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Crystal-phase quantum wires: One-dimensional heterostructures with atomically flat interfaces Pierre Corfdir, Hong Li, Oliver Marquardt, Guanhui Gao, Maciej R. Molas, Johannes K. Zettler, David van Treeck, Timur Flissikowski, Marek Potemski, Claudia Draxl, Achim Trampert, Sergio Fernandez-Garrido, Holger T Grahn, and Oliver Brandt Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b03997 • Publication Date (Web): 19 Dec 2017 Downloaded from http://pubs.acs.org on December 19, 2017

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Crystal-phase quantum wires: One-dimensional heterostructures with atomically flat interfaces Pierre Corfdir,1,*,** Hong Li,1,2 Oliver Marquardt,1 Guanhui Gao,1 Maciej R. Molas,3 Johannes K. Zettler,1,*** David van Treeck,1 Timur Flissikowski,1 Marek Potemski,3 Claudia Draxl,2 Achim Trampert,1 Sergio Fernández-Garrido,1 Holger T. Grahn,1 and Oliver Brandt1 1

Paul-Drude-Institut für Festkörperelektronik, Leibniz-Institut im Forschungsverbund Berlin

e. V., Hausvogteiplatz 5–7, 10117 Berlin, Germany 2

Institut für Physik and IRIS Adlershof, Humboldt-Universität zu Berlin, Zum Großen

Windkanal 6, 12489 Berlin, Germany 3

Laboratoire National des Champs Magnétiques Intenses, CNRS-UGA-UPS-INSA-EMFL, 25,

avenue des Martyrs, 38042 Grenoble, France Abstract In semiconductor quantum-wire heterostructures, interface roughness leads to exciton localization and to a radiative decay rate much smaller than that expected for structures with flat interfaces. Here, we uncover the electronic and optical properties of the one-dimensional extended defects that form at the intersection between stacking faults and inversion domain boundaries in GaN nanowires. We show that they act as crystal-phase quantum wires, a novel one-dimensional quantum system with atomically flat interfaces. These quantum wires efficiently capture excitons whose radiative decay gives rise to an optical doublet at 3.36 eV at 4.2 K. The binding energy of excitons confined in crystal-phase quantum wires is measured to be more than twice larger than that of the bulk. As a result of their unprecedented interface quality, these crystal-phase quantum wires constitute a model system for the study of onedimensional excitons. * Email: [email protected] ** Present address: ABB Corporate Research, 5405 Baden-Dättwil, Switzerland *** Present address: LayTec AG, Seesener Str. 10–13, 10709 Berlin, Germany Keywords:

GaN

nanowires,

quantum

wires,

crystal-phase

photoluminescence, density functional theory

ACS Paragon Plus Environment

engineering,

excitons,

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Coulomb correlations are enhanced in one-dimensional semiconductors compared to systems of higher dimensionalities.1,2 As a result, the oscillator strength of excitons in quantum wires becomes large,3 the photoluminescence (PL) spectrum of quantum wires is dominated by excitonic correlations even at high carrier densities,4,5 and exciton lasing has been observed in these structures.2,6 In addition, as a result of the broken translational symmetry perpendicular to the quantum wire axis, excitons can couple to a quasi continuum of photon states, leading to a large radiative decay rate.7 However, the interfaces of semiconductor heterostructures are usually not atomically flat, resulting in exciton localization along the quantum-wire axis. This localization introduces large wavevector components in the wavefunction of the exciton that significantly decrease the radiative recombination rate.7,8 Exciton localization in quantum structures usually occurs at local fluctuations in width and alloy content. This phenomenon has been extensively studied for quantum wells, but has also been reported for V-groove and pyramidal quantum-wire heterostructures8,9 as well as for ultrathin nanowires surrounded by air.10 Crystal-phase bandgap engineering in semiconductor nanowires has opened the possibility to fabricate heterostructures free of such fluctuations.11– 14

