Deformation of nematic liquid crystals by an electric field

Chapter 1. Introduction

2.1.3 Deformation of nematic liquid crystals by an electric field

Because of very widely important application via using electric field to reorient

the LCs, here we discuss in detail the affection by an electric field. The manifestation

of an electric field results in extra terms in the expression of the following free energy

density:

, (2.5)

We can cancel the first term due to independent of the direction of the director.

Considering the second term, the free energy of the nematic LCs concerned with an

electric field should be a minimum for a definite direction of the director relative to

the field direction due to the dielectric anisotropy Δε. As shown in Figure 2.8, if there

is a nematic LCs system with positive dielectric anisotropy (Δε＞0), the stable state

which should minimize the free energy is described by a director parallel to the

external field direction. In contrast, if the nematic LCs system with negative dielectric

anisotropy (Δε＜0), the stable state prefers to a director direction perpendicular to the

external field direction. In order to avoid the induced separation of charged impurities

forming electric double layer in LC cell, an alternating voltage across the LC cell. The

electric double layer model is shown in Figure 2.9. In view of an original state that the

direction of the director concerned with external field direction does not satisfy the

condition of minimum free energy, it leads to a sufficiently strong electric field to

generate a torque on the LCs which results in a reorientation of the director. We can

obtain a deformed state which owns lower free energy than the original state. The

equilibrium condition to cause a deformed stable state is the balance between the

electric torque and the restoring elastic torque of the LC. In addition, the stable state is

always obtained by the reorientation of director configuration when minimizing the

free energy of the system.

If we think of the electric energy in Equation (2.4), the

distribution of the director all over the system can be evaluated. According to

Equation (2.4), we can derive the critical field strength where the destabilizing electric

torque overcomes the stabilizing restoring elastic torque. Figure 2.10 are illustrated

several field-induced deformations of nematic LCs system. In Figure 2.10 (a), (b), and

(c), three fundamental situations are shown with different initial orientation of the

director. It is noted that the applied electric field is perpendicular to the director in

Figure 2.10 and the dielectric anisotropy Δε is positive so that the director prefers to

align parallel to the external field direction. Figure 2.10 (a) shows the result of a pure

splay deformation for a small director displacement. If having a higher field to the

deformation, we can obtain mainly a splay deformation with a combination of a bend

deformation. The threshold field Eo is given by

, (2.6) where d is the sample thickness.

Figure 2.10 (b) shows the result of a pure twist deformation. The threshold field Eo is

given by

, (2.7)

Figure 2.10 (c) shows the result of a small pure bend deformation. If having a higher

field to the deformation, we can obtain mainly a bent deformation with a little splay

deformation. The threshold field Eo is given by

, (2.8)

It must be emphasized that Equations (2.6)－(2.8) are derived under the simplifying

assumptions, where the interaction between the molecules and the surface is strong

and the electric conductivity is neglected here. According to (Uo is threshold

voltage), it indicates that the threshold voltage is independent of the sample thickness.

Similar deformations can be discussed in nematic LCs system with negative dielectric

anisotropy (Δε＜0). Then we can obtain the same critical field strength when the

electric field is perpendicular to the situation as shown in Figure 2.10. Figure 2.10 (d)

shows schematically the director alignment in a planar-twisted cell where the twist

angle is 90 degree. The threshold field Eo for a nematic LCs system with positive

dielectric anisotropy (Δε＞0) is given by

, (2.9) It should be emphasized here that a decrease of the anchoring energy leads to a

decrease of the threshold field Eo. In addition, for a tilted director alignment, there is

no threshold field theoretically. It means that the deformation starts at an infinite

small field strength.

