ÉCOLE CENTRALE de LYON

INSTITUT des NANOTECHNOLOGIES de LYON

CENTRE NATIONAL de la RECHERCHE SCIENTIFIQUE

____________________________________________________________________

Rybin Maxim

Graphene-photonic crystal hybrid structures for light harnessing

Electronique, Electrotechnique, Automatique

Scientific director:

Viktorovitch Pierre

Scientific director:

Obraztsova Elena

Lyon – 2013

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Résumé

La croissance continue de la complexité des systèmes rend inévitable le

développement de procédés technologiques pour lesquels différents types de

matériaux sont intégrés de manière hétérogène dans le but de réaliser une palette de

fonctionnalités, tout en miniaturisant la taille des dispositifs et en abaissant les coûts

de fabrication.

Cela est particulièrement vrai dans le domaine de la Photonique, pour laquelle

ces impératifs peuvent être atteints selon les lignes résumées ci-après :

- Miniaturisation photonique, dont la principale motivation réside dans la

nécessité d’assurer un faible budget thermique, ainsi qu’une bonne compatibilité

topologique avec les circuits microélectroniques, tout en bénéficiant du contrôle de

l’interaction lumière-matière offert par les microstructures photoniques.

- Intégration photonique hétérogène active/passive, combinant les matériaux

actifs (émission de lumière, caractéristiques non-linéaires) les plus efficaces avec les

matériaux passifs les mieux adaptés (conduction et confinement de la lumière), en

vue de tirer le meilleur parti de chacun.

Ce travail de thèse est consacré au développement de nouvelles approches

destinées à satisfaire les impératifs évoqués précédemment, l’objectif étant la

production de nouvelles classes de dispositifs photoniques associant les matériaux

silicium et graphène, exploitant les caractéristiques non-linéaires uniques de ce

dernier (absorption saturable ultrarapide et indépendante de la longueur d’onde) et

les remarquables capacités du premier pour la fabrication de structures photoniques

miniaturisées permettant un fort confinement de la lumière en utilisant les procédés

de fabrication avancés et bas coût de la microélectronique silicium.

Concernant la miniaturisation photonique, il est proposé de mettre en oeuvre

une stratégie de confinement de type diffractif à base de structures périodiques à fort

contraste d’indice pour le contrôle spatio-temporel de la trajectoire des photons.

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Cette stratégie, au cœur des récents développements de la Micro-Nano-Photonique,

est usuellement répertoriée sous la nomination de l’approche « Cristal Photonique ».

Selon cette approche le matériau silicium a été utilisé en raison de ses remarquables

caractéristiques photoniques : son indice optique élevé (autour de 3,5) en fait un

excellent candidat pour la réalisation de cristaux photoniques ; cela s’est avéré

particulièrement vrai dans la configuration dite membrane, dans laquelle un cristal

photonique 1D est formé dans une couche mince de silicium sur isolant, en

l’occurrence la silice (SOI). Il a été démontré, théoriquement et expérimentalement,

que ces cristaux photoniques 1D peuvent se comporter comme des résonateurs,

adressables par la surface verticalement, c’est-à-dire comme des réservoirs de

photons où l’énergie électromagnétique peut être accumulée et stockée

temporairement de manière à assurer un couplage efficace (absorption) au matériau

graphène, moyennant un coût très réduit en termes de la puissance incidente

(réduction théorique d’un facteur 25, facteur 7 réalisé expérimentalement). Le

résonateur à base de cristal photonique 1D conçu et réalisé dans ce travail fournit

également un « sous-produit » photonique très attractif : il se comporte comme un

réflecteur compact très efficace, dont les caractéristiques spectrales peuvent être

contrôlées à volonté.

Un travail important à été consacré à la synthèse du graphène par méthode de

dépôt en phase vapeur sur des substrats de nickel et de cuivre : une analyse détaillée

de l’influence des paramètres de dépôt et des mécanismes de croissance a été réalisée.

Il a été démontré que ces substrats peuvent être utilisés pour la production de une à

quelques monocouches de graphène couvrant une surface d’environ 2cm2, de très

haute qualité structurale, comme validé par spectroscopie Raman. Il a été montré que

les échantillons obtenus possèdent des propriétés optiques non-

linéaires remarquables: notamment, le temps de relaxation des électrons excités dans

le matériau a été analysé par des méthodes spectroscopiques pompe-sonde dans la

gamme spectrale 1100-1700nm. L’effet de saturation de l’absorption a été étudié

autour de 10.5µm, et la saturation de l’absorption a été observée.

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La prochaine étape de ce travail sera la démonstration de l’absorption saturable

de graphène intégré avec un résonateur photonique silicium membranaire, pour une

puissance incidente réduite : cet aspect est en cours d’investigation dans les

Institutions à Moscou et Lyon où ce travail de thèse a été réalisé. Nombre d’autres

étapes sont attendues dans le futur, pour lesquelles la combinaison du graphène et du

silicium proposé dans cette thèse devraient conduire à la production d’une variété de

composants photoniques compacts originaux, incluant des dispositifs absorbant

saturables très rapides ainsi que des modulateurs optiques également très rapides et

accordables en longueur d’onde.

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Content

Introduction ................................................................................................................. 7

Chapter 1. Graphene and photonic crystals (literature review) ............................ 9

1.1 Graphene ............................................................................................................. 9

1.1.1 Atomic structure and band structure............................................................ 9

1.1.2 Synthesis .................................................................................................... 11

1.1.3 Optical properties and optical diagnostic tools of graphene...................... 18

1.2 Photonic crystals ............................................................................................... 23

1.2.1 Introduction to photonic crystals ...............................................................23

1.2.2 Resonant membrane reflector based on surface addressable photonic

crystal waveguiding structure. ............................................................................ 30

Chapter 2. Synthesis and investigation of graphene : experimental results [A2,

A3, A6, A8, A9] .......................................................................................................... 35

2.1 Original equipment for graphene synthesis by CVD method........................... 35

2.2 Methods for graphene transferring.................................................................... 38

2.3 Synthesis of graphene and its identification by optical methods...................... 40

2.3.1 Nickel foil of 50 micron thickness............................................................. 40

2.3.2 Nickel foil of 25 microns thickness ........................................................... 42

2.3.3 Copper foil of 25 microns thickness .......................................................... 46

2.4 Optical properties of graphene.......................................................................... 49

2.4.1 Pump-probe spectroscopy.......................................................................... 50

2.4.2 Absorbance in mid-IR range......................................................................54

Chapter 3. One-dimensional photonic crystals – simulation and fabrication..... 56

3.1 General concepts for design of reflective structures......................................... 57

3.2. Basic principles of computer simulation..........................................................62

3.3 Design and fabrication of weakly corrugated 1D PC membrane reflectors ..... 63

3.3.1 Simulation of structures ............................................................................. 63

3.3.2 Fabrication and characterization of structures ........................................... 67

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3.4 New design and fabrication of 1D PC membrane reflectors with adjustable

bandwidth and air filling factors close to 50% ....................................................... 71

3.4.1 Discovering new design of reflectors ........................................................ 71

3.4.2 Simulations of structures............................................................................ 73

3.4.3 Fabrication and characterization ................................................................79

Chapter 4. Combination of graphene with resonant 1D photonic crystal

membrane reflectors: theoretical and experimental measurements [A4, A7] .... 84

4.1 Concept of integration of a 1D photonic crystal membrane reflector with

graphene .................................................................................................................. 84

4.2 Simulation of enhancement of optical properties of graphene integrated with

PC ............................................................................................................................ 87

4.3 Experimental characterization of devices combining graphene and PC .......... 92

Conclusion.................................................................................................................. 96

Author’s publications.............................................................................................. 100

References ................................................................................................................ 101

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Introduction

Hybrid structure is a structure in which chemically different materials interact

with each other. The task of creating different hybrid structures are always

interesting and promising in terms of getting new and unique experimental results. In

most cases, hybrid structures are designed and studied in order to find new properties

or to change the properties of one of the used materials. In this work, in the first time

ever the idea to create hybrid structures based on photonic crystals and graphene for

changing the optical properties of the latter is proposed.

The study of graphene nowadays is one of the most popular topics in the field

of nanomaterials. In 2010, the Nobel Prize "for groundbreaking experiments

regarding the two-dimensional material graphene" was awarded to Konstantin

Novoselov and Andre Geim. Recall that graphene is a two-dimensional structure

where the carbon atoms are arranged in hexagons. Graphene is a constituent unit of

graphite and it has been used as a theoretical model to describe other forms of carbon

allotropes, such as fullerenes and nanotubes. Despite the fact that the first

experimental samples of graphene have been obtained recently (in 2004), there is

already a lot of studies on graphene applications in various areas. The number of

publications devoted to graphene grows exponentially as a function of time.

All of the features of graphene are based on its band structure. In the first

Brillouin zone of graphene, there are special points K and K', near those the

dispersion of the electron energy has a linear dependence on the wave vector. Thus,

graphene is a semiconductor with a zero band gap and the behaviour of the electrons

is described not by the Schrödinger equation (as in bulk semiconductors), but by a

two-dimensional Dirac equation for massless quasi-particles. Due to its specific

electronic structure graphene demonstrates unique electronic properties, such as

quantum Hall effect, ultra-high electron mobility, etc. Moreover graphene has

outstanding optical performance. Its optical absorption, equals to 2.3% of the

incident radiation intensity, does not depend on wavelength.

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The second constitute of the proposed hybrid structures is photonic crystal,

which is the crystal with a periodically repeating refractive index. Due to its specific

structure the photonic crystals allow to control the flow of light. It is possible to

create so-called "stop-band" for photons or to localize photons in space during a

certain time by selecting the parameters of photonic crystals. In nature, photonic

crystals are very close to us. The wings of butterflies are made of photonic crystals,

where its different coloring is determined by the reflection of a specific wavelength

of light, at which there is a stop-band for photons at certain incident angle. In modern

optoelectronics and optics, photonic crystals are widely used in devices such as

different reflecting surfaces, optical fiber waveguides or a vertical-cavity surface-

emitting laser.

Thus, a combination of graphene with photonic crystals can result in a tenfold

increase of the effective optical absorption in graphene comparing with a baseline

graphene light absorption which equals to 2.3% of the incident radiation intensity.

This increase of absorption in graphene makes possible to observe the nonlinear

optical effects in the two-dimensional carbon material at lower intensities of the

incident radiation. For example, the effect of saturation of absorption occurs when

the power density is more than 0.1 mW/cm2, but such power cannot be obtained on

the microchip, and also this power value is close to the threshold of material

degradation. So, the described problem is actual and has no solution at present time.

This urgent problem is one of the tasks solved in this thesis.

In this work I present a complete cycle of the problem solution. At first, the

installation for the synthesis of graphene was created and linear and non-linear

optical properties of synthesized graphene were studied. Then the necessary

parameters of photonic crystals have been chosen on the base of computer simulation,

and the experimental structures were fabricated. At the final step the model of hybrid

structure based on graphene and photonic crystal was studied using computer

methods and the samples with desired properties were produced. The effect of

enhancement of graphene optical absorbance in case of its combination with

photonic crystal has been demonstrated.

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Chapter 1. Graphene and photonic crystals (literature review)

1.1 Graphene

1.1.1 Atomic structure and band structure

Carbon is one of the most interesting elements of the periodic table. It has a lot

of allotropes and some of them, diamond and graphite, for instance, were well

known for a long time, while the others were discovered a few decades ago

Fig. 1. Graphene is a two dimensional form of carbon. As a base of all carbon

structures, it can be transformed in allotropes with different dimensionalities [7]:

a) 0-dimensional structure – fullerene;

b) 1-dimensional structure – nanotube;

c) 3- dimensional structure – graphite, containing several graphene layers.

a) b) c)

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(fullerenes [1] and nanotubes [2]).

Earlier a two dimensional carbon form, graphene, was investigated theoretically

[3, 4, 5]. In fact the existence of such a structure was not admitted and it was

considered as a virtual model for describing the other carbon forms (figure 1). But

just nine years ago the experimental results on graphene production have been

published [6]. The atomic structure of graphene is a two dimensional hexagon lattice

of carbon atoms [7, 8, 9]. There are two atoms in its unit cell, marked as A and B in

figure 2a. Each of these atoms forms a sublattice of equivalent atoms linked by a

translation vector rA=me1+ne2, where n and m are integers. In figure 2a the two sub-

lattices of atoms are colored in red and green, respectfully.

The energy band structure of graphene is described by Dirac equation instead of

Schrödinger equation (as it is usual for bulk materials). It can be interpreted as a

result of the atomic structure, which consists, as mentioned above, of two equivalent

carbon sub-lattices A and B (figure 2c). The quantum-mechanical transition between

these sub-lattices brings to the formation of two groups of energies, and their

crossing in the special point K and K’ of the first Brillion zone leads to the cone-like

energy spectrum (figure 2b). As a result the quasi particles in graphene demonstrate a

Fig. 2. Atomic and electronic structures of graphene. a) An elementary cell is shown in

yellow color; e1 and e2 are translation vectors. b) A valence zone touches a conduction

zone in the special points K and K’ of the first Brillion zone. c) A central lattice junction

(A) in the environment of nearest atoms; the red dashed circle shows the nearest

neighbours from the same crystal sublattice (A), and the green dashed circle shows the

atoms from the other sublattice (B).

a) b) c)

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linear dispersion characteristic: E=hkvF, like the massless relativistic particles (for

instance, photons), but instead of the light velocity there is a Fermi velocity vF≈c/300.

The quasi particles in graphene behave differently from the particles in metals or

semiconductors, where the energy spectrum can be approximated by parabolic

dispersion equations.

1.1.2 Synthesis

The theoretical investigation of graphene started long before the production of

experimental samples. A freestanding two dimensional carbon film should be

thermodynamically unstable according to the calculations of 30-40 years of previous

century, and this was a reason for the formation of carbon structure on the surfaces of

bulk materials. The first steps of fabrication of single carbon layer were done in the

1960-70 years using either colloidal solutions of graphite oxide [10, 11] or chemical

vapor deposition techniques from hydrocarbons onto metallic substrates [ 12 ].

Alternatively, so-called epitaxial method has been developed, consisting in a high

temperature treatment of silicon carbide under vaporization of silicon, thus resulting

in the formation of carbon film [13, 14]. However, all these methods resulted in

production of the several layer (around 20-30 layers) films, which are not a single

layer graphene film, in fact. A more detailed review of the listed methods of thin

carbon films fabrication can be found in reference [15]. The description of a few

main methods of graphene preparation is proposed below to the reader, since the

fabrication process has a strong influence on the properties of the final samples.

A new step of the graphene investigation has occurred after the first preparation

and characterization of graphene monolayer samples in 2004 by the Manchester

group headed by A. Geim and K. Novoselov [6]. A single layer, transferred onto

silicon substrate with an intermediate 300 nm thick oxide layer, has been obtained by

a mechanical cleavage of graphite with an adhesive tape. The graphene-oriented

activity has been triggered after the first publication about unique electronic

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properties of the novel carbon material – graphene. The optical and mechanical

properties have been investigated as well, the technology of graphene fabrication has

been developed in parallel. A few common technologies which are the mainstream in

graphene fabrication area should be highlighted among all of the variety of

fabrication processes. The advantages and drawbacks of every technology are

described to justify the method which has been selected in the present work for the

preparation of graphene samples.

1. A micromechanical cleavage of the highly ordered pyrolytic graphite

(HOPG) [6, 16, 17];

2. A chemical method used a colloidal dispersion based on compounds

consisting of graphene layers [18, 19, 20];

3. An epitaxial growth on the surfaces of different monocrystalline substrates

[ 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33] or a thermal

decomposition of SiC [34, 35, 36, 37];

4. A chemical vapor deposition of hydrocarbons on the surfaces of nickel [38,

39, 40, 41, 42, 43] or copper [44,45, 46, 47].

A few words about the first method: a few monolayer thick film is detached

from the bulk pyrolytic graphite by a sticky tape. A single layer can be formed on the

tape by repeating the same procedure several times. Then the carbon film is

transferred onto a silicon substrate capped with a 300 nm thick silicon dioxide layer:

the graphene layer is bonded to the silica top layer via the Van der Waals forces

(figure 3). However, a lot of few layer graphene

flakes with a thickness up to 100 layers and a

lateral size about 100 µm are transferred onto the

substrate as well. Thereby the detection of a single

piece of graphene monolayer with the size of few

tens of microns on the few cm2 substrates is a

heavy task. In any case such method for the

graphene production shows the maximum quality

of the fabricated samples. They are appropriate for

Fig.3. A scheme of graphene

fabrication by a

micromechanical cleavage.

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the electronic and transport measurements and can be used for fabrication of

experimental prototypes of different electronic devices, for instance, a quantum

transistor [6, 16, 17]. But a considerable drawback of this method is its fully

incompatibility with a scalable and mass graphene production.

