric constants, some parameterscan be found in [136]. The formulas are as follows:

Lorentz Model: For single-pole,

ε(ω) = ε∞ +(ε0 − ε∞)ω2

p

ω2p − ω2 − 2iωδp

(2.39)

where ε0 is the static permittivity, ε∞ is the relative permittivity at infinite fre-quency, ωp is the frequency of the pole pair (the resonant frequency of the medium),and δp is the damping coefficient.

Drude Model: For single-pole,

ε(ω) = 1.0− ω2p

ω(ω + iγ)(2.40)

where ωp is the bulk plasma frequency, γ is the damping rate.In order to describe the exciton-polariton contribution to the dielectric constant

of QDs, we use the frequency-dependent effective dielectric constant [137, 138] asshown below:

εQD(ω) = ε∞

[1 +

6ωLT

π2(ωex − ω − iγ)

](2.41)

where ε∞ is the dielectric constant of the QD material (bulk), ~ωex is the excitonenergy, and ωLT is the exciton-polaritonic transverse-longitudinal splitting of thepolariton dispersion branches (the width of the polaritonic stop band).

2.3. COMPUTATIONAL SKILLS IN OUR FDTD SIMULATION 29

For FDTD study of the propagation of an incident EM wave across the QD,Eq. (2.41) has been reformatted to be

εQD(ω) = ε∞

[1 +

6ωLTωex

π2(ω2ex − ω2 − iγω)

](2.42)

in the vicinity of the exciton resonance.We have to fit the parameters in ε expression by using the n and k values in

different frequency ranges.

2.3 Computational skills in our FDTD simula-

tion

In additions to the above mentioned computational aspects, the FDTD simulationrequires further input parameters, such as: the size of the computational domain,the boundary condition(s), spatial grid sizes, temporal grid sizes, and the lengthof time (time steps). In the following, we will introduce how to choose parametersfor effective computations and how to check the simulation results during thecomputing progress in addition to the common method of comparing the resultswith literatures. There are several simulation skills that have been used to getmore accurate results.

(1) Air domain test: In FDTD simulations, it is quicker to run a simulationwithout any fine structures inside the computational domain. From this air-domaintest, we can check the optimized parameters for the desired wavelength, EM com-ponents, power and amplitude of the light source, and whether the boundaries(periodic or PML) are set rightly. While considering a complex structure in thecomputing, finer grids should be used; if the metal or other dispersive materialis used in the simulation, there should be larger space between the PML and thestructures. A desired PML reflection value and the number of layers are alsoneeded to be properly set.

(2) Longer time test: Running a longer-time test simulation to make surethat steady states are reached without dispersion.

(3) Smaller temporal and spatial grid test: The spatial grid must be smallenough to resolve the shortest wavelength of the light to be simulated. This is gen-erally decided by the wavelength in the material(s) to be simulated. Moreover, insome cases, it can be related to the geometry of the photonic structures. Typically,the size of grid must resolve the wavelength in time and is less than λ/10 (λ isthe wavelength in the largest-ε material in the computational domain). Runninga smaller-grid simulation (including both temporal and spatial grids) to see if theresult remains the same as the coarser-grid simulation, and also check if it meetsthe source settings or Fresnel equations, etc. Then the expected grids scales whichcan lead to accurate results without dispersion will be proper set.

(4) Relation between temporal grid and spatial grid size: Smaller spa-tial grid, more accurate results will be got. However, more computer memory and


time will be also required. To obtain a stable FDTD simulation, one must obeythe Courant condition which relates the spatial and temporal step size:

δt ≤ 1

c√

( 1δx

)2 + ( 1δy

)2 + ( 1δz

)2(2.43)

where c is the speed of light in vacuum. Smaller spatial grid size gives smallertemporal grid size. Thus, more time is needed to reach the steady state.

(5) The conservation of energy: If we have not considered the absorption ofthe material and not involved active source inside the system, the energy flowingin the system must be the same as the energy flowing out of the system when thesteady state is reached. The Poynting vector shows the flow of energy:

S = E ×H (2.44)

(6) CW simulation instead of pulse simulation: For more accurate resultsin frequency domain, CW simulation scanning is better than the pulse simulation,because the pulse generally has a wide frequency and narrow pulse width, thusmay cause more unstable progress when the incident wave meets the geometries.The FFT or DFT calculation depends very much on the amount of samples andthe length of time.

(7) Boundary conditions: The boundary conditions at the edges of thecomputational domain must be carefully set and checked, especially the PMLabsorbing BC. While considering the line or plane wave source, the PML in x orx− y direction can cause light scattering due to the truncation of the source. Andthe dispersive material such as metal should be set far from the PML to obtainmore accurate results.

2.4 Discrete Fourier Transform

In a pulse simulation, we usually transform the temporal results from the FDTDcalculation to the frequency domain by using the discrete Fourier transform (DFT).Assuming E(nδt) as the time response of the electromagnetic component from theFDTD calculation, its DFT is given by

E(N,ω) =N∑

n=0

E(nδt) exp(−inωδt) (2.45)

where δt is the FDTD time interval, N is the number of time steps in the sim-ulation. If the signal time is infinitely long, its discrete-time Fourier transform(DTFT) is

E(∞, ω) =∞∑

n=0

E(nδt) exp(−inωδt) (2.46)

2.5. FINITE ELEMENT METHOD 31

which provides a continuous-time Fourier transform of the function E(t):

E(ω) =

∫ ∞

0

E(t) exp(−iωt)dt (2.47)

DFT integration should be run up to the time when the FDTD simulationstops. According to the uncertainty principle, if we use only a finite-length E(nδt)with n ≤ N , this finite sampling time will result in an inadequate frequencyresolution in the Fourier spectrum, which is proportional to 1/(Nδt) [139]. Someoscillations and/or errors may occur to the DFT results if the simulation is stoppedtoo early. So, it is necessary to run the simulation for a sufficiently long time toget a reasonable frequency resolution. At least, the simulation should be run longenough for the time-domain fields to decay.

According to the Nyquist-Shannon sampling theorem, if the signal x(t) has ahighest frequency of B Hz, the time interval for the sampling should be less than1/(2B) second [139]. Considering the signal E(nδt) (sampling interval δt) fromthe FDTD simulation as an example, if its bandwidth is B, the sufficient conditionfor exact reconstruction from samples should satisfy:

δt < 1/(2B) (2.48)

Moreover, we should choose the nonzero time-domain signals to do the FFT orDFT calculations.

2.5 Finite element method

The finite element method (FEM) is also used to numerically solve the partialdifferential equations (PDEs). FEM usually uses unstructured meshes, which isdifferent from the squared grids used in FDTD. For example, the 2D computationaldomain is always divided into triangles in FEM, so it is easy for FEM to solvePDEs on complicated geometries. The time-resolved results cannot be achievedstraightforward in FEM because all FEM codes use frequency-domain methods,i.e., steady state of EM wave at a single wavelength will be obtained in FEM. Itshould repeat the simulations at different wavelengths to get the results over abroad wavelength range. [140].

Chapter 3

Light-matter interaction in nanophotonic structures

The interaction of light with matter can take many forms: (1) light absorptionand fluorescence based on quantum optics (absorption and emission of photons);(2) light scattering including reflection, refraction and diffraction based on waveoptics. If there is no polariton induced during the light-matter interaction, thematerial is normally referred to as passive, while the material is called active whenpolariton becomes induced.

In this chapter, we focus on the light absorption and fluorescence. The lightscattering will be introduced in Chapter 4. We first show macroscopic light-matterinteraction phenomena in EM optics. After that, quantum mechanism related tothe light absorption and emission in nano photonic structures (such as QWs/QDs)is introduced.

3.1 Electron in electromagnetic field

The nature of light-matter interaction in nano photonic structures is the electron-EM field interaction. The Hamiltonian describing an electron with an electroniccharge −e in the electromagnetic field of (A, φ) is

1

2m0

(p− eA)2 − eφ + V0(r)

=p2

2m0

− eφ + V0(r)− e

m0

A · p +ie~2m0

∇ ·A +e2

2m0

A2 (3.1)

where V0(r) is the potential energy of the system in the darkness, m0 the freeelectron mass, and p = −i~∇ is the electron momentum. In the above equation,p2/(2m0) + V0(r) is the Hamiltonian of electron in the darkness. For the electro-magnetic field of optical radiation, the scale potential φ is small and neglected, the∇ ·A is also neglected according to the Lorentz gauge[141]. Considering:

|eA · pm0

| : | p2

2m0

| = 2e|A|p

33

34CHAPTER 3. LIGHT-MATTER INTERACTION IN NANO PHOTONIC STRUCTURES

0

500

1000

1500

2000

2500

0 500 1000 1500 2000 25000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0sola

r spectr

a (

Wm

-2µm

-1)

(a)

outside atmosphere

sea level

e∗

A/

p (

10

-6)

(b)

wavelength (nm)

Figure 3.1: (a) Solar radiation spectra and (b) ratio of e|A|/p in solar cells. Theregion between two dashed lines shows the visible light region: 380-750 nm.

|e2A2

2m0

| : |eA · pm0

| = e|A|2p

(3.2)

the ratio of e|A|/p shows the electron-EM wave (light-matter) interaction.

Fig. 3.1(a) shows the solar radiation spectra.

Using an electron speed of 104 m/s (in common semiconductors), m0 = 9.1 ×10−31 kg, e = 1.6× 10−19 C in Eqs. (3.3), we got the plot of ratio e|A|/p as shownin Fig. 3.1(b).

W = nph~ωc , e|A| = e

√nph~2εω

, ω = 2πc/λ (3.3)

As can be observed in Fig. 3.1(b), e|A|/p in the whole solar spectral range isvery small so that in the following we only consider the light matter interaction inthe form of A · p and the term containing A2 is neglected.

The value of e|A|/p at sea level is much smaller at some wavelengths due tothe light absorption by the atmosphere. e|A|/p is large in visible-light regionand some NIR wavelength regions. In this thesis, we tried to find a good optical

3.2. PHOTONS IN SEMICONDUCTORS 35

E1

E2

E1

E2hνhν

absorption emission

(photon)

(a) (b)

Figure 3.2: Illustration of light (photon) absorption and emission.

coupling structure to enhance the light-matter interaction in solar cell over broadwavelength.

3.2 Photons in semiconductors

Electronics and photonics have joined together in semiconductor optoelectronicdevices where photons can generate free electrons and electrons can generate andcontrol the motion of photons. Semiconductors are broadly used in optical de-tectors, sources (light-emitting diodes and lasers), amplifiers, waveguides, sensors[9, 35, 92, 142, 143, 144, 145, 146]. Semiconductor materials absorb and emitphotons by undergoing transitions between different electronic energy levels [3].

