Influence of Metal Deposition on Exciton−Surface Plasmon Polariton

Apr 2, 2013 - Excitons were generated in the metal coated nanowires by .... Torr and evaporation rate of ∼0.1 nm/s. ... The CL detection ..... value...
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Influence of Metal Deposition on Exciton−Surface Plasmon Polariton Coupling in GaAs/AlAs/GaAs Core−Shell Nanowires Studied with Time-Resolved Cathodoluminescence Yevgeni Estrin,† Daniel H. Rich,*,† Andrey V. Kretinin,‡ and Hadas Shtrikman‡ †

Department of Physics and The Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, P.O.B 653, Beer-Sheva 84105, Israel ‡ Braun Center for Submicrometer Research, Condensed Matter Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel S Supporting Information *

ABSTRACT: The coupling of excitons to surface plasmon polaritons (SPPs) in Au- and Al-coated GaAs/AlAs/GaAs core−shell nanowires, possessing diameters of ∼100 nm, was probed using time-resolved cathodoluminescence (CL). Excitons were generated in the metal coated nanowires by injecting a pulsed high-energy electron beam through the thin metal films. The Purcell enhancement factor (FP) was obtained by direct measurement of changes in the temperaturedependent radiative lifetime caused by the nanowire excitonSPP coupling and compared with a model that takes into account the dependence of FP on the distance from the metal film and the thickness of the film covering the GaAs nanowires. KEYWORDS: GaAs/AlAs core−shell nanowires, surface plasmon polariton, cathodoluminescence n important field in nanotechnology research is the design of plasmonic metal/semiconductor composite structures to obtain novel optical device properties for a variety of applications in biological labeling/sensing,1,2 light-emitting diodes,3,4 lasers,5 and solar cells.6 By an appropriate choice of a metal possessing a surface plasmon frequency, ωsp, which is reasonably close to the excitonic transition energy of the nanocrystal, exciton coupling to surface plasmon polaritons (SPPs) can be enhanced. The enhancement of the photoluminescence (PL) efficiency of InGaN/GaN quantum well (QW) samples coated with thin films of Ag has been presented before.7−10 The results demonstrate an enhancement of the internal quantum efficiency by transfer of energy between excited electron−hole (e−h) pairs and propagating SPPs. A similar SPP-enhanced PL has been observed in the GaAs/ AlGaAs QW system in which samples were coated with Au.11 Notably, SPP-enhanced emission was also observed in CdSe quantum dots (QDs) that were dispersed on evaporated Au films12 and GaN/AlN QD samples prepared using thin Ag films.13 In particular, one-dimensional III−V nanowires may play an important role in the development of electronic devices at the nanoscale as well as in the aforementioned photonic applications.14−20 Light absorption and resonant optical modes in nanowires can be tuned by altering the diameter and cross-sectional shape.21,22 Semiconductor core−shell nanowires, in which a narrower band gap core is embedded

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© 2013 American Chemical Society

within a wider band gap material, are of significant importance for fabricating devices with enhanced optical properties or ballistic electronic transport properties.15,23 Detailed time- and polarization-resolved PL studies of GaAs/AlGaAs core−shell nanowires demonstrate the long exciton lifetimes and enhanced luminescence efficiency provided by the AlGaAs shell.24−26 The III−V nanowires are commonly nucleated and grown via a vapor−liquid−solid (VLS) mechanism using Au droplets or by self-assisted catalyst-free growth.27−29 In this work, we investigated the optical properties and carrier relaxation dynamics of Al- and Au-coated GaAs/AlAs/GaAs core−shell nanowires dispersed on Si substrates using time-resolved cathodoluminescence (CL). The nanowires were grown by self-assisted VLS growth in a high purity molecular beam epitaxy (MBE) system. The metal-coated nanowires, having diameters of ∼100 nm, provide a system in which the electron−hole pairs can be created, diffuse, and recombine in varying proximity to the surface. The variable distance from the surface, at which excitons recombine, results in a range in the expected Purcell enhancement factor (FP) which describes the enhanced radiative recombination rate due to coupling of the excitons to the SPP modes of the metal film. The SPPs can be converted to free-space photons if the propagating SPPs in the Received: January 2, 2013 Revised: February 27, 2013 Published: March 21, 2013 1602

