Young's Modulus of Wurtzite and Zinc Blende InP ... - ACS Publications

May 23, 2017 - Lappeenranta University of Technology, P.O. Box 20, Lappeenranta FI-53851, Finland. § ... ITMO University, Saint Petersburg 197101, Ru...
0 downloads 0 Views 4MB Size
Download PDF
Letter pubs.acs.org/NanoLett

Young’s Modulus of Wurtzite and Zinc Blende InP Nanowires Mikhail Dunaevskiy,*,†,∥ Pavel Geydt,‡ Erkki Laḧ deranta,‡ Prokhor Alekseev,† Tuomas Haggrén,§ Joona-Pekko Kakko,§ Hua Jiang,§ and Harri Lipsanen§ †

Ioffe Institute, Saint Petersburg 194021, Russia Lappeenranta University of Technology, P.O. Box 20, Lappeenranta FI-53851, Finland § Aalto University, P.O. Box 15100, Espoo FI-00076, Finland ∥ ITMO University, Saint Petersburg 197101, Russia ‡

S Supporting Information *

ABSTRACT: The Young’s modulus of thin conical InP nanowires with either wurtzite or mixed “zinc blende/wurtzite” structures was measured. It has been shown that the value of Young’s modulus obtained for wurtzite InP nanowires (E[0001] = 130 ± 30 GPa) was similar to the theoretically predicted value for the wurtzite InP material (E[0001] = 120 ± 10 GPa). The Young’s modulus of mixed “zinc blende/wurtzite” InP nanowires (E[111] = 65 ± 10 GPa) appeared to be 40% less than the theoretically predicted value for the zinc blende InP material (E[111] = 110 GPa). An advanced method for measuring the Young’s modulus of thin and flexible nanostructures is proposed. It consists of measuring the flexibility (the inverse of stiffness) profiles 1/k(x) by the scanning probe microscopy with precise control of loading force in nanonewton range followed by simulations. KEYWORDS: Nanowires, Young’s modulus, scanning probe miscroscopy, Wurtzite, InP

V

It should be noted that thin InP NWs may exhibit a wurtzite structure.16 As far as we know, at the moment, there are only a few publications in which the Young’s modulus of wurtzite InP is estimated. There is a paper on measuring the deformation potential in wurtzite InP NW that may indicate the possibility of some differences between the Young’s modulus in wurtzite (WZ) and zinc blende (ZB) InP.17 Also, our group attempted to measure the Young’s modulus of wurtzite InP NWs;18 unfortunately, the mentioned work18 contained some methodological inaccuracies, and because of this, it partly contained erroneous results of experiments. In the present study, the advanced measuring procedure for registering the bending of thin cone-shaped NWs with scanning probe microscope (SPM) was developed and used to determine the Young’s modulus of InP NWs. A total of three series of samples (S1, S2, and S3) of conical InP NWs were studied. They had different geometric parameters (length L ∈ [2,3] μm, average radius Rmid ∈ [15,45] nm, and cone angle α ∈ [1°,1.5°]) and crystal structure (wurtzite or mixed “zinc blende/wurtzite”) shown in Table S1. These NWs were grown in metalorganic vapor-phase epitaxy (MOVPE) chamber by vapor−liquid−solid mechanism under

arious types of semiconductor nanowires (NWs) have been intensively investigated in recent years. Several ingenious ideas of creating advanced devices based on NWs are proposed for sensorics,1−3 nanoelectronics,4,5 photovoltaics,6,7 and piezotronics.8 A number of research groups are inspired to build effective photovoltaic devices based on III−V NWs. An important problem of these devices is the high density of surface states, which leads to the charge carrier depletion in thin NWs. To solve this problem, one must either use surface passivation of the NWs or use materials with initially low density of surface states.9,10 InP has a low density of surface states; hence, solar cells based on InP NWs have one of the highest efficiencies (∼13%) among the NW-based photovoltaic elements.11 Therefore, the study of the InP NWs properties seems to be a beneficial task. When designing the NW-based devices, it is important to know not only their electrical characteristics but also their mechanical properties. Thin NWs have a low bending stiffness coefficient due to their high aspect ratio. This can lead to considerable bends of NWs and even their breakage. Therefore, it is important to reveal information about the elastic strength of thin NWs. Few crucial studies have shown that the effective Young’s modulus of thin NWs (ZnO, GaAs, etc.) is significantly different from the tabulated values for corresponding bulk materials.12−15 In this paper, the Young’s modulii of thin InP NWs with radii in the range 17−40 nm will be studied. © 2017 American Chemical Society

