ARTICLE pubs.acs.org/JPCC
Dielectric and Lattice Vibrational Spectra of Cu2O Hollow Spheres in the Range of 110 THz Yu-ping Yang,*,† Wen-zhong Wang,† Zhen-wei Zhang,‡ Liang-liang Zhang,‡ and Cun-lin Zhang‡ † ‡
School of Science, Minzu University of China, Beijing 100081, P. R. China Beijing Key Laboratory for Terahertz Spectroscopy and Imaging, Key Laboratory of Terahertz Optoelectronics, Ministry of Education, Department of Physics, Capital Normal University, Beijing 100048, P. R. China ABSTRACT: The transmitted spectra of Cu2O hollow spheres have been measured in the range of 110 THz and analyzed by the classical dispersion theory and group theoretical analysis. Two strong phonon resonances are observed at v1 = 4.54 THz (148.3 cm1) and v2 = 4.91 THz (163.5 cm1), corresponding to the transverse optical (TO) phonon and longitudinal optical (LO) phonon modes, respectively. In addition, we have identified a possible surface optical (SO) phonon mode located between the TO and LO phonon frequencies and have observed that a forbidden phonon mode at 9.36 THz (312 cm1) is activated due to the imperfect lattice of the Cu2O hollow spheres. The optical and dielectric parameters are also derived and discussed based on the Lorentz model of dielectric response.
1. INTRODUCTION Cuprous oxide (Cu2O) is a p-type metal oxide semiconductor with a direct band gap energy of 2.17 eV and a large excitonic binding energy of ∼140 meV.1 Cu2O nanostructures are reported to have potential applications in solar energy conversion, catalysis, gas sensors, carriers, and drug delivery.2 In the past decade, various morphological Cu2O products, such as hollow spheres, wires, cubes, cages, and octahedrons, etc., have been synthesized by different methods.3 In particular, the Cu2O hollow nanospheres and microspheres have high surface area, a large fraction of void space, as well as a low dielectric constant. They also exhibit some special electrical, magnetic, thermal, optical, and surface properties owing to their structural hierarchy and geometry. Zhu et al.4 reported that hollow Cu2O microspheres can greatly enhance the immobilization of the DNA probe on the electrode surface and improve the sensitivity of DNA biosensors. Gao et al.5 measured the optical limiting properties of the thin-shell spheres of Cu2O by using nanosecond laser pulses and demonstrated promising applications in the protection of human eyes or optical sensors from high-power laser irradiation. In addition, other potential applications of these materials are diverse, ranging from catalysis, drug delivery, artificial cells, light fillers, acoustic insulation, and photonic crystals.6 Study of the lattice vibrations in Cu2O material can help to gain an understanding of the nature of the electronphonon interaction. During the past 50 years, some lattice-dynamical calculations have been performed by Huang,7 Caratatos,8 and Carabatos and Prevot9 using the available zone-center frequencies. Furthermore, the phonon spectra in the Cu2O single crystal have been measured by the Infrared (IR),1012 Raman resonance (RR),1315 and exciton luminescence.16 The measured lattice vibrational frequencies of single-crystal Cu2O are listed in r 2011 American Chemical Society
Table I. However, no phonon characterizations have so far been performed on Cu2O hollow spheres. In addition, uncertainties in the phonon intensities due to the imperfections in the lattice have led various authors to assign differing frequencies to the same zone-center modes. For example, Dawson et al.12 and Heltemes11 assign 149 cm1 to the Γ15(LO) mode, whereas Yu and Shen21 give 149 cm1 to the Γ15(TO) mode. Also, because of phase insensitivity, the IR and Raman techniques can not be used to measure the detailed phonon dispersion relations. Terahertz time-domain spectroscopy (THz-TDS) is an excellent complement to the optical studies because it probes both amplitude and phase of the far-infrared spectrum. Consequently, THz-TDS provides the complex-valued, frequency-dependent optical properties and does not require a KramersKronig analysis. Recently, THz-TDS has been used to study dielectric and phonon properties in nanomaterials such as ZnO tetrapod structures,17 CuS nanoparticles,18 and PbSe nanocrystal arrays.19 Another reason one needs to characterize the phonon mode of Cu2O by THz-TDS is that Cu2O may be an ideal choice for high power terahertz generation due to its high exciton gain and rather high excitonic binding energy.24 Huber et al.25,26 reported that THz pulses may couple resonantly to the intraexcitonic transitions between 3p and 2s excition states, and femtosecond THz spectroscopic technology can explore novel quantum optical processes and shed new light on the complex phase diagram of electronhole excitations in Cu2O crystal. However, scattering with phonons and free carriers leads to high THz absorption and ultrafast nonradiative relaxation of the excited states to the lowest Received: December 1, 2010 Revised: March 12, 2011 Published: May 10, 2011 10333
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Table I. Frequencies of Zone-Center Phonons in Single-Crystal Cu2O Γ15 (cm1) reference
method
Γ25 (cm1)
Γ0 12 (cm1)
TO
LO
Γ0 2 (cm1)
Compann20
RR
Yu and Shen21
RR
Heltemes11
IR
Dawson et al.12
IR and RR
100
110
Reydellet et al.15
IR and RR
100
108
Compaan et al.22
RR and photoluminesecse
110
176
O’Keeffe10
IR
105
150
348
Petroff et al.16 Beg et al.23
photoluminescense inelastic neutron scattering
107 105
147 146
347
109 88
110
85 87
154 149
154
146
149
146.3
148 150
149.3
348 308 350
Figure 2. Schematic diagram of the ABCD THz-TDS spectrometer.