We can derive theoretically the equation of motion of the director (the dynamics

of the field-induced deformations) which presents the balance of the elastic and

viscous forces and the external electric field. Considering a particular case of a pure

twist deformation, it means that the system is not accompanied by a change in

position of the centers of gravity of LC molecules (in contrast to splay and bend

deformations). The equation of motion can be written as:

, (2.10)

where θ is the angle between the local director and the substrates, z is the coordinate

perpendicular to the substrate, t is the time, and γ1 the rotational viscosity. In general,

Equation (2.10) must be solved numerically. However, for some simplifying

assumptions, we can derive the following result for the switching times of the

dielectric reorientation as follows:

, (2.11)

where U is voltage and Uo is the threshold voltage, and

, (2.12)

Equations (2.11) and (2.12) are also valid for bend and splay deformations if small

deviations from the initial orientation of the director. Owing to depend on the initial

orientation of the director, in Equation (2.12), different elastic constants can be

replaced K2, for a planar layer K1, for a homeotropic layer K3, and for a planartwisted

layer K1 (K3 – 2K2)/4. Finally, it worth noting that the switching times are mainly

determined by the rotational viscosity γ1 and the sample thickness d from Equations

(2.11) and (2.12). In particular, Δε and the driving voltage are the crucial factors to

affect the rise time.

2. 2.1 Semiconductor nanowires and nanorods [5]

Nanoscale materials have attracted tremendous interest and attention over the

past decade for their vast areas of applications ranging from electronics to

pharmaceuticals.

One-dimensional (1D) nanostructures such as nanowires, nanobelts and

nanotubes have become the focus of intensive research owing to their fascinating

properties, unique applications in macroscopic physics and fabrication of nanoscale

electronic and optoelectronic devices. Semiconductor nanowires have demonstrated

significant potential as fundamental building blocks for electronic and photonic

devices and offer substantial promises for integrated nanosystems. The rectifying

properties of semiconductor nanowires-based electronics demonstrated the versatility

of the nanowires-based electronics device.

Quantum confinement effects of the semiconductor nanowires on the other hand,

produce unique optical properties that can be applied to nanophotonic devices.

Notably, the key feature of semiconductor nanowires that has enabled much of their

success has been the growth of materials with reproducible electronic and optical

properties that can be in turn, integrated into functional nanoscale devices.

Consequently, nano-devices based on semiconductor materials such as field-effect

transistors (FETs) [6], lasers [7], light emitting diodes (LEDs) [8] and sensors [9]

have been demonstrated.

Quantum size-confinement plays an important role in determining the energy

levels of 1D nanostructures when its diameter is below the critical Bohr radius. Lu et

al. found that the absorption edge of Si nanowires display significant blue shift as

compared with the indirect bandgap (~1. 1 eV) of bulk silicon [10-12]. They observed

sharp, discrete features in the absorption spectra and relatively strong band-edge

photoluminescence (PL). These different optical features mainly resulted from

quantum-confinement effects and also the variation in growth direction for these Si

nanowires [13]. In contrast to quantum dots, light emitted from nanowires is highly

polarized along the longitudinal axes. One-dimensional nanostructures have thus far

been primarily synthesized by lithography and epitaxial techniques on semiconductor

substrates [14–16]. Free standing nanowires, on the other hand, of many

semiconductors have recently been formed by a growth technique using nanosized

liquid droplets of the metal solvent [17–20]. This technique has the advantage of

being able to produce heterogeneous structures along the nanowire, such as p-n

junctions [17] and superlattices [18]. Optical properties of the nanowires formed using

the above technique have been studied by photoluminescence (PL) and absorption

spectroscopy, which showed a blueshift of the peak energy due to the quantum

confinement effect and giant polarization anisotropy in PL and optical absorption.

Those properties provide the potential for new applications of the semiconductor

nanowires. For example, Wang et al. [21] showed a prominent anisotropy in the PL

intensities in the direction parallel and perpendicular to the long axes of an individual,

isolated indium phosphide (InP) nanowires (Figure 2.11), whose polarization ratio is

0.96, but that of numerous InP nanowires grown on a substrate [22] (Figure 2.12), where

some of them were inclined from nomal of substrate, is only 0.5. The magnitude of the

polarization anisotropy could be quantitatively due to the large dielectric constant

contrast between the nanowires and the surrounding environment, as opposed to

quantum mechanical effects such as mixing of valence bands.