Crystal-phase quantum wells are induced by twin boundaries and basal plane stacking

faults (BSFs) intersecting nanowires axially, but also by inversion domain boundaries (IDBs) of type IDB* running along the length of the nanowires.15 For instance, I1 BSFs in GaN have been shown to act as three-monolayer-thick quantum wells of zincblende material with atomically flat interfaces that confine excitons along the [0001] direction.12,16 Due to these perfect interfaces, the radiative decay rate of the exciton in I1 BSFs is enhanced by its coherent macroscopic polarization.14 Both, I1 BSFs and IDB*s, have been observed in GaN nanowires grown by molecular-beam epitaxy and give rise to excitonic transitions labeled (I1,X) and (IDB*,X), respectively.17,18 Dimitrakopulos et al.19 reported the observation of intersecting I1 BSFs and IDB*s in planar GaN. I1 BSFs and IDB*s may also coexist in single GaN nanowires, and their intersection may possibly behave as a crystal-phase quantum wire. In this letter, we first show using transmission electron microscopy that intersecting IDB*s and I1 BSFs indeed exist in GaN nanowires and then demonstrate theoretically that the onedimensional defect created by this intersection has no broken bonds and binds excitons. In photoluminescence spectra of GaN nanowires with strong (I1,X) and (IDB*,X) transitions, we observe an additional emission doublet at 3.36 eV that we attribute to intersecting IDB*s and I1 BSFs. Using time-resolved as well as magneto-photoluminescence experiments, we show


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that the defect acts as a crystal-phase quantum wire. In addition, we determine the binding energy and oscillator strength of the quantum-wire exciton to be about 67.5 meV and 5.8 × 106 cm 1, respectively. Both of these values are large, reflecting the fact that excitonic effects −

in I1 BSF/IDB* crystal-phase quantum wires are strongly enhanced with respect to both the bulk and two-dimensional crystal-phase quantum structures such as the I1 BSF and the IDB* alone. Figure 1(a) shows a cross-sectional transmission electron micrograph of an ensemble of GaN nanowires grown on Si(111) at a substrate temperature of 750 °C (see Methods). When grown at this low substrate temperature, the nanowire ensemble consists of a dense (1010 cm 2) −

matrix of short and coalesced nanowires interspersed by long nanowires with a density on the order of 108 cm 2. As shown previously by a combination of convergent beam electron −

diffraction and dark-field transmission electron microscopy imaging,18 the short nanowires are N polar, while the long and thin ones are either Ga polar, or exhibit a Ga-polar core surrounded by an N-polar shell with a tubular inversion domain boundary at the core/shell interface. High-resolution transmission electron micrographs taken on two long and thin nanowires from the same sample are shown in Figs. 1(b) and 1(c). The defects perpendicular to the axis of the nanowire in Fig. 1(b) are I1 BSFs. In wurzite GaN crystals, I1 BSFs are formed by the removal of one basal layer (Aa) in the (0001) plane followed by a 1/3 shift, resulting in a ...AaBbAaBbCcBbCcBb... stacking sequence along the nanowire axis as shown in Fig. 1(d). The contrast variation across the section of the nanowire in Fig. 1(c) arises from a polarity inversion with an IDB* situated in the center. In this structure, the polarity is inverted with respect to the (10 1 0) defect plane. Different IDB structures have been proposed for the wurtzite structure. The so-called Holt-type IDBs exhibit Ga-Ga and N-N bonds, and the formation energy for this defect configuration is large.15 In contrast, the IDB* is created by interchanging Ga and N atoms on one side of a (10 1 0) plane followed by a 1/2 [0001] shift as shown in Fig. 1(e). Each atom remains fourfold coordinated by forming Ga-N bonds across the boundary, and the formation energy of this defect is consequently very low.15 Fiorentini20 calculated the potential across an IDB* and showed that this defect acts as a type-II quantum well that attracts holes. Accordingly, excitonic transitions associated with this defect have been observed for both GaN epilayers21 and nanowires.17,18 In nanowires, IDB*s span over


