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Dielectric confinement effect in ZnO quantum dots embedded in amorphous SiO2 matrix
View the table of contents for this issue, or go to the journal homepage for more 2007 J. Phys. D: Appl. Phys. 40 6071
(http://iopscience.iop.org/0022-3727/40/19/046)
J. Phys. D: Appl. Phys. 40 (2007) 6071–6075 doi:10.1088/0022-3727/40/19/046
Dielectric confinement effect in ZnO
quantum dots embedded in amorphous
SiO
2
matrix
Yu-Yun Peng
1, Tsung-Eong Hsieh
1,3and Chia-Hung Hsu
21Department of Materials Science and Engineering, National Chiao-Tung University, 1001 Ta-Hsueh Road, Hsinchu, Taiwan 300, Republic of China
2Research Division, National Synchrotron Radiation Research Center, Hsinchu, Taiwan 300, Republic of China
E-mail:[email protected],[email protected]@nsrrc.org.tw
Received 21 June 2007 Published 21 September 2007
Online atstacks.iop.org/JPhysD/40/6071
Abstract
The dielectric confinement effect on the blue shift Eg(a)of the ZnO
quantum dots (QDs) embedded in the SiO2matrix is evaluated by applying a
multi-shell two-electron system model. The experimental measurement and the calculations of various dielectric structures indicate that the composite matrix structure provides a better estimation of the blue shift of the ZnO QDs–SiO2system than the multi-shell structure. The proportionality factor
xdefined in this work exhibits a dependence of the dielectric confinement energy on the specific dimension ratio (the b/a ratio) and the dielectric constant εmatrixof the outer matrix. The result of the calculation also shows
the limit of the two-electron system in estimating the ground-state energy of samples with high dot density. However, the correlation shows the existence of the strong dielectric confinement effect in ZnO QDs–SiO2thin films and
allows a better understanding of the semiconductor QDs–dielectric systems.
1. Introduction
Research on semiconductor quantum dots (QDs) coated with or embedded in various dielectric materials has attracted much attention in recent years. The unique characteristics of such nanostructures are affected not only by the quantum confinement [1] resulting from the nanoscale dimension but also by the dielectric confinement on the electron energies [2–7] and the polarization effect at the unstable surface of QD [8–10]. Previous studies reported that the dielectric environment could effectively change the optical [11–13] and transport [14–17] properties of semiconductor QDs. Many techniques have also been proposed to build a nanostructured semiconductor with a low dielectric-constant matrix into a single-electron device and deliver specific luminescence [12,13] and single-electron tunnelling [1,15,16] properties. Besides distinct optical and electrical properties, a single-electron device enables the integration in a bioenvironment 3 Author to whom any correspondence should be addressed.
with extremely low power consumption and small current operation, which is quite significant in the application to biotechnology.
The realization of semiconductor QD/dielectric systems in functional devices requires an in-depth understanding of the dielectric effect. The theory of the interaction of the attractive electron–hole Coulomb force and the effect of surface dielectric polarization on semiconductor QDs was introduced in the early 1980s [18,19]. Surface polarization is induced when charge accumulation in a QD encounters a dielectric mismatch at the QD/matrix interface. Such a polarization effect can lead to a great influence on the confined electron states [20–23], as a result of the creation of extra energies by a single electron interacting with its induced polarization. Further, two (or more) electrons in a QD will interact with the induced polarization created by each other and result in more extra energies. Therefore, the extent of the dielectric confinement is determined by the magnitude of the surface polarization. Consequently, a QD embedded in a glass matrix or liquid solution generally produces stronger confinement than a QD epitaxially grown, due to the substantial
Y-Y Peng et al
Table 1. The variations of the optical bandgaps Egand the corresponding parameters of ZnO QDs–SiO2thin films. The radius
aof ZnO QDs was obtained by the histogram with a Gaussian curve fitting and the b/a ratio is the specific dimension ratio. In ZnO QD–SiO2thin films, b is the distance from a dot centre to the surface of the neighbouring dot. With the ZnO volume ratio obtained by the x-ray reflectivity measurement, the b/a ratio could be calculated by assuming the randomly distributed QDs in a closest-packing arrangement. The dielectric constant εmatrixwas estimated by the Maxwell-Garnett approximation [32].
a(nm) Eg(eV) VZnO(%) b/a εmatrix 1.76 3.77± 0.04 13.86 2.865 4.376 1.90 3.65± 0.03 19.55 2.446 4.583 2.09 3.57± 0.05 22.75 2.276 4.703 2.52 3.44± 0.04 38.95 1.740 5.345 2.78 3.39± 0.04 43.56 1.638 5.540 3.09 3.31± 0.03 57.26 1.409 6.155 3.27 3.28± 0.04 77.36 1.178 7.168
difference in the dielectric constant and the higher barrier potential.
