1. Introduction

In recent years, two major approaches were developed in the nanofabrication: top-down and bottom-up fabrications [1,2]. The nanotubes and nanowires made from the bottom-up fabrication have demonstrated their values in novel nano-devices such as nano-generators, nano-actuators and nano-lasers [3–5]. In contrast, the periodic nanostructures from the top-down fabrication have also been designed for various applications, including nanorods for light emitting diode (LED), photonic crystals for nanolasers, and periodic metal stripes for acoustic transducers. In order to design those devices, the modification of the fundamental mechanical and optical properties needs to be known when the size is down to the nanoscale. For the optical property, the size-dependent strain relaxation in GaN-based nanorod-LED had been observed through the optical measurement [6]. For the mechanical characteristic, the AFM-based bending technology [7], MEMS-based in situ testing [8,9], and electromechanical resonance in situ testing technology [10,11] have been developed to acquire the mechanical parameters of the nanostructures vibrating up to the MHz range. As for the study of high frequency (>GHz) vibrations, some optical methods were also proposed, such as Raman spectroscopy, X-ray diffraction, and time-resolved pump-probe spectroscopy [12–14]. With these methods, the mechanical properties under nanoscale had been observed to be different from those of bulk materials, including softening or stiffening effects in the nanowires, nanoshells, and nanoparticles. As for the elastic modules of GaN nanowires, discrepancies were reported by different groups, attributed to different growth methods [7–11]. Utilizing the top-down fabricated nanostructures directly from the bulk materials and on top of a crystallized substrate, the mechanical property of nanostructures would be different from those of previous reports on nanowires all fabricated using bottom-up methods while the mechanical properties of the top-down fabricated nanorods would be independent of the growth conditions. Currently no report can be found on the mechanical characteristics of 2D arrayed piezoelectric GaN nanorods directly top-down fabricated on top of a bulk substrate. Not only that the aspect ratio of our studied 2-D arrayed GaN nanorods is different from those of previously reported GaN nanowires [7–11], but also the crystal-quality connection between our nanorods and their GaN substrate would provide distinct mechanical boundary condition from that of individual nanowires either free or in contact with heterostructures or nanoparticles in liquid.

In this letter, we report our attempt to use time-resolved femtosecond spectroscopy to excite and observe the high-frequency confined acoustic vibrations in the 2-D arrayed piezoelectric GaN nanorods directly top-down fabricated on top of a bulk substrate. Diameter-dependent radial breathing vibrations of GaN nanorods were successfully excited and temporally resolved. By analyzing the spectra of femtosecond excited radial breathing vibrations, the elastic constant of 2-D arrayed GaN nanorods can be deduced. Our rod-diameter dependent study indicates a reduced sound velocity when the diameter is one the order of or below 50nm. The confined acoustic vibration modes of nanostructures could be induced and detected by the femtosecond laser pump-probe spectroscopy [12,15,16]. When the photon energy of pump light was above the bandgap of GaN, the pump light was absorbed and then induced temperature increases. For the radial symmetric GaN nanorods, several different confined acoustic modes could be induced after the initial thermal expansion. Generally, three different confined acoustic modes in thin nanorods or nanowires were observed with different technologies in previous reports, which include the bending mode, the extensional mode, and the radial breathing mode [12,16]. For lower-aspect-ratio 2-D arrayed nanorods, the breathing mode corresponding to the vibration in the radial direction should be the dominant confined acoustic mode and the acoustic mode frequency is expected to be inversely proportional to the diameter of individual nanorod. After the excitation process, the relative change of the reflective probe light from the 2-D arrayed GaN nanorods would be induced due to the expansion of the breathing mode, which perturbed the volume fraction of 2-D arrayed GaN nanorods. For studying the relation between the breathing mode frequency and diameter of nanorods, we designed nanorods with different diameters but with a similar aspect-ratio (AR).

