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Determination of n-type doping level in single GaAs nanowires by cathodoluminescence Hung-Ling Chen, Chalermchai Himwas, Andrea Scaccabarozzi, Pierre Rale, Fabrice Oehler, Aristide Lemaitre, Laurent Lombez, Jean-Francois Guillemoles, Maria Tchernycheva, Jean-Christophe Harmand, Andrea Cattoni, and Stéphane Collin Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b02620 • Publication Date (Web): 16 Oct 2017 Downloaded from http://pubs.acs.org on October 18, 2017

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Determination of n-type doping level in single GaAs nanowires by cathodoluminescence Hung-Ling Chen,† Chalermchai Himwas,† Andrea Scaccabarozzi,†,‡ Pierre Rale,† Fabrice Oehler,† Aristide Lemaître,† Laurent Lombez,‡,¶ Jean-François Guillemoles,‡,¶ Maria Tchernycheva,† Jean-Christophe Harmand,† Andrea Cattoni,† and Stéphane Collin∗,†,‡ †Centre for Nanoscience and Nanotechnology, CNRS, University Paris-Sud/Paris-Saclay, France ‡Institut Photovoltaïque d’Ile-de-France (IPVF), Antony, France ¶Institut de Recherche et Développement sur l’Energie Photovoltaïque (IRDEP) EDF/CNRS/Chimie Paris Tech, Chatou, France E-mail: [email protected]

Abstract We present an effective method to determine the doping level in n-type III-V semiconductors at the nanoscale. Low-temperature and room-temperature cathodoluminescence (CL) measurements are carried out on single Si-doped GaAs nanowires. The spectral shift to higher energy (Burstein-Moss shift) and the broadening of luminescence spectra are signatures of increased electron densities. They are compared to the CL spectra of calibrated Si-doped GaAs layers whose doping levels are determined by Hall measurements. We apply the generalized Planck’s law to fit the whole spectra taking into account the electron occupation in the conduction band, the bandgap narrowing

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and band tails. The electron Fermi levels are used to determine the free electron concentrations, and we infer nanowires doping of 6 × 1017 to 1 × 1018 cm−3 . These results show that cathodoluminescence provides a robust way to probe carrier concentrations in semiconductor with the possibility of mapping spatial inhomogeneities at the nanoscale. Keywords: Cathodoluminescence, GaAs, nanowire, n-type doping, generalized Planck’s law.

Recent development of optoelectronics takes advantage of light confinement in nanostructures such as lasers, 1 light emitting diodes, 2 solar cells, 3 and hybrid III-V/Si devices. 4–7 Optimal performances require the control and the characterization of semiconductor doping with sub-micrometer characteristic lengths for both p and n regions. Radial junctions in nanowires are a noteworthy example. 8,9 III-V semiconductor nanowires (NWs) may constitute a new route toward high efficiency photovoltaic cells. 10,11 Nanowire arrays show antireflection properties and are beneficial for absorbing tilted incident or diffuse sunlight. 12 The highest conversion efficiency demonstrated for a GaAs single-junction was recently published with an efficiency of 15.3% at 1 sun with an axial junction. 13 Moreover, semiconductor NWs can relax significant misfit strain without dislocation formation and thus allow more flexible material designs. 14 Direct growth of III-V semiconductors on lattice-mismatched silicon provides an elegant way for the fabrication of multi-junction III-V/Si solar cells. A monolithic GaAs NW solar cell on Si bottom cell has already been demonstrated with the observation of voltage addition of the bottom and top cell and an efficiency of 11.4%. 5 Dopant incorporation mechanism in NWs might be very different depending on the growth method, and characterization of NW doping is not straightforward. Traditional Hall measurements for single NWs require sophisticated lithography steps, 15 and they are hindered by the requirement of good ohmic contacts to the doped NW. Nanowire field-effect transistors can also be fabricated to investigate majority carrier mobility and concentration, 16 but the accuracy is limited due to uncertainty of the gate capacitance and contact resistance. Atom probe tomography 17 is also used to investigate dopant concentration at the nanometer scale, 2


