Nondestructive Complete Mechanical Characterization of Zinc Blende

Jun 28, 2016 - We have developed and demonstrated an experimental method, based on the picosecond acoustics technique, to perform nondestructive ...
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Nondestructive Complete Mechanical Characterization of Zinc Blende and Wurtzite GaAs Nanowires Using Time-Resolved Pump− Probe Spectroscopy Pierre-Adrien Mante,*,†,‡ Sebastian Lehmann,‡,§ Nicklas Anttu,‡,§ Kimberly A. Dick,‡,§,∥ and Arkady Yartsev*,†,‡ †

Department of Chemical Physics, ‡NanoLund, §Department of Solid State Physics, and ∥Center for Analysis and Synthesis, Lund University, S-221 00 Lund, Sweden S Supporting Information *

ABSTRACT: We have developed and demonstrated an experimental method, based on the picosecond acoustics technique, to perform nondestructive complete mechanical characterization of nanowires, that is, the determination of the complete elasticity tensor. By means of femtosecond pump− probe spectroscopy, coherent acoustic phonons were generated in an ensemble of nanowires and their dynamics was resolved. Specific phonon modes were identified and the detection mechanism was addressed via wavelength dependent experiments. We calculated the exact phonon dispersion relation of the nanowires by fitting the experimentally observed frequencies, thus allowing the extraction of the complete elasticity tensor. The elasticity tensor and the nanowire diameter were determined for zinc blende GaAs nanowires and were found to be in a good agreement with literature data and independent measurements. Finally, we have applied this technique to characterize wurtzite GaAs nanowires, a metastable phase in bulk, for which no experimental values of elastic constants are currently available. Our results agree well with previous first principle calculations. The proposed approach to the complete and nondestructive mechanical characterization of nanowires will allow the efficient mechanical study of new crystal phases emerging in nanostructures, as well as size-dependent properties of nanostructured materials. KEYWORDS: Femtosecond laser, nanowires, zinc blende, wurtzite, elasticity tensor

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observed. Recent experiments have demonstrated the possibilities to observe multiple modes leading to the determination of elasticity and diameter of polycrystalline NWs.18 However, it is still challenging to observe a large number of vibrational modes and thus complete mechanical characterization cannot be achieved in materials with a large number of independent elastic constants. Furthermore, NWs can be grown in crystal phases that are metastable in the corresponding bulk counterpart of the material, like wurtzite (WZ) for most III−V semiconductors.19,20 It opens the way to the development of new devices based on crystal phase engineering,21 but the mechanical properties of these new phases have not yet been probed. Thus, a complete mechanical characterization of the NWs is much needed for fundamental understanding of properties of various crystal phase and their applications. Femtosecond pump−probe spectroscopy, and in particular its applications to the study of coherent acoustic phonons (CAPs), picosecond ultrasonics,22−27 is a convenient tool to

emiconductor nanowires (NWs) offer unique physical properties with a vast tunability, and as such are elementary pieces for nanoelectronics1 and nanophotonics.2 Much of the NW behavior and properties can be related to its mechanical properties. For instance, the mobility of electrons is typically limited by electron−phonon scattering,3 whereas the thermal behavior, which is of great interest for NW thermoelectrics,4 is governed by phonon group velocity.5 Mechanical properties also play a central role in devices, for example, in nanoelectromechanical systems (NEMS)6 or in NW-based battery applications, where mechanical cracks are responsible for their reduced lifetime.7 The mechanical properties of a material, such as Young’s modulus and Poisson ratio, are determined by its elasticity tensor,8 and the knowledge of this tensor is necessary for a large variety of applications from the simulation of straininduced effects9 to optomechanics.10 Measurement of the NWs’ mechanical properties have thus been a central issue in recent years.11−18 A complete mechanical characterization of NWs remains a challenge despite numerous experimental methods that have been employed.11 Indeed, using state of the art experimental characterization methods, elasticity studies remain limited to Young’s modulus12−14 or to an incomplete elasticity tensor15 due to the limited number of vibrational modes © XXXX American Chemical Society

