Luminous Efficiency of Ordered Arrays of GaN Nanowires with

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Luminous efficiency of ordered arrays of GaN nanowires with sub-wavelength diameters Christian Hauswald, Ivano Giuntoni, Timur Flissikowski, Tobias Gotschke, Raffaella Calarco, Holger T. Grahn, Lutz Geelhaar, and Oliver Brandt ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.6b00551 • Publication Date (Web): 06 Dec 2016 Downloaded from http://pubs.acs.org on December 13, 2016

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Luminous efficiency of ordered arrays of GaN nanowires with sub-wavelength diameters Christian Hauswald,†,‡ Ivano Giuntoni,† Timur Flissikowski,† Tobias Gotschke,†,¶ Raffaella Calarco,† Holger T. Grahn,† Lutz Geelhaar,† and Oliver Brandt∗,† †Paul-Drude-Institut fur ¨ Festkörperelektronik, Leibniz-Institut im Forschungsverbund Berlin e. V., Hausvogteiplatz 5–7, 10117 Berlin, Germany ‡Present address: DILAX Intelcom GmbH, Alt-Moabit 96b, 10559 Berlin, Germany ¶Present address: OSRAM Opto Semiconductors GmbH, Leibnizstr. 4, 93055 Regensburg, Germany E-mail: [email protected]

Abstract

Keywords: nanowire, gallium nitride, photoluminescence, luminous efficiency, finite-element method, finite-difference time-domain

We investigate the spontaneous emission from ordered arrays of GaN nanowires (NWs) with well-defined diameters, representing the building blocks for light-emitting as well as light-detecting devices integrated on Si substrates. The luminous efficiency of these arrays is observed to decrease by more than an order of magnitude when the NW diameter is increased from 120 to 240 nm. A detailed analysis of both steady-state and transient photoluminescence data reveals that this quenching is not caused by a corresponding decrease of the internal quantum efficiency. Hence, we examine the coupling of light into and out of the NW arrays by appropriate numerical simulations. While the change in absorbance is minor in the investigated diameter range, the extraction efficiency for thin NWs is enhanced by an order of magnitude as compared to thick NWs. This phenomenon primarily originates in the efficient coupling of the spontaneous emission to free space for sub-wavelength diameter NWs. Additionally, our results show that light, which after extraction from a NW propagates laterally, may be diffracted at the periodic array and redirected into free space, thus further enhancing the extraction efficiency for certain NW diameters.

The linear optical response of a bulk material is fully described by the wavelengthdependent complex refractive index n(λ). 1 However, if the material is structured on a scale comparable to or smaller than the wavelength of the light it interacts with, the optical response is additionally affected or even governed by the geometry and dimensions of the nanostructure. 2,3 For example, it has been shown that absorption resonances occur in ordered InAs and InP nanowire (NW) arrays that can be tuned by changing the NW diameter, 4,5 enabling the fabrication of InP NW-based solar cells with a conversion efficiency exceeding the ray limit. 6 These applications of NW-based structures as lightharvesting devices have motivated several theoretical 7–11 as well as experimental 12–17 studies of the light absorption by semiconductor NW arrays. For NW-based light-emitting devices, it is not light absorption but light extraction that—besides the internal quantum efficiency—critically affects the wall-plug efficiency of the device. Light extraction from an array of NWs is a much more formidable

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problem than light absorption by this array, both from a theoretical and experimental point of view. Valuable qualitative insights have been obtained from theoretical studies of the modal properties and waveguiding effects in single NWs using both analytical 18–20 and numerical approaches. 21 However, a quantitative determination of the extraction efficiency requires the consideration of the spatial distribution of the spontaneously emitting dipoles within the NW and their coupling to the various modes supported by the individual NW. In a dense NW array, effects originating from the interaction of the NWs have to be taken into account as well. Experimentally, the external quantum efficiency or the wall-plug efficiency of actual light-emitting devices can be measured, but to disentangle the various additional contributions to this quantity (such as contact resistance, injection efficiency, carrier leakage, etc.) is far from trivial and can be done only on an empirical basis. In this Letter, we investigate the luminous efficiency of ordered arrays of GaN NWs on Si substrates by a combined experimental and theoretical approach. Experimentally, we use both continuous-wave (cw) and time-resolved (TR) photoluminescence (PL) spectroscopy to access the external and the internal quantum efficiencies directly, respectively, without the complications arising from an electrical operation of the device. Theoretically, we quantitatively determine the absorbance of the NW array by fully three-dimensional finite-element method (FEM) simulations and the extraction by finite-difference time-domain (FDTD) simulations using randomly positioned point sources to mimic the spontaneous emission of donor-bound excitons detected experimentally. Our work shows light extraction to be the decisive factor for the experimentally observed twentyfold enhancement of the luminous efficiency with decreasing NW diameter. Our approach allows us to discriminate contributions from the material and the geometry and provide a guide to optimize the geometry of ordered NW arrays to be used