Figure 1. (a) Low- and (b) high-magnification SEM images of Cu2O hollow spheres. (c) XRD pattern of the as-prepared Cu2O hollow spheres.
bound exciton level. These processes can be deeply understood by the spectroscopic information. In this work, we present a direct and unambiguous observation of the transverse optical (TO) phonon and longitudinal optical (LO) phonon frequencies of Cu2O hollow spheres in the broad THz spectral region. By means of Lorentzian fitting of the THz spectra, a possible surface optical (SO) phonon peak located between the TO and LO phonon frequencies was identified with a frequency in agreement with the predicted value. In addition, the optical and dielectric parameters are derived, and the Lorentz model of dielectric response provides good fits on the measured data in the frequency range from 1 to 10 THz.
2. EXPERIMENTAL METHODS The synthesis of Cu2O hollow spheres was carried out at room temperature.27 In a typical procedure, 0.25 g of CuSO4 solution with concentration of 8 M was added into 5H2O and was dissolved in 100 mL of deionized water under constant stirring by a magnetic stirrer, and then 1 mL of N2H4 3 H2O solution with a concentration of 8 M was added into the above solution. The color of the solution gradually turned red. After stirring for 10 min, the red precipitate was centrifuged and washed several
times with deionized water and ethanol. As discussed in ref 27, X-ray diffraction (XRD) and transmission electron microscopy (TEM) were used to characterize the identity, crystal structure, and size of the products. The low-magnification image in Figure 1(a) clearly reveals that a large quantity of spherical particles with a narrow size distribution was achieved. The highmagnification image in Figure 1(b) demonstrates that the spherical-shaped particles are micrometer-scale hollow spheres with an average diameter of about 550 nm. The broken sphere as marked by an arrow in Figure 1(b) clearly indicates that the spheres prepared via our present template-free room temperature method are hollow. Figure 1(c) shows the typical XRD pattern of the as-prepared Cu2O hollow spheres. The XRD pattern contains five peaks that are clearly distinguishable and broadened. All of the diffraction peaks can be perfectly indexed to the 110, 111, 200, 220, and 311 peaks of cubic Cu2O (JCPDS No. 5-666, Pn3m). No characteristic XRD peaks arising from impurities are detected, indicating that the product is composed of the pure Cu2O phase. Before the measurement of the THz spectrum, the as-prepared Cu2O nanospheres were pressed into a 1-cmdiameter, 0.117-mm-thick pellet to ensure physical stability and planar interfaces. The pellet was fixed by two stainless steel plates with a 5-mm-diameter aperture at the center. The THz-TDS system used to characterize the Cu2O hollow spheres was an air-biased-coherent-detection (ABCD) spectrometer,28 which is schematically shown in Figure 2. A Ti-sapphire amplified laser (Spectra-Physics Hurricane) with a central wavelength of 800 nm, 85 fs (FWHM) pulse duration, 750 μJ pulse energy, and 1 kHz repetition rate is used as the optical source. The laser beam is separated into two beams by an optical beam splitter: one beam with 75% energy passing through a motorized delay line and a 100 μm thick type-I beta BBO crystal, 10334
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Figure 3. Time-resolved THz pulses through the free-space and Cu2O nanospheres. (Inset is the corresponding amplitude spectra.)
