This is an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of the article or any adaptations for non-commercial purposes. Letter Cite This: Nano Lett. 2019, 19, 4702−4711 pubs.acs.org/NanoLett Phonon Engineering in Twinning Superlattice Nanowires Marta De Luca,† Claudia Fasolato,†,‡ Marcel A. Verheijen,§ Yizhen Ren,§ Milo Y. Swinkels,† Sebastian Kölling,§ Erik P. A. M. Bakkers,§ Riccardo Rurali,*,∥ Xavier Cartoixà,⊥ and Ilaria Zardo*,† † Departement Physik, Universität Basel, 4056 Basel, Switzerland ‡ Dipartimento di Fisica e Geologia, Università degli Studi di Perugia, 06123 Perugia, Italy § Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands ∥ Institut de Ciència de Materials de Barcelona (ICMAB−CSIC), Campus de Bellaterra, 08193 Bellaterra, Barcelona, Spain ⊥ Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain * S Supporting Information ABSTRACT: One of the current challenges in nanoscience is tailoring the phononic properties of a material. This has long been a rather elusive task because several phonons have wavelengths in the nanometer range. Thus, high quality nanostructuring at that length-scale, unavailable until recently, is necessary for engineering the phonon spectrum. Here we report on the continuous tuning of the phononic properties of a twinning superlattice GaP nanowire by controlling its periodicity. Our experimental results, based on Raman spectroscopy and rationalized by means of ab initio theoretical calculations, give insight into the relation between local crystal structure, overall lattice symmetry, and vibrational properties, demonstrating how material engineering at the nanoscale can be successfully employed in the rational design of the phonon spectrum of a material. KEYWORDS: Phonon engineering, twinning superlattices, nanowires, Raman spectroscopy, DFT calculations D esigning materials with tailor-made phononic properties is crucial for many open problems within condensed matter and nanoscience, such as engineering efficient thermo- where only the crystal structure changes, while the atomic species and the nature of chemical bonding stay the same. This type of superlattices can be realized in nanowires (NWs),20−22 electric materials1,2 and keeping a low thermal budget in as the great progresses made in recent years in their synthetic nanoelectronics,3 as well as to envisage devices that can use growth23 enabled the epitaxial growth of novel crystal heat for information processing.4−6 Superstructures consisting phases,24,25 which in bulk can only be observed under extreme of a periodic arrangement of two materials, that is, super- conditions of temperature and pressure. The controlled lattices, can successfully exploit wave interference phenomena, switching between different crystal phases during the growth such as the formation of forbidden bandgaps and the opened the way to crystal phase engineering where unconven- modification of the density of states and group velocities of tional polytypes can be juxtaposed in an ordered fashion to the phonons, to control the heat flow by tuning the material’s most common polymorphs and create crystal phase super- thermal conductivity.7−10 A connection between the super- lattices. Because of the specific nature of these interfaces, it is lattice periodicity and coherent versus incoherent heat of great fundamental and applied interest to assess to what transport has been established, outlining two transport regimes extent one can tune by design the properties of these systems, dominated either by the corpuscular nature of phonons or by similarly to what can be achieved with conventional super- wave interference effects.11,12 Rough or defective interfaces lattices26,27 or phononic crystals.28 have been shown to significantly reduce the coherence of Twinning superlattices (TSLs)29,30 are a limiting case of phonon transport13 and thus much of the rich physics these crystal phase superstructures, where the only polytype exhibited by phononic superlattices is directly connected to present exhibits a periodic 60° rotation of the crystal lattice. the sharpness of the interfaces defining the superstructure.14 This is a unique metamaterial which locally is constituted by Typical issues that degrade the quality of ordinary hetero- junctions, for example, lack of sharpness of the interface, lattice Received: April 30, 2019 mismatch, and interdiffusion, become negligible or irrelevant in Revised: June 14, 2019 crystal phase superlattices,15−19 which are “homojunctions” Published: June 16, 2019 © 2019 American Chemical Society 4702 DOI: 10.1021/acs.nanolett.9b01775 Nano Lett. 2019, 19, 4702−4711 Nano Letters Letter Figure 1. Nanowire twin superlattice. (a) BF TEM image of a typical TSL nanowire investigated in this study. (b) Relation between position along the NW in (a) and extracted TSL period. (c) Schematic of a twin plane where spheres of different colors represent different types of atoms. (d) BF TEM image acquired at the top of the NW displayed in (a). (e) HAADF STEM image acquired in the position marked by the red square in (d). The red triangles indicate the position of the twin planes. The measured twin period is 32.6 nm. (f) BF high-resolution TEM image acquired at the bottom of the NW displayed in (a). (g) HAADF STEM image acquired in the position marked by the red square in (f). The red triangles indicate the position of the twin planes. The measured twin period is 11.4 nm. (h) Three-dimensional atomic reconstruction of a model TSL nanowire with six TSL periods. one single crystal phase but has the overall symmetry of a direction. Along the nanowire growth direction, regularly different one and that in III−V compounds has been obtained spaced twin planes can be