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Exciton states of quantum confined ZnO nanorods
Chemical Physics Letters 462 (2008) 100–103
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Exciton states of quantum confined ZnO nanorods Sun Young Kim a, Yun Seon Yeon a, Seung Min Park a,*, Jeong Hyun Kim b, Jae Kyu Song a,* a b
Department of Chemistry, Kyunghee University, 1 Hoegi-dong, Dongdaemoon-gu, Seoul 130-701, Republic of Korea School of Chemical and Biological Engineering, Seoul National University, Seoul 151-744, Republic of Korea
a r t i c l e
i n f o
Article history: Received 15 April 2008 In final form 24 July 2008 Available online 29 July 2008
a b s t r a c t Photoluminescence (PL) of zinc oxide (ZnO) nanorods with an average thickness of 5 nm and a length of 30 nm is blue-shifted compared to the bulk due to quantum confinement effects. The exciton states remain relatively stable at a high carrier density due to a smaller exciton size and an enhanced exciton binding energy in the quantum confined nanorods, whereas the electron-hole plasma states are formed in the bulk at the similar carrier density. A linear dependence of the PL intensity on the excitation intensity also corroborates the assumption that the stable exciton states are responsible for the undisturbed emission at a high carrier density. Ó 2008 Elsevier B.V. All rights reserved.
Semiconductor nanocrystals such as quantum dots and quantum rods are of intense scientific and technological interest, because electronic structures of nanocrystals can be tailored by changing their sizes and shapes [1–3]. Zinc oxide (ZnO) has a wide band gap (3.37 eV) and a large exciton binding energy (60 meV) at room temperature. The wide band gap is suitable for UV/blue optoelectronic applications, and lasing actions have been reported in ZnO nanowires, bulk particles, and thin films [4–8]. The large exciton binding energy affords stable exciton states at room temperature for better optical applications. However, a high carrier concentration is usually required for a sufficient optical gain. As the exciton (carrier) density approaches ‘Mott density’, electronhole plasma (EHP) states are formed [9–11]. Although EHP process for emission is common for conventional laser diode operation, the optical gain by the EHP recombinations is lower than that by the exciton-related processes, because binary recombination of free carriers in EHP has a lower efficiency than exciton recombination [7]. To keep up the exciton states beyond the Mott density, a low dimensionality is suggested to be an alternative approach, because quantum confinement effects can alter the properties of exciton states [12–16]. In addition, nanoparticles show enhancements of the exciton oscillator strength and the quantum efficiency, where nanorods provide a better optical gain than quantum dots due to a larger absorption cross section and a lower nonradiative decay [17]. In this Letter, we present experimental evidence of the stable exciton states in ZnO nanorods beyond the Mott density of the bulk, i.e., the carrier density regime where EHP recombination is observed in the bulk, which is suggested to stem from quantum confinement effects in the nanorods. The synthesis of ZnO nanorods in nonhydrolytic conditions was carried out in a nitrogen atmosphere using standard Schlenk tech* Corresponding authors. Fax: +82 2 966 3701 (J.K. Song). E-mail addresses: [email protected] (S.M. Park), [email protected] (J.K. Song). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.07.079