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in light-emitting devices such as multicolor LEDs 22 monolithically integrated on Si substrates.

Results The GaN NWs under investigation were synthesized by plasma-assisted molecular beam epitaxy on pre-patterned Si(111) substrates employing selective-area growth (SAG) 23 and contain spatially ordered arrays of GaN NWs with a length of 800 nm, a NW-to-NW pitch between 360 and 1000 nm, and welldefined diameters between 120 and 240 nm. Figure 1(a) shows an optical micrograph of several closely-spaced ordered NW arrays with different diameter and pitch. Each array has a size of 30×30 µm2 . The different colors of the arrays under white light illumination are a direct consequence of the difference in the coupling of light into the respective array, similarly to observations made for ordered InAs NW arrays. 4 Figure 1(b) displays an exemplary bird’s-eye view scanning electron micrograph highlighting the degree of selectivity and homogeneity of the GaN NWs under the employed growth conditions. Topview scanning electron micrographs of the five ordered GaN NW arrays under investigation in this letter are shown in Figs. 1(c)– 1(g). These arrays exhibit a constant NW-toNW pitch p = 360 nm and a variation in average NW diameter induced by a variation in the hole size of the underlying SiOx mask. A statistical analysis of the top facets of several hundred NWs of each array (see methods section for details) reveals average effective diameters d∗ for these five arrays of 120, 140, 162, 200 and 240 nm. Figure 1(h) displays the diameter distribution of the array shown in Fig. 1(g), for which a standard deviation of σ = 6 nm is extracted. This value is similar for all investigated ordered GaN NW arrays and significantly smaller than the value obtained for typical self-induced GaN NW ensembles of about 25 nm, 24 underlining the improved homogeneity of NWs fabricated by means of SAG.


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Ishizawa 29 for homoepitaxial GaN NW arrays obtained by SAG. The observation of a systematically higher PL intensity for GaN NW arrays with decreasing NW diameter (and constant pitch) is unexpected, because the excited volume decreases quadratically with the diameter. At first glance, we would thus expect a corresponding decrease in intensity rather than an increase. This expectation is based on the fact that the PL intensity IPL is proportional to the absorbance A, and the assumption that A scales with the total volume. IPL , however, also depends on the internal quantum efficiency ηint and the extraction efficiency ηextr : IPL /IL ∝ ηlum = Aηint ηextr

tum efficiency may decrease with increasing diameter. In order to examine this hypothesis, we investigate the internal quantum efficiency of the different NW arrays by performing lowtemperature (10 K) TRPL spectroscopy. The dominating recombination channel of the GaN NWs at low temperatures are excitons bound to neutral donors [cf. Fig. 2(a)]. Hence, we focus our analysis on the decay of this particular state. Figure 2(b) depicts the PL intensity transients of the (D0 , XA ) transition for GaN NW arrays with different average diameter d∗ . All transients are biexponential with almost identical decay times τf and τs for the fast and slow components, namely, about 90 and 800 ps, respectively. This characteristic biexponential decay of GaN NWs is caused by a re-population of the (D0 , XA ) state by the energetically lower lying (A02 , XA ) state, with the latter having a longer effective lifetime. 24 The decay time τf of the fast component represents the actual effective lifetime of the coupled (D0 , XA )/XA system, 24 which we previously found to be dominated by a fast nonradiative recombination process and to be thus almost equal to the nonradiative lifetime τnr . 33 As Fig. 2(c) shows, τf (as well as τs ) is essentially independent of the NW diameter. Since the internal quantum efficiency of the GaN NWs is directly proportional to this effective lifetime, ηint = τf /τr ≈ τnr /τr , where τr is the radiative lifetime of the (D0 , XA ) state, it is tempting to conclude that ηint does not depend on the NW diameter for the investigated samples. However, this conclusion would be premature, as ηint explicitely depends not only on τnr (via τf ), but also on τr . Since τf ≈ τnr because τnr ≪ τr , an increase of τr by a factor of 20 with increasing diameter would explain our experimental result, but would not noticeably affect the value of τf [although we would expect a systematic increase of τs , the decay time of the slow component, which we do not observe—see Fig. 2(c)]. We can envisage two phenomena in ordered GaN NW arrays that might, in principle, increase the radiative lifetime with respect to its value in

