Ab initio investigations of the lattice parameters in ZnMgO alloys
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1201-H05-33
Ab initio investigations of the lattice parameters in ZnMgO alloys Markus Heinemann, Marcel Giar and Christian Heiliger I. Physikalisches Institut, Justus Liebig University, 35392 Giessen, Germany
ABSTRACT We perform density functional theory calculations to determine equilibrium lattice parameters of wurtzite Zn1-xMgxO alloys for Mg concentrations x ranging from 0 to 31.25 %. We use the local density approximation (LDA) as well as the generalized gradient approximation (GGA) for the exchange correlation functional. For the lattice constants a and c we find a deviation from Vegard’s law and a constant unit cell volume independent of the Mg concentration.
INTRODUCTION ZnO with a band gap of about 3.4 eV has caught recent attention as a wide band gap semiconductor because it can be used for opto-electronic devices such as light emitting diodes with an operational range from blue to ultraviolet. Therefore, it is advantageous to use band gap modulations which are usually done by substituting bivalent metals (i.e. Mg) for Zinc. Much effort has been made to improve methods for the synthesis of ternary alloys like Zn1–xMgxO. Recent experimental works have successfully investigated the influence of increasing Mg concentration on Zn1–xMgxO thin films grown by pulsed laser deposition (PLD) [1] or plasma assisted molecular beam epitaxy (PAMBE) [2]. The thermodynamic solubility has been found to be within in a range of x=0 and x≈0.4 experimentally [2] as well as theoretically [3, 4]. Also the composition dependence of lattice parameters and the band gap has been investigated in detail. Recent theoretical investigations using the LDA [3] and the GGA [5] state a slightly increasing lattice parameter a and a decreasing lattice parameter c with increasing Mg concentration. These results are consistent with the results obtained by PLD [1]. Since LDA underestimates the lattice parameters, we additionally perform first principle calculations using the GGA method and compare both theoretical methods to experiments.
THEORY AND COMPUTATIONAL METHODS In this work we use a density functional theory (DFT) method to calculate the structural properties of Zn1–xMgxO alloys. We use the projector augmented wave method (PAW) [6-8] implemented in the ABINIT programme package [9-11]. For the exchange correlation we choose the Perdew-Wang 92 LDA functional [12] as well as the Perdew-Burke-Ernzerhof GGA functional [13]. The PAW+LDA and PAW+GGA pseudopotentials treat as valence electrons the 3s2, 3p6, 3d10 and 4s2 electrons for Zn, the 2s2, 2p6 and 3s2 for Mg, and the 2s2 and 2p4 electrons for O.
The calculations are carried out in a 2×2×2 supercell. For the LDA calculations a 3×3×2 kpoint mesh is used in the first Brillouin zone. The energy cut-off for the plane wave basis and for the double grid are set to 820 eV and 1360 eV, respectively. These values ensure convergence of the cell parameters a and c within a range less than a tenth of a percent. For GGA it is necessary to choose a 6×6×4 k-grid and 820 eV and 1900 eV for the plane
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