niques, as described in other studies [18,19]. Briefly, the nanorods were synthesized using a mixture of trioctylphosphine oxide (TOPO, 99%) and tetradecylphosphonic acid (TDPA, 98%) as stabilizing ligands, which was added to a mixture composed of zinc acetate (99.99%) and dioctyl ether (99%). After addition of 1,12dodecanediol (>97%), the mixture was heated to 250 °C and maintained at this temperature for 2 h. The prepared nanorods were examined without further treatments such as post-annealing. The synthesized nanorods were characterized by transmission electron microscopy (TEM, Technai 30). Relatively uniform-sized ZnO nanorods with an average size of 5 nm (thickness) 30 nm (length) are found, as shown in Fig. 1a. In order to obtain photoluminescence (PL) spectrum (Fig. 1b), nanorods drop-coated on glass substrates were excited with a He-Cd laser (325 nm). For comparison, PL spectrum of ZnO bulk powders (Aldrich) drop-coated on glass substrates was also obtained, where the exciton emissions are found at the peak energy of 3.25 eV with a FWHM of 0.13 eV. The peak energy and the FWHM are not identical to the known values of ZnO bulk (3.28 eV and 0.10 eV, respectively [20]) presumably due to impurities in ZnO in addition to the homogeneous broadening [15,20–22]. On the other hand, the emission peak of the nanorods in UV region is blue-shifted by 0.05 eV compared to that of the bulk, which is ascribed to the quantum confinement effects. When the dimension of a ZnO nanoparticle is comparable to a Bohr radius of the exciton (1.4 nm 6 aex 6 2.3 nm [14,23]), the band gap increases. According to an effective mass approximation, the band gap depends on the size of spherical nanoparticles [24]:
DEg ðRÞ ¼
p2 h2 2R2
1 1 1:8e2 þ þ Esol ðRÞ me mh eR
ð1Þ
where DEg(R) is the shift of the lowest excited state such as the exciton state in the spherical nanoparticle with a radius of R, me
101
S.Y. Kim et al. / Chemical Physics Letters 462 (2008) 100–103
a
20 nm
b
Wavelength (nm) 600
550
500
450
400
350
bulk
the nearly absent visible emission in the PL spectrum strongly suggests the good crystal quality of the nanorods, i.e., a low defect density such as the oxygen vacancy in the nanorods. In order to study the exciton states of ZnO nanorods at high carrier densities, nanorods were excited with the third harmonic (355 nm) of a Nd:YAG laser (Surelite I, Continuum, 20 Hz, 6 ns) using a UV microscope objective. The emission was collected by the same objective, spectrally resolved by a monochromator, and detected by a photomultiplier tube. Fig. 2a shows PL spectra of the nanorods as a function of the excitation intensity, where the emission peak of the nanorods is hardly shifted upon the increase in the excitation intensity. For comparison, PL spectra of the bulk obtained in the same excitation intensity range are presented in Fig. 2b. The emission peak of the bulk becomes red-shifted with an increase in the excitation intensity, which is plotted in Fig. 3a. The red-shift observed in the bulk is closely related to the EHP states, where the exciton–exciton scattering emission is not observed due to the reduced crystallinity of the bulk powder [9,11]. With the increase in the carrier density, the band gap decreases due to exchange and correlation effects. In addition, the Coulomb interactions between an electron and hole become screened. When an average exciton–exciton distance is comparable to the exciton diameter at a high exciton density (above the Mott density), the exciton states become destabilized to form EHP states, while the band gap decreases [9–11]. The amount of the red-shift in the bulk
a nanorod 2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
Energy (eV)
20.0 mJ/cm2 11.2 mJ/cm2
Fig. 1. (a) The transmission electron microscopy (TEM) image shows relatively uniform-sized ZnO nanorods with an average size of 5 nm (thickness) 30 nm (length). (b) Photoluminescence (PL) spectra of ZnO nanorods and bulk powders drop-coated on glass substrates. The emission of the nanorods in the UV region is blue-shifted compared to that of bulk. The dotted line indicates the peak position of the bulk powders.
