Chapter 2 Theoretical background
2.2 Quantum effect
2.2.1 Quantum confinement effect
Models explaining the confinement of charged particles in a three-dimensional potential well typically involve the solution of Schrodinger’s wave equation using the Hamiltonian[25]
V U
Variation between treatments generally originates from differences in expressions assigned to V0 which normally will is accompanied by the Coulombic interaction term U. Boundary conditions are imposed forcing the wave functions describing the carriers to zero at the walls of the potential well. Two regimes of quantization are usually distinguished in which the crystallite radius R is compared with the Bohr
radius of the excitons or related quantities: weak confinement: and strong confinement: .
aB
R≥ aB
R<
In the first case crystallite radius is larger than the exciton. As a consequence, the motion of center of mass of the exciton is quantized while the relative motion of electron and hole given by the envelope function φ(re −rh) is hardly affected. In the second case the Coulomb energy increases roughly with R-1, and the quantization energy with R-2, so that for sufficiently small values of R one should reach a situation where the Coulomb term can be neglected.
2.2.1.1 Weak confinement [26]
Coulomb-related correlation between the charged particles handled through the use of a variational approach involving higher-order wave function of the confined particles, and we can not neglect the electron hole Coulomb potential. The Schrodinger equation may be written as
− − ∇ Ψ+ + e− h Ψ= tΨ
with M =me +mh,
Ψ and consider Coulomb interaction first, then we get − ∇R +V R R = EcΨ
Here is resulting from the inclusion of Coulomb interaction. Then we consider the confinement potential
Eex and the absorption energy of a photon is
t c ex g Eex
The size quantization band states of the electron and hole dominates for the kinetic energies of electron and hole are larger than the electron-hole Coulomb potential, and the effect of the Coulomb attraction between the electron and hole can be treated as a perturbation. Then the Schrodinger equation becomes
− − ∇ Ψ+V Ψ =EΨ
and the energy of a electron or hole is
, 1,2,3...
The absorption energy of a photon is
2.2.2 Density of states (DOS)
The concept of density of states (DOS) is extremely powerful. Important physical properties such as optical absorption, transport, etc., are intimately dependent upon this concept. The density of states is the number of available electronic states per unit volume per unit energy interval around an energy E. If we denote the density of states by N(E), the number of states in an energy interval dE around an energy E is N(E)dE. To calculate the density of states, we need to know the dimensionality of the system and the energy vs. wave vector relation or the dispersion relation that the electrons obey.[27]
2.2.2.1 Density of state for a three-dimensional system
In a three dimension system, the k-space volume between vector k and k + dk is (see Figure 2-2) 4πk2dk. We had shown above that the k-space volume per electron state is 3(2π/L). Therefore, the number of states of electron in the region between k and k+ dk are
Denoting the energy and energy interval corresponding to k and dk as E and dE, we
see that the number of electron states between E and E+ dE per unit volume is
= , then the equation becomes
3 2
2.2.2.2 Density of states for lower-dimensional systems
If we consider a 2-D system, a concept that has become a reality with use of quantum wells, similar arguments tell us that the density of states for a parabolic band is
We notice that as the dimensionality of the system changes, the energy dependence of the density of states also changes. In three-dimensional systems we have a E1/2-dependence as shown in Figure 2-3. In 2-D systems there is no energy dependence (Figure 2-3), while in 1-D systems, the density of states has a peak at E=0
(Figure 2-3). The variations related to dimensionality are extremely important and is a key driving force to lower dimensional systems.
2.3 X-ray diffraction
2.3.1 Lattice parameters
Most metals exhibit crystalline structures. The most common types of such structures are the simple cubic (SC), the face-centered cubic (FCC) and the wurtzite structure, etc. By diffracting X-rays with a wavelength comparable to the lattice constant, the lattice constant can be found by means of the diffraction pattern. For hexagonal unit cell which is characterized by lattice parameters a0 and c0, the plane spacing equation for the hexagonal structure is:[28]
2 wavelength of x-ray source. So the equation becomes
2
thus the lattice parameters can be estimated.