Received: February 23, 2016 Revised: June 10, 2016

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Figure 1. (a) ZB and (c) WZ GaAs NWs observed using SEM with a 30° tilting angle of the substrate with insets highlighting the morphology of the NW and scale bars of 1 μm. (b) ZB and (d) WZ GaAs NWs observed using overview TEM, SADP, and HRTEM. The SADP pattern of the ZB NW reflects the fact that apart of being twinned it consists of only ZB.

perform mechanical characterization.24 However, it is often limited to the sole generation of the longitudinal mode.22 Therefore, the determination of the elastic properties is not straightforward.24 Up to now, this technique has mostly been applied to study confined acoustic vibrations in NWs, such as breathing modes15,27 or extensional modes.14 However, due to the limited amount of information that can be retrieved from the observation of these modes it was not possible to perform a complete mechanical characterization of the NW. Recently, propagation of CAPs in a NW has been observed,23,28 which has opened the way to the characterization of isotropic materials.18 Nevertheless, the experimental method is rather complicated, because it involves multiple experiments with spatially separated pump and probe laser beams, and as such has limited practical value. Moreover, the complete characterization of anisotropic materials, as for example WZ, by the proposed approach18 remains problematic due to the large number of independent elastic constants. In this Letter, we have developed and demonstrated a simple and reliable experimental method based on picosecond acoustics, which allows the complete mechanical characterization of NWs. By performing femtosecond pump−probe spectroscopy experiments on an ensemble of NWs, we observed generation of multiple confined and propagating CAPs. We attributed the experimentally observed frequencies of these CAPs to acoustic branches of the dispersion relations of the NWs probed at a specific wave vector. We then extracted the mechanical properties by fitting the phonon dispersion relations of the NWs to our experimental data. As a demonstration, we applied this method to an ensemble of zinc blende (ZB) GaAs NWs and obtained a good agreement with the experimentally determined values from literature. In addition, due to the low number of independent elastic constants in ZB materials we also obtained the diameter of these NWs, by using it as a fitting parameter, and observed a good agreement with dimensions measured by scanning electron microscopy (SEM). We then took advantage of this

technique to perform a complete mechanical characterization of WZ GaAs NWs, a crystal phase that is metastable in bulk. The studied samples consist of monocrystalline intrinsic GaAs NWs, either in the ZB or WZ crystal phase standing perpendicular on a ⟨1̅1̅1̅⟩-type oriented GaAs substrates. The NWs were grown by use of metal organic vapor phase epitaxy following the vapor−liquid−solid growth mode29 and using gold seed particles.20,30 A detailed description of the NWs growth can be found elsewhere31,32 (Supporting Information). SEM in a LEO Gemini 1560 setup and high-resolution transmission electron microscopy (HRTEM) in a JEOL 3000F, including the acquisition of selected area diffraction patterns (SADPs) in TEM, were carried out to study the morphology and crystal structure of the NWs (Figure 1). The average dimensions, as obtained from SEM images and using the softwares NanoDim33 and ImageJ,34 respectively, are 103 ± 3 and 1860 ± 31 nm for the diameter and length of ZB NWs, and 68 ± 4 and 1583 ± 28 nm for the diameter and length of WZ NWs. For the given values, the diameter at half height of the NWs was extracted. However, the diameters at the tip and at the bottom of the NW were also measured in the case of the zinc blende NWs that exhibits tapering to prove that the average diameter and the diameter extracted at half height are equivalent. In the SEM images, we observe a pyramidal base at the bottom of the NWs. This base has the same crystallinity as the NWs and is much more pronounced in the case of WZ. Ultrafast pump−probe spectroscopy experiments were performed using a regeneratively amplified, mode-locked Yb:KGW (Ytterbium-doped potassium gadolinium tungstate) based femtosecond laser system (Pharos, Light conversion) operating at 1030 nm and delivering pulses of 200 fs at a 2 kHz repetition rate. This laser is then used to pump two noncollinearly phase-matched optical parametric amplifiers (NOPAs). A first one (Orpheus-N, Light Conversion) was used to generate pump pulses centered at 550 nm with a pulse duration of 35 fs. The second NOPA (also an Orpheus-N, Light Conversion) generated probe pulses with about 40 fs pulse duration at wavelengths ranging from 650 to 850 nm that B

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Figure 2. (a) Schematic representation of the experimental scheme. (b) Transient reflectivity (raw signal) obtained with a pump wavelength of 550 nm and probe wavelength of 850 nm on an ensemble of GaAs ZB NWs. Inset: Transient reflectivity after removal of the electronic and thermal contributions.