by which the 400 nm second harmonic (SH) is produced. The fundamental (ω) and SH (2ω) beam are focused in dry nitrogen with an effective focal length 150 mm lens. The predominantly p-polarized broadband THz emission from the laser-induced plasma is collimated and refocused by a pair of parabolic mirrors (P1 and P2) and then propagated through the sample located at the focal point of the parabolic mirror P2. The transmitted beam is collimated and refocused by P3 and P4. The residual 25% optical energy is reflected by a high resistivity silicon beam splitter as the probe beam. Then, the THz radiation is detected by the air plasma. The entire THz beam path is purged with dry nitrogen to eliminate the absorption lines of water vapor.
3. RESULTS AND DISCUSSION The transmitted THz pulses and corresponding amplitude spectra of the reference and sample pulses are illustrated in Figure 3. The THz pulses are measured over a scan duration of 5 ps to avoid the reflection from the back side of the Cu2O pellet. This situation in turn limits the frequency resolution of the numerical Fourier transforms. To perform a numerical interpolation between the measured frequency points, the measured pulses in the time domain were extended with zeros (zero-padding) to a total time duration of 20 ps, four times the measured scan duration. The spectra peaks are around 2 THz and extend beyond 10 THz. Outside this range, the amplitudes of the spectral components are too low, and the relative phase shows considerable scatter as they drop into the noise level of the measurements. Figure 4(a) presents the frequency-dependent power absorption coefficient of the Cu2O pellet, which was extracted from the experimental data using the well-known amplitude transmission function of a parallel dielectric slab.29 As can be seen, the absorption baseline increases with increasing frequency, and three prominent resonance lines are located at 4.45 (148.3 cm1), 4.91 (163.5 cm1), and 9.37 THz (312 cm1), respectively, which is an indication that remarkable changes at corresponding frequencies occur in the extinction coefficient k and the refractive index n. Cu2O has a simple cubic structure with two molecules per unit cell. The structure belongs to the O4n = Pn3m space group. There are three acoustic and 15 optical phonon branches. Using the group symmetry notations from Bouckaert et al.,30 the zerocenter phonons are classified as 3
0
2
0
0
Γ ¼ 33 Γ15 þ 3 Γ25 þ Γ25 þ Γ12 þ Γ2
ð1Þ
Figure 4. Absorption coefficients (a), extinction coefficients (b), and refraction indexes (c) of the Cu2O pellet (without zero pad, filled circles b; four times zero pad, open circles O).
In a perfect lattice, only two optical 3Γ15 modes whose frequencies have previously been reported around 146 and 609 cm1 are infrared active.11,12 However, due to imperfections in the lattice, particularly in nanomaterials, the optical selection rules are relaxed, and most of the zone-boundary phonons along with the otherwise unallowed zone-center phonons, such as the longitudinal optical (LO) phonon and Γ0 2 mode, are also activated.10,12,21 In common with the lattice-dynamical calculations performed by Carabatos and Prevot,9 the measured absorption peaks located at 4.45 (148.3 cm1), 4.91 (163.5 cm1), and 9.37 THz (312 cm1) can be assigned to Γ15(TO), the activated Γ15(LO), and Γ0 2 phonon modes, respectively, as indicated in Table II. Apart from that, a blue shift of ∼0.14 THz (4.6 cm1) due to quantum confinement was observed in Cu2O hollow spheres. The frequency-dependent dielectric function is determined by the measured extinction coefficient and refractive index through the relationship: ε(ω) = (n þ ik).2 The calculated complex dielectric constants of the Cu2O hollow spheres are presented in Figure 5. It is clear that the average values of εr are about 3.25 and much smaller than the value of the bulk Cu2O crystal (Table II) due to the large fraction of void space in Cu2O hollow spheres. The complex dielectric function of the Cu2O hollow spheres can be represented by the Lorentz model of dielectric response31 εm ðωÞ ¼ ε¥ þ
Sj ω2
∑j ω2TOj ωTOj 2 iΓ ω j
ð2Þ
where ε¥ is the high-frequency dielectric constant. The summation term in eq 2 is over all the lattice oscillations, with the jth resonant frequency ωTOj, resonant width Γj, and resonant strength Sj, respectively. Using eq 2, both the real and imaginary parts of ε achieve the best fit (solid curves in Figure 5) to the experimental data with ε¥ = 3.2, ωTO/2π = 4.48 ( 0.05, ωLO/2π = 4.90 ( 0.05, and ωΓ0 2/2π = 9.32 ( 0.05 THz. The three best fitting resonances are in good agreement with the measured absorption peaks. It is interesting to note that the LO phonon mode in Figure 4(a) exhibits noticeable asymmetric broadening on the low-frequency side. A closer inspection of this feature, as shown in Figure 6, suggests that the broad absorption consists of a superposition of 10335
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Table II. Frequencies of Zone-Center Phonons in Cu2O Hollow Spheres Γ15 (THz) reference 11
Cu2O sample
method
TO
SO
LO
Γ0 2 (THz)
ε¥
ε0
Heltemes
single crystal
IR
4.38
4.47
6.6
7.6
Dawson et al.12
single crystal
IR and Raman
4.39
4.48
6.5
7.4
3.2
3.9
Carabatos et al.9
single crystal
rigid-ion model
4.29
present work
hollow sphere
THz-TDS
4.45
Figure 5. Complex dielectric constant of the Cu2O hollow spheres with the real part εr (a) and the imaginary part εi (b).