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the whole nanowire length and may exhibit a planar or tubular geometry [the IDB* in Fig. 1(c) is of the latter type], depending on whether the Ga- and N-polar nanowires are next to each other or form a core/shell structure, respectively.18 In addition to I1 BSFs and IDB*s, we also observe nanowires that contain both types of defects. The high-resolution transmission electron micrograph in Fig. 1(c) shows an example for the intersection of an I1 BSF with an IDB* in one particular nanowire. Similar observations were already made by Dimitrakopulos et al.19 for GaN layers grown on sapphire substrates. Based on a topological theory of interfacial defects and transmission electron microscopy experiments, they proposed that the stacking sequence at the intersection of an I1 BSF and an IDB* is similar to the one at the center of the periodic cell displayed in Fig. 1(f). Clearly, there is no Ga-Ga or N-N bond involved in the central I1 BSF/IDB* junction [Fig. 1(f)], a finding suggesting that this linear extended defect does not introduce nonradiative centers15,19 and thus may give rise to radiative transitions detectable by PL spectroscopy. To clarify whether the I1 BSF/IDB* junction in Fig. 1(f) can bind excitons, we have calculated the electrostatic potential profile in the plane perpendicular to the axis of the I1 BSF/IDB* quantum wire by density-functional theory (DFT) (see Methods). The microscopic electrostatic potential at the I1 BSF/IDB* is calculated by taking the difference ∆V between the potential at each ion site and the average potential of the respective species in the periodic cell shown in Fig. 1(f). To construct the two-dimensional potential map displayed in Fig. 2(a), ∆V was interpolated. The positive value at the center of the cell indicates that holes are attracted by the I1 BSF/IDB* junction while electrons are repelled. In other words, I1 BSF/IDB* junctions act as type-II quantum wires, with the electron remaining in the vicinity of the defect only as a result of the attractive Coulomb potential induced by the hole. Note that the band offsets existing between the matrix and the junctions, which is not considered in this calculation, may additionally confine electrons. To verify that the electrostatic potential alone can already give rise to a bound state for excitons, we have computed the energy and wavefunction of an exciton bound to an I1 BSF/IDB* junction using an eight-band k·p model. We assume that the wavefunction of the exciton is given by Ψ ( re, rh ) = Φe (xe, ye )Φh (xh , yh ) χ (ze − zh ) , where Φe and Φh are the electron and hole envelope functions in the plane perpendicular to the quantum wire and χ describes


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the relative motion of the exciton along the axis of the quantum wire. We assume that 1/4

χ (ζ ) = 2 (πλ 2 ) exp (−ζ 2 λ 2 ) , with λ being a variational parameter.22 The potentials for the electron and the hole (Ve and Vh, respectively) have been deduced from the slowly varying part of the DFT potential in Fig. 2(a), and have been set to zero away from the defect. In this way, the result of our k·p simulations is not affected by artifacts introduced by the additional junctions included in the periodic cell in Figs. 1(f) and 2(a). The potential Ve used as input for the k·p simulations is shown in Fig. 2(b). Due to the type-II band alignment at the I1 BSF/IDB* junction, it is essential to account in our calculations for the Coulomb interaction between the electron and the hole, which can be achieved using the effective potential method.23 In this framework, Ve and Vh are replaced by effective potentials V!e and V!h , respectively, that take into account the kinetic energy of the internal motion of the exciton as well as the electron-hole interaction. Φe, Φh, and λ are optimized until the energy of the exciton is minimized (see Supporting Information for more details). As depicted in Fig. 2(c),

V!e exhibits a nearly circular symmetry in the ( 1 2 1 0) plane and becomes minimal at a distance of about 3.3 nm away from the junction. Our calculations demonstrate that the electrostatic potential at the I1 BSF/IDB*s junction is sufficient for creating a bound state for excitons. However, since V!e is shallow [Fig. 2(c)], the 2

electron charge density Φe displayed in Fig. 2(d) is spread out over a large area in the (11 2 0) plane. Similarly, the extent of the exciton wavefunction along the I1 BSF/IDB* axis is large (λ = 9 nm). In contrast, Φh

2

is pinned at the I1 BSF/IDB* junction [Fig. 2(e)]. Consequently,

both, the absolute square of the electron-hole overlap integral Φe Φh

2

and the exciton

binding energy EB, are found to be comparatively low, namely, 0.07 and 7 meV, respectively. These values would probably change significantly if we would be able to derive the band offsets between the wurtzite matrix and the planar defects in addition to the electrostatic potential, which potentially may turn the band alignment to type I. In addition, the separation of the on-axis and in-plane motions of the exciton in Ψ(re, rh ) leads to a significant underestimate of EB when λ is much larger than the Bohr radius in the bulk.24 In any case, we would expect radiative excitonic transitions associated with the I1 BSF/IDB* junctions at low temperatures. The transition energy of the I1 BSF/IDB* exciton is predicted within the present approximate treatment to be 3.344 eV.