(1)

with the laser intensity IL and the luminous efficiency ηlum . In the work by Kishino and Ishizawa 29 , the higher PL intensity for decreasing NW diameter was ascribed to an increase of ηint due to an improved filtering of threading dislocations originating from the heteroepitaxial GaN buffer layer. In fact, the thinnest NWs studied in their work were found to be free of threading dislocations, in contrast to thicker ones. 29 In the present work, a similar mechanism is conceivable. At the early stage of SAG, multiple nucleation of GaN may occur in the holes of the mask, depending on their diameter. 23 Subsequently, these multiple nuclei coalesce to form a single NW. 30 Because of the mutual misorientation of the individual nuclei, each coalescence event may induce the formation of dislocations at the coalescence boundaries. 31,32 With increasing diameter of the holes and thus of the NWs forming upon further growth, the density of these boundary dislocations may increase drastically. If the boundary dislocations act as nonradiative recombination centers for excitons, analogously to the a- and c-type threading dislocations in GaN layers or the thick NWs investigated in Ref. 29, the nonradiative lifetime of the excitons and thus the internal quan-


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the bulk. First, an ordered GaN NW array acts as a two-dimensional photonic crystal due to its periodic arrangement 34 and may suppress spontaneous emission of a given wavelength. 35,36 This effect, however, depends very sensitively on the specific combination of NW diameter and pitch and will not lead to the experimentally observed monotonic decrease of the luminous efficiency with increasing diameter and constant pitch [cf. Fig. 2(a)]. This monotonic change in luminous efficiency with diameter is also observed for NW arrays with very different pitch as depicted in Fig. 2(d), which displays the integrated PL intensity for 19 different GaN NW arrays with NW diameters between 120 and 240 nm and a pitch between 360 and 1000 nm. The behavior seen in this figure is clearly incompatible with that expected for effects arising from the existence of a photonic bandgap. Second, Fermi-level pinning occurs at the M-plane sidewalls of GaN NWs, resulting in surface band bending and thus radial electric fields. For a given background doping, 37 the strength of this field is directly proportional to d∗ , i. e., it increases by a factor of two for the NW arrays under investigation. This increase in the strength of the field may result in a corresponding increase of the radiative lifetime of the (D0 , XA ) state as discussed in detail in Ref. 38. The lower the binding energy of the exciton, the stronger this effect, i. e., the (D0 , XA ) state with its binding energy of 7 meV quenches already for fields for which the free A exciton with its binding energy of 26 meV is not affected at all. 39 The inset of Fig. 2(a) shows the near band-edge spectral range of the arrays with NW diameters of 120 and 200 nm on a semi-logarithmic scale. The intensity of the (D0 , XA ) and the XA transitions are seen to decrease to the same extent, an observation which is clearly inconsistent with the behavior expected for an intensity quenching by electric fields. Our experimental results strongly suggest that the quenching of the PL intensity is not related to the internal quantum efficiency of