References

[1] P. J. Collings and M. Hird, R. A. Stradling and P. C. Klipstein, Introduction to

Liquid crystals Chemistry and Physics (Taylor & Francis, 1997).

[2] P. J. Collings, Liquid crystals (Nature’s Delicate Phase of Matter) (Princeton

University Press, 1990).

[3] de Gennes, P. G.; Prost, J. The Physics of Liquid Crystals; Clarendon (Oxford,

1993).

[4] P. C. Yeh, and C. Gu, Optics of Liquid Crystal Displays (Wiley, New York, 1999).

[5] A. A. Balandin and K. L. Wang, Handbook of Semiconductor Nanostructures and

Nanodevices 4 (American Scientific Publishers, Los Angeles, California, USA,

2006).

[6] R. Martel, T Schmidt, H. R. Shea, T. Hertel, and P. Avouris, Appl. Phys. Lett. 73,

2447 (1998).

[7] J.C. Johnson, H. J.Choi, K. R. Knutsen, R D. Schaller, R Yang, and R. J. Saykally,

Nature Mater. 1, 106 (2002).

[8] H. M. Kim, T W. Kang, and K. S. Chung, Adv Mater. 15, 567 (2003).

[9] A. Kolmakov, Y. Zhang, G. Cheng, and M. Moskovits, Adv Mater. 15, 997 (2003).

[10] X. Lu, T. Hanrath, K. P. Johnston, and B. A. Korgel, Nano Lett. 3, 93 (2003).

[11] T. Hanrath and B. A. Korgel, J. Am. Chem. Soc. 124, 1424 (2001).

[12] J. D. Holmes, K. P. Johnston, R. C. Doty, and B .A. Korgel, Science 287, 1471

(2000).

[13] M. V Wolkin, J.Jorne, P. M. Fauchet, G. Allan, and C. Deleme, Phys. Rev. Lett.

82, 197 (1999).

[14] Y. Arakawa and H. Sakaki, Appl. Phys. Lett. 40, 939 (1982).

[15] T. Someya, H. Akiyama, and H. Sakaki, Phys. Rev. Lett. 74, 3664 (1995).

[16] P. Ils, M. Michel, A. Forchel, I. Gyuro, M. Klenk, and E. Zielinski, Appl. Phys.

Lett. 64, 496 (1994).

[17] M. S. Gudiksen, L. J. Lauhon, J. Wang, D. C. Smith, and C. M. Lieber, Nature

_London_ 415, 617 (2002).

[18] Y. Wu, R. Fan, and P. Yang, Nano Lett. 2, 83 (2002).

[19] T. Mokari, E. Rothenberg, I. Popov, R. Costi, and U. Bnin, Science 304, 1787

(2004).

[20] J. Goldberger, R. He, Y. Zhang, S. Lee, H. Yan, H-J. Choi, and P. Yang, Nature

(London) 422, 599 (2003).

[21] J. F. Wang, M. S.Gudiksen, X. EDuan, Y. Cui, and C. M. Lieber, Science 293,

1455 (2001).

[22] N. Yamamoto, S. Bhunia and Y. Watanabe, Appl. Phys. Lett. 88, 153106 (2006).

Figure 2.1 The schematic showing of isotropic liquid phase.

Figure 2.2 The schematic showing of nematic liquid crystal phase.

(a)

(b)

Figure 2.3 The schematic showing of (a) smectic-A liquid crystal phase,

(b) smectic-C liquid crystal phase.

Figure 2.4 The schematic showing of cholesteric liquid crystal phase,

where is the director.

**Figure 2.5 The schematic showing of smectic-C* liquid crystal phase.**

(a) (b)

(c)

Figure 2.6 The schematic showing of (a) splay, (b) twist, and (c) bend

deformations in liquid crystal.

