E1(A) Electronic Band Gap in Wurtzite InAs Nanowires Studied by

Letter pubs.acs.org/NanoLett

E1(A) Electronic Band Gap in Wurtzite InAs Nanowires Studied by Resonant Raman Scattering Ilaria Zardo,*,†,‡ Sara Yazji,† Nicolas Hörmann,† Simon Hertenberger,† Stefan Funk,†,‡ Sara Mangialardo,§ Stefanie Morkötter,† Gregor Koblmüller,† Paolo Postorino,§ and Gerhard Abstreiter†,‡ †

Walter Schottky Institut and Physik Department, Technische Universität München, Am Coulombwall 4, D-85748 Garching, Germany ‡ Institute for Advanced Study, Technische Universität München, Lichtenbergstrasse 2a, D-85748 Garching, Germany § Dipartimento di Fisica, Università di Roma Sapienza, P.le Aldo Moro 5, I-00185 Roma, Italy ABSTRACT: We report on resonant Raman experiments carried out on wurtzite InAs nanowires. Resonant conditions have been obtained by tuning either the excitation energy or the band gap through external high pressure at fixed excitation energy. A complete azimuthal study of the Raman spectra with two laser excitation lines (2.41 and 1.92 eV) has also been performed on a single wire. The measured E2H mode resonance indicates that the E1(A) gap is about 2.4 eV, which is considerably reduced with respect to the zinc-blende InAs E1 gap. These findings confirm recent theoretical calculations of crystal phase induced bandstructure modifications. KEYWORDS: InAs nanowires, electronic band structure, optical properties, resonant Raman spectroscopy

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Bulk InAs (ZB structure) has been investigated by Raman spectroscopy for laser excitation energies near the E1 and E1+ΔSO gap.8,18,19 The observation of a sharper resonance of the forbidden 1LO(Γ) and of the 2LO(Γ) with respect to the TO resonance indicates that intraband Fröhlich coupling is the electron−phonon mechanism involved in InAs, similar as observed for other polar zinc blende semiconductors.3,4 A slight difference in the energy values of the Raman scattering cross section gap and the optical gap was also found by varying the temperature.19 Pressure-dependent Raman experiments were also carried out on bulk InAs, and both the allowed TO and LO resonances were observed at approximately the E1 energy gap.11 In this work, resonant Raman scattering experiments were performed on single InAs nanowires, consisting of a predominant WZ structure with stacking faults,20 changing the laser excitation energy in the range from 1.92 to 2.71 eV. Furthermore, the resonant Raman condition was also obtained at a fixed excitation energy by varying the applied pressure, and experiments on nanowire bundles were carried out. Electronic Band Structure Probed by Resonant Raman Spectroscopy. A typical high-resolution transmission electron microscopy (HR TEM) image together with the corresponding selected area diffraction (SAD) pattern of a sample grown exactly under the same conditions of the sample investigated by Raman spectroscopy is shown in Figure 1. Both diffraction patterns and high-resolution (HR) TEM images

emiconductor nanowires have attracted a lot of attention in recent years, since they are promising candidates for novel electronic and photonic devices at the nanoscale.1,2 The understanding of the modifications of electronic and optical properties under shape and dimensional restrictions is a fundamental task for nanowire applications. Resonant Raman scattering has been extensively used in the past decade for the investigation of bulk zinc-blende (ZB) and diamond semiconductors, since it provides detailed information of the electronic resonances and electron−phonon interaction.3,4 Many bulk semiconductors have been studied in the energy region of the E0, E0+ΔSO as well as E1, E1+ΔSO critical points,3−8 leading to the understanding of the electron− phonon coupling mechanisms, which can be either deformation potential or Fröhlich coupling. Additionally, in III−V semiconductors resonant Raman scattering can be induced by pressure tuning of the band gaps keeping the excitation energy fixed.4,9−11 In this sense, resonant Raman scattering is a useful tool for the investigations of basic physical properties and changes due to different crystal structure or to the confinement in materials at the nanoscale. It has been shown already that for GaAs the Fröhlich coupling is stronger in nanowires than in the bulk material.12,13 Furthermore, it is well-known that semiconductor nanowires can crystallize in the wurtzite (WZ) structure, which is not stable in the bulk material.14,15 Resonance conditions in light scattering experiments demonstrate the changes in the electronic band structure16 and in the electron−phonon interaction12,13,17 arising from the specific nanowire structure. © XXXX American Chemical Society