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thin metal film are scattered by the surface/interface roughness or grain boundaries of the polycrystalline metal film, owing to the momentum change associated with the scattering that enables a matching with the ω vs k light dispersion relation.9,10 Due to the opacity of the metal with respect to light/laser excitation from the top surface, CL is shown to be a particularly useful probe for the metal/nanowire (or more generally for metal coated nanostructure systems) in that the high-energy electron beam can easily penetrate the metal film and create excess e−h pairs in the semiconductor nanostructure. The GaAs/AlAs/GaAs nanowires were grown by molecular beam epitaxy (MBE) using the self-assisted VLS method,28−30 on (111)-oriented silicon bearing a native oxide layer. After water removal at ∼200 °C, the Si wafer was outgassed overnight at high temperature (∼600 °C) in a separate chamber, before being transferred into the MBE growth chamber. The growth was initiated by condensation of Ga at the point defects in the SiO2 layer and carried out at ∼640 °C and a group V/III (As4/Ga) ratio of ∼100. Uniform diameter GaAs nanowires were grown with a high aspect ratio, no significant tapering, and a pure zinc-blende structure, as revealed by careful transmission electron microscopy (TEM) analysis. For growth of the uniform ∼6 nm AlAs shell and ∼12 nm GaAs capping layer, the temperature was lowered to 520 °C. The GaAs capping layer protects the AlAs shell from oxidation when exposed to air. A typical scanning electron microscopy (SEM) image of the as-grown GaAs/AlAs/GaAs core−shell nanowires can be seen in Figure 1a. Nanowires, having widths of ∼100 nm and lengths of ∼12 μm, were harvested and dispersed onto heavily doped ptype Si wafers coated with a ∼20-nm-thick layer of Al to minimize the effects of charging during the CL measurements. A characteristic hexagonal prism shape was observed for such wires, consistent with previous studies of the shape of selfassisted MBE-grown GaAs nanowires.30 Slightly tilted SEM top views of a single GaAs/AlAs/GaAs core−shell nanowire showing the tip and the base are presented in Figure 1b and c, respectively, which clearly reveal the hexagonal shape. A typical TEM image of a single GaAs/AlAs/GaAs core−shell wire taken from the same sample, showing a uniform structure with no defects, is presented in Figure 1d. The inset on the left shows an electron diffraction pattern revealing the zinc-blende structure. The inset on the right shows a high-resolution TEM image of a cross-section taken from a GaAs/AlAs/GaAs core− shell nanowire possessing the same nominal structure but having slightly different thicknesses, displaying the typical hexagonal shape. The wire growth is along a ⟨111⟩ direction, and the facets on the hexagonal prism belong to the {011} family.30 Of relevance is also the native oxide layer that forms on the surface of the GaAs capping layer of the nanowire. TEM showed that an oxide layer with thickness of 2−3 nm formed on the capping layer, and such an image is presented in the Supporting Information. The Au and Al films were deposited at near normal incidence onto the nanowires which were maintained at room temperature in a separate metal evaporation system with a pressure of ∼1 × 10−6 Torr and evaporation rate of ∼0.1 nm/s. To ensure a flat surface, the nominal thickness (t0) of the deposited metal film was ∼20 nm. High resolution field-emission SEM images of the bare, Al-, and Au-covered nanowires are shown in Figure 2a−c. Roughness with feature sizes less than ∼10 nm is observed on both the Al- and Au-covered nanowires. Differences in the roughness between the two metals can be

Figure 1. SEM image of the as-grown GaAs/AlAs/GaAs core−shell nanowires taken from a side view in (a). The nanowires exhibit a uniform aspect ratio greater than ∼100. Slightly tilted SEM top views of a single GaAs/AlAs/GaAs core−shell nanowire showing the tip and the base in (b) and (c), respectively, which clearly reveal the hexagonal shape. A typical TEM image of a single GaAs/AlAs/GaAs core−shell wire taken from the same sample, showing a uniform structure with no defects, is presented in (d). The inset on the left shows an electron diffraction pattern revealing the zinc-blende structure. The inset on the right shows a high-resolution TEM image of a cross-section taken from a GaAs/AlAs/GaAs core−shell nanowire possessing the same nominal structure but having slightly different thicknesses, displaying the typical hexagonal shape.

