Bandgap Energy of Wurtzite InAs Nanowires - American Chemical

Letter pubs.acs.org/NanoLett

Bandgap Energy of Wurtzite InAs Nanowires Michele B. Rota,† Amira S. Ameruddin,‡ H. Aruni Fonseka,‡ Qiang Gao,‡ Francesco Mura,§ Antonio Polimeni,† Antonio Miriametro,† H. Hoe Tan,‡ Chennupati Jagadish,‡ and Mario Capizzi*,† †

Dipartimento di Fisica, Sapienza Università di Roma, Piazzale A. Moro 5, 00185 Roma, Italy Department of Electronic Materials Engineering, Research School of Physics and Engineering, The Australian National University, Canberra, ACT 2601, Australia § Dipartimento di Chimica, Sapienza Università di Roma, Piazzale A. Moro 5, 00185 Roma, Italy ‡

ABSTRACT: InAs nanowires (NWs) have been grown on semi-insulating InAs (111)B substrates by metal−organic chemical vapor deposition catalyzed by 50, 100, and 150 nm-sized Au particles. The pure wurtzite (WZ) phase of these NWs has been attested by high-resolution transmission electron microscopy and selected area diffraction pattern measurements. Low temperature photoluminescence measurements have provided unambiguous and robust evidence of a well resolved, isolated peak at 0.477 eV, namely 59 meV higher than the band gap of ZB InAs. The WZ nature of this energy band has been demonstrated by high values of the polarization degree, measured in ensembles of NWs both as-grown and mechanically transferred onto Si and GaAs substrates, in agreement with the polarization selection rules for WZ crystals. The value of 0.477 eV found here for the bandgap energy of WZ InAs agrees well with theoretical calculations. KEYWORDS: Wurtzite InAs nanowires, bandgap energy, polarization degree, steady-state photoluminescence

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compounds. In particular, the bandgap of WZ InAs is not wellknown because of (i) poor detector sensitivity at 0.4−0.5 eV, the range where the WZ InAs bandgap is theoretically predicted to fall; (ii) the presence of strong absorption bands due to atmospheric water vapor at ∼0.5 eV; (iii) poor PL efficiency, due to strong nonradiative recombination processes, in particular Auger processes,32 and surface and bulk defects. However, it has been shown recently that surface defects can be efficiently removed by passivating InAs NWs with organic sulfides, with an ensuing huge reduction of PL line width.33 After the first report of light emission from both WZ and ZB phases in the PL spectra of InAs NW ensembles,21 only scattered and indirect values of the WZ InAs bandgap, ranging from 46 to 120 meV above the ZB bandgap energy (0.418 eV at 4.2 K),34 have been reported. A value of about 0.54 eV has been extrapolated from photocurrent measurements in InAs1−xPx ternary alloys.22 A very weak structure at 0.50 eV on top of a strong emission tail due to ensembles of thin NWs (50 nm average size) has been observed in PL spectra (peaked at 0.455 eV because of confinement effects) and attributed to WZ inclusions.23 Highly excited PL bands appear at an energy ∼0.3 eV higher than that of the ZB bandgap in 25 nm InAs/InP core/shell NWs.24 These bands were analyzed in terms of the combined effects of confinement, strain, and a theoretically predicted ZB−WZ bandgap energy separation of 55 meV.25 A

ndium arsenide (InAs) is a small bandgap semiconductor where Fermi level pinning with an ensuing accumulation of electrons at the surface makes it easy to achieve Ohmic contacts.1 Moreover, the small effective electron mass and large g-factor and mobility2 of InAs are fundamental properties in high performance nanoelectronics,3 spintronics, and quantum electronics.4,5 The potential of InAs for the development of nanoscale devices was soon realized and developed after the demonstration of III−V nanowires (NWs)6 using the vapor− liquid−solid technique (VLS), which was first introduced for the epitaxial growth of uniaxial Si NWs.7 The reduced NW dimensions (tens of nanometers in diameter and few microns in length) allow for the development of novel electronic and photonic nanoscale devices.8 Indeed, nearly defect-free axial heterostructures can be obtained between highly mismatched materials9,10 with a change in the material band structure along the length of the NW or in its radial plane, as in core/shell structures.11 This has resulted in the realization of devices such as single-electron transistors,12 field-effect transistors,13−15 inverters and logic gates,15 resonant tunnel diodes,16 quantum dots,17 solar cells,18 lasers,19 and photodetectors.20 As discussed in the following paragraph, phase controlled NWs have been used to ascertain the band structure of InAs,21−27 as well as other non-nitride III−V compounds such as GaP,28 GaAs,29,30 and InP.31 However, not much is known about the optical properties of InAs NWs grown in a hexagonal wurtzite (WZ) phase, which does not exist naturally in bulk InAs; the cubic zincblende (ZB) phase is characteristic of the bulk phase of InAs as well as of most other non-nitride III−V © 2016 American Chemical Society

