**6. Resonant Raman scattering in nanowires**

compositions as extracted by the comparison between experiment and calculation for the GaAs‐like TO modes are *x* = (0.22–0.24) for the sample with nominal *x* = 0.20, *x* = (0.17–0.22)

**Figure 9.** (a) Raman spectra (open circles) of In*x*Ga1‐*x*As nanoneedles (with the indicated nominal In content, *x*) capped with 30 nm of GaAs. Spectra were taken in the scattering geometry and were normalized to the GaAs‐like E2

phonon peak, whose energy is indicated by a dashed line in the spectra of the *x* = 0.12 sample. Red solid lines are Lorentzian fits to the data. The single contributions to a Lorentzian fit are represented by green solid lines in the *x* = 0.12 sample as an example. (b) Same as (a) for samples with the indicated GaAs shell thickness *t* and fixed In content (*x*

shell. (c) Frequency of various optical phonons as a function of indium composition. Symbols represent experimental data points taken under the (open circles) and (full squares) scattering configurations. Solid lines indi‐ cate theoretical estimations for ZB In*x*Ga1‐*x*As and dashed lines are linear fits to the data for the GaAs‐like and InAs‐like

H modes. (d) Energy of phonon modes for an In*x*Ga1‐*x*As NN with *x* = 0.16 a function of shell thickness. Symbols rep‐ resent experimental data points taken under the (full squares) and (open circles) scattering configura‐

In these NNs, the possible presence of strain was also probed by Raman spectroscopy. In **Figure 9(b)**, we display spectra recorded in configuration from NNs with different GaAs shell thickness *t* and same indium composition (nominal *x* = 0.16). The peaks' attribution is the same as in panel (a). Here, the GaAs LO phonon mode is also observed, but only in the sample with the thickest shell. Its energy (∼287 cm−1) is downshifted by ∼2 cm−1 with respect to the bulk, which could be due to tensile strain in the shell. The Raman shift of all modes as determined by Lorentzian fits to the spectra (the green solid lines in panel (b) are an example) are reported in panel (d) as full squares for data and open circles for data as a function of the nominal shell thickness. We do not observe any clear and consistent energy variation of the phonon modes with increasing shell thickness, neither an increase in their

tions. Dashed lines indicate the energy of the GaAs‐like A1/E1 (TO) and E2

Reproduced with permission from Ref. [28]. © 2014, American Chemical Society.

H phonon is indicated by a dashed line in the spectrum of the sample without

H modes for In*x*Ga1‐*x*As without shell.

H

for nominal *x* = 0.16, and *x* = (0.12–0.15) for nominal *x* = 0.12 [28].

= 0.16). The energy of the GaAs‐like E2

94 Raman Spectroscopy and Applications

E2

In this section, we highlight the power of Resonant Raman scattering (RRS) to investigate the electronic band structure and the electron‐phonon interaction in semiconductor NWs. This investigation is possible because the scattering cross section contains the electron‐radiation and the electron‐phonon interaction Hamiltonians, as well as electronic states for electron‐hole pair. In standard conditions, it is very difficult to have access to this information, due to summation over all the intermediate states, but if resonant conditions are achieved, the excitation energy matches electronic interband transitions and the electronic‐related terms in the scattering cross section are sizably enhanced. Resonant conditions between excitation energy and electronic states may be reached by varying either the energy of the excitation (using a tunable laser) or the energy of the electronic states (for instance by applying an external pressure at fixed excitation energy). Indeed, the energy gap of semiconductors typically increases with pressure, thus if the pressure dependence of the energy gap is known, pressure‐ dependent RRS measurements give information on the electronic band structure of the material. We will discuss both methods focusing on InAs NWs with WZ phase [30], because in III–V NWs with WZ phase the electronic band structure is poorly known and RRS has proved to be a necessary tool to shine light on this highly debated topic [31].

