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Femtosecond pump probe spectroscopy experiments were carried out to observe extensional modes of GaN nanorods. Different orders of extensional modes were generated and observed following the absorption of femtosecond light pulses. This observation confirms that with a diameter on the order of 100 nm, no mechanical change is expected compared to bulk GaN. We propose and demonstrate that the detection of these modes is achieved through the modulation of the Fabry-Pérot cavity formed by the nanorod array. The extensional modes change the nanorods length and thus modify the reflectivity of the rod-array cavity.
©2012 Optical Society of America
1. Introduction
Nanorods are promising materials in a wide variety of field, from biosensing [1,2] to electronics and optoelectronics [3]. In order to make applications possible, the knowledge of the toughness and mechanical behaviors of nanorods is a critical issue [4,5].First of all, a better understanding of the vibration of nanorods is necessary for their use in micro and nano electro mechanical systems. It is also important to document the variation of mechanical properties upon size reduction [6–8]. Optical methods for the characterization of mechanical properties of nanorods are extremely interesting, because of their ease of use. Raman spectroscopy [9,10], optical interferometry [11,12] or time resolved X-ray [13] and optical reflectivity [14–16] have been used to characterize the vibrations of nanorods.
GaN nanorods can be especially interesting for the purpose of electronics because of the piezoelectric properties of GaN and the possibility to generate electricity through these properties [17]. It is therefore a key issue to be able to elastically characterize GaN nanorods. The mechanical behavior of GaN nanorods has been studied in the MHz range through the observation of bending mode [7]. A diameter dependent variation of the Young's modulus has been observed. But, to the best of our knowledge, no observation of confined acoustic phonons (CAP), extensional or breathing mode, of GaN nanorods has been made.
In this paper, we report on the observation of multiple orders of extensional modes of an array of GaN nanorods. Our results are confirmed by finite element method simulation and the obtained Young's Modulus agrees well with the expected value. We then propose and demonstrate that the extensional modes are detected through modulation of the length of the Fabry-Pérot cavity formed by the nanorods.
2. Samples and experimental setup
Experiments were performed on GaN nanorods grown by plasma-assisted molecular beam epitaxy on a Si substrate [18]. The rods were grown along the [0001] direction and the average length of the rod is 1150 nm and the average width is 100 nm. The average length and width are obtained by doing the statistical average above a large number of measurements [19]. As it can be seen in the SEM pictures of Fig. 1 , these nanorods exhibit a large dispersion in radius and the average diameter is 100 nm.
The time-resolved femtosecond spectroscopy [20] experiments were carried on using a tunable Ti:sapphire oscillator and a conventional two-color pump and probe setup. The laser produces 100 fs optical pulses at a repetition rate of 76 MHz, centered at a wavelength tunable between 700 and 950 nm. We used an infrared probe and a frequency doubled pump and the spot diameter is slightly larger than 30 µm, we thus are sensitive to the average rod length and our experimental results are independent of the position on the sample.
3. Results
Long nanorod exhibits different vibration modes: breathing mode, bending mode and extensional mode [13]. The frequency of the breathing mode depends on the diameter of the rod and for bending mode, it depends on the cross section [13], since our nanorods have a large dispersion in diameter (Fig. 1), inhomogeneous broadening will make the detection of such modes difficult. On the other hand, the extensional mode solely depends on the length of the rod and the Young's Modulus E along the axis of the rod. For a rod with one free end and the other fixed, the frequency of the nth order extensional mode is given by [21]
where ρ is the mass density and l is the length of the rod. Therefore, the observation of the extensional mode allows the extraction of Young's modulus.The second harmonic generation is necessary for the pump to obtain photons with energy above the band gap of GaN nanorod and then to excite electron-hole pairs. The excited electron-hole pairs will modify the equilibrium position of atom and will launch an acoustic vibration. This generation mechanism is often referred to as displacive mechanism or deformation potential generation [22]. Since the penetration depth of the pump light (≈115 nm at 360 nm for bulk GaN) is small [23], the excitation is not homogeneous along the rod axis, therefore we expect to be able to generate not only fundamental, but also higher order extensional modes. We performed time resolved femtosecond spectroscopy to study the behavior of nanorods. In Fig. 2(a) , we reproduce the pump-probe trace obtained with a pump wavelength of 360 nm and a probe wavelength of 720 nm.
Fig. 2 (a) Transient reflectivity trace with a pump wavelength of 360 nm and a probe wavelength of 720 nm. (Inset) Transient reflectivity with background removed. (b) Fourier transform of transient reflectivity. (c) FEM simulation of the mode shapes.
