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The density functional perturbation theory (DFPT) is employed to study the structure, optical phonon modes and dielectric properties for wurtzite GaN and AlN under hydrostatic pressure. In order to calculate accurately the Born effective charges and high frequency dielectric tensors, we utilize two sum rules to monitor this calculation. The calculated optical phonon frequencies and longitudinal-transverse splitting show an increasing with pressure, whereas the Born effective charges and high frequency dielectric tensors are found to decrease with pressure. In particular, we analysed the reason for discrepancy between this calculation and previous experimental determination of pressure dependence of the LO-TO splitting in AlN. The different pressure behavior of the structural and lattice-dynamical properties of GaN and AlN is discussed in terms of the strengths of the covalent bonds and crystal anisotropy. Our results regarding dielectric Grüneisen parameter are predictions and may serve as a reference.

The group-III nitrides GaN and AlN are currently being actively investigated in view of their promising potential for short-wavelength electroluminescence devices and high-temperature, high-power, and high-frequency electronics [

The understanding the effect of pressure on the vibrational properties is quite important. Its knowledge allows one to correlate macroscopic thermodynamic parameters with properties on the atomic scale. The neutron scattering, electron energy loss spectroscopy, IR absorption, Raman spectroscopy, and diamond anvil cell etc. experimentally have been used to study phonons and related properties. Perlin et al. [_{1}) splitting slightly decreased and the LO-TO (A_{1}) splitting increases. Afterwards, Goñi et al. [_{1}) splitting under pressure. However, a decrease of the LO-TO splitting for both A_{1} and E_{1} modes in AlN was estimated in recent Raman measurements of Yakovenko et al. [_{1} and E_{1} modes. Perlin et al. [_{1} (TO), A_{1} (LO) phonon modes and effective transverse charge of wurtzite GaN by Raman scattering and means of tight-binding formalism. In contrast with the extensive range of experimental studies on the pressure effect on the phonon dispersion of semiconductors, theoretical works on the topic are relatively sparse. The pressure dependence of the LO-TO splitting in GaN and AlN is an issue of controversy. In a polar lattice, the splitting of the optical phonon modes is determined by two parameters, Born effective charge of the lattice ions and the screening of the Coulomb interaction, which depends on the electronic part of the dielectric constant in the phonon frequency regime.

In this work, we study the pressure effect on phonon and relevant properties for GaN up to 50 GPa and AlN up to 20 GPa by DFPT computations. Firstly, we calculate and analyse the evolution with pressure of the unit cell shape (i.e., c/a ratio) and unit cell geometry (i.e., internal parameter u) of GaN and AlN. In the following section, it will study pressure dependence of zone-center optical phonon modes and the LO-TO splitting of both the A_{1} and E_{1} modes. Next, it will calculate and discuss the pressure dependence of Born effective charge tensors

The interatomic force constants (IFC’s) describing the atomic interactions in a crystalline solid are defined in real space as [^{ }

Here,

The vibration frequencies

tor

where

The dielectric constant mainly is influenced by two factors which are the electron and phonon,

where

tive of the total electronic energy with respect to a perturbing electric field along directions α and β;

The Born effective charge is defined as the variation of the force on a given atom under the application of an electric field

where

The second sum rule guarantees that the charge neutrality is also fulfilled at the level of the Born effective charges. For every direction

By the above sum rules, we can monitor whether the calculation is well converged with respect to numerical parameters, like the number of plane waves, the sampling of BZ, and the number of points of the exchange-correlation grid.

We use a first-principles pseudopotential method base on the density functional perturbation theory with wave function represented in a plane-wave basis set. This work is performed employing the ABINT package [

In

The calculations were performed in two steps. In the first step, we calculate the total energy of the bulk wurtzite crystal as a function of the unit cell volume. Then, using the definition of pressure,

ficients of

is completely different. The values c/a (u) are remarkably smaller (larger) than the ideal values and decrease

(increase) with rising hydrostatic pressure, with a slope of

× 10^{−4}. Our results for c/a are in reasonable agreement with experimental studies of the lattice constants under pressure [

For most stable wurtzite-type structures c/a ratio and the u parameter are strongly correlated; If c/a decreases, then u increases in such a way that the inequivalent bond lengths R^{(1)} (along the c direction with bond length

^{(2)} are nearly equal, however, the tetrahedral angles are distorted. The bond lengths R^{(1)} and R^{(2)}

(in the hexagonal plane and is threefold degenerate with bond length

with the calculated one (0.3745). In the case of AlN there is, however, a larger deviation between the estimated value (0.3784) and the calculated one (0.3803). This finding can be attributed to the stronger covalent bonding of AlN, which preserves the ideal tetrahedral bond angles.

The pressure dependence of zone-center optical phonon modes and the LO-TO splitting of both the A_{1} and E_{1} modes are plotted in _{1} and E_{1}. In general, the agreement between our calculated values at zero pressure and other theoretical values [_{1} and E_{1} modes are almost constant or even increase slightly with increasing pressure. An increase of the LO-TO splitting for the A1 mode was found Manjόn et al. [

Taking the angular dispersion of the TO modes,

The LO-TO splitting is a function of Born effective charges Z^{*} and infrared dielectric constant

where

modes. It is a measure of the change in electronic polarization due to ionic displacements. For atom k,

Although there are four atoms in the unit cell of the wurtzite structure the nonsymmorphic space group

_{ } | _{ } | _{ } | _{ } | _{ } | ||
---|---|---|---|---|---|---|

GaN AlN | Calc. ^{a } Expt. ^{b } Expt. ^{c } Calc. ^{d } Calc. ^{a } Expt. ^{e } Expt. ^{f } Expt. ^{g } Calc. ^{h} | 3.10 3.9 3.55 3.1 3.05 4.08 4.35 4.05 3.00 | 3.08 3.94 3.3 2.96 5.07 5.33 4.52 3.80 | 3.42 4.4 3.2 3.5 3.48 4.00 3.70 4.00 3.50 | 3.432 3.6 3.50 4.77 3.60 4.00 | |

^{a}This work, ^{b}Ref. [^{c}Ref. [^{d}Ref. [^{e}Ref. [^{f}Ref. [^{g}Ref. [^{h}Ref. [

acoustic sum rule:

tensor are existent. Contrary to the effective charges, the form of the dielectric tensor is determined by the symmetry of the crystal and is expected to be diagonal for the wurtzite structure. The dielectric tensors

The calculated Born effective charge tensors at zero pressure agree well with the experimental data obtained from first-order Raman-scattering experiments [

Our results concerning

The average value

The pressure dependence of

to characterize the pressure dependence of the dielectric constants. For GaN and AlN, we have found that the

perpendicular and parallel components of

In summary, first-principles calculations in the framework of the DFPT are carried out to study the pressure

dependences of structure, phonon and dielectric properties for wurtzite GaN and AlN. Our results show that pressure dependence of the wurtzite parameters c/a are reasonably well, as measured by high pressure X-Ray diffraction studies. The calculated pressure dependence of optical phonon frequencies, Born effective charges, dielectric constants is agreement with other theoretical data available. However, the calculated pressure coefficients of optical phonon frequencies are smaller than other experimental values, and pressure dependence of the LO-TO splittings in AlN between calculated and experimental data is contrary. The pressure dependence of

HuanyouWang,YaqiChen,YalanLi,XiangyanHe, (2015) Dependence of the Structure, Optical Phonon Modes and Dielectric Properties on Pressure in Wurtzite GaN and AlN. Advances in Materials Physics and Chemistry,05,316-324. doi: 10.4236/ampc.2015.58031