graphene-photonic crystal hybrid structures for light …the second constitute of the proposed...
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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].
14
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,
15
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.
17
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].
18
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
19
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
References
1. H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl, R. E. Smalley,
“C60: Buckminsterfullerene”, Nature 318, 162 – 163 (1985).
2. S. Iijima, “Helical microtubules of graphitic carbon”, Nature 354, 56 –
58 (1991).
3. P. R. Wallace, “The Band Theory of Graphite”, Physical Review 71,
622–634 (1947).
4. D. P. DiVincenzo, E. J. Mele, “Self-consistent effective-mass theory for
intralayer screening in graphite intercalation compounds”, Physical Review B 29,
1685–1694 (1984).
5. T. W. Ebbesen, H. Hiura, “Graphene in 3-dimensions: Towards graphite
origami” Advanced Materials 7, 582–586 (1995).
6. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V.
Dubonos, I. V. Grigorieva, A. A. Firsov, “Electric field effect in atomically thin
carbon films”, Science 306, 666–669 (2004).
7. A. K. Geim, K. S. Novoselov, “The rise of graphene”, Nature Materials
6, 183 - 191 (2007).
8. M. I. Katsnelson, “Graphene: carbon in two dimensions”, Materials
Today 10 (1–2), 20–27 (2007).
9. B. T. Kelly, “Physics of Graphite”, Applied Science Publishers (1981).
10. H. P. Boehm, A. Clauss, G. Fischer, U. Hofmann, “Surface properties of
extremely thin graphite lamellae”, Proc. of the Fifth Conference on Carbon,
Pergamon Press, London, 73 (1962).
11. H. P. Boehm, A. Clauss, G. O. Fischer, U. Hofmann, “Dünnste
kohlenstoff-folien”, Z. Naturforsch. B, 17, 150 (1962).
12. M. Eizenberg, J. M. Blakely, “Carbon monolayer phase condensation on
Ni(111)”, Surface Science 82(1), 228–236 (1979).
102
13. A. J. Van Bommel, J. E. Crombeen, A. Van Tooren, “LEED and Auger
electron observations of the SiC(0001) surface”, Surface Science 48(2), 463–472,
(1975).
14. I. Forbeaux, J.-M. Themlin, J.-M. Debever, “Heteroepitaxial graphite on
6H-SiC(0001): Interface formation through conduction-band electronic structure”,
Physical Review B 58, 16396–16406 (1998).
15. B. Z. Jang, A. Zhamu, “Processing of nanographene platelets (NGPs)
and NGP nanocomposites: a review”, Journal of Materials Science 43(15), 5092-
5101 (2008).
16. K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S.
V. Morozov, A. K. Geim, “Two-dimensional atomic crystals”, Proceedings of the
National Academy of Sciences of the United States of America 102(30), 10451-
10453 (2005).
17. J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J.
Booth, S. Roth, “The structure of suspended graphene sheets”, Nature (London) 446,
60 (2007).
18. K. P. Loh, Q. Bao, P. K. Ang, J. Yang, “The chemistry of graphene”,
Journal of Materials Chemistry 20, 2277-2289 (2010).
19. S. Park, R. S. Ruoff, “Chemical methods for the production of
graphenes”, Nature Nanotechnology 4, 217-224 (2009).
20. O. C. Compton, S. T. Nguyen, “Graphene Oxide, Highly Reduced
Graphene Oxide, and Graphene: Versatile Building Blocks for Carbon-Based
Materials” Small 6, 711–723 (2010).
21. S. Marchini, S. Günther, J. Wintterlin, “Scanning tunneling microscopy
of graphene on Ru(0001)”, Physical Review B 76, 075429-1 – 075429-9 (2007).
22. Y. Pan, H. Zhang, D. Shi, J. Sun, S. Du, F. Liu, H.-J. Gao, “Highly
Ordered, Millimeter-Scale, Continuous, Single-Crystalline Graphene Monolayer
Formed on Ru (0001)”, Advanced Materials 21, 2777–2780 (2009).
103
23. P. W. Sutter, J.-I. Flege, E. A. Sutter, “Epitaxial graphene on
ruthenium”, Nature Materials 7, 406 - 411 (2008).