There are groups of close electronic energy levels which form bands in a semi-conductor material. The electrons-filled band is the valence band and the emptyband above the top of valence band is conduction band. The space between thesetwo bands is the energy gap. Electrons and holes can interact with photons. Theabsorption of a photon can generate an electron-hole pair and the recombinationof the electron-hole pair can result in the emission of a photon, see Fig. 3.2.

3.3 Wave functions of electrons in nano struc-

tures

Quantum well infrared photodetectors (QWIPs) usually contain one or more QWsmade of semiconductor materials [147]. QW is a sandwich semiconductor structureconsisting of a thin layer of material whose bandgap is smaller than that of thesurrounding material, forming conduction-band and valence-band rectangular po-tential wells in which electrons and holes are confined. A common material for thewell is GaAs, and the barrier material is aluminium gallium arsenide (AlGaAs).Fig. 3.3(a) shows a schematic energy band structure of such a GaAs/AlGaAs QWstructure.

Eqs. (3.4) and (3.5) show the energy relations including the potential energy


0 10 20 30 40 50 60 70-0.40

-0.35

-0.30

-0.25

-0.20

-0.15

-0.10

0AlGaAs

GaAs

E0

E1

E2

-V0

AlGaAs

Schematic energy

band structure of a

GaAs/AlGaAs QW structure

(b)

Energ

y (

eV

)

E2

E1

QW Barrier

Sample growth direction (nm)

Barrier

E0

(a)

Figure 3.3: (a) Schematic energy band structure of a GaAs/AlGaAs QW struc-ture. (b) First three bound states of a finite GaAs/AlGaAs QW structure with anAlGaAs barrier width of 50 nm and a GaAs QW width of 20nm.

and kinetic energy in finite potential QW and barriers,

E = ~2k2w/2m∗

w − V0 (3.4)

E = ~2k2b/2m

∗b (3.5)

where mw and mb are the effective masses of the well material and barrier ma-terial, V0 is the potential barrier height. For a QW structure with 50 nm thickAl0.3Ga0.7As barrier and 20 nm thick GaAs QW, the wave functions of three low-est bound states are shown in Fig. 3.3(b). Here we find that wave functions canpenetrate into the barriers when the barrier well is finite, the wave will decay inthe barrier regions and more electrons will go into the barrier easier when the levelis near the top of the well [136].

Consider a QW which is confined along the z direction with an effective con-finement length LQW , and extended in the xy plane, the wave function can beexpressed as [146]:

ψi,k(x, y, z) =1√SQW

ψi(z)ei(kxx+kyy) (3.6)

where SQW is the extension area of the QW in xy plane and (x, y, z) is the positionof the electron in space. ∫

LQW

|ψi(z)|2dz = 1 (3.7)

For QD confined in 3D within an effective volume ΩQD, the electron state is

3.3. WAVE FUNCTIONS OF ELECTRONS IN NANO STRUCTURES 37

quantized and only denoted by its quantum index i, i.e., ψi(r), and

∫

ΩQD

|ψi(r)|2dr = 1 (3.8)

due to the wave function normalization.Most QDs grown by MBE and MOCVD methods are dome shaped [148, 149]

with a circular base of radius r and a height h (h/(2r) ≈ 1/4.5 for InAs QD inGaAs). We can model such a QD as a cylinder with a circular cross section (radiusr) in the xy plane and a height h along the z axis. For the low-energy levels in theconduction band, we can approximate the confinement potential as infinitely highso that we can separately solve the Schrodinger equation as a square QW with awidth h along the z direction and a cylindrical QW disk with radius r in the xyplane.

A cylindrical quantum wire extended along the z axis is described by

[− ~2

2m∗

(d2

dx2+

d2

dy2

)+ V (x, y)

]ψ(x, y) = Eψ(x, y) (3.9)

where

V (x, y) =

−V0 x2 + y2 ≤ a2

0 x2 + y2 > a2 (3.10)

where V0 ≥ 0. In the cylindrical coordinate of (x, y) = (ρ, φ) and by writingψ(x, y) = eimφJm(ρ),

d2Jm(ρ)

dρ2+

1

ρ

dJm(ρ)

dρ+

2m∗[E − V (ρ)]

~2− m2

ρ2

Jm(ρ) = 0 (3.11)

where m is an integer (negative or positive so the state of |m| is two-fold degener-ate).

Inside the quantum wire, q2 = 2m∗(E + V0)/~2, the above equation becomes

d2Jm(ρ)

dρ2+

1

ρ

dJm(ρ)

dρ+

(q2 − m2

ρ2

)Jm(ρ) = 0 (3.12)

The solutions to the above equation are called Bessel functions. For integer valuesof m, the Bessel function can be expressed as

Jm(ρ) =1

2π

∫ π

−π

e−i(mτ−qρ sin τ) dτ (3.13)

For ground state (m = 0) in x− y plane,

J0(ρ) =1

2π

∫ π

−π

eiqρ sin τ dτ (3.14)


The ground state wave function in space is [87]

ψ0(ρ, φ, z) =

√2

hsin

(πz

h

) 1

β√

πr2

∫ π

−π

eiqρ sin τ dτ (3.15)

where m∗ is the effective mass of electron, q2 = 2m∗(E + V0)/~2, and β a nor-malization factor (β = 3.26 for the ground state), V0 is the confinement energyof the conduction band electron. We can find the value of q for the ground statewhen we set the radial part of the wave function to zero at the edge of the QD(ρ = r) which gives q0r = 2.405. This wave function is a good approximation ofthe ground state electron wave function calculated in [150] for actual dome-shapedQDs, due to the small electron effective mass of the QD material.

We now consider a spherical CdSe QD in vacuum with a radius of R as shownin Fig. 3.4(a). The energy band gap of bulk CdSe material is 1.74 eV (roomtemperature), the exciton Bohr radius is 4.9 nm, the quantum confinement energiesfor the conduction-band electron and the valence-band holes are 4.95 eV and 2.5eV respectively. Fig. 3.4(b) shows the schematic energy band structure of QD.The effective masses of the electron and hole are m∗

c = 0.14m0 and m∗v = 0.46m0,

respectively, where m0 is the electron rest mass. Each single-particle state isdenoted by its energy and angular momentum number (`). Fig. 3.4(c) and (d)shows the CB electron states and VB hole states confined in a spherical CdSe QDwith a radius of 2 nm and 4 nm as a function of the angular momentum number(`). QD has a quantized energy spectrum due to the spatial confinements of thewave functions within the QD. With the increase of radius of QD (from 2 nm to 4nm), the number of confined states increases and the distance between two neareststates decrease. The QD bandgap thus decrease with an increasing size of QD asshown in Fig. 3.4(c) and (d).

3.4 Photocurrent in solid-state based QWs/QDs

From this section to the following sections, we take solid-state based QWs/QDsand chemical synthetic solution-based QDs as examples. Without loss of generality,light is assumed to be injected in z direction in these devices.

We consider intra-conduction-band optical transitions (transitions between twostates within the conduction band) for the infrared photodetectors. As we dis-cussed before, the major light-matter interaction is A · p, where A is the vectorfield of the EM field and p is the electron momentum. As A ∝ E, we use E ·p todescribe the light-matter interaction since E is obtained directly from our FDTDcalculations.

We first consider the QW. Denote ei as the quantized energy level confinedin the QW along the z direction, its wave function ψi, E the electric field ofthe incident radiation. The total wave function of the conduction-band electronconfined in the QW can be expressed as

ψi,kx,ky(r, t) = ψi(z) ei(kxx+kyy)e−i(ei+ekxky )t/~ (3.16)

3.4. PHOTOCURRENT IN SOLID-STATE BASED QWS/QDS 39

0 1 2 3 4 5 6 7-5-4-3-2-1012345

0 2 4 6 8 10 12 14 16 18-5-4-3-2-1012345

(a)

VB hole states

Angular momentum quantum number

Ele

ctr

on e

nerg

y (

eV

)

CB electron states

(c) R=2nm

(b)

Schematic energy band

structure of QD

4.95 eV 4.95 eV

0

-1.74 eV

-4.24 eV

R=4nm(d)

VB hole states

CB electron states

R

CdSe QD in vacuum

Figure 3.4: (a) CdSe QD in vacuum. (b) Schematic energy band structure of CdSeQD with a radius of 4 nm. Conduction-band (CB) electron states and valence-band (VB) hole states confined in a spherical CdSe QD with a radius of (c) 2 nmand (d) 4 nm as a function of the angular momentum quantum number.


Here the QW is grown along the z direction and extended in the xy plane. Inthe above equation, kx and ky are wave vectors in the xy plane, and ekxky =~2(k2

x + k2y)/2m

∗, m∗ is the effective mass of the conduction-band electron. Anincident photon will excite an electron originally in ψi,kx,ky to an extended state

ψk(r, t) = ψkz(z) ei(kxx+kyy)e−i(ekz +ekxky )t/~ (3.17)

where k = (kx, ky, kz). The wave function ψkz(z) of the extended state is notsimply in the form of eikzz. It is affected by the potential wells of QWs and QDs[147, 151]. Here ekz = ~2k2

z/2m∗.

The photoexcited electron occupying ψk, referred to as the photocarrier, willeventually be driven by an external bias to form the photocurrent. In a commonGaAs/AlGaAs QWIP, the transport of photocarriers can be well described by aneffective drift mobility of carriers in the bulk AlGaAs material [36]. Apart fromthe drift mobility of the carriers, the photocurrent JQW can be expressed as [146]

JQW(~ω) =

∫ ∫|〈ψi,kx,ky |E · ∇|ψk〉|2dtdk

=

∫ ∣∣∣∣∫

Ezψi(z)dψkz(z)

dzdz

∣∣∣∣2

(

∫ ∞

0

[ei(ei−ek−~ω)t/~ + ei(ei−ek+~ω)t/~]dt) dk

=

∫ ∣∣∣∣∫

Ezψi(z)dψkz(z)

dzdz

∣∣∣∣2

δ(ei − ekz + ~ω) dk (3.18)

where E = (Ex, Ey, Ez) is the electric field of the excitation photon and ~ω is thephoton energy. In the above expressions, we consider an incident electric field witha single photon energy ~ω so that ks in Eqs. (3.18) and (3.20) are determined bythe energy conservation δ functions.

For common device configurations in production, the incident radiation prop-agates along the z direction so that Ez = 0. An optical grating is thus necessaryfor QWIP to diffract the light for nonzero Ez.