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but it is a destructive and time-consuming technique, still limited to relatively high doping concentrations. Moreover, the assessment of the carrier concentration may be flawed by electrically inactive impurities. In this context, contactless methods such as photoluminescence (PL) 18,19 or terahertz spectroscopy 20 of NW ensembles are promising alternatives to provide a rapid feed-back for NW growth. For photovoltaic applications, luminescence is one of the most useful characterization tools. The increase in the luminescence efficiency is key to push the conversion efficiency toward the Shockley-Queisser limit, 21 as shown for record single-junction GaAs solar cells. 22,23 High purity semiconductors exhibit a single sharp peak from band edge recombination. Introducing impurity dopants creates shallow donor states (n-type) or acceptor states (ptype), and impurity states merge with adjacent bands at high concentration. 24 Thus, one can observe a deeper sub-bandgap absorption tail and wider luminescence spectra in doped semiconductors. Furthermore, direct-gap III-V semiconductors (GaAs, InP...) have different electron and hole effective masses. N-type GaAs is degenerate for doping concentration above 5×1017 cm−3 , hence the absorption edge and luminescence peak shift to higher photon energy (blueshift) due to filling of the conduction band. This phenomenon is referred to BursteinMoss shift. 25,26 Blueshift and broadening of PL spectra have been observed in highly-doped n-InP NW, 27,28 and cathodoluminescence has been used to evidence local variations in the doping concentration. 15,28 Calibrated PL was also used to assess the Fermi level splitting in InP micropilars. 29 Arab et al. have investigated electron concentration in GaAs NWs based on the full-width at half maximum (FWHM) of the PL peaks. 19 However, inhomogeneities may also contribute to the luminescence broadening. A quantitative spectrum analysis is still lacking and requires luminescence measurements at the nanometer scale, which cannot be simply achieved by PL due to the diffraction limit. In this work, we demonstrate the use of cathodoluminescence (CL) mapping of single GaAs NWs to assess the local carrier concentration with a nanoscale resolution. Si-doped GaAs NWs present a clear Burstein-Moss shift and a broadening of the CL spectrum. Ad-

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vanced model based on the generalized Planck’s law 30 is developed to fit the luminescence spectra and to extract the Fermi level. This approach is validated on a series of n-GaAs thin film samples, for which the carrier concentration calibrated by Hall measurements is in quantitative agreement with the one extracted from the proposed all-optical method. Single NW CL mapping demonstrates a good doping homogeneity along the wire axis. Statistical analyses performed on a wire assembly allow assessing wire to wire doping fluctuations with a concentration spread over 6 × 1017 to 1018 cm−3 range. GaAs NWs were synthesized by molecular beam epitaxy (MBE) on Si(111) substrates. A standard effusion cell was used for gallium. Arsenic was supplied by a solid-source cell equipped with individual valve and shutter, producing As4 molecules. Prior to the growth, the undoped Si(111) substrate was degassed in ultra-high vacuum at 450◦ C for 1 hour without removing the native oxide. Self-catalyzed vapor-liquid-solid (VLS) growth of GaAs NWs was carried out at 610◦ C for 60 min. Ga flux was set as to produce a GaAs planar growth rate on (001) substrates of 0.2 nm/s calibrated from reflection high-energy electron diffraction (RHEED) oscillations. V/III beam equivalent pressure (BEP) ratio was set to 12. At the end of the self-catalyzed NW growth, the Ga catalyst droplet was crystallized by exposing the sample to As4 flux (closing only Ga shutter) during 20 min while maintaining the substrate temperature at 610◦ C. Then, a Si-doped GaAs shell was grown at 465◦ C for 60 min with Ga flux reduced to half of the previous value and a V/III BEP ratio of about 68. The choices of comparatively lower substrate temperature and higher BEP ratio were made to inhibit the axial growth. The temperature of the Si cell was set to 1150◦ C, which is expected to produce n-type doping concentration of about 6 × 1018 cm−3 as calibrated on GaAs(001) planar films. The intrinsic GaAs core/Si-doped GaAs shell NWs have a total length of 4.1 ± 0.5 µm and a diameter of 300 ± 40 nm typically (see Fig. S1 in Supporting Information). The Si-doped GaAs shell thickness was estimated to 55 ± 5 nm by subtracting the GaAs core diameter grown under identical conditions from the diameter of the GaAs core/Si-doped GaAs shell structure. We also used three reference samples of Si-doped GaAs thin-films grown by MBE