observed. Bright-field (BF) TEM only with NWs. It is worth noting, however, that since their images show the ZB segments between consecutive twin planes discovery29,30 none of the functional properties of TSLs has with different contrast (Figure 1a). A twin acts as a mirror been reported so far. In particular, molecular dynamics plane, where the stacking of lattice planes ABCABC typical of a simulations of TSL in Si NWs have exposed the possibility pure ZB structure are changed into ABCACBA (Figure 1c). to tune the thermal conductivity in these systems by changing We define the TSL period (2L) as twice the distance between the distance between twin planes, namely the period of the two consecutive twin planes (Figure 1h). By analyzing the superlattice.31,32 In our report, we provide experimental variation of the contrast along the NW length, we obtain an evidence, corroborated and rationalized by ab initio calcu- estimation of the period. As displayed in Figure 1b, in our lations, of such modified properties and of their tunability. sample the period changes along the nanowire length: at the We study GaP TSLs where periodically arranged twin planes bottom of the NW, a first segment (∼500 nm) exhibits a with distances L ranging from 4 to 20 nm, separate zincblende constant period of about 10 nm; it is followed by a transition (ZB) segments.15 Therefore, although the twin defects region (500−600 nm) with increasing period from 10 to 30 themselves can in a way be considered as the shortest possible nm; at the end of the NW, a final segment (∼600 nm) has a wurtzite (WZ) inclusion, these NWs are made exclusively of constant period of about 30−40 nm. All the investigated TSL ZB GaP. Yet, the periodic twin arrangement confers a NWs exhibit very similar structural characteristics. The hexagonal symmetry to the NW as a whole. As we will discuss variation of the twin spacing along the NW length is shown below, this unusual crystal lattice is an excellent test-bed for by TEM and high-angle annular dark-field (HAADF) scanning monitoring how the existence of an overall periodicity affects TEM (STEM) images taken at the different location along the the phononic properties of the material in terms of number, NW (Figure 1d−g). Experimental TEM details along with frequency, and symmetry of the phonon modes arising from TEM images and periods’ estimation on five NWs are provided the superstructure. Indeed, we show that we can rationally in Supporting Information 1. design the phononic properties by tuning the superlattice The spatial dependence of the twin spacing characteristic of period. Moreover, we find that the TSL phonons are keeping our NWs enabled us to investigate the phononic properties of their coherence over tens of nanometers at room temperature, TSL NWs for different TSL periods under otherwise identical which is a clear indication that the defect-free and atomically conditions. sharp interfaces of TSL NWs make them the ideal super- Hexagonal Superstructure. We probed the phonons of structure to study coherent phonons and wave interference. TSL NWs by inelastic light-scattering experiments. The Results. Twinning Superlattice Nanowires. We grow GaP expected phonon modes at the Γ-point of the Brillouin zone nanowires by metal−organic vapor phase epitaxy using the were computed with ab initio density functional perturbation vapor−liquid−solid growth technique. We analyze the theory (DFPT) calculations33 within the local density structural properties of the wires by transmission electron approximation (LDA) with the ABINIT code.34,35 We also microscopy (TEM), which shows that the wires have ZB computed the corresponding Raman susceptibility tensors and structure, uniform diameter, and are grown along the ⟨111⟩ expected theoretical Raman spectra,36 as detailed in the 4703 DOI: 10.1021/acs.nanolett.9b01775 Nano Lett. 2019, 19, 4702−4711 Nano Letters Letter Figure 2. Twin superlattice phonon modes and hexagonal symmetry. (a) Calculated spectrum of a GaP twin superlattice with 9 nm period length. (b) Calculated reference spectra of bulk GaP in the ZB (black solid line) and wurtzite (red solid line) crystal phase. (c) Measured spectrum of a GaP twin superlattice nanowire with 9 nm period length (open circles). Deconvoluted Lorentzian components of the data fitting arising from the superlattice are displayed, along with the fit result (solid lines). (d) Measured reference spectra of GaP from a bulk ZB substrate (black circles) and a wurtzite nanowire (red circles) with superimposed fit results (solid lines). All theoretical and experimental spectra were obtained in the x̅(yy)x configuration. All spectra in panels a−d are normalized to the most intense peak contribution. (e) Residual plot (lines + circles) of the fit of the data displayed in panel c performed excluding the modes arising from the superlattice. The fit of the residual plot along with its Lorentzian components (only those arising from the superlattice) are displayed (solid lines). (f) Residual plots (lines + circles) of the fit of the data displayed in (d). The scale of panels e and f goes between −2.5% and 5% of the scale in panels c and d. Computational Methods. Polarization-resolved Raman scatter- 2. The single NWs (both TSL and WZ) were placed with the ing experiments and calculations were performed in back- long axis along the z-axis of the reference system. In particular, scattering geometry. The incident photon wavevector (ki) is the WZ [01̅10], [21̅1̅0], and [0001̅] axes were along x, y, and antiparallel to the x-axis and the scattered photon wavevector z, and the TSL [011], [21̅1], and [111̅] axes were along x, y, (ks) is parallel to x. As a consequence, the incident and and z. The reference bulk GaP