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CHAPTER 3
Electro-optic Properties of II-VI Semiconductor Nano-clusters and
Electro-optic Chromophores
3.1 Introduction
Optical properties of CdSe(S) nano-clusters and polymeric electro-optic
chromophores have fully been investigated in the last chapter. Efforts in this chapter will
be focused on the electro-optic properties of those materials. Conclusions reached in last
chapter will be used to explain experimental results. In this chapter, several points will be
fully explored: why CdSe nano-clusters possess very high electro-optic properties in
comparison with its bulk counterpart; why ESA and field assisted ESA techniques allow
even higher electro-optic performance; and how the electro-optic coefficient varies with
the number of bilayers (film thickness), and proton irradiation, and other factors. First of
all, measurement of electro-optic coefficients is a very critical issue in this chapter.
Accurate and reliable measurement of the electro-optic coefficient of samples is not easy,
so a separate section is assigned to this problem.
3.1.1. Electro-optic properties of semiconductor nano-cluster materials
Property changes of materials at the nano-level as a result of surface effects and
quantum size effects have been widely obsevered. First, nano-particles exhibit thermal,
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electrical, magnetic, acoustic, optical, mechanical, dielectric, super-conductive and
chemical properties which are different from those of bulk materials and large size
particles. When particle size reaches several nano-meters, the band gap and energy level
spacing of metals increase, so a metal becomes an insulator. The resistance of an
insulator correspondingly decreases and may it become a conductor. Additionally, ferro-
magnetic materials become para-magnetic, ferro-electric materials transform to para-
electric, brittle ceramic materials become plastic, and strength and hardness also increase
in a similar way.
In the traditional theory of the origin of second harmonic generation in terms of
electro-optic coefficient (r33, r13), the basic structural requirement of materials is non-
symmetry or the lack of an inversion center. This is the case in polymer and crystal
electro-optic materials. Because of this restriction, only a small potion of bulk materials
are electro-optic materials. Of the 32 crystals classes, 20 are noncentrosymmetric (1).
These are candidates for electro-optic materials with SHG or Pockels effects, but the lack
of an inversion center is not sufficient to guarantee SHG or Pecokels effects. Only few
crystals exhibit this phenomenon, such as LiNbO3, KDP, α-quartz crystal etc.. For
semiconductor nano-clusters, the origin of SHG and Pockels effects is not the lack of an
inversion center, instead they are due to (1) quantum confinement effect, (2) surface
effect and (3) defect and trap states. If the stimulation energy is higher than the exciton
oscillation energy, excitons will be formed. These are located underneath the conduction
band in the energy band diagram. But if the stimulation energy is lower than the exciton
oscillation energy, no exciton will be formed. Excitons are not stable, in that they tend to
decay to lower energy state. When they interact with phonons, they will lose some
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energy. In nano-clusters, the exciton concentration is higher than in bulk materials. This
is the main reason for the electro-optic and nonlinear optic phenomena of nano-clusters.
In addition to this, surface and defect states resulting in dangling bonds, and trap states
cause the separation of electrons and holes. Dielectric mismatch between the cluster and
the surrounding matrix (such as polymer, glass) produce a dipole moment layer around
the clusters, and permanent dipole moments have been observed(2,3,4). All those effects
are enhanced greatly with the decrease of particle size, so large electro-optic and
nonlinear optic effects result. Most research activities of the electro-optic and nonlinear
optic effects of nano-clusters are focused on third harmonic generation (THG) and
electro-optic Kerr effects, because they do not need the asymmetric structure. But under
certain conditions, such as in the presence of an external field, or by introducing internal
field during our ESA process, many dipole moments will aligned at an average direction,
so second order electro-optic effect and second harmonic generation (SHG) effect
(Pockels effect) can be observed.
In order to evaluate the potential of nano-materials for related applications, it is
important to have the nonlinear susceptibility χ(3) divided into the real part Re(χ(3)) and
the imaginary part Im(χ(3)). The latter term corresponds to a slow response. Both the
magnitude of Im(χ(3)) and the ratio Im(χ(3)) / Re(χ(3)) can be decreased by the effect of
confinement(7). Like the linear properties of a given material, the nonlinear properties of a
given material at frequency ω can be fully described by the refractive index n(ω) or the
relative dielectric constant εr(ω) or the susceptibility χ(ω). They are related by
εr(ω) =n(ω)2 = 1+ χ(ω) , (3.1)
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where the real part and the imaginary part of ∆n or ∆χ lead to nonlinear refraction and
nonlinear absorption, respectively. Nonlinear refraction is responsible for the many
nonlinear optical phenomenal, such as self-phase modulation (SPM) and solition
propagation, which are very important in optical communication.
There are two physical mechanisms behind the third-order nonlinearity: resonant
and nonresonant nonlinearity. The first type (above the bandgap) requires real excitations
of charge carriers. In steady state, the number density N of excited carriers is proportional
to the total absorption (αI) and ∆χ is proportional to intensity I . When the frequency ω
of the incident field is close to that of an optical transition of the medium, it produces a
large optical Kerr effect. The resulting response is controlled by the decay time (τr) of the
excited charges and it is slow, about 0.1-1 ns, so the population of excited carriers cannot
follow the high frequency modulation of the optical intensity and the dispersion of χ(3) is
large in this case. Whenever an incident radiation pulse duration τp is shorter than τr , N
fails to reach its steady state value. In this case, the effective susceptibility χ(3)eff is useful.
It is related to the steady state value χ(3) by(5)
χ(3 eff = (τp/τr) χ(3) . (3.2)
The energy level scheme of SDGs (semiconductor nano-crystals dispersed in
glasses) in the resonant regime is shown in Figure 3-1. Carriers are first excited to level 1.
From here, they relax down to level 0 with rate constant k, or are trapped at level 3 with
rate constant k’. If the lifetime T1 of level 1 is longer than the laser pulse duration τp, the
response can be characterized by an effective susceptibility which takes the transient
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nature of the response into account and which is a function of the delay of the backward
pump pulse or of the probe in nonlinear absorption. Three effects contribute to this
response, namely
(1) The population of level 1 leads to saturation of the 0→ 1 transition,
(2) The population of level 1 leads to induced absorption between levels 1 and 2,
and
(3) The carriers in level 3 (the trapping level) create a static electric field of the form
E0 = 24 R
q
πε , (3.3)
which modifies the optical response.
Fig. 3-1. Relevant energy levels for SDGs (semiconductor nano-crystals
dispersion in glasses) in the resonant regime.
0
1
2
3
hω21
hω10 K
K’
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By using the nonlinear absorption technique to study SDGs, the exact role of free
and trapped carriers has been elucidated. Particles without traps give rise to the fast (free-
carrier) component, with a lifetime T1 decreasing from about 1 ns to 30 ps upon
darkening. Particles with traps, in which case the carriers are very quickly trapped, give
rise to a slow response, with darkened particles no longer contributing to the nonlinear
response. Figure 3-2 is a simple energy level scheme diagram comparing a bulk
semiconductor and a micro-ctystallite, and surface states and trap states are indicated.
Bulk Semiconductor Nano-cluster
Conduction Band
Fig. 3-2. Schematic energy level scheme diagram for the bulk
semiconductor and for the micro-crystallite.
Deep trapShallow trap
Valence band
Distance
Eg
Delocalizedmolecularorbitals
Deep trap
Surface state
Cluster size
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The second type of the third-order nonlinearity is the nonresonant nonlinearity,
which is caused by the nonlinear motion of bound charges as the photon energy of the
emission beam is between Eg/2 <hω<Eg (below the bandgap). It has a very quick
response time on the order of about one femtosecond, although the χ(3) is smaller than in
the resonant case. The frequency dispersion of the fast χ(3) is negligible when frequency
is well below the spectral region of linear absorption. At frequencies below the bandgap,
there is no state available for electrons to be excited through a one-photon process, the
third-order nonlinearity is purely non-resonant, and the ionic contribution to χ(3) is
negligible, so the non-resonant electronic linearity is the primary contribution to χ(3). It
Fig. 3-3. Plots of Imχχχχ(3) and Reχχχχ(3) as a function of frequency,
ωωωω0 is the resonance frequency.
ωωωω
Im χχχχ(3)
Re χχχχ(3)
ωωωω0
χχχχ(3)
A
B
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has a very fast response, fast enough to produce refractive index change capable of being
modulated at very high frequencies. This is of the practical importance in optical
communication. On the other hand, the resonant third-order susceptibility of the SDGs is
large, but as absorption and speed of response are considered, the overall figure of merit
for device applications is not satisfactory.
The χ(3) term becomes complex near resonance. At near resonance close to an
optical transition, Imχ(3) is large, and losses are larger. In Figure 3-3, position A is
appropriate for the resonant case, while position B is appropriate for the non-resonant
case.