Received: January 23, 2017 Revised: April 23, 2017 Published: May 23, 2017 3441

DOI: 10.1021/acs.nanolett.7b00312 Nano Lett. 2017, 17, 3441−3446

Letter

Nano Letters

(ΔE ≈ 85 meV) of the photoluminescence spectral line related to interband transitions (see Figure S1b). Part of the NWs have grown approximately normally to the surface. It was impossible to carry out accurate SPM measurements of the bend of these NWs. However, the major part of NWs in each array was inclined (at a small angle of 10−20°) to the substrate’s surface. The SPM experiments, i.e., measurement of the bending profiles, were performed exactly on these slightly inclined InP NWs. It should be noted that the angle of inclination of the SPM cantilever to the studied sample surface is approximately 14°. Thus, NWs that were “tilted toward” the inclined SPM cantilever (Figure 1d) were chosen for measurements. This allowed the acquisition of the most-stable geometry of the SPM bending experiment when the axis of force application is locally perpendicular to the surface of the bent NW. We used SPM “Multimode 8” (Bruker), providing the PeakForce Tapping mode and regime of quantitative nanomechanics (QNM).19 To work with superflexible InP NWs, we have chosen SNL-10 and ScanAsyst-Air probes (both from Bruker) with low stiffness coefficients in the range of 0.06−0.4 N/m. A specific feature of the investigated InP NWs was that they had extremely low bending stiffness due to the low radius-tolength ratio (R/L ≈ 10−2). For example, cylindrical NW with radius R = 20 nm and length L = 2 μm has a bending stiffness coefficient k ≈ 0.005 N/m. Therefore, when acting onto the NW, even with considerably small force (F = 1−5 nN), the obtained bending will be hundreds of nanometers. Such a value is excessively high for accurately tracking the bending movement of the nanowire by SPM devices. This means that, by usual methods of SPM, it is impossible to obtain a stable image of thin NWs. To solve the above-mentioned problems, we used the PeakForce mode. This regime was specifically designed to minimize the SPM force acting on the surface and makes it possible to investigate soft matter or even NWs with low bending stiffness. When operating in this PeakForce mode, we were able to controllably reduce the force acting on the surface down to 0.05 nN and maintain it during scanning with a high level of accuracy. Working with such small forces allowed us to obtain low-noise images of the inclined InP NWs and even not to bend them during the scanning. This was an important step necessary for further increasing the accuracy of the measurement of a NW’s bending. It is worth noting that previously researchers were utilizing the method of load curves F(z) measurement at some points of NWs in most studies dedicated to measurement of NW Young’s moduli.14,20,21 The bending stiffness value knw was determined from the load curves procedure. Then, using the value of the bending stiffness, it is possible to determine the value of NW Young’s modulus according to formula 1:

catalytic Au droplets on (111) Si substrate with native oxide at 450 °C. The V/III ratio for S1 and S2 was 400 and 200 for sample series S3. The geometrical parameters of NWs were determined by high-resolution transmission electron microscopy (Figure 1a) and scanning electron microscopy (Figure 1c) and then by scanning probe microscopy. The type of crystal structure for InP NWs was determined by electron diffraction (Figures 1b and S1a). The orientation of the WZ NWs long axis was [0001]. The orientation of the ZB/WZ (predominantly ZB) NWs long axis was [111]. The wurtzite crystal structure of the S1 sample was also confirmed by the blue-shift

