Colorful InAs Nanowire Arrays - American Chemical Society

Mar 12, 2012 - A striking observation is optically visible colors of the array, which we show can be tuned depending on the geometrical parameters of ...
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Colorful InAs Nanowire Arrays: From Strong to Weak Absorption with Geometrical Tuning Phillip M. Wu,*,†,‡ Nicklas Anttu,*,†,‡ H. Q. Xu,†,¶ Lars Samuelson,† and Mats-Erik Pistol† †

Division of Solid State Physics and The Nanometer Structure Consortium (nmC@LU), Lund University, Box 118, S - 22100 Lund, Sweden ¶ Key Laboratory for the Physics and Chemistry of Nanodevices and Department of Electronics, Peking University, Beijing 100871, China S Supporting Information *

ABSTRACT: One-dimensional nanostructure arrays can show fascinatingly different, tunable optical response compared to bulk systems. Here we study theoretically and demonstrate experimentally how to engineer the reflection and absorption of light in epitaxially grown vertical arrays of InAs nanowires (NWs). A striking observation is optically visible colors of the array, which we show can be tuned depending on the geometrical parameters of the array. Specifically, larger diameter NW arrays absorb light more effectively out to a longer wavelength compared to smaller diameter arrays. Thus, controlling the diameter provides a way to tune the optically observable color of an array. We also find that arrays with a larger amount of InAs material reflect less light (or absorb more light) than arrays with less material. On the basis of these two trends, InAs NW arrays can be designed to absorb light either much more or much less efficiently than a thin film of an effective medium containing the same amount of InAs as the NW array. The tunable absorption and low area filling factor of the NW arrays compared to thin film bode well for III-V photovoltaics and photodetection. KEYWORDS: InAs, vertical nanowire array, reflectance, absorptance, photodetection, photovoltaics

T

photonic crystal where a well studied and controllable in-plane photonic band gap15−17 can be employed for example for lasing.18 However, when the III-V NW arrays are considered for concentrator photovoltaics19 and photodetection, the light is incident along the nanowire axis, that is, along the out-of-plane direction that does not exhibit a photonic band gap,17 in a wavelength region where the III-V material shows large values of the absorption coefficient. Thus, separate studies of the optical response of an absorbing, photonic NW array are highly motivated. In order to obtain an adequate theoretical description of the optical response of a densely and closely packed periodic NW array, full electrodynamic modeling is needed.20 Theoretical studies of the absorptance of square vertical arrays of NWs of the III-V materials GaAs4 and InP5 predict that the absorptance depends not only on the area filling factor, defined here as f = π[(D/2)/p]2, but also on the specific values of D and p, where D is the NW diameter and p the period of the array. Furthermore, these theoretical studies indicate that an increasing value of D at a constant f gives a higher absorptance at long wavelengths.4,5 This can be understood from a wavelength dependent critical diameter DC(λ) of NW arrays. For D < DC, the absorptance of the array drops off quickly.7

he use of vertical arrays of nanowires (NWs) as the active region for photovoltaics and photodetection has gained considerable recent interest.1−12 For III-V NWs, this is largely due to the expectation that NW arrays can absorb light at efficiencies at least as high as bulk material5,7,10 and the fact that NWs can be grown on cheap substrates,1 which would substantially reduce material production costs. Furthermore, the NW geometry allows for the epitaxial growth of axial heterostructures in material combinations that would not be possible in bulk layer growth due to large lattice mismatch.13 This gives a large freedom in the choice of the band gap of each axial segment and, therefore, gives for photovoltaics the prospect1 of a very high efficiency by matching14 the solar spectrum closely with the band gaps of a multijunction NW solar cell. However, the current prototype single-junction III-V NW array solar cells have shown low efficiencies and further optimization is needed.1,8,9 To enable the full potential of the III-V NW arrays for applications in photovoltaics and photodetection, it is critical to consider how light interacts with the NWs. In particular, it is necessary to understand how the absorptance, the fraction of incident light of a given wavelength absorbed in the NWs, and the reflectance depend on the geometrical parameters of the NW arrays. By combining materials with different refractive indexes, for example, the high refractive index III-V material and the void/ air in a NW array, the propagation of light can be affected strongly.15,16 Indeed, a NW array represents one type of a © 2012 American Chemical Society