overlapping lines. After subtracting the baseline, the THz spectrum in the range of 4.05.4 THz was fitted to a sum of three Lorentzians, shown individually by the blue dashed lines in Figure 6. It is clear from an inspection of Table II that two big peaks (I and III) correspond to the TO and LO phonon modes, respectively. A new small peak II at 4.82 THz is located between the TO and LO phonon frequencies. For the nanostructured semiconductor, due to the high surface-to-volume ratio, optical absorption in the low-frequency region is dominated not only by the lattice vibration of the interior atoms but also by the surface vibration of the surface atoms. On the basis of the classical electromagnetic theories for polariton modes given by Ruppin and Englman,32 the surface optical phonon mode can be observed when microcrystals are about 1 order of magnitude smaller than the wavelength of an incident radiation, which is satisfied in the present experiment. In addition, the peak of the surface phonon should be located between the bulk TO and LO phonon frequency. The SO phonon mode is further identified by calculating the SO mode frequency, ωSO, using the following expression (ref 32) ω2SO ε0 þ εm ð1=L 1Þ ¼ ε¥ þ εm ð1=L 1Þ ω2TO
ð3Þ
where ωTO is the frequency of the TO phonon mode; εm is the dielectric constant of the host medium; and L is the depolarization factor which depends on the particle shape. In the case of Cu2O hollow spheres, εm = 1 and L = 1/3. In addition, ε0 and ε¥ are the static and high frequency dielectric constants, respectively, and their values are monitored by the LO mode frequency with respect to the TO mode frequency in a way described by the LanddaneSachsTeller (LST) relation33 ω2LO ε0 ¼ 2 ωTO ε¥
ð4Þ
4.83
4.77
9.24
4.91
9.37
Figure 6. Broad feature of absorption in the range of 45.4 THz. The circles are the measured data, and the solid curve is a nonlinear leastsquares fit to the data based on the sum of three Lorentzian functions. The dotted curves are Lorentzian functions determined by the fitting procedure with line centers at 4.45, 4.82, and 4.91 THz and all lines with FWHM linewidths of ∼0.19 THz.