Received: December 7, 2012 Revised: May 7, 2013

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dx.doi.org/10.1021/nl304528j | Nano Lett. XXXX, XXX, XXX−XXX

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Figure 1. Representative HR-TEM image of an InAs nanowire (a), showing the characteristic layer stacking where predominant WZ segments are distinguishable, and the corresponding SAD pattern (b). Both the SAD pattern and the high-resolution HR-TEM image were recorded in the [110] zone axis corresponding to the side facet of the NW. Note that the distinct WZ sensitive reflections 11̅2 and 1̅12 are marked by white arrows. The white circle marks the diffraction spot characteristic for the growth direction, which can be indexed as 002 or 111 for WZ or ZB, respectively. Continuous streaks parallel to the growth direction reveal the presence of stacking disorder. Figure 2. (a) Schematic of the scattering configuration used for the excitation-dependent resonant Raman measurements. Both the incident and the analyzed light are parallel to the nanowire crystal direction x (backscattering configuration). θ denotes the angle between the incident polarization (εi) and the nanowire axis z. The polarization of the incident and analyzed light (εi,s) was selected either parallel to the nanowire axis (θ = 0, left schematic) or orthogonal to it (θ = 90°, right schematic). In terms of Porto notation, the first case corresponds to the x(z,z)x̅ configuration, while the second to the x(y,y)x̅ configuration. (b) Raman spectra collected on a single InAs nanowire with a 150 nm diameter, for five different excitation energies in the x(z,z)x̅ and (c) x(y,y)x̅ configurations.

were recorded in the [110] zone axis corresponding to the side facet of the NW. The SAD pattern evidences an overall WZ dominant crystal phase, indicated by distinct WZ sensitive reflections 11̅2 and 1̅12. Moreover, the WZ stacking is interrupted by regions of disordered stacking along the growth direction, as also indicated in the SAD pattern by the weak streaks parallel to the growth direction. Polarization-dependent Raman spectroscopy enables us to probe phonon modes with a defined symmetry. Selected spectra collected from a single nanowire, with different excitation energies and for the two scattering configurations indicated, are shown in Figure 2. The polarization of excitation and detection are selected to be parallel and oriented either parallel or perpendicular to the nanowire growth axis, which corresponds to the [111] direction, as illustrated in the schematic in Figure 2a. In the so-called Porto notation, these scattering configurations correspond to x(z,z)x̅ and x(y,y)x,̅ respectively, where x is the scattering direction, which is parallel to the [110] direction, and the terms in the brackets are the polarization of the incident and scattered light. The intensities of the spectra shown have already been corrected for the efficiency of the setup, as explained in the following. The spectra exhibit an asymmetric peak at about 215 cm−1, in the region of the transversal optical (TO) mode, and the longitudinal optical (LO) mode at 237.5 cm−1, more pronounced for higher excitation energies. The 2LO mode at 475.5 cm −1 , is visible only in the x(y,y)x̅ scattering configuration for high excitation energies and more clearly when the excitation energy is 2.41 eV. Polarization-dependent Raman studies enabled us to distinguish two contributions to the peak at about 215 cm−1, namely, the ZB-like TO(A1+E1) mode at about 217.5 cm−1, to which we will refer in the following as TO, and the E2H WZ mode at about 213.7 cm−1, arising from the WZ structure along the nanowire axis.21 Since the difference in energy between the TO and E2H modes is small (∼4 cm−1), their individual resonant behavior is not easily distinguishable. In the following, when spectra have been analyzed using just a single Lorentzian fitting curve in the spectral range of the two modes, we will refer generally to it as TO* mode. However, the TO(A1) is strongly predominant in the x(z,z)x̅ configuration, while the E2H is strongly predom-