The second popular

technique of graphene

fabrication is chemical. A

variety of chemical approaches

exists for production of

graphene-based solutions

(figure 4). At first, a method of

graphene production from

graphite oxide has been

proposed [48, 49, 50, 51]. This

effective approach for

separation of graphite layers is

based on the strong chemical oxidants, for instance, on oxygen and halogen. As a

result of oxidation of internal graphite layers, the distance between non oxidized

layers increases while the coupling energy between these layers decreases. A

possibility of separation of graphite layers increases. This allows synthesizing the

graphene oxide flakes with lateral sizes of a few hundreds of microns. Then a

subsequent graphene reduction from graphene oxide is achieved with a chemical

reaction using hydrazine, for instance. The procedure of oxidation of bulk graphite

accompanied by increasing the interlayer distance is well known from the beginning

of the nineteenth century. The oxidation order and the chemical composition of

prepared samples depend on the experimental conditions, on the initial materials and

on the quality of chemical reagents. The investigations have shown that the surface

of oxidized materials usually contains the hydroxyl and epoxy groups while the

edges of the sample end by the carboxyl and carbonyl groups. This results in

reduction of electrical and optical propertied of graphene.

Fig. 4. Routes for graphene formation from different

carbon materials [51].

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Another chemical approach for graphene fabrication is a liquid exfoliation of

graphite [52, 53, 54]. The easiest way to separate graphite into single graphene layers

is to exploit a surface-active agent (surfactant) which can penetrate between graphite

layers. After mechanical treatment (sonication) this graphite can be separated into

single graphene flakes. Such method has already been proved as efficient for

separation of single carbon nanotubes from bundles [55, 56, 57]. The formation of

suspended monolayer (with a little admixture of a few layer graphene), can be

achieved using a long-time impact of a high intensity sonication and centrifugation.

The samples produced by this method have a lateral size less than 100 microns. The

chemical methods can be used for graphene production in case of the low quality

conditions of the samples for optics [58] or for energy production [59], because the

samples have a small lateral size and may have different functionalization during the

chemical treatment. They can also be used to produce the composite materials for

chemical applications [60, 61].

The next method, which differs radically from the previous one and which has

been demonstrated in the same time, is the epitaxial growth on the surfaces of

monocrystals, such as ruthenium [21, 22, 23] (figure 5), iridium [24, 25, 26],

platinum [27, 28, 29], palladium [30, 31] and nickel [32, 33]. A temperature

dependence of the carbon solubility in transition metals is a basis of this method. The

saturation of metal with carbon occurs during the temperature treatments exceeding

1000°C and in the atmosphere of alcohol or hydrocarbons. Then the solubility of

carbon decreases with decreasing the temperature in high or ultra-high vacuum and,

at the expense of crystalline compression, the carbon atoms are pushed out by the

metal and form the graphene domains on the surface of material. Undoubtedly there

are certain conditions of graphene synthesis, specific to each metal, but the

mechanism of the synthesis is always the same. The advantage of this method is the

formation of ultra thin graphene film containing one, two or three layers and the

large-scale samples. The other benefit of the method is a possibility to investigate the

crystalline structure of graphene by a scanning tunnelling microscopy. On the other

hand, the transferring process cannot be done without damaging the metal substrates,

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which are expensive consumable materials. Thereby the epitaxial method is not so

convenient for a large-scale graphene production with a further fabrication of device

and it is not so popular from the practical point of view, while it is used for

fundamental investigations.

One more method of epitaxial growth of graphene is based on a thermal

decomposition of silicon carbide [34, 35]. The 6H-SiC(0001) substrate is heated up

to 1500-2000°C with the rate of 2-3 degrees per second in vacuum or in argon

atmosphere with pressure 10-900 mbar. Then it cooled down with the same rate

after a while. The method seems to be very simple and effective but as it was shown

in the references [36, 37], the quality of graphene samples strongly depends on the

quality of initial silicon carbide crystal. The general advantage of this method, first

of all, concerns the area of the synthesised graphene sample which can amount the

size of the substrate. The other thing, which should be mentioned, is a possibility to

perform the electrical measurements without transferring of graphene from the

substrate because the silicon carbide is a semiconductor. But in any case the device

fabrication is not possible with the graphene synthesised by this method because the

transferring of the sample is very difficult.

Fig. 5. In situ microscopy of graphene epitaxy on Ru(0001). a) A time-lapse sequence of

LEEM images showing the initial growth of a first-layer graphene island on Ru(0001) at

850°C. Numbers indicate the elapsed time in seconds after the nucleation of graphene

island. b) A schematic cross-sectional view of the preferential, carpet-like expansion of

the graphene sheet (g) across ‘downhill’ steps, and suppression of the growth in the

‘uphill’ direction [23].

a)

b)

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There are a lot of other methods for graphene production, which are less

popular and used only in specific areas, for instance, the “un-zipping” of carbon

nanotubes resulting in formation of graphene nanoribbons or using the thermally

expanded graphite for graphene fabrication, etc.: the reviews of other methods are

presented in references [50, 62, 63, 64, 65].

Finally, I cannot miss to conclude the review of graphene fabrication methods

with the most promising method, which has already demonstrated a possibility of

large-scale, high quality and mass production of graphene. This is a chemical vapor

deposition (CVD) technique from carbonaceous gas onto polycrystalline substrate of

nickel [38, 39, 40, 41, 42, 43] or copper [44, 45, 46, 47].

In 2008 two groups published in parallel papers about results on graphene

monolayer fabrication by CVD method on a nickel polycrystalline substrate in the

first time [40, 41]. A rise of amount of papers devoted to CVD growth of graphene

started from that time. A fabrication of graphene on the copper foils by CVD method

has been published in 2009 [45]. However, the mechanisms of graphene growth on

nickel and copper are different: they are usually combined together because the same

equipment is used for both.

So, let us start with the description of CVD growth process on a nickel

polycrystalline substrate. The synthesis of graphite on nickel foils by chemical vapor

deposition was known since 1976 [66]. A possibility to form around 400 Å thick

graphite films at temperature of 900°C has been shown. Earlier, in 1952, the

dependences of carbon solubility in nickel in different conditions have been

determined [67] (figure 6a). The mechanism of graphene formation on the nickel

surface is simple (figure 6b): the nickel polycrystalline substrate is heated in a

mixture of carbonaceous gas, hydrogen and argon with different pressures (from

millibar to atmosphere pressure). The gas decomposes into carbon and compounds

with deposition of carbon on the nickel substrate top when its temperature is around

650°C, since the nickel is a catalyst of the reaction.

Then, with the increasing of substrate temperature, carbon diffuses inside the

material due to the thermal expansion of the metal. The heating stopped after 800°C.

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Finally, in course of cooling down

(to room temperature) the nickel

substrate the carbon atoms are

pushed out from the bulk of metal

and form the graphite-like film

because its lattice constant is very

close to that of nickel. According

to publications, the thickness of

carbon film depends on the

synthesis conditions and reaches a

few hundreds of nanometers. For

the appropriate process conditions

(a thickness of nickel substrate

and its maximum temperature, the

synthesis duration and the pressure

in chamber, the gas concentration

and a cooling rate) it is possible to

obtain a film with a thickness

down to one graphene layer. The

described method has already been

demonstrated as a good technique

for graphene production for

different applications in optics [68] and nanoelectronics [44].

The process of graphene formation on a copper substrate differs significantly

from that on nickel [47]. Due to the fact that carbon solubility in copper is 1000

times less than in nickel, there is no diffusion of carbon inside the copper after its

deposition of the metal surface. But with the copper temperature increasing a

probability of graphene film formation and an area covered with it increase.

According to the literature [47], it is impossible to form a thick graphene film on top

of copper substrate because the copper serves as a catalyst for decomposition of

a)

b)

Fig. 6. a) Illustration of carbon segregation at

nickel surface [40]; b) Experimental results

on solubility of carbon in nickel [67].

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carbonaceous gas, and after its coverage with a graphene monolayer the gas

decomposition becomes difficult. This method seems to be very promising for a

mass graphene production. The well-known commercial firm “Samsung” uses this

method for their scientific research focused on graphene integration for fabrication of

transparent conductive flexible substrates for future touch screens.

In the present work the method of chemical vapor deposition of graphene on

both nickel and copper foils is described in details and applied for production of

samples with a desired thickness and a high quality. Also a detailed analysis of

influence of every parameter of the process on the graphene characteristics is

presented (see chapter 2.3).

1.1.3 Optical properties and optical diagnostic tools of graphene

As it was mentioned above the unique properties of graphene are based on its

band structure. In this work a special attention is paid to the optical diagnostics of

graphene, especially to Raman spectroscopy and light absorption spectroscopy

techniques, because they are used for graphene identification and characterisation.

The Raman effect in graphene is observed at every excitation wavelengths due to the

linear dispersion characteristics of electrons in graphene near the special K and K’

points of the first Brillouin zone. The absorbance of graphene has unusually flat

dependence on the incident wavelength, as also described below.

Let us first describe more carefully the Raman effect in graphene and show its

usefulness as an efficient diagnostic tool for graphene [69, 70, 71, 72, 73, 74, 75].

The Raman spectra of bulk graphite and graphene, registered with excitation at 514.5

nm, are shown in Figure 7a. There are two most intense bands: G peak at ~ 1580

cm-1 (the name comes from “general” – this peak appears both in graphene and in

graphite, it has the same position and shape for these materials); 2D band at ~ 2680

cm-1 [76]. It is the second order of a D-peak, which corresponds to “disorder” in

graphite and graphene and has position at ~ 1350 cm-1. The D-peak is not seen in

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defect-free graphite [77] since the zone-boundary phonons do not satisfy the Raman

fundamental selection rules, in turn the double-phonon Raman scattering is observed

in every graphite and graphene samples but with deferent positions and shapes.

Raman spectroscopy usually is used for graphene determination. It is possible to

confirm a presence of graphene monolayer if a Raman spectrum of material satisfies

a few conditions. G-peak should have a position at 1580 cm-1 like in a graphite

sample. The 2D band of graphene should have much higher (usually from 2 to 5

times) intensity comparing to its G band, in case of graphite it is vice versa, see

figure 7a (note that figure 7a is rescaled to show a similar 2D intensity). The shape

and position of 2D band of graphene and graphite have significant differences. In

figure 7b it is clearly seen that the 2D band of single layer graphene film shifts to

lower energy compares to thicker graphene film. Moreover a bandwidth of this band

increases with increasing of layers and the shape changes as well. But the 2D band

shape stops changing if graphene film thickness becomes more then 5 layer and a 10

layer graphene film has the same 2D band as bulk graphite. Finally to distinguish

monolayer graphene from bilayer it is necessary to focused more carefully on 2D

Fig. 7. a) A comparison of Raman spectra for bulk graphite and graphene. The spectra

were normalized on the height of 2D peak at 2680 cm-1. b) The evolution of 2D band shape

depending on the number of graphene layers.

All spectra were registered with an excitation wavelength 514.5 nm [70].

a) b) G

G

2D

2D

20

band. In figure 8 the Raman spectra

for both single and double layer

graphene films are shown. As it can

be seen from the figure 8 the 2D

band of monolayer graphene has

tight single peak with position at

2680 cm-1 and a bandwidth around

25-30 cm-1 , but in case of bilayer it

splits into 4 components with

increasing of bandwidth up to 60-70

cm-1 and a central position shifts to

2700 cm-1. A very accurate

explanation of this effect is presented in references [70, 74, 75].

Thereby the Raman spectroscopy shows a strong difference between single and

double layer graphene films and thicker graphene films. It means that Raman

spectroscopy is a very efficient technique for thin layer graphene detection and

characterisation.

Switching over to absorption spectroscopy of graphene it should be noticed that

measurements of graphene absorbance basically aimed not at investigation of

graphene optical properties but at diagnostics of synthesised samples and at

determination of its structure (eg an indirect measurement of the film thickness). The

optical properties of graphene are resulting from its band structure. Since electrons in

graphene have no energy gap and the dispersion characteristic is linear, the material

absorbs the light in a very wide range of wavelengths. The electrons in graphene

propagate with high velocities and its interaction with photons is described by a fine-

structure constant 137

12

==c

e

ℏα and does not depend on any material properties. In

references [78, 79] it is shown theoretically and experimentally that the absorbance

of graphene monolayer equals to πα ≈ 2.3%. An increase of graphene layer number

contained in the film results in the increase of absorbance of graphene with the

a) monolayer

b) bilayer

G

2D

G 2D

Fig. 8. Raman spectra of monolayer (a) and

bilayer (b) graphene films. An excitation

wavelength is 514 nm [75].

21

coefficient 2.3% per layer. Thereby the absorbance spectrum of graphene film allows

to estimate the number of graphene layers. In figure 9a the absorbance spectra of one

and two graphene layers are shown. In fact, the absorption measurements are very

informative for characterisation of synthesised graphene samples.

For further application of graphene in optics, it is also interesting to know the

non-linear characteristics of the material. It is established that the non-linear optical

properties are the result of a high non-linear electric susceptibility. In graphene the

non-linear electric polarization brought by the interaction of intensive

electromagnetic radiation can be expanded versus the electric field E as:

)EEEE EEE EEE(PPP (4)(3)(2)(1)0nonlinlin …++++=+= χχχχε (1.1)

The electric susceptibility of high order (χ(3),… χ(n)) results in different non-

linear effects such as saturation of absorption [80], optical shift of frequency [81] or

generation of second harmonic [82, 83], which are observed in graphene. The effect

of saturation of absorption has already been investigated in carbon nanotubes and

graphene. And as this effect is demonstrated in this work it is necessary to describe it

in more details.

Fig. 9. a) Looking through one-atom-thick crystals. A photograph of a 50-mm aperture

partially covered by graphene or its bilayer. The line scan profile shows the intensity of

transmitted white light along the yellow line [78]; b) Scheme of relaxation process of

exited by photons electrons.

a) b)

22

The effect of saturable absorption is a decreasing of material absorbance with

increasing the incident light intensity. Mostly this effect is observed in material when

the incident intensity is very close to the threshold of material destruction. Such

intensity is usually achieved with the ultra-short laser pulses. With enough power

intensity of incident light the excitation of carriers from a ground state to higher

energy levels is faster than its return. In this case the carriers occupy the high energy

levels and it results in saturation of absorption or, in the other words, transparency of

the material. The non-linear absorbance is related to the concentration of excited

carriers. If we consider a two level system, the non-linear absorbance equals to:

0

1)( ααα +

+=

sat

sat

N

NN

(1.2)

where α(N) – the absorbance, N – the induced concentration of carriers

(electrons or holes), Nsat – the saturable concentration of carriers (the concentration

which corresponds to the threshold of saturation Isat when the absorbance decreases

down to 50%) [84]. The concentration of carriers can be also written via intensity I

of incident flux, as ωταℏ

IN = , where τ – the carrier recombination time, ω – the

frequency of radiation. Thanks to linear dispersion characteristics and the absence of

energy band gap in graphene the absorption is possible for any quantum energies.

While a short laser pulse with the frequency ω is absorbed by graphene, the non-

equilibrium distribution of electrons and holes appears in conduction and valence

zones, correspondingly (figure 9b). According to Pauli Exclusion Principle, no two

identical electrons may occupy the same quantum state simultaneously, consequently

the absorbance on graphene decreases during the time of electron relaxation (τ1

corresponds to intra-band relaxation and τ2 to inter-band).

The described optical properties and the methods for graphene diagnostics were

investigated in this work and the results are presented in the experimental section

(chapter 2).

23

1.2 Photonic crystals

An overview of the literature on the unique carbon material – graphene was

provided in the previous part of the manuscript. It reported the methods of its

preparation, an overview of its unique properties and presented its possible

applications in optics and optoelectronics. In this section, which may seem to have

no connection with graphene, the photonic crystal structures are described. But, as

will be shown later, the integration of graphene with photonic crystals will be the

next step in the research and application of graphene in terms of the control of

electromagnetic radiation. As it was shown, graphene absorbs 2.3% of incident

radiation in a wide wavelength range, and graphene has nonlinear optical properties,

which are currently commonly used in lasers. Graphene is an effective saturable

absorber, and this property can be used to implement a regime of passive mode

locking in lasers for generation of ultra short (subpicosecond) pulses. But, in order to

exploit the non-linear properties of graphene, a high power density of the incident

radiation is requested, which is often not possible with micro-and nanodevices. Thus,

in the course of the work, the problem of finding solutions to reduce the power

density of the electromagnetic radiation requested to threshold nonlinear optical

behavior in graphene is addressed. And one of the examples of these structures is

well-known photonic crystals, which provide the ability to control electromagnetic

radiation. A description of the structures and principles of control of the propagation

of photons through them comes below.

1.2.1 Introduction to photonic crystals

In 20th century the scientists have studied to control electrical properties of

certain materials. The transistor revolution in electronics was a confirmation of

advances in semiconductor physics. But in the last few decades, a new goal was set.

24

It is to control the optical properties of materials. A vast range of technological

developments can be possible if there would be an opportunity to construct materials

that respond to incident light over a desired range of wavelength by perfectly

reflecting it, or allowing it to propagate in required directions, or confining it in a

desired volume. Such structures were theoretically studied at first in 1972 by Bykov

from USSR (now Russia) [85] and the first experimental samples were obtained by

John [86] and Yablonovitch [87]. The name of these structures is Photonic Crystals

(PC).