observed with the aluminum deposition showing more spots and hillocks, possibly owing to differences in grain size and morphology. To better quantify the roughness of the metal films on the nanowires, we performed atomic force microscopy (AFM) measurements for the three cases, as shown in Figure 2d−f. A line scan analysis of the AFM images, with scans along a line parallel to the nanowire length near the top, is shown in Figure 2g. The root-mean-square (RMS) roughness is 0.54, 1.05, and 1.31 nm for typical scans along the bare, Au-, and Alcovered nanowires, respectively. The roughness observed for the bare nanowire is attributed to possible variations in the oxide layer thickness. A variety of feature sizes, ranging from ∼10 to ∼50 nm is observed in the AFM images and line scans for the metal coated nanowires. CL imaging and spectroscopy were previously used to determine the propagation distance of SPPs near the surface plasmon resonance of Ag and Au films, and the propagation lengths varied from a few hundred nanometers to several micrometers.31,32 Therefore, differences in the polycrystalline morphology, surface roughness, and size scale between the Al- and Au- coated wires are expected to be small in comparison to the wavelength of light and typical SPP 1603

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propagation lengths. Such roughness is not expected to influence the CL intensity measurements. The CL experiments were performed on a modified JSM5910 scanning electron microscope (SEM). The CL detection system has been described previously in detail and measures emission in a far-field detection geometry.33 Electron beam energies (Eb) ranging from 7 to 15 keV and e-beam currents (Ib) ranging from 0.3 to 2 nA were used to excite and create excess carriers in the GaAs nanowires. A GaAs:Cs photomultiplier tube operating in the 380−890 nm spectral range enabled photon counting of the luminescence which was dispersed by a monochromator with a 0.25 m focal length. The spectral resolution was set to ∼1 nm. The samples were mounted in the SEM on a variable temperature and vibration isolated cold stage that was cooled with a closed-cycle cryocooler and were maintained at temperatures ranging from 50 to 300 K. Time-resolved CL experiments were performed by the method of delayed coincidence in an inverted single photon counting mode.33 Electron beam pulses of 50 ns width with a 1 MHz repetition rate were used to excite the sample. Sets of CL spectra and CL decay transients of the GaAs near band-edge (NBE) emission for e-beam excitation of a single bare nanowire are shown in Figure 3 for temperatures in the 50−210 K range. The intensities of the CL spectra in Figure 3a have been normalized so that each spectrum displays approximately the same peak height, and scaling factors are shown to indicate the relative CL intensity for each temperature. As the temperature increases, the CL spectra are observed to red-shift in accordance with the temperature dependence of the GaAs bandgap, and the CL spectra broaden from 20.4 to 54.3 meV as the temperature is raised from 50 to 210 K. CL transients of the bare and Au-covered nanowires are shown in Figures 3b and c, respectively. The transients were acquired for emission wavelengths near the CL peak intensity at each temperature. The carrier lifetimes were extracted from the slopes of the CL transients at each temperature, assuming a single exponential decay whose fits are illustrated by the red lines running through the data in Figures 3b and c. The carrier lifetimes depend on the temperature and generally increase in the temperature range shown. The deposition of Au on the nanowires is found to markedly reduce the carrier lifetimes relative to the values for the bare nanowires, as shown in

Figure 2. High-resolution field-emission SEM (a−c) and AFM (d−f) images of the bare, Al-, and Au-covered GaAs/AlAs/GaAs core−shell nanowires. The SEM and AFM images are shown with the same size scale, as indicated in (a). A line scan analysis of the AFM images is shown in (g) for each nanowire in which a height vs distance scan is presented along a line parallel to the nanowire length and near the top of the nanowire.

Figure 3. Stack plot of local CL spectra in (a) acquired for a point e-beam excitation of a bare GaAs/AlAs/GaAs core−shell nanowire at various temperatures and local CL decay transients in (b) and (c) for the bare and Au-covered nanowires, respectively, at various temperatures. The relative peak heights of each CL spectrum have been adjusted to display approximately the same height, and scaling factors are shown for the various temperatures. The red lines in (b) and (c) show the results of a linear fit in the semilog plot for obtaining the carrier decay time, τ. 1604

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Figure 4. Histogram analysis of the integrated CL intensities (a−c) and carrier decay times (τ) (d−f) for the bare, Au-, and Al-covered GaAs/AlAs/ GaAs core−shell nanowires dispersed at various angles on the Si substrate.

