**3. Size effects in the Raman spectra of semiconductor nanowires**

In a 3D‐crystal with N atoms per primitive unit cell, the phonon dispersion (namely, the relation between the frequency and the wavevector of lattice vibrations) is composed of 3N branches (three of them are acoustic and the remaining 3N−3 are optical). Along high‐symmetry directions the phonons are classified as transverse or longitudinal according to whether their displacements are perpendicular or parallel to the direction of the phonon wavevector *q*, respectively. Due to momentum and energy conservation rules, only the optical lattice modes at *q* = 0 (Γ point) can be studied by one‐phonon spectroscopic techniques (infrared spectroscopy for odd parity modes and Raman scattering for both odd and even parity modes). In III–V ZB crystals and group IV crystals with the diamond structure, such as Si and Ge, there are six‐ phonon branches (because there are two atoms per primitive unit cell): two transverse and one longitudinal acoustical modes (TA and LA, respectively) and two transverse and one longitu‐ dinal optical modes (TO and LO, respectively). The TO and LO near Γ are degenerate only in group IV crystals since the two atoms in the unit cell are identical.

**Figure 5.** (a) Raman spectra recorded every 100 nm along a Ge NW with diameter of 86 nm. (b) Peak position (open circles, bottom scale) and FWHM Γ (full triangles, top scale) of the degenerate TO/LO modes as a function of the posi‐ tion. Solid lines are guides to the eyes. (c) Bottom: energy shift Δ*ω* from the crystalline Ge Raman peak position (298 cm−1). Top: broadening Δ*Γ* with respect to the natural FWHM of the crystalline Ge Raman peak (3.4 cm−1). Open circles are the experimental values; solid lines come from the theoretical model.

In nanostructured materials it is usually observed that the energy of TO and LO modes is very similar to the bulk case. Differences may arise due to phonon confinement effects when scaling down the size of the crystal. Indeed, whenever the sizes of the "phonon wave packet" are comparable to the crystal size, an uncertainty in wavevector is introduced, which results in a contribution to the Raman peak at frequencies different from that at the Γ point. In other words, there is a relaxation of the *q* = 0 momentum conservation rule. As a consequence, the Raman line shifts (in a direction depending on the phonon dispersion) and broadens. **Figure 5(a)** shows Raman spectra taken along a single Ge nanowire consisting of a crystalline Ge core, whose diameter is inhomogeneous along the NW length, surrounded by an amorphous Ge layer [16]. The main band, attributed to the degenerate TO/LO phonons of the core, display variations in intensity and energy along the NW axis. Panel (b) shows the peak energy (open circles) and the full width at half maximum (FWHM) Γ (full triangles) of the phonon band as a function of the position (with steps of 100 nm). Since the downshift is mostly accompanied by a broadening, these effects point to phonon confinement in the core. By using a proper model and taking the experimental lattice constant of Ge NWs from the literature, an estimate of the size of the nanocrystal is determined by our experimental downshift (Δ*ω*) and broad‐ ening (ΔΓ) of the TO/LO band, as displayed in panel (c). The observed Δ*ω* correspond to a crystal size between 5 and 30 nm, in excellent agreement with the TEM analysis [16], while the broadening gives values between 5 and 10 nm. We believe that the broadening data are less reliable because the inhomogeneity of the core in diameter (definitely probed by a ∼1 µm laser spot) creates an additional broadening of the phonon band, resulting in crystal sizes smaller than the real ones.

dinal optical modes (TO and LO, respectively). The TO and LO near Γ are degenerate only in

**Figure 5.** (a) Raman spectra recorded every 100 nm along a Ge NW with diameter of 86 nm. (b) Peak position (open circles, bottom scale) and FWHM Γ (full triangles, top scale) of the degenerate TO/LO modes as a function of the posi‐ tion. Solid lines are guides to the eyes. (c) Bottom: energy shift Δ*ω* from the crystalline Ge Raman peak position (298 cm−1). Top: broadening Δ*Γ* with respect to the natural FWHM of the crystalline Ge Raman peak (3.4 cm−1). Open circles