inant in the x(y,y)x̅ configuration, which will be used later. It is important to point out that the E2H mode is peculiar of the wurtzite structure.15 The possibility to study its resonant behavior through polarized Raman scattering will give us informations on how the crystal phase affects the electronic band structure. The Raman scattering cross section R(ω) for both TO* and LO mode have been determined at each scattering configuration. For this purpose, the measured Raman intensities have to be corrected by factors that take into account the dependence on the incident frequency ωi, on the spectral response of the setup f(ωs,εs), where ωs and εs are the frequency and polarization of the scattered light, respectively, and on the reflection coefficient of the material for the incident and scattered light. At room temperature, the reflection coefficient does not contribute significantly to the shape of the resonance near the E1 gap for InAs,19 so it will be neglected. The measured intensities of the Raman peaks are: I(ω) ∝ ωi4R(ω)f (ωs , εs⃗ )I

where I is the Raman intensity as unaffected by the setup efficiency. Usually, the measured intensities are divided by the intensity of the Raman peaks collected from a material with constant R(ω), so that the contributions of ωi and f(ωs,εs) are removed. For this purpose, calcite or fluorite is usually used.22 In this work, we used the Raman signal collected from the Si(111) substrate on which the wires were transferred, since the scattering cross sections RSi(ω) of Si relative to CaF2 is known from the literature.7 In this way, the reference-intensities were collected under the same experimental conditions of the B


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nanowires with different diameter. The TO* mode in x(y,y)x̅ configuration, that is, mainly the E2H, shows an increase in intensity in the energy region 2.41−2.60 eV. Apparently two separate resonances can be observed in the proximity of the two energy values, but the limited number of experimental points does not allow determining exactly at what energy the maximum occurs. The TO* in x(z,z)x̅ configuration, that is, mainly the TO(A1), and the LO in both configurations continuously gain intensity with increasing energy, and no maxima are visible in the investigated energy range. The resonance profiles for InAs nanowires with WZ structure, as shown in Figure 3a and b, clearly differ from what was observed in bulk InAs at room temperature.19,24 No resonance of the TO and LO modes is observed at the E1 ZB InAs gap (∼2.5 eV). In WZ crystals, the band structure can be approximated with the so-called quasi-cubic model, resulting in a sequence of the valence levels Γ9v, Γ7v+, and Γ7v−, as depicted schematically in Figure 3c: the Γ9v with heavy hole character, the Γ7v+ with light hole character, and Γ7v− given by the crystalfield splitting. Furthermore, the transition Γ9v−Γ7c can be excited with electric field with polarization perpendicular to the c axis, while the Γ7−Γ7 transition is allowed with polarization either parallel or perpendicular to the c axis.25 Let us consider now the coupling of electronic states with the different phonon mode symmetries. While the E2H mode couples with states Γ9v−Γ7c, the modes with symmetry A1 couple with Γ7−Γ7 as well as Γ9−Γ9, and E1 couple with Γ7−Γ7 as well as Γ9−Γ7.26 The symmetry of the relevant phonon modes, along with their coupling with electronic states, is summarized in Table 1. In a

measurements on the nanowires. For the nanowires (nw) we obtain: R nw(ωi) ∝ Inw(ωi)R Si(ωi)/ISi(ωi)

where Inw(ωi) and ISi(ωi) are the measured Raman peak intensities of the nanowire and Si respectively, normalized to the laser power (counts/(W·s)). The Raman scattering cross sections of the TO* (squares) and LO (circles) modes for the polarization configuration x(z,z)x̅ (open symbols) and x(y,y)x̅ (filled symbols) are shown in Figure 3a and b. Here, the error bars arise from the average of the Raman scattering cross section of four investigated nanowires with different diameters ranging from 90 to 220 nm. We would like to underline that the analysis of these measurements did not show any dependence or even any substantial difference in the resonance behavior of

