69 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,
66
Embed
CHAPTER 3 Electro -optic Properties of II -VI …Electro -optic properties of semiconductor nano -cluster materials Property changes of materials at the nano -level as a result of
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
69
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
76
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
77
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.
78
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