2.3.2 Debye-Scherer formula [29]
Consider now the path difference between successive planes when the incident beam remains fixed at the Bragg angle θ as Figure 2-4, but with the diffracted ray leaving at an angle θ+ ∆θ, corresponding to the intensity I in the spectrum line an angular
distance ∆θ away from the peak. The path difference between waves from successive planes is now [30]
)
with BC and CE being the path differences between the successive incident beams, and d is the interplanar distance. If ∆θ is small, we can write cos∆θ=1 and sin∆θ=∆θ, in which case
BC+CE =2dsinθ+d∆θcosθ =nλ+d∆θcosθ,
where λ is the wavelength of the incident X-ray. Therefore the phase δ per interplanar distance is
θ θ
Since a phase difference of 2nπ produces the same effect as zero phase, we can write the effective phase difference as
θ θ λ
δ = 2π d∆ cos .
We obtained the result that the distribution of intensity I in a spectrum line a distance R from the grating is effectively
and the maximum intensity is
2
where φ is the amplitude at unit distance from the grating, N is the total number of
grating apertures, and δ is the phase change per aperture; or
N will change much faster than 2
δ , the sine square function will reach its
first minimum before
The solution to the equation yields the required phase change corresponding to the half maximum. It may be obtained
where λ is the wavelength of the x-ray source, and D is the size of the particles.
2.4 Photoluminescence characterization[31]
An electron was excited from the valence to the conduction band by absorption of a photon. In this process, we bring the system of N electrons from the ground state to an excited state. We need for the understanding of the optical properties of the electronic system of a semiconductor is therefore a description of the excited states of the N-particle problem. The quanta of these excitations are called “excitons”.
Indeed excitons in semiconductors form, to a good approximation, a hydrogen or positroium like series of states below the gap. For simple parabolic bands and direct-gap semiconductor one can separate the relative motion of electron and hole and the motion of the center of mass. This leads to the dispersion relation of excitons in Figure 2-5.
and wave vector of the exciton.
The exciton state has an effective Rydberg energy modified by the reduced mass of electron and hole and the dielectric constant of the medium in which these particles move. Some of the defects can bind an exciton resulting in a bound exciton complex (BEC). In Figure 2-6 we visualize excitons bound to an ionized donor (D
Ry*
+X), a neutral donor (D0X), and a neutral acceptor (A0X). An ionized acceptor does not usually bind an exciton since a neutral acceptor and a free electron are energetically more favorable. The binding energy of an exciton (X) is the highest for a neutral acceptor (A0X complex), the lower for a neutral donor (D0X) and the lower
still for an ionized donor (D+X). The binding energy Eb of exciton to the complex usually increases according to
EDb+X <EDb0X < EAb0X.
The binding energy is defined as the energetic distance from the lowest free exciton state at k=0 to the energy of the complex. There is a rule of thumb, known as Hayne’s rule, which relates the binding energy of the exciton to the neutral complex with the binding of the additional carrier to the point defect.
2.5 Raman spectroscopy
Raman spectroscopy is based on the Raman effect [32]. When photons from a laser are scattered from a crystal with emission or absorption of phonons, the energy shifts of the photons are small, but can be measured by interferometric techniques.
Usually, the phonon wave vectors are very small compared to the size of the Brillouin zone so that the interactions are only with zone center phonon. Thus, one can have interaction with either the zone center acoustic phonons or the optical phonons.
Once again, one can write the conservation laws for energy and momentum. It must be remembered that the wavevectors containing the refractive index n,
)
where q and q’ are the photon wavevectors in free space. The upper sign corresponds to a phonon absorption (the process is called anti-Stokes scattering) while the lower sign corresponds to an emission (Stokes scattering). Since q and q’ are very small, G has to be zero. The anti-Stokes and Stokes scattering are shown in Figure 2-7. The anti-Stokes mode is usually much weak than the Stokes mode, and it is Stokes-mode scattering that is usually monitored.