Table 1. Relevant Phonon Modes along with the Scattering Configurations and the Electronic Transitions and According Electric Field Polarization with Which They Are Coupled phonon mode

scattering configuration

electronic transition

electric field polarization

E2H A1 E1

x(y,y)x̅ x(z,z)x̅ x(y,y)x̅

Γ9v−Γ7c Γ7−Γ7, Γ9−Γ9 Γ7−Γ7, Γ9−Γ7

E⊥c E∥,⊥c E∥,⊥c

recent work, Belabbes et al. calculated the quasiparticle band structures of four polytypes (3C, 6H, 4H, and 2H) of GaP, GaAs, GaSb, InP, InAs, and InSb.23 According to their calculations, the E1(A) gap from the heavy hole valence band of the 2H InAs has an energy of about 2.4 eV, while the E1(A) gap from the light hole valence band at the A point has an energy slightly higher than 2.6 eV. The gap from crystal-field split-off valence band at the A point has a much higher energy. The resonance of the E2H at about 2.4 eV can be therefore explained by the coupling with the E1(A) gap. Instead, the increasing intensity of the TO(A1) in the investigated energy region can be explained by the sum of the transitions from light hole and crystal-field split-off valence band. Furthermore, effects of the presence of stacking faults and twin defects cannot be excluded, and it would affect mainly the TO mode, smoothing the resonance profile arising from the two different structures. The redshift of the E1 transition in InAs nanowires with an intermixture of zinc-blende and wurtzite phase with respect to the ZB bulk was already reported.27 However, a resonant profile was observed only in the x(y,y)x̅ scattering configuration, probably due to the different ratios of WZ and ZB phases.27

Figure 3. Raman scattering cross section of the TO* (a) and LO (b) modes for polarization configuration x(z,z)x̅ (open symbols) and x(y,y)x̅ (filled symbols). The TO(A1) is strongly predominant in the x(z,z)x̅ configuration, while the E2H is strongly predominant in the x(y,y)x̅ configuration. The experimental points are the result of the average cross section obtained for four nanowires with different diameters. Solid lines are guides to the eyes. (c) Sketch of the InAs WZ (ZB) band structure between the Γ and A (L) point of the first Brillouin zone according to ref 25. In the first case, the allowed optical transitions for the electric field parallel or orthogonal to the c axis are shown. C


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absolute intensities of the TO* and LO modes are shown in Figure 5 as a function of the applied pressure.

A further indication of the resonant behavior of the scattered light perpendicular to the nanowire axis, is given by the complete azimuthal study of the Raman spectra with two laser excitation lines, namely, 2.41 eV (514.5 nm) and 1.92 eV (647.1 nm). The results are shown in Figure 4.

Figure 5. Intensity of the TO* (a) and LO (b) modes of InAs nanowires bundles as a function of the applied pressure. The different symbols indicate two different measured nanowire bundles (pos1 and pos2). (c) Average on the peaks intensities over the two different bundles. The dashed lines indicate the pressure at which the resonance occurs in bulk InAs for this specific excitation wavelength, due to the pressure dependence of the E1 gap: E1(eV) = 2.49 (eV) + 0.074 P (eV/GPa).11 The solid lines are a guide to the eyes.

Figure 4. Azimuthal dependence of the E2H mode (a−b) and of the A1-TO mode (c−d) for 514.5 and 647.1 nm, respectively. The filled (empty) symbols indicate scattered light with polarization perpendicular (parallel) to the nanowire axis (z direction). θ is the angle between the polarization of the incident light and the nanowire axis z, as schematically depicted in Figure 2a.

The different symbols in Figure 5a and b indicate results obtained from two different bundles measured. The slight difference between the two bundles can be addressed to the difficulty in focusing, especially when the methanol−ethanol mixture exhibits a liquid−solid transition (∼3 GPa); the general behavior is similar. With increasing pressure, the TO* mode shows an increase of the absolute intensity, with a first maximum around 4 GPa and a second one around 6.5 GPa. For higher pressures the TO* is still visible, but its intensity abruptly decreases at ∼7 GPa. The LO intensity decreases continuously with increasing pressure, becoming barely visible at ∼3 GPa, and it disappears completely around 7 GPa. The different resonance profiles of the two modes can be seen in Figure 5c, where the average intensities of the two modes measured for the two different bundles are plotted. The pressure for each data point is estimated as the average between the initial and the final pressure at each step. For ZB structure, the dependence of the E1 energy gap as a function of pressure is known from literature.11 Using 2.71 eV excitation energy, we expect the resonance for the ZB phonon modes at ∼3 GPa (this value is indicated by the dashed lines in Figure 5). Nevertheless the intensity increase for the TO* mode is observed at a pressure slightly higher than 3 GPa accordingly with a value of the E1gap slightly lower than the 2.71 eV. This finding thus strongly supports the result obtained by the wavelength-dependent Raman study discussed in the previous section. Interestingly, assuming for the E1 WZ band gap the same pressure dependence of the E1 ZB gap11 but an energy value of 2.4