3π R4 (1) 4 L3 where k is the stiffness coefficient of a NW, E is the Young’s modulus, R is the radius of a NW, and L is the length of a NW. It should be emphasized that this approach is justified in the case of thicker NWs with R higher than 50 nm. However, in the case of NWs with R ≈ 10 nm, the use of this method can lead to large errors and nonreproducibility of experimental results. The reason is that for measuring the bending stiffness coefficient k, one must first obtain an SPM image of inclined k=E

Figure 1. (a) HRTEM image of the end of an InP nanowire (S1 sample); (b) electron diffraction pattern indicating wurtzite structure of InP nanowires at the S1 sample; (c) scanning electron microscopy image of an ensemble of InP nanowires; (d) scheme of SPM bending profile measurement; (e) orientation of SPM X-axis relating to the long axis of the nanowire. 3442

DOI: 10.1021/acs.nanolett.7b00312 Nano Lett. 2017, 17, 3441−3446

Letter

Nano Letters NWs and then move the SPM-probe in a specified XY location on the NW surface and only then measure the load curve F(z). Due to the nonideal operation of the SPM probe XY displacement system (drift and creep), the error in XY positioning may exceed the diameter of thin NW. Therefore, the SPM probe can fail to come into contact with the NW, while in almost all cases, the probe will not measure the top part of NW. This will lead to the fact that instead of the normal bending of the nanowire a partially lateral bending of the NW will occur. Additionally, in this case, unstable probe−nanowire contact and slipping of the SPM probe during measurement of load curves F(z) may occur. In the course of our experiments with thin InP NWs, we faced the above-mentioned set of methodological difficulties18 and, as a result, completely abandoned the method of load curves F(z). We propose a following advanced SPM method of measuring the bending profiles w(x) on the inclined InP NWs with different small load forces Fpeak. The X-axis direction of the scanning should be set to be parallel to the long axis of the NW (Figure 1e). It is important to note that the Y-step between the lines (Δy) in the scan should be significantly smaller than the radius of the NW (Δy < RNW). This will allow at least one or two scan profiles to be detected when the SPM probe moves exactly through the top part of the NW without slipping from it. When the value of the load force (Fpeak = 0.05, 1, 2, and 5 nN) will increase, the bending of the NW will also increase. This will lead to a change in the registered topography of inclined NW. Our experiments show that the bending of InP NWs is close to zero when working with ultralow load force Fpeak = 0.05 nN. Therefore, by subtracting the height profile obtained for the load force 0.05 nN from the topographic profile of inclined NW obtained for the higher load force, e.g., 5 nN, one can get the bending profile w(x) for the force of 5 nN represented by formula 2: w(x)5 nN = h(x)5 nN − h(x)0.05 nN

(2)

Similarly, one can get bending profiles for various values of peak force w(x)1 nN, w(x)2 nN, w(x)10 nN, etc. In the course of our measurements, we have observed a linear increase of bending profiles with increasing of load force values, i.e., w ≈ Fpeak (Figure 2d). This means that in this range of applied forces, the bending of the NW is described by the Hooke’s law. For all experiments described in this paper, we have chosen the load force values so as to not reach the nonlinear bending conditions. After the measurements of the bending profiles of InP NWs, control measurements with ultralow peak force were always carried out to detect possible plastic deformations. It should be noted that no residual plastic deformations were detected for all investigated NWs. Measured bending profiles w(x)F1, w(x)F2, ..., w(x)Fi were divided by the magnitudes of corresponding load forces applied to the NWs to get their inverse stiffness (or flexibility) profiles f(x)=1/k(x). It was especially important that the flexibility profiles f(x) obtained for different forces were found to be almost equal and repeatable because the bending of the NWs was proportional to the load force w ≈ Fpeak. Flexibility profiles obtained with four or five different load forces were averaged to diminish the noise. Then, the averaged flexibility profile was analyzed using formula 3 for a conical beam, which allowed us to extract information about the Young’s modulus of conical InP NWs. It is worth noting that it is more convenient to analyze not the k(x) profile but exactly the flexibility profile 1/k(x) because