In nanostructured materials it is usually observed that the energy of TO and LO modes is very similar to the bulk case. Differences may arise due to phonon confinement effects when scaling down the size of the crystal. Indeed, whenever the sizes of the "phonon wave packet" are comparable to the crystal size, an uncertainty in wavevector is introduced, which results in a contribution to the Raman peak at frequencies different from that at the Γ point. In other words, there is a relaxation of the *q* = 0 momentum conservation rule. As a consequence, the Raman line shifts (in a direction depending on the phonon dispersion) and broadens. **Figure 5(a)** shows Raman spectra taken along a single Ge nanowire consisting of a crystalline Ge core, whose diameter is inhomogeneous along the NW length, surrounded by an amorphous Ge layer [16]. The main band, attributed to the degenerate TO/LO phonons of the core, display variations in intensity and energy along the NW axis. Panel (b) shows the peak energy (open circles) and the full width at half maximum (FWHM) Γ (full triangles) of the phonon band as a function of the position (with steps of 100 nm). Since the downshift is mostly accompanied by a broadening, these effects point to phonon confinement in the core. By using a proper model and taking the experimental lattice constant of Ge NWs from the literature, an estimate of the size of the nanocrystal is determined by our experimental downshift (Δ*ω*) and broad‐ ening (ΔΓ) of the TO/LO band, as displayed in panel (c). The observed Δ*ω* correspond to a crystal size between 5 and 30 nm, in excellent agreement with the TEM analysis [16], while the

group IV crystals since the two atoms in the unit cell are identical.

88 Raman Spectroscopy and Applications

are the experimental values; solid lines come from the theoretical model.

In the context of size effects in NWs, in addition to phonon confinement also the high surface‐ to‐volume ratio of NWs plays a role and creates differences with the bulk. As a matter of fact, the surfaces represent a new physical boundary. The crystal symmetry might be affected by the existence of the edges, which lead to a rearrangement of the lattice and can activate silent modes. Also, specific modes associated to the surface, such as surface optical (SO) modes or breathing modes, may appear [17]. The SO phonons are created at the interface between different materials with different dielectric constants and propagate along the interface. They are activated by a breaking of the translational symmetry of the surface potential, likely due to diameter variations along the NW length. Finally, since the surface atoms are "less bound" than the internal atoms, they "experience" a different local field. The propagation of optical phonons, where the oscillating dipoles, created by the out of phase oscillation of ions and cations, interact via a dipole‐dipole interaction, is most affected by this.

Besides the appearance of the SO modes, the peculiar cylindrical shape with nanoscale dimensions of the NWs gives rise to the so‐called dielectric mismatch effect, as will be discussed in the following. A representative example of the difference between NWs and the bulk is presented in **Figure 6** for zinc blende GaAs [18, 19]. In panel (a) we show a Raman spectrum of a ZB NW grown along the [111] direction (blue) and a spectrum of a (111)‐oriented GaAs wafer (black) tilted by 90°. The spectra were, therefore, collected in the same scattering geometry, namely, . The spectra are composed of a unique phonon mode, the E1(TO), at ∼267 cm−1, as expected, based on the experimental geometry and the Raman tensors for ZB. The FWHM of this mode in the NW spectrum is ∼2 cm−1 larger than in the bulk, which indicates a good crystal quality of the NW, the broadening being likely due to the presence of some twins in the crystal structure. Panel (b) displays the azimuthal dependence of parallel (full circles) and perpendicular (open squares) components of the scattered light of this mode for the bulk (left) and the NW (right). The measurements are performed as described in **Figure 4(a)** and **(b)**. In the bulk, the maximum intensity is found almost at the angles (*θ* ∼ −20° for the parallel component and *θ* ∼ 70° for the perpendicular) resulting from calculations based on Eq. (1). A same result is found in the NW for the parallel component. Instead, the perpendicular component is much less intense than in the bulk and it has no clear angular dependence. This difference points to a modification of the selection rules when passing from the bulk to the NW. This change can be attributed to the one‐dimensional geometry of the NW. Indeed, in cylindrical‐like crystals whose dielectric constant is larger than the one of the surrounding air, light absorption/emission is suppressed for light polarization perpendicular to the long symmetry axis because of image forces arising at the interface between the cylinder and its surroundings [20]. In NWs, this effect was observed also in photoluminescence measurements and it is strongly dependent on light wavelength and NW diameter. It exists in all NWs and in wurtzite NWs it has to be carefully taken into account when dealing with electronic selection rules [21]. In Raman spectroscopy, because of this effect the phonon modes are more efficiently excited for parallel polarization, as we observe.