is the effective mass of the electron, mh is the effective mass of the hole, e is the dielectric coefficient, and Esol (R) is the solvation energy. The first term is the band gap change due to the quantum confinement, while the second term is the Coulomb attraction related to the exciton binding energy. The shift of the lowest excited state of a spherical nanoparticle with the diameter of 5.0 nm is calculated to be 0.17 eV from Eq. (1). However, the ZnO nanorods investigated in this study are not in spherical shapes, which needs complex theoretical methods to be tested to figure out the shift of the lowest excited state. In fact, the band gap is also dependent on the length of the nanorods in the given diameter, although the band gap variation with respect to the length is not as sensitive as to the diameter [25,26]. In addition, the length dependence of the band gap is not significant beyond the aspect ratio of 2 [26]. For the rod shape, a recent study reports that the ZnO nanorod of a diameter of 2.2 nm (an effective diameter of 2.6 nm) and a length of 43 nm shows the shift of 0.23 eV [15], suggesting that the shift in the diameter of 5.0 nm is in the range of 0.04–0.06 eV, if the shift is only sensitive to the diameter. This range coincides with the observed blue-shift of the emission (0.05 eV), which supports that the UV emission results from the exciton recombination in the quantum confined ZnO nanorods. The broad green emissions around 2.5 eV do not appear clearly in the nanorods. The mechanism of the green emission has been extensively investigated, and the oxygen vacancy is generally accepted as the origin of the green emission [7,18,19]. We note that
5.6 mJ/cm2 2.8 mJ/cm2 1.0 mJ/cm2
2.9
3.0
3.1
3.2
3.3
3.4
3.3
3.4
Energy (eV)
b 20.0 mJ/cm2 11.2 mJ/cm2 5.6 mJ/cm2 2.8 mJ/cm2 1.0 mJ/cm2
2.9
3.0
3.1
3.2
Energy (eV) Fig. 2. (a) Excitation intensity dependence of photoluminescence (PL) in ZnO nanorods. The PL is not shifted with an increase in the excitation intensity. The dotted line indicates the peak position at the excitation intensity of 1 mJ/cm2. Overall shape of PL is virtually unchanged with an increase in the excitation intensity. PL spectra are offset for clarity. (b) Excitation intensity dependence of PL in ZnO bulk. The PL is red-shifted with an increase in the excitation intensity. The dotted line indicates the peak position at the excitation intensity of 1 mJ/cm2. PL spectra are offset for clarity.
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a
nanorod bulk
3.30
Peak center (eV)
ing to a smaller exciton radius with a decrease in the nanoparticle size [12]:
3.32
aex ¼
3.28 3.26 3.24 3.22 3.20 0
5
10
15
20
25
2
Excitation intensity (mJ/cm )
b
400
nanorod bulk
Intensity (a.u.)
300
200
100
0 0
5
10
15
20
25
2
Excitation intensity (mJ/cm ) Fig. 3. (a) Excitation intensity dependence of peak positions of photoluminescence (PL). The emission peak in the bulk is red-shifted with an increase in the excitation intensity, whereas emission peak in the nanorods is not shifted as much. (b) Excitation intensity dependence of the total PL intensity. The emission intensities of the bulk are not linear over the excitation intensity, whereas the emission intensities of the nanorods are nearly linear.
is observed to be about 0.04 eV at the excitation intensity of 20 mJ/ cm2pulse. The carrier density is estimated according to the model that one absorbed photon creates one carrier [11]:
np ¼
Iexc s hmexc L
ð2Þ
where Iexc is the excitation power, hmexc is the photon energy, s is the characteristic time, and L is the effective length. Because the lifetime of the excited carrier is reported to be 200 ps in the bulk [5], which is smaller than the pulse width of the excitation laser (6 ns), s is set to be 200 ps [11]. The effective length of 500 nm (the average diameter of the bulk powder) is used for the bulk, because the diameter of the bulk powder is between the penetration depth of the excitation laser (50 nm) and the diffusion length (1 lm) [11]. Then, the carrier density is estimated to be about 2 1019 cm3 at the excitation intensity of 20 mJ/cm2pulse. Therefore, the observed shift (0.04 eV) in the bulk seems to agree well with other studies [9–11], because the band gap renormalization is estimated to be 0.10 eV (the exciton binding energy in addition to the observed shift). In the confinement regime, however, Coulomb interactions and quantum confinement effects show distinctive dependences on the size of nanoparticles. In other words, while the exciton size is determined by the interactions between the electron and the hole in the bulk limit, the exciton size in nanoparticles is mainly dependent on the boundaries of the confinement potential [12–14], lead-
1 1 R
ð3Þ