24. R. van Gastel, A. T. N’Diaye, D. Wall, J. Coraux, C. Busse, N. M.
Buckanie, F.-J. Meyer zu Heringdorf, M. Horn von Hoegen, T. Michely, B.
Poelsema, “Selecting a single orientation for millimeter sized graphene sheets”,
Applied Physics Letters 95, 121901-1 – 121901-3 (2009).
25. J. Coraux, A. T. N‘Diaye, C. Busse, Thomas Michely, “Structural
Coherency of Graphene on Ir(111)”, Nano Letters 8(2), 565–570 (2008).
26. T. N'Diaye1, J. Coraux, T. N. Plasa, C. Busse, T. Michely, “ Structure of
epitaxial graphene on Ir(111)”, New Journal of Physics 10, 043033 (2008).
27. T.A. Land, T. Michely, R.J. Behm, J.C. Hemminger, G. Comsa, “STM
investigation of single layer graphite structures produced on Pt(111) by hydrocarbon
decomposition”, Surface Science 264(3), 261–270 (1992).
28. P. Sutter, J. T. Sadowski, E. Sutter “Graphene on Pt(111): Growth and
substrate interaction”, Physical Review B 80, 245411-1 – 245411-10 (2009).
29. M. Gao, Y. Pan, L. Huang, H. Hu, L. Z. Zhang, H. M. Guo, S. X. Du,
and H.-J. Gao, “Epitaxial growth and structural property of graphene on Pt(111)”,
Applied Physics Letters 98, 033101-1 – 033101-3 (2011).
30. S.-Y. Kwon, C. V. Ciobanu, V. Petrova, V. B. Shenoy, J. Bareño, V.
Gambin, I. Petrov, S. Kodambaka, “Growth of Semiconducting Graphene on
Palladium”, Nano Letters 9 (12), 3985–3990 (2009).
31. Y. Murata, E. Starodub, B. B. Kappes, C. V. Ciobanu, N. C. Bartelt, K.
F. McCarty, S. Kodambaka, “Orientation-dependent work function of graphene on
Pd(111)”, Applied Physics Letters 97, 143114-1 – 143114-3 (2010).
32. D. Usachov, A. M. Dobrotvorskii, A. Varykhalov, O. Rader, W. Gudat,
A. M. Shikin, V. K. Adamchuk, “Experimental and theoretical study of the
morphology of commensurate and incommensurate graphene layers on Ni single-
crystal surfaces”, Physical Review B. 78, 085403-1 – 085403-9 (2008).
104
33. Yu. S. Dedkov, M. Fonin, U. Rüdiger, C. Laubschat, “ Graphene-
protected iron layer on Ni(111)”, Applied Physics Letters 93, 022509 (2008).
34. E. Rollings, G. Gweon, S. Zhou, B. Mun, J. Mcchesney, B. Hussain, A.
Fedorov, P. First, W. Deheer, A. Lanzara, “Synthesis and characterization of
atomically thin graphite films on a silicon carbide substrate”, Journal of Physics and
Chemistry of Solids 67(9-10), 2172-2177 (2006).
35. L. B. Biedermann, M. L. Bolen, M. A. Capano, D. Zemlyanov, R. G.
Reifenberger, “Insights into few-layer epitaxial graphene growth on 4H-SiC(0001)
substrates from STM studies”, Physical Review B 79, 125411-1 – 125411-10 (2009).
36. C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li,
J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, W. A. de Heer, “Electronic
Confinement and Coherence in Patterned Epitaxial Graphene”, Science 312 (5777),
1191-1196 (2006).
37. K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J.
L. McChesney, T. Ohta, S. A. Reshanov, J. Röhrl, E. Rotenberg, A. K. Schmid, D.
Waldmann, H. B. Weber, T. Seyller, “Towards wafer-size graphene layers by
atmospheric pressure graphitization of silicon carbide”, Nature Materials 8, 203-207
(2009).
38. A.-S. Johansson, J. Lu, J.-O. Carlsson, “TEM investigation of CVD
graphite on nickel”, Thin Solid Films 252(1), 19–25 (1994).
39. A. N. Obraztsov, E. A. Obraztsova, A. V. Tyurnina, A. A. Zolotukhin,
“Chemical vapor deposition of thin graphite films of nanometer thickness”, Carbon,
45(10), 2017–2021 (2007).