Al-covered nanowires, consistent with an enhancement in the radiative recombination rate due to exciton-SPP coupling. The absence of nanowires in the 40−50° range in Figure 4a−c is purely accidental, as the nanowires were dispersed with random angles on the Si substrates for the bare, Au-, and Al- covered nanowire samples. We note that, despite the nearly identical internal reflection geometries for the Au- and Al-covered wires, the reflectivity of Al is lower than the reflectivity of Au by ∼12% at λ = 820 nm due to an interband transition in Al,35 and as such this cannot account for the observed large differences in the integrated CL intensities. Thus, the CL intensity enhancement likely results from an enhanced exciton-SPP coupling in the Au-covered wires. In addition, a statistical analysis of the carrier lifetimes of the GaAs nanowires was performed, and histograms of the decay times measured at T = 50 K for the bare, Au-, and Al-covered wires are shown in Figure 4d−f. These results show that the average lifetimes (τ) for the bare, Al-covered, and Au-covered wires are ∼2.0, 1.3, and 1.1 ns, respectively. Moreover, we have performed time-resolved CL measurements and CL integrated intensity measurements, I(T), for temperatures ranging from 50 to 300 K to determine the temperature dependence of the radiative lifetime (τR) and nonradiative lifetime (τNR). We have extracted τR(T) from τ(T) and I(T) using a procedure which we have previously described for time-resolved CL studies of InGaN/GaN quantum wells, presented in the Supporting Information.36 The results for τ(T) and τR(T) are shown in Figure 5a and b, respectively, for the bare, Al-covered, and Au-

Figures 3b and c. An analysis of the temperature dependence of the radiative lifetimes for the bare, Au-, and Al-covered wires is presented below. To account for variations among the wires, we have performed a statistical analysis of the integrated CL intensities (I) and carrier decay times (τ) for emission from single bare, Au-, and Al-covered wires for T = 50 K. The e-beam was injected into each individual nanowire through the metal film at a point above its center. The dispersal of wires on the Si substrate with random orientations has allowed for a statistical analysis of the integrated CL emission intensity for various orientation angles (θ) relative to the optical axis of the CL detection system.34 By comparing coated nanowires with two different metals, whose deposition geometries are nearly identical, we can compare the effects of exciton-SPP coupling and luminescence intensity enhancements for the Au and Al metal coatings. Since the Au/GaAs surface plasmon resonance energy (ℏωSP = 1.804 eV) is much closer to the GaAs band gap energy (ℏωGaAs = ∼1.51 eV at 50 K) than in the case of Al/ GaAs (ℏωSP = 2.700 eV), as determined by the calculated ω vs k dispersion relations described below, we would expect a CL intensity enhancement for the Au-covered wires relative to that for the Al-covered wires. Histograms of the integrated NBE CL emission for T = 50 K are shown in Figure 4a−c for the bare, Au-, and Al-covered nanowires, with each panel summarizing the mean and standard deviation of the integrated CL intensities and lifetimes. The Au-covered nanowires exhibit an average CL intensity that is ∼3.1 times greater than that for the 1605

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Figure 5. Results for the carrier decay times τ(T) in (a) and radiative lifetimes τR(T) in (b) for the bare, Al-covered, and Au-covered GaAs/AlAs/ GaAs core−shell nanowires.

Figure 6. Experimental energy-dependent Purcell enhancement factors for the Au- and Al-covered GaAs/AlAs/GaAs core−shell nanowires. The Purcell enhancement factors are given by FP(ω) = τR(bare)/τR(metal) in the energy range of the GaAs near band edge emission (T = 50 to ∼300 K).

covered wires. To assess the enhancement as a result of exciton coupling to SPPs, we obtain the energy-dependent Purcell enhancement factors as FP(ω) = τR(bare)/τR(metal) which are shown in Figure 6 for the time-resolved CL measurements of the bare, Al-covered, and Au-covered nanowires. The data represent values obtained for different temperatures in the 50−