was a (111)B substrate tilted in scattered light polarization vectors, εi and εs, lie in the yz plane, order to lie in the xz plane and to have the (011) surface lying which is the plane of the sample. εi and εs can be separately on the yz plane. controlled to obtain the desired scattering geometries. The The calculated spectrum of a GaP TSL with 9 nm period scattering configuration is expressed in the Porto notation, length is shown in Figure 2a. For comparison, the reference ki(εi, εs)ks: the outer terms, from left to right, refer to the calculated spectra of bulk ZB and WZ GaP are also shown in excitation and scattering direction of the light, respectively, and Figure 2b. The spectrum of the TSL in Figure 2a features the the inner bracket refers to the excitation and detection transversal optical (TO) mode at ∼362 cm−1 similarly to the polarizations. The main scattering geometries used in this work one of ZB GaP, but it also exhibits a quite pronounced EH 2 are the x̅(zz)x, x̅(yy)x, and x̅(zy)x. In the calculations, the mode, which is characteristic of a hexagonal symmetry like in nonanalytical corrections suitable to the specific scattering WZ.37,38 The presence of the EH 2 mode in the TSL NW is a geometry were applied as explained in Supporting Information clear indication that the overall symmetry of a TSL is 4704 DOI: 10.1021/acs.nanolett.9b01775 Nano Lett. 2019, 19, 4702−4711 Nano Letters Letter a Table 1. Calculated and Experimental Frequencies of TO, LO, and EH 2 modes for GaP ZB, WZ, and TSL TO (cm−1) LO (cm−1) EH −1 2 (cm ) ZB WZ TSL ZB WZ TSL WZ TSL theory 362.2 360.1 361.6 391.9 (396.5) 391.2 391.7 354.7 355.6 exp. 366.2 363.0 365.5 402.6 400.2 402.4 356.3 357.3 a Experimental frequencies refer to the samples of Figure 2c,d. The TSL period is 9 nm. The scattering configuration used both for experiments and −1 calculations is x̅(zz)x for the TO and LO modes and x̅(yy)x for the EH 2 . The error on the experimental values is ±0.5 cm . The value between parentheses for the calculated LO frequency of the ZB has been obtained by renormalization of the non-analytical corrections using the experimental value of the dielectric constant. hexagonal. Indeed, its corresponding space group is P63mc analytical correction to the calculation due to the larger values (#186), which is the same as the WZ structure. Notably, the of the LDA dielectric constant (ε = 12.9) with respect to Raman spectrum of the TSL also consists of several phonon experiment (ε = 11.1),45 leading to a smaller TO−LO splitting. modes on the higher wavenumber side of the TO mode, which Indeed, the discrepancy between the calculated and measured are neither observed in the ZB nor in the WZ phase but arise LO frequencies decreases if we renormalize the nonanalytical from the backfolding of the phonon dispersion due to the correction using the experimental value of the dielectric different lattice parameter introduced by the superlattice.39−41 constant (see value in parentheses in the table). According to our calculations, all those modes are transverse Because a difference between experimental and theoretical optical modes. frequencies occurs regardless of the crystal symmetry involved Single NWs were transferred on a Si(100) substrate and (ZB, WZ, TSL), when comparing theory to experiment we will polarization-dependent spatially resolved measurements were focus on the relative shift in the frequencies induced by the performed at room temperature and at 5.5 K. We performed different crystal symmetries and not on the absolute frequency measurements using two different excitation wavelengths; here, values. The agreement between theoretical and experimental we present results obtained with λexc = 514.5 nm at room frequency shifts is indeed very good. In going from the ZB to temperature (spectra acquired with λexc = 632.8 nm or at 5.5 K, the WZ phase, TO and LO modes downshift by different, showing consistent results, can be found in the Supporting consistent amounts in both the theoretical and the Information). In Figure 2c,d, we display the experimental experimental data. The frequencies of the modes in the TSL spectra corresponding to the theory in Figure 2a,b with the are in between the ZB and the WZ values, closer to the ZB. TSL and WZ spectra acquired on NW samples. In the The EH 2 mode, arising from the back-folding of the TO mode measured spectrum of a GaP TSL NW with 9 nm period in both WZ and TSL, upshifts by ∼1 cm−1 when going from length shown in Figure 2c, the TO and EH 2 modes are clearly the WZ to the TSL structure. The dependence of TO and EH 2 visible as in the computed spectrum. Differently from the frequencies on the TSL period will be discussed in more detail computed spectrum, the experimental one also exhibits a below (see, e.g., Figure 5). longitudinal optical (LO) mode at ∼402 cm−1 and a broad As predicted by the calculations, in the TSL experimental shoulder below the LO mode. The latter is ascribed to a spectrum displayed in Figure 2c, we also detect significant surface optical (SO) mode due to the finite size of the NW.42 spectral features between the TO and LO modes. Although the The LO mode is also present in the reference GaP spectra, finite full width at half-maximum (fwhm) of the phonon modes acquired on bulk ZB and on the WZ NW and depicted in prevents one from resolving each component of the spectrum Figure 2d. This mode is forbidden by selection rules in the by eye, a careful quantitative analysis clearly exposes the adopted scattering geometry and is indeed absent in the presence of numerous, well-defined phonon modes between theoretical results. The forbidden LO mode arises in both bulk the TO and LO modes, whose Lorentzian contributions to the