Investigation of the higher order Raman Spectra from experimental and theoretical perspectives

Z.Azdad Möri

The author independently carried out all calculations, measurements, and data interpretations presented in this work

Higher-order Raman scattering processes are inherently challenging to investigate due to the significant reduction in scattering cross-sections compared to first-order Raman scattering. This reduction leads to weaker signal intensities, making experimental detection and analysis considerably more difficult.
To date, the existing literature on higher-order Raman scattering in gallium phosphide (GaP) is limited exclusively to its zinc blende (ZB) crystalline phase. In contrast, the wurtzite (WZ) phase of GaP is metastable and typically occurs only in nanostructured forms such as nanowires. Mapping higher-order Raman processes in these low-dimensional systems presents additional challenges, stemming from size effects, surface states, and reduced signal strength.
Nonetheless, recent advances in resonant Raman techniques have enabled enhanced detection of higher-order phonon modes in such nanostructures. In particular, exploiting surface-phonon-polariton (SPhP) resonances provides a powerful, non-invasive approach to amplify Raman signals without perturbing the intrinsic vibrational properties of the material—a common drawback when using plasmonic resonances, which can strongly modify the local electromagnetic environment and alter the phonon dynamics. The use of SPhP-enhanced Raman scattering thus offers a promising pathway for comprehensive characterization of higher-order vibrational modes in WZ-GaP nanowires and similar polar semiconductor nanostructures.
Although surface-phonon-polariton (SPhP) resonances are not discussed in detail in this section (see Project section), the signal enhancement techniques employed here enabled high-resolution mapping of the second-order Raman spectrum. This detailed spectral information allowed for direct comparison with the two-phonon density of states (2PDOS) calculated using ab initio methods within the Quantum ESPRESSO framework.

We begin by examining the higher-order Raman spectra using a 514nm wavelength laser as an excitation source to probe the bulk GaP in its zinc blende (ZB) structure and comparing the observed features with those reported in the existing literature. Following this, we present the calculated phonon dispersion relations along the high-symmetry directions of the Brillouin zone. Finally, we perform a detailed comparison between the experimental Raman features and the theoretical predictions to establish correlations with specific phonon modes and their combinations.
The obtained spectra under the three main polarization. The Spectra display high spectral resolution with very distinguished features

Raman Spectra of Bulk GaP under three different polarization

To interpret the higher-order Raman spectra from first-principles calculations, it is essential to analyze the phonon dispersion relations and consider all possible decay channels and selection rules associated with overtone and combination modes. This task is computationally intensive, as it requires fine sampling of the Brillouin zone and careful treatment of anharmonic effects and symmetry constraints. In this work, we generated the phonon dispersion of bulk GaP using density-functional perturbation theory (DFPT). Prior to the DFPT calculations, a rigorous convergence study was conducted to optimize the choice of pseudopotentials, plane-wave energy cut-offs, and structural parameters. The phonon calculations were performed using the ph.x module of the Quantum Espresso package . following a self-consistent ground-state calculation using pw.x The results of such a calculation are displayed below together:

Phonon dispersion of Zinc Blend GaP

The calculation of the projected density of state serves to compute the two phonon density of state as follow [1]:

DOS 2 (ω; q; \pm) = \frac{1}{N_{q}} \sum_{q_{1}, q_{2}, j_{1}, j_{2}} δ (ω \pm ω_{q_{1} j_{1}} - ω_{q_{2} j_{2}}) δ_{q \pm q_{1}, q_{2} + G},

where G is a reciprocal lattice vector. The sign ± correspond to absorption and emission processes, respectively.
Such calculation results in the following graph:

Simulated 2PDOS for all the possible q vectors vs measured Raman spectra under ZZ and ZY configuration

A detailed investigation reveals the contribution of two-phonon processes in the measured Raman spectra. This is particularly evident under the cross-polarization configuration ZY, where the resonant overtones of the transverse acoustic (TA) and longitudinal acoustic (LA) phonons exhibit relatively weaker intensity. Under these conditions, the reduced background from overtone features enhances the clarity of the spectra, making it possible to achieve a one-to-one identification of all vibrational modes and their corresponding symmetries.

With the establishment of a robust methodology, the first measurement of higher-order Raman spectroscopy in wurtzite gallium phosphide (GaP) is demonstrated. The study begins with a comparison between the Raman spectra of the zinc blende and wurtzite phases. Subsequently, the phonon dispersion of wurtzite GaP is calculated, followed by the computation of the two-phonon density of states, in line with the previously established approach.

Measured Zinc-Blend and Wurzite Raman signal under X(ZZ)X polarization

From the measured spectra, additional modes can be identified in the wurtzite structure that are not present in the zinc blende counterpart. This is expected, as the number of atoms per unit cell differs between the two crystal structures. Although the signal from the nanowires is relatively noisy, one can clearly observe pronounced and broader features below 300 cm⁻¹ when compared to the zinc blende sample.

This enhancement suggests:

Increased contribution from acoustic phonons, either as overtones or in mixed modes (e.g. TA+LA).
Relaxation of selection rules due to:
- Finite-size effects in nanowires.
- Differences in phonon dispersion for the wurtzite phase, which may lead to new or shifted low-energy modes.

These modes likely involve zone-boundary acoustic phonons becoming partially Raman-active due to broken translational symmetry.

In order to verify the above claims we first calculate the phonon dispersion and it's projected phonon density of state (PDOS). The result is displayed below:

Phonon dispersion of Wurzite GaP with it's correspond PDOS

It is evident from the phonon dispersion of wurtzite GaP that the degeneracy between the lower and higher branches of the acoustic modes is lifted. This results in distinct features that can be identified in the higher-order Raman spectra.

Difference between Raman spectra of ZB and Wurzite GaP

These features originate from zone-boundary phonons, which become Raman-active due to the symmetry breaking inherent in the nanowire structure. Contrary to the bulk spectra, the nanowires do not exhibit selection rules for the TA and LA modes, confirming the relaxation of these rules. When compared to the two phonon density of state shown below

Raman spectra under three polarization of Wurzite GaP and the first direct measurement of the Two phon density of state with it's correspond 2PDOS

While the correct attribute of each peak to it's corresponding mode is an undergoing work. This experiment showed for the first time higher order Raman phonon spectra of Wurzite GaP nanowire

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