Figure 2.7 The schematic showing of three principal viscosity coefficients η

₁

, η

_2,

and η

_3.

Figure 2.8 Nematic LC under an external bias (a) △ε> 0 (b) △ε< 0.

Figure 2.9 The ionic charges induced by an external field in LC cell.

Figure 2.10 The schematic showing of basic geometries of the dielectric

reorientation of nematic liquid crystals (

^△ε>0)

. On the left hand side, the

initial states distinguish by different starting orientations. On the right

hand side, the deformed states above the threshold are illustrated.

Figure 2.11 Polarized excitation and emission spectraof nanowires. (A) Excitation spectra of a 15-nm-diameter InP nanowire. These spectra were recorded with the polarization of the exciting laser aligned parallel (solid line) and perpendicular (dashed line) to the wire axis. The polarization ratio, ρ, is 0.96. Inset, plot of the polarization ratio as a function of energy.

(B) Emission spectra of the same wire as in (A). These spectra were taken with the excitation parallel to the wire, while a polarizer was placed in the detection optics. The polarization ratio of the parallel (solid line) to perpendicular (dashed line) emission is 0.92. The spectra were taken with integration times of 10 s. Inset, plot of the polarization ratio as a function of energy. Reprinted with permission from J. F. Wang et al., Science 293.

1455(2001).

Figure 2.12 CL spectra from the nanowire region and substrate region taken for the p(solid spots) and s(open spots) polarization directions. The polarization ratio, ρ, is only 0.5. Reprinted with permission from Appl.

Phys. Lett. 88, 153106 (2006).

Chapter 3 Experiment

3.1 Micro-Photoluminescence [1]

3.1.1Principles and Applications of Micro-Photoluminescence

For a perfect semiconductor crystal, a light source with photon energy higher

than the band gap of the semiconductor crystal will excite the carriers to their excited

states. As soon as the excitation occurs, all excited electrons and holes will relax to

the bottom of the conduction band and the top of valence band, respectively, and then

the radioactive recombination may occur under the condition of momentum

conservation as shown in Figure 3.1. When the maximum of the valence band and the

minimum of the conduction band occur at the same value of the wave vector k,

transitions are direct and the material is a direct-gap semiconductor (for instance,

GaAs and GaN). For a direct-gap material, the most probable transition is across the

minimum energy gap which is between the most probably filled states at the minimum

of the conduction band and the states most likely to be unoccupied at the maximum of

the valence band. If the band extreme do not occur at the same wave vector k, the

transition is indirect. To hold the condition of momentum conservation in such an

indirect-gap material (for example, Si and Ge), the participation of phonons is

required. Such a process is also called a phonon-assisted process. Therefore, the

recombination of electron-hole pairs must be accompanied by the simultaneous

emission of a photon and a phonon. The probability of such a process is significantly

lower as compared with direct transitions. The radioactive recombination that is

caused by the incandescence coming from hot source is called photoluminescence

(PL). As shown in Figure 3.2, for example, if there is a multiplicity of excited states,

only transitions from the lowest excited state can generally be observed at low

temperatures because of rapid thermalization [2]. Figure 3.3 illustrates the process of

photoexcitation, as well as different processes that may cause light emission. If a

photon with its energy higher than the band gap of the sample, an electron in the

valence band will be excited to conduction band and soon dribbles down to the

bottom of conduction band by reaching thermal equilibrium with the lattice, i.e.,

emitting phonons. Figure 3.3(a) is an interband transition. In this case, a direct

recombination between an electron in the conduction band and a hole in the valence

band results in the emission of a photon of energy Eg =hν Although this recombination

occurs from states close to the corresponding band edges, the thermal distribution of

carriers in these states will lead, in general, to a broad emission spectrum. If the

semiconductor is pure, the recombination will be between electrons in the conduction

band and holes in the valence band. As the temperature is sufficiently low (e.g., less

than 25 K for GaAs), an electron and a hole will form a bound state due to the

Coulomb interaction. This electron-hole pair is the so-called exciton. The

recombination of an exciton will give rise to sharp-line luminescence with energy of