When light is scattered from the surface of sample, the scattered light is found to contain mainly wavelengths that were incident on the sample (Rayleigh scattering) but also different wavelengths at very low intensities (few parts per million) that represent an interaction of the incident light with material. The interaction with acoustic phonons is called Brillouin scattering while the interaction with optical is call Raman scattering. Optical phonons have higher energies than acoustic phonons giving larger photon energy shifts. Hence Raman scattering is easier to detect than Brillouin scattering. Subsequently, Raman scattering is a vibrational spectroscopic technique that can detect both organic and inorganic species and measure the crystalline of solids.
Figure 2-1 Schematic of the rotes that one could follow within the scope of sol-gel processing.
Figure 2.2 Geometry used to calculate density of states in three, two and one dimensions.
Figure 2.3 Variation in the energy dependence of the density of states in a) three-dimensional b) two- dimensional c) one- dimensional systems.
Figure 2-4 The crystalline planes of the materials.
Figure 2-5 A pair excitation in the scheme of valence and conduction bands (a) in the exciton picture for a direct gap semiconductor (b).
Figure 2-6 Visualization of an exciton bound to an ionized donor (a), a neutral donor (b), and a neutral acceptor(c)
Figure 2-7 The picture of anti-Stokes and Stokes scattering processes.
Chapter 3 Experiment detail
3.1 Sample preparation
We produce monodisperse ZnO colloidal spheres by sol-gel method. Sol-gel method was chosen due to its simple handling and narrow size distribution. The ZnO colloidal spheres were produced by a one-stage reaction process similar to that described by Seelig et al [33], and reactions were described as the following equations: Eq. (1) is the hydrolysis reaction for Zn(OAc)2 to form metal complexes. We increased the temperature of reflux from RT to 160oC and maintained for aging. The zinc complexes will dehydrate and remove acetic acid to form pure ZnO as Eq. (2) during the aging time. Actually, the two reactions described above proceed simultaneously while the temperature is over 110oC. All chemicals used in this study were reagent grade and employed without further purification. In a typical reaction, zinc acetate dihydrate (99.5% Zn(OAc)2, Riedel-deHaen) was added to diethylene glycol (99.5% DEG, EDTA). The first thing we notice is that we can control the quantum dots size with domination concentration of zinc acetate in the solvent (DEG). This point will be examined later. Then the temperature of reaction solution was increased to 160℃ and maintained for different aging time.
White colloidal ZnO was formed in the solution that was employed as the primary solution. Jezequel[34] et al., reported that this method produce monodisperse ZnO
primary reaction was performed as described above, and the product was placed in a centrifuge. The supernatant (DEG, dissolved reaction products, and unreacted ZnAc and water) was decanted off and saved, and the polydisperse powder was discarded.
Finally, the supernatant was then dipped on substrates (SiO2/Si (001) or SiO2) and dried at 150℃.
3.2 Microstructure and optical properties
3.2.1 X-ray diffraction
The crystal structures of the as-grown powder were inspected by Bede D1 diffractometer at Industrial Technology Research Institute using a CuK X-ray source (λ=1.5405Å). We used small angle diffraction. The ω was fixed at 5∘, the scanning step was 0.04∘, scanning rate was 4 degree/min and count time was 1.00 second. Figure 3-2 shown XRD ω-2θ scans geometry. The dashed lines mean the trajectory of the incident beam and the detector to be in motion.
The sizes of the nanocrystallites can be determined by X-ray diffraction using the measurement of the full width at half maximum (FWHM) of the X-ray diffraction lines. The average diameter is obtained by
θ λ cos
89 . 0
D= B , where D is the average diameter of the nanocrystallite, λ is the wavelength of the X-ray source, and B is the FWHM of X-ray diffraction peak at the diffraction angle θ.