and NW samples from the use of a high NA objective (see spectrum are displayed by solid lines. Figure 2e is particularly Supporting Information 3) and in the case of the WZ and TSL revealing in this sense. It shows the residual plot of a fit of data NWs also possibly from size effects responsible for a relaxation displayed in Figure 2c where we include only the EH 2 , TO, SO, of selection rules. The SO mode is also revealed in the and LO modes and a broad Gaussian to account for the spectrum collected from the WZ NW but absent in the contribution of the TSL modes between TO and LO modes; spectrum collected from the bulk (011) GaP, confirming its for comparison, in Figure 2f we provide also the residual plot origin. Both of these features (the finite size effects and the of the fit of the data collected on the two reference systems high NA of the objective) are not accounted for in the including the EH 2 , TO, LO, and SO modes. In the case of the theoretical modeling and thus this disagreement is not WZ GaP NW and the bulk ZB GaP, the obtained residual surprising. Finally, notice that the TO mode in the oscillates within 2% of the measured intensity, which confirms experimental spectra of the ZB, WZ, and TSL is broadened that all necessary contributions to the fits were already to the low-frequency side. This effect, well-known in bulk included in Figure 2d. Instead, the residual of the analysis of GaP,43,44 is due to the strong anharmonicity of the material, as the TSL spectrum, including the TSL broad contribution further discussed in the Supporting Information 4. between TO and LO, strongly increases in the range of Table 1 displays a comparison between the calculated (first frequencies between the TO and LO modes and has clearly row) and measured (second row) frequencies of the TO, LO, distinguishable features that can be fitted by Lorentzian peaks, and EH 2 modes for GaP ZB, WZ, and TSL. Our computed further corroborating the quantitative analysis of Figure 2c. frequencies agree well with the experimental results with a Tunability of the Phononic Properties. As discussed small underestimation which is within 4 cm−1 for all modes previously, the spacing between the twin planes varies along with the exception of the LO. The disagreement of the latter is the length of the NW, being always shorter at the bottom than larger because of the known underestimation of the non- near the tip. This feature is especially appealing because it gives 4705 DOI: 10.1021/acs.nanolett.9b01775 Nano Lett. 2019, 19, 4702−4711 Nano Letters Letter Figure 3. Tunability of the phononic properties in twin superlattices. (a) Calculated spectra of a GaP TSL with 4 nm (open stars and blue solid line) and 9 nm (open triangles and cyan solid line) period length. (b) Measured spectrum of a GaP TSL nanowire with ∼9 nm period length. Deconvoluted components of the data fitting are displayed (EH 2 mode in black dashed line, TO, SO, and LO modes in gray solid line). (c) Measured spectrum of a GaP TSL nanowire with ∼12.5 nm period length. Deconvoluted components of the data fitting are displayed. The intensity scales of the spectra in (b,c) are directly comparable. (d) Intensity vs wavenumbers of the calculated (empty symbols) and measured (filled symbols) phonon modes arising from the SL from the spectra displayed in panels a−c. Colors refer to the corresponding period length. Stars are for 2L = 4 nm, triangles are for 2L = 9 nm, circles are for 2L = 12.5 nm, as summarized in the legend. Vertical dashed lines show the good agreement between calculated and experimental phonon frequencies of the TSL with period of 9 nm. This is also evident in Table 2. The blue diamond refers to data acquired on a NW with ∼26 nm period length. All theoretical and experimental spectra were obtained in the x̅(yy)x configuration. In order to allow a fair comparison, all calculated and experimental frequencies are expressed as frequency shifts from the TO mode of the relative sample. Similarly, we have rescaled all the experimental intensities so that the EH 2 mode intensity retrieved experimentally on NW with the 9 nm period matches the EH 2 intensity calculated for a TSL with the same period. Table 2. Calculated and Experimental Frequencies of the Folding-Originated Modes for GaP TSL Expressed as Frequency Shifts from the TO Modea TSL mode 1 TSL mode TSL mode TSL mode TSL mode TSL mode TSL mode 7 (cm−1) 2 (cm−1) 3 (cm−1) 4 (cm−1) 5 (cm−1) 6 (cm−1) (cm−1) theory 7.6 9.5 14.0 18.9 23.5 27.0 29.0 exp. 7.9 9.6 14.4 20.2 24.6 29.3 a Experimental frequencies refer to the spectra displayed in Figure 3b. The TSL period in both theory and experiment is 9 nm. The scattering configuration used both for experiments and calculations is the x̅(yy)x. The error on the experimental values is ±1.5 cm−1. access to TSLs with different periods within a single NW. It is Figure 2a) with another with a shorter period of 4 nm. As worth mentioning here that the probed region of the NW is expected, a shorter period results in fewer peaks. limited to the laser spot size, and therefore at the two NW ends The quantitative calculation unveils that the fewer the peaks, we probe phonons arising from a constant TSL period. Our the higher their intensity. Indeed, in the limiting case of a computed Raman spectra predict the possibility of tuning the vanishing period we retrieve the WZ case where there is only number and intensity of the spectral features with wave- one very intense folded mode (EH 2 ). numbers beyond the TO by controlling the period of the TSL. Figure 3 also displays the experimental Raman spectra This is shown in Figure 3a, where we compare the computed acquired from two NWs with slightly different periods: 9 nm in Raman