3.1.2 Electro-optic properties of electro-optic chromophores
Electro-active polymer and polymeric devices have attracted attention in the
development of optical systems such as LANs (local area networks), optical fiber sensors
and integrated optics because polymers offer many features which make them ideal
materials for optical devices. For example polymeric materials offer dielectric constants
that are much (about ten times) lower than their inorganic counterparts. This results in a
lower velocity mismatch between microwaves and optical waves and has led to the
demonstration of high band-width modulators. In addition, polymeric materials can be
processed on virtually any substrates of interest with greater ease and versatility than bulk
crystals. There is a large variety of potential material properties and a variety of methods
for patterning. They are relatively inexpensive, and may be processed by melt, solution
spinning and other techniques. They can have good optical properties and, by chemical
modification, their linear and nonlinear opticalproperties can be altered. They have
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adaptable electrical properties and are compatible with many semiconductor-processing
steps such as lithography, electroding and plasma etching (7).
A suitable species of polymers for electro-active devices should contain
molecules possessing second order hyperpolarizability which are organized in such a way
that there is no macroscopic center of symmetry to provide an even distribution of
optically nonlinear molecules. Electro-optical polymers are mainly chromophores or
dyes. A chromophore is a conjugated molecule that contains an electron-donating group
on one end and an electron-accepting group on the other end. Typically, they consist of a
donor, a π electron bridge and acceptor segments. Molecular hyperpolarizability β can be
predicted by quantum mechanical theory (8) as
β = (µee- µgg )µge2/Ege
2 , (3.4)
where µee- µgg is the difference between excited and ground state dipole moments, µgeis
the transition dipole moment, and Ege is the optical (HOMO-LUMO) gap. This equation
indicates a quadratic relationship between β and the bond length alternation (or Eg). β is
related to the degree of ground state polarization, which depends primarily on the
structure (the structure of the π-conjugated system, and the strength of the donors and
acceptors. The µee-µgg term indicates that as the electrons interact with the oscillating
electric field, they show a preference to shift from one direction to the other along the
axis of the molecule. Electro-optic and nonlinear optical properties of electro-optic
polymers are mainly determined by the length of the π-conjugated system, and the
strength of donor and acceptor groups.
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A chromophore can be dissolved as a guest in an inert transparent polymeric host
to form a solid solution or these species can be chemically bound to polymers. These
molecules must then be induced to point at least statistically in a common direction.
Provided that there is significant microscopic second order hyperpolarizability in the
direction of the molecular ground state dipole moment of the guest, the required
orientation can be induced by the application of an external electric field, or by internal
field via the ESA process discussed above. The molecules experience an energy
minimum when they are aligned with their dipole moment in the field direction and,
within the limits set by Boltzmannn statistics, they take up this preferred orientation.
Since the idea of using polymers as electro-optic materials for optoelectronics was raised,
a wide variety of such materials have been synthesized and studied, and three main
classes have emerged, as shown in Figure 3-4. These are discussed below.
Guest-host systems In such systems, the nonlinear chromophore is dissolved in a
host polymer without any chemical attachment between the dye and the polymer
backbone. When the dye concentration in the matrix is increased, crystallization, phase
separation or concentration inhomgeneities rapidly occur, thus limiting the chromphore
density in the material, and resulting in lower optical quality and electro-optic efficiency.
Moreover, the orientation stability of such solid solution is generally insufficient, even at
room temperature. However the investigation of this kind of system permits us to
understand the influence of parameters such as the guest chromophore size in comparison
with the polymer free cavity volume and that of the doped polymeric glasses to rubber
transition temperature (Tg) on the poling dynamics and relaxation. It has been
subsequently concluded that the electro-optic efficiency and stability is achieved if the
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active molecules are attached to the polymeric backbone. In that arrangement, two kinds
of systems have been explored, the first one is main-chain polymers where the nonlinear
chromophore is axially incorporated along the polymer chains. Unfortunately the
orientation efficiency of such systems remains poor, due to such dominating effects as
chain folding. No significant improvements have been obtained yet in this direction. The
second system is that of the side-chain polymers which has led to interesting applications.
Side-chain polymers In this configuration the nonlinear chromophores are
chemically tethered to the polymer backbone as a side chain pendant group. For such
materials, a dye molar concentration close to 100% can be reached. However, for a
Fig. 3-4. Three kinds of electro-optic polymers.
E-O chromophores
Cross linking function
Guest-host systems
Side-chain systems Cross-linked systems
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number of systems, the electro-optic efficiency of this polymer saturates for a nonlinear
chromophore molar concentration of about 40%. Furthermore, as the optical quality
decreases as the dye density increases, a trade-off has to be found.
The attachment of the chromophores to the polymer backbone should also hinder
its rotation in the matrix and thus improve the poled order stability. Another way to
improve the thermal stability of such a structure is generally to use higher Tg as
compared to that of guest-host systems.
Cross-linked systems Cross-linked polymers can be classified according to the
nature of the chemical attachments between the components of the system, as follows.
1. Guest-host or side chain systems, where the NLO chromophores are not
directly involved in the cross-linking process that occurs between groups located
on the polymer backbone.
2. Systems with difunctional nonlinear molecules, involved in the cross-linking
process resulting in chromophores attached by both ends to the polymer chains.
Cross-linked materials have widely been studied, involving, respectively, thermal
or photo-chemistry processes. The process must be optimized as cross-linking will
compete with the poling procedure and a satisfactory trade-off between electro-optical
efficiency and stability will have to be sought. Since the poling process requires
sufficient dipole mobility, cross-linking must occur during or after chromophore
orientation which may turn out to be contradictory. On the other hand, some cross-linking
processes are destructive because incursions to higher temperature or UV irradiation may
destroy the nonlinear units.
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Organic molecules with extended conjugated π-electron systems are good
candidates for nonlinear optical materials (9).
The β value (the hyperpolarizability) increases with the increasing number of
electron donors and acceptors. These molecules usually exhibit strong permanent
electronic dipole moment along their molecular axis. For third order nonlinear materials,
no centro-symmetry is required. In this case the magnitude of the nonlinear effect shows
a fifth power dependence on the length of the π–electron system that may comprise
double and/ or triple bonds.
Great progress has been made in chromophore-containing EO polymeric materials
over the past 10 years. By understanding the molecular origins of hyperpolarizability,
more than 100 species have been synthesized, some of them having exceptionally high
EO coefficients (r33>100 pm/V)(10), and by using these kinds of polymeric EO materials,
high performance modulators have been made.
3.2. Measurements of Electro-optic Pockels and Kerr coefficients
Measurement of electro-optic Pockels and Kerr coefficients can be implemented by
our fabricated ellipsometric and MZI type setups. Measurements are made under different
conditions including variable modulation voltage, poling voltage, temperature, and
thickness of films. The electro-optic Pockels coefficient have been measured by using
both ellipsometric and MZI type setups and it corresponds to the second order
nonlinearity (SHG) response of films. The electro-optic Kerr coefficient has been
measured by using the ellipsometric setup; it corresponds to the third order nonlinearity
(THG) response of films.
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Electro-optic tensor rijk has been defined in chapter1 by equation 1.1, where i, j, k can
all be x, y, or z, because rijk relates a second-rank tensor to a vector it is itself third rank
(three subscripts). It can be represented as 6×3 matrix and, it is symmetric, must follow
that rijk = rjik. Any symmetric matrix can be diagonalized through a coordinate
transformation, so electro-optic tensor can also be expressed as 3×3 matrix in the new
coordinate system. Distinguished from the electro-optic crystals, the poled electro-optic
polymeric films have a C∞v symmetric geometry. According to Kleinmann’s symmetry
rules (10, 11), r113 and r333(in an MZI type setup, if an ellipsometric setup is used for
measurement, electro-optic Pockels coefficients are denoted as r13 and r33, respectively)
are the only nonzero elements of the linear electro-optic tensor, and r1133 and r3333 are the
only nonzero elements that describe the quadratic electro-optic effect.
Two different techniques are usually used to investigate the electro-optic properties of
thin film polymer materials. The first popular configurationis the ellipsometric technique
(12, 13) utilizing a single laser beam, where the transmission amplitude modulation is
detected that results from beating the modulation of a wave polarized in the plane of
incidence (p wave) against that of a wave polarized perpendicular to the plane of
incidence (s wave). This measurement is relatively easy to perform, but allows only for
determination of the difference r333-r113. In order to separate these two coefficients, one
has to make an assumption concerning that relation between r333 and r113. For a weak
poling field condition in thin film polymers r333/r113 = 3(12, 13, 14). For our materials, a
small correction to this ratio is required.