2. Sample preparation

The scanning electron microscopy (SEM) images of the fabricated 2-D arrayed GaN nanorods are shown in Fig. 1 . In order to pattern the nano-diameter nanorods with a short-period and a high-density, E-beam lithography, thermal evaporation, and inductive coupled plasma reactive ion etching (ICP RIE) were utilized. Metal masks were used for RIE to achieve a high AR of rods. First e-beam lithography resist (Zep-520A) was coated on top of a 3μm-thick GaN film and the thickness of resist was 120nm. The 2-D arrayed pattern was fabricated on the resist by the e-beam lithography. The sample was then loaded into an evaporation chamber for the deposition of 30-nm metal film and the subsequent lift-off process of metal was performed by dimethylsulfoxide. Next, we used the ICP RIE system to dry etch the 2-D arrayed GaN nanorods. The etching gas and RF power were Cl₂/BCl₃ mixture and 200W, respectively [17]. After the ICP RIE process, the residual metal mask on top was removed with the selective chemical wet etching and potassium hydroxide (KOH) was utilized to decrease the defect density on the side walls of fabricated rods [18]. Finally, the geometry of 2-D arrayed GaN nanorods was observed by the field emission SEM (FEI Nova 600i). The diameters of the fabricated GaN nanorods were from 35 nm to 350nm nm and the heights were between 100nm to 1080nm.

 

Fig. 1 Top SEM views of the fabricated 2D-arrayed GaN nanorods on GaN substrates. The average rod diameters are (a) 324nm, (b) 250nm, (c) 230nm, (d) 183nm, (e) 135nm, (f) 52nm, (g) 40nm, (h) 35nm. (i) The side view SEM image of (e).

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3. Experimental details

For the femtosecond transient reflectivity measurement, a degenerate femtosecond pump-probe system was adopted with a Ti:sapphire laser. The frequency-doubled 360-nm UV femtosecond laser pulse was generated by a beta barium-borate (BBO) crystal and was divided into a pump beam and a probe beam. The average powers of the pump and probe beams were 30mW and 5mW, respectively. Finally, the pump and probe light were incident into the 2-D arrayed GaN nanorods with the same aspheric lens and the reflectivity of the probe light was detected by a biased Si detector. A pump-probe spot size of 20μm diameter (full width at half-maximum intensity) can be estimated at the focal plane by measuring the ratio of the focused pump and probe powers through a 10μm-diameter pin-hole. The spot size covered more than forty nanorod periods in its diameter.

4. Results and Discussion

The crystal class of the metal-organic-chemical-vapor-deposition-grown GaN film is of a hexagonal wurtzite structure with a reported elastic stiffness constant (C₁₁) of 365 ± 2 GPa [19] while the high quality GaN film was grown on a c-plane sapphire substrate. Based on the hexagonal structure, the sound velocity can be deduced from the slowness of curve with the density, stiffness constant and Poisson ratio of the well-known GaN crystal. The frequency f of the radial breathing mode can then be predicted by [16]

One example trace of the experimentally measured transient reflection change on the 2-D arrayed nanorod sample with a 135 nm diameter was shown in Fig. 2(a) . On top of the carrier-dynamics background, an oscillatory signal was observed to last for 500ps after the excitation of the pump light (inset of Fig. 2(b)). Through the Fourier transform analysis, the observed 33 GHz central frequency is in agreement with the prediction of the radial breathing mode model shown in Eq. (1). The oscillation bandwidth was 5 GHz, reflecting a slow damping process.

 

Fig. 2 (a) Measured probe reflection change as a function of time delay. The sample is with a 135nm diameter and a 220nm period. The inset scheme shows the geometry of a nanorod. D, d1, d2 and L are average diameter, top diameter, bottom diameter and height of a nanorod, determined by top and side SEM views. AR: aspect ratio. (b) An oscillation frequency of 33GHz was revealed in the fast-Fourier-transformed spectrum. The inset figure illustrates the observed oscillatory signal after removing the carrier dynamics background of (a).

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The periods and aspect ratios of 2-D arrayed GaN nanorods could be designed to be different to study the possible frequency shift contributed from surface acoustics effects [20]. We first studied the effect of rod periodicity on the observed oscillatory frequency for 150 ± 10 nm-diameter and 240 ± 10 nm-diameter GaN nanorods. As shown in Fig. 3(a) , our study indicates that the observed oscillatory frequency does not have a significant dependency on the periodicity within our studied range. We also investigated the aspect ratio (AR) dependency. The result for 240 ± 10 nm diameter GaN nanorods is shown in Fig. 3(b). The shift of the observed central frequency would be less than 1 GHz as the AR of rod was greater than 2. It is important to notice that with a 600ps scanning period in the transient measurement, our corresponding frequency resolution was only 1.8 GHz. In order to reduce the effect of the frequency shift due to different AR, in the following diameter-dependency study we selected only the samples with AR greater than 2.