**Figure 6.** (a) Raman spectra of a NW grown along the [111] direction (blue) and of a (111)‐oriented GaAs wafer (black) recorded in the same scattering geometry, . (b) Azimuthal dependence of the TO mode of the bulk GaAs (left) and of the NW (right). Full circles and open squares represent the components of the Raman signal along the *z*‐ and *y*‐ axes, respectively. Solid lines are squared sine fits to the data.

#### **4. Assessment of the crystal phase of nanowires**

The crystallization of NWs in a crystalline phase that is not stable in the bulk form is one of the consequences related to the large surface‐to‐volume ratio of NWs, since the "unusual" crystal structure formation is favored for certain ranges of the relevant interface energies. For instance, non‐nitrides III–V materials (such as GaAs, InAs, InP, etc.) that are notoriously stable in the cubic ZB phase in the bulk form can crystallize in the hexagonal wurtzite (WZ) phase when grown in the NW form under suitable VLS conditions. The occurrence of WZ in the lattice of these NWs is one of the most surprising findings in NWs and it provided the unprecedented opportunity to investigate this poorly known crystal phase. Many studies indicate that the WZ phase is favored in NWs featuring a high surface‐to‐volume ratio, such as in small diameters NWs [22], but an exhaustive picture of the reasons why WZ is formed in NWs is still lacking in the literature. It is worth stressing that the electronic and optical properties of the NWs strongly depend on their crystal phase [23] and thus engineering the crystal phase switching leads to the realization of heterostructures with additional degrees of freedom enabling novel optoelectronic devices [24, 25].

The differences between ZB and WZ properties are given by their different crystal structures. The ZB crystal is formed by two interpenetrating face‐centered‐cubic Bravais lattices (each of a different atomic species), whereas WZ is constructed from two interpenetrating hexagonal‐ close‐packed lattices. The differences between ZB and WZ crystals are best understood by observing their structures in the [111] direction (that is the [0001] direction in WZ, usually known as the *c*‐axis), along which both crystals look like stacked hexagonal layers, as shown in **Figure 7(a)** for a generic III–V crystal. Clearly, WZ and ZB are made by identical atoms within each layer, but these layers are alternated according to a different stacking sequence: ABABAB in WZ and ABCABC in ZB. The length of the unit cell of the WZ phase along the [0001] direction is double of the cell of the ZB phase in the [111] direction [26]. Due to these crystallographic similarities, the principal features of the WZ electronic and phononic band structure can be understood starting from the ZB band structure and applying folding arguments. We will discuss in detail the phonon band structure, as it can be probed mainly by the Raman spec‐ troscopy.

selection rules [21]. In Raman spectroscopy, because of this effect the phonon modes are more

**Figure 6.** (a) Raman spectra of a NW grown along the [111] direction (blue) and of a (111)‐oriented GaAs wafer (black) recorded in the same scattering geometry, . (b) Azimuthal dependence of the TO mode of the bulk GaAs (left) and of the NW (right). Full circles and open squares represent the components of the Raman signal along the *z*‐ and *y*‐

The crystallization of NWs in a crystalline phase that is not stable in the bulk form is one of the consequences related to the large surface‐to‐volume ratio of NWs, since the "unusual" crystal structure formation is favored for certain ranges of the relevant interface energies. For instance, non‐nitrides III–V materials (such as GaAs, InAs, InP, etc.) that are notoriously stable in the cubic ZB phase in the bulk form can crystallize in the hexagonal wurtzite (WZ) phase when grown in the NW form under suitable VLS conditions. The occurrence of WZ in the lattice of these NWs is one of the most surprising findings in NWs and it provided the unprecedented opportunity to investigate this poorly known crystal phase. Many studies indicate that the WZ phase is favored in NWs featuring a high surface‐to‐volume ratio, such as in small diameters NWs [22], but an exhaustive picture of the reasons why WZ is formed in NWs is still lacking in the literature. It is worth stressing that the electronic and optical properties of the NWs strongly depend on their crystal phase [23] and thus engineering the crystal phase switching leads to the realization of heterostructures with additional degrees of

The differences between ZB and WZ properties are given by their different crystal structures. The ZB crystal is formed by two interpenetrating face‐centered‐cubic Bravais lattices (each of a different atomic species), whereas WZ is constructed from two interpenetrating hexagonal‐ close‐packed lattices. The differences between ZB and WZ crystals are best understood by observing their structures in the [111] direction (that is the [0001] direction in WZ, usually known as the *c*‐axis), along which both crystals look like stacked hexagonal layers, as shown in **Figure 7(a)** for a generic III–V crystal. Clearly, WZ and ZB are made by identical atoms within each layer, but these layers are alternated according to a different stacking sequence: ABABAB

efficiently excited for parallel polarization, as we observe.