Joannopoulos in his book “Photonic Crystals: Molding the Flow of Light

(Second Edition)” [88] gave a very good description of photonic crystals: “As

electrons behave in solid states there is an optical analogue in the photonic crystal, in

which the atoms or molecules are replaced by macroscopic media with different

dielectric constants, and the periodic potential is replaced by a periodic dielectric

function (or, equivalently, a periodic index of refraction). If the dielectric constants

of the materials in the crystal are sufficiently different, and if the absorption of light

by the materials is minimal, then the refractions and reflections of light from all of

the various interfaces can produce many of the same phenomena for photons (light

modes) that the atomic potential produces for electrons. One solution to the problem

of optical control and manipulation is thus a photonic crystal, a low-loss periodic

dielectric medium. In particular, it is possible to design and construct photonic

crystals with photonic band gaps, preventing light from propagating in certain

directions with specified frequencies (i.e., a certain range of wavelengths, or “colors”

of light)”.

In figure 10a the simplest possible photonic crystal is shown. It consists of

alternating layers of different material and the period of repetition is close to incident

wavelength. The dielectric constant changes in one direction, and in two others it is

constant. As an example of such a PC, the Bragg grating is widely used as a

distributed reflector in vertical cavity surface emitting lasers. Besides, such

structures are widely used as antireflecting coatings which allow to decrease

25

dramatically the reflectance from the surface and are used to improve the quality of

lenses, prisms and other optical components.

Two-dimensional (2D) PC can have a comparatively large variety of

configurations, because it possesses periodicity of the permittivity along two

directions, while in the third direction of the medium is uniform [89]. A good

example of the 2D PC is porous silicon with periodically arranged pores, which is

represented by the silicon substrate with etched holes (figure 10b). Another example

of 2D PC is a periodically arranged system of dielectric rods in air. 2D PC can also

be found in nature. For instance, the pattern on the butterfly’s wing and its rainbow

play is caused by the light reflection from the microstructure on the wing.

Three-dimensional (3D) PC has permittivity modulation along all three

directions [89]. At that, the number of possible PC configurations is much larger than

in case of 1D or 2D PC. Many works are dedicated to the design of new geometric

configuration of 3D PC, which discover new possibilities of their application. The

most known naturally formed 3D PC is a valuable stone opal (figure 10c). This stone

is known by its unique optical properties. When turned around, it plays different

colors. It consists of a number of microspheres placed at nodes of a face-centered

cubic (FCC) lattice. Reflectance of such a structure strongly depends on the radiation

incident angle. So when one turns it around, it starts to reflect the radiation with

different wavelengths. Thus, optical properties of PCs are determined by the

existence of the periodic modulation of the permittivity or the refractive index of the

medium and the observed effects have a strong analogy to the solid state, as it was

written above, the periodically arranged structure of atoms in crystal lattice. Such a

Fig. 10. Examples of 1D PC (a), 2D PC (b) and 3D PC (c) [89].

a) b) c)

26

similarity between the physics of PCs and solid-state physics gives the possibility to

draw the analogy between some properties and computation methods applied to

solid-state and PCs physics.

The simplest approach for analyse different types of photonic crystal structures

is to imagine that a plane wave prоpаgates through the material and for further

calculations it is always considered the sum of the multiple reflections and

refractions that occur at each interface. This model could be useful for 1D PC but for

more complicated structures of 2D or 3D photonic crystals it is usually used the

analysis of a photonic band structure which is similar to electronic band structure in

semiconductors.

As an example the band structures of three types of multilayer structures are

presented in figure 11. Let us consider a structure of alternating layers (as in figure

10a), and the light flux is incident on the structure in perpendicular to the layers

direction. At first the layer are the same, for instance gallium arsenide, thereby the

flux goes through bulk material. In this case the dispersion characteristics of photons

in the material is described by [88]

( )=ck

kωε , (1.3)

taking into account that in a homogeneous medium, the speed of light is

reduced by the index of refraction (see figure 11a). The centre plot in figure 11 is for

a nearly-homogeneous medium. It looks almost like the homogeneous case but the

difference is in the presence of a gap in frequency between the upper and lower

branches of the lines. This gap occurs due to coupling each other of propagating and

counter-propagating waves through diffraction processes. The width of the gap

increases with the coupling rate, which corresponds to the magnitude of the periodic

modulation of the optical index. The figure 11c shows indeed that the gap widens

considerably with increasing of the difference between the dielectric contrasts of

materials [88].

27

Many of the promising applications of two- and three-dimensional photonic

crystals to date hinge on the location and width of photonic band gaps. For example,

a crystal with a band gap might make a very good, narrow-band filter, by rejecting

all (and only) frequencies in the gap. A resonant cavity, carved out of a photonic

crystal, would have perfectly reflecting walls for frequencies in the gap.

The other approach to control the light propagation which is a very widely used

in photonics, it is a waveguide. The simplest way to describe it is to consider the

infinite semiconductor or dielectric slab (for instance the glass), which perform total

internal reflection. This phenomenon takes place if light rays within the glass that is

incident on the interface with any lower-index medium at too shallow an angle. In

this case flux is totally reflected and remains confined within the glass (forming a

planar waveguide). The phenomenon of refraction of a light beam at an interface

between two dielectrics ε1 and ε2 is usually described by the Snell’s law: n1·sinθ1 =

n2·sinθ2, where n1, n2 are the refractive indexes of mediums, θ1 and θ2 are incident

and refracted angles accordingly (see figure 12a where ε1> ε2). If θ1 > Arcsin(n2/n1),

Fig. 11. The photonic band structures for on-axis propagation, as computed for three

different multilayer films. In all three cases, each layer has a width 0.5a. (a): every layer

has the same dielectric constant ε=13. (b): layers alternate between ε of 13 and 12. (c):

layers alternate between ε of 13 and 1 [88].

a) b) c)

28

then correspondingly to the Snell’s law sinθ2 > 1, this inequation has not got

solutions and this results in totally reflected of incident beam. The critical angle θC =

Arcsin(n2/n1) can be determined only if n2 < n1, thereby total internal reflection effect

is possible only within the higher-index medium.

Snell’s law can be described also in terms of the combination of two

conservation laws. The first is conservation of frequency ω (from the linearity and

time-invariance of the Maxwell equations). And the second is conservation of the

component k|| of k that is parallel to the interface. In other words, k|| = |k|·sinθ, and

|k| = nω/c from the dispersion relation. So the Snell’s law is obtained by setting k||

equal on both sides of the interface. Further let us try to understand the band

structure of the electromagnetic modes in a thin plane of any high-index material

surrounded by air (or any lower-index material) with thickness a as it is presented in

figure 12b.

In the book “Photonic Crystals: Molding the Flow of Light (Second Edition)” of

a) b)

c)

Fig. 12. (a) A flat interface between two dielectrics ε1 and ε2. (b) An infinite slab of

dielectric material. (c) Harmonic mode frequencies for a plane of dielectric material of

thickness a and ε = 11,4. Blue lines correspond to modes that are localized in the plane.

The shaded blue region is a continuum of states that extend into both the plane and the air

around it. The red line is the light line ω = ck. This plot shows modes of only one

polarization, for which H is perpendicular to both the z and k directions [88].

29

Joannopoulos [88] there is a very clear explanation of it: “First, consider the modes

that are not confined to the glass, and extend into the air and out to infinity. Far away

from the glass, these modes must closely resemble free-space plane waves. These are

superposition of plane waves with 22

|| ⊥+== kkcckω for some perpendicular

real wave vector component k⊥. For a given value of k||, there will be modes with

every possible frequency greater than ck||, because k⊥ can take any value. Thus the

spectrum of states is continuous for all frequencies above the light line ω = ck||,

which is marked with a red line in figure 12c. The region of the band structure with

ω > ck|| is called the light cone. The modes in the light cone are solutions of Snell’s

law (less than the critical angle). In addition to the light cone, the glass plate

introduces new electromagnetic solutions that lie below the light line. Because ε is

larger in the glass than in air, these modes have lower frequencies relative to the

values the corresponding modes would have in free space. These new solutions must

be localized in the vicinity of the glass. Below the light line, the only solutions in air

are those with imaginary 222

|| / ckik ω−±=⊥ , corresponding to fields that decay

exponentially (are evanescent) away from the plane. Those solutions correspond to

the index-guided modes, and it is expected that for a given k|| they form a set of

discrete frequencies, because they are localized in one direction. Thus, the discrete

bands ωn(k||) below the light line are shown in figure 12c. In the limit of larger and

larger |k|||, one obtains more and more guided bands, and eventually one approaches

the ray-optics limit of totally internally reflected rays with a continuum of angles θ >

θC”.

To conclude the introduction it should be said that real micro and nanophotonic

devices based on 3D PC structures are very complicated in fabrication and the most

used PC are 1D or 2D. A 1D photonic crystals can be formed by a stacked structure

consisting of a large amount of layers of two different materials which are repeated

one after another: it is used mostly as a Bragg mirror in many different applications.

Considering 2D PC, it turns very uneasy to form a periodical structure in two

30

dimensions which has infinite size (in wavelength scale) in the third dimension. In

the real practical 2D PC, use is made of a PC slab. A two dimensional photonic

crystal is formed in a high index dielectric material (eg semiconductor) with

micrometers or even portion of micrometer thickness and several tens or hundreds of

micrometers in lateral dimensions. Thereby in this case we can image the

combination of waveguide (which was described above) and PC. Such kind of

structures is very useful for harnessing the light and the next section will demonstrate

how it is possible to combine free space and waveguided modes and will describe the

phenomena which are under operation in such approach.

1.2.2 Resonant membrane reflector based on surface addressable photonic

crystal waveguiding structure.

In photonic crystals, which are strongly corrugated periodic structures, strong

diffraction coupling between optical modes occurs; these diffraction processes affect

significantly the surface dispersion characteristics.

The essential manifestations of these disturbances consist in:

– The opening of multidirectional and large photonic bandgaps (PBG).

– The presence of flat photonic band-edge extremes (PBE), where the group

velocity vanishes, with low curvature (second derivative) 1/PBG.

These are the essential basic ingredients of the two optical confinement schemes

achievable with photonic crystals (PBG/PBE confinement schemes) and that make

them the most appropriate candidates for the production of a wide variety of compact

photonic structures.

As it was described in the previous section, in the PBG scheme, the propagation

of photons is forbidden, at least in certain directions. This is in particular true when

they are trapped in a so-called localized defect or microcavity and the related optical

modes are localized: in this case the propagation of photons is fully prohibited.

31

Opening of large PBG (in the spectral range) provided by the PC, allows for a very

efficient trapping of photons, which can be made strongly localized in free space.

In the PBE scheme, the PC operates around an extreme of the dispersion

characteristics where the group velocity of photons vanishes. It should be noted,

however, that the dispersion characteristics apply strictly for periodic structures with

infinite size and in steady state; therefore, the concept of zero group velocity is fully

true only under these particular extreme conditions. The real-world situation is

actually finite and transitory. It is therefore more appropriate to speak in terms of

slowing down of optical modes (so-called Bloch modes for a periodical structure),

which remain, however, delocalized. It can be shown that the lateral extension of the

area S of the slowing-down Bloch mode during its lifetime τ is proportional to ατ

[ 90 ]. As mentioned above, one essential virtue of PC is to achieve very low

curvature α at the band-edge extremes, thus resulting in strong slowing down and

thus, in very efficient PBE confinement of photons. Although the PBE scheme

provides weaker confinement efficiency than with the PBG approach, it results in an

improved control over the directionality or spatial/angular resolution of the light.

The vertical confinement of photons is based on refraction phenomenon. In the

configuration that is usually adopted, the light is guided in a high-index

semiconductor membrane surrounded with low-index cladding or barrier layers (for

example an insulator like silica or simply air): this is the so-called membrane

approach. In mono-mode operation conditions, the thickness of the membrane is very

low, around a fraction of a µm. For passive devices, silicon is often used for the

membrane material, especially in the silicon on insulator (SOI) configuration, which

is fully available in the world of microelectronics (see [91]).

However, full confinement of photons in the membrane waveguiding slab is

achieved only for those optical modes that operate below the light-line. This mode of

operation is restricted to devices that are meant to work in the sole waveguided

regime, where waveguided modes are not allowed to interact or couple with radiated

modes. For waveguided modes whose dispersion characteristics happen to lie above

the light line, coupling with the radiated modes is made possible, the waveguided

32

“state” of the related photons is transitory, and the photonic structure can operate in

both waveguided and free-space regimes. Thereby the surface addressable photonic

crystal stricture means the PC slab which exploits the waveguided modes above the

light line.

A simple illustration of the approach, which exploits the surface addressable PC

membrane structure, is the use of a plain photonic crystal membrane as a

wavelength-selective transmitter/reflector: when light is incident on this photonic

structure, in an out-of-plane (normal or oblique) direction, resonances in the

reflectivity spectrum can be observed. These resonances, so-called Fano resonances

[92], arise from the coupling of external radiation to the guided modes in the

structures, whenever there is matching of the wavelength λ0 and of the in-plane k||

component of the incident wave k-vector with those of the guided modes (see Figure

13). Accurate tailoring of the spectral characteristics of the Fano resonances (shape,

spectral width) is made possible by the design of the 2D PC membrane (type of 2D

PC, strength of the periodic corrugation, symmetry of the waveguided mode,

membrane thickness [93]).

In brief, the lateral kinetics of photon within the membrane and below the beam

must be slowed down to fully preserve constructive interferences of the incoming

Fig. 13. Illustration of the resonant coupling between a waveguided mode and a radiated

mode [93] .

a) b)

33

light with the waveguided photons. Those

essential features of resonant coupling

mechanisms of radiated light to a PC

membrane are illustrated in figure 14. The

ability of high index contrast PCs to slow

down photons and to confine them laterally,

especially at the high-symmetry points (or

extremes) of the dispersion characteristics,

lends to the production of devices with very

compact lateral size. It is to be noted, in

addition, that for real devices with limited

lateral size, efficient slowing down of

photons within their physical boundaries

results in minimizing unwanted diffraction

losses induced by the latter. A variety of

passive as well as active devices operating above the light-line and based on a plain

PC membrane have been reported. For example, very compact passive reflectors

showing a large bandwidth (a few hundreds of nanometers) and consisting in a 2D

PC formed in an InP membrane suspended in air have been reported. The large

bandwidth is obtained for specific designs of the 2D PC, which allow, among other

features, for a very strong coupling rate 1/τc of waveguided modes with the radiation

continuum [94, 95]. The 2D PC membrane can be also designed in such a way as to

result in very strong Fano resonance that is for weak coupling rate 1/τc. Use of such

strong Fano resonances has been made for the demonstration of very low threshold

and very compact surface-emitting Bloch mode laser [96, 97], as well as of optically

controlled microswitches [98].

As it was written in the beginning of the chapter the idea of describing of

photonic crystal structures was to prove that the PC could be as an effective addition

device for light harnessing to provide the light confinement for further integration

with graphene. In this subsection the strategy of photons confinement was observed.

Fig. 14. Essential features of resonant

coupling mechanisms of radiated light

to a PC membrane. The symbols are

defined in the text.

34

It means that the bonding of PC membrane reflectors with graphene can result in the

increasing of time interaction of coming photons with absorbing material. In turns it

results in enhancement of absorbance in graphene. This principle is described in

details in the fourth chapter. And the design and the fabrication of appropriate PC

structures are described in the third chapter in details as well.

35

Chapter 2. Synthesis and investigation of graphene : experimental results

[A2, A3, A6, A8, A9]

2.1 Original equipment for graphene synthesis by CVD method

The original experimental setup for chemical vapor deposition was designed

and assembled during this work. As it was mentioned in the literature review, the

CVD-method of graphene fabrication is based on the decomposition of carbon-

containing gas onto the catalytic substrate at high temperature. To implement this

method, it was necessary to design the installation in such way that the sample can

be heated to a temperature of over 1000°C. Another characteristic feature of the

setup is to have the ability to control the temperature and the rates of heating and

cooling.

The most common installation method for chemical vapor deposition is a

commercial model using a quartz tube furnace with a filament heater. In such an

installation the temperature of the substrate cannot be controlled with high accuracy

and there is no possibility to control the cooling and heating rates of the sample.

Therefore, several important features were taken into account in the design of the

system:

• Vacuum chamber with a base vacuum pressure not exceeding 10-4 bar;

• Possibility to introduce several gases;

• Ability to heat the sample above 1000°C, and precise control of temperature

with accuracy of 1degree;

• Control of heating and cooling rates of the sample and measuring the

electrical parameters of the foils during the experiment (current, voltage,

resistance).

Thereby the setup was constructed taking into account the listed requirements.

The scheme of it is shown in figure 15. The heating of the metal substrate is

performed by Joule effect by injecting a high current. Temperature of the substrate is

controlled by a double wavelength infrared pyrometer through the window in the

36

chamber, and the change rate of temperature can be easily controlled by a

programmable direct current source connected to the computer. The vacuum

chamber is equipped with cooled walls and inlets of methane, hydrogen and argon.

The sample is placed on the electrodes, which are connected to a DC-source. An

additional distinctive feature of the installation for the synthesis of graphene lies in

the absence of any flow of gases. It should be noted that commercial equipments for

the synthesis of graphene by CVD method is based on the gas flow. As an example,

to set the desired pressure in the chamber and the concentration of methane in the

mixture with hydrogen, the chamber should be filled with hydrogen up to a pressure

with the subsequent addition of methane. For instance, to realize the synthesis of

graphene at a chamber pressure of 200 mbar and 10% methane, it is needed to fill the

chamber with hydrogen up to a pressure of 180 millibars, and then 20 mbar of

methane should be added.