 

Fig. 3 (a) The observed oscillatory frequency as a function of rod periodicity for 150 ± 10 nm-diameter (black solid squares) and 240 ± 10 nm-diameter (red solid triangles) GaN nanorods. (b) The observed oscillatory frequency as a function of aspect ratio for 240 ± 10 nm diameter GaN nanorods. The observed frequency is 21 ± 1.5GHz while the aspect ratio is higher than 2.

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Figure 4(a) summarizes the observed oscillatory frequency as a function of rod diameter. For nanorods with a diameter ranging between 135nm and 324nm, our observed central oscillatory frequency agrees well with the characteristic frequency of radial breathing mode following Eq. (1) while the v_r of bulk GaN and τ_n are taken as 7744 m/s and 2.05 [19,21,22], respectively. We assumed that τ_n was fixed for different rod diameters due to similar excitation and boundary conditions. The excellent agreement between the measured diameter-dependent oscillation frequency and Eq. (1) confirms our suggestion that the observed oscillatory signals are contributed from the radial breathing oscillations of the fabricated nanorods. When the diameters of the 2D arrayed GaN nanorods were below 50 nm, the vibrational frequency of the observed breathing mode was found to be lower than the theoretical prediction. With τ_n as a dimensionless constant in Eq. (1), the relatively low breathing mode frequency would indicate a lower sound velocity in nanorods with a diameter less than 50nm. Therefore, the elastic stiffness constant (C₁₁) can then be deduced from the measured results with the formula, v_r = (c₁₁/ρ)^1/2 where ρ is the density of GaN. Thus derived C₁₁ elastic stiffness constant of nanorod as a function of rod diameter is shown in Fig. 4(b). We can notice that the C₁₁ elastic constant is significantly lower for GaN nanorods with a diameter smaller than 50 nm. With a 35nm rod diameter, our experimental method found that the C₁₁ value decreases by 48% in comparison with the bulk counterpart.

 

Fig. 4 (a) The observed oscillatory frequency versus the diameter of nanorod. Rod diameter ranges from 324nm to 35 nm. The horizontal error bars represent the diameter nonuniformity based on the SEM images and the vertical error bars represents full-width half-maximum of the amplitude in Fourier-transformed oscillatory spectra. The black curve is the result of the theoretical calculation on the radial breathing mode based on Eq. (1) with v_r = 7744 m/s and τ_n = 2.05. (b) Elastic stiffness constant (C₁₁) as a function of GaN rod diameter. The black dashed line represents the bulk C₁₁ value.

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It is important to notice that different diameter dependencies on elastic stiffness constant in c-axis GaN nanowires have been predicted in different theoretical calculations [8,23–25], depending on different assumptions in the inter-atomic potentials on wire surface. In Ref. 8, molecular dynamics simulation with a Stillinger-Weber potential (SW-MD) was adopted to simulate the elasticity of c-axis GaN nanowires. Reference 8 predicted that the elastic stiffness constant should increase as the diameter of nanowire was smaller than 20nm. In Ref. 24, the density-functional theory was adopted for the theoretical calculation and the elastic stiffness constant was predicted to decrease when the wire diameter was smaller than 10 nm. All previous experiment attempts [8] to measure the size dependence of the elastic stiffness constant in GaN nanowires were all with a diameter equal to or larger than 55 nm, while no diameter dependency on the elastic constant can be found [8]. The difference between our results and previous theories [8,23–25] might be resulted from the specific surface conditions of the top-down fabricated GaN nanorods. It was known that dry-etching can increase the surface defect density on the side walls of GaN nanorods [7] and the follow-up KOH wet-etching could modify the defect density [18]. Other possible reasons include the non-perfect rod shapes and studied GHz frequency range.

4. Conclusion

In summary, we not only successfully excited and observed the radial breathing mode in 2D-arrayed GaN nanorods by femtosecond transient reflectivity spectroscopy, but also found that a slow sound velocity existed for rods with a diameter smaller than 50nm. The corresponding elastic stiffness constant of the 2D arrayed GaN nanorods was acquired in our measurement and was found to be much reduced. Our observation further implied that the observed softening effect appeared in the radial direction of rods and could be a critical parameter modification to be considered in the development of future nanoelectromechanical system.