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on semi-insulating GaAs(001) substrates. The electron concentrations were determined by Hall measurement: 5.3×1017 cm−3 (sample A), 1.7×1018 cm−3 (sample B), and 5.8×1018 cm−3 (sample C). Si dopant in GaAs is known to be amphoteric, depending on whether Si incorporates in Ga (SiGa ) or As (SiAs ) sites. It is normally utilized as n-type dopant for GaAs thin film grown on GaAs(001), with typical free electron concentrations up to 7 × 1018 cm−3 . 31 At higher doping levels, the lattice strain becomes the driving force for increasing proportions of Si to occupy As sites. 32 For self-catalyzed VLS growth of GaAs NWs on (111) surface, Si incorporation is more complex and p-type doping has been observed. 33,34 On the other hand, shell-doping on NW facets of {110} family was identified as n-type by measuring local vibration modes of SiGa or SiAs using Raman spectroscopy. 35 Here we circumvent these difficulties by using NW core-shell structure for which only the shell is doped to unambiguously investigate the electron concentrations from the Si impurities incorporated during the shell growth. We performed CL measurements using an Attolight Chronos cathodoluminescence microscope. After growth, the NWs were transferred on a conductive Si substrate as a support to facilitate charge evacuation during CL measurements. Single NWs were excited by electron beam with 4 − 6 kV acceleration voltage and impinging current of about 1 nA. Luminescence was collected through an achromatic reflective objective with a numerical aperture of 0.72, and was recorded on an Andor Newton CCD camera (1024×256 pixels, pixel width 26 µm) through a Horiba dispersive spectrometer (grating: 150 grooves/mm, dispersion per pixel: 0.53 nm). The spectral resolution is estimated to 3 nm or less. Luminescence spectra were corrected for the optical response of the collection and detection system. According to CASINO Monte Carlo simulation of the interaction volume for a 4 kV (resp. 6 kV) electron beam in GaAs, the depth of the generation volume is about 50 nm (resp. 70 nm) with a cut-off defined as 80% of the maximum energy (see Supporting Information). For the NWs considered in this study the shell thickness is about 55 nm so that most of the excitation is located in the shell region. Figure 1 shows a SEM image and cathodoluminescence

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maps of a single NW (NW-1) at 30 K. A luminescence spectrum is recorded for each pixel and its integrated CL intensity is presented in Figure 1(b), where the outline of the NW is superimposed (white solid contour). Within the NW contour shown in Figure 1(b), basic characteristics such as peak energy and FWHM are extracted and plotted in Figure 1(c) and (d), respectively. In order to avoid effects related to high injection level, we have verified that the peak energy and FWHM remain within small variation of 2 meV when decreasing the e-beam current by one order of magnitude and by comparing CL with PL (see Fig. S3 in Supporting Information). Note that these CL maps exhibit spatial inhomogeneities at the scale of a few tens of nanometers. The electron beam spot size is smaller than 10 nm, and the generation volume spreads laterally over about 35 nm in diameter (see Supporting Information). The actual spatial resolution is also impacted by the diffusion length of minority carriers and may vary over the area of the NW depending on the material properties and defects. In these growth conditions, the NW has a zinc-blende (ZB) crystal structure except at the upper end of the wire where a mixed ZB and wurtzite (WZ) structure can be found due to crystallization of the catalyst droplet (tip, lower left in Figure 1(a)). For this reason, the top region is more difficult to analyze, 36–39 and it will be disregarded in the present doping investigation. In the vicinity of the wire sidewalls, geometrical effects could contribute to a decrease of the CL intensity, but we also observe a redshift of the peak that may be attributed to surface band bending. 40,41 For further analysis, we consider an average spectrum extracted from the center region of the CL maps (dashed contour in 1(c) and (d)) where the NW emits single peak luminescence, with peak energy and FWHM varying within less than 10 meV. The temperature dependence of CL spectra is shown in Figure 2(a). The CL intensities were normalized by the maximum and shifted vertically for clarity. The evolution of the peak energy is plotted as a function of the temperature, along with their half width at higher and lower energy side (Figure 2(b)). We observed a blueshift compared to the bandgap of intrinsic GaAs calculated using the Varshni equation, 42,43 and the single peak emission

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constant and ν the photon frequency. Second, we need to model the impact of doping on the absorption coefficient. Urbach first noticed the exponential decay of the absorption coefficient below the bandgap 49 . The tail states may arise from several causes. At sufficiently high dopant concentration, the wave functions of impurity dopants overlap and merge with the adjacent band. Local fluctuations of electrostatic potential from ionized impurities also perturb conducting electrons and holes, thus smear both band edges. 50 A simple method to model the absorption band tail used by Katahara and Hillhouse consists in convoluting the ideal absorption with a decay function. 51 As we only observed simple exponential decays in the lower-energy part of CL spectra, an Urbach tail with an adjustable energy parameter γ is chosen. 1 α0 (hν) = 2γ