Figure 3. (a) Fourier transform of the transient reflectivity signals obtained with a probe wavelength of 650 or 850 nm on ZB GaAs NWs. The Fourier transform displays multiple acoustic modes. BBS, backward Brillouin scattering; Q, quadrupolar mode; B, breathing mode; 2B, second order breathing mode. (b) Experimental frequencies and consequently fitted/extracted phonon dispersion relations of ZB GaAs NWs (black lines) with the branches that participate in the signals highlighted (green lines). The experimental frequencies detected by forward scattering modes (blue dots), backward Brillouin scattering at 650 nm (red triangle), and at 850 nm (blue triangle) and the double of the wave vector of the HE11 optical guided mode wave vector at 650 (dashed red line) and 850 nm (dashed blue line) are also represented.

In the Fourier transforms of Figure 3a, multiple peaks are observed and each of them corresponds to a specific acoustic mode. To perform mechanical characterization, we proceed as follows: first we attribute each of these frequencies to a specific phonon mode, that is, a phonon branch at a given wave vector, as seen in Figure 3a. Then, we calculate the phonon dispersion relations, assuming infinitely long NWs and using the mechanical properties and the diameter of the NWs as parameters. Then we fit the frequencies obtained from the phonon dispersion relation to the experimental frequencies. The best fitted dispersion relations are shown in Figure 3b). The identification of each mode relies on the understanding of the generation and detection processes, a detail study of which can be found elsewhere.35 Briefly, guided optical modes within the NWs can exhibit modified electric fields due to confinement. For example, the electric field can exhibit a 2-fold symmetry, which is the case for the HE11 mode, the fundamental guided optical mode. The amplitude of CAPs generated by the absorption of light is directly proportional to the density of photoexcited carriers.25 The displacement field of the acoustic modes that can be generated is thus dependent on the symmetry of the electric field distribution of the guided optical modes. Therefore, only a limited set of CAPs are generated. These modes are the longitudinal and breathing modes, which are axisymmetric, and the quadrupolar mode that has a 2-fold symmetry, as well as their higher orders. It is

are time delayed with respect to the pump by a delay stage. The pump beam was chopped at a frequency of 1 kHz using a mechanical chopper. Both beams are sent on the sample and the modifications of the reflectivity of the probe induced by the pump are monitored (Figure 2a). Figure 2b displays a transient reflectivity signal obtained on the ZB sample at a pump wavelength of 550 nm and a probe wavelength of 850 nm. The absorption of the pump pulse induces the generation of electron−hole pairs, leading to an abrupt change of the sample reflectivity at 0 ps in Figure 2b. On longer time scale, the reflectivity returns to its original value when excited electrons transfer their excess energy to the lattice. In addition to this contribution, we observe an oscillatory component, which was isolated by fitting the reflectivity with multiple exponentials and is given separately in the inset of Figure 2b. These oscillations are due to CAPs generated by a combination of the deformation potential, defined as the modification of the equilibrium position of atoms due to the excitation of electrons, and thermoelastic effects, that is, dilatation induced by the temperature rise in the sample.25 Performing a Fourier transform of the oscillatory signal reveals multiple frequency components of the generated CAPs. Such Fourier transforms of the transient reflectivity signals obtained at a probe wavelength of 650 and 850 nm are reproduced in Figure 3a. C