Figure 2. (a) SPM image of the inclined inP nanowires; (b) 3D SPM image of one of the InP nanowires when scanning it with ultralow force Fpeak = 0.05 nN; (c) cross-section profile h(x)0.05 nN; (d) bending profiles for various values of peak force w(x)1 nN, w(x)2 nN, w(x)5 nN; (e) flexibility profile 1/k(x) measured on the InP NW and smooth fitting curve using formula 3 for a conical beam. 3443

DOI: 10.1021/acs.nanolett.7b00312 Nano Lett. 2017, 17, 3441−3446

Letter

Nano Letters

measurement of their bending profiles. This was followed by the precise measurement of the “height of horizontally lying NWs” and then recalculated into their average radius, as discussed in our previous work.14 As a result of this work, the Young’s moduli for 16 InP NWs (for samples S1, S2, and S3) were calculated. Figure 3 shows

it reaches zero when approaching the base of a NW. If one tries to analyze the profile k(x), then stiffness will reach infinity at the approach to the NW base, creating problems for data simulation and analysis of the elastic modulus. Moreover, we should note that the method of measurement for the flexibility profiles, 1/k(x), is superior to the method of measurement of load curves, F(z). The reason is that the flexibility profile already contains information on a series of stress tests conducted over the entire length of the NW. This significantly improves the accuracy of the measurement of Young’s modulus with its statistical repeatability. It should also be emphasized that the developed method of measurement of flexibility profiles with precise SPM force control mode is universal and can be applied to any thin and flexible onedimensional objects (NWs, fibrils, asbestos tubes, nanotubes, etc.) or two-dimensional thin and flexible membranes (graphene). Because in this study we were investigating the NWs with conical shape, in terms of the continuum theory of elasticity, we derived a formula (see equations S.1−S.6) that relates the flexibility profile 1/k(x) of a conical NW and the Young’s modulus E of its material: 1 4 1 1 x3 = 4 k(x) 3π E R mid (1 + a(x − L /2))(1 − aL /2)3

Figure 3. Dependence of the measured Young’s modulus on the average radius of conical InP nanowires.

(3)

Here, Rmid is the average radius of a NW, L is the length of a NW, a = α/2Rmid is an auxiliary coefficient associated with the cone angle tangent α, and x is the coordinate of the SPM probe when acting onto the NW. It should be emphasized that formula 3 becomes equal to formula 1 for a NW of constant circular cross-section when a → 0. The numerical simulation of experimental data for the flexibility profile using formula 3 allows us to obtain the value of Young’s modulus E and the coefficient a = α/2Rmid. Figure 2a shows an image of the array of inclined InP NWs as well as an image of one of the NWs (Figure 2b) when it was scanned with ultralow force Fpeak = 0.05 nN and its crosssectional height profile h(x)0.05 nN (Figure 2c). The bending profiles obtained with increasing load force values (1, 2, and 5 nN) are presented in Figure 2d. Figure 2e demonstrates the flexibility profile 1/k(x) measured for this certain NW and smooth fitting curve using formula 3 for a conical beam. As a result of this fit, we obtained: (a) the value of Fit1 = E·Rmid4 and (b) the value of Fit2 = α/2Rmid. From scanning electron microscopy (SEM) data (Figure S1c), we recognized the typical value of the cone angle α for the array of NWs. This allowed us to determine the average radius of the NW Rmid = α/(2Fit2). Then, knowing the average radius Rmid of the NW, one can get the value of Young’s modulus E = Fit1/Rmid4. Here, we must strongly emphasize that an accurate determination of a NW’s radius is crucial for the accurate determination of the Young’s modulus of the NW’s material. The above-described method makes it possible to calculate the NW radius as a result of experimental data fit. Furthermore, control experiment was performed using a high-resolution SEM (resolution Δ ≈ 1−2 nm) to check the accuracy of our modeled determination of radius for 6 NWs. It has been found that values of average radii of the NWs measured with highresolution SEM were 7−10% higher than those estimated from the SPM data fitting. We considered this to correct the obtained values of Young’s modulus. Besides that, the rest part of the NWs were intentionally broken by the SPM probe after