The second conventional technique used in electro-optic property studies is based on
Mach-Zehnderinterferometry.(15, 16) This technique, although tedious, allows a
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straightforward independent determination of the electro-optic coefficients r113 and r333.
In this discussion, we report Mach-Zehnder interferometric measurements of the linear
electro-optic modulation and the ratio of the linear electro-optic coefficients r333 and r113.
Then, we report the simple ellipsometric measurements of the quadratic electro-optic
modulation, and use the value of ratio obtained by the Mach-Zehnder measurements to
calculate the quadratic electro-optic coefficients r1133 and r3333 because it is difficult to
derive the formulas to calculate them based on Mach-Zehnder data.
3.2.1 Linear electro-optic coefficient measurement by ellipsometric setup
The ellipsometric experimental setup is shown in Figure 3-5, and Figure 3-6 is a
diagram of the ellipsometric setup, based on a transmission configuration of the
ellipsometric method. In this configuration, the modulation of the refractive index of the
sample by the externally applied AC electric field (we refer to this as the modulating
field) causes a phase retardation between the s- and the p-polarized components of the
incident beam. The input beam, polarized at 45o with respect to the plane of incidence
(this results in equal components of s and p polarizations), passes through the sample,
propagates through the compensator and analyzer, and impinges onto a photodetector,
which operates in the photovoltaic mode. The signal from the detector is amplified by the
current/voltage transducer/amplifier (UDT Tramp), and measured using both a DC
voltmeter (Hewlett Packard digital multimeter 34401A), and a lock-in amplifier (Stanford
Research Systems SRS 850 DSP). The magnitude of the detected light intensity depends
on the phase shift ψsp between the s and the p components of the light polarization, and
can be expressed as
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),2
(sin2 spmd II
ϕ= (3.5)
where Id is the intensity arriving at the detector in our experimental setup, Im is the
incident intensity, and ψsp is the phase difference between the s and p polarizations after
the beam passes through the sample, the compensator, and the analyzer. At point Ic=Im/2,
the Id - ψsp curve is at its most linear region. Applying an ac field to the sample when
operated in this region yields a modulation in the phase difference, δϕsp, which results in
Fig. 3-5. Ellipsometric setup.
Laser, He-Ne laser; H, half-wave plate at 632.8nm; P, polarizer; S, sample; C,
compensator; A, analyzer; D, silicon photodetector; AMP, amplifier; VDC, voltmeter;
HVP, high-voltage probe; LOCK-IN, lock-in amplifier; OSC, oscilloscope; WG,
waveform generator; HV, high voltage amplifier; PC: computer.
Laser P S C A DH
HousingHVP
AMP
PC
HV WG OSC LOCK-IN VDC
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Fig. 3-6. Picture of ellipsometric setup.
a modulation of the transmitted intensity, Iac. For small modulations, Iac is related to δϕsp
by the expression
.spcac II δϕ= (3.6)
For a single beam pass through the sample in this geometry, the phase difference between
the s and the p polarizations is given by
),coscos
(2
s
s
p
pspsp
nnd
ααλπϕϕϕ −=−= (3.7)
where αs,p is the angle of incidence inside the sample with respect to the sample normal
for the s and p polarizations, respectively, d stands for the thickness of the sample, and
np,s is the refractive index for the p and s polarization components, respectively. Since the
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applied field is perpendicular to the film plane, ns=no, and np is related to no and ne by the
index ellipsoid
.cossin1
2
2
2
2
2o
p
e
p
p nnn
αα+= (3.8)
The modulated phase difference δϕsp is given by
.ee
spo
o
spsp n
nn
n∆
¶¶
+∆¶¶
=ϕϕ
δϕ (3.9)
For our polymer based samples, the nonzero components of the electro-optic tensor are
only r13 and r33 due to the C∞v symmetry of this medium (17, 18). Therefore, ∆no and ∆ne
are related to the elements of the electro-optic tensor r13 and r33 by
)(10.3,2
1
)(10.3,2
1
333
133
bd
Vrnn
ad
Vrnn
acee
acoo
=∆
=∆
where Vac is the modulating voltage. Using equations (3.10) with the approximation that
n=no≈ne, allows one to derive the following expression
,sin
1.
)sin2(
)sin(.
2222
2322
1333 θθθ
πλ
nn
n
IV
Irr
cac
ac
−−=− (3.11)
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where θ is the external angle of incidence.
The Advantage of this setup is that it is simpler than the MZI. A primary
disadvantage is that one can only get γ33−γ13. Τhen, using approximate relation
γ33=3γ13, one can obtain γ33 and γ13.
The ESA thin film material samples were sandwiched between two-ITO coated
glass substrates. Since our samples are very thin, to prevent short circuits from occurring
between the two ITO electrodes, a glass ring spacer of thickness 99 µm with a central
hole of diameter 2 mm which allows the incident beam to impinge the sample directly,
was placed between one ITO electrode and the film. Finally, the samples were sealed
with UV-curable epoxy. Before making measurements, the samples were irradiated by an
UV-light (wavelength = 365nm) source for 30 mins to ensure that the epoxy sealed
firmly. A high voltage amplifier (Trek 610C) provided the sinusoidal waveform at the
level of ~2 V/µm as the modulating field. No poling field was applied. The magnitude of
the AC modulating voltage applied to the sample was measured using a high voltage
passive probe (Tektronics P6015). The employed laser intensity incident on the sample is
220 mW/cm2 at 632.8nm. The modulation of the laser beam was detected by a silicon
photodetector coupled with a transducer-amplifier, and measured using a lock-in
amplifier. For each experimental point, the data were collected for 200 seconds and the
average was taken. To calculate the electro-optic coefficients by equation 3.11, we need
to determine the actual modulating voltage across the film. According to electromagnetic
field theory, the applied voltage is given by Vac = V0d/n2(d+l). Here, d stands for the
thickness of films, l is the thickness of the air gap, V0 is total voltage across the samples,
and n is refractive index of the films. Its value varies between 1.5-1.6 at 632.8 nm with
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different materials and thickness of the samples, n2 is the dielectric constant at high
frequency. In this experiment, the response of each electronic device, namely the high
voltage amplifier, the high voltage probe and the transducer amplifier was determined at
each measured frequency to ensure a proper characterization of the electro-optic
modulation of the samples. The highest measured modulating frequency, 10 kHz, was
limited by the bandwidth of the high voltage amplifier supplying the modulating voltage.
3.2.2. Linear Electro-optic coefficient measurement by MZI setup
The electro-optic properties of the sample materials were measured by
employing the conventional Mach-Zehnder interferometric setup shown in Figure 3-7 (15,
16, 19) and Figure 3-8 is a picture of the setup. The experimental arrangement was arranged
on a vibration-isolated table. In addition, a plastic glass housing was used to reduce the
influence of air fluctuations on the stability of the interferometer. The reference arm of
the interferometer contains a glass wedge, which can be slowly translated by a stepper
motor to produce a controllable phase shift between the two interfering optical beams.
The electro-optic sample is mounted on a rotation stage and placed in the signal arm of
the interferometer. When a modulating voltage is applied to the sample, a change in the
refractive index, as well as a change in the path length due to the change in the refraction
angle, occurs. The resulting phase modulation of the signal beam is (15, 16, 19) :
),(2
snnsac ∆+∆=∆Φλπ
(3.12)
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where λ is the optical wavelength, n is the refractive index of the material, and s is the
optical path length given by s=d/cosα; here, d is the thickness of the sample and α is the
angle of refraction. This phase shift causes a modulation of the light intensity exiting the
interferometer, and the relationship between the phase and intensity modulation can be
expressed as
,22minmax
,
II
I rmsacac −
=∆Φ (3.13)
where Iac.rms is the modulated intensity due to the ac electric field, and Imax and Imin are the
maximum and the minimum intensities associated with a π phase shift of the reference
beam due to the wedge translation. For the case of s-polarized light obliquely
illuminating the sample, a general formula for the r113 coefficient of the material can be
determined from equations 3.12 and 3.13 with the approximation that ne ≅ no = n; it is
given as
.sin2
)/sin1(..
222
2/322
minmax
,
,113 θ
θπ
λ−
−−
=n
n
II
I
nVr rmsac
rmsac
(3.14)
Here, Vac,rms is the modulating voltage applied to the sample and θ is the external angle of
incidence signal beam on the sample. For p-polarization of the laser beam, we can obtain
the expression relating to the coefficients r113 and r333 as
.sin2
)/sin1(..
2cossin
22
2/322
minmax
,
,
2113
2333 θ
θπ
λαα−
−−
=+n
n
II
I
nVrr rmsac
rmsac
(3.15)
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Therefore, by measuring the modulation for both light polarizations and from
equations 3-14 and 3-15, one can obtain independent values for r113 and r333.