the band gap minus the binding energy of the exciton. Figure 3.3(b) shows an

excitonic transition. If the semiconductor contains impurities, several new

recombination paths via the impurity states open up. Electrons from the conduction

band may recombine with neutral acceptors which become negatively charged after

recombination (as shown in Fig. 3.3(c)). Neutral donors may recombine with holes in

the valence band, becoming positively charged (as shown in Fig. 3.3(d)). At higher

impurity concentrations electrons bound to donors may recombine directly with holes

bound to acceptors, giving rise to donor–acceptor pair luminescence (as shown in Fig.

3.3(e)). A third category of impurities is isoelectronic impurities, where the impurity

has the same valency as the atom it replaces in the host lattice. The isoelectronic

impurities may bind excitons, which can give luminescence, substantially below the

energy of free excitons. Luminescence studies are, in general, a very powerful method

for obtaining information about impurities, also at low concentrations. It should also

be noted that not all recombination between electrons and holes results in light

emission, since there may also be efficient nonradiative recombination paths. PL is

one of the most useful optical methods for the semiconductor industry [2, 3], with its

powerful and sensitive ability to find impurities and defect levels in silicon and group

III-V element semiconductors, which affect materials quality and device performance.

A given impurity produces a set of characteristic spectral features. This fingerprint

identifies the impurity type, and often several different impurities can be seen in a

single PL spectrum. In another use, the full width at half maximum (FWHM) of PL

peak is an indication of sample quality and crystallinity, although such analysis has

not yet become highly quantitative. Besides, PL is sensitive to the strain field inherent

in the semiconductor heterostructures, and can measure the magnitude and the

direction of the strain field. Photoluminescence can also determine the band gaps of

semiconductors. This is very important for binary (AxB1-x) and ternary (AxB1-xC)

alloys whose gaps vary with the compositional parameter x which must be accurately

known for applications. When the relation between gap energy and x is known, the PL

measurement of gap can be inverted to determine x. From this, a two-dimensional

map of alloy composition can be obtained as the exciting laser beam is scanned across

the surface of the sample, which is a useful tool to determine inhomogeneity.

Among the optical characterization methods, PL are probably the best developed

to carry out such spatial scanning, with commercial equipment available. An

interesting PL measurement with the aid of a polarizer can help us study the optical

anisotropy of semiconductor heterostructures. By way of this method, we are able to

investigate the microstructure of the sample and the mechanism of the radioactive

recombination of the electrons and the holes in detail.

3.1.2 The Apparatus for Micro-Photoluminescence Measurement

The micro-PL arrangement is the most straightforward measurement in optical

system as shown in Figure 3.4. The excitation source can be any laser whose photon

energy is higher than the band gap of the materials to be examined, and whose power

is sufficient to excite an adequate signal. In our measurements, a laser beam with 374

nm is focused into a microscope to be the excitation source. The luminescence from

sample is again focused into the microscope and pass through optical fiber then enters

a TRIAX 320 spectrometer. Finally, a high response H5783 photomultiplier tube is

employed as the detector. The signal from detector switched by SACQ2 sends to

computer. These photons can be generated at continuous powers of watts. Usually,

tens of mW are often adequate to give good signals. The intensity of the Micro-PL

signal apparently depends on the quality of the materials to be examined, the handling

ability of the system, and the sensitivity of the detector.

3.2 Transmission Electron Microscope (TEM)

A main TEM system consists of electron gun, condenser system and objective

lens. The electrons are generated and accelerated to required high energy by electron

gun. A condenser system is set up of different magnetic lenses and apertures makes it

possible to get either a parallel beam (micro probe for TEM) or a convergent beam

with selected convergence angles (nano probe for STEM and CBED). Furthermore,

the beam can be scanned (STEM) or tilted (DF-TEM). Most important objective lens

in the microscope since it generates the first intermediate image, the quality of which

determines the resolution of the final image. Images and diffraction pattern can

directly be observed on the viewing screen in the projection chamber or via a TV

camera mounted below the microscope column. Images can be recorded on negative

films, on slow-scan CCD cameras or on imaging plates. Schematic representation of

TEM is shown in Figure 3.5.