90 Raman Spectroscopy and Applications

axes, respectively. Solid lines are squared sine fits to the data.

**4. Assessment of the crystal phase of nanowires**

freedom enabling novel optoelectronic devices [24, 25].

**Figure 7.** (a) Schematic drawing of the atomic arrangement in zinc blende (left) and wurtzite (right) structures of a III– V semiconductor. Each letter represents a bilayer. (b) Phonon dispersion of a typical III–V semiconductor (GaAs). The phonon branches of the ZB structure (solid lines) are folded to give rise to the phonon branches of the WZ structure (dashed lines). (c) Atomic displacements corresponding to the Raman active optical phonon modes in the WZ struc‐ ture.

**Figure 7(b)** shows how the phonon dispersion of a III–V WZ crystal can be obtained by folding the one of the ZB structure along the [111] direction, namely from the Γ to the L point. We can consider only this high symmetry direction because we will deal with one‐phonon Raman scattering, which probes only phonons close to the Γ point. As discussed in the previous section for ZB GaAs crystals, there are six‐phonon branches: 2TA, 1LA, 2TO, and 1LO. We stress that the dispersion curves of the TA modes are relatively flat near the zone edge and their energies are much lower than the LA phonon energy due to the covalent nature of bonds in these crystals. The LO phonon has higher energy than the TO phonons near Γ due to the ionic character of the bonds and the macroscopic electric field connected with the long wavelength LO phonon, at variance with group IV crystals where they are degenerate because no extra charge is carried by the two identical atoms in the unit cell.

In WZ, four new modes appear at the Γ point of the Brillouin zone. The folded modes are indicated with red dashed lines. Group theory predicts eight‐phonon normal modes at the Γ point: 2A1 + 2E1 + 2B1 + 2E2. Considering our scattering geometry described in **Figure 4** and the crystallographic axes of a typical WZ NW grown along the [0001] direction, only the A1(LO), E1(TO), E2 H, and E2 L modes can be experimentally observed. The atomic displacements associated to these modes are sketched in panel (c). The notation E1 and A1 denote modes vibrating perpendicular and along the growth axis, respectively. Since A1 and E1 modes are also found in ZB, the appearance of E2 H and E2 L modes in the Raman spectrum of III–V NW is the unambiguous signature of a WZ phase.

Polarization‐resolved Raman measurements provide a reliable way to address the crystal phase of a given NW. To obtain such information it is necessary to calculate the selection rules for the modes specific to that crystal phase by using Eq. (1) and compare them with the experimental results. The Raman tensors of all existing crystal structures can be found in [27]. As summarized in table I in [19], in WZ III–V NWs grown along the [0001] direction (parallel to the *z*‐axis in **Figure 4**) in backscattering configuration the A1(TO) is expected to be observed only in the and configurations, the E2 H and E2 L only in , and E1 (TO) in . Experimentally, the selection rules can be probed by measuring the dependence of the scattered intensity on the incident and scattered polarizations as done in **Figure 6**. **Figure 8** shows how this was made in GaAs NWs [19]. In panel (a) the Raman spectra obtained under the four main polarization configurations on the same pure‐phase ZB NW of **Figure 6** are displayed. Only the A1/E1(TO) mode is visible and its intensity is maximum in the configuration, as clear also in the right panel of **Figure 6 (b)**. The reason for the sizable decrease in its intensity whenever the incident or scattered light are polarized perpendicular to the NW is the dielectric constant mismatch that we discussed in Section 3. In panel (b) of **Figure 8** we show the same measurement taken on a region of pure WZ phase in a mixed WZ/ZB NW. The E2 L is not observed due to its very low energy, the A1(TO) and E1 (TO) are almost degenerate in GaAs and appear at ∼266 cm−1. In the A1/E1 peak should be mainly E1 and in and mainly A1. The shoulder at ∼290 cm−1 can be ascribed to the theoretically forbid‐ den A1(LO), here most probably activated by the tilted facets of the hexagonal cross‐section of the NW that are not perpendicular to *ki* . Most importantly, we observe the E2 H mode at ∼256 cm−1, with the highest intensity in the configuration, as distinctive of the WZ phase. Its full azimuthal dependence in (c) for detected polarizations parallel (full circles) and perpen‐ dicular (open squares) to the NW axis nicely confirms this attribution: the maximum intensity of both detected polarizations is found when the polarization of incident light is perpendicular to the NW axis, though for the parallel detected polarization the dependence is less clear due to the low intensity.