the dependence of obtained Young’s moduli E(R) from the average radius of InP NWs. It can be seen that there are two qualitatively different regions on the graph: (1) thin (R < 27 nm) WZ nanowires with a Young’s modulus of 130 GPa and (2) thicker (R > 27 nm) “mixed ZB/WZ” nanowires with a Young’s modulus of 65 GPa. This difference can be explained in terms of two following approaches: (1) a “core−shell” model with a hard shell and (2) real difference in the Young’s moduli of WZ and “mixed ZB/WZ” nanowires. Indeed, one can try to explain the experimentally observed dependence of the Young’s modulus on the NWs radius in the framework of the core−shell model.22,23 For that, it is necessary to assume that the surface layer of InP NW is hard and has a high value of the Young’s modulus Eshell > Ecore. In this case, the dependence of Young’s modulus on the radius is described by formula 4: ⎛ E − Ecore ⎛ rs r 2 r 3 r 4 ⎞⎞ ⎜ E = Ecore⎜1 + 8 shell − 3 s2 + 4 s3 − 2 s4 ⎟⎟ ⎝ Ecore D D ⎠⎠ D D ⎝ (4)

where rs is thickness of the surface shell layer, and D is the diameter of the NW.12 However, it is important to note that the fold increase in the Young’s modulus experimentally observed for the NWs with radii in the range of 20−30 nm (see Figure 3) cannot be described by formula 4 with realistic values of Eshell and rs. The latter circumstance is due to the fact that the native oxide on the surface of the InP nanowire is very thin. Highresolution transmission electron microscopy (HRTEM) imaging did not reveal any surface native oxide layers for wurtzite InP NWs, which were kept in room air for about 1 year (see Figure 1a). At the same time, HRTEM imaging for zinc blende InP NWs demonstrated a surface native oxide layer with a 1 nm thickness. Additional elemental mapping done with electron diffraction spectroscopy (EDX) also did not indicate the signal from oxygen, which can verify that the native oxide is very thin. Moreover, literature sources confer with this 3444

DOI: 10.1021/acs.nanolett.7b00312 Nano Lett. 2017, 17, 3441−3446

Letter

Nano Letters

So, in the case of WZ InP NW, the theoretically found value of Young’s modulus (120 ± 10 GPa) is in good agreement with our experimental value of 130 GPa. However, in the case of ZB InP NW, the measured value of Young’s modulus was 65 GPa, i.e., 40% lower than the value predicted by the theory (110− 120 GPa). We use the following considerations to explain this difference: (i) It was shown by molecular dynamics modeling in work by Moon33 that the 30% decrease from the expected Young’s modulus for ZnS NWs is explained by ZB/WZ mixing. Remarkably, the Young’s moduli for the “ZB[111]” and “WZ[0001]” directions in ZnS have approximately similar values. The reason for the decreasing of the Young’s modulus is that phase borders between ZB and WZ phases in polytypical NWs are potentially deformable, weak, or defect sites. They decrease the strength of the material and lead to formation of areas, providing significant deformability under extensive loads, which finally leads to fractures inside a nanostructure. (ii) A similar effect of decreasing of the Young’s modulus was experimentally observed by Lexholm for ZB InAs NWs.34 The value of modulus was reported to decrease from E[111] = 97 GPa (for bulk ZB InAs) until ∼40−55 GPa, when the diameter of the NWs decreased from 100 nm until 40−50 nm, i.e., the declining diameter reduced the Young’s modulus by ∼40−50%. It is interesting to note that calculated value of Young’s modulus for WZ InAs in the [0001] direction is 96 GPa, which is nearly the same as the ZB E[111] value (97 GPa). Consequently, we suppose that one of the possible factors affecting the decrease of experimentally measured Young’s modulus of NWs (like in our case) is the same effect caused by ZB/ WZ mixing. Therefore, we believe that the reason for a “reduced” value of the Young’s modulus measured for InP NWs with radii R > 27 nm is the ZB/WZ mixing. In conclusion, a developed scanning probe microscopy approach for the measurement of Young’s modulus of thin and flexible nanowires was presented in this work. The method involves measuring of the flexibility profiles, 1/k(x), in the regime of precise force control. A formula that relates the flexibility profile of the conical NW and its Young’s modulus was derived and utilized to analyze the bending of conical InP nanowires. With this approach, the Young’s modulus of the conical InP nanowires with wurtzite and zinc blende structure was directly measured with a scanning probe microscope. The obtained value of the Young’s modulus of wurtzite InP NWs (130 ± 30 GPa) was close to that for the WZ InP material in the [0001] direction (E[0001] = 120 GPa). The Young’s modulus of mixed “zinc blende−wurtzite” InP NWs (65 ± 10 GPa) appeared to be 40% less than the value predicted by the theory (E[111] = 110−120 GPa).