For QDIP devices, we approximate the wave functions of the confined andextended states as

ψi(r, t) = ψi(r) e−ieit/~ , ψk(r, t) = ψk(r) e−iekt/~ (3.19)

so that the photocurrent is

JQD(~ω) =

∫ ∣∣∣∣∫

E ·[ψ∗i (r)∇ψk(r)

]dr

∣∣∣∣2

δ(ei − ek + ~ω) dk (3.20)

QDs can thus be photoexcited by Ex and/or Ey.For the dome-shaped QDs, the intraband optical transition matrix from ground

state ψ0 to an extended plane wave in the conduction band

ψkρkz(ρ, φ, z) =1√Ω

ei(kρρ+kzz)

3.5. EXCITON-POLARITONS IN SOLUTION-BASED COLLOIDAL QDS 41

is [87]

α = E · 〈ψ0|∇|ψkρkz〉 = (Eρkρ + Ezkz)〈ψ0|ψkρkz〉 (3.21)

where Ω is the volume (i.e., πr2h) of the QD (wave function normalization). Forq0 6= 0, and after integration over φ which gives 2π, the optical matrix elementbecomes

α =2√

2(Eρkρ + Ezkz)

βhr2

∫ h

0

sin(πz

h

)eikzz dz

×∫ r

0

∫ π

−π

ei(kρρ+q0ρ sin τ) dτρdρ (3.22)

Including the energy conservation and the density of states for free electronsin the GaAs material, the photocurrent density spectrum is

J(~ω) =

∫|α|2δ(e0 − ek + ~ω)

2dk

(2π)3(3.23)

where k = (kρ, kz), ek = ~2k2/2m∗, e0 is the energy of the ground electron stateψ0(ρ, φ, z) in the QD, 2dk/(2π)3 is the density of states which can be converted to√

ekdek. Here we assume the normal QDIP device configuration with an externalbias applied along the z direction.

3.5 Exciton-polaritons in solution-based colloidal

QDs

Excitons are bound pairs of electrons (in the conduction band) and holes (in thevalence band) under the coulomb interactions. When an electron is excited fromthe valence band into the conduction band by a photon, it is also attracted bythe hole in the valence band under the Coulomb force [136]. As the exciton is thebinding of the electron with the hole, its energy is slightly smaller than that of theunbound electron and hole. Excitons have interesting optical properties and areimportant for the optoelectronic applications [141, 145].

An exciton-polariton is a mixing of a photon and an exciton, it is the basicoptical excitation of semiconductor system. Exciton states are coupled to the EMfield via the light-matter interaction Hamiltonian, so exciton-polaritons are theeigen modes of the Maxwell equations coupled with the exciton-equations in asemiconductor structure [152]. The theory of exciton polaritons of a QD has beendescribed in details in Ref. [24].

We use FDTD algorithm and the dielectric constant of QD described in Eq. (2.42)to study the propagation of an incident EM wave across the QD. The computa-tional volume is terminated by periodic boundaries in x and y directions, andPML absorbing boundaries are used in z direction to absorb the light passingthrough the QD or reflected from the QD so that they will not affect the power


(b) power at negative ε,

(-150:1200)(50:300)

(a) power at positive ε,

(-40:40)

-15

0

15

150-15

x axis [nm]

y a

xis

[nm

]

(-40:40)

Figure 3.5: Optical power distributions in and around the QD with a (a) positiveε′, (b) negative ε′, the diameter of QD is 10 nm. The insets are the optical powerdistributions in different scales. Blue is the lowest value and red is the highestvalue.

and electric field measurements. A plane-wave CW light source is used and put ata safe distance away from the QD so that the local field around the QD will notbe disturbed.

The power flux distributions at the cross section of the QD with a positive ε′

and negative ε′ are shown in Fig. 3.5. The background is the air (ε′ = 1). Theaccumulation of the power occurs in the vicinities of the upper and lower poles ofthe QD, at the same time, depletion is also observed around the left and right poles.The profiles are the results caused by the light diffraction of the sphere shapedQD. The sign of the power in and around the QD is handled by the dielectricparameter variation of the QD. The same sign modulations of the power insideQD due to the sign of ε′ are observed[93].

Now we consider interband transitions in the colloidal QDs for solar cell appli-cations. Optical matrix element of inter-band transitions from the VB state to aCB state is

Γji = 〈ψjuc|E · p|ψiuv〉 = E · pcv〈ψj|ψi〉 (3.24)

where pcv = 〈uc|p|uv〉 is the momentum matrix element, related to the commonlygiven material parameter Ep = p2

cv/2m0. Due to the quantized energy levels inQDs, these optical matrix elements are singular which are listed as sharp peaks asshown in Fig. 3.6.

In numerical calculations, the absorption between one VB state i and oneCB state j, including relaxation processes, can be also described by a Lorentzianpeak[153]


480 500 520 540 5600

80vacuumQD

2nd1st

1st

dQD

=3.4 nmO

ptical spectr

a

Wavelength [nm]

Absorption

2nd

Figure 3.6: Optical absorption spectra of the QD with a diameter of 3.4 nm with-out the exciton-polariton effect. Sharp peaks denote the singular optical matrixelement of Γji. The inset shows the schematic energy band structure of QD andcorresponding transitions.

Γabs(~ω) =∑ji

ΓjiΓ

π

1

(~ω − Eji)2 + Γ2(3.25)

where ~ω is the photon energy, Eji is the transition energy between CB state jand VB state i, and Γ is the relaxation energy. Γ also includes various energydissipations such as electron-phonon interactions at room temperature.

Optical absorption is possible when the photon energy equals to the energydifference between one VB state i and one CB state j and when Γji is not zero.

The photoluminescence (PL) peak is similarly described by the Lorentzianpeak:

Γlum(~ω) =A

2π

Γ

(~ω − (~ω0 −∆))2 + Γ2(3.26)

where ~ω0 = Ec0−Ev0 (Ec0 is the ground CB electron state, Ev0 is the ground VBhole state), ~ω is the photon energy, Γ is the relaxation energy, and A is a physicalconstant proportional to the optical transition matrix element Γj=0,i=0. ∆ denotesthe Stokes shift. The absorption and PL spectra are shown in Fig. 3.7(b). Theabsorption energy, normally defined as the energy of the first absorption peak, hasbeen widely used as a measure of the QD size [154, 155].

The excited exciton can contribute to the dielectric polarization of the QDmaterial and thus results in the effective dielectric constant of Eq. (2.41)(plottedin Fig. 3.7(a)). The small |ε′| with respect to ε∞ on the shorter-wavelength side


460 480 500 520 540 560 580 6000

50

100

150

520 540 560 580 600

0.1

0.2

0.3

0.4

0

10

20

30

450 500 550 600 650

(b)

∆

Optical spectr

a

Wavelength [nm]

absorption luminescence

exciton-polariton

effect

optical power inside QD

Die

lectr

ic c

onsta

nt

ε∞=12

ε'ε'' (a)

luminescence

absorptionCdSe - 3.4 nm

Figure 3.7: (a) Dielectric constant of QD and optical power inside QD. (b) Cal-culated optical spectra of the QD with a diameter of 3.4 nm. Red sharp peaksdenote the singular optical matrix element of Γji, while black thin and blue thicksolid lines are the absorption spectra without and with the exciton-polariton effect,respectively. The inset shows the experimental result of the Stokes shift.


of the exciton profile can induce a strongly enhanced EM field penetration in QD,so, optical absorption in this range is enhanced. While the wavelength is near theexciton peak, EM field penetration in QD is small due to the large |ε′|, the opticalabsorption at the ground-exciton resonance energy region (1st peak in Fig. 3.6) isreduced, which creates a gap between the first prominent absorption peak and theluminescence peak (i.e. Stokes shift ∆) as shown in Fig. 3.7(b) [93]. The shape ofthe theoretical absorption spectrum agrees well with the experimental data afterincluding the exciton-polariton effect.

In this chapter, I briefly introduced the light-matter interaction in QWs/QDs.The photocurrents in solid state QW/QDs and exciton-polaritons of colloidal QDsare studied. They are important for the performance of QWIP/QDIP and QDsolar cell. FDTD approach was used to simulate the EM wave propagation inthese QWs/QDs-based photovoltaic devices. More details will be shown in thefollowing chapter.

Chapter 4

Light manipulation in microphotonic structures

Light manipulation in micro and nano photonic structures can be realized in manyways, including the localized waveguide/cavity mode, diffraction on the geometricshape, the interference of diffracted waves, resonant excitation of surface-plasmon-polaritons, resonant excitation of exciton-polaritons. In this chapter, light manip-ulation in micro photonic structures will be discussed.

4.1 Dielectric PhC structures

4.1.1 Photonic band structure

Band structure is also called a band diagram or dispersion relation. Photons/lightare forbidden to propagate within certain energies (photonic bandgaps) in somedirections. If the gap covers all possible propagation directions, it is a completebandgap. The most famous structure for light control and manipulation is thePhC [4].

As shown in Chapter 1, several PhC structures have been found to presentband gaps for one or two polarizations. In order to create a complete photonicbandgap in three-dimensional (3D), one must arrange for the dielectric lattice tobe periodic along three axes, constituting a 3D photonic crystal [4]. For 2D case,the band structures for TE and TM modes are completely different. For example,in most situations, there are photonic band gaps for one polarization but not forthe other polarization. A 2D triangular lattice of air holes embedded in a dielectricslab presents a large bandgap for TE polarized waves and even a complete bandgapfor both polarizations for air holes with large radius [156]. However, a cubic latticeof rods in the air can present a bandgap for TM modes [9] and even a completeband gap for some sizes and shapes of rods [157]. Here we plot a 2D PhC bandgapas an example, see Fig. 4.1. It is calculated by the plane wave expansion (PWE)method [126]. Different refractive index “n” of rods, lattice constant “a” and rod

47

48CHAPTER 4. LIGHT MANIPULATION IN MICRO PHOTONIC STRUCTURES

0.0

0.2

0.4

0.6

0.8

b a

z

x

M

XΓ

(a)F

requency [2

πc/a

]

TM band structure

Γ X M Γ

(b)

Figure 4.1: (a) 2D PhC made of square lattice of dielectric columns. (b) TM(nonzero Ey, Hx and Hz) band structure of the PhC in (a). The inset shows theBrillouin zone which is shaded. b=0.55a and the dielectric refractive index n=3.0.

size “b” will change the band structure of PhC.

In the following subsections, we will show the light manipulation by the bandgapand band-modes of PhC.