consider only this high symmetry direction because we will deal with one‐phonon Raman scattering, which probes only phonons close to the Γ point. As discussed in the previous section for ZB GaAs crystals, there are six‐phonon branches: 2TA, 1LA, 2TO, and 1LO. We stress that the dispersion curves of the TA modes are relatively flat near the zone edge and their energies are much lower than the LA phonon energy due to the covalent nature of bonds in these crystals. The LO phonon has higher energy than the TO phonons near Γ due to the ionic character of the bonds and the macroscopic electric field connected with the long wavelength LO phonon, at variance with group IV crystals where they are degenerate because no extra

In WZ, four new modes appear at the Γ point of the Brillouin zone. The folded modes are indicated with red dashed lines. Group theory predicts eight‐phonon normal modes at the Γ point: 2A1 + 2E1 + 2B1 + 2E2. Considering our scattering geometry described in **Figure 4** and the crystallographic axes of a typical WZ NW grown along the [0001] direction, only the A1(LO),

associated to these modes are sketched in panel (c). The notation E1 and A1 denote modes vibrating perpendicular and along the growth axis, respectively. Since A1 and E1 modes are

Polarization‐resolved Raman measurements provide a reliable way to address the crystal phase of a given NW. To obtain such information it is necessary to calculate the selection rules for the modes specific to that crystal phase by using Eq. (1) and compare them with the experimental results. The Raman tensors of all existing crystal structures can be found in [27]. As summarized in table I in [19], in WZ III–V NWs grown along the [0001] direction (parallel to the *z*‐axis in **Figure 4**) in backscattering configuration the A1(TO) is expected to be observed

 . Experimentally, the selection rules can be probed by measuring the dependence of the scattered intensity on the incident and scattered polarizations as done in **Figure 6**. **Figure 8** shows how this was made in GaAs NWs [19]. In panel (a) the Raman spectra obtained under the four main polarization configurations on the same pure‐phase ZB NW of **Figure 6** are displayed. Only the A1/E1(TO) mode is visible and its intensity is maximum in the configuration, as clear also in the right panel of **Figure 6 (b)**. The reason for the sizable decrease in its intensity whenever the incident or scattered light are polarized perpendicular to the NW is the dielectric constant mismatch that we discussed in Section 3. In panel (b) of **Figure 8** we show the same measurement taken on a region of pure WZ phase in a mixed WZ/ZB NW. The

L is not observed due to its very low energy, the A1(TO) and E1 (TO) are almost degenerate in GaAs and appear at ∼266 cm−1. In the A1/E1 peak should be mainly E1 and in and mainly A1. The shoulder at ∼290 cm−1 can be ascribed to the theoretically forbid‐ den A1(LO), here most probably activated by the tilted facets of the hexagonal cross‐section of

cm−1, with the highest intensity in the configuration, as distinctive of the WZ phase. Its full azimuthal dependence in (c) for detected polarizations parallel (full circles) and perpen‐ dicular (open squares) to the NW axis nicely confirms this attribution: the maximum intensity

H and E2

L modes can be experimentally observed. The atomic displacements

H and E2

. Most importantly, we observe the E2

L modes in the Raman spectrum of III–V NW is

L only in , and E1 (TO) in

H mode at ∼256

charge is carried by the two identical atoms in the unit cell.

E1(TO), E2

E2

H, and E2

92 Raman Spectroscopy and Applications

also found in ZB, the appearance of E2

the NW that are not perpendicular to *ki*

the unambiguous signature of a WZ phase.

only in the and configurations, the E2

**Figure 8.** (a) Raman spectra of the ZB GaAs NW collected under the four main polarization configurations. The full azimuthal dependence is in the right panel of **Figure 6(b)**. (b) Same as (a) for a GaAs NW with WZ structure. (c) Azi‐ muthal dependence of the parallel (full circles) and perpendicular (open squares) components of the E2 H Raman mode with respect to NW growth axis. The solid red line is a squared sine fit to the data.