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the NWs. Thus, the explanation of this effect rather lies in the coupling of light with the arrays, which governs the absorbance as well as the extraction efficiency in Eq. (1). We first discuss whether our results can be understood in an effective medium approximation, which was recently successfully employed for the interpretation of Raman spectra obtained on GaN NW ensembles with high number densities and an excitation wavelength much larger than the average diameter of the investigated NWs. 40,41 Let us therefore assume that the ordered GaN NW arrays under investigation are represented by an 800 nm thick layer with an effective refractive index n˜ (λ, f ) according to the MaxwellGarnett approximation, 42 where f is the fill factor of the array, i. e., the ratio of the NW volume to the total volume of the layer. In this case, the reflectance, absorbance, and the extraction efficiency of the NW arrays can be calculated analytically. For f increasing from 0.1 to 0.45, corresponding to the diameter and pitch combination in Figs. 1(c)–1(g), the absorbance increases by a factor of about 3, but the extraction efficiency decreases by a factor of 2. Within an effective medium approximation, we would thus expect only a marginal increase in the PL intensity, rather than the factor of 4 expected from the naive consideration of the excited material volume. However, the effective medium approximation clearly fails to explain the observed decrease of the luminous efficiency by a factor of 20. The reason for this failure of the effective medium approximation to explain this observation manifests itself most clearly when examining the results for different values of the pitch p shown in Fig. 2(d). Within the effective medium approximation, the PL intensity should depend only on the fill factor f . The data shown in Fig. 2(d), however, demonstrate that both the pitch and the NW diameter influence the measured PL intensity and hence the luminous efficiency of an array. For a constant pitch p, arrays with a lower fill factor (i. e., a smaller average NW diameter) exhibit a larger luminous efficiency, while for NW arrays with similar d∗ and varying pitch


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p no strict correlation is observed. Hence, the ordered NW arrays under investigation cannot be treated as an effective medium with f as the sole parameter. We attribute this finding to the fact that the wavelength λ/n used to excite the material is comparable to the GaN NW diameter. Recent studies of the interaction of light with ordered InAs 4 and InP NW arrays 43 arrived at the same conclusion.

tor, i. e., the energy flux density between the various material interfaces. Figures 3(b)–3(d) display the light intensity (i. e., the absolute square of the electric field) in NWs with three different diameters exposed to an incident plane wave with λ = 325 nm. If the NW diameter is much smaller than the wavelength of the incident light divided by the refractive index of the material (for GaN, nλ=325 nm = 2.65 + 0.3i) the incoming plane wave transmits the NW array almost undisturbed and is reflected at the Si substrate [cf. Fig. 3(b)]. In this range, the NWs barely support the fundamental mode, which has an effective refractive index close to one (cf. Supporting Information). Qualitatively speaking, the majority of the light is guided outside of the NW and cannot be absorbed. When the NW diameter is increased above 50 nm, higher-order modes become allowed (i. e., exhibit an effective refractive index n ≥ 1, cf. Figs. 3 and 4 in the Supporting Information) and the absorbance strongly increases as shown by the large electric field inside the GaN NW in Fig. 3(c) and 3(d). After these first, qualitative insights, we now proceed to provide a quantitative analysis of the total absorbance A of ordered GaN NW arrays with different NW diameters under illumination of light with λ = 325 nm. Figure 3(e) displays the values obtained for A, R, and T from three-dimensional FEM simulations for a wide diameter range. The gray shaded area highlights the range of NW diameters investigated experimentally by PL spectroscopy in this paper (cf. Fig. 2). 46 In agreement with recent experiments 47 and simulations for other material systems, 7 the absorbance is dramatically reduced for NWs with d∗ ≪ 50 nm. A sharp onset of the absorbance is visible around d∗ = 50 nm, accompanied at the same time by a sharp decrease of both T and R. A maximum absorbance of A = 0.97 is reached at d∗ ≈ 90 nm, significantly higher than the absorbance of light for this wavelength in a planar GaN layer of A = 0.8. With increasing NW diameter, the absorbance slightly decreases to A ≈ 0.8 and then exhibits a sec-