assumption about the 1 nm thickness of native oxide layer on ZB InP.24 If the value of the thickness of the shell oxide layer rs = 1 nm is being put into the core−shell model, then a sloping of the E(R) dependence would be insignificant. This function with small sloping cannot adequately represent a drastic kink in Young’s modulus, which we have observed. The change took place in the narrow range 20−30 nm, while Young’s modulus increased twice. One can see (Figure S2a) that the modeled core−shell curve (Ec = 60 GPa, Es = 130 GPa (In2O3 Young’s modulus ≈ 130−150 GPa),25 and rs = 1 nm) overlaid at the experimental data E(R), which fits the region with R > 27 nm (InP NWs with mixed ZB/WZ structure and with 1 nm thick oxide) well enough. However, it does not adequately model the part of the plot with R < 25 nm (InP NWs with WZ structure). If one tries to fit all of the experimental data E(R) with a core− shell model, then the values of elasticity for core and shell will be strongly inadequate (see Figure S2b). In this case, the core of the NW have a negative Young’s modulus (Ec= −50 GPa), while the shell is superhard (Es = 1000 GPa). We highlight once more that consideration of influence of the oxide layer in the core−shell model seems reasonable only for NWs containing the ZB phase, having a nonzero thickness of the oxide shell (rs = 1 nm, R > 27 nm). We do not observe oxide layer for WZ InP NWs, which means that its influence onto the Young’s modulus is negligible. The influence of the nanowire surface atoms (without the oxide) onto the Young’s modulus of InP NWs was studied in details in theoretical work.26 The authors state that influence of the surface is being initiated for nanowires with radii in the range of a few nanometers (leading to decrease of the Young’s modulus), while for the range 20−40 nm (our case), this influence is negligible. Thus, the only remaining possible explanation is related with the real difference in Young’s moduli of WZ and “mixed ZB/ WZ” nanowires. Indeed, the right side of the graph in Figure 3 (Rmid > 30 nm, E ≈ 65 GPa) corresponds to the “mixed ZB/ WZ” NWs,27 while the left side (Rmid < 25 nm, E ≈ 130 GPa) corresponds to the NWs with wurtzite structure. From this reasoning, it follows that the wurtzite InP NWs have a Young’s modulus of approximately 130 GPa. The Young’s modulus measurement error for individual wurtzite NWs was approximately 50 GPa due to the strong influence of the radius of thin NWs (∼RNW4). Still, it is difficult to determine the NW’s radius with high accuracy, even with the help of high-resolution SEM. However, after averaging over six wurtzite NWs (see Figure 3), this error decreased down to ±30 GPa. Let us now carry out theoretical estimates of the axial Young’s modulus of wurtzite InP NW (E[0001]) and zinc blende InP NW (E[111]). Knowing the elastic coefficients for ZB InP and using the Martin transformation,28 it is possible to find values of the compliance matrix (Sij) for WZ InP. Then, from the values of the compliance matrix, one can get the Young’s modulus value in the given direction29 for WZ InP. These calculations were carried out (see the Supporting Information), and the following values were obtained: E[0001] = 112 GPa (based on Larsson et al. results)30 and E[0001] = 127 GPa (based on Wang et al. results).31 Therefore, evaluation of the Young’s modulus of WZ InP NWs along the long axis [0001] provides the value E[0001] ≈ 120 ± 10 GPa. In the case of ZB InP NW, the axial Young’s modulus value E[111] = 110 GPa was obtained using formula no. 1 from Brantley32 (see the Supporting Information).