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Next, we examine the optical transitions in GaN nanowires by PL spectroscopy. As mentioned above, the sample grown at 750°C and investigated by transmission electron microscopy in Figs. 1(a)-1(c) consists of a matrix of coalesced nanowires. As coalescence results in strain and in the formation of dislocations, the PL signal for this sample is broad and weak even at 10 K. In the following, we thus focus on GaN nanowire ensembles grown by molecular-beam epitaxy on Si(111) at substrate temperatures higher than 780 °C. The excitonic lines in the PL spectra of these samples at 10 K are narrow,25 facilitating the identification of PL lines potentially related to the I1 BSF/IDB*s junctions. Also, we restrict ourselves to PL experiments on ensembles of as-grown nanowires. As shown in Ref. 26, the dispersion process of nanowires on a substrate usually introduces strain, which may red- or blueshift the energy of the excitonic transitions by several meV, making it difficult to attribute photoluminescence transitions to specific crystallographic defects. Figure 3(a) shows PL spectra taken on ensembles of GaN nanowires at 10 K. These nanowires have been grown at substrate temperatures between 788 and 865 °C. Details about the growth process are given in the Methods section. The transitions located between 3.47 and 3.48 eV correspond to the near-band-edge (NBE) emission of GaN and consist of excitons bound to O and Si donors as well as free excitons.25 The transitions at 3.449 and 3.455 eV arise from localized and free (IDB*,X) complexes, respectively.18 The bands at 3.41 and 3.32 eV are related to exciton recombination at I1- and I2-BSFs, respectively.12,27 Weak phonon replica from the NBE, (IDB*,X), and (I1,X) transitions are also detected. The intensities of the (I1,X) and (I2,X) lines increase with increasing substrate temperature. This phenomenon is due to an increased Si incorporation in the nanowires grown at high temperatures that leads to a decrease in the formation energy of stacking faults.25 An additional doublet, with low- and high-energy components at 3.3535 and 3.3660 eV, respectively, also develops with increasing substrate temperature. These lines exhibit a full width at half maximum of 1 meV [Fig. 3(b)], a value much lower than that of the (IDB*,X), (I1,X), and (I2,X) bands. This doublet, labeled Y4, was already observed in both, GaN layers21 and nanowires.28,29 It was mostly ascribed to an exciton bound to a structural defect and in some reports specifically attributed to the recombination of excitons bound to a-type edge threading dislocations21 or a-type screw dislocations.30 We examine these possibilities in view of recent results on the impact of coalescence on the microstructure of GaN nanowires.31 Tilt and twist between two mutually disoriented nanowires may be accommodated elastically or


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plastically. In particular, while nanowire tilt gives rise to a-type edge dislocations with a line direction along the a axis, it is energetically favorable for the twist to be accommodated via elastic strain. Therefore, none of the defects proposed in Refs. 21 and 30 should occur in GaN nanowires. Note also that the study in Ref. 30 has been performed on a locally strained GaN layer as evident from the high emission energy of the donor-bound exciton line. Correcting for the energy shift caused by this strain, a-type screw dislocations in GaN nanowires should give rise to light emission at 3.335 eV, i. e., 18 meV lower energy than for the observed lowenergy component of the Y4 doublet [cf. Fig. 3(a)] and thus rather correspond to the Y5 line.21 Finally, as shown in the Supporting Information, the nanowires with strong Y4 lines are those with the lowest coalescence degree, a dependence opposite to the one expected if dislocations were at the origin of the Y4 doublet. Since this doublet is particularly intense in nanowire samples with prominent (IDB*,X) and (I1,X) bands [cf. Fig. 3(a)], we propose that it arises from exciton recombination at I1 BSF/IDB*s crystal-phase quantum wires. This idea is examined in detail in Figs. 3(b) and 3(c) by temperature-dependent PL experiments on the sample grown at a substrate temperature of 865 °C. The inset in Fig. 3(b) shows the temperature dependence of the PL spectra in the vicinity of the Y4 doublet. With increasing temperature, the intensity of the line at 3.3535 eV quenches, while that at 3.366 eV takes over and eventually dominates the PL spectrum at temperatures higher than 25 K. Similarly, with increasing excitation power, the PL intensity ratio between the lines at 3.366 and 3.3535 eV increases (see Supporting Information). The behavior of the Y4 doublet with increasing temperature and excitation power is reminiscent of that observed for donor-bound and free excitons, where the free exciton line takes over the donor-bound ones with increasing temperature and excitation power. Despite the fact that IDBs* and I1 BSFs are quantum wells with atomically flat interfaces, a similar behavior has also been observed for the (IDB*,X)18 and the (I1,X) transitions.32 In both cases, this phenomenon has been attributed to the presence of donors in the vicinity of planar defects that localize excitons at low temperatures.18,33 Accordingly, we attribute the line at 3.3535 eV to the recombination of excitons localized along the I1 BSF/IDB* junction and the line at 3.366 eV to excitons delocalized along the junction. The PL transients of these two lines at low temperatures are consistent with this hypothesis. As shown in Fig. 3(b), the PL intensity at 3.366 eV shows an almost instantaneous rise followed by a fast decay with an initial decay time of 32 ps. This decay time compares well with the 39 ps that it takes for the PL intensity at 3.3535 eV to reach a maximum. The decay time of 32 ps measured for the line at 3.366 eV therefore corresponds to