spectrum of a TSL with a period of 9 nm (the same of panel b and 12.5 nm in panel c (see Supporting Information 5 4706 DOI: 10.1021/acs.nanolett.9b01775 Nano Lett. 2019, 19, 4702−4711 Nano Letters Letter Figure 4. Dependence of the TSL phonon modes on the period lengths. (a) Raman map as a function of the position along the NW (step size: 0.15 μm) where the spectrum in Figure 2c was acquired. A SEM image of this NW is displayed on the left side of the map. Period decreases with increasing position, as indicated in the SEM image. The map was recorded in the x̅(yy)x configuration in order to highlight TSL-related features, and each line in the color plot was normalized to its maximum intensity (TO mode). (b) Raman spectra extracted from the map in the positions indicated by the arrows and dashed lines in (a). The x-scale is changed from panel a to panel b for sake of clarity. for different scattering configurations and for a discussion of between calculated and experimental frequencies of the TSL Raman selection rules). It is worth stressing that the twin with 9 nm period. period has been estimated by TEM measurements performed A one-dimensional Raman scan acquired along the length of on the very same wires after Raman measurements. Notice that the TSL NW studied in Figure 2 is displayed in Figure 4. The the period length of the NW in Figure 3b closely compares to spatially resolved investigation allows monitoring the changes one of the cases considered in our theoretical calculations in the Raman spectrum ensuing from the changes in the period (Figure 3a), thus we compare the frequencies of the modes of the TSL. Here, the period length decreases with increasing between the TO and LO modes originated from the back- position in the vertical scale. In Figure 4b, we display two folding in Table 2. The phonon frequencies are given as a representative Raman spectra extracted from the map in the relative shift with respect to the TO mode to get rid of the positions indicated by the arrows in Figure 4a. In the top part, slight underestimation of phonon frequencies by DFPT. the period is smaller and thus the intensity of the TSL folded- Considering the experimental error, we find a remarkable originated modes (EH 2 and the modes between TO and LO) is agreement between theory and experiment. Notice that the higher. In the bottom part, where the gold droplet is located, peak with 24.6 cm−1 frequency shift is quite broad, and thus it and the NW is slightly tapered, the LO mode is enhanced. This is probably resulting from a convolution of the separate 23.5 happens in all our measurements (see, e.g., Supporting and 27.0 cm−1 modes predicted by theory. Information Figures 6 and 7). The LO enhancement is due Let us now compare the spectra recorded on the NWs with the presence of the gold nanoparticle. Indeed, metal nano- slightly different periods (in Figure 3b,c) to demonstrate particles can affect the electromagnetic near-field profile in the experimentally the tunability of the phononic properties. The surrounding region, thus rendering forbidden modes greatly quantitative analysis of these spectra shows that at longer enhanced, a phenomenon very well-known for molecular samples in surface enhanced Raman scattering applications.46 periods, we observe a larger number of spectral features than at The map confirms that where the period is smaller, the shorter periods which is in line with the prediction of the intensity of the TSL folded-originated modes (EH 2 and the theory. It is interesting to observe that also the EH 2 peak, which modes between TO and LO) is higher. is the other characteristic signature of these TSLs, obeys the The period of the TSL not only determines the number, rule regarding its intensity, which is stronger for shorter frequency, and intensity of the folding-originated modes but it periods. A more quantitative comparison is carried out in also affects the frequency of the “bulklike” modes, namely TO Figure 3d, where we plot the intensity as a function of the and LO. In Figure 5a, we compare theoretical and Raman shift (calculated from the TO of the pertinent sample) experimental frequencies of TO mode as a function of the of all the measured and computed phonon modes extracted TSL period. We consider the WZ as a TSL with vanishing from fitting the spectra reported in Figure 3a−c. The NW with period and the ZB as a TSL with asymptotically long period 12.5 nm period shows one more peak between TO and LO (for the plot we set it equal to 1200 nm, i.e., about twice the than the NW with 9 nm period, which is in agreement with the laser spot) and plot the absolute frequency shifts from the expectation of an increased number of modes in a longer calculated and experimental TO mode of the ZB as open and period TSL, and the EH 2 mode is more intense in the NW with filled symbols, respectively. The theory predicts a gradual the shorter period. In the plot of the EH 2 mode, we also upshift with increasing period (i.e., decreasing frequency shift included the results obtained from a TSL period of ∼26 nm. with respect to the ZB TO). The experimental values nicely As expected, its intensity slightly decreases due to the increased reproduce this behavior. Although the shift of the TO mode period length. The relative spectrum and analysis are displayed with the TSL period is quite small, its observation is an in Supporting Information 6. We did not perform a important confirmation that we are probing the phonons of the quantitative analysis including ∼20 TSL modes between TO TSL and that our theory provides an accurate description of and LO because it would be affected by a non-negligible the physics involved. For the sake of completeness, we have degree