Simulation of the absorbance Consequently, we continue with explicitly solving Maxwell’s equations by appropriate numerical simulations to obtain quantitative values for A and ηextr . In order to simulate the absorbance A of ordered GaN NW arrays in dependence of the NW diameter and pitch, we solve Maxwell’s equations in three dimensions using the finite element method (FEM) as implemented in JCMSuite. 44 As the light source in the FEM simulations, we take a plane wave with λ = 325 nm corresponding to the wavelength of the He-Cd laser used for the PL experiments. Figure 3(a) schematically depicts the threedimensional simulation region with the hexagon representing the cross-section of one unit cell used for the simulations. The GaN NWs are represented by cylinders with diameter d∗ , since the influence of the actual hexagonal symmetry on the optical modes within the NWs and thus the absorption of light was shown to be negligible. 45 As in the actual sample, the NWs are assumed to have a length l = 800 nm and a center-to-center separation of p = 360 nm. All light transmitting the NW array is assumed to be absorbed by the semi-infinite Si substrate. The absorbance of the GaN NWs is calculated by A = 1 − R − T, where the transmittance T represents the amount of light transmitted through the NW array and absorbed in the Si substrate, while the reflectance R denotes the combined reflectance of the incident light at the top facet of the GaN NWs and at the substrate. The values of T and R are obtained by calculating the Poynting vec-


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ond resonance at d∗ = 220 nm with A = 0.94. For d∗ > 220 nm, it slowly approaches the expected value for planar GaN layers of A = 0.8. The observed resonances in absorbance are the so-called resonant leaky modes 12 and have been also observed for NWs in other material systems such as GaAs, 48 InAs, 8 and InP. 5,7,43 At these resonances, the incident light is coupled effectively into a guided mode inside the NW and thus the absorption is enhanced. In light of the unexpected decrease in luminous efficiency with increasing NW diameter, the main result from the three-dimensional FEM simulations is that the total amount of laser light absorbed by the ordered GaN NW arrays does not significantly change within the experimentally investigated NW diameter range. While the absorbance increases from 0.8 to 0.96 between 120 and 225 nm, the PL intensity was found to decrease by more than one order of magnitude in the same interval for a NW pitch of p = 360 nm (cf. Fig. 2). Consequently, this decrease is not caused by a corresponding change of the absorbance for the NW arrays under investigation.

count the actual nature of the emission centers dominating the PL spectra depicted in Fig. 2(a), i. e., excitons bound to neutral donors. These donors are incorporated inadvertently during growth into the GaN host lattice at spatially random positions. To account for this fact, we model these donor-bound excitons as discrete, randomly distributed radiating dipoles sources and directly compute the extraction efficiency within the frame of a finite-difference timedomain (FDTD) approach. 52 For a typical residual doping density of ND = 5 × 1016 cm−3 , 53 a single NW contains about 450–2000 dipole sources for the investigated range of diameters. In addition, we have to consider a statistically significant number of spatially random and microscopically different donor distributions for each NW diameter. Clearly, fully threedimensional FDTD simulations of this scenario would demand excessive computational resources. Assuming a cylindrical cross-section of the NWs, we can reduce the problem to a twodimensional one as depicted in Fig. 4(a). Within a modal picture, this elimination of one coordinate results in an overestimation of the effective indices of the guided modes. Furthermore, for a given NW diameter, the number of guided modes is actually larger in three dimensions when compared to the two-dimensional case (cf. Supporting Information). The essential physics, however, is grasped correctly within this simplified scheme. The ”NWs” referred to in the following in the discussion of Fig. 4 are all twodimensional. Figure 4(b) shows a schematic of the simulated structure. The GaN NWs are assumed to have a length of l = 800 nm and a diameter d∗ varying between 100 and 250 nm. The donor-bound excitons as emitting centers are represented by dipole sources as schematically depicted in Fig. 4(c). To account for the optical polarization of the (D0 , XA ) transition, only sources with transverse electrical field were considered. The spatial position of these dipoles is varied randomly for

Simulating the extraction efficiency Therefore, we finally consider the third factor which influences the PL intensity, namely, the extraction efficiency ηextr of the ordered GaN NW arrays [cf. Eq. (1)]. Most investigations of the extraction efficiency of NWs are based on studying their modal properties. 18,21,49–51 This approach is based on the computation of the effective indices of the guided modes and their reflection coefficients at the end facets (cf. Supporting Information). However, this approach gives no information about the efficiency with which the spontaneous emission of a radiating dipole is coupled into the respective modes. In other words, while this approach gives valuable qualitative insights, it is difficult to extract quantitative results. To mimic the physical processes involved in the PL emission of our samples as closely as possible, it is essential to take into ac-