The effects of the dielectric environment on various semiconductor QDs such as Si, InAs, InP and CdSe have been studied extensively [2–9]. The influence of the dielectric mismatch on the confinement energy of a QD has also been discussed based on the framework of the effective-mass approximation (EMA). This work investigates the dielectric confinement behaviour of a ZnO QD in the amorphous SiO2 matrix. The dielectric confinement energy produced
by the polarization effect is calculated by applying a multi-shell two-electron system model. Three dielectric structures are considered in the calculation and all exhibit similar confinement effects on a ZnO QD. In addition to the strong influence of the amorphous SiO2 dielectric on the optical
bandgap Egof ZnO QDs/SiO2nanocomposite films, the results
also illustrate the dependence of the dielectric confinement energy on the specific dimension ratio (b/a ratio) and the dielectric constant of the matrix εmatrix.
2. Experiment
ZnO QDs-SiO2 nanocomposite thin films were prepared by
the target-attached sputtering method without substrate heating and post annealing [24,25]. By changing the sputtering power and the Ar ambient pressure, the thin-film samples containing ZnO QDs with different dot radii and densities could be prepared. The microstructure was characterized by transmission electron microscopy ((TEM), Philips TECNAI 20 FEG Type). The ZnO volume ratios were calculated via the measurement of x-ray reflectivity performed in a Huber four-circle x-ray diffractometer operating at 50 kV and 200 mA with Cu-Kαradiation. The dot radius and volume ratio of each
specimen are listed in table1. Figure1shows several TEM images of the ZnO QDs-SiO2nanocomposite thin films with
different dot radii. It was found that ZnO formed nanoscale crystalline particles embedded in the amorphous SiO2matrix
[24,25]. TEM characterization revealed that the ZnO QDs with a small dot radius were completely surrounded by the amorphous SiO2matrix and well separated from each another.
In contrast, the coalescence of neighbouring QDs occurred in
Figure 1. TEM images of the ZnO QDs–SiO2nanocomposite films with different dot radii a. The increase in ZnO crystallinity can be observed in the samples with a high dot density.
samples with a large dot radius and a high dot density, and the crystallinity of ZnO QDs also increased.
The optical bandgap Eg of nanocomposite films was
determined via the absorption spectra obtained by a UV-visible spectrometer (SHIMADZU UV-1601PC) in the wavelength ranging from 250 to 800 nm. The variation of the Egwith the
dot radius is listed in table1. It is found that Egincreases from
3.28 to 3.77 eV with the decrease in the dot radius from 3.27 to 1.76 nm. The blue shift implies a stronger confinement effect than those of ZnO QDs embedded in air, water [26] and other dielectrics [27].
3. Results and discussion
3.1. Multi-shell two-electron system model
In order to demonstrate the influence of numerous dielectric interfaces on the dielectric confinement, a multi-shell two-electron system model was derived to evaluate the confinement effect in ZnO QDs-SiO2 nanocomposite films. The
multi-shell two-electron system model describes the two-electron ground-state energy of a spherical QD surrounded by periodic dielectric shell layers as illustrated in figure2(a). The model contains a centred QD with a radius of a and n surrounding shell layers. Overall, there are n interfaces in total, from the dot centre to the outermost dielectric. The thickness of the kth shell layer is denoted as b−a for k = odd and 2a for k = even. εk+1is the static dielectric constant of the kth shell.
When two electrons are put into the centred QD surrounded by a dielectric material, there arise three energy terms: the self-polarization energy Es(a), the direct Coulomb
energy Ec(a)and the induced polarization energy Ep(a).
The electrostatic interactions in the multi-shell two-electron system model can be solved by using the standard method [28] as well as that in the previous works presented by Babi´c et al [3] and Iwamatsu et al [4]. The self-polarization energy Es(a)is
Figure 2. (a) The schematic illustration of the multi-shell two-electron system model with n dielectric interfaces. (b), (c) and (d) are the three dielectric structures considered in the calculations: (b) structure 1, a single ZnO QD in the SiO2matrix, (c) structure 2 (composite matrix structure), a single ZnO QD within the ZnO–SiO2composite matrix and (d) structure 3 (multi-shell
structure), approximately the outer dielectric environment as a
multi-shell structure with periodic dielectric shell layers along the closest-packing direction.