During the work the nickel and copper foils were used for graphene formation.

Below comes a detailed description of the synthesis process. The synthesis of

graphene films on metal foils includes four steps:

1. Annealing of the foil in hydrogen;

2. Injection of methane;

3. Deposition of carbon on the nickel or copper substrates. Diffusion of carbon

inside the nickel, or formation of graphene film on the surface of the copper

substrate;

a) b)

Fig. 15. a) Scheme of CVD equipment for graphene synthesis. b) Photograph of the

installation.

37

4. Formation of the graphene film during cooling of the nickel substrate.

The metal substrate is held between the electrodes in the chamber. The camera

is washed and filled with hydrogen (or with a mixture of hydrogen and argon) up to a

pressure of 500 millibars. Then the heating of the substrate by passing a high current

is started. The linear increase of the current is set with the software. When the

temperature of the substrate reaches the required value, the current increase is

stopped, and then the temperature is held for the certain time. It was found that the

rate of current increase, the temperature and the annealing time are very important,

as they determine the size and quality of the grains produced in polycrystalline nickel

or copper foils. The transitional step, which includes cooling of the metallic substrate,

pumping of hydrogen to the required pressure and introduction of the methane to

obtain the desired concentration, occurs after annealing of the substrate. Further,

after the inlet of methane, the most important phase of synthesis takes place. It is the

decomposition of methane, the deposition of amorphous carbon on the surface of the

catalyst substrate and the further diffusion of carbon into nickel at temperatures

above 800°C (in case of using copper foil as a catalytic substrate the formation of

graphene film takes place directly on the surface of the foil). The current increase is

Fig. 16. Scheme of experimental process of graphene synthesis by CVD method on

nickel foils.

38

stopped and, like in case of annealing, the requested temperature is kept for 20

minutes or more, if necessary. Finally, the last stage consists in the cooling of the

substrate down to room temperature either “instantaneously” (that is by turning off

the current), or linearly by decreasing the current with the software. Figure 16 shows

the step by step scheme of the successive experimental steps for the formation of

graphene film on top of the nickel foil. The influence of all of the synthesis

conditions on the final result were found out and described. These relationships are

presented and discussed in the following paragraphs of this chapter (see section 2.3).

2.2 Methods for graphene transferring

After the sample synthesis the important stage of transferring process from the

catalytic substrate onto the arbitrary substrate starts. It is selected on the base of

targeted applications of graphene samples. In the present work, various methods of

graphene transfer have been tested, and the most suitable methods for different types

of samples, depending on the thickness of the graphene film and on the metal

substrate used during the synthesis, were determined.

1) The transferring process of the graphene film with an estimated thickness of

3 layers or less from nickel foils onto any substrate is the same as the process of

transfer of the graphene film from copper foils. It was carried out using a thermal

release tape** (TRT), and ammonium persulfate is used as an etchant. TRT is stuck

on the metal foil side covered with the deposited graphene film, and the other side of

the foil is polished to remove the graphene film. Next, the three-layer system (foil-

graphene-TRT) is gently put on the surface of a solution of ammonium persulfate

(with a concentration of 2 g in 10 ml of water), so that the foil floats on the surface

of the solution, and the polymer tape is on the air, and the metal foil is completely in

the solution. After 24 hours, the copper foil is fully etched by the solution, and the

* The thermal release tape (TRT) is a unique adhesive tape that adheres tightly at room temperature and can easily be peeled off just by heating. Product name is “Revalpha” produced by Nitto Denko.

39

“swimming” polymer tape with the graphene film remains on the surface of the

solution. In case of a nickel foil, ammonium persulfate does not chemically react

with the nickel, but only separates the graphene film and the nickel foil, and as a

result we obtain the polymer with graphene floating on the top of solution and the

nickel foil sinks in the solution. Then the polymer tape is washed with de-ionized

water, dried up and placed on the substrate. Next, the "substrate-graphene-polymer"

is heated up to 150°C on a hot plate: within a few seconds, the adhesive properties of

the polymer completely disappear, and it can be easily removed. As a result, the

graphene film is transferred without any damage, for example, on an oxidized silicon

substrate with oxide thickness of 300 nm or on any other substrate (figure 17).

2) To transfer the graphene films with thickness of more than 4 layers from a

nickel foil onto other substrate is significantly different from the process described

above for two reasons. First, as it is noted above, ammonium persulfate does not

interact with the nickel, but only breaks the bond between the first layer of graphene

and the nickel foil. In case of graphene film thickness of more than 4 layers it is

experimentally established that ammonium persulphate cannot separate graphene

from nickel. Therefore, the used etchant is a ferric chloride solution of the same

concentration. Second, using a TRT with graphene film containing more than 4

graphene layers, the separation of the tape during the heating occurs less efficiently.

As a result, the upper layers of the graphene films do not bounce off the polymer and

remain on it. Consequently, the use of TRT is impractical. Thus, the transfer process

is as follows (see figure 18):

Step 1. Removal of the graphene film on one side of the foil by grinding;

Fig. 17. Experimental scheme for transferring of graphene film with thickness less

then 5 layers.

40

Step 2. Placement in a ferric chloride solution so that the nickel foil is floating

on the surface of the solution, and the part covered by the graphene film is in the air;

Step 3. Waiting for complete etching of nickel - about 24 hours;

Step 4. Washing of the solution with de-ionized water to remove iron chloride;

Step 5. Fishing a floating graphene film by a required substrate.

2.3 Synthesis of graphene and its identification by optical methods

2.3.1 Nickel foil of 50 micron thickness

Nickel foils with a thickness of 50 microns were used in the first experiments of

graphene synthesis. A comprehensive study of the synthesis was achieved by step by

step changing the growth parameters.

At first, the methane concentration was changed from 5% to 50%, and the

chamber pressure was changed from 50 to 500 mbar (the other parameters were

constant), and the influence of these two parameters on the thickness of the sample

was revealed. Also it was found out that one of the key parameters of the graphene

film formation is the maximum temperature of the nickel substrate after introduction

of methane into the chamber (see figure 19). Since the solubility of carbon in nickel

is proportional to temperature (see Section 1.1.2, figure 6b), and the thickness of the

graphene film depends on the amount of carbon diffused into nickel, the film

thickness increases with the substrate temperature during synthesis. A series of

experiments was done to observe the impact of growth parameters on graphene film

Fig. 18. Experimental scheme for transferring of graphene film with thickness

exceeding 5 layers.

41

thickness. Three values of temperatures (900, 950 and 1000 Celsius degrees) were

selected. The experiments were done using three values of methane concentration

(5%, 20% and 50%) and three values of pressure in the chamber (50 mbar, 200 mbar

and 500 mbar). The synthesis parameters were combined with each other and, as a

result, 27 experiments were performed and the graphene samples obtained were

examined by optical absorption spectroscopy to estimate the film thicknesses (by

absorption coefficient of graphene film at visible wavelength range and taking into

account that a graphene monolayer absorbs 2.3% of intensity of incident light in a

wide wavelength range). The results are presented in figure 19.

It was found that the number of graphene layers in the film increases with

increasing the pressure in chamber and with increasing the methane concentration in

the mixture with hydrogen. Also with increasing the growth temperature (other

parameters of the experiments being kept unchanged) the graphene film thickness

increases significantly. A pressure of 500 millibars and a methane concentration of

5% were chosen as the most appropriate conditions for obtaining samples of

graphene with different thickness. Regarding the study of the effect of cooling rate of

the substrate on the thickness of graphene film, it was discovered that the thinnest

film is obtained when the cooling rate is “instantaneous”, while increasing the time

of cooling up to a few seconds results in the formation of a thick films (more than

tens of layers).

а) b) c)

Fig. 19. Dependences of thicknesses of graphene films on pressure on the chamber during

the experiments for three different concentrations of methane (5%, 20% and 50%) and for

three different temperatures of the substrates: a) 900°C, b) 950°C, c) 1000°C.

42

The following series of experiments was devoted to study the temperature

dependence of the film thickness. The pressure in the chamber was 500 mbar and the

concentration of methane was 5%. The fabricated samples were analyzed with an

optical absorption spectroscopy. The results of analysis of this series of samples are

shown in figure 20. The attention was paid to the fact that the optical linear

absorption spectra were registered from the sample areas which contain the

maximum number of graphene layers, while in the experiment a significant

temperature gradient (100°) from the foil center to the place of its attachment to the

contacts was detected. As a result, the graphene film was uneven, and the thickness

gradient was about 5 layers from the sample edge to its center.

2.3.2 Nickel foil of 25 microns thickness

As described above, the impact of almost all experimental parameters on the

quality of graphene films was studied by using a nickel foil with a thickness of 50

Fig. 20. Transmittance spectra of graphene films grown on nickel substrate with different

maximum temperature during the experiments.

43

microns. However, a serious drawback in using this substrate is the presence of a

strong temperature gradient during heating of the foil. This problem was solved by

using of a thin nickel foil and using a more appropriate geometric shape providing a

more uniform distribution of the current flow. The temperature gradient was reduced

in this way down to 20 degrees using 25 µm nickel foils. The dependences of the

graphene film thickness on the temperature in the case of using 25 µm nickel foil are

the same as for 50 µm foil. The temperature values providing the growth of 1 to 5

layers of graphene range from 870 to 930◦C. Figure 21 shows the photographs of

obtained samples and the corresponding optical absorption spectra for samples

containing a small number of graphene layers. However, the image shown in figure

21f indicates a non-uniformity of the area covered with graphene film. To increase

this area and to improve its uniformity it was proposed to increase the cooling rates

of the sample up to a few tens of seconds, but to reduce the amount of carbon

diffused inside the nickel. As a reminder, the previous experiments were done with

a) b) c)

d)

e) f)

g)

Fig. 21. Photograph of single (a), double (b) and triple (c) graphene layers on glass; d)

The transmittance spectra of graphene films; e) Photograph of a monolayer graphene film

on SiO2/Si substrate; f) Optical microscope image of graphene on SiO2/Si substrate; g)

Raman spectrum of a monolayer graphene film.

44

the instantaneous cooling rates and with the methane concentration of 5% and more.

In other words, the idea was: the lower is the cooling rates, the thicker and more

uniform is the graphene film obtained. And the less is the amount of carbon atoms

diffused inside nickel, the thinner is the graphene film obtained. So, the conditions

are listed below for the series of experiments carried out. At first, the cooling rates

were increased up to 10 degrees per second for values of methane concentration and

pressure in the chamber similar to those used in previous experiments (5% and 500

mbar). As a result, an increase of area covered by graphene film and increase of its

uniformity have been obtained. However, the film thickness increased as well up to

ten nanometers, corresponding to the presence of about 30 graphene layers. Further,

the experiments were made with methane concentrations ranging from 2% to 5% at

pressures ranging from 50 mbar to 500 mbar, to reduce the amount of diffused

carbon. In addition during the synthesis process the electrical resistances of nickel

foils were monitored in a real-time regime.

After foil annealing and methane inlet, the resistance of nickel foil was

measured and displayed as a function of its temperature. Then the heating was started

and a linear resistance increasing was observed with the substrate temperature

a) b)

Fig. 22. a) Dependences of resistance of nickel foil on its temperature before and after

methane introduction into the chamber (for different methane concentrations); b) The

dependences of temperature, at which the resistance starts to increase faster, on the

pressure in the chamber (for different methane concentrations).

45

increasing. A kink point has been revealed, where the resistance started to increase

rapidly, as evidenced from the change of the curve slope (figure 22a). This type of

resistance behavior was interpreted as a start of carbon diffusion into nickel. It may

be interpreted as the increasing of amount of carbon atoms penetrated inside the

nickel per time unit after this point. In addition, it was found that the substrate

temperature, at which the diffusion process starts, depends on methane concentration

and on pressure in the chamber (the corresponding dependences are presented in

figure 22b). As it can be seen from the figure, this temperature increases with

decreasing of methane concentration and with decreasing of pressure in the chamber.

This information about the beginning of carbon diffusion is very important,

because on its base we can control the amount of carbon penetrated inside the bulk

nickel by controlling the time period after the beginning moment. Another way to

control the carbon amount is to fix the maximal rise of temperature of the nickel foil

after reaching the kink point. For instance, a bilayer graphene film can be obtained if

the maximum temperature of nickel foil is 30 degrees higher than the temperature at

which the diffusion started (in conditions of methane concentration of 2% and the

pressure in chamber of 200 mbar). Therefore it is easy to obtain a thin graphene film

consisted of one, two or three layers. The photographs of thin graphene films are

shown in figure 21a, b, c. There are also the corresponded optical absorption spectra.

As a conclusion of described synthesis of graphene films on nickel foils it can

be highlighted that the nickel foils are an effective catalyst material for a few layered

graphene film synthesis (from three layers up to tens). But it is not the case with a

monolayer graphene synthesis because the process is very sensitive to parameters of

experiment such as methane concentration, pressure in chamber and maximum

temperature of the substrate and it is very difficult to produce a high quality

graphene monolayer. Thus, the synthesis of graphene films was extended to study

the mechanism of graphene formation on copper foils. The results of this study are

presented in the next section.

46

2.3.3 Copper foil of 25 microns thickness

As it was said in the literature review of the methods of graphene production,

the copper is a catalyst for decomposition of carbonaceous gas: moreover the copper

has a very low solubility of carbon as compared with nickel. It means that graphene

formation takes place directly on the metal surface. Since the mechanism of

graphene formation on copper differs from that on nickel, it was necessary to re-

examine the impact of every experimental parameters on the final result. Therefore,

the investigation of graphene synthesis on copper surface was done: the aim was to

perform a qualitative and quantitative characterization of graphene synthesis on

copper, as it was done in case of nickel foil. Table 1 shows the experimental

parameters used for the fabrication of a series of samples.

Table 1. Set of parameters used for synthesis of graphene films on copper foils

Number of

samples

Pressure in the

chamber (mbar)

Concentration of CH4 in the mixture with

H2 (%)

Maximum temperature of the substrate

(°С)

Cooling rates (s)

1 500 5 850 10 2 500 5 850 170 3 500 5 800 10 4 500 5 800 170 5 500 20 850 10 6 500 20 850 170 7 500 20 800 10 8 500 20 800 170 9 50 5 850 170 10 50 5 850 350 11 50 5 800 170 12 50 5 800 350 13 50 20 850 170 14 50 20 850 350 15 50 20 800 170 16 50 20 800 350

47

The samples were transferred onto the substrate silicon/silicon oxide using the

same procedure as in the case of transferring the thin graphene films from nickel.

Then the obtained samples were checked for uniformity in the optical microscope.

Part of the samples was investigated by scanning electron microscopy. The Raman

spectroscopy was used to evaluate the thickness of the samples and to reveal the

presence of defects (see chapter 1.1.3). Here are the main conclusions based on these

results:

1. At a pressure of 50 mbar, the coverage of the copper foil by graphene film is

more uniform than with a pressure of 500 millibars.

2. A cooling time of 170 seconds is the most suitable for formation of

graphene monolayer. Comparing the samples obtained at different cooling

rates (170 and 350 seconds), the observed trend was an increase in graphene

film coverage area for longer cooling time, accompanied by an increase of

sample № 8 sample № 13

50 µm 50 µm

Fig. 23. Optical microscope images of two graphene films (the parameters of synthesis

correspond to table 1) and their Raman spectra.

48

film thickness up to 3 layers.

3. From comparison of graphene growth at two different temperatures (800°C

and 850°C) it was found that the formation of graphene monolayer occurs

under higher pressure at 800°C than at 850°C. No specific dependences

have been revealed after comparison of samples grown with different

concentrations of methane in mixture with hydrogen.

Figure 23 shows the Raman spectra and images in the optical microscope of

two samples which were prepared according to Table 1 at numbers 8 and 13 and

transferred onto the substrate silicon/silicon oxide. It can be seen from the spectra

that two samples show the significant

Raman peaks with a frequency shift of

1350 cm-1, indicating the disordered

structure of graphene.

During the other series of

experiments, observation and studies of

dependences of sample quality on

synthesis parameters were emphasized. It

was noticed that the growth parameters

(such as concentration, pressure and

temperature) affect the number of layers in

the sample, but not its quality. Then we

concentrated on the behavior of other

parameters of the experiments which

influence on the quality of the samples. A

series of experiments in which the

synthesis time was increased from 5

minutes to 1 hour (figure 24) has been

performed. The Raman spectra of these

samples have shown that D-peak, being

responsible for a number of defects in the

Fig. 24. The Raman spectra of

graphene samples fabricated with

different synthesis time.

49

crystalline lattice of carbon film, decreased while the synthesis time increased. This

was interpreted as a peculiarity of the graphene growth on copper foils. As it was

mentioned in the literature review, the coefficient of carbon solubility in copper is

very low. It means that while the copper surface behaves as a catalyst for methane

decomposition at high temperature, the carbon atoms deposit onto the copper surface

and form a so-called “centers of growth” rather than diffuse inside the bulk of copper

substrate (as in the case of a nickel catalytic substrate). Over time the new carbon

atoms are added to these growth centers, and the islands start to grow up in size.