40. Q. Yu, J. Lian, S. Siriponglert, H. Li, Y. P. Chen, S.-S. Pei, “Graphene
segregated on Ni surfaces and transferred to insulators”, Applied Physics Letters 93,
113103-1 – 113103-3 (2008).
41. A. Reina, X. Jia, J. Ho, D. Nezich, H. Son, V. Bulovic, M. S.
Dresselhaus, J. Kong, “Large Area, Few-Layer Graphene Films on Arbitrary
Substrates by Chemical Vapor Deposition”, Nano Letters 9 (1), 30-35 (2009).
105
42. K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H.
Ahn, P. Kim, J.-Y. Choi, B. H. Hong, “Large-scale pattern growth of graphene films
for stretchable transparent electrodes”, Nature 457, 706-710 (2009).
43. H. Cao, Q. Yu, R. Colby, D. Pandey, C. S. Park, J. Lian, D. Zemlyanov,
I. Childres, V. Drachev, E. A. Stach, M. Hussain, H. Li, S. S. Pei, Y. P. Chen,
“Large-scale graphitic thin films synthesized on Ni and transferred to insulators:
Structural and electronic properties”, Journal of Applied Physics 107, 044310-1 –
044310-7 (2010).
44. S. Bae, H. Kim, Y. Lee, X. Xu, J.-S. Park, Y. Zheng, J. Balakrishnan, T.
Lei, H. R. Kim, Y. I. Song, Y.-J. Kim, K. S. Kim, B. Özyilmaz, J.-H. Ahn, B. H.
Hong, S. Iijima, “Roll-to-roll production of 30-inch graphene films for transparent
electrodes”, Nature Nanotechnology 5, 574–578 (2010).
45. X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A.
Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, Rodney S. Ruoff,
“Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper
Foils”, Science 324, 1312-1314 (2009).
46. X. Li, Y. Zhu, W. Cai, M. Borysiak, B. Han, D. Chen, R. D. Piner, L.
Colombo, R. S. Ruoff, “Transfer of large-area graphene films for high-performance
transparent conductive electrodes”, Nano Letters 9(12), 4359-63 (2009).
47. C. Mattevi, H. Kim, M. Chhowalla , “A review of chemical vapour
deposition of graphene on copper”, Journal of Materials Chemistry 21, 3324-3334
(2011).
48. S. Stankovich, R. D. Piner, S. T. Nguyen, R. S. Ruoff, “ Synthesis and
exfoliation of isocyanate-treated graphene oxide nanoplatelets”, Carbon 44, 3342–
3347 (2006).
49. D. A. Dikin, S. Stankovich, E. J. Zimney, R. D. Piner, G. H. B.
Dommett, G. Evmenenko, S. T. Nguyen, R. S. Ruoff, “Preparation and
characterization of graphene oxide paper”, Nature 448, 457-460 (2007).
106
50. S. Gilje, S. Han, M. Wang, K. L. Wang, R. B. Kaner, “A Chemical
Route to Graphene for Device Applications”, Nano Letters 7 (11), 3394–3398
(2007).
51. E.D. Grayfer, V.G. Makotchenko, A.S. Nazarov, S.J. Kim, V.E
Fedorov, “Graphene: chemical approaches to the synthesis and modification”,
Russian Chemical Reviews 80 (8), 751-770 (2011).
52. Y. Hernandez, V. Nicolosi, M. Lotya, F. M. Blighe, Z. Sun, S. De, I. T.
McGovern, B. Holland, M. Byrne, Y. K. Gun'Ko, J. J. Boland, P. Niraj, G. Duesberg,
S. Krishnamurthy, R. Goodhue, J. Hutchison, V. Scardaci, A. C. Ferrari, J. N.
Coleman, “High-yield production of graphene by liquid-phase exfoliation of
graphite”, Nature Nanotechnology 3, 563 - 568 (2008).
53. C. E. Hamilton, J. R. Lomeda, Z. Sun, J. M. Tour, A. R. Barron, “High-
Yield Organic Dispersions of Unfunctionalized Graphene”, Nano Letters 9 (10),
3460–3462 (2009).