4.1.2 Multiple beam splitting from PhC waveguide

Multiple beam splitting and directional emission (90 beaming effect) are veryimportant for the free-space optics (FSO) in which light propagates between twopoints in free space. Different from an optical communication technology basedon optical fiber, FSO is useful when the optical fiber connections are impracticalin many situations.

Recently, directional emission and beam splitting of light coming out of PhCwaveguides (PCWs) have been developed by using the bandgap character of PhC,and they are also useful for efficient coupling between waveguides and PCW edge-emitting lasers [7]. Many methods such as changing the refractive index of thesurface layer, using grating layers [158] or coupling waveguides [159], surface cor-rugation [160, 161], concave corrugated surface [162], point defects near the surface[8] and tapered exit [163] can be used to obtain directional emission in PCWs. Forbeam splitting, PCW structures have also been developed. Different from closed-type PCWs on the chips [164], the open-type Y-shaped splitting from the PCWto the out free space has also made progress. It can be successfully realized bythe self-collimation PhCs [165] and corrugated-surface PCW [166]. However thecorrugated surface is very complicated in manufacturing. A simpler PCW designfor multiple beam splitting of light should be proposed to reduce the cost.

We have designed a simple PhC waveguide with removable rods at the exit to

4.1. DIELECTRIC PHC STRUCTURES 49

-20 -10 0 10 20-30

-20

-10

0

10

20

30

40a

a

-20 -10 0 10 20

x axis [a]

b

-20 -10 0 10 20

z a

xis

[a]

c

a

a1

2 3

Figure 4.2: (a) Simple waveguide. (b) and (c) Y-shaped waveguides with removablerods at the exit. b=0.55a, dielectric refractive index n=3.0.

realize beam splittings[9] (Fig. 4.2).

In the 2D FDTD simulation, the lattice constant is a, a short line source (widthL=1.0a) located in the PhC waveguide is used, the incident direction is in the zdirection (perpendicular to the PhC rods), refractive index of rods n=3.0, b=0.55a,the incident Gaussian TM polarized light is described by:

H(x, z, t) = [Hx(x, z, t), 0, Hz(x, z, t)]E(x, z, t) = [0, Ey(x, z, t), 0] (4.1)

The domain is terminated by periodic boundaries in the x directions to produceperiodic arrays and PML absorbing boundaries along the z direction [135]. Att = 0 when the line light source is switched on, Ey(x, z, 0) = Hx(x, z, 0) = 1,Hz(x, z, 0) = 0 at the source plane (line), CW is used for the calculation.

Fig. 4.2 shows optical field Ey distributions in three different PCW structuresfor the same wavelength (λ=1.95a) in bandgap. Fig. 4.2 (a) shows the referencePCW, the optical field diverges rapidly after exiting this simplest waveguide dueto the diffraction. Whereas by simply adding and removing rods at the exitsand modifying their positions, the beam is split and the interference between thesplit beams generates three and five highly concentrated beams from the PCW.Fig. 4.2 (b) and (c) shows one-to-three and one-to-five beam splittings those arewell concentrated and separated from each other.

In the following subsections, we will use the dispersion photonic bands (band-modes) of PhCs to diffract light in the light-absorbing devices.

4.1.3 Light diffraction and funneling in solar cell and QDIP

(1) PhC in solar cells


Light diffraction and funneling are important for the light-absorption in thephotovoltaic devices such as thin film solar cells and QDIP. Many optical lossesmay reduce the light trapping in solar cells, such as reflection from the front surfacewhich prevents light from entering the solar cell, and poor absorption of light dueto the thin thickness of the solar cells. In order to reduce the reflection from thedevice surface, anti-reflection coating layer is used [121]. The second importantissue is to increase pathways and traveling time of photons inside active region inthe solar cell to enhance the light absorption by dye molecules and colloidal QDs(light-matter interaction) [95, 120] in the solar cell.

Light diffraction has been realized by conventional optical dielectric gratings[36, 167]. From the geometrical optics approach, Yablonovitch and Cody haveshown that the ability to funnel light into a thin film solar cell is normally limitedto 4n2, where n is the refractive index of the absorbing medium [168]. However,when the wave effects of light is considered, the limit is not strictly right. Inwave optics regime, light diffraction can enhance the path length of photons tosurpass the conventional limit 4n2. This is because wave optics approaches aimto enhancing absorption in the most interesting range in contrast to geometricaloptics approach that treats all wavelengths equally. When the film thickness orthe period of a periodic grating is comparable to or smaller than the wavelength,wave optics phenomena occur [5, 6]. The limit in the geometrical optics regimehas been surpassed in subwavelength regime [169, 170].

Plasmonic effect excited by metal-particles can improve the light harvestingin the solar cells [88, 89, 90]. PhCs have also been certified to exceed the 4n2

absorption limit and improve the light trapping by superposing light diffractionand interference in the lattice [5, 6]. Micro rods, nano wires and PhCs [14, 171,172, 173, 174, 175, 176] were used in the active layer region to funnel light in solarcells, PhC back-reflectors and forward-scatters were also used to enhance the lighttrapping inside the active layer [177, 178]. Most of these structures focus on thedesired wavelengths.

Some PhC structures in solar cells include the light absorbing materials insidethe rods, e.g., periodic silicon or organic rods standing in the z direction on thexy plane form a 2D PhC [171, 172], while others use PhC patterned electrodeswith silicon, dye moleculars or QDs embedded inside them [14, 173, 174, 175, 176].They all can improve light-matter interactions significantly. A 2D PhC structureis expected to be superior to a 1D one for solar cell applications, because there canbe more resonances in a 2D lattice to trap the light. However, 2D PhC fabricationis more complicated than 1D ones.

We have designed a 2D PhC structure as shown in Fig. 4.3 (c) to realize efficientlight diffraction and funneling in solar cells.

In the 2D FDTD simulation, the plane-wave (line source) incident direction isin the z direction, the incident TE polarized CW light is described by:

E(x, z, t) = [Ex(x, z, t), 0, Ez(x, z, t)]H(x, z, t) = [0, Hy(x, z, t), 0] (4.2)

4.1. DIELECTRIC PHC STRUCTURES 51

0.5 1.0 1.5 2.00.0

0.2

0.9

1.0 (e)

ITO

ITO

TiO2 + QDs

A

A

A

AAB

A e-

BB e-

...

light

(c)

light

(b)

light

(a)

(c)

(b)

(a)

Wavelength [a]

Diffr

acte

d e

nerg

y Light

ITO (Indium tin

oxide)

transparent

electrolyte

(d)

Figure 4.3: (a) Simple diffraction gratings. (b) and (c) PhC structures, b=0.55a,dielectric refractive index n=1.75. (d) Solar energy diffraction. (e) Model solarcell based on PhC structures (b) and (c). “A” is TiO2 with QDs, “B” is ITO,transparent electrolyte is filled in the other space.


Power flows:

Sz(x, z, t) = Ex(x, z, t)Hy(x, z, t)Sx(x, z, t) = −Ez(x, z, t)Hy(x, z, t) (4.3)

The domain is terminated by periodic boundaries in the x directions to produceperiodic arrays and plane wave source, PML absorbing boundaries are used alongthe z direction [135]. At t = 0, Ex(x, z, 0) = Hy(x, z, 0) = 1, Ez(x, z, 0) = 0 at thesource plane (line), the refractive index of rods is n=2.75, the lattice constant is a,b=0.55a. During the light propagation, a large Ez component in z direction (thedirection of the incident light) will indicate a good ability of light diffraction. Theaveraged 〈E2

z 〉 can be understood as diffracted light energy [179].The PhC lattice structures in Fig. 4.3 (b) and (c) are also working in the wave

optics regime, they can diffract incoming beams into highly oblique angles, whichincreases the pathways of photons inside the solar cell; on the other side, the reso-nance modes with a high photon density of states can increase the traveling timeof photons inside the solar cell. These effects can help to maximize the probabil-ity of absorption. Fig. 4.3 (d) shows the comparison of diffracted energy in thesame area of a common rectangular groove grating [167] in Fig. 4.3 (a) (substraterefractive index n=2.75[115], depth of rectangular groove=0.15a, period=0.6a, fill-ing factor=1/3) and two PhC structures in Fig. 4.3 (b) and (c), which indicatesa significant improvement of the light trapping effect in subwavelength photonicstructures. There are only a few individual resonances in the perfect PhC (Fig. 4.3(b)), while the light diffraction in the comb-shaped structure (Fig. 4.3 (c)) happensover a broadband.

With the rapid development of nanofabrication techniques and lithographictechniques for stacked PhC structures [14, 20], the PhC structure can be formedby a stack of dielectric rods by etching an alternant sequence of indium tin oxide(ITO, dielectric refractive index n=1.17 [180]) films and TiO2 (n=2.75[115]) filmsembedded with light-absorbing QDs. Absorbed photons can excite electrons fromthe valence band to the conduction band in the QD, then electrons will be injectedinto the TiO2 rods [181], and further diffuse to the ITO rods and ITO films,thus forms the photocurrent. Transparent organic solvent-based, non-corrosiveelectrolytes (disulfide/thiolate redox couple, n ≈1 [182]) can be filled in otherspace. A model solar cell based on the PhC structure is shown in Fig. 4.3 (e).

(2) PhC in QDIPsFor dome-shaped QDs, the contribution of Ez (in the propagating direction)

to light-matter interactions inside QDs is enlarged [87]. Model QDIP with QDsembedded in the PhC framework is proposed to create large Ez component andimprove the optical absorption efficiency in the QDIP (see Fig. 4.4). For example,InAs QD-layers are embedded in the GaAs slab. In infrared FPAs, the light isinjected from below the bottom of the substrate to avoid the light reflection frommetallic contact layer on the top of the FPAs. 2D square lattice PC structures areshown in Fig. 4.4 (b) and (c). The air holes in the PhC structures are extended


(a) (b) (c)

x

zlight

substrate

QD layers

Figure 4.4: (a) QDs layers. Schematic PhC structures with holes in slab: (b)perfect PhC structure, (c) PhC structure with cavities. Radii of the air holes are0.3a, dielectric refractive index of slab n=3.3.

along the y direction. At t = 0, Ex(x, z) = Hy(x, z) = 1, Ez(x, z) = 0 are set at theplane wave source (TE polarized) in 2D FDTD simulation. We adopt the dielectricrefractive index of n=3.3 for GaAs slab in the wavelength region from 2 to 12 µm[115]. The lattice constant is a, radius of the air holes is 0.3a. The domain isterminated by periodic boundaries in the x directions to produce periodic arraysand PML absorbing boundaries along the z direction [135].