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are determined by its geometry and elastic properties. In the case of ZB materials, there are three independent elasticity tensor components C11, C12, and C44. Defining these components is equivalent to determining the complete elasticity tensor of the material. In our study, we were able to observe experimentally at least five frequencies, so we are potentially capable to not only completely characterize the elastic properties but also to determine the diameter of the NWs. To do so, we calculated the dispersion relations of ⟨11̅ 1̅ ⟩̅ type oriented NWs using the RUS method23,39 to fit the experimental frequencies. We simultaneously extracted the elastic constants and the diameter by minimizing the rootmean-square deviation between the simulation and the experimental frequencies for the quadrupolar, fundamental, and second order breathing and the backward scattered longitudinal mode. The best fitted to the experimental frequencies dispersion curves obtained by variation of C11, C12, C44 and the NW diameter D are shown in Figure 3b. To prove the uniqueness of the solution, we proceed as follows: first, at a given diameter we demonstrate that only a unique set of elastic constants can reproduce the experimental frequencies, and then we show that for a given set of elastic constants, only one diameter fits the data (see Supporting Information). We find that the values of the elastic constants we obtain are in good agreement with the bulk values reported in the literature.40 Similarly, the fitted diameter D = 110 nm agrees with the D = 103 nm measured by SEM (Figure 1a). The elastic constants and diameter, D, extracted from the experimental data are given in Table 1.

interesting to note that the guiding of optical modes enables the generation of the quadrupolar mode, which is considered as inactive in conventional time-resolved experiments.36 Regarding the detection mechanism, we consider Brillouin scattering of light by phonons in NWs that has been recently investigated.35,37 Brillouin scattering corresponds to the process of emission or absorption of an acoustic phonon by light. Because light and sound can only propagate along the NW axis due to the guiding effect, scattered light can only propagate in the same or opposite direction as the incident light, which corresponds to forward and backward scattering, respectively. In the case of forward scattering, energy and momentum conservation impose that light is scattered by zone-center phonons, q = 0, while for backward scattering the relation q = 2k between the wave vector of light (k) and of sound (q) has to hold. As a consequence, the frequencies originating from backward scattering are dependent on the probe wavelength, which is in contrast to forward scattering. Additionally, backward Brillouin scattering has been only observed for the longitudinal mode.28 Thanks to these considerations we have greatly reduced the complexity of identification of the observed acoustic frequencies: only a few modes can contribute to the signal and we can further sort them by performing probe wavelength dependent experiments. In Figure 3a, we reproduced the Fourier transforms of the signals obtained with a probe wavelength of either 650 or 850 nm. A single peak is shifting when changing the probe wavelength. We can thus attribute this mode to the backward Brillouin scattering of the longitudinal CAP of the NW. By performing optical simulations, using the scattering matrix method,38 we obtained for these small-diameter NWs an effective refractive index, n ∼ 1, for this mode, which leads to an acoustic wave vector of q = 2k = 19 μm−1 at 650 nm and q = 2k = 14 μm−1 at 850 nm. These two wave vectors/frequencies couples, which are displayed in Figure 3b as the red and blue triangle, will be used to perform the fit of the dispersion relation of the lower acoustic mode. Next, we focus on the frequencies that are independent of the probe wavelength. According to phonon dispersion relations in NWs,23 the longitudinal mode, that is, the mode that we observe due to backward Brillouin scattering (probe wavelength dependent), is the dilatational mode of lowest frequency. From Figure 3b, it is apparent that this mode has the lowest frequency as it goes to zero at q = 0. Detection of a mode at lower frequency than the backward Brillouin mode cannot originate from forward scattering because there is no mode of lower frequency at q = 0. Therefore, the probe wavelength independent frequency observed at around 5 GHz is not resulting from forward scattering, but probably from the pyramidal base or the extensional mode of the NWs.14 The remaining three modes, which have frequencies higher than the backward Brillouin scattering mode correspond to the forward scattering of light by the quadrupolar (Q), the fundamental (B), and the second order (2B) breathing modes of the NWs. The breathing modes are often the ones dominantly excited by short light pulse CAPs due to their high symmetry.15,27 The quadrupolar mode is detected due to polarization of the pump beam that breaks the rotational symmetry of the electric field in the NWs, consequently enabling generation of this mode.35 As we understand now the origin of each peak observed in the Fourier transform, we can use them to characterize the properties of the NWs. The frequencies of vibrations of a wire