Received: December 26, 2011 Revised: February 23, 2012 Published: March 12, 2012 1990

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Reflectance spectra were measured with an optical probe (Filmetrics F40) attached to a Zeiss optical microscope. The light was incident onto the sample through a 20× objective of numerical aperture of NA = 0.5 oriented at normal angle to the sample, that is, the illumination is from a cone with 30° half angle. Reflected light was collected with the same 20× objective, from a square spot of an area of 20 μm × 20 μm (well within each nanowire square array area of 50 μm × 50 μm). The background and the baseline calibrations were performed with a Si reference substrate. Theoretical simulations were carried out by solving the Maxwell’s equations with the scattering matrix method.28 In this way, we take into account the wave properties of the light and its interaction with the NWs. The incident light of a given wavelength is a plane wave incident from air in the directions given by the angles θinc and ϕinc, and either TE or TM polarized, see the schematic in Figure 1a. We calculate the

The experimental scattering spectrum of a single GaAs NW lying on a substrate was shown to be dominated by strong, welldefined resonances.21 However, the measurements of the reflectance of periodic, vertical InP NW arrays did not show such resonances but showed for all wavelengths reduced values compared to the reflectance of a bare InP substrate.6,22 Thus, there exists a clear need for further studies to elucidate the optical response of arrays of III-V NWs. Advances in nanoscale fabrication and lithography over the last few decades now allow for experimental fabrication of periodic NW arrays with periodicities 300 nm < p < 900 nm,23,24 that is, comparable in scale to the visible light spectrum. Here, we investigate both experimentally and theoretically the optical response of an array of InAs NWs when the NW diameter and length, and the array period are varied. The array periods p range from 900 nm down to subwavelength length scales of 300 nm, and the NW diameters are in the range 40 nm < D < 110 nm. These NWs are grown by chemical beam epitaxy (CBE), which produces NWs with little tapering. We have chosen to work with InAs over other materials such as Si, GaAs, and InP due to the large absorption coefficient α associated with InAs25 (for wavelengths λ > 500 nm the α of InAs is at least a factor of 20 larger than that of Si, a factor of 3 larger than that of GaAs, and a factor of 2 larger than that of InP). We measure the reflectance spectra of the NW arrays, compare these with simulated reflectance spectra, and find good agreement. We find for each array a wavelength λhalfway below (above) which the reflectance is low (high). This wavelength shifts to a longer wavelength when the NW diameter is increased. We see this behavior also in a tunable and observable color where arrays of NWs with a large D show a red-shifted color compared to arrays of NWs with a smaller D. Furthermore, the optical response of the NW array cannot be determined solely by the filling factor f, which shows that an effective medium description with f as the only parameter is not applicable for the NW arrays here. We find also that a larger amount of InAs in the NW array, as quantified by f L, where L is the length of the nanowires in the array, leads to a reduced reflectance. These two trends that relate the optical response to the geometrical parameters can be used as a design guide for NW arrays. We use the geometrical parameters of three example NW arrays to model the absorptance spectra. We find that the absorptance drops rapidly for λ > λhalfway. Our results show that arrays of NWs of small diameters absorb less (by almost half as much in some arrays) at long wavelengths than a thin film of an effective medium containing the same amount of InAs as the NW array due to a decreased coupling of the electric field of the incident light into the NWs. In contrast, for shorter wavelengths the NW arrays can absorb much stronger than such thin films. A proper use of such control over the absorptance of the NW array will allow for creative design of III-V NW arrays for photovoltaic and photodetection applications, and we provide a simple guideline for this. InAs nanowires were grown in a high vacuum chemical beam epitaxy (CBE) unit.26,27 Electron beam lithography (EBL) defined gold (Au) seed dots were arranged in square lattices, each with an area of 50 μm × 50 μm, on an InAs growth substrate. To change the density, we varied the center-to-center separation between neighboring dots, that is, the period of the lattice. The diameter of the Au dots was controlled by changing the electron beam dose. The details of the CBE growth are included in the Supporting Information document.