Then they coalesce and form a graphene monolayer. An area of islands increases

with the synthesis time increasing. The number of boundaries reduces, and the

quality improves. Thereby the quality of samples increases with the synthesis time

increasing while the other process parameters are fixed.

From this extensive experimental study on graphene synthesis onto both nickel

and copper foils it can be concluded that the nickel catalytic substrate is very

efficient for growth of a few graphene layer film of high quality, but with the copper

foils it is easy to obtain a monolayer graphene with almost no defects.

2.4 Optical properties of graphene

Besides the investigation of graphene synthesis by CVD method on nickel and

copper foils, the study of optical properties of prepared graphene samples in a wide

wavelength range is presented in this work as well. Since one of the aims of the work

is the fabrication of optical devices based on graphene and photonic crystals, one of

the objects was to proof the availability of graphene for usage in optical systems.

Thereby the pump-probe spectroscopy with solid-state lasers was used to

characterize the non-linear optical properties of graphene in the near-infrared range.

The investigation of graphene in a mid-infrared range was done using bulk lasers

with different gases as active media (CO or CO2).

50

2.4.1 Pump-probe spectroscopy

Among the methods to study photoexcited carrier dynamics the ultrafast

transient absorption spectroscopy (often referred as to pump-probe spectroscopy) is

one of the most informative. Pump-probe technique allows one to trace the ultrafast

dynamics of photoexcited carriers in time domain. A femtosecond resolution of this

method allows one to study a mechanism which is responsible for the ultrafast

excitation and relaxation processes on a time scale of several femtoseconds.

Understanding of this mechanism in graphene is essential for various optical and

electronic applications.

In pump-probe spectroscopy, two light pulses are used. The pump pulse is

typically much stronger than the probe pulse, which is delayed with respect to the

pump pulse. Pump and probe pulses may have different center wavelengths.

Moreover, the probe beam may have a wide spectrum being a femtosecond

continuum. The femtosecond time resolution is obtained by sending one of the pulses

through an optical delay line (typically motorized). A relatively strong pump beam

initiates changes in the absorption coefficient of the medium. These changes can be

visualized by the probe pulse, which enters the sample later with respect to the pump.

Thus by monitoring the dependence of the absorption coefficient on the pump pulse

intensity and the pump-probe delay, one can obtain information on the dynamics of

the photoexcited carriers.

Despite the increased interest in recent years for the experimental and

theoretical study of the dynamics of carriers in graphene and graphite thin films, the

physical mechanisms that caused a superfast optical nonlinearity still remain unclear.

As it is described in section 1.1.3., there exist two distinct time scales in differential

transmission spectra. Specifically, a fast initial decay of the pump-induced

transmission lasts for some tens of femtoseconds, while a slower relaxation process

takes place in subpicosecond time scale. The fast decay is ascribed to the Coulomb-

51

induced carrier scattering, while the slower process is associated with the carrier

cooling due to electron−phonon coupling.

Below the results of a «pump-probe» study of induced absorption changes (∆A)

in two graphene samples are presented. This study consists of two pump-probe

experiments: with pump wavelengths blue and red shifted with respect to the probe

Fig. 25. Time-resolved absorbance change ∆A measured for the samples containing 5 and

15 graphene layers. In the contour plots, ∆A is presented as a function of the time delay

between the pump and probe pulses (vertical axis) and the probe wavelength/energy

(horizontal axes). The top panels: ∆A contour plots, when the probe photon energy was

higher than the pump photon energy (blue-shifted probe). The bottom panels: ∆A contour

plots obtained when the probe photon energy was lower than the pump photon energy (red-

shifted probe).The center panels: spectra of instantaneous (taken at a zero time delay

between pump and probe) absorbance (∆A) spectra normalized on a pump pulse energy (ε) .

The open and filled circles represent the experimental data obtained for the blue- and red-

shifted probes, correspondingly. The relevant average values are presented by the blue and

red solid lines. The pump wavelengths are shown with the blue and red arrows.

52

wavelength. The top panels in figure 25 represent the ∆A contour plots, when the

probe photon energy was higher than the pump photon energy (blue-shifted probe).

The bottom panels show the ∆A contour plots obtained when the probe photon

energy was lower than the pump photon energy (red-shifted probe). These

experiments allow to explore the dynamics of carriers excited into the higher energy

states compared to ћωpump .

The measurements were carried out for two samples of graphene films with a

thickness of 5 and 15 layers of graphene. The «pump-probe» measurements were

carried out in the spectral range of 1100-1700 nm and the values of wavelength

ranges of pump and probe pulses in the experiments were set by the capability of the

experimental equipment. The first series of «pump-probe» experiments were done

using the pump in the spectral range of 1100-1250 nm and the probe in the range of

1200-1700 nm. In the second series of experiments the pump had longer wavelength

(1500-1800 nm) as compared to the probe wavelengths (1000-1700 nm).

A rapid change in absorption, after the arrival of the pump pulse, over the entire

investigated spectral range was observed in all «pump-probe» experiments with

different samples. It should be noted that the induced change in the absorption was

observed in the longer-wavelength (λprobe > λpump) and in the shorter-wavelength

(λprobe < λpump) part of the spectrum, compared to the wavelength of the pump. The

induced change in absorbance ∆A measured at various pumping in two samples of

graphene films is shown in figure 25. The contour images in figure 25 show the

value of ∆A as a function of wavelength of the probe light and the time delay

between the «pump» and «probe» pulses. The intensity and wavelength of the pump

were slightly adjusted, depending on the measured sample, to obtain the best

transient signal of absorption intensity variation. Figure 25 clearly shows that in all

experiments the femtosecond pump pulse created a negative change in absorption, i.e.

the decrease in absorption (or increase in transmitting) of the sample and it

corresponds to the effect of saturation of absorption. The positive changes in the

absorption magnitude were not observed at any time delay.

53

Figure 25 (the middle row) also shows the spectra of induced absorption

changes recorded at zero time delay between the pump and probe pulses. It can be

seen that the value of ∆A registered from samples has the minimum intensity in the

range 1300 ± 100 nm regardless of the excitation wavelength. The presence of such

spectral features indicates the maximum quasi-equilibrium distribution of the excited

electrons (holes) in the conduction (valence) band, corresponding to energy of 1 eV.

And, as it is seen in figure 25, the position of the maximum distribution does not

change during 1 ps. The lack of energy redistribution of carriers within the area

suggests that the sub-picosecond time of the electron-hole recombination is the main

channel of relaxation of the excited state.

∆A relaxation kinetics was obtained for the two samples and the two variants of

excitation schemes shown in figure 26. The measurements were normalized to unity

to determine and compare the characteristic relaxation times of the kinetics obtained

in the experiment, and it was approximated by the function:

Fig. 26. Temporal profile of the normalized ∆A for samples with the different number of

layers. The probe wavelength is set to 1300 nm while the pump wavelength is 1150 nm

(blue-shifted probe, B∆A) or 1550 nm (red-shifted probe, R∆A). The blue squares and red

circles represent the experimental data. The results of the bi-exponential fits for the blue-

and red-shifted probe are shown by the blue and red solid lines, respectively. Two decay

constants obtained for each sample are presented in the insets.

54

21 /2

/1

ττ xx eAeAA −− +=∆ (2.1)

where τ1 and τ2 are the relaxation times of intraband relaxation of

photoexcitated carriers and interband relaxation of photoexcitated carriers

accordingly (see chapter 1.1.3). Thus, the characteristic relaxation times of the

induced change in absorption for all samples were defined: τ1 = 250 ± 30 fs and τ2 =

2400 ± 400 fs. No explicit dependences of the characteristic relaxation times on the

wavelength of the pump or on the thickness of the sample were found in the

experiments.

2.4.2 Absorbance in mid-IR range

The optical absorption phenomena in graphene in the medium infrared spectral

range were also investigated in the present work. At first, the experiments were

performed to measure the linear absorption in graphene by the infrared Fourier

spectroscopy in a wide wavelength range (from 2 to 11 µm). A CaF2 substrate was

used for the experiment, since it is transparent in this wavelength range. In figure 27a

the green plot corresponds to the optical transmission spectrum of graphene. The

graphene film consists of around 25 layers, and the absorbance value of 60% in a

visible spectral range is practically unchanged in the whole range measured. The

transmission coefficient remains constant regardless of the wavelength of the

incident radiation. It means that graphene film could be used as an optical element at

a very wide wavelength range.

The transmission dependences on the incident power density of CO2 laser

operating in the single-pulse mode at the wavelength of 10.55 microns were

measured to confirm the effect of absorption saturation in the graphene film in the

mid-infrared spectral range. Figure 27b shows the dependence of optical

transmission of graphene film (with an approximate thickness of 10 layers) on the

power density of the incident laser pulse at a wavelength of 10.55 microns. The

change in transmittance up to 12% is seen from figure 27b.

55

Thereby graphene synthesized by CVD method demonstrated non-linear optical

properties in a wide wavelength range from IR to middle-IR. The relaxation times of

exited electrons were obtained using pump-probe measurements and it equals to 250

fs for intraband relaxation and 2400 fs for interband relaxation. Also the threshold of

saturation of absorption was found out at the wavelength 10.55 µm using CO2 laser.

These data suggest that graphene possesses the properties of a saturable absorber.

This makes graphene a promising material for realization of mode locking regime in

wide wavelength range.

a) b)

Fig. 27. a) Linear transmittance of a pristine( black) and covered with multi-layered

graphene (red) calcium fluoride. The green line corresponds to transmittance of multi-

layered graphene b) Dependence of the transmission of a multilayer graphene on the peak

intensity of incident light. The horizontal line (T = 75,9%) shows the graphene

transmission for a weak (2.7 mW) diode laser radiation with λ = 635 nm. The solid curve

corresponds to the calculated dependence 86.58

100 exp 0.046333

TI

= ⋅ − − + , where I is taken

in kW/cm2.

56

Chapter 3. One-dimensional photonic crystals – simulation and fabrication

As it was mentioned in the literature review of the dissertation it is possible,

using photonic crystals, to control the propagation of electromagnetic radiation by

creation of a photonic band gaps or localization of radiation in the membrane. The

second approach is the basis of the principle of reflection of light from the PC

membrane slab, as it was described in section 1.2.2. On the other side, the part of this

work is devoted to studies of graphene, namely, the investigation of graphene

synthesis by chemical vapor deposition, and its linear and nonlinear optical

properties. As it was shown in the previous chapter, a single graphene layer exhibits

an absorption coefficient of 2.3% which does not depend on the wavelength of

incident radiation; moreover, the absorption coefficient increases by 2.3% per each

added layer for the multiple layer graphene structure. The nonlinear optical

properties of graphene were demonstrated as well and it was shown that the effect of

absorption saturation is observed in graphene for incident power densities in excess

of 0.1 MW/cm2. This property allows using graphene as a saturable absorber for

realization of mode locking regime and generation of ultrashort laser pulses. When

getting a high power density of the incident radiation is not possible, or when the

degradation of graphene film is observed at high incident power density, it is needed

to decrease the threshold of power density, at which the effect of absorption

saturation appears. An effective solution of this problem lies in the integration of

graphene with reflective membranes based on photonic crystals. The photons are

localized and stored in the membrane, and therefore, the time of their interaction

with the electrons in graphene increases, i.e., the effective absorbance can be

increased by several times. A more detailed description of the integration of

graphene with reflective structures is presented in Chapter 4. In the present chapter a

description of the design and fabrication of reflective structures based on one-

dimensional photonic crystals is presented. Below the principle of reflection from the

PC membrane slab, computer simulation of the various structures of PC crystals and

methods for their manufacturing are described.

57

3.1 General concepts for design of reflective structures

As shown in the literature review of this manuscript, photonic crystals

integrated in a waveguide slab can act as a narrowband reflective membrane. For

fabrication of such structures detailed theoretical calculations, which are based on a

computer simulation of the reflective characteristics of membranes depending on the

parameters of these membranes, are required. But, in turn, it is needed to understand

the basic principles of the behavior of photons in reflective membranes based on

photonic crystals in order to have an opportunity to interpret the results of computer

simulations. This section will discuss the principles of light reflection from the

structures based on 1D PC in the context of problems considered in this manuscript.

In this work, it is proposed to apply a photon confinement strategy (based on

the diffractive phenomena in the high index contrast periodically structured

materials) to control the spatial-temporal trajectory of photons. This strategy is in the

heart of quite a few recent developments in the field of Micro-Nano-photonics, along

the line which has been widely referred as the Photonic Crystal (PC) approach.

Along this line, silicon material is often used owing to its remarkable photonic

characteristics: its high refractive index (around 3.5) makes it a very good candidate

as a photonic crystal material and an excellent optical “conductor". This is

particularly true when it is used in the so called “membrane configuration", where

the photonic crystal can be formed in a Silicon on Insulator (SOI) layer, which is

widely used in micro-electronics. In the proposed configuration, a surface (vertically

addressable) photonic resonance is generated in the PC silicon membrane structure

which behaves as a wavelength selective reflector [99, 93]. Use is made of the Fano

resonance effect resulting from the resonant coupling of incident radiation with

waveguided slow Bloch modes in the photonic crystal membrane [100, 101].

For a better understanding of this idea, at first, we consider a three-layer

structure formed from a standard SOI substrate including a thick silicon substrate

covered by a silica layer of 2 µm, and a 220 nm thick silicon membrane layer on top

of it. The injection of an electromagnetic wave guided in the silicon membrane

58

cannot be obtained in the vertical direction because the parallel component of the

normal incident light is equal to zero. But in the presence of a periodic patterning of

the silicon layer the latter behaves as a diffraction grating and can provide the

missing amount of k||-component. Thus a resonant injection of incoming photons into

the waveguide can be achieved. But this diffraction grating assisted injection process

is not irreversible and these photons are not fully waveguided: owing to the presence

of the periodic grating, they are indeed emitted back to free space after a certain time,

which called the lifetime of the waveguided modes. This lifetime is inversely

proportional to the bandwidth (BW) of the resonance peak (Fano resonance [102]) in

the reflectivity spectrum. A thorough description of this Fano resonance effect,

resulting from the resonant coupling of a waveguided slow Bloch mode with free

space propagating modes can be found in Ref. [93]: in brief, it results from the

resonant coupling promoted by the periodic grating of the external radiation with the

guided modes in the structures, whenever there is a good matching between the in-

plane component of the wave vector of the incident wave and the wave vector of the

guided modes. The periodic grating is simply obtained by the patterning of the

silicon layer consisting in the formation of periodically repeated air slits, thus

resulting in a 1D PC membrane slab, where incident photons are resonantly inserted

and confined.

It will be helpful to explain the phenomena which is described above more

carefully and using appropriate formulas [103]. At first, it should be considered a 1D

PC membrane excited by an incident light beam normal to the membrane (figure

28a), meaning that we operate at the Γ point of the photonic crystal. As indicated in

figure 27b and 27c, the spectral resonance, at frequency ω0, is associated with a

Bloch mode at the centre of the Brillouin zone where the group velocity vanishes.

Then, near this point, the dispersion curve can be characterized by its curvature α,

defined by, in the parabolic approximation:

20

1

2kω ω α= + (3.1)

59

The bandwidth of the reflectivity peak is related to the coupling rate, τc,

between the guided Bloch mode and the incident beam. Then, the quality factor of

the resonance is:

0 0 cQλ ω τ

δλ= = (3.2)

As it will be discussed below, the behaviour of the PC membrane around a

given resonance is completely determined by the parameters α and τc.

For real devices, the lateral size of the illuminated area is limited, and the

resonant coupling efficiency, η, of incoming photons to the guided mode is

controlled by the lateral escape rate, 1/τg, of the wave-guided mode out of this area. It

a) b)

c) d)

Fig. 28. a) Schematic view of a 1D PCM (period Λ) excited by a normal incident beam; b)

band structure the 1D PCM (the Γ Bloch mode is indicated by a red circle); c)resulting

reflectivity spectrum of the 1D PCM; d) reflectivity at resonance as a function of the beam

width [103].

60

can be easily argued that g

g c

τη

τ τ=

+ , which means that τg must be significantly

larger than τc in order to reach a large coupling efficiency [104].

The effect of the lateral kinetics of photons is illustrated in figure 28d, where

the reflectivity maximum (at resonance) is plotted as a function of the beam width:

the coupling efficiency tends to 100% above a beam width which corresponds to the

mean free path of photons in the PC membrane before they escape towards free-

space. This lateral extension of the mode can be estimated as [93]:

cw ατ≈ (3.3)

This approximate formula shows that the ability of high-index-contrast PC

membrane to slow down photons, confining them laterally, allows a very good

control over the lateral escape rate and lends itself to the production of devices with

very compact lateral size.

As discussed above, the resonance bandwidth is determined by the coupling rate

τc between leaky wave-guided Bloch modes and free space radiated modes. From

first order perturbation theory, this coupling rate is proportional to the overlap

integral:

( , ) ( ) ( )G RE x z E z x dxdzε∆∫∫ (3.4)

where the integral is evaluated over a unit cell of the PCM and:

− ER(z) and EG(x, z) are the incoming plane-wave and wave-guided fields for

the unpatterned (or homogeneous) membrane,

− ∆ε(x) is the dielectric periodic variation applied to the homogeneous

membrane.