In terms of eqs 3 and 4, by using the following parameters of Cu2O hollow spheres, ε¥ = 3.2, ωTO/2π = 4.45, ωLO/2π = 4.91 THz, one can obtain the static dielectric constants ε0 = 3.89 and the frequency of the SO mode to be ωSO/2π = 4.83 (161 cm1) THz. The asymmetric line shape of the strong line at 4.91 THz in Figure 6 may indicate the presence of another close and weaker line. The excellent numerical fit to the observed line shape used the strong line at 4.91 THz together with a weaker line at 4.82 THz. Consequently, the weaker line is tentatively identified with the predicted surface optical phonon mode with a frequency of 4.83 THz. Table II summarizes the lattice vibrational frequencies of the Cu2O single crystals and hollow spheres. The assignments discussed above have been listed together with several other more tentative assignments made by other authors. Finally, we compared the LO phonon frequency in the present work with that determined by IR spectra. The IR reflection of single-crystal Cu2O measured by Heltemes11 showed only a strong band at the transverse optical (TO) frequency (ωTO/2π = 4.38 THz) because LO phonons are Raman active and do not contribute to the IR absorption. Consequently, the LO frequency (ωLO/2π = 4.47 THz) was obtained from the zeros of εr, the real part of the dielectric constant. However, uncertainties in the phonon intensities due to the imperfections in the lattice may lead to ambiguous assignment for the LO frequency, as indicated in Tables I and II. In our case, there can be little doubt about this assignment because the second band vLO = 4.91 THz is too strong to represent anything but a fundamental process, i.e., the corresponding longitudinal optical phonon. 10336
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4. CONCLUSION Ultrabroad bandwidth THz-TDS has been used to study the dielectric and lattice resonances in Cu2O hollow spheres. We have been able to measure three of the six zone-center optic phonon frequencies, including the forbidden LO and Γ0 2 phonon modes, and we have identified a possible surface optical (SO) phonon. It has been found that the rigid-ion model gives good agreement with our measurements. In addition, the measured refractive index, power absorption, and complex dielectric function are also obtained and discussed based on the Lorentz model of dielectric response. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This Project was partly supported by the National Natural Science Foundation of China (Grant No. 11074312), the National Key Basic Research Special Foundation of China (Grant No. 2007CB310408), the “985 Project” (Grant no. 98503-008006, 98503-008017), and “211 Project” of Ministry of Education of China. We thank D. Grischkowsky and Weili Zhang for their fruitful discussions and carefully checking our English. ’ REFERENCES (1) Musa, A. Q.; Akomolafe, T.; Carter, M. J. Production of Cuprous Oxide, a Solar Cell Material, by Thermal Oxidation and a Study of its Physical and Electrical Properties. Sol. Energy Mater. Sol. Cells 1998, 51, 305. Zhang, J. T.; Liu, J. F.; Peng, Q.; Wang, X.; Li, Y. Nearly monodisperse Cu2O and CuO nanospheres: preparation and applications for sensitive gas sensors. Chem. Mater. 2006, 18, 867. (2) Chang, Y.; Teo, J. J.; Zeng, H. C. Formation of colloidal CuO nanocrystallites ans their spherical aggregation and reductive transformation to hollow Cu2O nanosphere. Langmuir 2005, 21, 1074–1079. Yang, M.; Zhang, Y.; Pang, G.; Feng, S. Preparation of Cu2O hollow nanospheres under reflux conditions. Eur. J. Inorg. Chem. 2007, 3841–3844. (3) Xu, H.; Wang, W. Template synthesis of multishelled Cu2O Hollow spheres with a single-crystalline shell wall. Angew. Chem., Int. Ed. 2007, 46, 1489–1492. (4) Zhu, H.; Wan, J.; Xu, G. Fast Synthesis of Cu2O Hollow Microspheres and Their Application in DNA Biosensor of Hepatitis B Virus. Cryst. Growth Des. 2009, 9 (1), 633–638. (5) Gao, J.; Li, Q.; Zhao, H.; Li, L.; Liu, C.; Gong, Q.; Qi, L. One-Pot Synthesis of Uniform Cu2O and CuS Hollow Spheres and Their Optical Limiting Properties. Chem. Mater. 2008, 20, 6263–6269. (6) Ma, Y.; Qi, L. Solution-phase synthesis of inorganic hollow structures by templating strategies. J. Colloid Interface Sci. 2009, 335, 1–10. (7) Huang, K. The long wave modes of the Cu2O lattice. Z. Phys. 1963, 171, 213–225. (8) Carabatos, C. Lattice Vibrations of Cu2O at the Long Wave Limit. Phys. Status Solidi 1970, 37, 773. (9) Carabatos, C.; Prevot, B. Rigid Ion model lattice dynamics of Cuprite (Cu2O). Phys. Status Solidi B 1971, 44, 701. (10) O’Keeffe, M. Infrared Optical Properties of Cuprous Oxide. J. Chem. Phys. 1963, 39, 1789. (11) Heltemes, E. C. Far-Infrared properties of Cuprous Oxide. Phys. Rev. 1966, 142, 803. (12) Dawson, P.; Hargreave, M. M.; Wilkinson, G. R. The dielectric and lattice vibrational spectrum of cuppous oxide. J. Phys. Chem. Solids 1973, 34, 2201–2208.
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