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.7b00312. Additional details of establishment of size, geometrical features, and crystal composition; calculation of the stiffness for a conical NW; the estimation for WZ InP 3445

DOI: 10.1021/acs.nanolett.7b00312 Nano Lett. 2017, 17, 3441−3446

Letter

Nano Letters

■

(19) Young, T. J.; Monclus, M. A.; Burnett, T. L.; Broughton, W. R.; Ogin, S. L.; Smith, P. A. Meas. Sci. Technol. 2011, 22, 125703. (20) Ma, J.; Liu, Y.; Hao, P.; Wang, J.; Zhang, Y. Sci. Rep. 2016, 6, 18994. (21) Barth, S.; Harnagea, C.; Mathur, S.; Rosei, F. Nanotechnology 2009, 20, 115705. (22) Calahorra, Y.; Shtempluck, O.; Kotchetkov, V.; Yaish, Y. E. Nano Lett. 2015, 15, 2945−2950. (23) Chen, Y.; Gao, Q.; Wang, Y.; An, X.; Liao, X.; Mai, Y.; Tan, H. H.; Zou, J.; Ringer, S. P.; Jagadish, C. Nano Lett. 2015, 15, 5279−5283. (24) Zemek, J.; Baschenko, O. A.; Tyzykhov, M. A. Thin Solid Films 1993, 224, 141−147. (25) Bartolomé, J.; Hidalgo, P.; Maestre, D.; Cremades, A.; Piqueras, J. Appl. Phys. Lett. 2014, 104, 161909. (26) Dos Santos, C. L.; Piquini, P. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 075408. (27) Ikejiri, K.; Kitauchi, Y.; Tomioka, K.; Motohisa, J.; Fukui, T. Nano Lett. 2011, 11, 4314−4318. (28) Martin, R. M. Phys. Rev. Lett. 1972, 6, 4546. (29) Chen, Y.; Burgess, T.; An, X.; Mai, Y.; Tan, H. H.; Zou, J.; Ringer, S. P.; Jagadish, C.; Liao, X. Nano Lett. 2016, 16, 1911−1916. (30) Larsson, M. W.; Wagner, J. B.; Wallin, M.; Hakansson, P.; Froberg, L. E.; Samuelson, L.; Wallenberg, L. R. Nanotechnology 2007, 18, 015504. (31) Wang, S. Q.; Ye, H. Q. Phys. Status Solidi B 2003, 240, 45−54. (32) Brantley, W. A. J. Appl. Phys. 1973, 44, 534. (33) Moon, J.; Cho, M.; Zhou, M. J. Appl. Phys. 2015, 117, 214307. (34) Lexholm, M.; Karlsson, I.; Boxberg, F.; Hessman, D. Appl. Phys. Lett. 2009, 95, 113103.

Young’s modulus in the [0001] direction E[0001] and for ZB InP Young’s modulus in the [111] direction E[111]; and core−shell modeling. Tables showing geometric parameters and crystal structure of InP NWs. Figures showing electron diffraction, and photoluminescence and scanning electron microscopy images for InP NWs. (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: mike.dunaeff[email protected]ffe.ru. ORCID

Mikhail Dunaevskiy: 0000-0001-6038-223X Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was financially supported by Russian Foundation for Basic Research grant no. 14-02-01118 and by the Government of Russian Federation (grant no. 074-U01). P.A. acknowledges an RFBR grant (no. 16-32-00295 mol_a) for financial support. The work was supported by the Moppi project of Aalto Energy Efficiency Program. The fabrication of the NWs was performed in the Micronova clean room facilities of Aalto University.