formed when an electron inside the centred QD interacts with the polarization potential created itself and can be expressed as
Es(a)= e2 8π εoε1a 2π2 ∞ l=0 a2l+1Al 1 0 jo2(π x)x2l+2dx (1)
with the coefficient Algiven by
Al= (l + 1) n k >0 k= odd 1 a2l+1 Sk [1 + ((k− 1)/2)(1 + (b/a))](2l+1) + n k >0 k= even 1 a2l+1 Sk [(b/a) + ((k− 2)/2)(1 + (b/a))](2l+1) (2) Sk= εk− εk+1 εk+1+ l· (εk+ εk+1) . (3)
jois the spherical Bessel function of zero order and Skis the
dielectric mismatch coefficient for the self-polarization. The direct Coulomb energy Ec(a) arises when more than two
electrons are put into the centred QD and interact with each other and is given by
Ec(a)=
2.578 ε1a
. (4)
The induced polarization energy Ep(a) depicts the
interaction energy of the electron with the image charge created
by another electron, expressed as Ep(a)= e2 4π εoε1a n k >0 k= odd 1 a · Pk 1 + ((k− 1)/2)(1 + (b/a)) + n k >0 k= even 1 a Pk (b/a)+ ((k− 2)/2)(1 + (b/a)) , (5) Pk= εk− εk+1 εkεk+1 , (6)
where Pkis the dielectric mismatch coefficient for the induced
polarization. Both Es(a)and Ep(a)are related to the b/a
ratio, the parameter characterizing the multi-shell structure in the calculation. Hence, the concurrent effect on the blue shift Eg(a)of the QD as illustrated in figure2(a) can be ascribed
to the size-dependent quantum confinement energy EBrus
g (a)
and the dielectric confinement energy Edielectric
g (a)due to the
dielectric mismatch. It can be expressed as [2–4,23,29] Eg(a)= EgBrus(a)+ Egdielectric(a)= EgBrus(a)
+ [2Es(a)+ Ec(a)+ Ep(a)], (7)
EBrusg (a)= ¯h 2π2 2a2 1 m∗e + 1 m∗h − 1.8e2 εoε∞a. (8) EBrus
g (a)represents the quantum localization of the electron–
hole via a shielded Coulomb interaction in a single QD, i.e. the ground-state regardless of the polarization in Brus’ model [2,19]. m∗e and m∗h are the effective masses of the electron and hole, respectively, and ε∞is the high-frequency dielectric constant of the QD. In our calculation, the quantum localization and the perturbation energy of the Coulomb interaction are both related to the wave functions of the electron and hole which can be characterized by the effective radius aeff. Thus, we replace a
by aeffin equations (4) and (8). We note that the real dot radius
awas adopted in equations (2) and (5) since the perturbation energies of the potential generated by the dielectric mismatch with the electron wave function are mainly constrained by the real dimension of the potential well, the effective radius aeff
can be obtained by applying the finite potential model with the following equation [31] aeff= a + ¯h 2m∗b(Vo− Ee(a)) , (9)
where Vois the finite barrier potential, m∗bis the effective mass
of electron in the barrier region (SiO2matrix) and Ee(a)is
the electron confinement energy term in EBrus g (a).
3.2. Confinement behaviours in various dielectric environments
To evaluate the confinement behaviour of a reality ZnO QDs/SiO2 system, we designed three dielectric structures
based on the multi-shell two-electron system model:
(1) structure 1: a single ZnO QD embedded in the SiO2matrix
Y-Y Peng et al
Table 2. The parameters for the calculation of the dielectric confinement energy of QD in various dielectric structures. Structure 1 Structure 2 Structure 3
QD ZnO ZnO ZnO
Dielectric environment SiO2matrix ZnO–SiO2composite matrix ZnO/SiO2multishell
n 1 1 n
b/a ∞ ∞ a
ε ε1= εZnOε2= εSiO2 ε1= εZnOε2= ε( a)
matrix ε1= ε3= ε5= . . . = εZnOε2= ε4= ε6= . . . = εSiO2
aListed in table1.
Note: εZnO= 8.5, ε∞= 6, m∗e= 0.3mo, m∗h= 0.8mo[30]; εSiO2= 3.9, m∗b= 0.5mo; Vo= 4.3 eV = φZnO− φSiO2, φ= work function.
Figure 3. A comparison of experimental and calculated blue shifts
Egof different dielectric structures based on the multi-shell two-electron system model.
(2) structure 2 (composite matrix structure): a single ZnO QD embedded in the composite ZnO–SiO2matrix (figure2(c))
of which the dielectric constants εmatrixare calculated by
the Maxwell-Garnett approximation [32] with the ZnO volume ratio obtained from the measurement of x-ray reflectivity;
(3) structure 3 (multi-shell structure): a single ZnO QD embedded in the multi-shell dielectric environment comprising an alternative arrangement of SiO2and ZnO
shell layers (figure2(d)).