After a fast increase of the reflectivity at time zero, produced by photogenerated carriers on a femtosecond time scale, we observed a slow decay due to electronically and thermally induced variation of the refractive index. After the removal of this thermal and electronical background represented by the red trace on Fig. 2(a), we obtained the signal shown in the inset of Fig. 2(a). We used a three exponential decay function to fit this background [24]. On this signal, one can observe different oscillations. These oscillations are independent of the probe polarization. In order to obtain their frequencies, we realized the Fourier transform of this signal (Fig. 2(b)). We observe three vibrations with frequencies 1.53, 4.76 and 7.68 GHz. First one remarks the ratio between these frequencies. Between the second and the first, we have a 3.1 ratio, and between the third and the first frequency, a ratio of 5.0. Moreover, if we use the third frequency and Eq. (1) to extrapolate Young's Modulus along the growth direction of the rod, taking a 1150 nm rod length and a density of 6.095 g cm-3 [25], we obtain a modulus of 304 ± 15 GPa, which is in good agreement with value of 305 GPa reported in literature for bulk GaN [7]. Indeed, as reported in Ref. [7], we don't expect to observe any change in mechanical properties for 100 nm diameter rod.
To further confirm that we were probing extensional modes, we realized finite element method (FEM) simulation to obtain the mode shape and to confirm the frequencies. We modeled the nanorod as a cylinder of radius 50 nm and of length 1150 nm. We use the elastic constants and the density of GaN provided by Ref. [25]. We fixed one end of the nanorod while other boundaries remain free. The results of the FEM calculation exhibit a lot of different frequencies. To be able to observe the relevant solution we can use two criteria to sort the frequencies. First, since we have a large dispersion in the rod diameter, we only consider the mode that have a weak dependency on the radius. The other criterion comes from our experimental setup; the laser spot (30 µm) is larger than the nanorod diameter, and we can consider that the deposited energy is homogenous at the rod top surface. Therefore, we only consider the modes that have an axial symmetry. By using these two criteria, we can find three modes with similar frequencies as the one observed experimentally. The mode shape and the frequency of these three vibrations are depicted in Fig. 2(c). Comparing with the experimental results, we further confirm from this simulation that the experimentally observed vibrations are extensional modes.
4. Detection mechanism
Now we know that these observed frequencies come from extensional modes, we then focus on the detection mechanism. In the case of metallic nanorods, the detection of CAP is done through the coupling of light with plasmons [26]. However, for semiconductor nanowire, there is little report on the detection of CAP by light. In Ref. [13], authors report on the detection by light of CAP in InAs nanorods, but the investigation on the detection mechanism is not the purpose of their report. In the following, we propose a model for the detection of the extensional modes.
The model we propose can be understood as follows: since our sample is composed of a Si substrate with a layer of GaN nanorods grown on top of it, this structure can also be regarded as a Fabry-Pérot cavity if the photon energy is lower than the energy of GaN bandgap, which is the case for our infra-red probe. Then the vibration induced by the pump beam, will modify the length of the cavity, and as a consequence, the reflectivity will be modified [27,28]. The reflectivity R of this Fabry-Pérot cavity, if we consider there is no loss, is given by
withl is the length of the cavity, i.e. the nanorod length, 𝜆 is the probe wavelength and θ is the angle between the light in the GaN layer and the normal to the cavity. In this equation, T1-2 refers to the transmittance from medium 1 to medium 2 and r1-2 is the reflection coefficient from medium 1 to medium 2. To confirm that our sample contains such a Fabry-Pérot cavity, we realized the reflectivity spectrum of our sample at a 45° incidence angle (Fig. 3 ).In Fig. 3, we can observe oscillation in the reflectivity coming from the constructive and destructive interference induced by multiple reflections in the cavity. We also fit the experimental data using Eq. (2). This fitting allow us to estimate the effective refractive index of our structure. Similarly to the results obtained by other groups [23], we can reproduce the full spectrum by using the refractive index of bulk GaN multiplied by a scaling factor that depends on the filling fraction, in our case 0.6. The deviation between the experimental reflectivity spectrum and the simulation can be coming from possible scattering, however our purpose here is to retrieve the effective refractive index by fitting the oscillations.
From Eqs. (2) and (3), we can see that if the length of nanorods l is modified, which is the case for extensional modes, then the reflectivity will be changed. Consequently, the amplitude of the transient reflectivity should be proportional to the derivative of the reflectivity as a function of the rod length:
Different parameters can be tuned to verify experimentally that the signal is proportional to this expression, for example the wavelength. However we don't have the opportunity to explore a large range of wavelength since we need the energy of the pump beam to be above bang gap to generate the extensional modes. Therefore, we decided to tune the angle of incidence. Figure 4(a) represents the derivative of the Fabry-Pérot reflectivity with respect to the length l of the nanorod as a function of the angle of incidence of the probe light on the sample θ’, which can be linked to θ by Snell’s law, at a wavelength of 730 nm and a rod length of 1150 nm.