The polarization of scattered light was chosen either parallel (empty symbols) or perpendicular (full symbols) to the nanowire axis, while the polarization of incident light was varied by the angle θ with respect to the nanowire axis, as illustrated in the schematic in Figure 2a. In this case it was possible to resolve the TO and the E2H modes at 217.5 and 214.7 cm −1 , respectively. The E 2 H mode is observed predominantly in the x(y,y)x̅ scattering configuration for both excitation energies, and the intensity increases considerably when exciting with 2.41 eV (see Figure 3a−b). The TO mode instead is predominant in the x(z,z)x̅ scattering configuration, but the intensity does not change significantly for these excitation energies. Pressure-Induced Resonant Raman Spectroscopy. In addition we have performed high-pressure Raman measurements on InAs nanowire bundles. It is well-known that the energy gap of semiconductors increases with applying pressure, as also observed for InAs bulk material.11 This means that resonant Raman scattering is also observed, keeping the excitation energy fixed and varying the energy gap with pressure. Pressure-dependent measurements give information on the electronic band structure of the investigated material. The polarization of the incident and the scattered light was not selected, since the polarization is affected by the diamonds of the pressure cell and the experiment was carried out on nanowire bundles rather than on a single nanowire, exciting with 2.71 eV. The spectra are fitted with two Lorentzian curves, in correspondence of the TO* and LO mode regions. The D


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scans could be performed on the same nanowires measured with Raman spectroscopy. The diameter of the wires was extrapolated from the AFM profile. Nanowires with different diameters in the range 90−220 nm were studied. Raman measurements were performed in backscattering geometry on single InAs nanowires at room temperature, with four different lines of an Ar+ laser and one line of a Kr+ laser, with excitation wavelengths in the range 457.9−647.1 nm, corresponding to energies between 1.92 and 2.71 eV, and with a spectral resolution of about 1 cm−1. For each excitation wavelength at least four nanowires with different diameters were investigated. The nominal laser power was kept below 500 μW in order to avoid local heating effects.31 The laser beam was focused on the selected wire with a 100× objective (NA 0.95). The scattered light was collected by a XY Raman-Dilor triple spectrometer with a multichannel charge couple device detector. The polarization of incident and scattered light was also selected: for each nanowire, spectra with incident and scattered light parallel and perpendicular to the nanowire axis were collected. Therefore, the scattering configurations were x(z,z)x̅ and x(y,y)x̅, in the so-called Porto notation, respectively, where z is the nanowire growth direction, corresponding to the [111] direction, and x the scattering direction, which is parallel to the [110] direction. In the case of the complete azimuthal study of the Raman spectra, the polarization of the incident light was varied by an angle θ, while the polarization of the scattered light was selected either parallel or perpendicular to the nanowire axis. Pressure-dependent measurements were performed by exciting bundles of nanowires with the 457.9 nm line of the Ar+ laser (2.71 eV). A screw clamped opposing-plate DAC, furnished with high quality type II diamonds with culets of 750 μm in diameter was employed for applying hydrostatic pressure. The nanowires were loaded together with a ruby microsphere in a sample chamber of 150 μm diameter and 60 μm heights under working conditions, located in the center of a stainless steel gasket. A methanol−ethanol mixture (4:1) was used as pressure transmitting medium, and the ruby microsphere was used for the determination of the pressure inside the chamber, through the ruby-fluorescence technique.32 Raman spectra were collected in backscattering geometry using a 50× objective (NA 0.42). For each pressure step, spectra recorded from two different bundles of nanowires were recorded. The pressure was measured before and after collecting Raman spectra. In this case, the polarization of incident and scattered light was not selected, since it is not conserved through the diamond.