300 K range, whose exciton transition energies follow approximately the Varshni relation for the temperature dependence of the bulk GaAs bandgap.37,38 To develop a reasonable model and calculate FP(ω) for the metal−nanowire system, we first observe that the diameter of the nanowire (∼100 nm) is large compared with (i) the 1606

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penetration depth of the SPP field into the semiconductor near resonance and (ii) the typical exciton dipole to metal film separation, both of which are ∼10 nm for SPP-induced field enhancements in quantum heterostructures and nanostructures.6−13 Therefore, we expect that the largest enhancement of CL intensity and decrease in radiative lifetime will occur in regions of the nanowire where excitons recombine in closest proximity to the metal films. Assuming a small curvature of the wire for excitons recombining within ∼10 nm of the metal, we expect that the two-dimensional (2D) SPP energy dispersion model for a metal film covering a flat dielectric material will provide a reasonable model from which the ω vs k dispersion relations can be calculated for both Au- and Al-covered wires.39 From the solution of Maxwell’s equations with a matching of boundary conditions at the interfaces of the vacuum/metal/ GaAs system, we have calculated the ω vs k dispersion relations which include the effects of losses for both Al and Au films possessing varying thicknesses on GaAs, as shown in Figure 7.

plasmon states per unit area can be calculated from the dispersion relations in Figure 7 and is given by ρ2D(ω) = (1/ 4π)∂k2/∂ω. For a dielectric in the transparency region (i.e., |ε″(ω)| ≪ |ε′(ω)|), the energy density of the electric field in the layer is given by uE(ω,z) = [∂(ωε′)/∂ω][|E(z)|2/8π].45 However, for metals with dissipation, the expression for the energy density is uE(ω,z) = (ε′ + 2ωε″/γ)[|E(z)|2/8π] where γ is the damping constant which can be estimated from the Drude model.46,47 The propagation of electromagnetic waves along the metal/GaAs interface yields analytical solutions for the in-plane electric field, Exi, in the ith layer (such that i = 1 to 3 represent the vacuum, metal, and GaAs regions, respectively) of the form Exi ∝ exp(ikx)exp(−kziz) with k2zi = k2 − (ω2/c2)εi. The denominator of eq 1 can easily be integrated to yield an analytical solution for FP(z) that is given by FP(z) = 1 +

πc 3e−2kz3z ⎡ e−2kz2t ω 2⎢ k + ε′2 + ⎣ z1

(

×

We have used the energy dependence of the dielectric constants (i.e., ε(ω) = ε′(ω) + iε″(ω)) of GaAs, Au, and Al that are found in the literature,40−43 and the formalism for the SPP dispersion relation calculation has been previously described.7,8,44 The Purcell factor, FP, is given by πc 3 |E(z)|2 ∞ u (ω , −∞ E

4ω 2 ∫

z′)dz′

)(

1 − e−2k z2t kz2

)+

∂(ωε ′3 ) 1 ⎤ ∂ω kz3 ⎥ ⎦

(2)

Using the appropriate dielectric functions of Au, Al, and GaAs,40−43 we have plotted FP(z) for metal thicknesses (t) of 10, 20, and 30 nm and for ℏω = 1.42 eV (TGaAs ≈ 300 K), as shown in Figure 8a. As expected from the energy differences between the GaAs NBE emission at room temperature (∼1.42 eV) and the surface plasmon frequencies for Au (ℏωsp ≈ 1.804 eV) and for Al (ℏωsp ≈ 2.700 eV), the values of FP(z) in close proximity to the metal (i.e., for z < ∼10 nm) for Au/GaAs are at least an order of magnitude larger than those for Al/GaAs. To develop a model for the average Purcell enhancement factor, ⟨FP⟩, for exciton recombination in the metal-covered wires subject to the present e-beam excitation conditions, we expect that a relatively uniform e−h pair excitation density occurs across the cross-section of the wire (∼100 nm) owing to (i) the size of the e−h generation volume for a beam energy of 15 keV and (ii) the minority carrier diffusion length, both of which are ∼1 μm. Therefore, in the simplest model, we calculate the effective Purcell enhancement factor (⟨FP⟩) as an area average over the 2D cross-section of the wire (neglecting recombination in the thin AlAs shell). We considered nanowire cross-sectional shapes of hexagonal, circular, and square, for comparison, as illustrated in the inset of Figure 8a for the first two shapes. The dimensions of the nanowire used in the calculations are given by r0 = 50 nm, r1 = 32 nm, and r2 = 38 nm for a 100 nm diameter GaAs/AlAs/GaAs core−shell nanowire possessing a ∼12-nm-thick GaAs capping layer surrounding a ∼6-nm-thick AlAs shell. In this model, we assume that half of the wire is covered by a thin metal film of variable thickness (t), whereas the other half is bare due to shadowing during the metal deposition. The local thickness of the metal on the nanowire surface is taken as t = t0 cos α, where α is the angle between the impinging metal beam and surface normal during the metal deposition. The results of the averaging for the case of hexagonal nanowires are shown in Figure 8b in which ⟨FP⟩ is plotted vs ℏω for Au and Al covered wires for film thicknesses (t0) ranging from 10 to 30 nm. The energy range of the GaAs NBE emission for temperatures between 50 and 300 K is shown on the graph for comparison. As observed in Figure 8b, the expected average Purcell factor