54. J. Wang, Y. Hernandez, M. Lotya, J. N. Coleman, W. J. Blau,
“Broadband Nonlinear Optical Response of Graphene Dispersions”, Advanced
Materials 21 (23), 2430–2435 (2009).
55. C. A. Furtado, U. J. Kim, H. R. Gutierrez, L. Pan, E. C. Dickey, P. C.
Eklund, “Debundling and Dissolution of Single-Walled Carbon Nanotubes in Amide
Solvents”, Journal of the American Chemical Society 126 (19), 6095 – 6105 (2004).
56. S. M. Bachilo, M. S. Strano, C. Kittrell, R. H. Hauge, R. E. Smalley, R.
B. Weisman, “Structure-Assigned Optical Spectra of Single-Walled Carbon
Nanotubes”, Science 298, 2361 – 2366 (2002).
57. B. J. Landi, H. J. Ruf, J. J. Worman, R. P. Raffaelle, “Effects of Alkyl
Amide Solvents on the Dispersion of Single-Wall Carbon Nanotubes”, the Journal
Physical Chemistry B 108 (44), 17089–17095 (2004).
58. Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang,
F.Bonaccorso, D.M. Basko, A.C. Ferrari, “Graphene Mode-Locked Ultrafast laser”,
ACS Nano 4, 803-810, (2010).
107
59. X. Wang, L. Zhi, K. Müllen, “Transparent, Conductive Graphene
Electrodes for Dye-Sensitized Solar Cells”, Nano Letters 8 (1), 323–327 (2008).
60. S. Stankovich, D. A. Dikin, G. H. B. Dommett, K. M. Kohlhaas, E. J.
Zimney, E. A. Stach, R. D. Piner, S. T. Nguyen, R. S. Ruoff, “Graphene-based
composite materials”, Nature 442, 282-286 (2006).
61. T. Ramanathan, A. A. Abdala, S. Stankovich, D. A. Dikin, M. Herrera-
Alonso, R. D. Piner, D. H. Adamson, H. C. Schniepp, X. Chen, R. S. Ruoff, S. T.
Nguyen, I. A. Aksay, R. K. Prud'Homme, L. C. Brinson, “Functionalized graphene
sheets for polymer nanocomposites”, Nature Nanotechnology 3, 327 - 331 (2008).
62. D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A.
Dimiev, B. K. Price, J. M. Tour, “Longitudinal unzipping of carbon nanotubes to
form graphene nanoribbons”, Nature 458, 872-876 (2009).
63. L. Jiao, L. Zhang, X. Wang, G. Diankov, H. Dai, “Narrow graphene
nanoribbons from carbon nanotubes”, Nature 458, 877-880 (2009).
64. K. A. Worsley, P. Ramesh, S. K. Mandal, S. Niyogi, M. E. Itkis, R. C.
Haddon, “Soluble graphene derived from graphite fluoride”, Chemical Physics
Letters 445 (1–3), 51–56 (2007).
65. M. Choucair, P. Thordarson, J. A. Stride, “Gram-scale production of
graphene based on solvothermal synthesis and sonication”, Nature Nanotechnology
4, 30 - 33 (2009)
66. C. Bernardo, L. S. Lobo, “Evidence that carbon formation from
acetylene on nickel involves bulk diffusion”, Carbon 14 (5), 287–288 (1976).
67. J. J. Lander, H. E. Kern, A. L. Beach, “Solubility and Diffusion
Coefficient of Carbon in Nickel: Reaction Rates of Nickel‐Carbon Alloys with
Barium Oxide”, Journal of Applied Physics 23, 1305 (1952).
68. B. Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, D.
Y. Tang, “Atomic Layer Graphene as Saturable Absorber for Ultrafast Pulsed
Lasers”, Advanced Functional Materials 19, 3077-3083 (2009).
108
69. A. Gupta, G. Chen, P. Joshi, S. Tadigadapa, P.C. Eklund, “Raman
Scattering from High-Frequency Phonons in Supported n-Graphene Layer Films”,
Nano Letters 6 (12), 2667–2673 (2006).
70. A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F.
Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, A. K. Geim, “Raman
Spectrum of Graphene and Graphene Layers”, Physical Review Letters 97, 187401-1
– 187401-4 (2006).
71. A. Das, B. Chakraborty, A. K. Sood, “Raman spectroscopy of graphene
on different substrates and influence of defects”, Bulletin of Materials Science 31
(3), 579-584 (2008).