CdSe nanocluster/polymer thin film samples were sandwiched between two ITO-
coated glass substrates. The samples were then sealed using UV-curable epoxy. Before
making measurements, the samples were irradiated by an UV-light source for several
hours to ensure that the epoxy fully cured and sealed firmly. A high voltage amplifier
(Trek 610C) provided the sinusoidal waveform at a level of ~1 V/µm as the modulating
field. No external poling electric field was applied across the sample. The magnitude of
the AC modulating voltage applied to the sample was measured using a high voltage
passive probe (Tektronix P6015) and an oscilloscope (Tektronix TDS 210). The
employed laser beam intensity incident on the sample was 220 mW/cm2 at 632.8nm. The
modulation of the laser beam was detected by a silicon photodetector (UDT Pin 10)
coupled with a transducer-amplifier (UDT Tramp), and measured using both a lock-in
amplifier (Stanford Research Systems SRS850 DSP) and a dc multimeter (Hewlett
Packard Digital 34401A). The data acquisition was performed with the help of a PC
computer. For each experimental point, data were collected for 200 seconds and the
average was taken. In this experiment, the response of each electronic device, namely the
high voltage amplifier, the high voltage probe and the transducer amplifier, was
determined at each measured frequency to ensure a proper normalized characterization of
the electro-optic modulation of the samples. The highest measured modulating frequency,
10 kHz, was limited by the bandwidth of the high voltage amplifier supplying the
modulating voltage.
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3.2.3 Quadratic electro-optic coefficient measurement by ellipsometric setup
As we mentioned above, since it is difficult to derive concise equations to
calculate r1133 and r3333 from the Mach-Zehnder configuration data, we employed the
conventinal ellipsometric setup to investigate the quadratic electro-optic modulation. The
experimental setup is the same as that shown in Figures 3-5 and 3-6. In this
configuration, the modulation of the refractive index of the sample by the externally
applied AC electric field causes a phase retardation between the s- and the p-polarized
components of the incident beam. The input beam, polarized at 45o with respect to the
plane of incidence (this results in equal amplitude components of the s and p
polarizations), passes through the sample, propagates through the compensator and
analyzer, and impinges onto a photodetector, which operates in the photovoltaic mode.
The signal from the detector is amplified by the current/voltage transducer/amplifier, and
measured using both a DC voltmeter and a lock-in amplifier. This lock-in amplifier
allows us to measure the modulated signal intensity either at the fundamental frequency
(linear) or at second harmonic frequency (quadratic). By follow the same derivation of
equation 3.5 through equation 3.9 in section 3.2.1, the modulated phase difference δϕsp is
given by (15, 16)
.ee
spo
o
spsp n
nn
n∆
¶¶
+∆¶¶
=ϕϕ
δϕ (3.16)
If we take both linear and quadratic electro-optic modulations into account, ∆no and ∆ne
are related to the elements r113, r333, r1133, and r3333 of the electro-optic tensor, by
92
)(17.3,)(2
1
)(17.3,)(2
1
33333333
11331133
bd
V
d
Vrrnn
ad
V
d
Vrrnn
acacee
acacoo
+=∆
+=∆
where Vac is modulating voltage. Evaluating the derivations with the approximation that
n=no≈ne, equation 3.16 can be written
).()sin(
)sin2(sin.
22/322
222
oesp nnnn
nd ∆−∆−
−=∆θ
θθλπϕ (3.18)
Let us write Vac as
),cos( tVV ACac ω= (3.19)
where VAC represents the amplitude of the modulating voltage, ω is modulating radian
frequency, and E = Vac/d is modulating electric field across the sample. Substituting for
Vac with equation 3.19 in equation 3.17, we have
)].2cos1(2
cos[(2
12
211333333
)1133330 td
Vrrt
d
Vrrnn ACAC
e ωω +−
+−=∆−∆ (3.20)
Using equation 3.6 and separating the fundamental frequency and second harmonic
frequency terms, we have
93
,sin
1.
)sin2(
)sin(.
2222
2322
113333 θθθ
πλ
nn
n
IV
Irr
crms
ac
ac
−−=− (3.21)
for the linear electro-optic modulation in the ellipsometric configuration and
,sin1
.)sin2(
)sin(.
)( 2222
2322
2
2
11333333 θθθ
πλ ω
nn
n
IV
dIrr
crms
ac
ac
−−=− (3.22)
for the quadratic electro-optic modulation in the same configuration. Here θ is the
external angle of incidence, and I2ωac is the intensity of the modulating signal at the
second harmonic frequency, as we mentioned above, which can be measured by the lock-
in amplifier. Vacrms can be measured using the oscilloscope and Ic can be measured by the
multimeter. The difference r3333-r1133 can be obtained according to equation 3.22. Then,
using the appropriate r3333/r1133 ratio, we can separate the two electro-optic coefficients,
r3333 and r1133.
In practice, even though a lock-in amplifier is used, it is most important to isolate
various noise contributions effectively. To reduce low frequency mechanical noise, a gas
floated optical table should be used, and all optical components (expect for laser) should
be put in a plastic housing. For high frequency electric and magnetic noise isolation, all
wires should be shielded by metal foil. Al foil is usually widely used. It is good in low
frequency, but at very high frequency (>1000Hz), an alloy foil composed of high
permeability magnetic metal (like µ metal) is highly recommended. Since most noise is
picked up from the detector, special attention should be placed on this. Before
94
measurement are made, the noise spectrum is measured to determine the optimum
measurement frequency (with minimum noise), and all optical parts are carefully aligned
to accomplish good M-Z interferometer performance in terms of extinction ratio (Imax-
Imin/ Imax>70%). Finally, a standard sample is used to calibrate the interferometer. Each
time before measurement, the extinction ratio is checked to ensure reliable results.
Fig. 3-7. Mach-Zehnder interferometric setup for linear electro-optic effect
measurements.
HVP
PC
HV LOCK -IN
AMP
VDC OSC WG
L1 λ/2 P
M
M M
M
L
BS
BS
S θ
Housing
D
PH
W
95
L1, He-Ne laser; λ/2, half-wave plate at 632.8nm; P, polarizer; S, sample; D, silicon
photodetector; AMP, amplifier; VDC, multimeter; HVP, high-voltage probe; LOCK-IN,
lock-in amplifier; OSC, oscilloscope; WG, waveform generator; HV, high voltage
amplifier; PC: computer; W, glass wedge; BS’s, beamsplitters; M’s, mirrors; PH, pin
hole; L, lens.
Fig. 3-8. Picture of Mach-Zehnder interferometric setup.
3.3 Results and discussion
3.3.1 Polymer matric nano-cluster electro-optic films
A. r333/r113 ratio of ESA films
96
From symmetry consideration, the value of r333/r113 of isotropic electro-optic
materials should be 3(20, 21). It is assumed that the poled glassy chromophore thin film is
uniaxial and belongs to the C∞v point group, so r13 = r51. If there is no interaction between
chromophores, based on standard rigid gas model, one can predict r33 = 3r13 . This
conclusion has long been used for polymeric electro-optic materials, but for many
organic electro-optic materials such as L-B films, liquid crystals, and organic crystals,
which display a fair degree of anisotropy, r33/r13 ≠ 3. Figure 3.9 shows the ratio of r333/r113
of a CdSe/PDDA ESA film calculated from the measured data obtained with the Mach-
Zehnder setup. One can see that the ratio varies between 4.1 and 4.5 at different
modulating frequencies. Other samples give the same result: r333/r113 > 3. This means that
Fig. 3-9. Modulation frequency dependent of r333/r113 ratio
of nano-cluster CdSe/PDDA ESA film.
2
3
4
5
6
1 10 100 1000 10000
Modulation Frequency (Hz)
r 333
/r13
3
CdSe/PDDA film, thickness 150nm
97
ESA films can not be treated as an ideal isotropic system with C∞v symmetry. Some
modified new relationship has been derived (22), in which the extent of anisotropy
(dispersion factor) is considered. Results in Chapter 2 indicate that ESA films are indeed
anisotropic, because of the internal field. So the Mach-Zehnder setup is more appropriate
for the electro-optic coefficient measurement of ESA films.