Therefore, the controlling parameters of the bandwidth are the symmetry of the

photonic crystal, for the in-plane overlap, and the thickness of the membrane, for the

vertical overlap.

It is well demonstrated [105] that, for Bloch modes at the Γ point, PCMs exhibit

two kinds of modes:

61

− Modes whose symmetry forbids the coupling to free-space, resulting in a zero

coupling (or infinite Q factor).

− Modes which can couple to free-space, leading usually to moderate Q factors

due to the strong diffraction efficiency of high index contrast gratings.

The previous general considerations have been used as a simple guideline for

the design of resonant PC reflectors with the desired narrow bandwidth, or large Q

resonance, which are requested to maximize the absorption of a single graphene

layer well beyond 2.3%, when both structures are combined together. It will be

shown that the requested quality factor and the corresponding bandwidth are

respectively close to 103 and around a few nm for the maximum achievable

absorption (around 50%) of a single graphene layer combined with the membrane

resonant reflector. In order to reach this target, two approaches are proposed:

- The first rather trivial approach consists in using weakly corrugated 1D PC

crystal with low filling factor of the low index material (periodic array of silicon

stripes separated by very thin air slits), with a period a allowing the structure to

operate at the Γ point. The adjustable weak corrugation results in a weak coupling

strength and therefore in an adjustable narrow bandwidth. For this period the

diffraction conditions are met for an incoming optical beam to be coupled with a

wave-guided slow Bloch mode if aneff=λ , where effn is the effective index of the

Bloch mode and λ the operation wavelength.

- The second approach, which is original, consists in starting with a strongly

corrugated (low index material filling factor on the order of 50%) 1D PC with 2a

period. At the wavelength aneff=λ , the 1D PC operates at the 1rst Brillouin

boundary below the light line where waveguided Bloch modes are efficiently slowed

down but are not accessible from free space (the diffraction conditions are not met,

in particular at the Γ point). Addressing these slow Bloch modes at the Γ point is

made possible if a double periodicity ( 22

aa ×= ) is superimposed to the

2

a period

62

PC structure. It is therefore possible to excite highly confined waveguided Fano

resonance with adjustable bandwidth in the PC slab membrane by adjusting

accordingly the strength of the double period perturbation.

Those two approaches will be developed in details in sections 3.3 and 3.4.

Before, we present briefly in the following 3.2 section the basic principle of

computer simulation.

3.2. Basic principles of computer simulation

One of the aims of the work was searching the appropriate design of the 1D PC

membrane reflectors for its further fabrication. Computer simulation of one-

dimensional photonic crystal structures is performed by using two methods. The first

method is based on Rigorously Coupled Wave Analysis (RCWA) and is

implemented in a commercial program “GSolver” from the Grating Solver

Development Company. This algorithm gives a numerical solution of Maxwell’s

equations for a periodic grating structure that lies at the boundary between two

homogeneous linear isotropic infinite half spaces: the substrate, and the superstrate.

The solution is rigorous in the sense that the full set of vector Maxwell’s equations

are solved with only the following two simplifying assumptions: 1) a piecewise-

linear approximation to the grating construction, and 2) a truncation parameter for

the Fourier series representation of the permittivity (and impermitivity) within each

grating layer. GSolver is set up to work with linear isotropic homogeneous materials.

Within GSolver, a grating is specified by a series of thin layers. Each layer consists

of (box shaped) regions of constant indices of refraction. By allowing the scale of

this approximation to decrease, a spatially-continuous grating structure can be

approximated to any desired accuracy. This method was used to simulate the

reflective membranes based on one-dimensional photonic crystals with infinite

spatial dimensions.

63

The second method is called the method of Finite Difference Time Domain

(FDTD). This method is a numerical analysis technique used for modelling

computational electrodynamics (finding approximate solutions to the associated

system of differential equations). Since it is a time-domain method, FDTD solutions

can cover a wide frequency range with a single simulation run, and treat nonlinear

material properties in a natural way. The FDTD method belongs to the general class

of grid-based differential time-domain numerical modelling methods. The time-

dependent Maxwell's equations (in partial differential form) are discretized using

central-difference approximations to the space and time partial derivatives. The

resulting finite-difference equations are solved in either software or hardware in a

leapfrog manner: the electric field vector components in a volume of space are

solved at a given instant of time; then the magnetic field vector components in the

same spatial volume are solved at the next instant of time; and the process is repeated

over and over again until the desired transient or steady-state electromagnetic field

behavior is fully evolved. This method was implemented in a commercial application

of RSoft, called FullWAVE. This software was used to simulate the reflective

membranes based on one-dimensional photonic crystals with finite spatial

dimensions.

3.3 Design and fabrication of weakly corrugated 1D PC membrane

reflectors

3.3.1 Simulation of structures

As it was described above the

easiest may to construct the

reflectors based on 1D PC is to

fabricate the grating with a low

corrugation of membrane (silicon

Fig. 29. Scheme of the reflector based on 1D PC

waveguided slab.

64

layer on dielectric substrate – Silicon On Insulator – SOI substrate). The scheme of

Fig. 30. Reflectivity dependences for wide ranges of silicon filling factor (from 0 to 1) and

incident wavelength (from 1450 nm to 1700 nm) for 6 different periods of structures (from

500 nm to 850 nm).

65

such structure is shown in figure 29. The computer simulation using RCWA method

was performed to find out the necessary parameters of the reflective structure to get

the required reflectivity spectrum. It was determined that there are three parameters

of such type of structure: silicon film thickness, filling factor (FF) and period (p) of

1D PC. In our case the simulations were done for silicon film thickness of 220 nm,

which is a standard Si membrane thickness of available SOI substrates. The other

two features of the reflectors were assigned before starting the simulations:

1) The resonance peak position was chosen around 1550 nm with an accuracy

of 20 nm (1.53-1.57 µm). This value of reflective peak was chosen because

it is planed to use the reflectors in optical communications in future, and its

operational wavelength is 1.55µm.

2) The quality factor of the reflective structure should be from 50 to 1500, it

corresponds to a bandwidth of reflective peak from 1 nm to 30 nm. Such

range of quality factor was chosen to match with the absorbance of graphene

to be integrated in the structures.

For a resonance wavelength around 1.5 µm, the period approximately should

equals to µmn

aeff

7.05.0 −≈= λ. Thereby the simulations were started from

discovering the rough value of FF and p. The corresponded reflectivity maps are

shown in figure 30. The simulations of the reflectivity are performed for 6 different

values of the period spanning from 0.5 to 0.85 µm and are represented in figure 30 as

contour maps in which the intensity of reflectivity is colored: wavelengths

correspond to X axis and filling factors correspond to Y axis.

As it is observed from the figure 30, the reflective peaks in the 1.55µm

wavelength range correspond to period of structure ranging from 550 nm to 750 nm

and filling factor from 0.7 to 0.97. Then the simulations were refined and limited to

this narrowed range of periods and filling factors (figure 31). The plots show that the

reflective peak positions and bandwidths strongly depend on the combination of

silicon filling factor and period of structures for fixed silicon layer thickness of 220

nm. For a better understanding of the maps it is helpful to explain how it should be

66

read. If one images a line parallel to axis X corresponding to any value of filling

factor (the example with the line corresponding to filling factor of 0.85 is shown in

figure 31c) then a structure with these parameters (period 650 nm and silicon filling

factor 0.85) has a reflectivity spectrum where the values of reflectivity corresponds

to colors crossed by the line. In more details it means that the reflectivity peak of

considered structure has the position of 1572 nm and it is non symmetric with

slanting slope to lower wavelength and sudden slope to higher wavelength. The

bandwidth of this peak is around 23 nm (the quality factor equals to λres/∆λ = 68). If

such reasoning is extended to the other values of filling factors and periods then the

required quality factor in the range from 50 to 1500 can be obtained and the

combination of parameters of 1D PC can be found out.

Fig. 31. Accurate reflectivity dependences with the same parameters of structures as

shown in previous figure.

67

As a conclusion of these simulations it should be noted that with increasing of

the filling factor and decreasing of the period, the quality factor of membrane

increases and vice versa. The most applicable period and silicon filling factor values

range respectively from 590 nm to 690 nm and from 0.78 to 0.92.

3.3.2 Fabrication and characterization of structures

For the production of 1D PC membrane reflectors, the initial SOI substrate

consisted of a 1mm thick silicon substrate, a 2 µm thick silicon dioxide layer and a

220 nm silicon membrane was used. Moreover for further fabrication process, the

SOI substrate was covered by 80 nm silica layer (it is usually used as protecting

mask for etching of silicon).

The fabrication process consisted of electron beam lithography and reactive ion

plasma etching. The lithography experiments were done using a scanning electron

Fig. 32. Fabrication scheme of 1D PC structure in SOI substrate.

68

microscope «FEI Inspect F» with additional equipment for lithography with

resolution of 20 nm. Reactive ion plasma-chemical etching was carried out on a

commercial installation Alcatel Nextral 110 with a maximum power of 300 W, feed

gases O2, Ar, H2, CHF3, SF6 from 1 to 50 standard cubic centimeters per minute and

working pressure in the chamber from 5 to 100 millitorr.

In the preliminary experiments, silicon patterning was done using reactive ion

etching with plasma in a mixture of argon gas, and sulfur hexafluoride (SF6) in order

to create the required structure (stripes) of silicon.

The lithography process consisted of several stages: spin coating deposition of a

resist with thickness of several hundred nanometers, direct electron-beam

lithography with a spatial resolution down to 20 nm, and use of developer and fixer

to create a clear picture of the resist. The result is a five-layer system: "substrate -

insulator - silicon - silicon oxide - resist structure" (see figure 32). The next

technological step was reactive ion plasma etching. First, silicon oxide mask was

etched using a mixture of argon and trifluoromethane (CHF3), followed by oxygen

plasma etching, which is used to remove resist. The final step is etching of both silica

and silicon layers. The etching parameters were chosen so that the full etching of 220

nm thick silicon coincided with the etching time of 80 nm silicon oxide.

A few samples were fabricated by the method described above. And two of

them had a reflectivity peak in the wavelength range which can be observed in

available equipment. Before the reflectivity measurements the scanning electron

microscopy (SEM) was used for observation of the samples (see figure 33). The

SEM measurements show that the quality of fabricated samples is not so good: as it

can be seen from the images (figure 33): the edges of silicon stripes are not sharp.

The presence of sidewall roughness introduces light scattering and, as a result, the

reduction of intensity of reflectivity peak (optical loses in the other words) can be

observed. Moreover the parameters (period, silicon filling factor, depth of silicon

etching) of expected structures did not fully correspond to the real fabricated

structures. The reason of this discrepancy is likely to be the non optimized reactive

ion etching process. The parameters which were used in the experiments were

69

chosen from the default options of the equipment. But for the different purposes of

accurate experiments, it is useful to calibrate such parameters of RIE as

concentration of gases in the mixture, flow rates, pressure in the chamber, etc. This

calibration was done in further experiments (see the section 3.4.3).

The reflectivity spectra measured in the present work were obtained with a

home-made installation. It consists of a commercial diode laser of B&W Tech

company model BWC-SLD9A-CE with the generation of radiation in the

wavelength range from 1.4 µm to 1.65 µm and a commercial spectrum analyzer

Advantest Q8384 with resolution of up to 20 picometers.

The reflectivity spectra which were measured from fabricated samples are

presented in figure 34a and 34b by red plots. In the same figures the reflectivity

spectra of expected structures are presented as well in blue color. It is clearly

observed that the experimental results are not in agreement with the simulation data

of designed structure. The measured spectra of fabricated structures demonstrate red

shifts of 130-150 nm as compared with the spectra of expected structures. It was

supposed that the discrepancy between simulation and experimental results appeared

because of RIE process, which was not calibrated for required aim, and it resulted in

incomplete etching of silicon. It means that a portion of the silicon layer was left

over, resulting in a red shift of the reflectivity peak. The quality of the etching

Fig. 33. SEM images of 1D PC reflective membrane. Sample #1 and #2.

70

process was accounted for by simulation of different structures with incomplete

etching of silicon layer to adjust experimental results with corresponding structures

(figure 34 a and b, green and black plots). Simulated reflectivity spectra apply to

three structures with different thicknesses of non etched silicon layer. The reflective

peak shifts from the expected spectrum of structure with fully etched silicon to

longer wavelength range with increasing of non etched silicon. There is a matching

between the positions of the reflectivity peak measured from fabricated 1D PC

structure and the peak which was obtained from simulation of structure, if thickness

of left silicon layer equals to 119 nm.

The figures 34c and 34d show a comparison of the experimental results and

simulations both with and without roughness of structures. The roughness was

Fig. 34. Adjustment of the simulation to experimental for two different types of real

samples : incomplete RIE of silicon (a, b) and sidewall roughness (c, d).

a) b)

c) d)

71

simulated by adding a thin absorbing layer (3 nm) at the edge of the silicon stripes of

1D PC structures. It is clearly noticed that the influence of roughness to the

reflectivity characteristics of the membranes depends on the quality factor of

membranes. The Q-factor of the membrane that is shown in figure 34c is much lower

than that in figure 34d. The roughness decreases reflectivity in figure 34c by 10%

and in figure 34d decreasing of reflectivity is about 50%. It means that it is strongly

necessary to fabricate a perfect structure without any roughness if a reflective

membrane with a high Q-factor is desired.

As it was noted above the quality of 1D PC structures of obtained samples is

low because the process of etching of silicon layer is hard to adjust for fabrication of

such designed 1D PC structures. For instance, if the quality factor of PC reflector is

requested to be 1000 (corresponded bandwidth is 1.55 nm for resonance wavelength

of 1.55 µm) then the parameters of 1D photonic crystal should be the next: period –

590 nm and silicon filling factor – 0.92 (from the figure 31a). The air slits and silicon

stripes should be therefore 47.2 nm and 542.8 nm wide, respectively. It means that

the air slits are too narrow for implementing of precise dimensions and sharp edges

of the silicon stripes during the electron-beam lithography and reactive ion etching.

The design should be changed to relax the fabrication process.

For instance, the silicon filling factor is desirable to be approximately equal to

0.5 while the air slits and silicon stripes being not narrower than 200 nm. To achieve

this target, a new design of reflective membranes is proposed. It is described in

details in the next section.

3.4 New design and fabrication of 1D PC membrane reflectors with

adjustable bandwidth and air filling factors close to 50%

3.4.1 Discovering new design of reflectors

72

If an incident beam impinges a periodic structure of period a along the vertical

direction, its in-plane k vector is zero: diffraction phenomena provides an in-plane

momentum = a

π2. Matching with a waveguided mode of effective index neff and at

wavelength λ can occur provided that: λππ effnx

a

⋅⋅=

22. As it was said in section

3.1, in case of low corrugation, the period a can be adjusted to meet this condition

(effn

aλ= ) and 1D PC substrate can perform coupling between free-space and

waveguided modes by exploiting the Bloch modes of 1D PC near the Г point of the

first Brillouin zone and above the light line. But as it was shown in previous

subsection 3.3, there is a problem to fabricate narrow air slits (10-20% of period of

500-600 nm) which width equals to 50-100 nm. So a new approach for design of

narrowband reflective structures was proposed.

The demand for new design of 1D PC structures is to get wide air slits and wide

silicon stripes with widths not less than 200 nm and the possibility to adjust the

quality factors of the reflective membrane. So as it was previously mentioned, if the

resonance peak in reflectivity spectrum of 1D PC structure should be obtained, it is

necessary to do the structure such way that it is possible to address the slow Bloch

mode above light line in dispersion characteristic.

At first let us start from periodical PC structure with strong corrugation (period

is 500 nm and silicon filling factor is 0.5). The wavelength is chosen to operate at the

first Brillouin zone boundary; it is meant to couple to slow Bloch modes at the band

edges of the stop band opened up at the first Brillouin zone; however, these Bloch

modes are below the light line and cannot be coupled to incoming free-space radiated

modes. In these conditions, the PC membrane behaves as a plain non-structured

membrane with regard to free space modes, with an effective index in between 1 and

the Si optical index 2. In order to meet diffracting resonant interaction conditions for

vertically incident radiated modes (gamma point), the double periodicity can be

introduced as it was proposed in section 3.1 (the second approach). Addressing a

73

slow Bloch mode results in a resonant reflectivity peak, whose bandwidth is

controlled by the "strength" of the double periodicity (for example the amount of

difference between to adjacent Si stripes within a double period).

3.4.2 Simulations of structures

As in previous simulations described in 3.3.1 the characteristics of reflectors

should be the same but one more condition was added:

• reflective peak should be around 1.55 µm;

• quality factor of reflective peak is in the range from 50 to 1500

(corresponding bandwidth range from 1 nm to 30 nm);

• widths of air slits and silicon stripes should be not less then 200 nm.