Z

hν−Eg −∞

ε αideal (hν − ε) exp − dε γ

(3)

The bandgap Eg is here a fitting parameter to account for the bandgap narrowing effect. 52,53 For hν > Eg , we use either Sturge data 54 or a parabolic model for the absorption of undoped GaAs (αideal ). In the case of parabolic absorption, we fix α = 14800 cm−1 at hν = 1.6 eV for all doping levels, since absorption of doped GaAs converges at energies above 1.6 eV. 55 Thirdly, the band filling effect should be taken into account. It is especially crucial for degenerate n-type GaAs. Not only the absorption tail goes deeper into the bandgap with increasing electron density, but also the absorption edge shifts to higher photon energy. The occupation probability is described by the Fermi-Dirac distribution for electrons in the conduction band fc and in the valence band fv . The correct absorption term is: α(hν) = α0 (hν) × (fv − fc ) fv − fc =

1 exp

εh −Ef v kT

+1

(4)

1

− exp

εe −Ef c kT

+1

with photon energy equal to the energy difference between electrons and holes: hν = εe − εh , and the excess energy hν − Eg is weighted between electrons and holes (see Supporting 12


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Information). Finally, spontaneous emission inside a homogeneous material is isotropic. Due to the spectral variation of the absorption coefficient close to the bandgap, low-energy photons might have a larger probability than high-energy photons to escape through the front surface. Therefore, external luminescence spectrum may be redshifted as compared to the internal emission rate given by Equation (2). For a homogeneously excited slab of thickness d, P. Würfel derived an analytical form for the external luminescence spectrum as a function of the material absorptivity: 30 φ(hν) =

2π (hν)2 A(hν) h3 c2 exp hν−(Ef c −Ef v ) − 1 kT

(5)

A(hν) = (1 − R(hν)) [1 − exp (−αd)] R is the reflectivity on the front surface of the planar film. In general, local excitation is used in CL or PL and the injection profile decreases in depth. As minority carriers diffuse, the final carrier concentrations depend on the density of non-radiative recombination centers and eventual electric field. d can be described as a characteristic length scale over which carriers are generated, travel and recombine radiatively. 51 In the presence of nanostructures or optical resonances, this macroscopic approach might fail. Here, d is considered as a fitting parameter. The results of the fit are displayed in Figure 6(a) for planar layers. For doping concentrations below 2 × 1018 cm−3 , Sturge measurements of the absorption coefficient is used. The corresponding semi-insulating GaAs has an ionized impurity concentration between 3 × 1016 and 1017 cm−3 , and presents an Urbach tail of energy width about 6 meV at room temperature. 54 This absorption tail is replaced by the γ parameter to fit the sharp spectrum of sample (A). For high doping concentrations (samples B and C), Coulombic enhancement of absorption close to the gap is screened by high carrier concentrations, so the absorption edge raised less rapidly and a parabolic model provides an accurate fit of the emission spec-

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free electron mass. The non-parabolicity of the conduction band is corrected by introducing a dimensionless coefficient β: 43,57

n = Nc F1/2

where Fj (x) =

1 Γ(j+1)

R∞ 0

Ef c − Ec kT

tj dt exp(t−x)+1

15βkT − F3/2 4Eg

Ef c − Ec kT

is the Fermi integral of order j, Nc = 2

(6)

2πm∗e kT h2

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the conduction band effective density of states and β ≈ −0.83 at room temperature. 43 The result of the non-parabolicity correction is plotted in Figure 6(b) (green line). The electron Fermi levels extracted from experiments are in good agreement with the theoretical curve for moderate doping, but not for highly doped semiconductors. Szmyd et al. had a similar discrepancy between the measured Fermi level and calculation from pure GaAs band structure. 58 They suggested a deformation of the conduction band when GaAs is heavily doped, so a larger band curvature effective mass should be adopted for n-GaAs. The same phenomenon was also noted for n-type InP NWs. 28 We replace the effective mass m∗e by the value calculated as a function of the electron density n proposed by Raymond 59 (red curve in Figure 6(b)). The result is better matched with the fit for highly doped n-GaAs. The remaining discrepancy may be due to the formation of a conduction band tail that lower the Fermi level at a given electron concentration 50 or to the inaccuracy of the correction for the conduction band structure of highly doped n-GaAs. Nevertheless, the electron Fermi level still provides a reasonable measure to determine the electron concentration between 5 × 1017 to 5 × 1018 cm−3 , i.e. in the doping range relevant for NW-based devices. The bandgap narrowing and band tail broadening are in competition with the increase of the electron Fermi level. During the fit, we allow the absorption curve to shift in photon energy (assuming that the conduction and valence bands shift rigidly toward each other). The bandgap narrowing in highly-doped semiconductor originates from increased carrier-impurity ion and carrier-carrier interactions. 60 Figure 6(c) shows the evolution of the bandgap (blue) with electron concentration. The bandgap narrowing of p-type GaAs is well studied and