where aex is the exciton radius and R is the nanoparticle radius. A recent study calculates that the exciton radius is 0.98 nm for the ZnO quantum dot of a diameter of 5.3 nm [16], which is smaller than the Bohr radius of the exciton in the bulk. Thus, the spatial overlap of excitons in nanoparticles occurs at a higher exciton density, and the critical exciton (carrier) density such as the Mott density in the nanorods is expected to be higher than that in the bulk. For example, the Mott density of the nanorods can be higher (up to 10 times) than that of the bulk, when the exciton radius of the nanorods is similar to that of the quantum dot. Accordingly, the exciton states of nanorods are stable even at a high carrier density, where the EHP states are readily formed in the bulk. However, a direct comparison may not be possible without more information on the carrier density calculated with the absorption cross sections and lifetimes of the nanorods. In our preliminary study, the absorption efficiency of the nanorods is estimated to be similar to that of the bulk. Although the lifetime measurements remain for further studies, the lifetimes of the nanorods with a diameter of 29 nm are similar to those of the bulk [5,6,27], suggesting that the lifetimes of the nanorods with a diameter of 5 nm might not be much different from the bulk. On the other hand, because the diameter of the nanorods (5 nm) is smaller than the penetration depth (50 nm), the effective length (L) in Eq. (2) is 50 nm in the nanorods, while L is 500 nm in the bulk, resulting in a higher carrier density in the nanorods at the same excitation intensity. Therefore, the carrier density of the nanorods is supposed not to be smaller than that of the bulk, unless the lifetime or the absorption efficiency of the nanorods is more than 10 times smaller. In PL spectra of the nanorods obtained in the same excitation intensity range, however, the emission peak of the nanorods is not shifted as much as that in the bulk (Fig. 3a), presumably because the EHP states are not formed in the nanorods even above the Mott density of the bulk due to a smaller exciton size. The stable exciton states at a high carrier density are also explained by the enhanced exciton binding energy. With a decrease in the nanoparticle size (R), the second term of Eq. (1) related to the exciton binding energy increases with R1, which results in the exciton binding energy of 0.29 eV in the spherical nanoparticle with the diameter of 5.0 nm [24]. Using the temperature dependence of the shift in PL spectra, the exciton binding energy is estimated to be 0.13 eV in a quantum dot (diameter of 5.3 nm) [16]. Because the exciton binding energy is also dependent on the length of the nanorods [13], it is not easy to estimate the exact exciton binding energy in the nanorods. However, the recent study finds that the exciton binding energy in the ZnO nanorod of a diameter of 2.2 nm (an effective diameter of 2.6 nm) is 6–10 times larger than that in the bulk [15], which suggests that the exciton binding energy in ZnO nanorod with the diameter of 5.0 nm is larger than 0.10 eV. Thus, the large exciton binding energy in the nanorods can stabilize the exciton state even at a high carrier density. In other words, the exciton states in the nanorods at a high carrier density are affected by the confinement energies, the screened Coulomb interactions, and the band gap renormalization effects. With the increase in the exciton density, the Coulomb interactions are screened and the exciton binding energy decreases. However, the exciton state in the nanorods is not influenced as much due to its large binding energy that originates from quantum confinement effects, resulting in the stable exciton states at a high carrier density. Another evidence for the stable exciton states beyond the Mott density of the bulk is found in a nearly linear increase in the PL intensity as a function of the excitation intensity, as presented in
S.Y. Kim et al. / Chemical Physics Letters 462 (2008) 100–103
Fig. 3b. While the total PL intensity of the bulk levels off at the high carrier density regime due to a less efficient emission of the EHP states [7], the PL intensity of the nanorods shows a nearly linear dependence on the excitation intensity, supporting that the exciton states are mainly responsible for the emission of the nanorods above the Mott density of the bulk. Therefore, the emission efficiency of the nanorods can be larger than that of the bulk at a high carrier density, because the exciton recombination has a better efficiency than the binary recombination of free carriers in EHP states. In summary, the ZnO nanorods synthesized in nonhydrolytic conditions exhibit strong UV emission. The absence of visible emission indicates that the nanorods have a low level of defects such as oxygen vacancy. Due to the quantum confinement effects, the emission band is blue-shifted in the nanorods. With an increase in the excitation intensity, the PL spectra of the nanorods remain nearly unchanged, which gives a sharp contrast to the red-shift observed in the bulk ZnO. Because of a smaller exciton size and an enhanced exciton binding energy, the exciton states of the nanorods are stable at a high excitation intensity that the EHP states are formed in the bulk. A linear dependence of the PL intensity on the excitation intensity also suggests that the exciton states are stable in the nanorods beyond the Mott density of the bulk, which promises a more efficient exciton-related emission in the ZnO nanorods for applications of ZnO nanorod-based laser with a lower lasing threshold and an improved optical gain. Acknowledgement This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund, KRF-2006-331-C00145).