eV at ambient pressureas found in the wavelength dependent studythe resonance with the excitation wavelength should occur at about 4.2 GPa, in good agreement with the measurements. Since the polarization of incident and scattered light was not selected, it is not possible to assign the resonance of the TO(A1+E1) or to the E2H. The LO mode does not show any resonance, but a continuously decreasing intensity, as expected from a gap which is already bigger than 2.71 eV at ambient pressure. This is in agreement with the coupling with the gaps from the light hole valence band and the gap from crystal-field split-off valence band at the A point. Finally, it is interesting to note that the TO* intensity does not decrease significantly for pressures higher than the ZB E1 gap, as observed in the bulk material.11 The diminution of the intensity at ∼7 GPaand the disappearance of the LO modecan be related to the structural phase transition that occurs for the zinc blende material, associated with the metallization of the system.11,28 Nevertheless the spectrum can be fully recovered after depressurizing the diamond anvil cell (DAC), indicating a reversible structural transition. The presence of the TO* signal over 7 GPa, though with strongly reduced intensity, as well as the recovery of the signal after depressurizing can be explained by an incomplete structural transition. Conclusions. As expected, nanowires with mainly WZ structure and high density of stacking faults along the nanowire axis show a different behavior with respect to the pure ZB material. The resonance profiles obtained here are remarkably different from those observed in bulk ZB InAs and provide an experimental confirmation of the calculated bandstructure of WZ InAs. The resonance profile of the E2H mode has a peak around 2.4 eV, indicating the coupling with the E1(A) gap of the WZ structure. This is confirmed by the shift to higher energy of the pressure-dependent resonance profile. Instead, the TO(A1+E1) mode does not exhibit a resonance in the investigated energy range. From the excitation energy dependent measurement, we can deduce that the resonance is shifted to energies higher than 2.71 eV, possible due to the transitions from the light hole valence band and the gap from crystal-field split-off valence band at the A point. The pressure dependent measurements confirm that with increasing pressure, and consequently increasing the relevant energy gap, the LO mode is moving out of resonance conditions, leading to a significantly decreasing intensity. We want to stress that the present method, based on a combined Raman resonant scattering technique, can represent a new sensible experimental tool for band structure investigation of nanosized semiconductor samples. Methods. Catalyst free InAs nanowires were grown by solid-source molecular beam epitaxy on Si (111) substrate covered by ultrathin amorphous SiOx, as discussed in refs 29 and 30. The nanowires present mainly WZ crystal structure with a high density of stacking faults and twin defects.20 TEM was performed using a FEI Titan 80-300 and a JEOL JEM 2011, where both diffraction patterns and (HR) TEM images were recorded in a ⟨110⟩ zone axis corresponding to the facet of the nanowire. During TEM analysis the size of the SAD aperture was adjusted to the full length of the nanowire to gain representative diffraction pattern information of the whole nanowire. For statistical analysis a total of five nanowires were characterized. For Raman scattering experiments on single nanowires, the nanowires were transferred by isopropanol drop casting onto a patterned Si substrate, so that atomic force microscopy (AFM)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Addresses

I.Z.: Applied Physics, Photonics & Semiconductor Nanophysics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands. N.H.: Helmholtz Institute Ulm (HIU)Electrochemical Energy Storage, Albert-Einstein-Allee 11, 89069 Ulm, Germany. Author Contributions

I.Z. and S.Y. contributed equally. Notes

The authors declare no competing financial interest. E


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ACKNOWLEDGMENTS

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REFERENCES

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We thank M. Bichler and H. Riedl for excellent experimental help and Markus Döblinger for scientific discussion. This work was supported financially by the DFG via the excellence cluster Nanosystems Initiative Munich (NIM) and the SFB 631. I.Z., S.F., and G.A. are also thankful for the support by of the Technische Universität MünchenInstitute for Advanced Study, funded by the German Excellence Initiative, and G.K. would also like to acknowledge financial support from the EU Marie Curie FP7 Reintegration Grant.

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E1(A) Electronic Band Gap in Wurtzite InAs Nanowires Studied by

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