Ez = 0 in the initial light source. Fig. 4.5 shows that when the light wavelengthis in the photonic band of PhC, the PhC lattice can diffract the injected radiationto other directions, which results in nonzero Ez component in the QDs region. Atthe same time, the light propagates slowly in the lattice; created resonance modescan trap the energy in the slab; created multiple pathways inside the active regioncan enhance the absorbing ratio, these are useful for the light-QDs interaction.We compare the amplitude of Ez in the perfect PhC and the PhC with cavities inFig. 4.5. Note that when the wavelength in slab (3a/3.3) ≤ PhC lattice constant(a), rods in perfect PhC can create more resonance modes, however, when thewavelength is larger (9a/3.3) than lattice constant (a), the periodic cavities inFig. 4.4 (c) can provide larger area resonance in the slab[183]. Lattice constant ofPhC and size of cavity can be modified to realize the maximum light trapping ondifferent wavelengths.

4.2 Metallic PhC structures

Metals and doped semiconductors can reflect all the light with a frequency be-low plasma frequency[136]. Metallic waveguides and cavities are widely used to


X Axis

Z A

xis

(d)(c)(b)(a)

λ=3a λ=3a λ=9a λ=9a

Figure 4.5: Amplitude of Ez in PhC structures with holes in slab, (a) and (c) arefor perfect PhC structure, (b) and (d) are for PhC structure with cavities, radiiof the air holes are 0.3a, dielectric refractive index of slab n=3.3. λ refers to thewavelength in air.

control microwave propagation. A metallic cavity wall reflects EM waves and ametallic waveguide allows light propagation only along its axis. It would be ex-tremely useful to control EM waves with frequencies outside the microwave regimesimilarly, such as visible light and IR radiation. Metallic PhC structures includingreflective metallic gratings and SPP-supported metallic gratings have been usedin QWIP/QDIP [35, 36, 86, 87, 110, 146].

4.2.1 Reflective metallic gratings

Conventional reflective metallic structures contain periodic holes or gratings inthe metallic film on the top of the pixel in QWIPs (Fig. 4.6(a))[35, 36]. Theyshow mainly a near field light diffraction effect and the wavelength of the optimaldiffraction depends on the grating geometry very much. In dense-pixel photodetec-tor arrays where the optical pixels are small, the gratings become less effective[110].Total internal reflection structures were proposed [111, 112] to avoid the crosstalkfrom substrate. However, the severe crosstalk caused by the diffraction from thecorners of the neighboring pixels in common gratings is strong despite some under-fill is used between the pixels. Such crosstalk from corner diffraction is difficult tobe minimized. Moreover, such a crosstalk travels ahead of the useful signal fromthe corner diffraction in local pixel since light transmission in the underfill is faster.This crosstalk is blockaded in the concave pixel structure (Fig. 4.6(b))[146]. In thisstructure, one-concave metallic reflector per-pixel can effectively diffract and focusthe electric field components to deeper absorbing layers in QWIP/QDIP withoutcausing inter-pixel crosstalk.

Photocurrents in these two structures are studied by 3D FDTD simulations.


QWs/QDsinside

metallic reflective layer and dielectric insulation layer

incident light

common layer and substratesubstrate

QWs/QDs

Au/Agpixel

(a) (b)incident light

pixel

Figure 4.6: (a) One-pixel structure with conventional metallic reflective gratings.(b) FPA structure with concave pixel structure (one-reflector-per-pixel).

The incident radiation is simulated by a pulsed TE-polarized plane wave withcentral wavelength of 4 µm and a broad wavelength range from 2 to 10 µm,Ex(x, y, z, t)|t=0 = 1, Ey(x, y, z, t)|t=0 = Ez(x, y, z, t)|t=0 = 0 at the source plane,the propagation direction of the incident light is still along the z axis. Refractiveindices of QW and QD materials are set to be n=3.3 (for III-V materials in infraredregion)[115]. The dielectric constant of Ag film is described by Eq. (2.39) and fit-ted according to the parameters in [115]. The size of one pixel is 7.9 µm, and thethickness of absorbing layer is 2.75 µm. 3×3 gratings are set in the conventionalreflective metallic structure. The domain is terminated by periodic boundaries inthe x and y directions to produce periodic arrays and PML absorbing boundariesalong the z direction [135].

Considering that the QW width and QD size are very smaller than the lightwavelength, the electric-field inside QW can be seen as z-independent in one QW,thus

JQW =

∣∣∣∣∫ ∫

Ez(x, y, z)

[∫

QW

ψi(z)dψkz(z)

dzdz

]dxdy

∣∣∣∣2

∝∣∣∣∣∫ ∫

Ez(x, y, z)dxdy

∣∣∣∣2

(4.4)

where Ez(x, y, z) is the average electric field component Ez in the QW plane at z.

For the QDs layer at z, r = R + r′, where R is the center of the QD, r′ shows


the position in the QD,

JQD =∑R

∣∣∣∣E(R) ·∫

QD

ψ∗i (r′)∇ψk(r′)dr′

∣∣∣∣2

∝∑R

|E(R)|2 =

∫ ∫|E(x, y, z)|2 dxdy (4.5)

From Eq. (4.4) and (4.5), JQW is proportional to the square of the sum of theelectric field in the QW plane due to perfect coherence of wave function and Ez inthe xy plane, while JQD is proportional to the sum of the squared electric field inthe QD layer because the wave functions in different QDs are totally not coupled.When the device is processed into the pixel structure, E field modes exist at thexy plane so that Eq. (4.4) can be modified as Eq. (4.5) in a pixel structure. Weconsider the photocurrents

Jx(z, t) =

∫ ∫|Ex(x, y, z, t)|2 dxdy

Jy(z, t) =

∫ ∫|Ey(x, y, z, t)|2 dxdy

Jz(z, t) =

∫ ∫|Ez(x, y, z, t)|2 dxdy (4.6)

from the deepest absorbing layers in Fig. 4.6 (b). Jz plays a major role for QWIP,and Jx + Jy + Jz can work integrally for QDIP.

The temporal developments of the photocurrents excited by the infrared pulseare shown in Fig. 4.7. Fig. 4.7 (b) shows that much larger Jy and Jz are obtainedin a broad time domain at the deepest absorbing layer in concave pixel structure asshown in Fig. 4.6(b), which are smaller in Fig. 4.7(a). This is because the intensityof the diffracted radiation (Ey and Ez) in the conventional grating structure ofFig. 4.6(a) will be small when the active layer is located at a far distance fromthe diffraction surface[36]. However, the diffraction starts early when the lightwave reaches the edges of the elliptical mirror in the concave structure, and theelectric fields Ey and Ez sustain large values for a longer time in the concave pixelstructure due to the sustained diffractions, thus will generate large Jy and Jz inthe deeper layer than the conventional gratings [146].

The Ex and Ez distributions in the concave pixel structure at three differenttimes shown in Fig. 4.8 can also certify above results. A strong focused Ex alsoleads to a strong focused Ez component. The electric-field mode distribution inthe pixel structure can result in different currents from different layers in theactive region. As some part of the detector material is removed in the concavegrating structure, total Jx will be decreased, however, Jy and Jz will be enhancedobviously. Besides, pixels in the concave structure can be very close to each otheras the metal has a good reflection of the infrared light.

Choi et al. have successfully fabricated the ladder-shaped metallic mirrors onQWIPs [112], the structure works quite well except that photocurrents are sensi-tive to both the angle of the reflective structure and polarization of injected light.


10-3

10-2

10-1

100

101

T

Photo

curr

ent

com

ponents

a grating

Jx=1647

Jy=59

Jz=236

Jx(t)

Jz(t)

Jy(t)

Time [fs]

200100 300 700

concavebJ

x=1483

Jy=187

Jz=984

Figure 4.7: Photocurrents from the deepest absorbing layers in the pixel structuresof Fig. 4.6 excited by a radiation pulse (wavelength 2 ∼ 10 µm). (a) Conventionalreflective grating. (b) Concave reflective grating. Thin black solid lines are Jx(t),thick blue solid lines are Jy(t), red dashed lines are Jz(t). T (vertical dashed lines)denotes the time when the pulse reaches the top interface between absorbing layerand metal.

focusing (b)

137 fs6

7

8

9

10

11

Ez

x axis [µm]

z a

xis

[µm

]

(a')

6

7

8

9

10

11

Ex

106 fs

(a)

1 2 3 4 5 6 7

(b')

(c)

174 fs

(c') C

2.8

C

3.15

Figure 4.8: Spatial distributions of (a,b,c) E2x and (a’,b’,c’) E2

z excited by a radi-ation pulse in the concave pixel structure at three different times. Arrows markthe motion of the electric field.


It should be noticed for the concave metallic mirrors that extra thin electrical iso-lation layer should be added between the metallic mirror and the detector materialto avoid the shorting out in the detectors. With proper modifications, the concavereflector can be expected to enhance photocurrents in solar cell devices.

4.2.2 Surface plasmon polaritons in metallic gratings

Ebbesen et al. reported the light transmission through a subwavelength hole arrayin Ag film in 1998[184] and found the transmission is large when the wavelength islarger than the period of holes and almost ten times the diameter of the hole. Asthe result will vary with parameters such as the period of holes, the thickness of themetal film and the size and shape of the hole, the physical mechanisms have beenunderstood in several ways, in which the main explanation is the excitation of sur-face plasmon polaritons (SPP) [124, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194].SPPs can propagate in a wave form at the interface between a negative-permittivitymaterial (such as metal or doped dielectric) and a positive-permittivity material.The amplitude of SPP decays exponentially with the increasing distance away fromthe interface, which means that the SPP is bound to the interface. Due to the EMfield confinement near the interface, metallic film with hole arrays are exploitedto create enhanced E field in the absorbing-material region in QWIPs/QDIPs[86, 87].

Using the similar FDTD settings as those in the last subsection, we numericallysimulated the SPP excitation and transmission through the interface between bulkGaAs and Au film with hole array. Period of the hole array is 3µm, the diameter ofthe hole is 1600nm, and the thickness of Au film is 150nm. The dielectric constantof Au is described by Eq. (2.39) and fitted according to the parameters in [115].Fig. 4.9 shows the temporal development of the electric field E2

x and E2z at different

z positions, calculated by the surface integral of the electric field components onplanes subdividing the z axis. There is no E2

z created if no metal film is set. Whenthe Au film with hole arrays is introduced, the reflection and transmission of E2

z

are created by the diffraction of the injected pulse. The optical field transmitslargely on the Au-GaAs interface with a nonzero z component due to both thesurface plasmon and geometric diffraction. Optical field Ez near the Au-GaAsinterface is dominated by the surface plasmon, while Ez in the region far awayfrom the metal-semiconductor interface is due to the geometric diffraction becausethe decay time is short. It is found that the metallic film needs to be quite thinand with large holes in order to optimize the magnitude of Ez.