Figure 7. Calculated ω vs k surface plasmon dispersion relationships for various thicknesses (as indicated by the arrows) of Au (a) and Al (b) deposited on GaAs. The effects of losses are taken into account by including the imaginary part of the dielectric constants for Au, Al, and GaAs.

FP(z) = 1 +

∂(k 2) ∂ω

2ωε ′′2 γ

ρ2D (ω) (1)

where uE(ω,z) is the electric energy density for each material region and E(z) is the un-normalized plasmon electric field at a distance z from the metal/GaAs interface.7,8 The 2D density of 1607

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Figure 8. Calculated Purcell enhancement factor, FP, as a function of distance (z) from the metal/GaAs interface of the nanowire in (a) for ℏω = 1.42 eV and the calculated average Purcell enhancement factor ⟨FP⟩ as a function of energy (ℏω) for e−h recombination in the Au- and Al-covered GaAs/AlAs/GaAs core−shell nanowires with a hexagonal shape in (b). The results are shown for Au and Al film thicknesses of 10, 20, and 30 nm (a) and for various Au and Al film thicknesses (t0) ranging from 10 to 30 nm (b). The shaded (green) vertical bar in (a) shows the position of the AlAs shell layer relative to the metal/GaAs interface at z = 0. A schematic of the GaAs/AlAs/GaAs core−shell nanowire structure is shown in the inset of (a) for wires possessing hexagonal and circular (tapered) shapes, where r0 = 50 nm, r1 = 32 nm, and r2 = 38 nm. The energy range of the GaAs NBE emission, for temperatures between 50 and 300 K, is shown by the shaded vertical bar in (b).

Figure 9. Calculated average Purcell enhancement factor, ⟨FP⟩, vs energy (a) and vs the minimum effective metal-exciton separation (teff) (b). The calculations were performed for a Au and Al film thicknesses (t0) of 20 nm on the GaAs/AlAs/GaAs core−shell nanowires possessing hexagonal, circular, and square cross sections, with a radius (r0) of 50 nm, in the energy range of the GaAs near band edge emission (T = 50 to 300 K). A schematic of the model structure is shown in the inset of Figure 8a for hexagonal and circular (tapered) nanowire shapes.

for ℏω = 1.42 eV is reduced in comparison to the maximum values near the metal/GaAs interface (z ≈ 0) shown in Figure 8a. This is due to the assumption of a roughly uniform density for e−h pair generation and recombination over the crosssectional area of the wire. Moreover, in Figure 9a, we show the calculated values of ⟨FP⟩ for the energy range associated with the NBE emission in GaAs from 50 to 300 K. The calculations of ⟨FP⟩ for a metal thickness of t0 = 20 nm are shown for nanowires possessing hexagonal, circular, and square cross sections, for comparison. For the circular cross-section, two cases were considered in which the

metal film thickness was both constant (t = t0) and allowed to vary as t = t0 cos α (i.e., a tapered film coverage, as illustrated in the inset of Figure 8a). The calculations for the hexagonal and circular (tapered) cross sections yield the largest values of ⟨FP⟩ in Figure 9a as a result of local enhancements in FP caused by the proximity of excitons to segments of the Au films having reduced thicknesses (t ≪ 20 nm). While the calculations agree qualitatively with the experimental results in that the values of ⟨FP⟩ for the Au-covered nanowires are larger than those for the Al-covered nanowires at all energies, it is clear that the model 1608

