Phonon dispersions of cubic GaN. The dispersions produced by DFT are denoted by the solid line while the one in dashed line is produced by the ABCM.
Phonon dispersions of wurtzite InN. The dispersions produced by DFT are denoted by the solid line while the one in dashed line is produced by the ABCM. Note that the former adopted the same kind of pseudo-potential (PBE) but with a higher electronic wavefunction energy cutoff to account for more atoms inside the unit cell while the latter used force constants from the cubic counterpart. This figure is aimed to show how ABCM worked for a wurtzite lattice.
Schematic graph of the atomic arrangement inside one unit cell. The direction of z-axis is the same as the  direction. Note that planes perpendicular to the z axis are of no quantum confinement.
Schematic graph for the quantum well device. The periodic boundary conditions imply an infinite number of InN-GaN layers inside the device. The phonon bands derived apply best to the region well away from the substrate and surface.
Phonon dispersion for the InN-GaN MQW with 10 sub-unit cells. Note that the flatness along Γ-A direction is due to the confinement.
Phonon dispersion for the InN-GaN MQW with 2 sub-unit cells. Note that the confinement along the Γ-A direction is reduced compared with Figure 5 . The frequencies splitting at Γ point can be explained by the inequivalent dipole moment viewed from different directions (Γ-A or Γ-M). This dipole moment is expected to be present in nitride compounds in the wurtzite phase.
Vibrations in the InN-GaN MQW with 2 sub-unit cells at Γ-A direction. The stacking order along the Γ-A direction is N1/In1/N2/In2/N3/Ga1/N4/Ga2. A horizontal arrow (in blue) denotes a longitudinal mode while a vertical (in red and black) one denotes a transverse mode. The cross mark in the plot represents the mixed mode. Note that the arrows only show the vibrating direction and do not contain information on magnitudes. The arrows in red and black denote a different vibration pattern within the plane perpendicular to the Γ-A direction.
Specific heat for the InN-GaN MQW with 10 sub-unit cells. The specific heat curve of the MQW falls between the curves of InN and GaN. The specific heats of the bulk materials at 300 K are and for GaN and InN, respectively. In the previous work, specific heat of GaN was measured within (Ref. 34 ) while that of InN was around . 35,36
Thermal conductivity at c direction for the InN-GaN MQW and the bulk counterparts. Though the thermal conductivity of bulk GaN is quite high, the overall thermal conductivity of the MQW is limited by that of the bulk InN.
Frequency dependent thermal conductivity at c direction for the 10 sub-unit cells InN-GaN MQW. Only the low frequency phonon modes contribute to the thermal conductivity at this direction.
Lattice constants and frequencies at high symmetry points for cubic InN and GaN. The lattice constant was calculated by minimizing the system energy.
Force constants for the ABCM. All the FCs are in unit N/m except for which was calculated by taking the lattice constant and electron charge as 1. The subscript n and p denote a negatively or positively charged target ion. is the ion-ion interaction force constant while and are the force constants for anion-BC and cation-BC, respectively. β denotes the bond bending force constant while is the Coulombic pre-factor.
Wurtzite InN phonon frequencies at high symmetry points (in unit THz). Data of the column this work were generated by the modified ABCM. The Inelastic X-ray Scattering (IXS) is from the Serrano et al. 27
Wurtzite GaN phonon frequencies at high symmetric points (in unit THz). Data of the column this work were generated by the modified ABCM.
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