The new offered design of 1D PC reflective membrane consists of so-called

“double period” structures where two periodic arrays of silicon stripes and air slits

are presented and one of the silicon array is moved laterally (see figure 36a). The

resonance peak in the reflectivity spectrum of described structure should have

symmetric shape in order to avoid any losses during the further integration of the

structure with graphene. To achieve the symmetric peak in reflectivity spectrum of

“double periodic” structure it is necessary to obtain the minimum of reflectivity in

spectrum at presumable resonance wavelength (1.55 µm) of the initial “single

period” structure which is a constituent part of “double period” structure. The

dependences of reflectivity of “single period” structure on filling factor for several

values of period are shown in figure 35.

As it can be seen on the maps the reflectivity has the minimum in the

wavelength range around 1.55 µm in different combination of period and FF:

• for p=500 nm FF =0,45…0,55;

• for p=600 nm FF =0,45…0,67;

• other values of periods has not good performance of minimum background.

74

To conclude these simulations it should be noted that the single period of

structure should be roughly equal to 500 nm and the silicon filling factor - 0.5. It

means that the corresponded resonance “double periodic” structure should have the

period around 1000 nm and it must have two silicon stripes and two air slits with the

value of each width of 250 nm.

The second step of simulations is to introduce the displacement of one silicon

stripe array in a “double periodic” structure. This results in appearance of resonance

peak in the reflectivity spectra of structures. The resonance wavelength can be now

adjusted by an appropriate choice of the period (keeping the silicon FF roughly

constant), in such a way as to coincide with conditions for minimum of the

reflectivity spectrum at certain wavelength in order to obtain a nice symmetric peak.

The searching for parameters which influence on the reflective peak position and on

its bandwidth followed further. A rough simulation to find out the dependences in

principle has been done. As it can be seen in figure 36a the “new” design of the

Fig. 35. Reflectivity dependences on different parameters of structures.

75

structure consists of two periodic gratings with the same silicon stripes (a=b) but

with the different air slits which have a little bit shift from each other of few percents

(if it is shifted by 1% it means that difference between air slits will be 2%). The

reflectivity spectra of structures with difference between air slits from 2% to 14% are

shown in figure 36b.

An adjusting the combination of silicon filling factor and period to achieve its

influence on the position of the resonance peak was a next step of computer

simulations. All of the simulation data is not presented but after its studying next two

rules were determined:

a)

b)

Fig. 36. a) The scheme of structure (the superposition of two structures with resembling

parameters); b) The reflectivity of structures with the same value of silicon stripes and

different air slits (a=b=25%; c>d; p=990 nm on pic. A, the absolute value are

a=b=247,5 nm and c+d=495 nm).

76

1) With increasing the silicon filling factor the period should be decreased

in order to obtain the resonance peak around 1.55 µm. In case of increasing the

silicon filling factor more than 0.58, the structure period should be less then 930 nm.

It means that the air filling factor equals to 0.42 or 390.6 nm. But taking into account

that this value for two arrays, the width of one air slit will be less then 195.3 nm and

it does not meet the condition for 1D PC fabrication. Thereby the silicon filling

factor can be not less than 0.58 for “double periodic” structure or 0.29 for “single

periodic structure”.

2) With decreasing the silicon filling factor less then 0.48 the period is

required to be more than 1.05 µm, besides the intensity of reflective peak decreases

less then 70%. And the second fact is not acceptable because the further integration

of structure with graphene requests to have 100% of intensity of reflective peak for

Fig. 37. Reflectivity maps. Dependences of reflectivity on period for four types of air slit.

77

the best coupling of confined photons with the absorbing material.

To summarize the simulation, the silicon filling factor of 0.52 was chosen as the

most appropriate value for obtaining a nice symmetric reflective peak around the

resonance wavelength 1.55 µm. The reflectivity maps of the “double period”

structure with a selected silicon filling factor of 0.52 and different values of

discrepancy between the air slits are demonstrated in figure 37. As it can be seen

from the contour maps the bandwidth of reflective peak can be easily adjusted by

playing with widths of air slits in two arrays. With increasing the discrepancy

between the air slits in “double periodic” structure its quality factor decreases. In

order to obtain the reflective peak at 1.55 µm the period of structure should be

around 1 µm and in this case the widths of silicon stripes and air slits will have

values more then 200 nm. Thuswise all of the conditions were met and the

parameters of 1D PC structure were found out.

Finally, the last step of simulation of reflectors based on 1D PC was the

investigation of lateral losses in the membrane which can appear due to a finite

lateral size of structure and a finite size of incident beam. As it was introduced in

section 3.1 it is necessary to provide a fully coupling of the free-space mode with the

waveguided mode for 100% reflectivity efficiency of membrane reflectors. To

understand the real behaviour of electromagnetic field in 1D PC structure the FDTD

method was used for simulation of finite size structures and beam fluxes with

different sizes. In figure 38 the maps of electric field are presented. For better

understanding these maps, there is a brief description: the 1D PC structure has the

size of 100x100 µm and it is shown as a grating parallel to axis Y; the source is

shown as a grey block and it stays at 3 µm from the PC structure; the light

propagates from right to left; besides the profiles of intensity of electric filed are

shown in figure above each map, the profiles correspond to the yellow lines, which

are parallel to the axis X and lie in the map center. As it can be seen from the maps

the intensity of the reflective electric field increases with increasing of the width of a

light source and it has a limit value where the intensity of reflectivity equals to 100%.

This maximum of source width depends on the bandwidth of PC reflector (see figure

78

38d). It was concluded that the size of 1D PC structure should be not less than 60x60

µm.

To summarise the described simulations several appropriate structures were

selected to proceed further with the fabrication. The parameters of selected structures

Fig. 38. Contour maps of electric fields of source with a different width ( from 10 to 40

µm) (a, b, c). Dependence of intensity of reflectivity maximum on width of the incident

light flux for different types of structures (different bandwidths) (d).

a) b)

c)

d)

79

are shown in the table below.

Table 2. Set of data of sizes of simulated reflective structures based on 1D PC

and its bandwidths.

name of

structure period

filling

factor

difference between

air slit bandwidth

2.1 52 %

2.2 54 %

2.3

990 nm

56 %

3.53 % 35 nm 1.5 nm

3.1 56.3 %

3.2 58.4 %

3.3

950 nm

60.5 %

5.79 % 55 nm 2.2 nm

4.1 54.1 %

4.2 56.2 %

4.3

970 nm

58.3 %

7.73 % 75 nm 4.5 nm

5.1 52 %

5.2 54 %

5.3

990 nm

56 %

9.6 % 95 nm 7 nm

The next section is about the fabrication and characterization of the “double

periodic” 1D PC structures.

3.4.3 Fabrication and characterization

As a reminder it should be noted that in the section 3.3.2 there was the

description of method of 1D PC fabrication from SOI substrate and the problem was

to achieve a high sharpness of sidewalls of silicon stripes. It was proposed the

80

roughness of silicon sidewalls is due to reactive ion etching. During the fabrication

process the sulfur hexafluoride (SF6) was used for etching of silicon, but it is known

that this gas does not show high selectivity of etching process between silicon and

silica. It means that the hard mask of silica, which was used in previous experiments

on fabrication, could not fully protect the silicon layer and it was etched as well as

silicon. The second problem is a fluoridation of the silica during the etching process

and further etching becomes more chemical but not mechanical and it results in

roughness of sidewalls. Thereby it was purposed to change the active environment

from SF6 gas to Cl2 gas because chlorine does not damage silica and presents a very

high selective silicon etching. There was no possibility to use chlorine gas with

reactive ion etching equipment but the chlorine usage was available in induced

coupled plasma RIE equipment (ICP RIE).

In additional the lithography process was improved a lot to obtain the matching

between design structures and real experimental samples. During a lot of attempts to

fabricate necessary PC structures, the problem of mismatching of design and

obtained samples was observed. To solve this problem it was proposed to calibrate

initial design of 1D PC structures. As it is known that the technology of electron

beam lithography consists of following steps: 1) covering the substrate by resist; 2)

Fig. 39. Scanning electron microscope images of two different 1D PC structures formed

on SOI substrate with different parameters of silicon filling factor and period.

81

direct electron beam lithography on resist using preliminary prepared design; 3)

using developer to form pattering on resist. In our case due to multilayer substrate

(silicon-silica-silicon-silica) it is important to take into account that the electrons

shined on the resist scatter inside the resist, reflect from the multilayer substrate.

Thereby the lithography design was improved by adjusting the dose factor. The

adjustment was done by using computer simulation of electron propagation through

the resist and multilayer substrate. As result the samples were obtained with sharp

sidewalls and good matching between designed structures and fabricated samples

(see figure 39).

The values of width of silicon stripes which were formed on silicon layer with

and without corrections of design are given in table 3. As it can be seen from the

table, the accuracy without corrections is not less then 30-50 nm and with corrections,

it is around 10-15 nm.

Table 3. Set of data of measurements of width of fabricated samples with and

without design corrections and its comparing with expected values.

experiment results designed width of silicon stripes

without corrections With corrections

structure #2: 255 nm 287 nm 267 nm

structure #4: 280 nm 321 nm 290 nm

structure #5: 260 nm 297 nm 270 nm

At the last step of investigation of fabricated samples the reflectivity

characteristics were measured. The comparisons of simulation and experimental

results of reflectivity characteristics of the structures with different parameters are

shown in figure 40. It confirms that the fabrication technique which was developed

has a very good potential to produce samples based on SOI substrate. Moreover the

experimental results show a good matching with simulation data. The accuracy of

matching between of experiment and simulation is around 10-20 nm (concerning the

position of resonance reflective peaks). It means that the theoretical proposal

82

(described in section 3.3.1) to use a new original approach for achievement of

narrowband reflective structures is applicable and can be used for other different

aims.

As conclusion of this chapter, it should be repeated that two principles of

reflection from 1P PC structures based on SOI substrate were proposed, so-called

“single periodic 1D photonic crystal” and “double periodic 1D PC”. Both of these

approaches were realized in experiments using two different types of fabrication

technologies. It was shown that chlorine is a more appropriate gas for silicon etching

compared with sulfur hexafluoride. Also it was shown that correction of design using

Fig. 40. Simulation (red plots) and experimental measurements (black plots) of

reflectivity characteristics of structures with different parameters corresponded to date

from table 2 (designations of “c” and “d” are presented on figure 35a).

83

computer simulation is needed to obtain a high accuracy between designed and

fabricated samples.

The next chapter presents the investigation of integration of graphene with 1D

PC structures which were described in this chapter.

84

Chapter 4. Combination of graphene with resonant 1D photonic crystal

membrane reflectors: theoretical and experimental measurements [A4, A7]

4.1 Concept of integration of a 1D photonic crystal membrane reflector

with graphene

The main target of this work is to integrate graphene with photonic crystal for a

variety of potential applications which have been presented in the introduction of the

manuscript. In the present section I give a detailed description of the physical

concepts underlying such integration of graphene with PC structures. Let us remind

that graphene absorbs 2.3% of the incident light intensity mostly independently of

the wavelength and also has non-linear optical properties: as a result graphene is

attractive not only for electronics, but also for optics and photonics. The effect of

saturable absorption was observed in graphene films and already has been used in

lasers for formation of self-mode locking regime and generation of ultra-short (sub-

picosecond) pulses [106, 107]. In more details, the electrons of a ground state of a

saturable absorber material are excited to the upper energy state. With the increasing

of the incident light power density at a rate such that there is insufficient time for

them to decay back to the ground state, the ground state becomes depleted, and the

absorption saturates. For graphene, the saturation of absorption appears if the power

density of the incident fluence is higher than 0.4mJ/cm2, and this parameter is almost

the same as for other passive mode-lockers e.g. SESAM. Now I propose to combine

graphene material with an optical resonator, where photons can be efficiently

confined, thus resulting in an enhancement of the effective graphene absorbance and

allowing for reaching saturation of absorption at a reduced incident optical power.

The optical resonator, which was described in details in previous chapter, consists of

a reflective resonant structure based on a one-dimensional (1D) photonic crystal (PC)

membrane slab. In brief, the idea of bonding the graphene with such a structure is

based on the peculiarity of the reflection of this membrane (see chapter 3). Thus a 1D

PC membrane slab, where incident photons are resonantly inserted and confined,

85

allows for light harnessing. If now a graphene layer bonded onto the reflective

structure is considered, the photons confined inside the slab will interact with the

electrons in graphene. The longer the lifetime of photons in the slab (or the narrower

the BW of the resonant reflector), the longer they will be interacting with electrons in

the graphene, thus resulting in an enhanced absorbance of carbon film (see a scheme

in figure 41). Note however that the maximum attainable absorbance (50%:

developed later) is achieved under the so-called critical conditions where the control

of the photon lifetime in the slab is equally shared by the absorption rate and by the

free space re-emission rate of photons.

Let us define the equations which describe these critical conditions. At first, the

reflective structure covered by absorbing material (graphene film, for instance) and

the normally incident light should be considered. In this case a part of incoming

photons will be reflected, other part will be transmitted and some of photons will be

absorbed by the graphene film. The reflectivity of the structure depends on the

incident wavelength and on photon lifetime in the slab (see relation below). The

latter is just controlled by the coupling of waveguided modes with free space

radiated modes and by the absorption of confined waveguided modes in the slab by

absorbing material. Moreover the photon lifetime related to the absorption can be

Fig. 41. a) Scheme of reflection from the 1D PC membrane. b) Scheme of

enhancement of absorbance in graphene combined with 1D PC reflective membrane.

a) b)

86

represented by the absorption coefficient of the material, the effective index of the

PC membrane and the light velocity.

Thereby, the reflectivity of the PC membrane reflector as a function of the

incident light pulsation (ω) is given below:

( )

2

2

2 201 4

PCR

ττ

ω ω τ

=

+ − (4.1)

with 1 1 1

PC Aτ τ τ= + , where

1

A eff

c

nα

τ= ; τPC is a photon lifetime related to

coupling of incoming photons from free space with waveguided mode; τA is a photon

lifetime related to the coupling of confined photons with electrons in the absorbing

material (graphene film); ω0 is a resonance wavelength of reflective structure based

on 1D PC; neff is an effective index of the PC membrane; α is the absorption

coefficient of the material; c is the light velocity.

At resonance (ω = ω0):

2

2

1

1 PC

A

Rττ

=

+

(4.2)

2

2

11

2

+=−=

A

PC

A

PC

RT

ττ

ττ

(4.3)

And the absorbance of graphene film is defined as:

22

222

21

2

1

2

1

+

=

+

=−−=

PCeff

PCeff

A

PC

A

PC

n

c

n

c

TRA

τα

τα

ττττ

(4.4)

87

In case of absence of graphene film: α=0, then |R|2 = 1, |T|2 = |A|2 = 0. The

condition for maximum absorbance is eff

PC A

n

cτ τ

α= = , in this case

2 2

max50%A A= = and |R|2 = |T|2 = 25%.

Let us elucidate what will happen if this condition is not met. For τPC < τA then

confined photons cannot experience a full coupling with absorbing material and this

results in a reduced absorbance (less than 50%). In the other case, if τPC > τA then too

many photons will interact with electrons of absorbing material and the resonance

will be killed, as a result the absorbance will decrease and the reflectivity as well but

transmittance will increase beyond 25%.

As it was mentioned above the photon lifetime related to coupling of incoming

photons with free space mode corresponds to the bandwidth of the resonance

reflective peak of PC structure. Thereby to obtain the best result in enhancement

graphene absorbance the bandwidth should be adjusted. The computer simulation of

graphene bonding with PC reflectors is presented below.

4.2 Simulation of enhancement of optical properties of graphene integrated

with PC

After complete theoretical and experimental investigation of 1D PC reflective

membranes, the study of influence of graphene films on reflective characteristics of

membranes was started. At the first step the simplest example was considered where

a graphene monolayer covers a reflector based on 1D photonic crystal with single

periodicity (see section 3.3). Then the computer simulation of characteristics of PC

structures without graphene and covered by single graphene layer was done and it is

presented in figure 42. Simulated reflectivity spectra of PC structures with different

parameters of silicon filling factor and period are shown in figure 42a. As it can be

seen these parameters define the Q-factor (or bandwidth) of structures. Further, if the

structures are covered by graphene monolayer, the reflectivity (figure 42b) is reduced

88

due to absorption in graphene. The reduction of reflectivity increases with decreasing

of bandwidth (or increasing of quality factor), but in case of too narrow bandwidth,

the reduction of reflectivity does not fully correspond to absorption in graphene. For

a better understanding, the absorbance of graphene bonded with PC structure with

different Q-factor was calculated (plots of figure 42c). It should be noticed that the

maximum of absorbance is around 50% and this value corresponds to the bandwidth

of 1.4 nm (black spectrum). Meanwhile, the reflectivity is reduced down to around

25% (figure 42b black spectrum) whereas the transmittance of the structure reaches

25% (see figure 42d black spectrum). This situation corresponds to the so called

Fig. 42. a) Simulation of reflectivity spectrum of PC structure without graphene; b)

Simulation of reflectivity spectrum of PC structure covered by graphene; c) Simulation

of absorbance spectrum of graphene bonded with PC; d) Simulation of transmittance

spectrum of PC structure covered by graphene.

a) b)

c) d)

89

critical conditions where the control of the photon lifetime in the slab is equally

shared by the absorption rate and by the free space re-emission rate of photons, as

already mentioned above. In case of very narrow bandwidth of peak (0.5 nm) photon

lifetime related to coupling waveguided modes with free space modes is longer than

the photon lifetime related to coupling of confined waveguided photons with

absorbing material and as a result the resonance is killed. Thereby reflectivity in this

case decreases (red plot in figure 42b), absorbance decreases as well (red plot figure

42c) and transmittance increases (red plot figure 42d).