Received: June 1, 2016 Revised: July 27, 2016 Published: July 28, 2016 5197

DOI: 10.1021/acs.nanolett.6b02205 Nano Lett. 2016, 16, 5197−5203

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Figure 1. SEM top-view images of 80 nm (a) and 160 nm (b) InAs NWs mechanically transferred onto Si substrates. Scale bars are indicated on each image.

nanoparticles with diameter of 50, 100, and 150 nm. Those nanoparticles, dispersed on the substrate, act as catalysts for the VLS growth of the NWs. However, the resulting NW size is usually greater than the nominal Au droplet diameter because of a competing radial growth taking place during the VLS growth. WZ nanowires were obtained with a combination of low V/III ratio (2.9) and relatively higher growth temperature (500 °C), while ZB nanowires were promoted by using a combination of low growth temperature (400 °C) and higher V/III ratio (46.0). More details on growth method, mechanisms, and crystal structure characterization can be found elsewhere.39 Both vertically standing NWs (as-grown) and NWs mechanically removed from the InAs substrate and transferred onto Si or GaAs substrates were investigated by SEM carried out in a FEI Helios 600 NanoLab FIB system. A JEOL 2100F system operated at 200 kV and a Philips CM 300 system operated at 300 kV were used for TEM and HRTEM measurements, respectively, of single NWs transferred onto lacy carbon grids. PL measurements were carried out by exciting the samples with an Ar ion laser (λ = 514.5 nm) focused to a spot of approximately 400 μm diameter by a 40 cm lens and chopped at 375 Hz. Sample temperature ranging from 10 to 300 K was maintained by using a closed-cycle coldfinger He cryostat equipped with two sapphire (Al2O3) windows mounted at 90°. An unconventional PL setup was used in order to maximize the light collection and optimize the matching between the f/number of the signal collection system and that of the monochromator. The sample was excited by the laser beam at 45° angle. Photoluminescence, collected at 90° with respect to the laser beam, was collimated by a 5 cm CaF2 lens (2.5 cm in diameter) and then focused by a 10 cm CaF2 lens (2.5 cm in diameter), to a magnification factor of 2, onto the slit of a 0.25 m focal-length monochromator equipped with a 300 grooves/mm grating, 6 × 6 cm2, blazed at 2 μm. The PL signal was dispersed by the monochromator and finally detected by a liquid-N2-cooled InSb photodiode coupled to a lock-in amplifier. Measurements of the polarization degree of the PL bands were performed by using a KRS5 capacitive polarizer with a holographic grating of metallic wires that allows light transmission only for polarization perpendicular to the wires. Spurious features due to absorption by atmospheric water vapor and to the dependence of the monochromator response on light polarization were taken into account by normalizing polarized and unpolarized PL spectra to the system response. Sample Morphology and Structural Properties. An average effective size of 80 ± 10, 160 ± 15, and 220 ± 20 nm

