Phonon Deformation Potential Constants of Wurtzite ZnO: A First-Principles Study
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Phonon Deformation Potential Constants of Wurtzite ZnO: A First-Principles Study Kazuhiro Shimada, Tomoyasu Hiramatsu, and Hitoshi Kato Division of Electrical and Electronic Engineering, College of Science and Engineering, Kanto Gakuin University, Yokohama 236-8501, Japan. ABSTRACT We performed first-principles calculations to obtain the phonon deformation potential (PDP) constants of wurtzite ZnO. The results are in good agreement with available experimental data except for a few PDP constants. We also found that the phonon frequencies of the A1 and B2 modes have relatively stronger nonlinear characteristics than the other modes. INTRODUCTION Group-II oxides, such as MgO and ZnO, have been attractive materials for optoelectronic devices, transparent electronic devices, and piezoelectric devices. The earth abundance of these oxides increases the importance for application to these electronic devices. Crystals of these oxides are grown on suitable alternative substrates, and the lattice mismatch produces a strain in the grown oxides. Evaluation of the strain in the grown oxides is important for the fabrication of electronic devices, because these oxides are considered to have large spontaneous and piezoelectric polarization [1–8]. The strain can be evaluated by observing the change in phonon frequencies using Raman or IR spectroscopy measurements if the values of the phonon deformation potential (PDP) constants are known. However, there are only a few reports on the PDP constants of wurtzite ZnO under biaxial and uniaxial strains [9, 10]. In this paper, we report on the PDP constants of wurtzite ZnO predicted by first-principles calculations based on the density functional theory (DFT). COMPUTATIONAL METHOD Electronic ground states were determined on the basis of DFT [11]. The projectoraugmented-wave (PAW) pseudopotential [12] was used to describe electron-ion interaction in the Zn 3d104s2 and O 2s22p4 valence states. Electronic wave functions were expanded by planewaves up to a cutoff energy of 50 Ry together with a cutoff energy of 300 Ry for a charge density. We used Perdew–Zunger (PZ) parameterization [13] for the local density approximation (LDA) of the exchange-correlation energy. Brillouin zone k point integration was performed using Monkhorst–Pack 10 × 10 × 6 mesh k points [14]. Lattice parameters were fully optimized by minimizing the forces on atoms and the stress tensors within 2 × 10–7 Ry/a.u. and 0.01 GPa, respectively. To calculate the PDP constants, biaxial ( ε xx = ε yy ≠ 0 , ε zz = 0 ) and uniaxial
( ε xx = ε yy = 0 , ε zz ≠ 0 ) strains of ±1–2% were applied to the equilibrium crystal structure, and the internal strain was fully relaxed so that the forces on atoms became less than 2 × 10–7 Ry/a.u. The DFT calculations in this work were performed using the ab initio simulation package Quantum-ESPRESSO [15]. The change in phonon frequencies for applied strain is related to the PDP constants as:
~ Δω = a(ε xx + ε yy ) + bε zz = a~ (σ xx + σ yy ) + b σ zz ,
(1)
~ where a and b are the PDP constants,
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