■

REFERENCES

(1) Patolsky, F.; Lieber, C. M. Mater. Today 2005, 8, 20−28. (2) Cui, Y.; Wei, Q.; Park, H.; Lieber, C. M. Science 2001, 293, 1289−1292. (3) Tao, A.; Kim, F.; Hess, C.; Goldberger, J.; He, R.; Sun, Y.; Xia, Y.; Yang, P. Nano Lett. 2003, 3, 1229−1233. (4) Lieber, C. M. Sci. Am. 2007, 17, 64−71. (5) Cui, Y.; Zhong, Z.; Wang, D.; Wang, W. U.; Lieber, C. M. Nano Lett. 2003, 3, 149−152. (6) Krogstrup, P.; Jorgensen, H. I.; Heiss, M.; Demichel, O.; Holm, J. V.; Aagesen, M.; Nygard, J.; Fontcuberta i Morral, A. Nat. Photonics 2013, 7, 306−310. (7) Kim, S. K.; Day, R. W.; Cahoon, J. F.; Kempa, T. J.; Song, K. D.; Park, H. G.; Lieber, C. M. Nano Lett. 2012, 12, 4971−4976. (8) Wang, Z. L. Adv. Mater. 2007, 19, 889−892. (9) Alekseev, P. A.; Dunaevskiy, M. S.; Ulin, V. P.; Lvova, T. V.; Filatov, D. O.; Nezhdanov, A. V.; Mashin, A. I.; Berkovits, V. L. Nano Lett. 2015, 15, 63−68. (10) Haggren, T.; Jiang, H.; Kakko, J.-P.; Huhtio, T.; Dhaka, V.; Kauppinen, E.; Lipsanen, H. Appl. Phys. Lett. 2014, 105, 033114. (11) Wallentin, J.; Anttu, N.; Asoli, D.; Huffman, M.; Åberg, I.; Magnusson, M. H.; Siefer, G.; Fuss-Kailuweit, P.; Dimroth, F.; Witzigmann, B.; Xu, H. Q.; Samuelson, L.; Deppert, K.; Borgström, M. T. Science 2013, 339, 1057. (12) Chen, C. Q.; Shi, Y.; Zhang, Y. S.; Zhu, J.; Yan, Y. J. Phys. Rev. Lett. 2006, 96, 075505. (13) Song, J.; Wang, X.; Riedo, E.; Wang, Z. L. Nano Lett. 2005, 5, 1954−1958. (14) Alekseev, P. A.; Dunaevskii, M. S.; Stovpyaga, A. V.; Lepsa, M.; Titkov, A. N. Semiconductors 2012, 46, 641−646. (15) Gu, X. W.; Loynachan, C. N.; Wu, Z.; Zhang, Y. W.; Srolovitz, D. J.; Greer, J. R. Nano Lett. 2012, 12, 6385−6392. (16) De Luca, M.; Zilli, A.; Fonseka, H. A.; Mokkapati, S.; Miriametro, A.; Tan, H. H.; Smith, L. M.; Jagadish, C.; Capizzi, M.; Polimeni, A. Nano Lett. 2015, 15, 998−1005. (17) Chauvin, N.; Mavel, A.; Patriarche, G.; Masenelli, B.; Gendry, M.; Machon, D. Nano Lett. 2016, Just Accepted; 10.1021/ acs.nanolett.5b04646. (18) Geydt, P.; Dunaevskiy, M.; Alekseev, P.; Kakko, J.-P.; Haggrén, T.; Lähderanta, E.; Lipsanen, H. J. Phys.: Conf. Ser. 2016, 769, 012029. 3446

DOI: 10.1021/acs.nanolett.7b00312 Nano Lett. 2017, 17, 3441−3446