Fig. 4 (a) Theoretical amplitude of the acoustic signal as a function of the angle of incidence of probe light at a wavelength of 730 nm (b) Transient reflectivity at a probe wavelength of 730 nm obtained for different incident angle.
We can see that the amplitude of the signal should change sign at an angle close to 35° therefore we should be able to observe a sign change of the oscillation if we probe with an angle lower or higher than 35°. We thus realized experiments with a variable angle of incidence at a pump wavelength of 365 nm and 730 nm for the probe. The signals obtained are represented in Fig. 4(b). Because the second order mode has a longer life time than the fundamental mode, we focused on these oscillations, and as predicted by Eq. (4) we observe a sign change at an angle located around 35°. We can consequently ascribe the detection of the multiple orders of extensional modes to the modulation of the length of the Fabry-Pérot cavity.
In conclusion, we reported the observation of multiple orders of extensional modes of GaN nanorods by using time resolved femtosecond spectroscopy. This observation is confirmed by FEM simulations. As expected for such nanorods dimensions, with a radial diameter close to 100 nm, we did not observe any mechanical changes due to size reduction. We also proposed a detection mechanism for these extensional modes. We experimentally confirmed that the extensional modes are detected thanks to the modulation of the cavity length formed by the nanorods array.
Acknowledgments
The authors would like to thanks Professor Min-Hsiung Shih for his precious help on finite element simulation. This work was sponsored by the National Science Council of Taiwan, R.O.C. under Grant No. 99-2120-M-002-013.
References and links
1. K.-W. Hu, T.-M. Liu, K.-Y. Chung, K.-S. Huang, C.-T. Hsieh, C.-K. Sun, and C.-S. Yeh, “Efficient Near-IR Hyperthermia and Intense Nonlinear Optical Imaging Contrast on the Gold Nanorod-in-Shell Nanostructures,” J. Am. Chem. Soc. 131(40), 14186–14187 (2009). [CrossRef] [PubMed]
2. A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009). [CrossRef] [PubMed]
3. X. Duan, Y. Huang, Y. Cui, J. Wang, and C. M. Lieber, “Indium phosphide nanowires as building blocks for nanoscale electronic and optoelectronic devices,” Nature 409(6816), 66–69 (2001). [CrossRef] [PubMed]
4. K. L. Ekinci and M. L. Roukes, “Nanoelectromechanical systems,” Rev. Sci. Instrum. 76(6), 061101 (2005). [CrossRef]
5. E. W. Wong, P. E. Sheehan, and C. M. Lieber, “Nanobeam Mechanics: Elasticity, Strength, and Toughness of Nanorods and Nanotubes,” Science 277(5334), 1971–1975 (1997). [CrossRef]
6. C. Q. Chen, Y. Shi, Y. S. Zhang, J. Zhu, and Y. J. Yan, “Size Dependence of Young’s Modulus in ZnO Nanowires,” Phys. Rev. Lett. 96(7), 075505 (2006). [CrossRef] [PubMed]
7. C.-Y. Nam, P. Jaroenapibal, D. Tham, D. E. Luzzi, S. Evoy, and J. E. Fischer, “Diameter-Dependent Electromechanical Properties of GaN Nanowires,” Nano Lett. 6(2), 153–158 (2006). [CrossRef] [PubMed]
8. D. A. Smith, V. C. Holmberg, D. C. Lee, and B. A. Korgel, “Young's Modulus and Size-Dependent Mechanical Quality Factor of Nanoelectromechanical Germanium Nanowire Resonators,” J. Phys. Chem. C 112(29), 10725–10729 (2008). [CrossRef]
9. S. Piscanec, M. Cantoro, A. C. Ferrari, J. A. Zapien, Y. Lifshitz, S. T. Lee, S. Hofmann, and J. Robertson, “Raman spectroscopy of silicon nanowires,” Phys. Rev. B 68(24), 241312 (2003). [CrossRef]
10. H. Lange, M. Mohr, M. Artemyev, U. Woggon, and C. Thomsen, “Direct Observation of the Radial Breathing Mode in CdSe Nanorods,” Nano Lett. 8(12), 4614–4617 (2008). [CrossRef] [PubMed]