Figure 1. (a) Schematic showing InAs NWs of diameter D and length L. The NWs stand in an array of period p on top of an optically thick InAs substrate. The definitions of the azimuthal angle ϕinc and the polar angle θinc are also shown. The k vector of the incident light is given by kinc = [−sin(ϕinc)sin(θinc), cos(ϕinc)sin(θinc), cos(θinc)]2π/λ. Also, the polar angle θm of the mth diffracted order is indicated. The electric field ETE of TE polarized incident light is defined by ETE ⊥ez and ETE⊥ kinc, where ez is the unit vector in the z direction.The electric field ETM of TM polarized incident light is defined by ETM⊥ ETE and ETM⊥kinc. (b) Scanning electron microscope image of sample A at 30° tilt. The scale bar is 500 nm. Below this image are colors from the NW arrays A−G with the geometrical parameters listed in Table 1 (notice that D increases when going from sample A to sample G). These images, each with a size of 50 μm × 50 μm, are recorded directly from the Zeiss optical microscope.

transmittance T(λ) of light into the InAs substrate and the reflectance R(λ) of light back into air. The absorptance is obtained from energy balance as A(λ) = 1 − R(λ) − T(λ). We calculate also Rm, the reflectance of the mth diffracted order, that is, the fraction of incident intensity coupled to the mth diffracted order that propagates in a direction given by the angle θm. We use tabulated values of the wavelength dependent (complex-valued) refractive index n(λ) of InAs25 and for air, nair = 1 is used. To model the experimental conditions of unpolarized light incident through an objective of NA = 0.5 and collected with the same objective, we sum up the reflectances of diffracted orders with θm < 30° for given ϕinc and θinc and average over both TE and TM polarized incident light and over the incidence angles 0 < ϕinc < 360° and θinc < 30° of the NA = 0.5. We show in Figure 1b optical images of six NW arrays with different optical colors and a scanning electron microscope (SEM) image of one array (sample A) of ordered NWs. For 1991

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this study, we have grown a series of 42 square arrays, each covering a substrate area of 50 μm × 50 μm, with periods p in the range of 300 to 900 nm, diameters D in the range of 40 to 100 nm, and lengths L in the range of 600 nm to 6 μm. The geometrical parameters of the square NW arrays with the results shown in Figures 1b, 2, and 3 are tabulated in Table 1

Table 1. Geometrical Parameters of the Nanowire Arrays with the Results Shown in Figures 1, 2, and 3a sample

diameter (D)

length (L)

A B C E F G H I J

51 nm 65 nm 68 nm 91 nm 102 nm 108 nm 73 nm 62 nm 100 nm

1896 nm 1080 nm 1084 nm 1142 nm 704 nm 666 nm 1408 nm 1444 nm 690 nm

period (p) 335 327 320 440 320 310 500 435 320

nm nm nm nm nm nm nm nm nm

a

For a list of the geometrical parameters for all the 42 arrays investigated in Figure 4, see Supporting Information.