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Table 1: Peak energy, FWHM and optimal fit parameters (bandgap Eg , electron Fermi level Ef c , band tail γ, characteristic length d) for CL spectra measured at room temperature, and geometry of NWs (length, diameter). Sample A B C NW-1 NW-5 NW-6 NW-7 NW-8 NW-9 NW-10

Peak eV 1.426 1.433 1.455 1.434 1.433 1.433 1.434 1.434 1.433 1.432

FWHM eV 0.043 0.071 0.130 0.064 0.056 0.059 0.057 0.061 0.060 0.062

Eg eV 1.414 1.406 1.384 1.411 1.414 1.415 1.416 1.413 1.415 1.412

Ef c eV 0.019 0.053 0.113 0.016 0.033 0.029 0.031 0.005 0.001 0.031

γ eV 0.009 0.013 0.020 0.016 0.016 0.019 0.018 0.017 0.017 0.020

d nm 3000 1200 0 400 3200 3100 3300 200 600 2500

Length Diameter µm nm

3.0 4.4 3.8 5.1 3.8 2.2 3.5

260 300 290 310 240 180 270

experimental results seems to converge: the bandgap narrowing is proportional to p1/3 . 46,53 For n-type GaAs, the use of absorption measurements to determine the bandgap is influenced by the Burstein-Moss shift. Our bandgap values, obtained by fitting the luminescence spectra, are in agreement with that of Szmyd et al. 58 and with the theoretical calculation of Bennett. 61 Below the bandgap, either conduction or valence band tails are involved, as we observed a wider exponential tail in the low-energy side of the luminescence spectra. The magnitude of this tail (red curve in Figure 6(c)) gives also an indication of the carrier concentration. A simple empirical relation is deduced from thin film reference samples: γ = 6.077 × 10−9 × n0.3476

(7)

where n is expressed in cm−3 and the absorption tail γ in eV. The previous analysis is now used to assess the doping level of n-doped GaAs NWs. For NWs, the macroscopic description in Equation (5) is no more valid. We simply keep d as unknown parameter so that the product αd is best fitted to CL spectra measured at room temperature. An effectively large value of d in NWs may be attributed to a strong reabsorption effect near bandgap when the NW diameter matches an optical resonant mode.

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Figure 7 shows the CL spectrum of a NW (NW-1) measured at room temperature. The luminescence model (Equation (5)) provides a very good fit of the main luminescence peak. An additional signal at low energy is attributed to deep levels. 45,62 The fit parameters of every NW are given in Table 1. According to the FWHM of CL spectra, we predict electron concentrations of 6 × 1017 to 2 × 1018 cm−3 (see Figure 5). We note that all NWs present an absorption tail larger than bulk GaAs of comparable electron density, so the electron-donor ion and electronelectron interactions should not be the only reason for large absorption tails in NWs. Possible compensation might lead to the creation of acceptor-like states 62 or of a larger valence band tail. 45 The larger tails may also be related to surface states, and the increased of donor ionization energy at the proximity of the surfaces. 63 The full fit of CL spectra to retrieve the electron Fermi level seems to be more reliable than a simple deduction of the electron concentration from luminescence FWHM or peak energy, because unexpectedly large FWHM and different peak positions may come from unknown acceptor states. The length and diameter of each NW are also indicated in Table 1. Shorter wires may experience significant shadowing compared to longer wires, and have therefore thinner doped shells. Their electron concentration may be partly reduced due to the depletion layer induced by surface states. For a free electron concentration of 1018 cm−3 and a density of interface states of 1013 cm−2 eV−1 , the Fermi level is pinned near the mid-gap and the depletion width is about 32 nm (see Supporting Information). Consistently, we found lower electron Fermi levels for thinner Si-doped shells (see NW-8 and NW-9 in Table 1). In contrast, the depletion depth is significantly smaller than the nominal shell thickness of 55 nm and should not impact the measurements of the other NWs. Moreover, the depletion region may be reduced by partial band flattening induced by CL excitation. For larger diameters (NW-5, NW-6, NW-7 and NW-10), the fits of room-temperature CL measurement give Fermi levels 29 − 33 meV above the conduction band edge, resulting in electron concentrations of 6 × 1017 to 1018 cm−3 . In conclusion, we have determined the doping level of Si-doped n-type GaAs NWs with