References

[1] K. J Wu, Master Thesis, N. T. U., Taiwan (2006).；K. C. Chu, Doctoral

dissertation, N.T.U., Taiwan (2005).

[2] R. A. Stradling and P. C. Klipstein, in Growth and Characterisation of

Semiconductors (Hilger, 1990).

[3] S. Perkowitz, in Optical Characterization of Semiconductors: Infrard, Raman, and

Photoluminescence Spectroscopy (Academic Press, 1993).

Figure 3.1 Energy transition in (a) direct and in (b) indirect gap semiconductor between initial states and final states.

Figure 3.2 The schematic representation of low temperature

photoluminescence (after R. A. Strading and P. C. Klipstein).

Figure 3.3 Illustration of different processes that can give rise to light emission in semiconductor.

(a) The band to band recombination.

(b)Excitonic recombination.

(c)Free hole-neutral donor recombination.

(d)Free electron recombines with a hole on a neutral acceptor.

(e)Donor-acceptor recombination.

Figure 3.4 The schematic diagram of the experimental setup used in the optical measurement.

Figure 3.5 Schematic diagram of TEM.

Chapter4

Color-tunable light emitting device based on the mixture of CdSe nanorods and dots embedded in liquid crystal cells

4.1 Introduction

One-dimensional nanostructures, such as nanorods, nanowires, and nanotubes,

etc., have become a class of attractive materials as their geometric anisotropy gives

rise to unique physical properties [1-8]. For example, the emission and absorption

spectra arising from one-dimensional semiconducting wires can be highly anisotropic,

and hence serve as an excellent candidate for the application in polarized

optoelectronic devices. On the other hand, liquid crystal (LC) is an anisotropic fluid,

which is thermodynamically between isotropic fluids and crystalline solid. The most

useful property of LC lies in the fact that its molecular orientation can be easily

controlled via an external bias. On this basis, numerous applications have been

established, among which one prominent case should be ascribed to the liquid crystal

display (LCD). Combining zero and one-dimensional semiconductor nanostructures

with the well developed LCD technology, herein, we propose the feasibility of

designing a novel color-tunable light emitting device. We ingeniously demonstrate a

color-tunable emission device by embedding semiconductor nanorods and quantum

dots in a LC cell. The underlying mechanism is as follows. Nanorods will align along

the orientation of LC molecules due to a large alignment energy caused by the

enhanced anchoring force through ampled surface area in nanomaterials. When the

orientation of LC molecules is altered by an external bias, the reorientation of the

nanorods will follow that of liquid crystal through the minimized elastic energy of

interaction via the electric field. Because the emission of nanorods is strongly

anisotropic, and that of quantum dots is spherically symmetric, i.e. isotropic, we

therefore can fine-tune the ratio of the emission intensity between nanorods and

quantum dots. If we intentionally select nanorods and quantum dots with different

emissive wavelengths, the resulting emission color of this newly designed device

could thus be manipulated. Our result elaborated here should be very useful for the

future development of smart optoelectronic devices.

4.2 Experiment

4.2.1 Sample preparation

Syntheses of CdSe quantum dots and nanorods have been well documented

[9-12]. In this study, CdSe quantum dots were synthesized by a previously reported

protocol [12], and CdSe nanorods were synthesized according to the reported method,

except for a slight modification regarding the usage of surfactants [13]. In brief, a

selenium (Se) injection solution containing 0.073 g of Se was prepared by dissolving

Se powder in 1 ml of tri-n-octyl phosphine. 0.20 g of CdO and 0.71 g of tetradecyl

在文檔中液晶摻雜硒化鎘奈米柱與量子點製作可調控發光元件 (頁 22-0)