Table 1. Elastic Constants of ZB GaAs Obtained Using Time Resolved Spectroscopy and Comparison with Literature Values and Dimensions Extracted from SEM Micrographs ZB

C11 (GPa)

C12 (GPa)

C44 (GPa)

D (nm)

this work theory40 exp41 SEM

114 (±10) 124.2 118.4

56 (±15) 51.4 53.7

59 (±10) 63.4 59.1

110 (±5)

103 ± 3

We have thus demonstrated that, using the experimental technique we developed, it is now possible to nondestructively characterize the complete elasticity tensor, as well as the dimensions of ZB NWs. Next, we characterize the mechanical properties of the WZ phase of GaAs NWs. The WZ phase of GaAs is metastable in bulk form, which makes it difficult to access its mechanical properties. However, in NWs WZ GaAs is stable and can be grown with great control.19,32 Other III−V semiconductors, such as InAs, InP, and GaP, show a similar behavior.19,20 We thus applied the method we developed above to WZ GaAs NWs. The Fourier transform of the signal obtained with the pump wavelength of 550 nm and the probe wavelength of 650 and 750 nm can be seen in Figure 4a. Similarly to the ZB NWs, the Fourier transform spectrum displays numerous frequencies. However, the number of frequencies is larger than in the case of the ZB sample. These additional frequencies are coming from CAPs propagation in the substrate and vibrations of the pyramidal base that can be seen in Figures 1c and 4d. To identify these additional modes, we removed the NWs of the sample using ultrasound, leaving only the pyramidal base as seen in Figure 4d. We then performed experiments and compared the D

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Figure 4. (a) Fourier transform of the transient reflectivity signals obtained with a probe wavelength of 650 or 750 nm on WZ GaAs NWs. BBS, backward Brillouin scattering; Q, quadrupolar mode; B, breathing mode; 2B, second order breathing mode. (b) Experimental frequencies and consequently fitted/extracted phonon dispersion relations of WZ GaAs NWs (black lines), with the branches that participate in the signals highlighted (green lines). The experimental frequencies detected by forward scattering modes (blue dots), backward Brillouin scattering at 650 nm (red triangle) and 750 nm (blue triangle), and the double of the HE11 optical guided mode wave vector at 650 nm (dashed red line) and 750 nm (dashed blue line) are also represented. (c) Fourier transform of the transient reflectivity signals obtained with a probe wavelength of 650 nm on samples before and after removal of the NWs. (d) SEM image of the pyramidal base of the WZ NWs after removal of the NWs by ultrasound. The scale bar is 1 μm.

Table 2. Elastic Constants of WZ GaAs Obtained by Time Resolved Spectroscopy and Comparison with Literature Values WZ

C11 (GPa)

C12 (GPa)

C13 (GPa)

C33 (GPa)

C44 (GPa)

exp theory40

152 (±10) 147.6

42 (±15) 46

40 (±10) 33.4

165 (±10) 160.2

47 (±15) 42.4

scattering and then we assign the modes detected by forward scattering. When changing the wavelength from 650 to 750 nm, the peak observed at 14 GHz in Figure 4a shifts to 12 GHz. We thus attribute this peak to the scattering of the probe beam by the longitudinal CAPs. Similarly to ZB, for such small-diameter NWs we expect a close to unity effective refractive index. As a consequence, the wave-vectors of the detected phonons are q = 19 μm−1 and q = 16.5 μm−1 at 650 and 750 nm, respectively. We now consider the CAPs detected by forward scattering. Three modes that are not originating from the substrate or the pyramidal base are detected at 34, 50, and 131 GHz and are assigned to the quadrupolar mode and the fundamental and second order breathing mode, respectively. The determination of these modes is unambiguous because only these three modes can be generated due to the symmetry of the pump electric field. After assigning all the experimentally observed frequencies to specific CAPs, we can perform the mechanical characterization of the NWs. In the WZ crystal, it is not possible to characterize simultaneously the elasticity tensor and the dimensions with the five experimental frequencies we observe, as the tensor has five independent elastic constants C11, C12, C13, C33, and C44. In this study, we extracted the dimensions of WZ NWs from SEM images and used them to determine the elasticity tensor. The