In conclusion, the light movement in metallic PhC structures is affected bythe geometric diffraction, the PhC modes and the SPP effect. The geometricdiffraction and PhC modes always exist, and the SPP can create an additionaleffect to them. All these three factors are related to the geometric shape of theholes, holes’ size, the period of the hole array, the thickness of the metal film,the material properties and the polarization of the incident EM wave. We shouldconsider them synthetically while designing the devices.


0

100

200

300

400

500z metal film with holes

QWs/QDs

substrate

no metal film

z axis [µm]

Tim

e [fs

]

(a) E2

x

reflection transmission

source

0 2 4 6 8 100

100

200

300

400

500

reflection transmission

(b) E2

z

metal film

air semiconductor

Figure 4.9: Temporal developments and spatial distributions of (a) E2x and (b)

E2z . Left inset in (a) shows one-pixel structure with metallic gratings with holes

in metal film, and right inset shows the E2x in the absence of a metal film in which

case the Ez field is always zero.

Chapter 5

Summary of papers

Totally six papers are included in this thesis. Micro and nano structures for efficientlight manipulation and light-matter interaction have been investigated by finite-difference time-domain (FDTD) method, they can be used in integrated photoniccircuits, broadband photo-detection and solar-radiation trapping, etc. They aresummarized as follows.

Journal Paper 1Surface Plasmon wave excited by subwavelength hole arrays at metal-semiconductor

interface can diffract the electric field in near field region. With the assistant ofgeometric diffraction in far field region, the structure can create useful field compo-nent and enhance the electric fields in the active layers in QW infrared photode-tectors (QWIPs) and QD infrared photodetectors (QDIPs). By calculating thetransmission and diffraction of the infrared optical field through the grating andthe light-matter interaction between the transmitted optical field and electronsconfined in the QD, we studied the photocurrent enhancement in QDIP with anoptical grating of subwavelength hole array in a thin metal film. The light diffrac-tion due to the surface plasmon effect at the metal-semiconductor surface and thephotonic subwavelength hole array is dominant in increasing the photocurrent.

Journal Paper 2Utilizing the photonic crystal bandgap character, multiple-beam splitting to

free space from a V groove in a two-dimensional (2D) photonic crystal waveguide(PCW) has been realized by adding and modifying a few additional dielectric rodsat the exit of the PCW. Numerical study shows that one-to-two (one beam in andtwo beams out), one-to-three, and one-to-five beam splittings can be easily realizedover a wide bandwidth, the split beams have symmetric energy distributions andhigh directional transmissions. By moving the additional rods at the exit of thePCW asymmetrically, off-axis directional emission can also be realized. The designis very useful for the free space communication.

Journal Paper 3We have studied the exciton-polariton contribution to the Stokes shift in col-

loidal QDs by comparing the experimental spectrum and results from numericalcalculation. By using quantum mechanism of light-matter interaction and FDTD

61

62 CHAPTER 5. SUMMARY OF PAPERS

analysis of EM field going across the QD, we found that the optical excitationof an exciton in the QD will couple with the external excitation radiation (i.e.,exciton polariton) and affect the dielectric constant of the QD very much, whichleads to variations of the optical power inside the QDs, the power variation in QDcan contribute significantly to the Stokes shift, i.e., a shift between the first lightabsorption peak and the emission peak. This is useful in bio-photonics field.

Journal Paper 4We have studied theoretically the temporal developments of photocurrents ex-

cited by an infrared radiation pulse in quantum well/dot infrared photodetectors(QWIP and QDIP) with different optical coupling structures. The light diffractionby the conventional reflective grating structure is only significant in the vicinity ofthe grating surface. It also consists of large crosstalk from the corner-diffraction ofneighboring pixels. However, a concave metallic reflector can eliminate the inter-pixel crosstalk and also create an enhanced diffracted and focused electric field todeep active layers, which obviously increases the photocurrents in broad-band pho-todetectors. With proper modifications, the concave reflector can also be expectedto enhance photocurrents in solar cell devices.

Journal Paper 5We compared the diffraction efficiency of conventional grating, perfect photonic-

crystal (PhC) and comb-shaped PhC rods-lattice structures. It is shown that thephotonic band of the PhC structure is very dispersive in a broad wavelength regionso that PhC structures can efficiently diffract incident light from its initial inci-dent direction to other directions in the PhC lattice over a broadband includingthe wavelength region of solar radiation. Further light diffraction and funnelingcan be obtained by using comb-shaped PhC structure because comb-shaped PhCstructure can create extra resonance modes to trap the light, the light propagatesslowly and in many pathways in the whole PhC lattice, which will greatly en-hance light-matter interaction when light-absorbing elements (such as QDs) areembedded in the PhC structure. We also present a model QD solar cell with QDsembedded in a stacked PhC rods-lattice structure.

Conference Paper 1For MBE-grown QDs, they are in dome-shape and favor the E field that in

the injection direction. We present a model QDIP with QDs embedded in thePhC framework to create large Ez component and improve the optical absorptionefficiency in the QDIP. When the light wavelength is in the photonic band of PhC,the PhC lattice can diffract the injected radiation, which creates Ez componentin the active region. At the same time, the light propagates slowly in the lattice;the created resonance modes can trap the energy in the slab; the created multiplepathways inside the active region can enhance the absorbing ratio, which are alluseful for the light-QDs interaction. Different sizes of cavities can play key roleson different wavelengths.

Bibliography

[1] V. Vedral, Modern foundations of quantum optics, (Imperial College Press, London,2005).

[2] M. Born and E. Wolf, Principles of optics: electromagnetic theory of propagation,interference and diffraction of light, 7th ed. (Cambridge University Press, Cam-bridge, 1999).

[3] B. E. A. Saleh and M. C. Teich, Fundamentals of photonics, 2nd ed. (Wiley, Hobo-ken, 2007).

[4] J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals:Molding the flow of light, 2nd ed. (Princeton University Press, Princeton, 2008).

[5] P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, Opt. Express15, 16986 (2007).

[6] Z. Yu, A. Raman, and S. Fan, Opt. Express 18, A366 (2010) .

[7] H. Kurt, Appl. Phys. B, 95, 341 (2009).

[8] C.-C. Chen, T. Pertsch, R. Iliev, F. Lederer, and A. Tunnermann, Opt. Express,14, 2423 (2006).

[9] Z.-H. Chen, Z.-Y. Yu, Y.-M. Liu, P.-F. Lu, and Y. Fu, Appl. Phys. B: Lasers andOptics 102, 857 (2011).

[10] E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).

[11] S. John, Phys. Rev. Lett. 58, 2486 (1987).

[12] L. Rayleigh, Phil. Mag. 26, 256 (1888).

[13] T. Kato, H. Susawa, M. Hirotani, T. Saka, Y. Ohashi, E. Shichi, and S. Shibata, J.Crystal Growth, 107, 832 (1991).

[14] J. G. Mutitu, S. Shi, C. Chen, T. Creazzo, A. Barnett, C. Honsberg, and D. W.Prather, Opt. Express 16, 15238 (2008).

[15] V. P. Bykov, Sov. J. Quantum Electron. 4, 861 (1975).

[16] K. Ohtaka, Phys. Rev. B 19, 5057 (1979).

63

64 BIBLIOGRAPHY

[17] E. Yablonovitch, T. J. Gmitter, and K. M. Leung, Phys. Rev. Lett. 67, 2295 (1991).

[18] T. F. Krauss, R. M. DeLaRue, and S. Brand, Nature 383, 699 (1996).

[19] P. Russell, Science 299, 358 (2003).

[20] S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho,M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, Nature 394, 251 (1998).

[21] A. Y. Vlasov, X.-Z. Bo, J. C. Sturm, and D. J. Norris. Nature 414, 289 (2001).

[22] M. Qi, E. Lidorikis, P. T. Rakich, S. G. Johnson, J. D. Joannopoulos, E. P. Ippen,and H. I. Smith, Nature 429, 538 (2004).

[23] E. L. Ivchenko and G. E. Pikus, Superlattices and Other Heterostructures: Symme-try and Optical Phenomena, 2nd ed. (Springer, Berlin, 1997).

[24] Y. Fu, M. Willander, and E. L. Ivchenko, Superlatt. Microstruct. 27, 255 (2000).

[25] E. L. Ivchenko, Y. Fu, and M. Willander, Phys. Solid State 42, 1756 (2000).

[26] Y. Zeng, X.S. Chen, W. Lu, and Y. Fu, Eur. Phys. J. B 49, 313 (2006).

[27] Y. Zeng, Y. Fu, X. Chen, W. Lu, and H. Agren, Phys. Rev. B 74, 115325 (2006).

[28] O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I.Kim, Science, 284, 1819 (1999).

[29] M. Berggren, A. Dodabalapur, R. E. Slusher, Z. Bao, A. Timko, and O. Nalamasu,Electron. Lett. 34, 90 (1998).

[30] B. Temelkuran, E. Ozbay, J. P. Kavanaugh, G. Tuttle, and K. M. Ho, Appl. Phys.Lett. 72, 2376 (1998).

[31] B. Temelkuran, M. Bayindir, E. Ozbay, R. Biswas, M. M. Sigalas, G. Tuttle, andK. M. Ho, J. Appl. Phys. 87, 603 (2000).

[32] M. Bayindir, B. Temelkuran, and E. Ozbay, Phys. Rev. B, 61, 11855 (2000).

[33] H. Benisty, J. Appl. Phys. 79, 7483 (1996).

[34] A. Mekis, S. Fan, and J.D. Joannopoulos, Phys. Rev. B, 58, 4809 (1998).

[35] J. Y. Andersson and L. Lundqvist, J. Appl. Phys. 71, 3600 (1992).

[36] Y. Fu, M. Willander, W. Lu, and W. Xu, J. Appl. Phys. 84, 5750 (1998).

[37] M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, Opt. Lett. 23, 1331(1998).

[38] J. P. Kottmann and O. J. F. Martin, Opt. Express, 8, 655 (2001).

[39] A. Drezet, A. L. Stepanov, H. Ditlbacher, A. Hohenau, B. Steinberger, F. R.Aussenegg, A. Leitner, and J. R. Krenn, Appl. Phys. Lett. 86, 074104 (2005).