**Figure 10(a)** shows some spectra collected from a single WZ InAs NW with growth axis aligned with *z*, as sketched in **Figure 4**, under two scattering configurations, (solid line) and (dashed line). Five different excitation energies comprised between 1.91 and 2.71 eV were used. All spectra exhibit an asymmetric peak at about 216 cm−1, in the region of the TO mode, and an LO mode at ∼238 cm−1, more intense for higher excitation energies. The TO peak is asymmetric because it results from the convolution of two peaks: the A1/E1 (TO) mode at ∼218 cm−1, dominant in the configuration (where it is mainly A1), and the E2 H mode at ∼214 cm−1, dominant for . This is in agreement with the results shown in **Figure 8(b)** for WZ GaAs. In the following we will refer to the convoluted A1/E1 and E2 H modes simply as TO. The measured Raman scattering cross sections (carefully normalized for the spectral response of the setup) of the TO (black squares) and LO (red circles) modes for the configura‐ tion (open symbols) and (filled symbols) are shown in panel (b). The intensity of the TO in configuration, that is mainly the A1 (TO), and of the LO in both configurations, increases with energy in a monotonic way, while the intensity of the TO in configuration (where it is mainly given by the E2 H mode), displays a resonance in the 2.41–2.60 eV energy region, which can be correlated with the WZ band structure since the E2 H mode is peculiar to WZ phase. Actually, two separate resonances appear, but the number of experimental points is too limited to point out the exact energy at which the maxima occur.

These RRS data can be interpreted at the light of the following considerations. The three lowest energy electronic interband transitions in III–V WZ materials, labeled as A, B, and C, involve

**Figure 10.** Resonant Raman experiments on WZ InAs NWs. (a) Spectra collected on a single NW with five different excitation energies in the (solid line) and (dashed line) configurations. (b) Raman scattering cross sec‐ tion of the TO as defined in the text (black squares and left scale) and LO (red circles and right scale) modes for the configuration (open symbols) and (filled symbols). The error bars come from the average of the Ram‐ an scattering cross sections of NWs with four different diameters. Solid lines are guides to the eyes. Reproduced with permission from [30]. Copyright 2013, American Chemical Society. (c) Spectra of a NW bundle for different applied pressures from 0 to 8.5 GPa. Excitation energy is fixed at 2.71 eV. (d) Average on the peaks intensities over two different bundles. The pressure at which the resonance is expected to occur in bulk InAs (based on the known pressure depend‐ ence of the E1 band gap for this excitation energy) is indicated by a dashed line. The solid lines are a guide to the eyes.

the bottommost conduction band minimum, having a Γ7 symmetry, and the three valence band maxima, with Γ9 , Γ7, + , and Γ7, − symmetries (in order of increasing hole energy). Due to the anisotropy of the hexagonal crystal lattice, there are special selection rules for these transitions: A is allowed only for light polarized perpendicular to the NW growth (like in and configuration), B and C are allowed for both perpendicular and parallel polarized light (like in , , and configurations). If we consider now the coupling of electronic states with the different phonon mode symmetries, the E2 H mode, allowed in , couples with the A transition, while the A1 mode, in , couples with B and C, and E1, in , couples with A, B, and C [30]. According to theoretical calculations on WZ InAs, the E1 gap at A point involving the first valence band (the one with Γ9 symmetry at Γ) has an energy of ∼2.4 eV, the E1(A) gap involving Γ7, + band has an energy slightly higher than 2.6 eV, and the E1(A) gap involving Γ7, − band has a much higher energy. Therefore, the resonance of the TO in (mainly E2 H) at about 2.4 eV can be explained by the coupling between E2 H and the E1(A) gap involving the first valence band. We stress that the 2.4 eV value of the E1(A) gap is reduced with respect to the ZB InAs E1 gap, in agreement with band structure calcula‐ tions. The increased intensity with no resonance of the TO in (mainly A1) in the investigated energy region suggests that the resonance could be shifted to energies higher than 2.71 eV, which can be due to the sum of the contributions from the second and the third valence bands.

TO. The measured Raman scattering cross sections (carefully normalized for the spectral response of the setup) of the TO (black squares) and LO (red circles) modes for the configura‐ tion (open symbols) and (filled symbols) are shown in panel (b). The intensity of the TO in configuration, that is mainly the A1 (TO), and of the LO in both configurations, increases with energy in a monotonic way, while the intensity of the TO in configuration

WZ phase. Actually, two separate resonances appear, but the number of experimental points

These RRS data can be interpreted at the light of the following considerations. The three lowest energy electronic interband transitions in III–V WZ materials, labeled as A, B, and C, involve