spectrum of samples with and without NWs in Figure 4c. These experiments, performed with a probe wavelength of 650 nm, reveal that the vibrations at 4, 8, 24, and 62 GHz are not originating from the NWs but from the pyramidal base or the substrate. In Figure 4a, we see that the highest of these frequencies is changing when changing the wavelength. This frequency is located at 62 GHz for a probe wavelength of 650 nm and at 58 GHz for a probe wavelength of 750 nm. We attribute this peak to the backward Brillouin scattering of longitudinal CAPs in the substrate. Indeed, the frequency of Brillouin scattering is given by, f = 2nν/λ,22 with n as the refractive index, ν is the sound velocity, and λ is the probe wavelength. We can calculate the sound velocity ν along the ⟨1̅1̅1̅⟩-type direction, using the elastic constants of the ZB phase, as we determined earlier, and the refractive indexes, n = 3.83 at 650 nm and n = 3.66 at 850 nm,42 as ν = 5360 m·s−1. With this sound velocity, we obtain frequencies of 63 and 55 GHz at 650 and 750 nm respectively, which is in good agreement with our experimental data. We identified the CAPs originating from the pyramidal base and the substrate, so we can now focus on the CAPs from the NWs. We use the same method as the one we developed for the ZB samples. First, we perform probe wavelength dependent experiments to highlight CAPs detected by backward Brillouin E

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C11 + 2C12 + 4C44 3ρ C33 ρ

phonon dispersion relations from the experimental frequencies by using the elastic constants as fitting parameters and thus determined the complete elasticity tensor. We demonstrated and validated this procedure on ZB GaAs nanowires and then applied it to the mechanical characterization of GaAs nanowires in the WZ phase, a crystal phase only encountered at the nanoscale. Our study establishes an efficient method to nondestructively characterize nanowires, both mechanically and geometrically.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b00786. Nanowires growth, demonstration of the uniqueness of the determination of the mechanical properties and dimensions of the NWs, and details of light and sound coupling in nanowires.(PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] . *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was performed within NanoLund and was supported by NanoLund, the Swedish Research Council VR, the Swedish Foundation for Strategic Research SSF, the Crafoord Foundation, and the Knut and Alice Wallenberg Foundation.

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= 5350 m.s−1, and for the WZ phase:

REFERENCES

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= 5550 m·s−1. Thus, we observe a 4% increase of

the sound velocity in the WZ NWs. Thus, mechanical properties are an avenue to measure the relative ZB and WZ composition of a NW, because a substantial variation of the mechanical properties exists between these two phases; as a consequence, the effective sound velocity for long wavelength acoustic phonons will reflect the relative composition of the NWs. The control over the growth of ZB and WZ segments within a NW opens up many possibilities for electronic band structure engineering.45 Similarly, the differences in the mechanical properties can lead to improvement in term of phonon engineering. For example, the difference of mechanical properties could be used to open phononic bandgaps in a ZB/WZ NW superlattice and to control thermal transport.46 Our approach of determination of the elastic constants is also important for implementation of piezoelectric devices based on NWs.21 We have thus developed and demonstrated an experimental technique using picosecond acoustics that allows a nondestructive complete mechanical characterization of nanowires. By performing picosecond ultrasonics experiments on nanowires, we observed generation of coherent acoustic phonons at specific frequencies. We assigned the appearance of these frequencies to the backward and forward scattering of light by the generated coherent acoustic phonons. We calculated the F

DOI: 10.1021/acs.nanolett.6b00786 Nano Lett. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.nanolett.6b00786 Nano Lett. XXXX, XXX, XXX−XXX