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each simulation run. Two limiting cases are considered regarding the NW pitch: a standalone NW and a periodic array with pitch p = 360 nm. Figure 4(d) presents the computed extraction efficiency ηextr for different NW diameters. This quantity is obtained by normalizing the power radiated toward monitor M2 with the total power detected by monitor M1 , averaged over 70 different random dipole distributions. The calculated extraction efficiency decreases with d∗ , but not monotonically. A pronounced maximum occurs around d∗ = 140 nm and a secondary one at d∗ = 205 nm. The scaled PL intensity [solid squares in Fig. 4(d)] agrees fairly well with the simulated extraction efficiency except for the sample with the thinnest NWs, for which the simulated value is a factor of three lower than the experimentally obtained one. Before addressing the effect of a periodic array of NWs, it is important to understand the physical origin of the minima and maxima in the extraction efficiency predicted by the FDTD simulations. To do so, a modal picture is most instructive (for a detailed discussion, see the Supporting Information). For diameters below 120 nm, only one mode is allowed at λ = 357 nm corresponding to the wavelength of the (D0 , XA ) transition. Once the diameter approaches about 120 nm, a second guided mode is supported by the GaN NW. Thus, with increasing NW diameter, two counteracting effects influence the extraction efficiency: (i) For a given mode, the reflection coefficients at the NW-air and the NW-Si interfaces monotonically increase and decrease, respectively. Hence, the extraction efficiency for this mode continuously decreases with increasing NW diameter. 18,50 (ii) Higher-order modes are extracted more easily because of their low effective index. Consequently, the reflection coefficients of the mode at the top and bottom interfaces monotonically decrease and increase, respectively, with the order of the mode. The interplay of these two effects results in the maxima and minima in the extraction efficiency. Every time a new mode is supported by the

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NW, the extraction efficiency increases intermittently. 20 However, the overall result of an increasing diameter is a reduction of the light extraction from the top facet until the extraction equals that of a planar layer. 50 A qualitatively similar behavior is observed when the NW is placed in a periodic array as shown in Fig. 4(e). Quantitatively, however, the presence of neighboring NWs leads to an enhanced extraction efficiency for diameters around 110 and 220 nm. The reason for this enhancement is clear when comparing Figs. 4(f) and 4(g): a considerable fraction of the laterally propagating radiation from the stand-alone NW [Fig. 4(f)] is redirected by diffraction at the periodic array surrounding the emitting NW [Fig. 4(g)]. 54 Due to the large index contrast between GaN and air, the array possesses a photonic band gap for certain combinations of NW diameter and pitch that inhibits the lateral propagation of light. 54,55 For a pitch of 360 nm, light extraction is enhanced for diameters around 110 and 220 nm. As a result of the enhanced extraction, the simulated extraction efficiency now agrees very well with the experimental data for small diameters, but deviates by a factor of two for larger ones. As shown in the Supporting Information by a comparison between the modes in two and three dimensions, this deviation is not caused by the simplified two-dimensional model employed here. Rather, it is the imperfection of the NW arrays under investigation which is responsible for the remaining discrepancies. As evident from the top-view scanning electron micrographs depicted in Figs. 1(c)–1(g), the NWs exhibit a certain fluctuation not only in their diameter, but also in their pitch and shape. It is intuitively clear that these deviations from a perfectly uniform nanowire array will smear out the oscillatory dependence predicted theoretically. For example, the varying diameters could be accounted for by a convolution of the results depicted in Fig. 4(e) with the diameter distribution shown in Fig. 1(h). Likewise, the effect of the varying nanowire distances could be estimated by averaging the dependencies for dif-


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ferent values of the pitch. These considerations, however, give only qualitative insight into the behavior of a disordered array, we do not attempt here to further improve the agreement of experiment and theory within pour FDTD approach. Instead, the effect of disorder in the array is best described by multiple scattering of the emitted light resulting in a redistribution of the intensity from laterally guided modes to diffusively propagating photons. 56,57 In addition, multiple scattering may result in reabsorption within the array even for small absorption coefficients. In general, disorder in the nanowire array will thus easily obscure photonic crystal effects (including the inhibition of the spontaneous emission discussed above), but to clarify its quantitative impact on the extraction efficiency requires a dedicated theoretical effort.