BIBLIOGRAPHY 65

[40] Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, Nano Lett.5, 1726 (2005).

[41] Z. Liu, J. M. Steele, H. Lee, and X. Zhang, Appl. Phys. Lett. 88, 171108 (2006).

[42] J. M. Steele, Z. Liu, Y. Wang, and X. Zhang, Opt. Express, 14, 5664 (2006).

[43] P. Berini, Phys. Rev. B 61, 10484 (2000).

[44] J. C. Weeber, A. Dereux, C. Girard, J. R. Krenn, and J. P. Goudonnet, Phys. Rev.B 60, 9061 (1999).

[45] J. C. Weeber, Y. Lacroute, and A. Dereux, Phys. Rev. B 68, 115401 (2003).

[46] R. Zia, M. D. Selker, and M. L. Brongersma, Phys. Rev. B 71, 165431 (2005).

[47] J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, Phys. Rev. B 72,075405 (2005).

[48] I. V. Novikov and A. A. Maradudin, Phys. Rev. B 66, 035403 (2002).

[49] S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, Phys. Rev. Lett.95, 046802 (2005).

[50] S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen,Nature, 440, 508 (2006).

[51] S. I. Bozhevolnyi, J. Erland, K. Leosson, P. M. W. Skovgaard, and J. M. Hvam,Phys. Rev. Lett. 86, 3008 (2001).

[52] J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, Opt. Lett.22, 475 (1997).

[53] A. Mcmillan, C. D. Paavola, J. Howard, S. L. Chan, N. J. Zaluzec, and J. D. Trent,Nature Mater. 1, 247 (2002).

[54] S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A.G. Requicha, Nature Mater. 2, 229 (2003).

[55] J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet,G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, Phys. Rev.Lett. 82, 2590 (1999).

[56] N. E. Hecker, R. A. Hopfel, N. Sawaki, T. Maier, and G. Strasser, Appl. Phys. Lett.75, 1577 (1999).

[57] A. Neogi, C. Lee, H. O. Everitt, T. Kuroda, A. Tackeuchi, and E. Yablonovitch,Phys. Rev. B 66, 153305 (2002).

[58] S. Wedge, I. R. Hooper, I. Sage, and W. L. Barnes, Phys. Rev. B 69, 245418 (2004)

[59] T. D. Neal, K. Okamoto, A. Scherer, M. S. Liu, and A. K. Jen, Appl. Phys. Lett.89, 221106 (2006).

66 BIBLIOGRAPHY

[60] K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, NatureMater. 3, 601 (2004).

[61] A. V. Krasavina and N. I. Zheludev, Appl. Phys. Lett. 84, 1416 (2004).

[62] A. V. Krasavin, K. F. MacDonald, N. I. Zheludev, and A. V. Zayats, Appl. Phys.Lett. 85, 3369 (2004).

[63] A. V. Krasavin, K. F. MacDonald, A. S. Schwanecke, and N. I. Zheludev, Appl.Phys. Lett. 89, 031118 (2006).

[64] A. V. Krasavin, A. V. Zayats, and N. I. Zheludev, J. Opt. A: Pure Appl. Opt. 7,S85 (2005).

[65] J. A. Sanchez-Gil and J. G. Rivas, Phys. Rev. B 73, 205410 (2006).

[66] A. A. Govyadinov and V. A. Podolskiy, Phys. Rev. Lett. 97, 223902 (2006).

[67] P. Andrew and W. L. Barnes, Science, 306,1002 (2004).

[68] R. P. Van Duyne, Science 306, 985 (2004).

[69] A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, Phys. Reports, 408, 131(2005).

[70] E. Ozbay, Science 311, 189 (2006).

[71] C. Girard, Rep. Prog. Phys. 68, 1883 (2005).

[72] C. Girard and E. Dujardin, J. Opt. A: Pure Appl. Opt. 8, S73 (2006).

[73] S. A. Maier and H. A. Atwater, J. Appl. Phys. 98, 011101 (2005).

[74] S. A. Ramakrishna, Rep. Prog. Phys. 68, 449 (2005).

[75] C. M. Soukoulis, M. Kafesaki, and E. N. Economou, Adv. Mater. 18, 1941 (2006).

[76] J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, Rep. Prog. Phys.70, 1 (2007).

[77] W. L. Barnes, A. Dereux, and T. W. Ebbesen, Nature 424, 824 (2003).

[78] W. Nomura, M. Ohtsuand, and T. Yatsui, Appl. Phys. Lett. 86, 181108 (2005).

[79] L. Chen, J. Shakya, and M. Lipson, Opt. Lett. 31, 2133 (2006).

[80] M. Yan and M. Qiu, J. Opt. Soc. Am. B, 24, 2333 (2007).

[81] Y. Song, J. Wang, Q. Li, M. Yan, and M. Qiu, Opt. Express 18, 13173 (2010).

[82] J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. V. Duyne,Nature Mater. 7, 442 (2008).

[83] M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers,and R. G. Nuzzo, Chem. Rev. 108, 494 (2008).

BIBLIOGRAPHY 67

[84] E. Kretschmann and H. Raether, Z. Naturf. A 23, 2135 (1968).

[85] A. Otto, Zeitschrift fur Physik, 216, 398 (1968).

[86] J. Rosenberg, R. V. Shenoi, T. E. Vandervelde, S. Krishna, and O. Painter, Appl.Phys. Lett. 95, 161101 (2009).

[87] S. Hellstrom, Z.-H. Chen, Y. Fu, M. Qiu, R. Soltanmoradi, Q. Wang, and J. Y.Andersson, Appl. Phys. Lett. 96, 231110 (2010).

[88] S. Pillai, K.R. Catchpole, T. Trupke, and M. A. Green, J. Appl. Phys. 101, 093105(2007).

[89] D. Duche, Ph. Torchio, L. Escoubas, F. Monestier, J. J. Simon, F. Flory, and G.Mathian, Sol. Energy Mater. Sol. Cells 93, 1377 (2009).

[90] W.J. Yoon, K.Y. Jung, J. Liu, T. Duraisamy, R. Revur, F.L. Teixeira, S. Sengupta,and P.R. Berger, Sol. Energy Mater. Sol. Cells 94, 128 (2010).

[91] F.de Medeiros, E. Albuquerque, M. Vasconcelos, and G. Farias, Surface Sci. 600,4337 (2006).

[92] A. N. Poddubny and E. L. Ivchenko, Physica E 42, 1871 (2010).

[93] Z.-H. Chen, S. Hellstrom, Z.-J. Ning, Z.-Y. Yu, and Y. Fu, J. Phys. Chem. C , 115,5286 (2011).

[94] F. Ferdos, S. Wang, Y. Wei, M. Sadeghi, Q. Zhao, and A. Larsson, J. CrystalGrowth, 251, 145 (2003).

[95] Z. Ning, H. Tian, C. Yuan, Y. Fu, H. Qin, L. Sun, and H. Agren, Chem. Commun.47, 1536 (2011).

[96] Y. Alhassid, Rev. Mod. Phys. 72, 895 (2000).

[97] S. M. Reimann and M. Manninen, Rev. Mod. Phys. 74, 1283 (2002).

[98] W. G. van der Wiel, S. De Franceschi, J. M. Elzerman, T. Fujisawa, S. Tarucha,and L. P. Kouwenhoven, Rev. Mod. Phys. 75, 1 (2003).

[99] Y. Fu, E. Berglind, L. Thylen, and H. Agren, J. Opt. Soc. Am. B 23, 2441 (2006).

[100] C. Wang, L. Huang, B. A. Parviz, and L. Y. Lin, Nano Lett. 6, 2549 (2006).

[101] L. Huang, C. Wang, and L. Y. Lin, Opt. Lett. 32, 235 (2007).

[102] I. L. Medintz, H. T. Uyeda, E. R. Goldman, and H. Mattoussi, Natrue materials,4, 435 (2005).

[103] B. F. Levine, K. K. Choi, C. G. Bethea, J. Walker, and R. J. Malik, Appl. Phys.Lett. 50, 1092 (1987).

[104] B. F. Levine, J. Appl. Phys. 74, R1-R81 (1993).

68 BIBLIOGRAPHY

[105] J. Y. Andersson and L. Lundqvist, Appl. Phys. Lett 59, 857 (1991).

[106] J. Y. Andersson, J. Appl. Phys. 78, 6298 (1993).

[107] J. Y. Andersson, J. Alverbro, J. Borglind, P. Helander, H. Martijn, and M. ostlund,Proceeding of the SPIE, Infrared Technology and Applications XXIII, 3061, 740(1997).

[108] H. Schneider, M.Walther, C. Schonbein, R. Rehm, J. Fleissner, W. Pletschen, J.Braunstein, P. Koidl, G. Weimann, J. Ziegler, and W. Cabanski, Physica E, 7, 101(2000).

[109] H. Schneider, J. Fleissner, R. Rehm, M. Walther, W. Pletschen, P. Koidl, G.Weimann, J. Ziegler, R. Breiter, and W. Cabanski, SPIE 4820, 297-305 (2003).

[110] K.-K. Choi, K.-M. Leung, T. Tamir, and C. Monroy, IEEE J. Quantum Electron.40, 130 (2004).

[111] C. J. Chen, K.-K. Choi, M. Z. Tidrow, and D. C. Tsui, Appl. Phys. Lett. 68, 1446(1996).

[112] K.-K. Choi, D. P. Forrai, D. W. Endres, and J. Sun, IEEE J. Quantum Electron.45, 1255 (2009).

[113] H. Schneider and H.C. Liu, Quantum Well Infrared Photodetectors: physics andapplications (Springer, Berlin, 2007).

[114] J. Jiang, S. Tsao, K. Mi, M. Razeghi, G. J. Brown, C. Jelen, and M. Z. Tidrow,Infrared Phys. Technol. 46, 199 (2005).

[115] E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press, San Diego,1998).

[116] M. A. Green, Solar cells: Operating Principles, Technology and System Applica-tions, (Prentice-Hall, New Jersey, 1982).

[117] M. A. Green, A. W. Blakers, J. Shi, E. M. Keller, and S. R. Wenham, IEEE Trans.Electron Devices 31, 679 (1984).

[118] M. A . Green, Third Generation Photovoltaics: Advanced Solar Energy Conversion,(Springer, Berlin, 2003).

[119] M. A. Green, P. A. Basore, N. Chang, D. Clugston, R. Egan, R. Evans, D. Hogg,S. Jarnason, M. Keevers, P. Lasswell, J. O’Sullivan, U. Schubert, A. Turner, S. R.Wenham, and T. Younget, Solar Energy 77, 857 (2004).