the larger D = 73 nm (sample H). Thus, as previously predicted in theoretical studies of the absorptance,4,5 we find from these experimental measurements of the reflectance proof that the optical response of a NW array does not depend solely on the filling factor f, but also on the specific value of D. Furthermore, the reflectance of both arrays seems to approach that of a planar InAs substrate at long wavelengths. At short wavelengths, the arrays here show low reflectance values. This is in contrast to the situation in a recent study of sparse arrays of Si NWs where sharp dips in the reflectance were observed, and at wavelengths both above and below the dip the reflectance recovered the high values of the reflectance of a bare substrate.29 For further analysis, we define a halfway point of the reflectance. This halfway point is characterized by the wavelength λhalfway and reflectance value Rhalfway given by Rhalfway = R(λhalfway) where Rhalfway = [R(λ = 850 nm) + Rmin]/2 and Rmin is the minimum value of the reflectance for 400 nm < λ < 850 nm. For sample H, λhalfway = 561 nm and Rhalfway = 15.5%, while for sample I, λhalfway = 519 nm and Rhalfway = 15.8%. Thus, the array H that has a larger D shows a considerably larger λhalfway than the array I. However, the Rhalfway of the two arrays are very similar. Furthermore, we find for both arrays low values of R for λ < λhalfway. From the insets in Figure 2, we see the observable orange color of sample H and the yellow color of sample I. This red shift of the color of sample H compared to that of sample I can be understood from the larger value of λhalfway of sample H compared to that of sample I, that is, the reflected light of sample H consists to a larger degree of the long, red wavelengths. In Figure 2, the modeled reflectances of samples H and I are also shown. We find in general a good agreement between the modeled and experimental spectra, especially above λhalfway (λ ≳ 500 nm in this case). The small discrepancies between modeled and experimental spectra might arise from the assumption of a circular cross-section of the NWs in the modeling while in reality the NWs have hexagonal cross-section. We chose to work with a circular cross-section in the modeling since the orientation/rotation of the hexagons varies between the NWs in the experiments. Another cause for the discrepancies could be diffuse reflectance in the experiments arising from slight variations of the diameters and positions of the NWs compared to the perfect array assumed in the modeling. Lastly, we do not take into account in the modeling the effect of the Au particle on top of the NWs. To ascertain that the main part of the optical response comes from the NWs and not from the Au particles, we provide in the Supporting Information document (Figure S1), results from simulations that indicate that the Au

Figure 2. Data from experiment and simulation showing shifts of the reflectance spectra of two NW arrays with nearly equal filling factors f = 0.0169 (sample H) and f = 0.0161 (sample I). At long wavelengths, the NW arrays reflect nearly as well as the bare InAs substrate. The insets show optical images of the samples H (right image) and I (left image).

Figure 3. Experimental and simulation data of a NW array that shows much lower reflectance than a bare InAs substrate out to long wavelengths of 650 nm. The NW array parameters were L = 690 nm, D = 100 nm, and p = 320 nm, giving a filling factor of f = 0.0767. The inset shows an optical image of sample J.

(the complete geometrical parameter table of all 42 arrays is included in the Supporting Information). We start by considering two specific NW arrays, sample I and H, of very similar lengths L and filling factors f but different diameters D and periods p. Sample I has D = 62.2 nm and p = 435 nm, giving f = 0.0161. Sample H has D = 73.4 nm and p = 500 nm, giving f = 0.0169. For sample I, we have L = 1444 nm, and L = 1408 nm for sample H. Thus, the amount of InAs in the two NW arrays I and H, given by f L, differs by only 2%. Figure 2 presents the experimental reflectance R of these two arrays. All experimental measurements in this work were performed, as described above, with a normally oriented objective lens with numerical aperture NA = 0.5, and light illumination and collection were from the same NA. We see clearly that the array with the smaller D = 62 nm (sample I) shows a higher reflectance for nearly all λ than the array with 1992

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f L provide a useful array design guide for tailoring the reflectance properties of NW arrays. We study now the absorptance of NW arrays and show that λhalfway is relevant also for the absorptance A of a NW array. As a specific example, we show the simulated absorptances of the three NW arrays H, I, and J in Figure 5. When these

particle does not play a major role in the optical response of these NW arrays. In Figure 3, we present the reflectance of an array (sample J) that has NWs of a larger diameter than the arrays H and I considered above. Here, L = 690 nm, D = 100 nm, and p = 320 nm, which gives f = 0.0767. The amount of InAs in the NWs of sample J, given by f L, is approximately 120% more than in samples H and I. In contrast to the arrays H and I discussed above, the reflectance for this denser array is considerably lower than that of the substrate for all wavelengths. Furthermore, below λ = 650 nm, the reflectance is below 6.5%. For sample J, λhalfway = 708 nm and Rhalfway = 12.9%, and we see clearly also for this array that R stays low for all λ < λhalfway. Thus, λhalfway for array J is considerably larger than for arrays I and H, and Rhalfway of array J is lower than that of array I or H. This large value of λhalfway causes the dark-red color of sample J observed in the inset of Figure 3. In Figure 3, the modeled reflectance is also shown, and we find once again good agreement with experimental results. In order to provide a more general picture to correlate the observed experimental reflectance R with the geometrical parameters, we summarize in Figure 4a for all the 42 arrays