103
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Exciton states of quantum confined ZnO nanorods Sun Young Kim a, Yun Seon Yeon a, Seung Min Park a,*, Jeong Hyun Kim b, Jae Kyu Song a,* a b
Department of Chemistry, Kyunghee University, 1 Hoegi-dong, Dongdaemoon-gu, Seoul 130-701, Republic of Korea School of Chemical and Biological Engineering, Seoul National University, Seoul 151-744, Republic of Korea
a r t i c l e
i n f o
Article history: Received 15 April 2008 In final form 24 July 2008 Available online 29 July 2008
a b s t r a c t Photoluminescence (PL) of zinc oxide (ZnO) nanorods with an average thickness of 5 nm and a length of 30 nm is blue-shifted compared to the bulk due to quantum confinement effects. The exciton states remain relatively stable at a high carrier density due to a smaller exciton size and an enhanced exciton binding energy in the quantum confined nanorods, whereas the electron-hole plasma states are formed in the bulk at the similar carrier density. A linear dependence of the PL intensity on the excitation intensity also corroborates the assumption that the stable exciton states are responsible for the undisturbed emission at a high carrier density. Ó 2008 Elsevier B.V. All rights reserved.
Semiconductor nanocrystals such as quantum dots and quantum rods are of intense scientific and technological interest, because electronic structures of nanocrystals can be tailored by changing their sizes and shapes [1–3]. Zinc oxide (ZnO) has a wide band gap (3.37 eV) and a large exciton binding energy (60 meV) at room temperature. The wide band gap is suitable for UV/blue optoelectronic applications, and lasing actions have been reported in ZnO nanowires, bulk particles, and thin films [4–8]. The large exciton binding energy affords stable exciton states at room temperature for better optical applications. However, a high carrier concentration is usually required for a sufficient optical gain. As the exciton (carrier) density approaches ‘Mott density’, electronhole plasma (EHP) states are formed [9–11]. Although EHP process for emission is common for conventional laser diode operation, the optical gain by the EHP recombinations is lower than that by the exciton-related processes, because binary recombination of free carriers in EHP has a lower efficiency than exciton recombination [7]. To keep up the exciton states beyond the Mott density, a low dimensionality is suggested to be an alternative approach, because quantum confinement effects can alter the properties of exciton states [12–16]. In addition, nanoparticles show enhancements of the exciton oscillator strength and the quantum efficiency, where nanorods provide a better optical gain than quantum dots due to a larger absorption cross section and a lower nonradiative decay [17]. In this Letter, we present experimental evidence of the stable exciton states in ZnO nanorods beyond the Mott density of the bulk, i.e., the carrier density regime where EHP recombination is observed in the bulk, which is suggested to stem from quantum confinement effects in the nanorods. The synthesis of ZnO nanorods in nonhydrolytic conditions was carried out in a nitrogen atmosphere using standard Schlenk tech* Corresponding authors. Fax: +82 2 966 3701 (J.K. Song). E-mail addresses: [email protected] (S.M. Park), [email protected] (J.K. Song). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.07.079