3.2.2 Optical absorption spectra
Optical transmission or absorption measurements are routinely used by chemists to
determine the constituents of chemical compounds. They are also used in the semiconductor industry, but only for certain specialized applications. We can compute the band-gap of the semiconductors by the absorption spectra.
The excitation and emission spectra were measured using U-4001 Spectrometer (Japan Spectroscopy) at Industrial Technology Research Institute with a lamp source of 150 W xenon. Fist, we must find and take out background signal from preparation sample. Measurements were performed using a glass having a path length of 2 mm. The intensity of emitted light was detected at a right angle to the incident light. Finally, we measured preparation sample (ZnO solution dip on SiO2
glass). Judging from the above, it can be concluded that background signal was deleted as we measure preparation sample. The measurement was taken in the range from 300 nm to 400 nm.
3.2.3 Photoluminescence system
Photoluminescence (PL) provides a non-destructive technique for the determination of certain impurities in semiconductors. The shallow-level and the deep-level of impurity states were detected by PL system. It was provided radiative recombination events dominate nonradiative recombination.
In the PL measurements, the 325 nm line from a He–Cd laser was used as the excitation light. Light emission from the samples was collected into the TRIAX 320 spectrometer and detected by a photomultiplier tube (PMT). As shown in Fig. 3-3, the diagram of PL detection system includes mirror, focusing and collecting lens, the sample holder and the cooling system. We utilized two single-grating monochromators (TRIAX 320), one equipped with a CCD detector (CCD-3000), and
photon counter for detection. The normal applied voltage of PMT is 800 KV.
Moreover, we used a standard fluorescent lamps to calibrate our spectral response of spectrometer and detector. The PL signals are exposed about 0.1 sec at the step of 0.1 nm. The data are transmitted through a GPIB card and recorded by a computer.
The monochromator (TRAIX 320) has a focal length of 32 cm with an optional side exit slit and has three selective 600, 1200 and 1800 grooves/mm gratings. When the entrance and exit slits are both opened to about 50 µm, the resolution is about 0.1 nm for the monochromator with PMT. The low-temperature PL measurements were carried out using a closed cycle cryogenic system.
3.2.4 Raman system
Raman scattering is a very powerful probe for investigating the vibration properties of materials. It is also influential in understanding problems as diverse as the structure of amorphous insulators, and the conduction mechanisms in ionic conductors. The experimental setup of Raman spectroscopy consists mainly of three components: a laser system serves as a powerful, monochromatic light source and a computer controlled spectrometer for wavelength analysis of the inelastically scattered light.
Figure 3-4 show the experimental setup schematically. The Raman scattering was measured with an Ar-ion laser (Coherent INNOVA 90) as an excitation source emitting at a wavelength of 488 nm. The scattered light was collected by a camera lens and imaged onto the entrance slit of the Spex 1877C. Light passes through the entrance (S1) to be collimated by M1 onto G1 where it is dispersed onto M2. After passing through S2, which acts as the filter stage to determine the pass band, the light strikes the spatial-filter mirror (M3) and passes though a fixed slit, which eliminates much of the stray light. Again the light is collimated (M4), dispersed (G2), in an
opposing direction to cancel the effects of the initial dispersion, then focused (M5) onto the exit slit of the filter stage (S3) which controls the resolution of the next spectrograph stage. In this final stage, the light is again collimated (M6) and dispersed on whichever of the turreted gratings (G3, G4 and G5 as gratings of 600, 1200 and 1800 grooves/nm, respectively) is selected by the user. The camera mirror (M7) projects a flat image onto the focal plane where it is seen by CCD.
Chemical reagent Molecular formula Degree of purity
Source
Zinc acetate dehydrate Zn(CH3COOH)2‧2H2O 99.5% Riedel-deHaen
Diethylene glycol C4H10O3 99.5% EDTA
Table 3.1. Shows that chemical reagent was used with sol-gel experiment. process.