B. Comparison of electro-optic nano-cluster and bulk crystals, ESA and spin
coating of electro-optic films
Figure 3-10 shows how r33 varies with the modulation frequency of CdSe films
fabricated under different conditions. From this figure, it is concluded that r33 decreases
with increasing modulation frequency, ESA films have higher r33 than spin coated films,
and no poling voltage is needed, and the r33 of spin coated films vary with nano-cluster
concentration. For general conditions (normal temperature, pressure), CdSe crystal
belongs to the hexagonal (Wurtzite) system, has 6 mm symmetry structure, and the
crystal’s electro-optic coefficients are r33= 4.3(pm/v), r13=1.8(pm/v) (23). Compared with
the experimental results, it is interest that CdSe nano-clusters have much higher electro-
optic coefficients than their bulk crystal counterparts. This is because they have totally
different origins in their electro-optic effects. Lack of an inversion center in the
hexagonal crystal class is the basis of the electro-optic effect of bulk CdSe crystal,
although the electro-optic effect is small, like that most of other crystals. The origin of
the electro-optic effect of CdSe nano-clusters has been fully discussed in the introduction
section, for better understanding, some quantitative description is given below.
98
Many optical and dielectric properties of materials can be explained in terms of
oscillation and photo-phonon interactions. Absorption and electro-optic effects of nano-
clusters are both based on the oscillation of excitons. An exciton can be seen as an
oscillator with a certain special oscillation frequency, The oscillator strength of an
exciton can be repressed as
2
0
2
2
2uE
h
mf µ∆= , (3.23)
Fig. 3-10. r33 varies with modulation frequency of CdSe films fabricated
at different Conditions, poling voltage is 80 volts/micron.
where m is the mass of an electron, ∆E is the band energy, µ is the exciting energy, u0 is
electron and hole wave function. So 2
0u is the overlap factor. This is the probability of
finding electrons and holes at certain locations. As particle size decreases, electrons and
0
20
40
60
80
100
120
140
160
180
200
10 100 1000 10000
Frequency(Hz)
r 33
(pm
/V)
1: ESA2:Spin Coating, 5% CdSe3:Spin Coating, 1% CdSe
1
2
3
99
holes are confined in a smaller space, so2
0u , the overlap factor increases, and so does
the oscillator strength of excitons.
The oscillator strength is f/V (V is the volume of nano-clusters) which determines
the absorption coefficient of materials. As particle size decreases, f increases, and V
decreases, so f/V increases significantly. So does the absorption coefficient of nano-
clusters.
From another point of view, via Mie scattering theory, which is based on an exact
solution of Maxwell’s equations, in the case of microcrystallite interaction with
electromagnetic field by its transition dipole moment, absorption is determined by the
effective cross sectional area and relative dielectric constant (24) to be
+−=
2
1Im
8'
'32
εε
λπσ a
, (3.24)
where a is the radius of the cluster, ε’ is the ratio of dielectric coefficients of the clusters
to the dielectric coefficients of the matrix. The dielectric constant is spatially varying
constant (25)
( ) ( ) 1
0 2
/exp/exp1
111−
∞∞
−+−−
−−= her
rr ρρεεε
ε , (3.25)
where
2/1
*2
=LO
e
em
h
ωρ and
2/1
*2
=LO
h
hm
h
ωρ , (3.26)
100
and ωLO is the longitudinal-optical-phonon frequency (=4×1013 /S for CdSe).
The overall result is that the shape of the absorption spectrum and absorption
intensity of nano-clusters are functions of ε’ , and the absorption coefficient of nano-
clusters increases with the decrease of cluster size.
Some theories have been developed to solve the relationship between optical
absorption and nonlinear dielectric susceptibility, namely
απω
χ4
)2( nc= , (3.27)
where n is the refractive index, c is the speed of light in vacuum, and ω is the angular
frequency.
Based on four-wave mixing theory, the third order susceptibility is be calculated by
(26):
)1(3
8 22)3(
TI
nc
−=
ωηεα
χ , (3.28)
where I is pump intensity, and T is transmission.
By applying of Fermi-Dirac statistics in band filling, χ(3) is proportional to
absorption coefficient
101
0
)3( ~ωω
αχ−g
. (3.29)
Using a simple two level saturation model, χ(3) is proportional to the square of
absorption coefficient (27)
2)3( )(~ αλχ . (3.30)
It is found that equation 3.30 is better in agreement with experimental results.
This means that )3(χ is directly determined by absorption.
Electro-optic coefficient is proportional to nonlinear optic coefficient, the
coefficient is 2/ n4, because they have the same physical origin
r = 2χ(2)/n4 . (3.31)
So smaller cluster results in higher absorption and cause larger nonlinear optical
and electro-optic responses. In chapter 2 it is concluded that ESA films have higher
absorption than spin coated films. So ESA film should have higher electro-optic
coefficients than spin coated films, provided that their nano-cluster concentrations are
close, which also has been conformed in Chapter 2.
This is easy to understand, since electro-optic and nonlinear optic effects, optical
absorption, as well as other optical properties of materials are determined by photon-
phonon interaction, and the properties of oscillators (oscillation strength and frequency)
102
predominate the results of interaction. The basic nonlinear optical process can be viewed
as absorption of photons in materials. They interact with phonons, stimulate phonons to
emit other photons whose frequency is different from that of the input basic photons, and
whose intensity is normally weak. As for SHG, the process is an annihilation of two
photons at frequency ω and the simultaneous creation of a photon at 2ω. The conversion
efficiency is dependent on a phase matching condition. If the conversion process is to
conserve momentum and energy then
K(2ω)=2K(ω) , (3.32)
which leads to a maximum SHG, and high electro-optic response.
The Electro-optic effect with respect to absorption spectra is well illustrated by
the Kramars-Kronig equation
dss
ssP∫
∞
−=
022
''' )(2
)(ϖ
απ
ϖα . (3.33)
In this equation, α ' is the real part of the absorption coefficient, which corresponds to the
refractive index n, α '' is the imaginary part of absorption coefficient, which is correspond
to the extinction coefficient k(α=α ' + iα '', N = ε =n + ik), and P is determined by a
Cauchy integral. By knowing known the absorption spectra, one can calculate the
refractive index variation.
By taking advantage of the Kramars-Kronig equation in the study of the electro-
optic effect of quantum well structures, the strong electro-optic effect has also been
103
predicted and observed. Quantum well structure is very similar to that of multilayer films
made by the ESA technique. For example, for a GaAs(6nm)/Ga0.6Al0.4As(10 nm)
quantum well structure, and for an electric field of 80kV/cm, by using the Kramars-
Kronig equation, the calculated maximum variation of refractive index is ∆n=1.8%,
which is two orders of magnitude greater than the refractive index variation in its bulk
crystals (28). This result is consistent with experimental results. The enhanced electro-
optic effect originates from the enhanced quantum confinement in a quantum well
structure (enhanced 2-dimensional confinement). By comparison, it is not difficult to
predict the enhanced electro-optic effect in nano-cluster based films (enhanced 3-
dimensional confinement) and ESA films (enhanced 2-dimensional confinement).
C. Effect of poling voltage and nano-cluster concentration on electro-optic
coefficient of spin coated films
One of the most exciting results in the present research is that a significant
electro-optic effect is demonstrated even in the absence of a poling field, based on our
unique ESA process, as indicated by experimental results. This is because such a field has
been internally built up, as discussed in Chapter 2. This is very useful for modulator
devices since device fabrication can be simplified because no poling field is needed.
Figure 3-11 shows the r33 variation with poling voltage of the spin-coated CdSe
films. At low poling voltage, r33 increases with poling voltage almost linearly, but at
higher poling voltage, the increase becomes slow and finally reaches its maximum value.
Further increasing the poling voltage causes no more increase in r33.
104
Fig. 3-11. r33 variation with poling voltage of spin coated CdSe films.
In the absence of an external field, all ground state dipole molecular moments in
spin coated films (both electro-optic polymer films and CdSe nano-cluster/polymer films)
are randomly distributed, and the over all orientation angle is 0. When external fields are
applied, the dipole moments begin to be aligned gradually according to the amplitude of
the external field, and full orientation may ultimately be reached at a high field, where r33
achieves its maximum value. For poled electro-optic polymer films, χ(2) varies with
orientation angle as
)(cos)( 322)()2( ϕβχ ωω ffN= , (3.34)
so the electro-optic coefficient also varies with orientation angle as
CdSe-NOr65, frequency of modulation voltage = 300Hz
0
2
4
6
8
10
12
14
16
18
0 20 40 60 80 100 120
Polying voltage (V/micron)
r 33
(pm
/V)
1 % (Vol.) CdSe
5% (vol.) CdSe
105
4322)( /)(cos)(2 nffN ϕβγ ωω= , (3.35)
where β is the second order susceptibility of the nano-clusters or chromophores, N is the
number of nano-clusters or chromophores per unite volume, f(ω) and f(2ω) are the local
field factors which are simple functions of the refractive index at the fundamental
frequency and the double frequency (second harmonic generation), ϕ is the average angle
between the ground state dipole moment of the nano-clusters or chromophores and the
direction normal to the films, and cos3ϕ is the acentric order parameter. In order to have
a nonzero Pockel’s effect, such spin coated films must be poled before measurement, or
an electric field must be applied during measurement.