Figure 5. Modeled absorptances A of NW array samples H (L = 1408 nm, D = 73.4 nm, p = 500 nm), I (L = 1444 nm, D = 62.2 nm, p = 435 nm), and J (L = 690 nm, D = 100 nm, p = 320 nm). We show also the absorptances of the three thin films of an effective medium such that each thin film contains the same amount of InAs as the corresponding NW array. Each thin film is on top of an InAs substrate and has the same thickness as the length of the corresponding NW array. The simulation assumes the incident light from an objective of NA = 0.5.

absorptance spectra are compared to the reflectance spectra in Figure 2 and Figure 3, we find a complementary behavior where lower (higher) values of the reflectance correspond to higher (lower) values of the absorptance. Thus, the colors of the NW arrays seen in Figures 1, 2, and 3 that were found above to be caused by the reduced reflectance at short wavelengths can now also be understood as the complementary color to the wavelengths that are absorbed stronger. We also show in Figure 5 for each NW array the absorptance of a thin film of an effective medium that contains the same amount of InAs as the NW array. The effective refractive index of such a thin film is calculated as neff = (1 − f)nair + f nInAs and depends therefore only on the filling factor f. When considering samples H and I, we find that the absorptance of sample H is higher than that of sample I for all wavelengths considered, even though the absorptances of the thin films corresponding to H and I almost coincide due to the very similar filling factor f and length L of the two NW arrays. Specifically, array H absorbs better at longer wavelengths than the smaller D array I. For both array H with λhalfway = 561 nm and array I with λhalfway = 519 nm, the absorptance drops faster than the absorptance of the corresponding thin film when moving from λhalfway toward longer wavelengths. At the longest wavelength considered, λ = 850 nm, the absorptances of the samples H and I are considerably lower than the absorptances of the corresponding thin films. Thus, the NW arrays become more transparent for long wavelengths than the corresponding thin films, explaining also why the reflectances of these two arrays approach rapidly that of the substrate in Figure 2 for long wavelengths. The absorptance of the NW array J shows a peak at λ ≈ 580 nm in Figure 5. At 550 nm < λ < 650 nm in the vicinity of this peak, the NW array J absorbs stronger than the thin film of equal

Figure 4. (a) λhalfway, which is the observed wavelength at Rhalfway, as a function of D. (b) Rhalfway as a function of the amount of InAs in the NW array, i.e., f L where f = π[(D/2)/p]2 is the filling factor. In both panels, the green square denotes the results for NW array I, the red square denotes the results for NW array H, and the purple square denotes the results for NW array J.

fabricated in this study the dependence of the halfway wavelength λhalfway against D and in Figure 4b the halfway reflectance Rhalfway against f L, the amount of InAs in the NW array. From Figure 4a, we find that λhalfway shifts to longer wavelength as D is increased. Note here that each data point may have different filling factor and NW length, but the general trend is that by tuning D, we can tune the wavelength λhalfway. At each D, for λ < λhalfway we find in general low values of the reflectance for all the 42 samples. Specifically, R < Rhalfway for λ < λhalfway and R > Rhalfway for λ > λhalfway for all samples. This explains the different observable colors of the NW arrays in Figure 1b where an increase of the NW diameter gives a color that is observed as more red since the shorter wavelengths are reflected weaker than the longer wavelengths. From Figure 4b, we find that for larger f L, and thus larger amount of InAs in the NW array, the reflectance Rhalfway drops. As we describe more clearly below, these dependencies of λhalfway on D and Rhalfway on 1993