72. C. Casiraghi, S. Pisana, K. S. Novoselov, A. K. Geim, A. C. Ferrari,
“Raman fingerprint of charged impurities in graphene”, Applied Physics Letters 91,
233108 (2007).
73. Z. Ni, Y. Wang, T. Yu, Z. Shen, “Raman Spectroscopy and Imaging of
Graphene”, Nano Research 1 (4), 273-291 (2008).
74. D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, L.
Wirtz, “Spatially Resolved Raman Spectroscopy of Single- and Few-Layer
Graphene”, Nano Letters 7 (2), 238–242 (2007).
75. L. M. Malard, J. Nilsson, D. C. Elias, J. C. Brant, F. Plentz, E. S. Alves,
A. H. Castro Neto, M. A. Pimenta, “Probing the electronic structure of bilayer
graphene by Raman scattering”, Physical Review B 76, 201401(R)-1 – 201401(R)-4
(2007).
76. R. P. Vidano, D. B. Fischbach, L. J. Willis, T. M. Loehr, “Observation
of Raman band shifting with excitation wavelength for carbons and graphites”, Solid
State Communications 39, 341 (1981).
77. R. J. Nemanich, S. A. Solin, “First- and second-order Raman scattering
from finite-size crystals of graphite”, Physical Review B 20, 392 (1979).
109
78. R.R. Nair, P. Blake, A.N. Grigorenko, K.S. Novoselov, T.J. Booth, T.
Stauber, N.M.R. Peres & A.K. Geim, “Fine Structure Constant Defines Visual
Transparency of Graphene “, Science 320, 1308 (2008).
79. K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, T. F. Heinz,
“ Measurement of the Optical Conductivity of Graphene”, Physical Review Letters
101, 196405-1 – 196405-4 (2008).
80. G. Xing, H. Guo, X. Zhang, T.C. Sum, C.H.A. Huan “The Physcis of
Ultrafast Saturable Absorption in Graphene”, Optics Express 18, 4564-4573 (2010).
81. E. Hendry, P.J. Hale, J.Morger, A.V. Savchenko, S.A. Mikhailov
“Coherent Nonlinear Optical Response of Graphene”, Physical Review Letters 105,
097401-097405 (2010).
82. S. A. Mikhailov “Non-linear Electromagnetic Response of Graphene”,
Europhysics Letters 79, 27002 (2007).
83. J. J. Dean, H. M. van Driel “Second Harmonic Generation from
Graphene and Graphitic Films”, Applied Physics Letters 95, 261910-261913 (2009).
84. E. Garmie “Resonant Optical Nonlinearities in Semiconductors”, IEEE
Journal of Selected Topics in Quantum Electronics 6, 1094-1110 (2000).
85. V. P. Bykov, "Spontaneous Emission in a Periodic Structure", Soviet
Journal of Experimental and Theoretical Physics 35, 269–273 (1972).
86. S. John, "Strong localization of photons in certain disordered dielectric
superlattices", Physical Review Letters 58 (23), 2486–2489 (1987).
87. E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State
Physics and Electronics", Physical Review Letters 58 (20), 2059–2062 (1987).
88. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, R. D. Meade, “Photonic
Crystals: Molding the Flow of Light (Second Edition)”, Princeton University Press
(2008).
89. I. A Sukhoivanov, I. V Guryev, “Photonic Crystals: Physics and
Practical Modeling”, Springer (2009).
110
90. X. Letartre, J. Mouette, J. L. Leclercq, P. Rojo-Romeo, C. Seassal, P.
Viktorovitch, "Switching devices with spatial and spectral resolution combining
photonic crystal and MOEMS structures," Journal of Lightwave Technology 21,
1691-1699 (2003).
91. M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, H. Ryu,
“Waveguides, resonators and their coupled elements in photonic crystal slabs”,
Optics Express 12 (8), 1551-1561 (2004).
92. V. N. Astratov, D. M. Whittaker, L. S. Culshaw, R. M. Stevenson, M. S.
Skolnick, T. F. Krauss, R. M. De La Rue, “Photonic band-structure effects in the
reflectivity of periodically patterned waveguides”, Physical Review B 60, R16255
(1999).