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the characteristic time for the capture of excitons by donors distributed in the vicinity of the extended structural defect. These donor-bound excitons in I1 BSF/IDB* junctions then decay exponentially with an effective decay time of 260 ps, a value comparable to that reported for the donor-bound excitons in the fault-free material.34 The temperature (T) dependence of the radiative lifetime τr of an exciton with dimensionality n is proportional to Tn/2.12 To determine the dimensionality of the density of states of excitons giving rise to the Y4 doublet, we have thus performed temperature-dependent time-resolved PL experiments. The temperature dependences of τr for the NBE, (IDB*,X), (I1,X), and Y4 emission lines are shown in Fig. 3(d). For the (I1,X) line, this dependence was deduced directly from the temperature dependence of the PL lifetime.12 For the NBE, (IDB*,X), and Y4 lines, we followed the approach described in Ref. 35. For a population of excitons that decays via radiative and nonradiative channels, τr is inversely proportional to the PL intensity at zero time delay. Therefore, provided that the initial exciton density remains constant, the temperature dependence of τr can be deduced directly from that of the PL intensity at zero time delay. For the NBE, (IDB*,X), and Y4 lines,, the data displayed in Fig. 3(d) thus correspond to the inverse of the sum of the PL intensity at zero time delay of the corresponding localized and free exciton transitions. As shown in Fig. 3(d), τr for all excitonic bands remains nearly constant in the low-temperature range and increases at higher temperatures. Therefore, the excitons responsible for these transitions all exhibit a zerodimensional character at 5 K. This finding is in agreement with the fact that the NBE emission is dominated by O- and Si-bound exciton transitions, while for the (IDB*,X), (I1,X), and Y4 lines excitons are localized by these donors in the vicinity of the corresponding structural defect.18,33 For temperatures higher than 20 K, τr for the NBE increases with T3/2, reflecting the thermally activated dissociation of the bound exciton complex and the threedimensional character of the free A excitons (XA) in nanowires with a diameter of 50 nm.34 For the IDB*s and I1 BSFs lines, τr increases linearly with temperature, confirming that these planar defects both act as quantum wells.36 In contrast, the increase in τr for the Y4 follows a T1/2 dependence between 10 and 40 K, suggesting that excitons are free to move along the extended defect giving rise to the Y4 doublet exhibting a one-dimensional character.7 A quantitative analysis of the temperature dependence of τr for the Y4 doublet requires to take into account the thermal equilibrium between free 1D excitons and those at donors.8,36 In particular, the temperature dependence of τr depends on the density of donors even at temperatures larger than 25 K, i. e., when the majority of carriers becomes delocalized [cf. Fig.


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3(d)]. In the Supporting Information, we have derived τr for a quantum-wire exciton in the presence of donor impurities. The best fit to the temperature dependence of τr for the Y4 transition using this analytic expression is shown in Fig. 3(d). The increase in τr with increasing temperature is well reproduced by the model, demonstrating that the Y4 transitions arise from the recombination of one-dimensional excitons. This result supports the assignment of this doublet to I1 BSF/IDB*s crystal-phase quantum wires. From the fit in Fig. 3(d), we extract an oscillator strength for the I1 BSF/IDB*s quantum wire exciton of (5.8 ± 0.2) × 106 cm 1, a value about one order of magnitude larger than that −

reported for free excitons in GaAs/(Al,Ga)As quantum wires with a type-I band alignment.7 Consequently, I1 BSF/IDB* excitons couple to light very efficiently. A large oscillator strength also suggests strong excitonic effects at crystal-phase quantum wires. To estimate EB of excitons at I1 BSF/IDB* quantum wires, we have measured the diamagnetic shift of the excitonic transitions in a magnetic field for the nanowire sample grown at a substrate temperature of 865 °C. This shift can be written as:

ΔE = EB2 + ! 2ω c2 4 − EB

(1)

with ωc denoting the cyclotron frequency and ħ the reduced Planck’s constant. Figure 4 shows the blueshift observed for the XA line and the high-energy component of the Y4 doublet as a function of the external magnetic field. The inset displays spectra of the high-energy line of the Y4 doublet for different magnetic fields. Fits of the data with Eq. (1) yield a value of EB = 24.3 meV for the XA transition, in reasonable agreement with the exciton binding energy of 26 meV reported for bulk GaN.37 For the line at 3.366 eV, a much smaller blueshift is observed, corresponding to a value of EB = 67.5 meV for the I1 BSF/IDB* quantum-wire exciton. This value is much larger than the calculated one (EB = 7 meV) and thus implies that the I1 BSF/IDB* junction actually exhibits a type-I band alignment with a strong confinement of both, electrons and holes. In conclusion, we have shown that intersecting I1 BSFs and IDB*s occur in spontaneously formed GaN nanowires that bind excitons and act as crystal-phase quantum wires. Excitons bound to these quantum wires have been found to exhibit exceptionally large oscillator strength and binding energy. The strong excitonic correlation combined with the fact that the


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nanowire geometry improves light extraction38 in these crystal-phase quantum wires results in very efficient emission. The well-defined geometry of these crystal-phase quantum wires, their atomically flat interfaces, and the absence of compositional fluctuations makes them an ideal system for fundamental studies of one-dimensional excitons. Dimitrakopulos et al. proposed previously that BSFs could propagate through IDBs*.19 Particularly interesting in this context are the tubular IDB*s formed in Ga-/N-polar core/shell nanowires and their intersection with I1 BSFs forming perfect hexagonally shaped crystal-phase quantum rings. Since the circumference of the core can be as small as 20 nm (see, for example, Fig. 1 in Ref. 18), these structures may enable an unambiguous observation of the excitonic AharanovBohm effect.

METHODS Nanowire growth All nanowire ensembles formed spontaneously during radio frequency plasma-assisted molecular-beam epitaxy of GaN on Si(111) substrates. For the samples grown at substrate temperatures of 788, 829, and 865 °C, the as-received substrates were etched for 2 min in diluted (5%) HF and then annealed in the growth chamber for 30 min at 880 °C. After this annealing, the 7 × 7 surface reconstruction characteristic of a clean Si(111) surface appeared upon cooling to temperatures below 860 °C. Subsequently, the substrate temperature was set to the desired value for growth, and the substrate was exposed to the N plasma for 10 min before opening the Ga shutter to induce the spontaneous formation of GaN nanowires. The latter requires N-rich conditions.39 For all samples, the active flux provided by the N plasma source was kept equal to 7.4 × 1014 s 1 cm 2. As the Ga desorption rate increases −

−

exponentially with increasing substrate temperature, the impinging Ga flux was increased from 1.8 × 1014 to 1.8 × 1015 s 1 cm 2 when increasing the substrate temperature from 788 to −

−

865 °C. For all samples, the nanowires exhibit an average length of 2–3 µm, a mean diameter of about 50 nm, and a density on the order of 5 × 109 cm 2. For the sample grown at a −

substrate temperature of 750 °C in a different molecular-beam epitaxy system, the substrate was exposed to active N for 5 min before opening the Ga shutter, and the N and Ga fluxes


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during growth amounted to 1.2 × 1015 and 2 × 1014 s 1 cm 2, respectively.40 Note that PL −

−

spectra taken on the latter sample can be found in Ref. 18 (sample C). Transmission electron microscopy Cross-sections of GaN nanowires were prepared by using the standard strategy of mechanical grinding and dimpling the specimen followed by Ar-ion beam milling down to electron transparency. Transmission electron microscopy imaging was performed with a field emission microscope operated at 200 kV. The microscope is equipped with a CCD camera for image recording. High-resolution images are obtained by aligning the nanowires along the zone axis orientation, which is controlled by electron diffraction pattern. Photoluminescence spectroscopy Continuous-wave photoluminescence (PL) experiments at zero magnetic field were performed using the 325-nm line of a HeCd laser for excitation. For these experiments, the samples were mounted on the cold finger of a continuous-flow He cryostat capable of reaching temperatures between 5 and 300 K. The laser was focused down to a 30 µm diameter spot onto the surface of the sample. The PL signal was collected using a lens and dispersed by a monochromator with an 80-cm focal length and a 2400 lines/mm grating, providing a spectral resolution of about 250 µeV. The dispersed signal was then detected with an ultraviolet-sensitized liquid-nitrogen-cooled charge coupled device (CCD). The dynamic range of the CCD camera is about four orders of magnitude. Low-temperature magneto PL experiments were performed in Faraday configuration using a free-space optics-based insert placed in a superconducting magnet producing magnetic fields up to 14 T. The sample was mounted on top of an x-y-z piezoelectric stage kept in gaseous He at 4.2 K and excited with a HeCd laser emitting at 325 nm. For these experiments, the laser was focused down to a spot with a diameter of about 1 µm using an aspheric lens. The PL signal was collected by the same lens and directed to a 50-cm focal-length monochromator equipped with a CCD camera for detection. Time-resolved PL measurements were performed by focusing the second harmonic (325 nm) of an optical parametric oscillator pumped by a femtosecond Ti:sapphire laser (pulse width and repetition rate of 200 fs and 76 MHz, respectively). The sample was mounted on the coldfinger of a continuous-flow He cryostat allowing us to set temperatures between 5 and