In practice, when the poling voltage is high (>30volts/micron), poling should be
performed in a closed chamber filled with nitrogen, or the samples may be damaged by
electrical shorts. This is particularly important for ultrathin films. Electrical conductivity
arising from impurities can lead to attenuation of poling efficiency. In this case,
purification of the solution before film processing may be necessary, and the use of
conductive or semiconductor polymers as matrix materials should be avoided.
Photoconductivity may also be a problem for some electro-optic materials and should be
considered. With such materials it is better to apply poling fields in the dark.
Figure 3-12 shows how the r33 of spin coated CdSe/Nor-65 films varies with CdSe
concentration. This result tells us that the electro-optic coefficients of spin coated
CdSe/Nor-65 films depends on CdSe concentration, and at low concentration (< 10 vol.%
), r33 increases linearly with CdSe concentration. But at higher concentration, the slope of
the curve decreases and if higher concentration films were measured, the slope may
106
Fig. 3-12. r33 of CdSe/Nor-65 film verses CdSe concentration,
poling voltage 80 volts/micron, modulation frequency 300 Hz.
become 0 or negative. This means that there may be a critical concentration (around 30
vol. %), at which the maximum r33 can be found and for values above the critical
concentration, r33 may decreases with increasing concentration.
Due to the quantum size effect of semiconductor nano-crystals, increasing nano-
particle concentration leads to an increase of the electro-optic coefficient, because the
polarization P (number of dipoles per unit volume) is increased. But optical absorption is
also increased, so high concentration is not allowed for practical uses. For nonlinear optic
and electro-optic applications, the concentration is normally less than 10%(vol.). A low
concentration levels, the electrostatic interactions between the chromophores in the
polymer system and of cluster-cluster in nano-semiconductor system are very small.
Their electro-optic coefficients increase linearly with thickness, like in an ideal gas
0
5
10
15
20
25
30
35
40
45
0 10 20 30 40
CdSe concentration (vol. %)
r 33
(pm
/v)
107
model, but at higher concentrations, the electro-optic coefficient of the films does not
increase linearly with concentration, maximum values are reached at certain
concentration, and the mutual electrostatic interactions can not be ignored.
Assuming that the chromophores and nano-clusters are of aspheric structure, and
that their interactions cannot be ignored, if all forces affecting the order are considered,
and if a Gibbs distribution is applied, then the electric field-induced acentric order factor
can be calculated as
∫ ∫
ΩΩΩΩ>=< dEGdEG pp ),(/),(coscos 33 ϕϕ , (3.36)
where G(Ω, Ep) is the Gibbs distribution function. It can be expressed by
)/),(exp(),( KTEUEG pp Ω−=Ω . (3.37)
Here, U is the total electrostatic potential energy, It is composed of a poling field
interaction and an electrostatic chromophore – chromophore or cluster-cluster interaction,
including dipole-dipole interaction, induced dipole interaction, and dispersion interaction.
If the chromophore – chromophore or cluster-cluster interaction is ignored, we
can obtain the order parameter
<cos3ϕ> = µF/5kT=µf(0)Ep/5kT , (3.38)
108
where µ is the dipole moment, k is Boltzmann's constant, and f(0) is the effective poling
electric field factor. This expression is suitable for use in the low concentration case, such
as an ideal gas model in physical chemistry theory. If chromophore – chromophore or
cluster-cluster interactions must be considered, the result is
<cos3ϕ>=(µf(0)Ep/5kT)[1-L2(W/kT)] , (3.39)
where L is the Langevin function, W is the chromophore – chromophore or cluster-
cluster electrostatic energy, which is proportional to N2, and N is the number density of
chromophore/cluster. Comparing the two equations, [1-L2(W/kT)] is a modification
factor, that indicates how the system is away from the ideal case. This model is also
useful in magnetic and ferroelectric materials to study similar concentration effects.
From this equation, it can be concluded that [1-L2(W/kT)] increases
monotonously with chromophore/cluster spacing, or 1/N, from equation 3.34, and χ(2)
and r are proportional to N. The over all consequence is that there is a critical value of N
at which maximum χ(2) and r can be achieved. So a very high concentration is not
optimal, since both film quality (absorption, transparency, scattering and uniformity) and
electro-optic property will be degraded. For CLD the critical concentration is about 25
wt.% in (29). For our CdSe based spin coated films, the exact critical concentration is to be
determined by more experiments (using more samples with different concentrations
around 30 vol.%).
D. Frequency response of polymer matrix nano-cluster electro-optic films
109
Figures 3-13 and 3-14 show the results obtained for r333 and r113, respectively.
One can see that the maximum r333 at a modulating frequency of 30 Hz is 560 pm/V and
both electro-optic coefficients r113 and r333 undergo a rapid decrease at a frequencies less
than around 100Hz. At frequencies higher than 100Hz, they continue to decrease slowly
until reaching a diminished stable value. Figures 3-13 and 3-14 and all other experimental
results demonstrate the same temporal behavior of electro-optic films: electro-optic
coefficients decrease with increasing modulation frequency, and both ESA and spin
coated electro-optic films possess the same tendency. This behavior is related to the
dipole moments vary with the frequency of the applied field. Dipole moments are
introduced due to the following electric polarization mechanism contributions at
particular frequencies.
(a) Orientational polarization, where the dipoles align themselves when an
electric field is applied.
(b) Electronic polarization, where the applied field distorts the negatively-
charged electron cloud with respect to the positively-charged nucleus. This is
particularly important for nano-sized semiconductor particles. The formation
of excitons separates the electron cloud and the nucleus, and because they are
highly polarizable, they can substantially contribute to the electro-optic and
second-order nonlinear signals.
(c) Ionic or atomic polarization, where the positive and negative ions undergo
relative shifts with the application of an external field.
110
Fig. 3-13. r333 as a function of modulating frequency
measured using the Mach-Zehnder setup.
Fig. 3-14. r113 as a function of modulating frequency
measured using the Mach-Zehnder setup.
40
60
80
100
120
140
160
10 100 1000 10000
Modulation frequency (Hz)
r 113
(pm
/v)
CdSe/PDDA ESA film, thickness 150 nm
100
200
300
400
500
600
10 100 1000 10000
Modulation frequency (Hz)
r 333
(pm
/v)
CdSe/PDDA ESA film, thickness 150 nm
111
At low frequency, all polarization mechanisms contribute to the electro-optic
effect, so both ESA film and spin-coated films possess very high EO coefficients (r33). At
high frequency, the orientation polarization cannot follow the rapid change of the
external modulation field, so no longer contributes to the electro-optic response. At these
frequencies, only electronic polarization and ionic or atomic polarization mechanisms are
in effect. At higher frequencies, even the ionic and atomic polarization contributions
disappear, and only electronic polarization still applies. So the r33 decreases greatly with
frequency, but the value is still high compared with that of other electro-optic materials.
Other factors also affect the temporal behavior. One is the absorption transition
effect. As the pumping laser wavelength becomes very close to the wavelength of the
absorption peak (hν~Eg), nearly direct band gap (band to band) transitions result. As a
result electrons are excited almost to the conduction band, electrons and holes are well
separated, and the excition lifetime (decay time) is high, which results in a large but slow
nonlinear and electro-optic response. This is termed the resonant transition region. As the
pump laser wavelength becomes such that 1/2 Eg< hν< Eg, the electro-optic and nonlinear
response falls into a non-resonant transition region, sometimes termed the superradiative
decay region. Here, the energy of the pumping laser is not as high as that in the resonant
transition case, so the resulting electron-hole pairs are not well separated. In this case,
they are not stable at all, their lifetime is rather low, which generates a fast but low
electrooptic and nonlinear response. In our case, electro-optic coefficients are measured
by using a HeNe laser (wavelength 633 nm). From absorption and photoluminescence
spectra, the band to band transitions of the samples takes place from 500 through 550nm,
112
so the transition is in non-resonant region, but close to the resonant transition region. As a
result, large but slow electro-optic and nonlinear responses can be observed.
This result implies that there is a trade off between the speed and amplitude of the
electro-optic effect when this kind of material is used in devices. Enhancement of electro-
optic and nonlinear optical properties are at the sacrifice of switching time, or vice versa.
Together with optical absorption, it makes sense to define a figure of merit of such
materials by χ(n) / αλτ , where α is absorption coefficient, λ is wavelength and τ is decay
time. This defines the overall performance of such kinds of devices or materials. Trap or
surface states also introduce slow response, since normally, trap states have long
lifetimes, and lead to enhancement of χ(n) and r.
