Comparative study of the pressure dependence of optical-phonon transverse-effective charges and linewidths in wurtzite InN

We investigate the hydrostatic pressure dependence of the zone center optical phonons of $c$-plane and $a$-plane wurtzite InN epilayers grown on GaN substrates. The longitudinal to transverse mode splitting for the $A_1$ and $E_1$ modes was found to increase with increasing pressure, whereas the associated transverse effective charge decreases for both modes as $e_T^{*}\left(A_1\right)=2.93–9.9\times {10}^{-3}P$ and $e_T^{*}\left(E_1\right)=2.80–10.6\times {10}^{-3}P$ (in units of elementary charge and $P$ in GPa). These observations are well in line with results for other II–VI, III–V, and group-IV semiconductor compounds as far as the relation between the magnitude and sign of the pressure derivative of $e_T^{*}$ and the bond ionicity is concerned. As the latter increases so does $|\partial e_T^{*}/\partial P|$ with a sign change from positive to negative for bond ionicities around $f_i=0.46$ for compounds with anions belonging to the first row of the Periodic Table. A comparison of the results for InN and other nine tetrahedrally bonded compounds indicate that the pressure behavior of the transverse effective charge is mainly determined by the strength of the Pauli repulsion between cation valence electrons and those of the anion core. We also perform ab initio calculations in order to address the origin of the observed increase in linewidth of the $E_2^{\text{high}}$ mode which is found to arise from a pressure-induced increase in the rate of two-phonon decay processes. This broadening is associated with tuning into resonance of a steep edge in the two-phonon density of states around 460 ${\mathrm{cm}}^{-1}$ with the frequency of the $E_2^{\text{high}}$ mode.

Figure 1

Raman spectra of an $a$-plane and $c$-plane InN epilayer at different pressures and at room temperature. The spectra were vertically shifted for clarity. The full lines show representative least-squares fits to the Raman spectra using Lorentzian line shapes at ambient pressure.

Figure 2

(a) Pressure dependence of the zone-center optical phonons of wurtzite InN measured by Raman scattering. Solid lines are results of least-squares fits to the data points using linear relations. The full (open) symbols correspond to the $a$-plane ($c$-plane) sample. (b) Full width at half maximum (FWHM) for the $E_2^{\text{high}}, A_1\left(\text{TO}\right)$, and $A_1\left(\text{LO}\right)$ modes. The solid lines represent results of the calculations based on the Fermi-resonance model.

Figure 3

Ab inito calculations of the two-phonon density of states (2PDOS) for selected pressures. The corresponding frequency of the $E_1\left(\text{TO}\right), A_1\left(\text{TO}\right)$, and $E_2^{\text{high}}$ is also shown with dashed lines. The arrows indicate the intersection of the $E_2^{\text{high}}$ with the 2PDOS where strong coupling of the $E_2^{\text{high}}$ with second-order modes can be identified. The functions ${\rho }^{\pm }$ correspond to decay processes with phonon wave vectors $k\to k^{\prime }\pm k^{\prime \prime }$.

Figure 4

(a) Hydrostatic pressure dependence of the LO-TO splittings for the polar $A_1$ and $E_1$ modes. Solid lines are results of least-squares fits to the data points using linear relations. (b) Normalized transverse effective charge for both InN polar modes as well as the corresponding data for GaN, AlN, GaAs, ZnO, and SiC.

Figure 5

(a) The pressure derivative of the logarithm of the transverse effective charge as a function of the bond ionicity for several group-IV, III–V, and II–VI semiconductor compounds. The parameters needed for the calculation of the pressure coefficient of the transverse effective charges were obtained from this work and the literature [6, 8, 9, 33, 34]. (b) Values of the electron localization function (ELF) calculated in real space using ab initio pseudopotentials for three different pressures. The In atom is at the origin of the unit cell.