PL band, extending from 0.40 to 0.55 eV and peaked at 0.52 eV, was detected in WZ InAs films (20−40 nm thick).26 Finally, a lower bound of approximately 0.46 eV was derived for the WZ bandgap energy from broad, unresolved PL bands.27 A variety of methods have been used to theoretically estimate the difference between the energy gap of the InAs WZ and ZB phases, ΔEg. By disregarding the spin−orbit (s−o) interaction, ab initio first-principle pseudopotential methods found Eg = 0.114 eV (0.074 eV) for the WZ (ZB) energy gap within the local density approximation (LDA)35 and Eg = 0.611 eV (0.556 eV) for the WZ (ZB) energy gap by a dynamically screened exchange, or GW approximation.25 The inclusion of s−o interaction has led to an InAs WZ bandgap energy equal to 0.481 eV both in a calculation based on empirical pseudopotentials36 and in a detailed review of structure, energetic, and electronic states of III−V compound polytypes37 based on a novel LDA-1/2 approximate quasiparticle method.38 In the latter work,37 the energy gap of all different InAs polytypes has been estimated (0.411, 0.431, 0.440, and 0.481 eV for the 3C, 6H, 4H, and 2H polytypes, in order of increasing percentage of hexagonality), which results in an energy gap of WZ InAs being 70 meV greater than that of ZB InAs. In the present work, the bandgap energy of WZ InAs grown on a ZB InAs substrate is determined by photoluminescence spectroscopy of NWs with different sizes. The NW morphology is investigated by scanning electron microscopy (SEM), transmission electron microscopy (TEM), high-resolution TEM (HRTEM), and selected area diffraction pattern (SADP) measurements. A PL band peaked at 0.477 ± 0.001 eV at 10 K, namely, 59 ± 1 meV higher in energy than the ZB InAs bandgap, is for the first time clearly resolved from contributions due to the ZB InAs phase. This isolated band, an optical marker of the sample excellent quality, is still observed in NW ensembles, which were mechanically transferred onto Si and GaAs substrates, thus showing that this band does not originate from the InAs substrate. However, the independence of the energy of this band on NW size rules out carrier confinement effects in our samples. Finally, the WZ nature of this band is clearly determined by high values of its polarization degree (0.61−0.66) measured in NW ensembles both as-grown and mechanically transferred onto Si, a result that has not been reported before in the literature of InAs WZ NWs. Sample Growth and Experimental Setup. InAs WZ NWs were grown by Au-catalyzed metal−organic chemical vapor deposition (MOCVD) on semi-insulating InAs (111)B substrates using trimethylindium and AsH3 as group III and V precursors, respectively. The InAs substrates were treated with a poly-L-lysine solution followed by a solution of colloidal Au 5198


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Figure 2. (a) SEM and (b) TEM images of a 160 nm InAs NW. (c) HRTEM image of the same NW showing the absence of stacking faults or planar defects. (d) SADP image supporting a pure WZ crystal structure.

Figure 3. PL spectra taken at 11 K from 80 nm NWs as-grown (a) or mechanically transferred onto a Si substrate (b). Dashed red line in panel (a) is a fit to the spectrum by using three different Voigt contributions given by the dashed-dot green lines. Peak energies as determined by Voigt fits are indicated.

WZ crystal structure, f ree of stacking faults as demonstrated by the HRTEM image in panel (c), whose purity is confirmed by the SADP image in panel (d). The NWs grow with the WZ caxis perpendicular to the InAs (111)B substrate. Experimental Results and Discussion. PL spectra taken at 11 K on 80 nm NWs as-grown or mechanically transferred onto a Si substrate are shown in panels (a) and (b) of Figure 3, respectively, together with Voigt fits made to determine the peak emission energies. All spectra have been normalized for the system response. In panel (a), the band at 417 meV is due to the ZB bandgap free-exciton (FE), in good agreement with the value reported in the literature (418 meV at 4.2 K).34 The strong decrease in the relative contribution of this band to the PL spectrum of transferred NWs in panel (b) clearly highlights that this emission originates from the InAs ZB substrate (the weak signal still at 416 meV in panel (b) could be due to substrate debris formed in the transfer process, as shown in Figure 1a). The emission peaks at 382 and 403 meV are due to emission from defects, also in the ZB InAs substrate, as supported by a decrease of their relative contribution to the PL spectra with increasing temperature and excitation power (not shown here). The band at 476 meV in panel (a) is at an energy 59 meV higher than that of the ZB bandgap. It persists in the spectrum of transferred NWs, although peaked at a lower energy (470 meV, to be discussed in the following). This high energy band should be due, therefore, either to carrier