[120] Z. Ning, Y. Fu, and H. Tian, Energy Environ. Sci. 3, 1170 (2010).

[121] G. P. Smestad, Optoelectronics of solar cells, (SPIE Press, Washington, 2002).

[122] H.-D. Kim and V. P. Oleg, ACS Nano, 6, 1239 (2012).

BIBLIOGRAPHY 69

[123] A. Taflove, Computational Electrodynamics: The Finite-Difference Time-DomainMethod (Artech House, Norwood, 1995).

[124] K. J. Webb and J. Li, Phys. Rev. B 73, 033401 (2006).

[125] K. M. Ho, C. T. Chan, and C. M. Soukoulis, Phys. Rev. Lett. 65, 3152 (1990).

[126] Y. Zeng, Y. Fu, X. Chen, W. Lu, and H. Agren, Solid State Commun. 139, 328(2006).

[127] K. S. Yee, IEEE Trans. Antennas and Propagation, 14, 302-307 (1966).

[128] A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G.Johnson, Computer Physics Communications, 181, 687 (2010).

[129] S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).

[130] M. Qiu and S. He, Phys. Rev. B 61, 12871 (2000).

[131] M. Qiu and S. He, J. Appl. Phys. 87, 8268 (2000).

[132] A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D.Joannopoulos, S. G. Johnson, and G. W. Burr, Opt. Lett. 31, 2972 (2006).

[133] Y. Fu, Y. Zeng, and H. Agren, Appl. Phys. A 87, 167 (2007).

[134] J. P. Berenger, J. Computational Physics, 114, 185 (1994).

[135] J. P. Berenger, IEEE Trans. Antennas Propag. 45, 466 (1997).

[136] M. Fox, Optical Properties of Solids, (Oxford University Press, Oxford, 2001).

[137] Y. Fu, L. Thylen, and H. Agren, Nano Letters, 8, 1551 (2008).

[138] S. Hellstrom and Y. Fu, Phys. Rev. B, 82, 245305 (2010).

[139] F. J. Taylor, Principles of signals and systems, (McGraw-Hill, New York, 1994).

[140] J. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (Wiley, New York,2002).

[141] Y. Fu and M. Qiu, Optical Properties of Nanostructures, (Pan Stanford Publishing,Singapore, 2011).

[142] H. Kirmse, R. Schneider, M. Rabe, W. Neumann, and F. Henneberger, Appl. Phys.Lett. 72, 1329 (1998).

[143] S. Lee, I. Daruka, C. S. Kim, A. L. Barabasi, J. L. Merz, and J. K. Furdyna, Phys.Rev. Lett. 81, 3479 (1998).

[144] M. C. Tamargo, II-VI semiconductor materials and their applications, (Taylor andFrancis, New York, 2002).

[145] Y. Fu, S. Hellstrom, and H. Agren, J. Nonlinear Opt. Phys. Mater. 18, 195 (2009).

70 BIBLIOGRAPHY

[146] Z.-H. Chen, S. Hellstrom, Z.-Y. Yu, M. Qiu, and Y. Fu, Appl. Phys. Lett. 100,043502 (2012).

[147] Y. Fu, Superlattices Microstruct. 30, 69 (2001).

[148] L. Ouattara, A. Mikkelsen, and E. Lundgren, L. Hoglund, C. Asplund, and J. Y.Andersson, Appl. Phys. Lett. 100, 044320 (2006).

[149] X.-F. Yang, K. Fu, W. Lu, W.-L. Xu, and Y. Fu, J. Phys. D: Appl. Phys. 42,125414 (2009).

[150] Y. Fu, S. M. Wang, F. Ferdos, M. Sadeghi, and A. Larsson, J. Nanosci. Nanotech-nol. 2, 421 (2002).

[151] X.-J. Shang, J.-F. He, M.-F. Li, F. Zhan, H.-Q. Ni, Z.-C. Niu, H. Pettersson, andY. Fu, Appl. Phys. Lett. 99, 113514 (2011).

[152] H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Propertiesof Semiconductors, World Scientific, Singapore, 1986.

[153] Y. Fu, T.-T. Han, Y. Luo, and H. Agren, J. Phys. Condens. Matter, 18, 9071(2006).

[154] W. W. Yu, L. Qu, W. Guo, and X. Peng, Chem. Mater. 15, 2854 (2003).

[155] R. Xie, U. Kolb, J. Li, T. Basche, and A. Mews, J. Am. Chem. Soc. 127, 7480(2005).

[156] R. D. Meade, K. L. Brommer, A. M. Rappe, and J. D. Joannopoulos, Appl. Phys.Lett. 61, 495 (1992).

[157] M. Agio and L. C. Andreani, Phys. Rev. B 61, 15519 (2000).

[158] R. Moussa, B. Wang, G. Tuttle, Th. Koschny, and C.M. Soukoulis, Phys. Rev. B76, 235417 (2007).

[159] Q. Wang, J. Y. Zhang, C. C. Yan, and Y. P. Cui, Phys. Lett. A 373, 1097 (2009).

[160] E. Moreno, F. J. Garcıa-Vidal, and L. Martın-Moreno, Phys. Rev. B 69, 121402(2004).

[161] S. K. Morrison and Y. S. Kivshar, Appl. Phys. Lett. 86, 081110 (2005).

[162] E. H. Khoo, A. Q. Liu, T. H. Cheng, J. Li, and D. Pinjala, Appl. Phys. Lett. 91,221105 (2007).

[163] H. Kurt, IEEE Photon. Technol. Lett., 20, 1682 (2008).

[164] M. Bayindir, B. Temelkuran, and E. Ozbay, Appl. Phys. Lett. 77, 3902 (2000).

[165] W. Y. Liang, J. W. Dong, and H. Z. Wang, Opt. Express, 15, 1234 (2007).

[166] L. Jiang, W. Jia, H. Li, X. Li, C. Cong, and Z. Shen, J. Opt. Soc. Am. B, 26, 2157(2009).

BIBLIOGRAPHY 71

[167] T. K. Gaylord, W. E. Baird, and M. G. Moharam, Appl. Opt. 25, 4562 (1986).

[168] E. Yablonovitch and G. Cody, IEEE Trans. Electron Devices 29, 300 (1982).

[169] Z. Yu, A. Raman, and S. Fan, Proc. Natl. Acad. Sci. 107, 17491 (2010).

[170] M. A. Green, Prog. Photovolt: Res. Appl. 19, 473 (2011).

[171] J. Zhu, Z. Yu, S. Fan, and Y. Cui, Mater. Sci. Eng. R-Rep. 70, 330 (2010).

[172] X. Meng, G. Gomard, O. E. Daif, E. Drouard, R. Orobtchouk, A. Kaminski, A.Fave, M. Lemiti, A. Abramov, P. R. i. Cabarrocas, and C. Seassal, Sol. EnergyMater. Sol. Cells 95, S32 (2011).

[173] D. Duche, E. Drouard, J. J. Simon, L. Escoubas, Ph. Torchio, J. Le Rouzo, andS. Vedraine, Sol. Energy Mater. Sol. Cells 95, S18 (2011).

[174] D.-H. Ko, J. R. Tumbleston, L. Zhang, S. Williams, J. M. DeSimone, R. Lopez,and E. T. Samulski, Nano Lett. 9, 2742 (2009).

[175] S. Guldin, S. Huttner, M. Kolle, M. E. Welland, P. Muller-Buschbaum, R. H.Friend, U. Steiner, and N. Tetreault, Nano Lett. 10, 2303 (2010).

[176] K. S. Leschkies, R. Divakar, J. Basu, E. Enache-Pommer, J. E. Boercker, C. B.Carter, U. R. Kortshagen, D. J. Norris, and E. S. Aydil, Nano Lett. 7, 1793 (2007).

[177] R. Biswas, J. Bhattacharya, B. Lewis, N. Chakravarty, and V. Dalal, Sol. EnergyMater. Sol. Cells 94, 2337 (2010).

[178] B. Park, M. Kim, and Y. I. Lee, Sol. Energy Mater. Sol. Cells 95, 1141 (2011).

[179] Z.-H. Chen, S. Hellstrom, Z.-Y. Yu, and Y. Fu, Sol. Energy Mater. Sol. Cells 99,316 (2012).

[180] J. K. Kim, S. Chhajed, M. F. Schubert, E. F. Schubert, A. J. Fischer, M. H.Crawford, J. Cho, H. Kim, and C. Sone, Adv. Mater. 20, 801 (2008).

[181] G. P. Smestad, S. Spiekermann, J. Kowalik, C. D. Grant, A. M. Schwartzberg, J.Zhang, L. M. Tolbert, and E. Moons, Sol. Energy Mater. Sol. Cells 76, 85 (2003).

[182] M. Wang, N. Chamberland, L. Breau, J.-E. Moser, R.H.-Baker, B. Marsan, S. M.Zakeeruddin, and M. Grazel, Nat. Chem. 2, 385 (2010).

[183] Z.-H. Chen, Y. Fu, and Z.-Y. Yu, The European Conference on Lasers and Electro-Optics (CLEO/Europe), Munich, Germany, May 22, 2011.

[184] T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature, 391,667 (1998).

[185] H. Shin, P. B. Catrysse, and S. Fan, Phys. Rev. B 72, 085436 (2005).

[186] Y. Zeng, Y. Fu, X. Chen, W. Lu, and H. Agren, Phys. Rev. B 76, 035427 (2007).

72 BIBLIOGRAPHY

[187] L. Salomon, F. Grillot, A. V. Zayats, and F. de Fornel, Phys. Rev. Lett. 86, 1110(2001).

[188] J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Science, 305, 847 (2004).

[189] H. F. Ghaemi, T. Thio, D. E. Grupp, and T. W. Ebbesen, H. J. Lezec, Phys. Rev.B 58, 6779 (1998).

[190] P. Lalanne, C. Sauvan. J. P. Hugonin, J. C. Rodier, and P. Chavel, Phys. Rev. B68, 125404 (2003).

[191] E. Popov, M. Neviere, S. Enoch, and R. Reinisch, Phys. Rev. B 62, 16100 (2000).

[192] R. Muller, V. Malyarchuk, and C. Lienau, Phys. Rev. B 68, 205415 (2003).

[193] S. A. Darmanyan and A. V. Zayats, Phys. Rev. B 67, 035424 (2003).

[194] F. I. Baida and D. V. Labeke, Phys. Rev. B 67, 155314 (2003).

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