niques, as described in other studies [18,19]. Briefly, the nanorods were synthesized using a mixture of trioctylphosphine oxide (TOPO, 99%) and tetradecylphosphonic acid (TDPA, 98%) as stabilizing ligands, which was added to a mixture composed of zinc acetate (99.99%) and dioctyl ether (99%). After addition of 1,12dodecanediol (>97%), the mixture was heated to 250 °C and maintained at this temperature for 2 h. The prepared nanorods were examined without further treatments such as post-annealing. The synthesized nanorods were characterized by transmission electron microscopy (TEM, Technai 30). Relatively uniform-sized ZnO nanorods with an average size of 5 nm (thickness) 30 nm (length) are found, as shown in Fig. 1a. In order to obtain photoluminescence (PL) spectrum (Fig. 1b), nanorods drop-coated on glass substrates were excited with a He-Cd laser (325 nm). For comparison, PL spectrum of ZnO bulk powders (Aldrich) drop-coated on glass substrates was also obtained, where the exciton emissions are found at the peak energy of 3.25 eV with a FWHM of 0.13 eV. The peak energy and the FWHM are not identical to the known values of ZnO bulk (3.28 eV and 0.10 eV, respectively [20]) presumably due to impurities in ZnO in addition to the homogeneous broadening [15,20–22]. On the other hand, the emission peak of the nanorods in UV region is blue-shifted by 0.05 eV compared to that of the bulk, which is ascribed to the quantum confinement effects. When the dimension of a ZnO nanoparticle is comparable to a Bohr radius of the exciton (1.4 nm 6 aex 6 2.3 nm [14,23]), the band gap increases. According to an effective mass approximation, the band gap depends on the size of spherical nanoparticles [24]:
DEg ðRÞ ¼
p2 h2 2R2
1 1 1:8e2 þ þ Esol ðRÞ me mh eR
ð1Þ
where DEg(R) is the shift of the lowest excited state such as the exciton state in the spherical nanoparticle with a radius of R, me
101
S.Y. Kim et al. / Chemical Physics Letters 462 (2008) 100–103
a
20 nm
b
Wavelength (nm) 600
550
500
450
400
350
bulk
the nearly absent visible emission in the PL spectrum strongly suggests the good crystal quality of the nanorods, i.e., a low defect density such as the oxygen vacancy in the nanorods. In order to study the exciton states of ZnO nanorods at high carrier densities, nanorods were excited with the third harmonic (355 nm) of a Nd:YAG laser (Surelite I, Continuum, 20 Hz, 6 ns) using a UV microscope objective. The emission was collected by the same objective, spectrally resolved by a monochromator, and detected by a photomultiplier tube. Fig. 2a shows PL spectra of the nanorods as a function of the excitation intensity, where the emission peak of the nanorods is hardly shifted upon the increase in the excitation intensity. For comparison, PL spectra of the bulk obtained in the same excitation intensity range are presented in Fig. 2b. The emission peak of the bulk becomes red-shifted with an increase in the excitation intensity, which is plotted in Fig. 3a. The red-shift observed in the bulk is closely related to the EHP states, where the exciton–exciton scattering emission is not observed due to the reduced crystallinity of the bulk powder [9,11]. With the increase in the carrier density, the band gap decreases due to exchange and correlation effects. In addition, the Coulomb interactions between an electron and hole become screened. When an average exciton–exciton distance is comparable to the exciton diameter at a high exciton density (above the Mott density), the exciton states become destabilized to form EHP states, while the band gap decreases [9–11]. The amount of the red-shift in the bulk
a nanorod 2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
Energy (eV)
20.0 mJ/cm2 11.2 mJ/cm2
Fig. 1. (a) The transmission electron microscopy (TEM) image shows relatively uniform-sized ZnO nanorods with an average size of 5 nm (thickness) 30 nm (length). (b) Photoluminescence (PL) spectra of ZnO nanorods and bulk powders drop-coated on glass substrates. The emission of the nanorods in the UV region is blue-shifted compared to that of bulk. The dotted line indicates the peak position of the bulk powders.