has been estimated from several SEM top-view and tilted images of NWs whose VLS growth was catalyzed by 50, 100, and 150 nm Au particles, respectively. Hereinafter, NWs will be indicated in the text and Figures by their effective size. The NW density is equal to ∼0.9 and 0.09 μm−2 for the 80 and 160 nm NWs, respectively (density decreasing further to 0.035 μm−2 in the case of 220 nm NWs). The NWs have a hexagonal crosssection and appear to be all perpendicular to the substrate in the case of 160 nm NWs, but not in the case of 80 nm NWs, as confirmed by 45° tilted-view SEM images (not shown here). Both 80 and 160 nm NWs were also mechanically transferred onto Si or GaAs substrates. This procedure results in NWs lying horizontally on the Si substrate and roughly parallel with each other, as shown by the SEM images in Figure 1 for 80 nm (a) and 160 nm (b) transferred NWs. The mechanical transfer permits measurements of the polarization degree of NW emission and excludes contributions of the InAs substrate to the PL spectra. The average NW length is of order of 20 μm (or more) for 80 nm NWs and of 10 μm for 160 nm NWs. Finally, this mechanical transfer process may give rise to contaminations by substrate debris, as shown in Figure 1a in the case of 80 nm NWs. Standard SEM, TEM, HRTEM, and SADP images of a 160 nm NW are shown in Figure 2. The NWs are almost taper-free with an effective size greater than the Au droplet, as shown in a SEM (panel a) and TEM (panel b) image. The NWs have a 5199


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Figure 5. PL spectra taken at 11 K in 80 nm mechanically transferred NWs for different excitation powers. The dependence of the band integrated intensity on excitation power is given in the inset in a log− log scale.

of InAs, native surface defects can pin the Fermi level above the conduction band edge,43 thus giving rise to a surface accumulation layer and to a native n-doping. In the latter case, a fit would be required in order to determine precisely the bandgap energy, which is impeded here by the large, Gaussian broadening of the 477 meV band. The linear dependence on excitation power and the (moderate) blue shift would favor either an attribution of this emission band to free excitons or to band-to-band recombination in slightly n-type InAs. On the basis of the PL spectra shown in Figures 4 and 5, the bandgap energy is estimated therefore to be equal to 477 ± 3 meV. With regards to the ∼6 meV difference in the WZ peak energy when measured in the as-grown and mechanically transferred samples (see Figure 3), it changes with substrate material, as shown in Figure 6a for the spectra taken from 80 nm NWs transferred onto either Si or GaAs substrates (the spectra were taken at the same temperature and similar excitation power as in as-grown NWs). This energy shift might be attributed to the strain produced at low temperature by the different thermal expansion coefficients of InAs NWs and Si or GaAs substrates. Similar energy shifts were reported in the micro-PL spectra of single InP NWs dispersed on Si, InP, or SrTiO3 substrates.44 Therein, energy shifts were following a statistical distribution because of the randomness in the thermal contact between InP NWs and substrates,44 as observed also in the present work. This randomness is the most likely cause of the broadening of the WZ A band when NWs are transferred onto Si or GaAs substrates (see Figure 6a). Peak energy changes and line width broadenings are also observed in the case of NWs of different size transferred onto Si substrates, as shown in Figure 6b. Finally, the WZ origin of the high energy PL band has been confirmed by measurements of the polarization degree of the emitted light, ρ = (I⊥ − I∥)/(I⊥ + I∥), where I⊥ and I∥ are the intensities of the emitted light for polarizations either perpendicular or parallel, respectively, to the c-axis, namely, to the NW main symmetry axis. In fact, no polarization selection rules hold for the regular tetrahedron, Td, point group symmetry of the ZB phase. On the contrary, strict polarization selection rules apply to the C6v point group symmetry of the hexagonal close packed WZ phase. Only light polarized perpendicular to the WZ c-axis is absorbed or emitted for

Figure 4. PL spectra taken at 11 K in as-grown NWs with different sizes.

With regards to the decrease in the PL peak intensity with increasing NW size, it can be ascribed to the corresponding decrease in NW density illustrated in the section on sample morphology.41 The decrease in the full width at half-maximum (from 16 to 8 meV) with increasing NW size is mainly due, instead, to a decreasing contribution to the spectra of a low energy tail most likely due to emission from surface defects. The relative weight of surface defects, indeed, should decrease in thick NWs characterized by a lower surface-to-volume ratio. The dependence of the WZ band on excitation power (P) is shown in Figure 5. In the same figure, the inset shows, in a log− log scale, that the PL intensity integrated over the whole band depends almost linearly on excitation power over more than two decades. This suggests that this band is not due to an impurity emission. Instead, it can be confidently attributed to the A band, according to the WZ crystal terminology,36 namely, to band-to-band (or FE) transitions from the minimum of the lowest conduction band (CB), with Γ7c symmetry, to the maximum of the highest valence band (VB), with Γ 9v symmetry. A band filling would account for the slight (3 meV) blue-shift and broadening of this A band with increasing excitation power. This PL band thus provides an unambiguous and precise determination of the bandgap energy in WZ InAs. Actually, the value usually reported in the literature for the “band-gap” energy is that of the PL peak energy. In the case of band-to-band recombination in intrinsic materials, the PL peak energy is higher by kBT/2 than the bandgap energy (namely, ∼0.5 meV at 10 K). In the case of exciton recombination, it is instead lower than the bandgap energy by the free exciton binding energy, which should not differ much from that of the free exciton in bulk ZB InAs (1 meV).42 However, in the case 5200