The parameters for the calculation are listed in tables1and
2. The calculation result and experimental data are presented in figure 3. The dashed–dotted line represents EgBrus(a),
the quantum localization derived by Brus without considering the effect of the outer dielectric environment. The uppermost dashed line represents ESiO2
g (a), the dielectric confinement
behaviour in structure 1, i.e. a single ZnO QD completely surrounded by the pure SiO2matrix. Figure3shows that the
composite matrix structure (structure 2) and the multi-shell structure (structure 3) exhibit similar dielectric confinement tendencies. However, the multi-shell structure predicts larger blue shifts Eg(a)and the values are almost superimposed
with those of structure 1, especially for samples with a smaller dot radius and a larger b/a ratio. An analogous behaviour is observed in the experimental data as well. The figure reveals that the experimental blue shifts Eg(a)are much smaller than
those calculated by both the composite matrix structure and the multi-shell structure. As for samples with a larger dot radius and a small b/a ratio, they tend to have experimental Eg(a)
values closer to that predicted by Brus, indicating a weaker dielectric confinement.
Accordingly, we conclude that the composite matrix structure provides a better approximation of the blue shift Eg(a)than the multi-shell structure, in spite of the difference
between the calculation and the experiment result suggesting an inadequacy of the two-electron system. The reason is ascribed to the basic assumption of the two-electron system which takes into account only a single positively charged QD. The ground-state energy thereof is evaluated by considering the perturbations of the induced polarization potential on the energy of electrons in the single QD. In practice, each ZnO QD in the SiO2 matrix behaves as an individual positive
space charge. The dielectric confinement energy is affected by the neighbouring positive charges since the polarization potential induced by the charge accumulation is thus different. Moreover, figure 3 shows a larger deviation between the calculated and the experimental blue shifts Eg(a)for samples
with a large dot radius and a small b/a ratio. This leads us to believe in the existence of the weakening confinement without being considered in the two-electron system, such as the wave function tunnelling effect, which usually occurs between QDs when they are very close to one another [33–35].
3.3. The correlations of the dielectric confinement energy In addition to the dielectric confinement effect described above, the experimental Eg(a)can be further expressed in terms of
EBrus g (a):
Eg(a)= EgBrus(a)+ E dielectric g (a)= E Brus g (a) + x· ESiOdielectric 2 (a), (10)
where ESiOdielectric2 (a)is the dielectric confinement energy of a single ZnO QD in the pure SiO2matrix (structure 1) and x
is defined as the proportionality factor, representing the level of the similarity between the material system and structure 1. The proportionality factor x of each sample can be obtained through the calculation and the experiment result. Figure4
shows the relations of the proportionality factor x versus the b/aratio and εmatrix. x increases linearly with the increase in
the b/a ratio and declines with the increase in εmatrix. It is
quite apparent that when the b/a ratio increases, the system becomes more and more like structure 1 and the value of x becomes closer to unit. The increase in the b/a ratio represents the decrease in the total amount and density of ZnO QDs within the sample, implying that the value of εmatrixgradually
approaches the dielectric constant of the pure SiO2matrix. The
correlation of the proportionality factor x with the b/a ratio and εmatrix not only demonstrates the influence of the outer
dielectric environment over the ground-state energy of QDs in nanocomposite thin films but also provides a simple method 6074
Figure 4. The relationships of the proportional factor x with the b/a ratio and the dielectric constant of the composite matrix εmatrix. The curve fittings show a linear dependence of the proportionality factor
xwith the b/a ratio while a gradual decay with the dielectric constant of the composite matrix εmatrix.
to evaluate the dielectric confinement effect in semiconductor QDs–dielectric systems.
4. Summary
In this work, we investigate the dielectric confinement effect on the blue shift Egof ZnO QDs embedded in the SiO2dielectric
by applying the multi-shell two-electron system model. The blue shift Egof ZnO QDs with different dielectric structures
is also calculated by considering the two-electron ground-state energy. In conjunction with the experimental data, we find that the composite matrix structure provides a better estimation of the blue shift Eg of the ZnO QDs–SiO2
system in comparison with the multi-shell structure. The relations of the proportionality factor x with the b/a ratio and the composite dielectric constant εmatrixindicate that the
magnitude of the dielectric confinement energy depends on the similarity of the system with the structure containing only a single ZnO QD inside the pure SiO2 matrix. The
correlation of the calculation and the experimental result shows the modulability of electron energy states of ZnO QDs embedded in the dielectrics, which provides versatile engineering applications of the semiconductor QDs–dielectric systems in opto-electronic devices in the future.
Acknowledgments
This work is supported by the National Science Council (NSC) of the Republic of China under the contract of NSC95-2221-E-009-130. Y-Y P would like to acknowledge the NSC for the financial support given under the contract of NSC95-2112-M-213-005.
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