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amount of InAs used. Furthermore, for this array with λhalfway = 708 nm the absorptance is below that of the thin film at λ = λhalfway and drops faster for λ > λhalfway than for the thin film. Thus, we see also for this array that at the longest wavelength considered, λ = 850 nm, the absorptance is considerably lower than for the thin film. To elucidate the physical origin of the strong dependence of the absorptance on D, we turn to study the modeled28 electric field strength squared, |E|2, inside the NWs of samples I and H that contain the same amount of absorbing InAs material but differ in the value of D (and p). The absorption of light inside the NWs, that is caused by ohmic losses, is proportional to the product of |E|2 and the absorption coefficient of InAs for a given λ. We show in Figure 6 the simulated |E|2 distributions

contain the same amount of InAs, are similar at this long wavelength. In contrast, for λ = 650 nm the larger D sample H shows considerably larger |E|2 inside the NWs than sample I, which explains the higher absorptance (Figure 5) and lower reflectance (Figure 2) of sample H for λ = 650 nm. Furthermore, both samples show stronger |E|2 inside the NWs for λ = 650 nm than for λ = 850 nm, which explains why both of them absorbs better, when put in relation to the (wavelength dependent) absorptance of the effective medium thin film in Figure 5, at λ = 650 nm than at λ = 850 nm. When we compare the field strengths |E|2 inside the NWs at λ = 450 nm (Figure 6a,d) and at λ = 850 nm (Figure 6c,f), we find also here that they are weaker at the longest wavelength λ = 850 nm. This explains why the absorptances of the NW arrays at λ = 450 nm are closer to those of the effective medium thin films (Figure 5) than at λ = 850 nm. These results show that there is a strong D dependence of the coupling of the electric field of the incident light into the NWs. This coupling is weaker at longer wavelengths and explains the drop in the absorptance of a NW array compared to that of an effective medium thin film when moving toward the longer wavelengths in Figure 5. Thus, by tuning the diameter D of the NWs, a NW array can absorb equally well, or even stronger, than a thin film with the same amount of InAs (see, for example, the high absorptance of samples H, I, and J at λ < λhalfway in Figure 5, and specifically the peak in the absorptance of sample J at λ ≈ 580 nm). However, a NW array can be made to absorb also much less light than the thin film as seen from the absorptances for λ > λhalfway in Figure 5. This gives a guideline for tailoring the optical properties of NW arrays for photovoltaics and photodetection. First, the NW diameter D should be chosen large enough so that λhalfway is larger than or equal to the wavelength(s) of interest for absorption. Next, the desired level of absorption can be achieved by choosing an appropriate value for f L, the amount of absorbing InAs material in the array. In conclusion, we have studied how the geometrical parameters (diameter D, length L, and period p) of a square array of InAs NWs determine the reflectance and absorptance of the array, and we find very good agreement between theoretical calculations and experimental measurements. The InAs NW arrays have an optically observable color in the visible spectrum that red shifts with increasing D. We observe that NW arrays with larger D absorb more efficiently out to longer wavelengths than NW arrays with smaller D, whereas the reflectance shows the complementary behavior where NWs with smaller D reflect more efficiently to shorter wavelengths, which explains the observed red shift. By comparing arrays with equal L and area filling factor f, we find that the effective medium description is not applicable for these NW arrays. Specifically, with a proper choice of D and f L, an array of NWs can be made to absorb either much more or much less light than a thin film of an effective medium with an equal amount of InAs as in the NW array. Furthermore, the NW arrays tend to become more transparent, that is, absorb weaker, than such thin films at long wavelengths due to a decreased coupling of the electric field of the incident light into the NWs. We also see that arrays with larger f L show lower reflectance, or in other words absorb stronger, than arrays containing less InAs. These trends and results were used to construct a guideline for designing NW arrays for photovoltaic and photodetection applications.