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Figure 6. (a) Comparison of PL spectra, taken at T = 11 K and P = 25 W cm−2 from 80 nm NWs mechanically transferred onto Si or GaAs substrates, with the spectrum of as-grown NWs. (b) Comparison of PL spectra recorded at T = 11 K and P = 25 W cm−2 from 80 and 160 nm InAs NWs mechanically transferred onto Si substrates.

Figure 7. Low-temperature PL spectra of InAs NWs for different emitted light polarizations and experimental setups. (a) Bottom panel: PL from 80 nm InAs NWs mechanically transferred onto a Si substrate for light polarization perpendicular (red line) or parallel (blue line) to the NW c-axis. The configuration of laser excitation and light collection is shown in the inset. Top panel: polarization degree ρ = (I⊥ − I∥)/(I⊥ + I∥) vs photon energy. (b) Bottom panel: same as bottom panel in (a) but for 160 nm as-grown InAs NWs. The configuration of laser excitation and light collection is shown in the inset. Top panel: polarization degree ρ vs photon energy.

transitions at the bandgap energy, from the Γ7c conduction band minimum to the Γ9v valence band maximum.45 Notice that measurements of the polarization degree of the weak, blueshifted features previously attributed to emission from InAs WZ NWs have never been attempted.23,24,26 The PL polarization degree has been measured for two different experimental configurations, as shown for 80 nm NWs mechanically transferred onto a Si substrate, in Figure 7a, and for as-grown 160 nm NWs, in Figure 7b. In the first case, the laser light impinges on the sample at 45° with respect to the substrate, while the emitted light is collected at 90° with respect to the direction of the incident laser beam, with both the incident laser beam and the collected emission directions perpendicular to the NW c-axis (see the inset schematic). The A band emission polarized perpendicularly to the c-axis (red line) is stronger than that polarized parallel to that same axis (blue line), as expected for the WZ phase. In the top panel of Figure 7a, the polarization degree as a function of energy is shown. It is greater than +0.6 over the whole A band, while it is slightly negative in the energy region of the ZB emission. The second experimental configuration is shown schematically in the inset of the bottom panel of Figure 7b for an ensemble of as-grown 160 nm NWs. The laser light impinges on one edge of an as-grown sample in a direction parallel to the NW c-axis, while the emitted light is collected at 90° with

respect to the direction of the incident laser beam. The emitted light is polarized mainly perpendicularly to the c-axis, with a polarization degree ranging from +0.6 to +0.7 over the whole band (see the top panel of Figure 7b), as found for the transferred NWs. The dependence of the emitted light intensity on the angle θ between the infrared polarizer axis and the NW c-axis is shown in Figure 8 for the mechanically transferred 80 nm NWs of Figure 7a. This dependence has been determined by taking 24 PL spectra in steps of 15°. The PL intensity was then normalized to the response of the experimental apparatus for each measured angle θ and averaged over a 10 meV range around the PL peak energy. Subsequently, the value of the polarization degree was determined by fitting the function derived from the Malus’ law I(θ ) =

1+ρ 1−ρ cos2(θ − θ0) + sin 2(θ − θ0) 2 2

to the data (θ0 is an offset angle). The best fit to the data has been obtained for ρ = 0.66 ± 0.01 and is shown by the continuous line in the polar plot. The high values of ρ found in both configurations for the 80 and 160 nm NWs show conclusively the WZ nature of the A band and, therefore, the robustness of our methods to determine the bandgap energy of WZ InAs. Notice that the 5201