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predicts an ⟨FP⟩ which is considerably larger (by a factor of 5− 10) than the experiment. To account for this discrepancy, we first note that an oxide layer of 2−3 nm in thickness surrounds the outer GaAs capping layer of the nanowire. Therefore, we observe that when Au or Al is deposited on the nanowires, the actual minimum separation between the metal layer and the excitons in the nanowires is at least equal to the thickness of the oxide layer. However, additional effects caused by the absence of a complete surface passivation may influence the average minimum separation distance between the metal film and the excitons. The presence of the oxide layer may induce surface/ interface states in the gap, create a depletion layer, and lead to small band-bending effects near the oxide/GaAs interface. Band-bending near the surface of semiconductors has the wellknown effect of creating a “dead-layer” near the surface in which the density of photoexcited or e-beam excited electron− hole pairs is significantly reduced. Such effects have recently been observed in GaAs and ZnO nanowires.48,49 Unfortunately, without sufficient information regarding the Fermi-level pinning near the oxide/GaAs surface the effective width of such a “dead-layer” cannot be reliably estimated. Instead, we have included an additional step in our model for the calculation of ⟨FP⟩ in which the minimum effective metal− exciton separation (teff) is allowed to vary from 0 to 10 nm, as shown in Figure 9b for an energy of ℏω = 1.42 eV (i.e., close to the room-temperature band gap of GaAs). In this modified model, teff describes the minimum effective metal−exciton separation, due to a combination of the oxide layer thickness and band-bending effects near the oxide/GaAs interface, before the plasmon field begins to act on the excitons. The calculations in Figure 9b show an exponential decay in ⟨FP⟩ as a function of teff for the four cross-sectional wire geometries, which we believe is a plausible explanation for the reduced values of the experimental ⟨FP⟩ relative to the values for the ideal case shown in Figure 9a in which teff = 0. Consequently, the calculated values in our simple model approach the maximum experimental values of ⟨FP⟩ ≈ 3 for teff = 10 nm. Thus, the assumption of an effective metal−exciton separation of ∼10 nm appears to minimize the discrepancy between experiment and theory in these results. The calculations are also observed to be strongly dependent on the nanowire diameter, cross-sectional shape, and on local film thickness variations which depend on the metal evaporation geometry. In conclusion, the coupling of excitons to SPPs in Au- and Al-coated GaAs/AlAs/GaAs core−shell nanowires was probed using time-resolved CL. Excitons were generated in the metalcoated nanowires possessing nearly identical coating geometries by injecting a pulsed high-energy electron beam through the thin metal films. The average Purcell enhancement factor, ⟨FP⟩, was obtained by the direct measurement of the changes in the integrated NBE CL emission intensities and the temperaturedependent radiative lifetimes. To analyze the coupling of excitons to SPPs, a model was presented for ⟨FP⟩ which takes into account the dependence of FP on the distance from the metal film and the thickness of the film covering the GaAs nanowires possessing various cross-sectional shapes. The present study suggests a more general approach for treating metal-covered nanostructures in which exciton diffusion in the mesoscopic regime can influence the observed plasmonic effects.

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ASSOCIATED CONTENT

S Supporting Information *

Observation of the native oxide layer in high-resolution TEM, measurement of the integrated CL intensity of each nanowire, and determination of the temperature-dependent radiative lifetime. 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: [email protected] Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Ronit Popovitz-Biro of the Microscopy Unit, Weizmann Institute of Science for the professional TEM analysis. We also thank Einat Roth of the IKI for highresolution FE-SEM measurements and Jürgen Jopp and Roxana Golan of the IKI for the AFM measurements. H.S. acknowledges partial support from the Israel Science Foundation (grant 532/12 ISF) and from the Israeli Ministry of Science and Technology (grant 3-6799 IMOST).

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REFERENCES

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NOTE ADDED AFTER ASAP PUBLICATION Equations 1 and 2 have been updated. The revised version was re-posted on April 2, 2013.

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