Ref. 30 reports that CdSe quantum dots exhibit a large permanent dipole moment
of 25 ~ 47 debyes. It is well-known that this moment can be rotated and oriented by the
application of an external electric field.(31-33) When a modulating voltage is applied across
the sample, a modulating torque will be applied to the quantum dots. This results in an
orientation distribution induced by the external electric field at lower frequencies, at
which the quantum dots can respond. This orientation distribution of the permanent
dipole moment can contribute to the electro-optic modulation. At higher modulating
frequencies, because the quantum dots cannot follow the rapid modulation of the electric
field to complete their rotation, the permanent dipole moment no longer has significant
contribution to the electro-optic modulation.
To determine the typical frequency of orientation, let us review the tensor
components of the molecular second-order susceptibility. In the one-dimensional case (34,
35),
113
],)5/1()5/1[(~ 31*
113 AANr zzz −β (3.40)
and
],)5/2()5/3[(~ 31*
333 AANr zzz +β (3.41)
where N is number density of quantum dots, A1 and A3 are order parameters of the
Legendre polynomials,(31, 34, 35) and β*zzz is the only nonvanishing, local-field-corrected
second-order optical susceptibility of single quantum dots.
From Equations 3.40 and 3.41, one can see that the data in Figures 3-13 and 3-14
indicate the frequency dependence behavior of β*zzz. To fit the experimental data in
Figures 3-13 and 3-14, let us write
),/exp()/exp( 2021010* ffaffaazzz −+−+=β (3.42)
where the first term, a0, represents the contribution of pure electron movement, the
second term depicts the contribution from the permanent dipole moment orientation, and
the third term arises from the induced dipole moment contribution.(31-33) The terms a0, a1
and a3 are constant, f10 and f20 are two typical limiting frequencies for the permanent
dipole and induced dipole moments, respectively, and f is the modulating frequency.
Within Figures 3-13 and 3-14, the two typical frequencies obtained are f10 = 28.5
Hz and f20 = 5.8×104Hz. From the value of f10, one can see that a CdSe quantum dot
114
needs 1/2f10 = 17. 5 ms to complete its physical orientation due to a rotation of its
permanent dipole moment. Therefore, at lower frequencies (<100Hz), electro-optic
modulation mainly stems from the orientation of the permanent dipole moment. At
frequencies higher than 100 Hz, the electro-optic modulation mainly arises from the
induced dipole moment orientation and pure electron movement.
E. Quadratic electro-optic coefficient of polymer matric nano-cluster electro-optic
films
Figures 3-15 and 3-16 show the measured results for Kerr electro-optic coefficient
r1133 and r3333. The obtained maximum value of r3333 is 176×10-20m2/V2 at a modulating
frequency of 3 Hz. One can see that r3333 and r1133 have a similar frequency dependence to
that of the linear electro-optic coefficents r333 and r113. This indicates that the orientational
distribution of the CdSe quantum dots particularly contributes to the quadratic electro-
optic modulation.
115
Fig . 3-15. r1133 as a function of modulating frequency
measured with the ellipsometric setup.
Fig. 3-16. r3333 as a function of modulating frequency
measured with the ellipsometric setup.
0
50
100
150
200
250
1 10 100 1000 10000
Modulation Frequeccy (Hz)
r 333
3 (
10-1
0 m/V
)2
Sample: CdSe/PDDA Thickness: 150 nm
0
20
40
60
80
100
1 10 100 1000 10000
Modulation Frequeccy (Hz)
r 113
3 (1
0-10 m
/V)2
Sample: CdSe/PDDA Thickness: 150 nm
116
3.3.2 Polymeric electro-optic chromophore films
Structures of experimental electro-optic chromophores
Each electro-optic polymer is composed of an electron donor, an acceptor and a
π-conjugated bridge. The amplitude of the electro-optic response is determined by the
strength of the electron donor and acceptor and the length of π-conjugated bridge, as
indicated in the introduction section. The molecular structures of used chromophore
polymers are listed Figure 3-17 below
polypeptide
Lys-216N
H
H
Bacteriorhodopsin (bR)
117
Poly 1-[4-(3-carboxy-4-hydr0xyphenylazo)benzenesulfonamido]-1,2-ethanediyl sodium salt(PCBS)
CH2 CH
NH
SO2
NN
OHCOO Na
n
N
R
R O
CN
CNCN
R = O SiCH3
C4H9CH3
CLD-1
118
Fig. 3-17. Molecular structures of various polymers used in the present work.
n
Poly-S-119
CH
NH
SO2
NN
HO
SO3 Na
CH2
Poly(allylamine hydrochloride) (PAH)
n
Cl
CH
CH2
NH3
CH2
Cl
Poly(diallyldimethylammonium chloride) (PD
nCH2CH2
NCH3 CH3
CH2 CH2
119
A. ESA films verses spin coated films of CLD electro-optic chromophores
CLD e-o properties The CLD chromophore is by far one of the best electro-optic polymers. It has a
high electro-optic coefficient, good stability, and has been used in making commercial
optical devices showing superior performance (high bandwidth, low half wave voltage).
Films of CLD were fabricated by ESA and spin coating processes. For spin coated films,
31 wt. % CLD is dispersed in PMMA ( F.W. =38000, Tg=113°C ), and the films
(thickness=6 micron) were polyed by an electrical field of 20V/micro n at 103°C for 1hr.
Results are shown in Figures 3-18, 3-19 and 3-20. Like CdSe based films fabricated by
ESA and spin coating processes, the electro-optic coefficients of ESA films are much
higher than those of spin-coated films, and the reasons have been fully discussed before.
This result tell us that the ESA technique is effective for aligning and holding the dipoles
in films and intensifing the electro-optic effect for both nano-cluster based films and
polymeric films.
Fig. 3-18. Modulation frequency dependence of r113 of ESA CLD/PDDA film.
05
101520253035404550
1 10 100 1000 10000
Modulation Frequency (Hz)
r 113
(pm
/v)
40 bilayers100 nm
120
Fig. 3-19. Modulation frequency dependence of r333 of ESA CLD/PDDA film.
Fig. 3-20. Modulation frequency dependence of r333 and r113
of spin coating CLD/PDDA(wt. 31% CLD) film.
0
50
100
150
200250
300
350
400
450
1 10 100 1000 10000
Modulation Frequency (Hz)
r 333
(pm
/v)
40 bilayers100 nm
0
10
20
30
40
50
60
70
10 100 1000 10000
Modulation Frequency (Hz)
r 333
& r
113(p
m/V
) r333
r113
121
B. Effect of proton irradiation on electro-optic behavior of films
Figures 3-21 and 3-22 show the measured r33 and r13 of the PS-119/PDDA films
with and without proton irradiation. For these samples, the film thickness is 70 nm, and
no poling voltage has been applied. The chemical structure of PS-119, PDDA and PAH
are shown in Figure 3-17. In PS-119, the SO2 functional group acts as the electron donor,
and SO3- as the acceptor. They are separated by a π-conjugated bridge. Due to SO3
-, PS-
119 is water soluble. It can be dissolved in water as a polycation and attracts to the NH3+
in PAH and N+ in PDDA. Resulting films show very high electro-optic coefficients,
much higher than that of LiNbO3. Like CdSe doped EO films, their electro-optic
coefficients (both r33 and r13) decrease with the increase of the frequency of the
modulation voltage, but at high frequency (over 1000 Hz), r33 is still high. From the FT-
IR measurement of the films, proton irradiation can break the N=N double bonding in the
π-conjugated bridge, leading to damage of the conjugating structure, so causing a
decrease of the EO coefficient.
Recently extensive research work involving electro-optic polymers has been
performed and some very good E-O polymers with very high electro-optic response have
been synthesized, but still many problems prevent E-O polymer from extensive
applications. One of the most important problems with respect to their practical
application is their stability. Time, temperature, photochemistry, and electromagnetic ray
irradiation are among the primary reasons that cause decay of such polymers. The effect
of proton irradiation has been chosen for our research, because this is ignored by most
researchers and it is very important for the potential use of electro-optic polymer in
aerospace applications.
122
Fourier transform infrared (FT-IR) absorption spectroscopy is employed to detect
the structural changes of molecules caused by proton irradiation. In FT-IR spectroscopy,
some important groups for PS-119 are OH-1 (3400cm-1), O-2 ( 1250 cm-1), NH-2 ( 3100-
3300 cm-1), C6H6(1600 cm-1 ) and [-N=N-]-2 (1388-1393 cm-1 ). By proton irradiation, the
most likely chemical change with regard to the change in electro-optic property is [-N=N-
]-2 debonding. This gives raise to conjugation damage, and so decreases electrooptic and
nonlinear optical properties such as the electro-optic coefficient (r33, r13), and second
harmonic generation (SHG). From Figures 3-26 and 3-27, there are slight, but not
apparent, intensity changes of [-N=N-]-2 before and after irradiation. This means that to
some extent, debonding of of [-N=N-]-2 in the selected group of samples results but most
[-N=N-]-2s remain the same.