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However, in one case the increment in the WZ bandgap energy is slightly overestimated (17%);37 in the other case, it is underestimated (10%).25 Notice that the percentage increase ΔEg/Eg found here in the case of small gap InAs is greater than that experimentally found in the wider gap InP NWs (5%)47 and GaAs NWs (0.5%).30 Conclusions. The energy gap of WZ InAs has been conclusively determined in NW ensembles of different sizes, grown on InAs (111)B substrates by Au-catalyzed MOCVD technique. In the PL spectra of all these samples, a band peaked at an energy of 0.477 ± 0.003 eV, 59 ± 3 meV higher than that of the ZB bandgap, has been fully resolved. The peak energy of this band does not depend on the NW size, thus excluding any effect due to carrier confinement or built-in strains. The polarization degree of as-grown NWs and of those transferred onto a Si substrate is as high as 0.66, namely, the emission polarized perpendicular to the NW c-axis is five times stronger than that parallel to the same axis. The estimated increase in the bandgap energy of WZ InAs phase with respect to that of ZB InAs is in quite good agreement with most theoretical estimates. This increase is significantly greater than that experimentally found in larger bandgap III−V semiconductors, such as GaAs and InP, an issue still opened to further theoretical investigation.

Figure 8. Polar plot of light intensity averaged over a 10 meV energy range around the PL peak energy for mechanically transferred 80 nm NWs and reported vs the angle between the IR polarizer axis and the NW c-axis. The full line is a best fit of the Malus’ law to the data as obtained for ρ = 0.66.

polarization degree of WZ NWs can never be equal to 1, for both extrinsic and intrinsic reasons. First, NWs in the as-grown and transferred samples are not all parallel to each other, as shown by SEM images in Figure 1. Second, the dielectric mismatch between air and NW should lower the value of polarization degree as measured in WZ NWs (the absorption/ emission of electromagnetic radiation is smaller in the case of light polarized perpendicular to the NW c-axis).46 Finally, the NW c-axis should be perfectly perpendicular to the plane formed by the incident laser beam and the emitted light in order to obtain maximum polarization degree in the 45° configuration used in Figure 7a. The present determination of the WZ InAs bandgap energy is compared in Table 1 with previous experimental results and

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Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

exptl (eV)

a

(22) (26) (23) (27) ± 0.003a

theory (eV) 0.114 0.611 0.481 0.481

(35) (25) (36) (37)

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ACKNOWLEDGMENTS

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REFERENCES

A.P. acknowledges funding by Sapienza Università di Roma under “Ateneo Awards 2014” grant. The Australian authors acknowledge the Australian Research Council for financial support and Australian National Fabrication Facility and Australian Microscopy and Microanalysis Research Facility for providing access to some of the equipment used in this work. G. Ambrosio, Dr. M. De Luca, and A. Zilli are acknowledged for their contribution at an early stage of this work, and D. Tedeschi for useful discussions.

Table 1. Summary of Experimental Evaluations and Theoretical Estimates of WZ InAs Bandgap Energy Together with the Theoretically Estimated Increases with Respect to ZB ZB the ZB InAs Bandgap Energy, ΔEg/Eg = (EWZ g − Eg )/Eg (with Corresponding References) 0.540 0.520 0.500 0.458 0.477

AUTHOR INFORMATION

ΔEg/Eg 0.54 0.10

(1) Noguchi, M.; Hirakawa, K.; Ikoma, T. Phys. Rev. Lett. 1991, 66, 2243. (2) Milnes, A. G.; Polyakov, A. Y. Mater. Sci. Eng., B 1993, 18, 237− 259. (3) Jiang, X.; Xiong, Q.; Li, Y.; Lieber, C. M. Nano Lett. 2007, 7 (10), 3214−3218. (4) Fasth, C.; Fuhrer, A.; Samuelson, L.; Golovach, V. N.; Loss, D. Phys. Rev. Lett. 2007, 98, 266801. (5) Björk, M. T.; Fuhrer, A.; Hansen, A. E.; Larsson, M. W.; Fröberg, L. E.; Samuelson, L. Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 72, 201307. (6) Hiruma, K.; Murakoshi, H.; Yazawa, M.; Katsuyama, T. J. Cryst. Growth 1996, 163 (3), 226−231. (7) Wagner, R. S.; Ellis, W. C. Appl. Phys. Lett. 1964, 4 (5), 89−90. (8) Hu, J.; Odom, T. W.; Lieber, C. M. Acc. Chem. Res. 1999, 32, 435. (9) Ertekin, E.; Greaney, P. A.; Chrzan, D. C. J. Appl. Phys. 2005, 97, 114325. (10) Guo, Y. G.; Zou, J.; Paladugu, M.; Wang, H.; Gao, Q.; Tan, H. H.; Jagadish, C. Appl. Phys. Lett. 2006, 89 (23), 231917.