It should be added that the influence of graphene films on reflectivity depends

on the thickness of graphene films due to its absorbing possibility. Graphene films

with thickness from 1 to 5 layers and absorbance from 2.3% to 11.5% of incident

flux intensity accordingly were simulated. It should be added that the optical

property of graphene (refractive index) was taken from the literature where it was

measured by ellipsometry [108]. For single graphene layer the refractive index at

visible range equals to n=2.6-1.3i. The real number is the same as for thin graphite

film and the imaginary unit, which is responsible for absorbance, equals to 1.3 and

corresponds to graphene absorbance of 2.3% at the wavelength of 550 nm. Since in

our case the operational wavelength is around 1.55 µm, the imaginary part was

changed to achieve the initial absorbance of graphene. The value of imaginary part of

refractive index for 1.55 µm equals to 3.0. Besides, with increasing of the thickness

of graphene film from 1 layer to 5 layers, the imaginary part of the optical index also

increases from 3.0 to 3.4, by 0.1 for each additional layer: this variation of the

imaginary part with wavelength is a direct consequence of the flat absorption

spectrum of graphene (see the section 2.1.3).

The dependence of graphene absorbance on the bandwidths of PC structures is

given in figure 43a. Also the influence of a hard mask, which is in fact a silicon

dioxide layer acting as a spacer layer and which was used in fabrication process (see

the section 3.3.2), on absorbing characteristic of graphene was obtained. The

simulations were done for PC without silica layer (figure 42a) and for thickness of

silica layer of 80 nm (figure 43b). There are three features which should be discussed

90

accordingly to these results of simulation. The first one and the general feature of

these simulations is that with increasing of the amount of graphene layers deposited

onto PC reflector the maximum of absorbance of graphene film appears at wider

bandwidth of resonance reflective peak of PC membrane. This behavior can be

explained by absorbing property of graphene. The thicker graphene film the shorter

photon lifetime related to coupling of confined photons with absorbing material is

required as result the lower quality factor membrane is needed. In the other words,

the action of the resonance is maximum when its intrinsic lifetime (which is like the

inverse of its bandwidth) equals to the time required for photon absorption (the

critical condition, which was described in previous section). The second one concern

to the maximum of absorbance of graphene film, its value is more than 50% and it

can be explained by action of Fano resonance. The resonance is helpful in increasing

the absorbance as long as the absorbing rate gives it a chance that is the requested

time duration, to survive. If the absorbing rate increases beyond (that it is getting

larger than 1

PCτ ), then the Fano resonance is useless and photons are directly

absorbed by the graphene material. Absorption in excess of 50% can then be

observed as well as simulated.

Fig. 43. Dependences of absorbance of graphene films with different thicknesses

(from 1 to 5 layers) on the bandwidths of PC structures: (a) the graphene film is directly

bonded on top of the PC; (b) a 80nm thick silica spacer is inserted between the PC

membrane and the graphene.

a) b)

91

The last point is the difference between plots where the structure is used without

and with silica layer. This layer was added onto the structure because it was used in

real device during the fabrication process as a hard mask to protect silicon layer

during etching procedure. But in case of graphene bonding with PC structure the

silica acts as additional layer which has little influence on reflective characteristics of

initial PC reflectors but introduces significant changes in the dependence of

absorbance on the bandwidth of reflectors (the plots in figure 43a and 43b differ

from each other). To interpret this change the silica layer can be imaged as an

additional spacer between graphene film and PC structure. The moving away of

graphene film from the PC results in weakened of interaction of electromagnetic

field with absorbing material. For example, if graphene monolayer is considered on

top the PC reflector then for maximum of absorbance of graphene the bandwidth of

structure without silica layer should be around 2-3 nm (black plot in figure 43a) but

in presence of silica layer with 80 nm thickness the maximum of absorbance of

graphene monolayer corresponds to 0.5-1 nm bandwidth of PC reflector (see the

black plot in figure 43b). If the graphene film is further away from the PC structure a

stronger resonance is necessary in order to provide sufficient interaction between

confined photons and electrons in graphene.

To conclude the results of simulations, there are several rules of adjustment of

the structure for maximum possible absorbance in graphene:

1) absorbance of graphene film reaches the maximum value if the critical

conditions are satisfied. These conditions are met if the two photon lifetimes

match with each other: a) the photon lifetime related to coupling of confined

photons with absorbing material and represented by thickness of graphene;

b) the photon lifetime related to coupling of waveguided photons with free

space mode and represented by the bandwidth of reflector.

2) the thicker graphene film deposited onto PC membrane the wider bandwidth

of reflector is needed to get maximum absorbance of graphene film while

the other parameters are unchanged;

92

3) the further the graphene film stands from the PC slab (the presence of

thicker silica layer) the narrower the bandwidth of reflector is required while

the other parameters are kept the same;

The next and final step of the work was the experimental demonstration of

enhancement of graphene absorbance. This step is presented in the next section.

4.3 Experimental characterization of devices combining graphene and PC

As it was described in sections 3.3.2 and 3.4.3 the technology of fabrication of

reflectors based on 1D PC slab has been improved and, as a result, the samples with

different parameters of reflection peak were obtained. Among these samples one

sample had the appropriate parameters: it has a lattice period of 600 nm and a silicon

filling factor of 85%. This reflective structure demonstrates a resonance peak at 1.58

µm and its bandwidth equals to 30 nm. This reflective PC structure was used for

graphene bonding. To compare the value of enhancement of absorbance, a few

different graphene films were transferred onto PC reflective membrane one after one

and the reflectivity spectra were measured every time.

Figure 44 shows the reflectivity spectra of samples before and after graphene

deposition. The reflectivity of the clear PC membrane is around 90% at the

resonance wavelength (set of data #1, black plots correspond to experimental results

and red plots – to simulation data). The losses of 10% (as compared to a perfect

mirror) are attributed to the sidewall roughness of the silicon strips formed in the

RIE process (see the section 3.3.2). The simulation of this roughness has been also

done. The results of modeling (red plots) are in good agreement with the

experimental results (black plots). The graphene deposition resulted in a decrease of

the reflectivity due to absorption in carbon film. The measurements were done for

several different films and the simulations were used to estimate the appropriate

thickness of the graphene film. The simulation data of reflector bonded with

graphene layers is shown in figure 44. The decrease of the reflection peak intensity at

93

the resonance wavelength occurs as a result of optical absorption in the graphene

film and the drop of amplitude agrees with the number of graphene layers. The

reflectivity spectra were simulated for one to 4 graphene layers.

Thereby, according to the experimental results, the first attempt of graphene

deposition (shown in figure 43a) exhibits a decrease of reflectivity from 90% down

to 60% and the same value was obtained for four layered graphene film using

computer simulation. This means that the absorbance of four graphene layers is 30%

a)

b)

Fig. 44. Optical microscope images and the reflection characteristics of the PC

pristine structures (set of data number #1) and the structures covered with graphene films

(set of data number #2) with different thicknesses. The approximate thicknesses of

graphene films are four layers (a) and two layers (b).

94

instead of 9.2% for a freestanding four-layered graphene. The second attempt (figure

44b and the corresponding spectra) showed a reflectivity of 70% and the computer

simulation gave the same value for double-layered graphene. This means that 20% of

intensity is absorbed in the graphene film meanwhile the absorbance of suspended

double layered graphene equals to 4.6%.

The third experiment on graphene bonding has shown the best results

Fig. 45. Microscope image (a) and SEM image (b) of the PC covered with

graphene. c) Raman spectrum of graphene transferred on the PC structure.

d) Experimental reflectivity spectra of the initial structure (black plot) and of the

structure covered with a graphene monolayer (red plot).

a) b)

c) d)

95

demonstrated in figure 45. The optical microscope image is shown in figure 45a, but

due to thin graphene film, it is invisible. Thereby a SEM observation of the carbon

film is shown in figure 45b. The area selected in blue circle is mostly uniformly

covered by graphene: this area was used for Raman and reflectivity measurements.

The Raman spectrum of the sample shows a high 2D peak corresponding to a single

graphene layer and the imperceptible D-peak thus confirming the high quality of the

sample (figure 45c). Finally the reflectivity measurements of the 1D PC reflector

covered by graphene demonstrate the reduction of reflectivity peak from 87 to 71%

(figure 45d). Since the silicon does not absorb light in this wavelength range it was

concluded that the reduction of reflectivity corresponds to the absorption in the

graphene monolayer (as in previous experiments described above). Thereby the

absorbance of graphene bonded with 1D PC slab equals to 16%, compared to 2.3%

for the plain suspended graphene monolayer. The PC structure therefore enables a

seven-fold enhancement of the absorbance in graphene.

Finally, the main aim of the work has been achieved and the effect of

enhancement of optical absorbance of graphene has been observed. The maximum

theoretical enhancement of graphene absorbance has been shown with the value of

50% in case of integration of graphene in reflective structure based on 1D PC slab

with special parameters comparing with 2.3% for a free-standing graphene . In other

words, the enhancement of absorbance by 20 times can be reached. The experimental

results demonstrate the possibility to increase the absorbance of graphene by 7 times

even in case of using the reflector with a low quality factor (Q = λres / ∆λ ≈ 56). This

reduced increase as compared to the maximum attainable is due to the fact that

reflectors, which were used, had a quality factor lower than the optimum value (the

real value of Q-factor of used reflector was around 50 instead of around 500) as a

result of unwanted optical losses.

96

Conclusion

The continuous growth of system complexity makes it inevitable the

development of technological schemes where different material systems are

heterogeneously integrated to achieve a variety of functionalities, while

miniaturizing the size of devices and systems and decreasing the cost of the

fabrication process, both in time and consumption.

This is particularly true in the field of Photonics, where the requirements to be

met in order to achieve those goals can be summarized along the two following lines:

- Photonic miniaturisation, which the principal driving forces lie in the low

energetic-thermal budget requested by photonic integrated systems, in the

necessary topological and size matching with micro-electronic circuits and,

finally, in the capability offered by photonic micro-nano-structures of

harnessing the interaction or coupling between the electromagnetic field and

the matter.

- Active/passive photonic heterogeneous integration, which combines the most

efficient active (light emission, non-linear characteristics) materials with

passive (light conducting and confining) materials to take full advantage of

both.

In this work, novel approaches to meet the above recalled requirements have

been developed, aiming at the production of new classes of photonic devices

combining silicon and graphene materials, taking advantage of the unique optical

non-linear properties of the latter (ultra-fast and wavelength independent saturable

absorption) and of the remarkable capacity of the former to offer the ideal material

basis for the fabrication of highly confining miniaturized photonic structures along

the powerful and low cost technological procedures currently applied for silicon

microelectronics.

For photonic miniaturization it was proposed to apply a photon confinement

strategy where use is made of diffractive phenomena in periodically high index

97

contrast structured materials to control the spatial-temporal trajectory of photons.

This strategy is in the heart of quite a few of the recent developments in the field of

Micro-Nano-photonics, along the line which has been widely referred to as the

Photonic Crystal approach. Along this line, silicon material has been used owing to

its remarkable photonic characteristics: its high optical index (around 3.5) makes it a

very good candidate as a photonic crystal material and an excellent optical

“conductor”; this has proved particularly true when used in the so called membrane

configuration, where 1D photonic crystal is formed in a Silicon on Insulator eg silica

(SOI) layer. It has been demonstrated, theoretically and experimentally, that these 1D

photonic crystal can act as photonic resonators, which are surface addressable

vertically, and consequently as photon reservoirs where the electromagnetic energy

can be accumulated and made available for efficient coupling to (absorption by) the

graphene material, at a very reduced cost in terms of the incident electromagnetic

power (theoretically up to a 25 reduction factor, while a factor 7 was observed

experimentally). The 1D photonic crystal resonator designed and fabricated in the

work constitute also very attractive “photonic by-products” in that they behave as

very efficient and compact reflectors, whose spectral characteristics can be

monitored at will.

Considerable amount of work has been devoted to the synthesis of graphene by

chemical vapour deposition on nickel and copper substrate: a detailed study of the

influence of growth parameters and of growth mechanism has been performed. It

was demonstrated that these substrates may be used for the production of graphene

with coverage area over 2 cm2 and with high quality, as confirmed by Raman

spectroscopy. It was shown that the obtained samples have nonlinear optical

properties: namely, the relaxation time of the excited electrons in graphene was

studied by “pump-probe” spectroscopy in the spectral range from 1100 to 1700 nm.

The effect of saturation of absorption at a wavelength of 10.55 µm was investigated

and the absorption saturation was found to be 12%.

98

The next step of this work will be the demonstration of saturable absorption of

graphene heterogeneously integrated with 1D silicon membrane photonic resonator,

at a reduced incident power: this aspect is currently investigated in the Institutions in

Moscow and Lyon where this PhD thesis work was conducted. Many other steps are

expected to follow in the future, where the combination of graphene and silicon

proposed in this work should results in the production of a variety of compact

photonic devices including ultra-fast saturable absorber devices and ultra-fast, widely

tunable optical modulators.

99

Acknowledge

In conclusion, I would like to express my sincere gratitude to my supervisors

Professor Pierre Viktorovitch and Professor Elena Obraztsova for guidance and

support during my PhD studies. I also wish to thank the Head of Nanophotonics and

Photovoltaics group Professor Xavier Letartre, Head of the Lyon Institute of

Nanotechnologies Christian Seassal, Head of Natural Science Center Professor

Vitaly Konov for opportunity to work in such a pleasant atmosphere and to

participate in international conferences.

Furthermore, I am grateful to Michel Garrigues, Céline Chevalier, Romain

Peretti, Cécile Jamois, Christelle Monat and Radoslaw Mazurczyk for help me with

experiments in INL and teach me to work the equipments and for their support.

Also I’d like to thank Petr Obraztsov, Roman Sorochenko and Yuriy Klimachev

for giving me an opportunity to perform interesting experiments on investigation of

linear and nonlinear optical properties of graphene in Prokhorov General Physics

Institute and in Lebed Physics Institute. Special thanks to all co-authors of the work

presented in this Thesis.

I am grateful to all members of Laboratory of spectroscopy of nanomaterials in

GPI and all members of group of Nanophotonic and Photovoltanic in INL for

assistance in training classes for optical equipment and for interesting discussions of

experimental results, as well as a friendly and good working atmosphere in

laboratories.

Finally, I would like to thank my parents Tatiana, Gennadiy, my sister Varya

and my wife Galina Rybin’s for their love and involvement in my life.

100

Author’s publications

[A1]. Rybin M.G., Kolmychek P.K., Obraztsova E.D., Ezhov A.A. and Svirko

O.A., «Formation and Identification of Graphene», Journal of Nanoelectronics and

Optoelectronics 4, 239-242 (2009).

[A2]. Rybin M.G., Pozharov A.S., Obraztsova E.D «Control of number of

graphene layers grown by chemical vapor deposition», Phys. Status Solidi С 7 (11–

12), 2785–2788 (2010).

[A3]. Obraztsov P.A., Rybin M.G., Tyurnina A.V., Garnov S.V., Obraztsova

E.D., Obraztsov A.N. and Svirko Yu.P, «Broadband Light-Induced Absorbance

Change in Multilayer Graphene», Nano Letters 11 (4), 1540–1545 (2011).

[A4]. Rybin M.G., Garrigues M., Pozharov A.S., Obraztsova E.D., Seassal C.

and Viktorovitch P. «Photonic Crystal Enhanced Absorbance of CVD Graphene»,

Carbon Nanostructures, GraphITA2012, 195-202 (2012).

[A5]. Bykov A.Y., Murzina T.V., Rybin M.G., Obraztsova E.D. «Second

harmonic generation in multilayer graphene induced by direct electric current»,

Physical Review B 85, 121413(R) (2012).

[A6]. Sorochenko V.R., Obraztsova E.D., Rusakov P.S., Rybin M.G.

«Nonlinear transmission of CO2 laser radiation by graphene», Quantum Electronics

42 (10) 907 – 912 (2012).

[A7]. Rybin M.G., Pozharov A.S., Chevalier C., Garrigues M., Seassal C.,

Peretti R., Jamois C., Viktorovitch P. and Obraztsova E.D., «Enhanced optical

absorbance of CVD-graphene monolayer by combination with photonic crystal slab»,

Physica Status Solidi B, 249(12), 2530–2533 (2012).

[A8]. Rusakov P.S., Kondrashov I.I., Rybin M.G., Pozharov A.S., Obraztsova

E.D. «Chemical vapor deposition of graphene on copper foils», Journal of

Nanoelectronics and Optoelectronics 8, 78-81 (2013).

[A9]. Kondrashov I.I., Rusakov P.S., Rybin M.G., Pozharov A.S., Obraztsova

E.D. «Chemical vapor deposition of graphene on nickel from different gaseous

atmospheres», Journal of Nanoelectronics and Optoelectronics 8, 82-85 (2013).

101

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