Figure 6. Electric field strength squared, |E|2, in the substrate and in two NWs of a periodic NW array (color scale), and in the air between and on top of the NWs (grayscale) in a cross-section through the center of the NWs parallel to the x−z plane starting 100 nm into the substrate and ending 200 nm above the top of the NWs. The incident light is x-polarized and incident at normal angle from the top air side with |Einc| = 1, i.e., we consider TE polarized incident light with θinc = 0 and ϕinc = 0 (see Figure 1 for a schematic). (a−c) For a NW array with D = 62.2 nm, p = 435 nm, and L = 1444 nm. (d−f) For D = 73.4 nm, p = 500 nm, and L = 1408 nm. The wavelength is λ = 450 nm in (a,d), λ = 650 nm in (b,e), and λ = 850 nm in (c,f).

from a side-view of array H and array I for normally incident light (the optical response of normally incident light does not differ dramatically from the response after integration over the incident numerical aperture NA = 0.5; compare Figures 2 and 3 with Supporting Information Figure S1) for the wavelength λ = 450 nm, λ = 650 nm, and λ = 850 nm. We notice that the absorption coefficient of InAs tends to decrease with increasing wavelength,25 which is evident also in Figure 6 from the much shorter decay length of |E|2 inside the substrate for lower λ. When we compare |E|2 inside the NWs of sample H (D = 73.4 nm) and sample I (D = 62.2 nm) at λ = 850 nm (Figure 6c,f), we find similar values. This explains why the absorptance (Figure 5) and reflectance (Figure 2) of these two arrays, which 1994

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(17) Joannopoulos, J.; Johnson, S.; Winn, J.; Meade, R. Photonic Crystals: Molding the Flow of Light, 2nd ed.; Princeton University Press: New York, 2008. (18) Scofield, A. C.; Kim, S.-H.; Shapiro, J. N.; Lin, A.; Liang, B.; Scherer, A.; Huffaker, D. L. Nano Lett. 2011, 11, 5387. (19) Dimroth, F.; Kurtz, S. MRS Bulletin 2007, 32, 230. (20) Hu, L.; Chen, G. Nano Lett. 2007, 7, 3249−3252. (21) Brönstrup, G.; Leiterer, C.; Jahr, N.; Gutsche, C.; Lysov, A.; Regolin, I.; Prost, W.; Tegude, F. J.; Fritzsche, W.; Christiansen, S. Nanotechnology 2011, 22, 385201. (22) Naureen, S.; Sanatinia, R.; Shahid, N.; Anand, S. Nano Lett. 2011, 11, 4805−4811. (23) Mårtensson, T.; Carlberg, P.; Borgström, M.; Montelius, L.; Seifert, W.; Samuelson, L. Nano Lett. 2004, 4, 699−702. (24) Persson, A. I.; Fröberg, L. E.; Samuelson, L.; Linke, H. Nanotechnology 2009, 20, 225304. (25) Handbook of Optical Constants of Solids; Palik, E. D., Ed.; Academic Press: Orlando, FL, 1985. (26) Persson, A. I.; Larsson, M. W.; Stenstrom, S.; Ohlsson, B. J.; Samuelson, L.; Wallenberg, L. R. Nat. Mater. 2004, 3, 677−681. (27) Jensen, L. E.; Björk, M. T.; Jeppesen, S.; Persson, A. I.; Ohlsson, B. J.; Samuelson, L. Nano Lett. 2004, 4, 1961−1964. (28) Anttu, N.; Xu, H. Q. Phys. Rev. B 2011, 83, 165431. (29) Seo, K.; Wober, M.; Steinvurzel, P.; Schonbrun, E.; Dan, Y.; Ellenbogen, T.; Crozier, K. B. Nano Lett. 2011, 11, 1851−1856.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information contains the geometrical parameters of all 42 arrays in this study, a figure with results from modeling with and without the Au catalyst particle, and details of the CBE NW growth. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: (P.M.W.) [email protected]; (N.A.) nicklas.anttu@ ftf.lth.se Author Contributions

‡ These authors contributed equally to this work and are co-first authors.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Heiner Linke and David Lindgren for useful suggestions and discussions during the preparation of the manuscript. This work was supported by the Swedish Research Council (VR), the Swedish Foundation for Strategic Research (SSF), the Nanometer Structure Consortium at Lund University (nmC@LU), EU program AMON-RA (No. 214814), Nordic Innovation program NANORDSUN, Knut and Alice Wallenberg Foundation, E.ON AG as part of the E.ON International Research Initiative, and the National Basic Research Program of the Ministry of Science and Technology of China (Nos. 2012CB932703 and 2012CB932700).

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