**Figure 10.** Resonant Raman experiments on WZ InAs NWs. (a) Spectra collected on a single NW with five different excitation energies in the (solid line) and (dashed line) configurations. (b) Raman scattering cross sec‐ tion of the TO as defined in the text (black squares and left scale) and LO (red circles and right scale) modes for the configuration (open symbols) and (filled symbols). The error bars come from the average of the Ram‐ an scattering cross sections of NWs with four different diameters. Solid lines are guides to the eyes. Reproduced with permission from [30]. Copyright 2013, American Chemical Society. (c) Spectra of a NW bundle for different applied pressures from 0 to 8.5 GPa. Excitation energy is fixed at 2.71 eV. (d) Average on the peaks intensities over two different bundles. The pressure at which the resonance is expected to occur in bulk InAs (based on the known pressure depend‐ ence of the E1 band gap for this excitation energy) is indicated by a dashed line. The solid lines are a guide to the eyes.

region, which can be correlated with the WZ band structure since the E2

is too limited to point out the exact energy at which the maxima occur.

H mode), displays a resonance in the 2.41–2.60 eV energy

H mode is peculiar to

(where it is mainly given by the E2

96 Raman Spectroscopy and Applications

Let us now discuss high‐pressure Raman measurements on the same NWs [30, 32]. Measure‐ ments were performed by exciting bundles of NWs with 2.71 eV. Hydrostatic pressure was applied by using a screw clamped opposing‐plate diamond Anvil cell (DAC, as the one sketched in **Figure 10(d)**). The NWs were loaded together with a ruby microsphere in a sample chamber 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 determining the pressure through the ruby‐fluorescence technique [33]. Raman spectra were collected in backscattering geometry without filtering light polarization, since it is not conserved through the diamond and anyhow the orientation of NWs in the bundle is unknown. Raman spectra collected from an InAs bundle are shown in **Figure 10(c)** for increasing applied pressure up to 8.5 GPa. At ambient pressure (0 GPa), the Raman spectrum is similar to the spectra in panel (a): the broad peak at ∼216 cm−1is due to convolution of the A1/E1 (TO) mode and the E2 H TO mode (we continue to label the peak as TO), and the peak at ∼238 cm−1 is due to LO mode. We notice that the frequency of the TO and LO increases with pressure, the FWHM of the TO decreases with pressure, the intensity of the LO peak decreases after 3 GPa and vanishes for pressures higher than 6.4 GPa, and the intensity of the TO increases (with a first maximum around 4 GPa and a second one around 6.5 GPa) and then decreases drastically without vanishing. The absolute intensities of the TO and LO modes (after averaging between two different bundles) are plotted in panel (d) as a function of the applied pressure. Red circles refer to LO, black squares to TO. In bulk ZB InAs, the pressure at which the resonance is expected to occur (based on the known pressure dependence of the E1 band gap for 2.71 eV excitation energy) is ∼3 GPa, as indicated by a dashed line in panel (d). Here, the intensity increase for the TO mode is observed at a pressure slightly higher than 3 GPa due to a value of the E1‐gap slightly lower than the 2.71 eV. This finding confirms the results obtained by the energy‐dependent Raman study. Indeed, assuming for the E1 WZ band gap the same pressure dependence of the E1 ZB gap and an energy gap at ambient pressure of 2.4 eV as the one determined from data in **Figure 10(b)**, the resonance is expected at about 4.2 GPa, in good agreement with the measurements. Moreover, the continuous decrease in intensity of the LO mode with pressure agrees with what expected from a gap which is already bigger than 2.71 eV at ambient pressure: with increasing pressure, and consequently increasing the relevant energy gap, the LO mode is going far and far from resonance conditions, leading to a contin‐ uously decreased intensity. This confirms its coupling with the gaps from the second and third valence bands at the A point. The disappearance of the LO mode at 6.4 GPa could be related to the structural phase transition that occurs in the ZB material, associated with the metalli‐ zation of the system. We point out that the spectrum could be fully recovered after depressu‐ rizing the DAC, indicating a reversible structural transition.

We have shown that the present method, based on the combination of two RRS techniques, has proved to be a novel and powerful experimental tool for band structure investigation of nanoscale semiconductors.

In conclusion, we have provided valuable examples, mostly based on our experimental results, of how powerful is Raman spectroscopy in investigating all the most important aspects of the lattice dynamics of semiconductor nanowires.