Figure 3.1. Experiment equipment used for fabricating ZnO quantum dots (QDS).
separating solution
dip or spin coating on SiO2/Si(001)
Clear solution Centrifuge
heating up to 160 & ℃ difference aging time White colloidal formed
varying heating rate Counter flow apparatus
varying solution concentration Diethylene-glycol (DEG)
Zn(CH3COOH)2‧2H2O
Table 3.2. A flow chart of fabricate ZnO quantum dots (QDS) by sol-gel method.
Figure 3-2 XRD ω-2θ scans geometry for ZnO nanoparticles.
Figure 3-3 PL detection system.
Figure 3-4 Raman detection system.
Chapter 4 Results and discussion
4.1 HRTEM and X-ray diffraction
measurement
Shown in Fig. 4-1(a) is a typical high-resolution transmission electron microscope (HRTEM) image of the ZnO nanoparticles. Nanoparticles aged at 160 °C for 1 h and solution concentration of 0.06M was selected for particle size determination by HRTEM. The particles shape are predominantly spherical, many also exhibit surface facetting, as shown in the inset of Figure 4-1(a) where a step of one atomic layer can be seen. The nanoparticles are clearly well separated and essentially have some aggregation. Figure 4-1(b) show the size distribution of particles after aging at 160°C for 1 h (0.06M), obtained from analysis of more than 35 particles per sample.
The average diameter of the number-weighted particles obtained from a colloid aged at 160°C for 1 h (0.06M) was determined to be 4.36± 0.3 nm.
The XRD patterns of the prepared sample (ZnO solution dip on SiO2 glass) by the sol-gel process are shown in Figure 4-2. The diffraction lines are the powder X-ray diffraction pattern of the ZnO nanoparticles prepared in a different solution concentration. The diffraction pattern and interplane spacings can be well matched to the standard diffraction pattern of wurtzite ZnO, demonstrating the formation of wurtzite ZnO nanocrystals. All of the samples present similar XRD peaks that can be indexed as the wurtzite ZnO crystal structure with lattice constants a=3.253Å and c=5.219Å by Eq. 2-8, which are consistent with the value in the standard card (JCPDS 36-1451). No diffraction peaks of other species could be detected that indicates all
the precursors have been completely decomposed and no other crystal products were formed. It should be noted here that the full width at half maximum (FWHM) of the diffraction peaks increase with decreasing the concentration of zinc precursor duo to the size effect. The mean diameter of the ZnO nanocrystallites is evaluated from the FWHM of the (110) peak from 3.5nm to 12nm by Eq. 2-9 with the range of B from 0.75 to 2.45 , θ= 47.56 and λ (wavelength of incident X∘ ∘ ∘ -ray) is 1.5406Å. This value corresponds to the tail of the particle size distribution determined from HRTEM micrographs (Figure 4-2 (b)) and is close to the value of 4.2 nm obtained from the absorption data (see next section).
4.2 Absorption and Photoluminescence
Spectra
Fig. 4-3 illustrates the room temperature optical absorption (dotted lines) and PL (solid line) spectra of different ZnO quantum dots with reacting solution concentration from 0.04M to 0.32M with aging 1h at 160 . ℃ The photoluminescence (PL) spectra of the six samples, which were excited with the laser of wavelength 325nm, are shown in Fig. 4-3 (solid line). An ultraviolet-blue (UV blue) emission occurs above the band gap energy of bulk ZnO (3.3 eV) and shifts to higher energies (3.3–3.435 eV) as the QD size decreases (12–3.5 nm). Since the Bohr diameter of the exciton in bulk ZnO is on the order of 2.34 nm, we must consider the electron hole Coulomb interaction in our samples and the particles are in the moderate to weak confinement regime.
The absorption spectra are significantly blue-shifted compared to the bulk single