93. P. Viktorovitch, B. Ben Bakir, S. Boutami, J. Louis Leclercq, X.
Letartre, P. Rojo-Romeo, C. Seassal, M. Zussy, L. Di Cioccio, J.Marc Fedeli, “3D
harnessing of light with 2.5D photonic crystals”, Laser & Photonics Reviews 4, 401–
413 (2010).
94. C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J.
Chang-Hasnain, “Ultra-broadband mirror using low index cladded subwavelength
grating,” IEEE Photonics Technology Letters 16(2), 518–520 (2004).
95. S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J. L. Leclerq, P. Rojo-
Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, "Broadband and compact 2D
photonic crystal reflectors with controllable polarization dependence," IEEE
Photonics Technology Letters 18, 835 (2006).
96. Mouette J., Seassal C., Letartre X., Rojo Romeo P., Leclercq J.L.,
Regreny P., Viktorovitch P., Jalaguier E., Perreau P., Moriceau H., “Very low
threshold vertical emitting laser operation in InP graphite photonic crystal slab on
silicon,” Electronics Letters, 39 (6), 526-528 (2003).
97. M. Imada, S. Noda1, A. Chutinan, T. Tokuda, M. Murata, G. Sasaki,
“Coherent two-dimensional lasing action in surface-emitting laser with triangular-
lattice photonic crystal structure”, Applied Physics Letters 75, 316 (1999).
111
98. F. Raineri, C. Cojocaru, P. Monnier, A. Levenson1, R. Raj, C. Seassal,
X. Letartre, P. Viktorovitch, “Ultrafast dynamics of the third-order nonlinear
response in a two-dimensional InP-based photonic crystal”, Applied Physics Letters
85, 1880 (2004).
99. P. Viktorovitch, E. Drouard, M. Garrigues, J. L. Leclercq, X. Letartre, P.
R. Romeo, C. Seassal, “Photonic crystals: basic concepts and devices”, Comptes
Rendus Physique 8, 253–266 (2007).
100. L. Ferrier, P. Rojo-Romeo, E. Drouard, X. Letatre, and P. Viktorovitch,
“Slow Bloch mode confinement in 2D photonic crystals for surface operating
devices”, Optics Express 16(5), 3136–3145 (2008).
101. Y. Ding, Robert Magnusson, “Use of nondegenerate resonant leaky
modes to fashion diverse optical spectra”, Optics Express 12(9), 1885–1891 (2004).
102. U. Fano, “The Theory of Anomalous Diffraction Gratings and of Quasi-
Stationary Waves on Metallic Surfaces (Sommerfeld’s Waves)”, Journal of the
Optical Society of America 31, 213 (1941).
103. X. Letartre, P. Viktorovitch, C. Sciancalepore, T. Benyattou, B. Ben
Bakir, “Surface addressable Photonic Crystal resonators: general design rules and
applications”, ICTON 2012 Warwick - United Kingdom 2-5 July 2012.
104. X. Letartre, J. Mouette, J. L. Leclercq, P. Rojo Romeo, C. Seassal, and
P. Viktorovitch, “Switching Devices With Spatial and Spectral Resolution
Combining Photonic Crystal and MOEMS Structures”, Journal of Lightwave
Technology 21(7), 1691 (2003).
105. T. Ochiai, K. Sakoda, “Dispersion relation and optical transmittance of a
hexagonal photonic crystal slab”, Physical Review B 63, 125107 (2001).
106. H. Zhang, D.Y. Tang, L.M. Zhao, Q.L. Bao, K.P. Loh, “Large Energy
Mode Locking of an Erbium-Doped Fiber laser With Atomic Layer Graphene”,
Optics Express 20, 17630-17635 (2009).
112
107. B. Q. Bao, H. Zhang, Y. Wang, Z. Ni, Y. Yan, Z. X. Shen, K. P. Loh, D.
Y. Tang, “Atomic Layer Graphene as Saturable Absorber for Ultrafast Pulsed
Lasers”, Advanced Functional Materials 19, 3077-3083 (2009).
108. J. W. Weber, V. E. Calado, M. C. M. van de Sanden, “Optical constants
of graphene measured by spectroscopic ellipsometry”, Applied Physics Letters 97,
091904 (2010).
113