0.17 0.14

Present work shown for comparison.

theoretical estimates. In the case of theoretical calculations, the value of the percentage increase in the WZ InAs bandgap energy with respect to that of ZB InAs is also reported. These increases are, indeed, less affected by the well-known problems that LDA calculations suffer in evaluating absolute values of semiconductor bandgap energies. The agreement with the absolute energy values of the WZ bandgap energy theoretically estimated in refs 36 and 37 by including the spin−orbit interaction is very good, as well as the agreement with the difference in the energy gaps between the WZ and ZB phases (55 meV compared with our result of 59 ± 3 meV) estimated in ref 25 within an ab initio approach, which did not include spin−orbit interaction. 5202


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Nano Letters (11) Lin, H.-M.; Chen, Y.-L.; Yang, J.; Liu, Y.-C.; Lin, K.-M.; Kai, J.-J.; Chen, F.-R.; Chen, L.-C.; Chen, Y.-F.; Chen, C.-C. Nano Lett. 2003, 3, 537. (12) Nilsson, H. A.; Duty, T.; Abay, S.; Wilson, C.; Wagner, J. B.; Thelander, C.; Delsing, P.; Samuelson, L. Nano Lett. 2008, 8 (3), 872− 875. (13) Duan, X. F.; Huang, Y.; Wang, J.; Lieber, C. M. Nature 2001, 409, 66−69. (14) Cui, Y.; Lieber, C. M. Science 2001, 291, 851−853. (15) Huang, Y.; Duan, X. F.; Cui, Y.; Lauhon, L. J.; Kim, K. − H.; Lieber, C. M. Science 2001, 294, 1313−1317. (16) Björk, M. T.; Ohlsson, B. J.; Thelander, C.; Persson, A. I.; Deppert, K.; Wallenberg, R. L.; Samuelson, L. Appl. Phys. Lett. 2002, 81 (23), 4458−4460. (17) Borgström, M. T.; Zwiller, W.; Müller, E.; Imamoglu, A. Nano Lett. 2005, 5 (7), 1439−1443. (18) Czaban, J. A.; Thompson, D. A.; LaPierre, R. R. Nano Lett. 2009, 9 (1), 148−154. (19) Chin, A. H.; Vaddiraju, S.; Maslov, A. V.; Ning, C. Z.; Sunkara, M. K.; Meyyappan, M. Appl. Phys. Lett. 2006, 88, 163115. (20) Wang, J.; Gudiksen, M. S.; Duan, X.; Cui, Y.; Lieber, C. M. Science 2001, 293, 1455−1457. (21) Sun, M. H.; Leong, E. S. P.; Chin, A. H.; Ning, C. Z.; Cirlin, G. E.; Samsonenko, Y. B.; Dubrovskii, V. G.; Chuang, L.; ChangHasnanin, C. Nanotechnology 2010, 21, 335705. (22) Trägårdh, J.; Persson, A. I.; Wagner, J. B.; Hessman, D.; Samuelson, L. J. Appl. Phys. 2007, 101, 123701. (23) Koblmüller, G.; Hertenberger, S.; Vizbaras, K.; Bichler, M.; Bao, F.; Zhang, J.−P.; Abstreiter, G. Nanotechnology 2010, 21, 365602. (24) Zanolli, Z.; Pistol, M.−E.; Fröberg, L. E.; Samuelson, L. J. Phys.: Condens. Matter 2007, 19, 295219. (25) Zanolli, Z.; Fuchs, F.; Furthmüller, J.; von Barth, U.; Bechstedt, F. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 75, 245121. (26) Bao, J.; Bell, D. C.; Capasso, F.; Erdman, N.; Wei, D.; Fröberg, L.; Mårtensson, T.; Samuelson, L. Adv. Mater. 2009, 21, 3654−3658. (27) Möller, M.; de Lima, M. M., Jr.; Cantarero, A.; Chiaramonte, T.; Cotta, M. A.; Iikawa, F. Nanotechnology 2012, 23, 375704. (28) Assali, S.; Zardo, I.; Plissard, S.; Kriegner, D.; Verheijen, M. A.; Bauer, G.; Meijerink, A.; Belabbes, A.; Bechstedt, F.; Haverkort, J. E. M.; Bakkers, E. P. A. M. Nano Lett. 2013, 13 (4), 1559−1563. (29) Vainorius, M.; Lehmann, S.; Gustafsson, A.; Samuelson, L.; Dick, K. A.; Pistol, M.-E. Nano Lett. 2016, 16 (4), 2774−2780. (30) De Luca, M.; Lavenuta, G.; Polimeni, A.; Rubini, S.; Grillo, V.; Mura, F.; Miriametro, A.; Capizzi, M.; Martelli, F. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87, 235304. (31) Zilli, A.; De Luca, M.; Tedeschi, D.; Fonseka, H. A.; Miriametro, A.; Tan, H. H.; Jagadish, C.; Capizzi, M.; Polimeni, A. ACS Nano 2015, 9 (4), 4277−4287. (32) Fang, Z. M.; Ma, K. Y.; Jaw, D. H.; Cohen, R. M.; Stringfellow, G. B. J. Appl. Phys. 1990, 67, 7034. (33) Sun, M. H.; Joyce, H. J.; Tan, H. H.; Jagadish, C.; Ning, C. Z. Nano Lett. 2012, 12, 3378−3384. (34) Madelung, O., Ed.Landolt-Börstein: Numerical Data and Functional Relationships in Science and Technology. Semiconductors: Intrinsic Properties of Group IV Elements and III-V, II-VI and I-VII Compounds; Series III v. 22a; Springer-Verlag: Berlin,1987. (35) Murayama, M.; Nakayama, T. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 49, 4710−4724. (36) De, A.; Pryor, C. E. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 155210. (37) Bechstedt, F.; Belabbes, A. J. Phys.: Condens. Matter 2013, 25, 273201. (38) Ferreira, L. G.; Marques, M.; Teles, L. K. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 125116. (39) Joyce, H. J.; Wong-Leung, J.; Gao, Q.; Tan, H. H.; Jagadish, C. Nano Lett. 2010, 10 (3), 908−915. (40) (a) De Luca, M.; Polimeni, A.; Fonseka, H. A.; Meaney, A. J.; Christianen, P. C. M.; Maan, J. C.; Paiman, S.; Tan, H. H.; Mura, F.; Jagadish, C.; Capizzi, M. Nano Lett. 2014, 14 (8), 4250−4256. (b) De

