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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,

70

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

71

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)

72

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

73

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’

74

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

75

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

79

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

80

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.

81

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.

82

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

83

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

84

),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

85

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

86

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)

87

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

88

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)

89

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)

90

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.

91

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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