of arbitrariness (see Supporting Information 6). The also considered the hypothetical situation in which the TO vertical dashed lines in Figure 3d highlight the good agreement shifts arise from the fact that in our scattering volume, we have 4707 DOI: 10.1021/acs.nanolett.9b01775 Nano Lett. 2019, 19, 4702−4711 Nano Letters Letter and the TSL theoretical data is quite small, one might still conclude that the simplified model gives a reasonable prediction of the TO frequencies of the TSL. In this respect, it is very important to stress that a similar approach is incapable of predicting other crucial features observed in our experiments and calculations, such as the appearance of spectral features between the TO and the LO mode, which are remarkable and unambiguous signatures of the coherent phonon propagation enabled by the superlattice, as well as the intensity and frequency of the EH 2 mode. Namely, we have computed with the simple model of weighted crystal phase contributions also the intensity and frequency of the EH 2 mode Figure 5. Dependence of TO and EH 2 modes on TSL period. (a) (gray dashed curve in Figure 5b and inset, respectively) and Calculated (open circles) and experimental (filled circles) frequencies compared it with the computed and measured (open triangles of TO mode in the x̅(zz)x configuration for GaP ZB, WZ, and TSL and filled circles in Figure 5b, respectively). Only the ab initio expressed as absolute shifts from the calculated and experimental ZB calculation of the TSL crystal accounts for the observed TO mode. The error bar of experimental frequencies is ±0.1 cm−1 intensities, while those resulting from the weighted WZ/ZB (smaller than the absolute error given by the spectral resolution, which is equal to 0.5 cm−1) because the data were acquired with the segments are lower than the experimental intensities. Even same experimental alignment. The dashed gray curve was obtained more striking, the model of weighted crystal phase from a model computing the spectra in TSL as a linear combination contribution cannot account for a dependence of the frequency of the ZB and WZ phases, weighting each contribution by the of the EH2 mode on TSL period (see inset in Figure 5b). corresponding volume ratio: the total volume of one period Vtot is the Our results provide evidence that periodic twins with NW cross section times the period of the TSL; the volume of the WZ periods up to about 35 nm cannot be regarded as, for example, Vwz is equal to the NW cross section times 2c, where c is the thickness wurtzite inclusions in a zinc-blende structure and rather confer of an AB segment and 2 is the number of twin defects in every period; the crystal with a new symmetry resulting in new properties. the volume of the ZB is derived by difference, Vtot − VWZ. The inset On the other hand, we suggest that the model with weighted shows the difference between the theoretical and experimental data and the gray curve (open circles and filled circles, respectively). (b) crystal phase contribution can be a useful tool to predict Calculated (open triangles) and experimental (filled triangles) phononic properties with randomly occurring twins and/or intensity of the EH2 mode in the x̅(yy)x configuration for GaP ZB, crystal phase mixing where coherent phonon effects do not WZ, and TSL. To allow a fair comparison, because the Raman occur. intensity is not absolute we have rescaled the experimental intensities Finally, we stress that our experimental results are very so that the experimental EH 2 mode intensity of the NW with the 9 nm sound and reproducible, as testified from the fact that (i) five period matches the calculated one, as in Figure 3d. The dashed gray different TSL NWs with very similar structural characteristics curve is the EH 2 mode intensity obtained with the weighted model. show very similar Raman spectra (see Supporting Information The inset shows the theoretical and experimental EH 2 frequency with 7); (ii) measurements performed in the same scattering respect to the WZ EH 2 frequency as a function of TSL period. The geometry but with different excitation wavelengths on different dashed gray curve represents the EH 2 frequency shift provided by the weighted model. NWs exhibit consistent spectral features (see Supporting Information 8); (iii) data acquired at 5.5 K on the same NWs measured at room temperature in the same configuration show portions of ZB (namely, the segments sandwiched between consistent results (see Supporting Information 9). two consecutive TSL planes) and portions of WZ (namely, the The presence of the EH 2 mode and the other backfolded TSL planes, which can be viewed as WZ inclusions consisting peaks in the TSL NWs is an important indication that the of one single AB bilayer). Therefore, we develop a simple associated phonons are keeping their coherence over a few model where we weigh each contribution (ZB and WZ) with TSL periods, namely, that the mean free path of those phonons the corresponding volume ratio, and the TSL spectrum is is longer than the period length. This is clearly the case for the computed as a linear combination of the theoretical ZB and short period part of the NWs but also for the long period part, WZ spectra. We then analyze the obtained spectra to extract because also in that region we observe clear, though less the TO frequency shift as a function of TSL period. The results intense (as predicted by theory), TSL phonon modes. This are displayed by the gray dashed curve in Figure 5a. The inset observation agrees well with our calculated mean free paths of shows the difference between the data and the curve. By optical phonons of bulk GaP at room temperature, which can construction, the curve