Luca, M.; Polimeni, A.; Capizzi, M.; Meaney, A. J.; Christianen, P. C. M.; Maan, J. K.; Mura, F.; Rubini, S.; Martelli, F. ACS Nano 2013, 7 (12), 10717−10725. (41) However, by taking into account the different NW densities and active volumes of differently sized NWs, the PL efficiency of the 160 nm NWs is estimated to be roughly 1.5−2 times higher than that of the 80 nm NWs, which suggests that the main defects are surface defects. (42) Tang, P. J. P.; Pullin, M. J.; Phillips, C. C. Phys. Rev. B: Condens. Matter Mater. Phys. 1997, 55, 4376−4381. (43) Allen, R. E.; Humphreys, T. J.; Dow, J. D.; Sankey, O. F. J. Vac. Sci. Technol., B: Microelectron. Process. Phenom. 1984, 2, 449. (44) Anufriev, R.; Chauvin, N.; Khmissi, H.; Naji, K.; Gendry, M.; Bru-Chevallier, C. Appl. Phys. Lett. 2012, 101, 072101. (45) Birman, J. L. Phys. Rev. 1959, 114, 1490. (46) De Luca, M.; Zilli, A.; Fonseka, H. A.; Mokkapati, S.; Miriametro, A.; Tan, H. H.; Smith, L. M.; Jagadish, C.; Capizzi, M.; Polimeni, A. Nano Lett. 2015, 15 (2), 998−1005. (47) Mishra, A.; Titova, L. V.; Hoang, T. B.; Jackson, H. E.; Smith, L. M.; Yarrison-Rice, J. M.; Kim, Y.; Joyce, H. J.; Gao, Q.; Tan, H. H.; Jagadish, C. Appl. Phys. Lett. 2007, 91, 263104.

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Bandgap Energy of Wurtzite InAs Nanowires - American Chemical

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