C. Electro-optic coefficient versus film thickness (number of bilayers)
Figures 3-27 and 3-30 show how the electro-optic coefficient varies with the
thickness of BR and PS-119 films fabricated by the ESA process. Although very high
electro-optic coefficients can be achieved at low film thickness, the electro-optic
coefficient decrease with thickness. An assumption is that the extent of chromphore
alignment (or order) decreases with the increase of film thickness. Optical properties of
ESA electro-optic films have been discussed in Chapter two. Absorption and refractive
index both vary with film thickness, and they are closely related based on the oscillation
model of photon- phonon interaction. Many factors affect the electro-optic property of
films, but in the thickness-electro-optic property experiment, with all factors kept
123
Fig. 3-21. r333, r113 vary with frequency of modulation
voltage of PS-119/PDDA films.
Fig. 3-22. r333, r113 vary with frequency of modulation voltage
of proton irradiated PS-119/PDDA films.
0
100
200
300
400
500
600
700
800
900
10 100 1000 10000
M od ula tion Frequ ency (H z)
r 113,
r 333 (
pm/V
)
r1 13
r3 33
020406080
100120140160180
10 100 1000 10000
Modulation Frequency (Hz)
r 333
, r11
3 (p
m/v
)
r333
r113
124
Fig. 3-23. r333, r113 vary with frequency of modulation voltage of PCBS/PDDA films.
Fig. 3-24. r333, r113 vary with frequency of modulation voltage
of proton irradiated P S-119/PDDA films.
050
100150200250300350400450
10 100 1000 10000
Modulation Frequency (Hz)
r 113
, r33
3 (p
m/V
)
r113
r333
0
20
40
60
80
100
120
10 100 1000 10000
Frequency (Hz)
r 333
, r11
3 (p
m/v
)
r333
r113
125
Fig. 3-25. FT-IR of polys-119/PDDA ESA films with (1-A) and without (control-A)
proton irradiation.
Fig. 3-26. FT-IR of PCBS/PDDA ESA films with (3A) and without (control 3)
proton irradiation.
-0 .0 2
-0 .0 1 5
-0 .0 1
-0 .0 0 5
0
0 .0 0 5
0 .0 1
0 .0 1 5
0 .0 2
0 .0 2 5
0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0
W a v e n u m b e r (c m -1 )
Abs
orba
nce
Inte
nsity
c o n tro l-A
1 -A
-0.05
-0.03
-0.01
0.01
0.03
400 900 1400 1900 2400 2900 3400 3900
Wavenumber(cm-1)
Abs
orba
nce
3A
Control 3
126
constant, it seems that the only variable factor introduced by thickness variation in the
process of film fabrication and property measurement is the dipole moment orientation.
But why the dipole moment orientation varies with film thickness is still not clear. It is
probably because the substrate surface is either only slightly or not at all charged. But the
polymer molecules used in the ESA process (such as PS-119, PDDA) contain positive
and negative charge parts, so for the first few layers of ESA film growth on the surface,
dipoles align well, because of the weak electrostatic interaction between the film and
substrate. As more layers are grown on the other polymer layers, the orientation of a
molecular dipole moment is affected by its charged neighbors. Some of them can
intensify its orientation, but others, particularly its lateral neighbors, will interrupt its
orientation. The overall result is to decrease the orientation, so the net electro-optic
coefficient decreases.
Fig. 3-27. r333 of PS-119/PDDA at different thickness (240,378 and 540 bilayers).
0
5
10
15
20
25
30
10 100 1000 10000
Modulation Frequency (Hz)
r 333
(pm
/v)
1
2
3
1: 540 bilayers2: 378 bilayers3: 240 bilayers
127
Fig. 3-28. r333, r113 vary with poling voltage of PS-119/PDDA film(540 bilayers),
modulation frequency 1000 Hz.
Fig. 3-29. r33 vary with modulated frequency of BR/PDDA film.
0
1
2
3
4
5
6
7
8
0 2 4 6 8 10 12
Poling Voltage (v/um)
r 333
, r11
3 (
pm/v
)
r113
r333
128
Fig. 3-30. Electo-optic coefficient of ESA BR/PDDA films at different thicknesses.
From Figure 3-28, applying an electrostatic poling field to films is also effective
as a way to increase the electro-optic coefficient of ESA films.
D. Electro-optic property of films made by field-assisted ESA processing
The effect of an external field on the optical properties of ESA films has been
investigated in Chapter 2. Electrical field influences the electronic states of the
chromophores, and leads to changes in the absorption spectrum: peak position, optical
density and wavelength at maximum absorption. They all increase with the number of
bilayers, and films made under external fields have lower absorption and peak
wavelength than those of films without an applied external field. These can be described
by the order parameter, which can be determined in terms of absorbance. In the
experiment of electro-optic coefficient variation with film thickness, two kind of samples
0
50
100
150
200
250
300
350
400
0 20 40 60 80
Number of Bilayers
r333
& r1
13 (p
m/v
) r333
r113
BR film
129
are used. For one sample the electric field is applied during the process of film growth by
ESA and for the other sample, no field is applied. The other conditions (solution
concentration, pH value, substrate cleaning, dipping time, rinse) are exactly the same, so
the results are comparable. From Figure 3-31, it is apparent that samples fabricated under
the application of an external electrical field give a higher electro-optic coefficient. The
absorption of these samples has been studied in Chapter 2. It is concluded that better
orientation can be obtained by means of an external field during the process of ESA film
fabrication, so it is easy to understand why the electro-optic property of that film is
enhanced. Since even though the enhancement is not very significant, it is impossible to
apply high voltage to solution and substrates. This technology has been proven to be
Fig. 3-31. Electro-optic coefficient of PS-119/PDDA ESA films variation
with the number of bilayers with and without applied field in
the process of film growth, modulation frequency is 30 Hz.
0
200
400
600
800
1000
0 100 200 300 400 500 600
Number of Bilayers
r 333
(pm
/v)
1
2
PS-119/ PDDA ESA Films1: Applied Voltage 0.47 v2: Applied Voltage 0 v
130
useful to improve the properties of self-assembled LEDs in our group in the mid 1990s.
By applying the electrical field assisted ESA technology, the resulted polymeric LED
device achieved lower threshold voltage, higher luminescent efficiency and longer
lifetime.
3.4 Conclusions
CdSe nano-clusters have a much higher electro-optic coefficient than their bulk
crystal counterparts. They have totally different origins in their electro-optic effects. For
both nano-cluster-and chromophore based ESA films, their electro-optic coefficients are
higher than those of spin-coated films, and no poling voltage is needed. The reasons have
been fully discussed. This result means that the ESA technique is effective to align and
hold the dipoles in films and to intensify the electro-optic effect. The r33 of spin coated
films varys with nano-cluster concentration, and there is a critical concentration at which
the maximum electro-optic coefficient can be obtained.
The electro-optic coefficient of spin-coated CdSe films also varies with poling
voltage. At low poling voltage, r33 increases with poling voltage almost linearly, but at
higher poling voltages, the increase becomes slow and finally reaches its maximum
value. Further increasing in poling voltage causes no more increase in r33.
CdSe quantum dots need 17. 5 ms to complete their physical orientation due to a
rotation of its permanent dipole moment. Therefore, at lower frequencies (<100Hz),
electro-optic modulation mainly stems from the orientation of the permanent dipole
moment. At frequencies higher than 100 Hz, the electro-optic modulation mainly arises
from the induced dipole moment orientation and pure electron movement.
131
The ratio of the electro-optic coefficients r333/r113 > 3. This means that ESA films
cannot be treated as an ideal isotropic system with the C∞v symmetry, and interactions
should be considered.Quadratic Kerr electro-optic coefficients have a similar frequency
dependence to that of the linear electro-optic coefficents r333 and r113. This indicates that
the orientational distribution of the CdSe quantum dots particularly contributes to the
quadratic electro-optic modulation.
From the FT-IR measurement of the films, proton irradiation can break the N=N
double bonding in π-conjugated bridges, leading to damage of the conjugating structure,
so causing a decrease of the EO coefficient.
Finally, the effect of an external field and film thickness on the optical and
electro-optic properties of ESA films has been investigated. Electro-optic coefficient
decreases with thickness. Electrical field influences the electronic states of the
chromophores, and leads to changes in absorption spectrum: peak position, optical
density and wavelength at maximum absorption. These changes in optical properties
correspond to changes in electro-optic properties. Better orientation can be obtained by
means of the application of an external field during the process of ESA film fabrication.
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