intersects the WZ and ZB theoretical be as long as 50 nm. Noticeably, backfolded phonon modes data, while it does not provide an accurate estimate of the TSL were observed until now in “conventional” heterostructure TO theoretical frequencies (the difference is indeed about 0.5 superlattices with considerably shorter periods than the twin cm−1), which were computed by considering the whole TSL periods probed in this study.41 The maintenance of coherent crystal with its own symmetry and not as a weighted sum of phonon propagation over tens of nanometers is the essential large ZB and thin WZ portions. The same difference is requirement for its exploitation in thermal applications based observed in the experimental data as well. It is worth noticing on coherent phonons. Quite remarkably, most of our study, that for periods around 40 nm, the measured TO mode which provides the experimental demonstration of coherent frequency is very close to the one of the ZB structure and does phonons in NWs, was carried out at room temperature, and not differ significantly from the one of the simplified model, because already at room temperature we are probing coherent whereas the deviations for periods up to 30−35 nm lead us to phonons, low temperature conditions, which correspond to a infer the TSL period up to which we observe coherent phonon longer phonon mean free path, are not needed to unveil TSL- effects. However, as the discrepancy between the dashed curve originated phonon modes. 4708 DOI: 10.1021/acs.nanolett.9b01775 Nano Lett. 2019, 19, 4702−4711 Nano Letters Letter In conclusion, we have reported on the phononic properties cutoff of 38 Ha, an energy cutoff for the fine fast Fourier of GaP nanowires twinning superlattices by investigating them transform of 76 Ha, and a strict convergence criterion of the with inelastic light scattering. We have observed the EH 2 mode wave function residual norm of 10−22 were used. characteristic of the WZ crystal structure and a number of In order to properly account for the scattering geometry spectral features beyond the TO mode. The first of these used in the experiment, the Raman intensity of each mode n observations was unexpected, because the nanowires inves- has been calculated as tigated locally possessed a ZB structure. However, the twin defect stacking confers an overall hexagonal structure to the In ∝ |εiR nεs|2 system giving rise to this phonon mode. The second where Rn is the Raman susceptibility tensor calculated ab initio, observation was a direct result of the folding of the dispersion while εi and εs are the polarization vectors of the incident and relation determined by the periodic superstructure. Both of scattered light, respectively.51 Once the intensity for each these observations were unambiguously corroborated by ab phonon mode has been calculated, Raman spectra are initio theoretical calculations and by the dependence of these generated by summing up Lorentzian functions, each spectral fingerprints on the spacing of the twin planes. This fact associated to a calculated mode frequency. The Lorentzian supports the tunability of the phonon spectrum of these functions have a full width at half-maximum that is chosen to systems and paves the way toward the achievement of reproduce the experimental one. phononic properties by design.31,32,47 We suggest that future Raman Experimental Details. Raman experiments were heat transport experiments will show that this controlled performed by exciting the samples either with the 633 nm line tuning of the phonon spectrum also results in a measurable of a HeNe laser or with the 514.5 nm line of an Ar+Kr+ laser. modification of the thermal conductivity, because (i) our The incident power was kept below 1 mW to avoid heating or calculations demonstrate that also acoustic modes undergo the damaging effects. The samples were illuminated with a high same folding as optical modes (see Supporting Information numerical aperture (0.95) 100× objective (if not differently 10) and (ii) although high frequency optical phonons per se do specified), which allows a spatial resolution of about 600 nm not contribute significantly to the thermal conductivity, they for the 514.5 nm laser. The polarization of the incident laser play an important role in third- and higher-order phonon light and of the backscattered beam can be controlled and scattering processes that also involve acoustic phonons. selected by means of polarization optics. The scattered light Methods. Nanowire Growth. The zincblende GaP TSLs was collected by a T64000 triple spectrometer in subtractive NWs were grown in an Aixtron Close Coupled Showerhead mode, equipped with a 1.800 g/mm grating and a liquid MOVPE reactor. Prior to growth, we used soft contact nitrogen-cooled CCD detector, providing a spectral resolution lithography to make regular nanoholes pattern in a SiNx-coated of 0.5−1 cm−1. T = 5.5 K measurements were performed by GaP (111)B wafer. Then the Au-catalyzed GaP TSLs were loading samples in a He continuous-flow cryostat using the grown by the vapor−liquid−solid mechanism with a V/III 514.5 nm laser. ratio of 21.5 at 640 °C.48 Phosphine (PH3) and trimethyl gallium (TMGa) were used as precursors, and hydrogen chloride gas was used to prevent nanowire tapering. The ■ * ASSOCIATED CONTENT S Supporting Information wurtzite (WZ) GaP NWs were grown with the method The Supporting Information is available free of charge on the described in ref 49. ACS Publications website at DOI: 10.1021/acs.nano- Structural Investigation. TEM studies on NWs were lett.9b01775. performed using a probe-corrected JEOL ARM 200F trans- mission electron microscope operated at 200 kV in both BF Further structural characterization of the