11. J. M. Nichol, E. R. Hemesath, L. J. Lauhon, and R. Budakian, “Displacement detection of silicon nanowires by polarization-enhanced fiber-optic interferometry,” Appl. Phys. Lett. 93(19), 193110 (2008). [CrossRef]
12. M. Belov, N. J. Quitoriano, S. Sharma, W. K. Hiebert, T. I. Kamins, and S. Evoy, “Mechanical resonance of clamped silicon nanowires measured by optical interferometry,” J. Appl. Phys. 103(7), 074304 (2008). [CrossRef]
13. S. O. Mariager, D. Khakhulin, H. T. Lemke, K. S. Kjaer, L. Guerin, L. Nuccio, C. B. Sørensen, M. M. Nielsen, and R. Feidenhans’l, “Direct Observation of Acoustic Oscillations in InAs Nanowires,” Nano Lett. 10(7), 2461–2465 (2010). [CrossRef] [PubMed]
14. M. Hu, X. Wang, G. V. Hartland, P. Mulvaney, J. P. Juste, and J. E. Sader, “Vibrational Response of Nanorods to Ultrafast Laser Induced Heating: Theoretical and Experimental Analysis,” J. Am. Chem. Soc. 125(48), 14925–14933 (2003). [CrossRef] [PubMed]
15. S. N. Jerebtsov, A. A. Kolomenskii, H. Liu, H. Zhang, Z. Ye, Z. Luo, W. Wu, G. G. Paulus, and H. A. Schuessler, “Laser-excited acoustic oscillations in silver and bismuth nanowires,” Phys. Rev. B 76(18), 184301 (2007). [CrossRef]
16. J. Burgin, P. Langot, A. Arbouet, J. Margueritat, J. Gonzalo, C. N. Afonso, F. Vallée, A. Mlayah, M. D. Rossell, and G. Van Tendeloo, “Acoustic Vibration Modes and Electron Lattice Coupling in Self-Assembled Silver Nanocolumns,” Nano Lett. 8(5), 1296–1302 (2008). [CrossRef] [PubMed]
17. W. S. Su, Y. F. Chen, C. L. Hsiao, and L. W. Tu, “Generation of electricity in GaN nanorods induced by piezoelectric effect,” Appl. Phys. Lett. 90(6), 063110 (2007). [CrossRef]
18. L. W. Tu, C. L. Hsiao, T. W. Chi, I. Lo, and K. Y. Hsieh, “Self-assembled vertical GaN nanorods grown by molecular-beam epitaxy,” Appl. Phys. Lett. 82(10), 1601–1603 (2003). [CrossRef]
19. C. L. Hsiao, L. W. Tu, T. W. Chi, H. W. Seo, Q. Y. Chen, and W. K. Chu, “Buffer controlled GaN nanorods growth on Si(111) substrates by plasma-assisted molecular beam epitaxy,” J. Vac. Sci. Technol. B 24(2), 845–851 (2006). [CrossRef]
20. K.-H. Lin, C.-M. Lai, C.-C. Pan, J.-I. Chyi, J.-W. Shi, S.-Z. Sun, C.-F. Chang, and C.-K. Sun, “Spatial manipulation of nanoacoustic waves with nanoscale spot sizes,” Nat. Nanotechnol. 2(11), 704–708 (2007). [CrossRef] [PubMed]
21. L. D. Landau, E. M. Lifshitz, A. M. Kosevich, and L. P. Pitaevskii, Theory of Elasticity (Butterworth-Heinemann, 1986).
22. W. B. Gauster and D. H. Habing, “Electronic Volume Effect in Silicon,” Phys. Rev. Lett. 18(24), 1058–1061 (1967). [CrossRef]
23. H.-Y. Chen, H.-W. Lin, C.-Y. Wu, W.-C. Chen, J.-S. Chen, and S. Gwo, “Gallium nitride nanorod arrays as low-refractive-index transparent media in the entire visible spectral region,” Opt. Express 16(11), 8106–8116 (2008). [CrossRef] [PubMed]
24. P. C. Upadhya, Q. Li, G. T. Wang, A. J. Fischer, A. J Taylor, and R. P. Prasankumar, “The influence of defect states on non-equilibrium carrier dynamics in GaN nanowires,” Semicond. Sci. Technol. 25, 024017 (2010).
25. A. Polian, M. Grimsditch, and I. Grzegory, “Elastic constants of gallium nitride,” J. Appl. Phys. 79(6), 3343–3344 (1996). [CrossRef]
26. P. Zijlstra, A. L. Tchebotareva, J. W. M. Chon, M. Gu, and M. Orrit, “Acoustic Oscillations and Elastic Moduli of Single Gold Nanorods,” Nano Lett. 8(10), 3493–3497 (2008). [CrossRef] [PubMed]
27. O. B. Wright, “Thickness and sound velocity measurement in thin transparent films with laser picosecond acoustics,” J. Appl. Phys. 71(4), 1617 (1992). [CrossRef]
28. A. Devos, J.-F. Robillard, R. Côte, and P. Emery, “High-laser-wavelength sensitivity of the picosecond ultrasonic response in transparent thin films,” Phys. Rev. B 74(6), 064114 (2006). [CrossRef]