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300 K. The PL signal was dispersed by a 25-cm focal-length monochromator and detected by a streak camera operating in synchroscan mode. For all experiments, the energy fluence per pulse was kept below 0.1 µJ/cm2. The position of the grating has been kept constant when measuring the temperature dependence of the time-resolved photoluminescence of the different excitonic lines. For all PL experiments, the diameter of the laser spot at the surface of the sample is chosen such that the detected signal is averaged over at least several tens of nanowires. This ensemble average improves statistics and allows us to quickly find areas on the sample with a least one nanowire containing an I1 BSF/IDB* junction. Measurements on ensemble of nanowires also ensures enough statistics and, in particular, that the measured spectra are characteristic of the ensemble and not being dominated by wire-to-wire fluctuations in crystallographic defects.41 Accordingly, spatial variations in PL lineshape, intensity or lifetime were not significant.

Simulations DFT calculations were performed using the projector-augmented wave method as implemented in Vienna Ab initio Simulation Package (VASP). The 3d electrons of Ga and 2s electrons of N were treated as valence states. The energy cutoff of the plane-wave basis set was set to 400 eV. Exchange-correlation effects were treated by the local-density approximation (LDA). To model both defects, the I1-BSF and the IDB*, a periodic structure consisting of 20 bilayers along [1010] (x-direction) and 20 bilayers along [0001] (z-direction) was constructed. A 1 × 8 × 1 Monkhorst-Pack k-point mesh was used for Brillouin zone integrations. The atomic positions were optimized until all atomic forces converged to less than 0.01 eV/Å. This structure optimization turned out to be crucial for obtaining a reliable electrostatic potential. Electron and hole ground state wave functions and energies were computed using an eightband k·p model,42 implemented using the multiband k·p module of the SPHInX software library.43 The dimensions of the simulation cell were 40×40×0.25 nm3, discretized in 160×160×1 grid points along x, y, and z, with z denoting the quantum-wire axis. Periodic boundary conditions are inherent to the plane-wave framework of the software package. The material parameters for GaN were taken from Ref. 44, the spin-orbit splitting Δso was taken from Ref. 45, and the potential arising from the I1 BSF/IDB* was introduced as an additional


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contribution to the potential landscape. Strain arising from the I1 BSF/IDB* was neglected. The calculation of the electron and hole ground states was performed in two steps: first, the single-particle states were computed using only the bulk electronic properties of GaN and the potential arising from the I1 BSF/IDB*. In a second step, the energy and wavefunction of the exciton were obtained by the effective potential method. The electron (hole) state was computed under the influence of the effective potential V!h ( V!e ) arising from the hole (electron) and minimized against the variational parameter λ that describes the extent of the exciton wavefunction along the z-axis. ASSOCIATED CONTENT Supporting information It contains a description of the effective potential formalism used to compute the energy of excitons in I1 BSF/IDB* quantum wires, a scanning electron microscopy analysis of the shape of GaN nanowires grown by molecular-beam epitaxy on Si(111) substrates, additional photoluminescence experiments on the investigated GaN nanowire samples, and the derivation of the temperature dependence of the radiative lifetime of a quantum-wire exciton in the presence of donor impurities. AUTHOR INFORMATION Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS We would like to thank Vincent Consonni for providing an additional sample and Manfred Ramsteiner and Chiara Sinito for a careful reading of the manuscript. P. C. acknowledges funding from the Fonds National Suisse de la Recherche Scientifique through project 161032. J. K. Z. thanks the Deutsche Forschungsgemeinschaft within SFB 951 for funding. M. R. M. and M. P. acknowledge the funding from the European Research Council (MOMB project no. 320590). We also acknowledge the support of LNCMI-CNRS, a member of the European Magnetic Field Laboratory (EMFL). REFERENCES 1