nanowires, TEM mode and HAADF STEM mode. details on computational and spectroscopic methods and Computational Methods. We have performed ab initio analysis, and Raman spectra taken on different nano- DFPT calculations33 within the LDA with the ABINIT wires, with different scattering geometries, at low code34,35 of TSLs with a period of 3, 4, and 9 nm. The latter temperature, and with different excitation wavelengths compares directly with a periodicity of the twins found in some (PDF) of the samples investigated experimentally. We use hexagonal cells, containing N = 10, 12, and 30 monolayers, for the three TSLs studied. Notice that to satisfy periodic boundary ■ AUTHOR INFORMATION Corresponding Authors conditions an even number of twin defects, placed along the *E-mail: rrurali@icmab.es. ZB [111] crystal axis, must be included and thus the *E-mail: ilaria.zardo@unibas.ch. computational cells used in the calculations contain two twin ORCID planes. The Brillouin zone was sampled with a converged grid Marta De Luca: 0000-0001-6061-3261 of 16 × 16 × M, with M taking values of 3, 2, and 1 going from Sebastian Kölling: 0000-0002-6606-9110 the smallest to the largest cell. The calculations have been performed in a bulk system, as we do not expect the vibrational Erik P. A. M. Bakkers: 0000-0002-8264-6862 properties of NWs of these characteristic diameters to be Riccardo Rurali: 0000-0002-4086-4191 affected by confinement. We compute the Raman susceptibility Xavier Cartoixà: 0000-0003-1905-5979 tensor from the third derivative of the total energy: twice with Ilaria Zardo: 0000-0002-8685-2305 respect to the application of an electric field (i.e., incident and Author Contributions scattered light polarization vectors) and once with respect to I.Z. conceived the experiment. M.D.L. and C.F. performed the the phonon displacement coordinates, making use of the 2n + measurements. M.D.L., C.F., and I.Z. analyzed the exper- 1 theorem.50 Given the sensitivity of the energy derivatives to imental results. Y.R. and E.P.A.M.B. grew the samples. S.K. and the quality of the converged wave functions, a high plane wave M.Y.S. prepared the samples for TEM investigation, which was 4709 DOI: 10.1021/acs.nanolett.9b01775 Nano Lett. 2019, 19, 4702−4711 Nano Letters Letter performed by M.A.V., while M.Y.S. took SEM images. R.R. and (10) Li, D.; Wu, Y.; Fan, R.; Yang, P.; Majumdar, A. Thermal X.C. performed the theoretical calculations. R.R., I.Z., and conductivity of Si/SiGe superlattice nanowires. Appl. Phys. Lett. 2003, M.D.L. wrote the manuscript. All authors discussed the results 83, 3186. and commented on the manuscript. (11) Luckyanova, M. N.; Garg, J.; Esfarjani, K.; Jandl, A.; Bulsara, M. T.; Schmidt, A. J.; Minnich, A. J.; Chen, S.; Dresselhaus, M. S.; Ren, Notes Z.; Fitzgerald, E. A.; Chen, G. Coherent Phonon Heat Conduction in The authors declare no competing financial interest. Superlattices. Science 2012, 338, 936. ■ (12) Ravichandran, J.; Yadav, A. K.; Cheaito, R.; Rossen, P. B.; Soukiassian, A.; Suresha, S. J.; Duda, J. C.; Foley, B. M.; Lee, C.-H.; ACKNOWLEDGMENTS Zhu, Y.; Lichtenberger, A. W.; Moore, J. E.; Muller, D. A.; Schlom, D. This project has received funding from the European Research G.; Hopkins, P. E.; Majumdar, A.; Ramesh, R.; Zurbuchen, M. A. Council (ERC) under the European Union’s Horizon 2020 Crossover from incoherent to coherent phonon scattering in epitaxial research and innovation program (Grant Agreement 756365) oxide superlattices. Nat. Mater. 2014, 13, 168. (13) Wen, Y.-C.; Hsieh, C.-L.; Lin, K.-H.; Chen, H.-P.; Chin, S.-C.; and from the Swiss National Science Foundation research Hsiao, C.-L.; Lin, Y.-T.; Chang, C.-S.; Chang, Y.-C.; Tu, L.-W.; Sun, Grant (Project Grant 200021_165784). R.R. acknowledges C.-K. Specular Scattering Probability of Acoustic Phonons in financial support by the Ministerio de Economia,́ Industria y Atomically Flat Interfaces. Phys. Rev. Lett. 2009, 103, 264301. Competitividad (MINECO) under Grant FEDER-MAT2017- (14) Huberman, S. C.; Larkin, J. M.; McGaughey, A. J. H.; Amon, C. 90024-P and the Severo Ochoa Centres of Excellence Program H. Disruption of superlattice phonons by interfacial mixing. Phys. Rev. under Grant SEV-2015-0496 and by the Generalitat de B: Condens. Matter Mater. Phys. 2013, 88, 155311. Catalunya under Grant 2014 SGR 301. X.C. acknowledges (15) Caroff, P.; Dick, K. A.; Johansson, J.; Messing, M. E.; Deppert, financial support by the Ministerio de Economia,́ Industria y K.; Samuelson, L. Controlled polytypic and twin-plane superlattices in Competitividad under Grant TEC2015-67462-C2-1-R III−V nanowires. Nat. Nanotechnol. 2009, 4, 50. (16) Dick, K. A.; Thelander, C.; Samuelson, L.; Caroff, P. Crystal (MINECO/FEDER). The calculations have been performed phase engineering in single InAs nanowires. Nano Lett. 2010, 10, at the Red Española de Supercomputación (RES) within the 3494. project “Phonons dispersion relation in GaP crystal phase (17) Bolinsson, J.; Caroff, P.; Mandl, B.; Dick, K. A. Wurtzite− superlattices” (FI-2017-1-0026). Solliance and the Dutch zincblende superlattices in InAs nanowires using a supply interruption province of Noord-Brabant are acknowledged for funding the method. Nanotechnology 2011, 22, 265606. TEM facility. M.D.L. acknowledges support from the Swiss (18) Assali, S.; Gagliano, L.; Oliveira, D. S.; Verheijen, M. A.; National Science Foundation Ambizione Grant (Grant Plissard, S. R.; Feiner, L. F.; Bakkers, E. P. A. M. Exploring Crystal PZ00P2_179801). C.F. acknowledges financial support from Phase Switching in GaP Nanowires. Nano Lett. 2015, 15, 8062. (19) Thelander, C.; Caroff, P.; Plissard, S.; Dey, A. W.; Dick, K. A. 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