is the effective mass of the electron, mh is the effective mass of the hole, e is the dielectric coefficient, and Esol (R) is the solvation energy. The first term is the band gap change due to the quantum confinement, while the second term is the Coulomb attraction related to the exciton binding energy. The shift of the lowest excited state of a spherical nanoparticle with the diameter of 5.0 nm is calculated to be 0.17 eV from Eq. (1). However, the ZnO nanorods investigated in this study are not in spherical shapes, which needs complex theoretical methods to be tested to figure out the shift of the lowest excited state. In fact, the band gap is also dependent on the length of the nanorods in the given diameter, although the band gap variation with respect to the length is not as sensitive as to the diameter [25,26]. In addition, the length dependence of the band gap is not significant beyond the aspect ratio of 2 [26]. For the rod shape, a recent study reports that the ZnO nanorod of a diameter of 2.2 nm (an effective diameter of 2.6 nm) and a length of 43 nm shows the shift of 0.23 eV [15], suggesting that the shift in the diameter of 5.0 nm is in the range of 0.04–0.06 eV, if the shift is only sensitive to the diameter. This range coincides with the observed blue-shift of the emission (0.05 eV), which supports that the UV emission results from the exciton recombination in the quantum confined ZnO nanorods. The broad green emissions around 2.5 eV do not appear clearly in the nanorods. The mechanism of the green emission has been extensively investigated, and the oxygen vacancy is generally accepted as the origin of the green emission [7,18,19]. We note that
5.6 mJ/cm2 2.8 mJ/cm2 1.0 mJ/cm2
2.9
3.0
3.1
3.2
3.3
3.4
3.3
3.4
Energy (eV)
b 20.0 mJ/cm2 11.2 mJ/cm2 5.6 mJ/cm2 2.8 mJ/cm2 1.0 mJ/cm2
2.9
3.0
3.1
3.2
Energy (eV) Fig. 2. (a) Excitation intensity dependence of photoluminescence (PL) in ZnO nanorods. The PL is not shifted with an increase in the excitation intensity. The dotted line indicates the peak position at the excitation intensity of 1 mJ/cm2. Overall shape of PL is virtually unchanged with an increase in the excitation intensity. PL spectra are offset for clarity. (b) Excitation intensity dependence of PL in ZnO bulk. The PL is red-shifted with an increase in the excitation intensity. The dotted line indicates the peak position at the excitation intensity of 1 mJ/cm2. PL spectra are offset for clarity.
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a
nanorod bulk
3.30
Peak center (eV)
ing to a smaller exciton radius with a decrease in the nanoparticle size [12]:
3.32
aex ¼
3.28 3.26 3.24 3.22 3.20 0
5
10
15
20
25
2
Excitation intensity (mJ/cm )
b
400
nanorod bulk
Intensity (a.u.)
300
200
100
0 0
5
10
15
20
25
2
Excitation intensity (mJ/cm ) Fig. 3. (a) Excitation intensity dependence of peak positions of photoluminescence (PL). The emission peak in the bulk is red-shifted with an increase in the excitation intensity, whereas emission peak in the nanorods is not shifted as much. (b) Excitation intensity dependence of the total PL intensity. The emission intensities of the bulk are not linear over the excitation intensity, whereas the emission intensities of the nanorods are nearly linear.
is observed to be about 0.04 eV at the excitation intensity of 20 mJ/ cm2pulse. The carrier density is estimated according to the model that one absorbed photon creates one carrier [11]:
np ¼
Iexc s hmexc L
ð2Þ
where Iexc is the excitation power, hmexc is the photon energy, s is the characteristic time, and L is the effective length. Because the lifetime of the excited carrier is reported to be 200 ps in the bulk [5], which is smaller than the pulse width of the excitation laser (6 ns), s is set to be 200 ps [11]. The effective length of 500 nm (the average diameter of the bulk powder) is used for the bulk, because the diameter of the bulk powder is between the penetration depth of the excitation laser (50 nm) and the diffusion length (1 lm) [11]. Then, the carrier density is estimated to be about 2 1019 cm3 at the excitation intensity of 20 mJ/cm2pulse. Therefore, the observed shift (0.04 eV) in the bulk seems to agree well with other studies [9–11], because the band gap renormalization is estimated to be 0.10 eV (the exciton binding energy in addition to the observed shift). In the confinement regime, however, Coulomb interactions and quantum confinement effects show distinctive dependences on the size of nanoparticles. In other words, while the exciton size is determined by the interactions between the electron and the hole in the bulk limit, the exciton size in nanoparticles is mainly dependent on the boundaries of the confinement potential [12–14], lead-
1 1 R
ð3Þ