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high surface recombination rates. Cathodoluminescence mapping provides useful information on doping levels and impurities with nanoscale resolution, and is a rapid method applicable from the characterization of nano-objects to the inspection of industrial processes.

Acknowledgement This work was partly supported by the French ANR projects NANOCELL (ANR-15-CE050026) and HETONAN (ANR-15-CE05-0009). The Attolight cathodoluminescence tool was funded by public grants supported by the Region Ile-de-France in the framework of C’Nano IdF (nanoscience competence center of Paris Region), by the European Union (FEDER 2007-2013), and by the Labex GANEX (ANR-11-LABX-0014) and NanoSaclay (ANR-10LABX-0035) as part of the "Investissements d’Avenir" program managed by the French National Research Agency (ANR).

Supporting Information Available Supporting Information provides SEM images of GaAs NWs, CASINO simulation of electron beam interaction volume, comparison between CL and PL measurements, CL maps of each NW, and the detailed models used for the surface depletion, absorption coefficients and luminescence spectra. This material is available free of charge via the Internet at http://pubs.acs.org/.

References (1) Eaton, S. W.; Fu, A.; Wong, A. B.; Ning, C.-Z.; Yang, P. Nature Reviews Materials 2016, 1, 16028. (2) Guan, N.; Dai, X.; Messanvi, A.; Zhang, H.; Yan, J.; Gautier, E.; Bougerol, C.;

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Julien, F. H.; Durand, C.; Eymery, J.; Tchernycheva, M. ACS Photonics 2016, 3, 597–603. (3) Boriskina, S. V. et al. Journal of Optics 2016, 18, 073004. (4) LaPierre, R. R. Journal of Applied Physics 2011, 110, 014310. (5) Yao, M.; Cong, S.; Arab, S.; Huang, N.; Povinelli, M. L.; Cronin, S. B.; Dapkus, P. D.; Zhou, C. Nano Letters 2015, 15, 7217–7224. (6) Kim, H.; Farrell, A. C.; Senanayake, P.; Lee, W.-J.; Huffaker, D. L. Nano Letters 2016, 16, 1833–1839. (7) Molière, T.; Jaffré, A.; Alvarez, J.; Mencaraglia, D.; Connolly, J. P.; Vincent, L.; Hallais, G.; Mangelinck, D.; Descoins, M.; Bouchier, D.; Renard, C. Journal of Applied Physics 2017, 121, 035704. (8) Mariani, G.; Zhou, Z.; Scofield, A.; Huffaker, D. L. Nano Letters 2013, 13, 1632–1637. (9) Boulanger, J. P.; Chia, A. C. E.; Wood, B.; Yazdi, S.; Kasama, T.; Aagesen, M.; LaPierre, R. R. IEEE Journal of Photovoltaics 2016, PP, 1–7. (10) LaPierre, R. R.; Chia, A. C. E.; Gibson, S. J.; Haapamaki, C. M.; Boulanger, J.; Yee, R.; Kuyanov, P.; Zhang, J.; Tajik, N.; Jewell, N.; Rahman, K. M. A. physica status solidi (RRL) – Rapid Research Letters 2013, 7, 815–830. (11) Otnes, G.; Borgström, M. T. Nano Today 2016, 12, 31–45. (12) Ghahfarokhi, O. M.; Anttu, N.; Samuelson, L.; Åberg, I. IEEE Journal of Photovoltaics 2016, 6, 1502–1508. (13) Aberg, I.; Vescovi, G.; Asoli, D.; Naseem, U.; Gilboy, J.; Sundvall, C.; Dahlgren, A.; Svensson, K.; Anttu, N.; Bjork, M.; Samuelson, L. IEEE Journal of Photovoltaics 2015, PP, 1–6. 20


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