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FIGURE CAPTIONS Figure 1: (a) Cross-sectional transmission electron micrograph taken on an ensemble of GaN nanowires grown on Si(111) at a substrate temperature of 750 °C. The ensemble consists of short and thick Ga-polar nanowires interspersed by long and thin nanowires with a Ga-/Npolar core/shell geometry. (b) and (c) High-resolution transmission electron micrographs of single nanowires (b) with only I1 BSFs and (c) with I1 BSFs intersecting an IDB*. (d)–(f) Atom stacking sequence at (d) an I1 BSF, (e) an IDB*, and (f) an I1-BSF/IDB* junction with relaxed atomic positions in wurtzite GaN. Red and blue circles correspond to Ga and N atoms, respectively. The I1 BSF and the IDB* are marked by colored regions in the background. In (f), the intersecting I1 BSF and IDB* at the center of the cell give rise to a linear extended defect aligned along the [ 1 2 1 0] direction. The additional four junctions at the cell boundaries have been included to ensure periodic boundary conditions. Figure 2: (a) Microscopic electrostatic potential for the relaxed structure shown in Fig. 1(f). The I1 BSF/IDB* junction at the center of the cell repels electrons, while the artificial junctions at the cell boundaries are attractive centers. (b) Electronic potential Ve at an I1 BSF/IDB* junction used as an input for the k·p simulations. The x and y axes correspond to the [0001] and [10 1 0] directions, respectively. The IDB* and the I1 BSF are located at x = 0 and y = 0, respectively. (c) Electron effective potential at the I1 BSF/IDB* junction for λ = 9 nm. In (b) and (c), the potential is color-coded according to the scale on the right. (d) Electron and (e) hole charge densities in the plane perpendicular to the I1 BSF/IDB* junction. The squared modulus of the electron-hole overlap integral amounts to 0.07. Figure 3: (a) PL spectra recorded at 10 K on GaN nanowire ensembles grown at three different substrate temperatures. The spectra have been shifted vertically for clarity. The energy ranges for the near band edge (NBE), (IDB*,X), (I1,X), and (I2,X) transitions are highlighted using different colors. The transitions labeled with a dot correspond to phonon replica, while those indicated by a star arise from free excitons. (b)–(d) Results of additional PL experiments performed on the sample grown at a substrate temperature of 865 °C. (b) PL transients for the high- and low-energy components of the Y4 doublet. Inset: PL spectra at 5,


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20, and 50 K. The spectra have been normalized and shifted vertically for clarity. (c) Temperature dependence of τr for the NBE (squares), (I1,X) (circles), (IDB*,X) (triangles), and Y4 transitions (diamonds). The solid lines show the dependence expected for three-, two-, and one-dimensional excitons. (d) Temperature dependence of τr for the Y4 doublet. The line is a fit accounting for the presence of localization centers in the vicinity of the I1 BSF/IDB* quantum wires. Inset: Schematic energy diagram depicting the phonon-assisted coupling and the radiative decay (black and blue arrows, respectively) of localized and free excitons in I1 BSF/IDB* crystal-phase quantum wires. Figure 4: Diamagnetic shift of the free exciton (squares) and the high-energy component of the Y4 transition (triangles) for the sample grown at a substrate temperature of 865 °C. The lines are the result of fits with Eq. (1). Inset: High energy component of the Y4 PL doublet at 4.2 K and at magnetic fields of 0, 10 and 14 T. The spectra have been shifted vertically for clarity. The vertical lines are guides to the eye.


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Figure 1 - Corfdir et al.


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(c)

IDB*

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(d) I1 BSF

(f)

(e) IDB* (1010)

[0001]

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[0001]

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ΔV (eV)

1 0.3 2 3 3 4 0 5 2 6 7 -0.3 8 1 9 100 1 2 3 4_ 5 6 11 0 12 Distance along [1010] (nm) 13 ~ Ve (meV) Ve (meV) (c) 14 (b) 10 10 500 15 160 17 -10 0 18 -10 -20 -10 0 10 -20 -10 0 10 19 x (nm) x (nm) 20 21 20 2 (e) |Φh|2 22 (d) |Φe| 10-1 23 10-3 24 10-5 25 0 26 27 10-3 28 ||2 = 0.07 29 ACS Paragon Plus -4 Environment 10 -20 30 10 0 10 -20 -10 0 -20 -10 31 x (nm) x (nm)

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Crystal-Phase Quantum Wires: One-Dimensional ... - ACS Publications

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