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found to be essential to combine spectrally and temporally resolved PL data for NWs arrays with different pitch. Moreover, for a quantitative understanding of the coupling of light into and out of the NW arrays, an effective medium approach was found to be entirely inadequate, but required a full solution of Maxwell’s equations. The presented analysis is applicable to a wide range of material systems and facilitates the identification of the factor limiting the wall-plug efficiency of NW-based light-emitting devices.

Methods Nanowire growth The GaN NW arrays under investigation were fabricated in a single growth run on the same wafer. To obtain SAG, we employed plasma-assisted molecular beam epitaxy at a substrate temperature of 825 °C and a Ga/N flux ratio of 0.23. The selectivity was achieved by exploiting the preferential nucleation of the GaN NWs on a 13 nm thick AlN buffer layer as compared to a SiOx mask. The SiOx film was sputtered onto the AlN buffer layer and subsequently patterned by electron beam lithography into 30 × 30 µm2 fields consisting of hexagonally arranged holes with different pitch and diameter. 23 The hole diameter controls the diameter of the NWs emanating from it. For holes larger than 50 nm in diameter, multiple nucleation occurs within the holes. 23,30 NWs with the diameters investigated in the present work have thus experienced at least one coalescence event in their early stage of growth. The patterned areas are closely spaced in the center of the substrate, and the investigated NW arrays thus formed under virtually identical conditions.

Conclusion In conclusion, the experimentally observed quenching of the low-temperature PL intensity for ordered arrays of GaN NWs with their average diameter increasing from 120 to 240 nm is primarily caused by a decreasing extraction efficiency of each single NW. For NW arrays with a given pitch, the extraction of light is predicted to be additionally enhanced for certain NW diameters by the diffraction of laterally propagating light at the periodic array. However, this effect is not clearly observed experimentally due to the disorder in the NW arrays under investigation. The identification of these mechanisms as the actual origin of the observed quenching of the PL intensity with increasing NW diameter has proven to be highly nontrivial and required a combined experimental and theoretical approach. The internal quantum efficiency, for example, may in principle depend on the presence of structural defects, surface electric fields, and photonic crystal effects. To be able to exclude the internal quantum efficiency as the origin of the quenching, it was

Scanning electron microscopy The morphological properties of the asgrown SAG GaN NW arrays are studied by field emission scanning electron microscopy.


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Numerical simulations

In order to correlate the structural and optical properties of the different ordered NW arrays, we extracted the area A and perimeter P of the top facets of individual NWs from top-view micrographs using the open source software ImageJ. 58 As described in detail in Ref. 59, this procedure allows us to calculate the effective NW diameter d∗ = 4A/P, which takes into account the surface-to-volume ratio for NWs of arbitrary shape. 33

The absorption of the laser light in SAG GaN NW arrays was assessed by solving the full three-dimensional Maxwell’s equations by the finite-element method as implemented in the commercial software package JCMsuite. 44 For this simulation, we neglect the thin (13 nm) AlN buffer layer below the NWs as well as the sputtered SiOx mask. A hexagonal unit cell with periodic boundary conditions is employed in order to represent the hexagonal arrangement of the GaN NW array (cf. Fig. 1). The accuracy of the simulation results was verified by simulating the absorbance, transmittance, and reflectance of a planar GaN slab with varying thickness at normal incidence. The results were essentially identical to the analytically obtained values for A, R, and T using Eqs. (4)–(6) in Ref. 60. For the simulations, the complex index of refraction at λ = 325 nm was assumed to have a value of 2.65 + 0.3i for GaN and 5.16 + 3.2i for Si. 61 The extraction efficiency of light emitted by the NWs was determined with the finitedifference time-domain method using the open-source software Meep. 52 The radiative decay of donor-bound excitons was modeled by spatially random dipoles emitting femtosecond Gaussian pulses with a temporally random phase to account for the incoherent nature of spontaneous emission. The short pulse duration corresponds to a spectral linewidth of 5 nm. Since the exciton emission encompasses a noticeably narrower spectral range, we have considered only the power emitted in a 0.5 nm interval across the central wavelength of the pulse. For simplicity, the material refractive indexes have been considered constant over this wavelength range. In particular, the refractive index of GaN at λ = 357 nm was taken to be 2.69, i. e., the material is assumed to be transparent below the free exciton absorption edge. The extraction efficiency was calculated as the ratio between the power detected by monitor M2 and the overall power in the simulation window obtained by monitor M1