where aex is the exciton radius and R is the nanoparticle radius. A recent study calculates that the exciton radius is 0.98 nm for the ZnO quantum dot of a diameter of 5.3 nm [16], which is smaller than the Bohr radius of the exciton in the bulk. Thus, the spatial overlap of excitons in nanoparticles occurs at a higher exciton density, and the critical exciton (carrier) density such as the Mott density in the nanorods is expected to be higher than that in the bulk. For example, the Mott density of the nanorods can be higher (up to 10 times) than that of the bulk, when the exciton radius of the nanorods is similar to that of the quantum dot. Accordingly, the exciton states of nanorods are stable even at a high carrier density, where the EHP states are readily formed in the bulk. However, a direct comparison may not be possible without more information on the carrier density calculated with the absorption cross sections and lifetimes of the nanorods. In our preliminary study, the absorption efficiency of the nanorods is estimated to be similar to that of the bulk. Although the lifetime measurements remain for further studies, the lifetimes of the nanorods with a diameter of 29 nm are similar to those of the bulk [5,6,27], suggesting that the lifetimes of the nanorods with a diameter of 5 nm might not be much different from the bulk. On the other hand, because the diameter of the nanorods (5 nm) is smaller than the penetration depth (50 nm), the effective length (L) in Eq. (2) is 50 nm in the nanorods, while L is 500 nm in the bulk, resulting in a higher carrier density in the nanorods at the same excitation intensity. Therefore, the carrier density of the nanorods is supposed not to be smaller than that of the bulk, unless the lifetime or the absorption efficiency of the nanorods is more than 10 times smaller. In PL spectra of the nanorods obtained in the same excitation intensity range, however, the emission peak of the nanorods is not shifted as much as that in the bulk (Fig. 3a), presumably because the EHP states are not formed in the nanorods even above the Mott density of the bulk due to a smaller exciton size. The stable exciton states at a high carrier density are also explained by the enhanced exciton binding energy. With a decrease in the nanoparticle size (R), the second term of Eq. (1) related to the exciton binding energy increases with R1, which results in the exciton binding energy of 0.29 eV in the spherical nanoparticle with the diameter of 5.0 nm [24]. Using the temperature dependence of the shift in PL spectra, the exciton binding energy is estimated to be 0.13 eV in a quantum dot (diameter of 5.3 nm) [16]. Because the exciton binding energy is also dependent on the length of the nanorods [13], it is not easy to estimate the exact exciton binding energy in the nanorods. However, the recent study finds that the exciton binding energy in the ZnO nanorod of a diameter of 2.2 nm (an effective diameter of 2.6 nm) is 6–10 times larger than that in the bulk [15], which suggests that the exciton binding energy in ZnO nanorod with the diameter of 5.0 nm is larger than 0.10 eV. Thus, the large exciton binding energy in the nanorods can stabilize the exciton state even at a high carrier density. In other words, the exciton states in the nanorods at a high carrier density are affected by the confinement energies, the screened Coulomb interactions, and the band gap renormalization effects. With the increase in the exciton density, the Coulomb interactions are screened and the exciton binding energy decreases. However, the exciton state in the nanorods is not influenced as much due to its large binding energy that originates from quantum confinement effects, resulting in the stable exciton states at a high carrier density. Another evidence for the stable exciton states beyond the Mott density of the bulk is found in a nearly linear increase in the PL intensity as a function of the excitation intensity, as presented in
S.Y. Kim et al. / Chemical Physics Letters 462 (2008) 100–103
Fig. 3b. While the total PL intensity of the bulk levels off at the high carrier density regime due to a less efficient emission of the EHP states [7], the PL intensity of the nanorods shows a nearly linear dependence on the excitation intensity, supporting that the exciton states are mainly responsible for the emission of the nanorods above the Mott density of the bulk. Therefore, the emission efficiency of the nanorods can be larger than that of the bulk at a high carrier density, because the exciton recombination has a better efficiency than the binary recombination of free carriers in EHP states. In summary, the ZnO nanorods synthesized in nonhydrolytic conditions exhibit strong UV emission. The absence of visible emission indicates that the nanorods have a low level of defects such as oxygen vacancy. Due to the quantum confinement effects, the emission band is blue-shifted in the nanorods. With an increase in the excitation intensity, the PL spectra of the nanorods remain nearly unchanged, which gives a sharp contrast to the red-shift observed in the bulk ZnO. Because of a smaller exciton size and an enhanced exciton binding energy, the exciton states of the nanorods are stable at a high excitation intensity that the EHP states are formed in the bulk. A linear dependence of the PL intensity on the excitation intensity also suggests that the exciton states are stable in the nanorods beyond the Mott density of the bulk, which promises a more efficient exciton-related emission in the ZnO nanorods for applications of ZnO nanorod-based laser with a lower lasing threshold and an improved optical gain. Acknowledgement This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund, KRF-2006-331-C00145).
103
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