Influence of excitation frequency on A$_{1}$(LO) and E$_{2}$ Raman modes in In rich In$_{1-x}$Ga$_{x}$N thin films

MBE grown In$_{1-x}$Ga$_{x}$N ($x$ = 0, 0.1, 0.3 and 0.54) thin films with bandgap energies varying from 0.77 to 1.85 eV have been investigated using Raman spectroscopy with 1.58 and 2.41eV excitation energies. The carrier mobility for InN film is 900 cm$^{2}$/V$\cdot $s and decreases with increasing $x$ with its value being 20 cm$^{2}$/V$\cdot $s for In$_{0.46}$Ga$_{0.54}$N . We observe a one-mode behavior of the A$_{1}$(LO) and E$_{2}$ modes. An enhancement in intensity of A$_{1}$(LO) and 2A$_{1}$(LO) replica modes in In$_{1-x}$Ga$_{x}$N films with bandgap energies close to the excitation energy is observed. For samples with $x \quad >$ 0, the A$_{1}$(LO) mode shows a higher intensity relative to E$_{2 }$mode which indicates a resonant enhancement of the A$_{1}$(LO) mode due to Fr\"{o}lich interaction. We find that the energies of longitudinal optical modes (A$_{1}$(LO) and 2A$_{1}$(LO)) vary nonlinearly, unlike the E$_{2}$ mode, with increasing Ga fraction. The width and asymmetry of the A$_{1}$(LO) band is higher for the lower excitation energy (1.58 eV). This is perhaps due to the structural disorder in the deeper regions of the films or due to the distribution of regions with different indium fractions. This may explain the lower carrier mobilities observed in In$_{1-x}$Ga$_{x}$N films with higher values of $x$.