Photoluminescence spectroscopy In order to investigate the optical properties of the SAG GaN NWs at low temperatures, the as-grown samples were mounted in a cold-finger cryostat. Cw-PL spectroscopy was performed by exciting the NWs with the 325 nm (3.814 eV) line of a He-Cd laser focused onto the sample with an excitation power density of less than 1 W/cm2 . Using a near-ultraviolet objective with a numerical aperture of 0.32, the diameter of the laser spot focused onto the sample was about 3 µm. Consequently, our measurements typically average over about hundred NWs of a given array with pitch p = 360 nm. The PL signal was spectrally dispersed by a monochromator providing a spectral resolution of 0.25 meV and detected with a cooled charge-coupled device. TRPL measurements were performed by exciting the ensemble with the second harmonic (325 nm) of pulses with a duration of about 200 fs from an optical parametric oscillator synchronously pumped by a femtosecond Ti:sapphire laser, which itself was pumped by a frequencydoubled Nd:YVO4 laser. A low excitation density corresponding to an energy fluence of about 1 µJ/cm2 per pulse was chosen to ensure well-resolved excitonic lines. The spot size in the TRPL measurements was about 3 × 11 µm2 . The transient PL signal was dispersed by a monochromator providing a spectral resolution of 4 meV and detected by a streak camera with a temporal resolution of 50 ps.


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[see Fig. 4(b)]. To avoid undesired reflections at the borders of the simulation window, perfectly matched layers (PML) were used as boundary conditions. A grid size of 2.5 nm has been used for the spatial discretization of the geometry. After performing 70 independent calculations and averaging the corresponding results, the calculated extraction efficiency had sufficiently converged.

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InAs nanowire arrays: from strong to weak absorption with geometrical tuning. Nano Lett. 2012, 12, 1990–1995. (5) Aghaeipour, M.; Anttu, N.; Nylund, G.; Samuelson, L.; Lehmann, S.; Pistol, M.E. Tunable absorption resonances in the ultraviolet for InP nanowire arrays. Opt. Express 2014, 22, 29204–29212. (6) Wallentin, J.; Anttu, N.; Asoli, D.; Huffman, M.; Aberg, I.; Magnusson, M. H.; Siefer, G.; FussKailuweit, P.; Dimroth, F.; Witzigmann, B.; Xu, H. Q.; Samuelson, L.; ¨ Deppert, K.; Borgstrom, M. T. InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit. Science 2013, 339, 1057–1060.

Acknowledgement We thank A. Tahraoui and W. Anders as well as N. Koo and J. Kim (AMO GmbH) for processing the patterned AlN/Si(111) wafers used for SAG of GaN NWs. We are also grateful to A.-K. Bluhm for scanning electron microscopy of the asgrown GaN NW arrays and to Pierre Corfdir for fruitful discussions, valuable suggestions, and a critical reading of the manuscript. This work has been funded by the German BMBF joint research project MONALISA (Contract No. 01BL0810).

(7) Anttu, N. Geometrical optics, electrostatics, and nanophotonic resonances in absorbing nanowire arrays. Opt. Lett. 2013, 38, 730–732.

Supporting Information Available

(8) Anttu, N.; Abrand, A.; Asoli, D.; ˚ berg, I.; Samuelson, L.; Heurlin, M.; A ¨ M. Absorption of light in InP Borgstrom, nanowire arrays. Nano Res. 2014, 7, 816– 823.

The following files are available free of charge. Room temperature photoluminescence measurements, additional simulation of the absorbance, dispersion and reflection coefficients of guided modes.

(9) Kim, S.-K.; Song, K.-D.; Kempa, T. J.; Day, R. W.; Lieber, C. M.; Park, H.-G. Design of nanowire optical cavities as efficient photon absorbers. ACS Nano 2014, 8, 3707–3714.

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Luminous Efficiency of Ordered Arrays of GaN Nanowires with

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