First Principles Study of the Optical Properties of Alkaline-Earth Metal Nitrides
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Computational Materials Science 49 (2010) 400–406 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci First principles study of the optical properties of alkaline-earth metal nitrides M. Dadsetani *, R. Beiranvand Physics Department, Faculty of Science, University of Lorestan, Lorestan, Iran article info abstract Article history: A detailed analysis of the optical properties of alkaline-earth metal nitrides (Be3N2,Mg3N2 and Ca3N2) has Received 10 January 2010 been performed, using the full potential linearized augmented plane wave (FP-LAPW) method within Received in revised form 9 May 2010 density functional theory. The exchange correlation potential is treated by the generalized gradient Accepted 11 May 2010 approximation within Perdew et al. scheme. The real and imaginary parts of the dielectric function Available online 12 June 2010 (x), the optical absorption coefficient I(x) the refractive index n(x), the extinction coefficient k(x) and the electron energy loss function are calculated within the random phase approximation (RPA). Keywords: The calculated results show a qualitative agreement with the available experimental results in the sense Metal nitrides that we can recognize some peaks qualitatively, that is, ones that are due to single particle transitions. Optical properties DFT Furthermore, the interband transitions responsible for the structures in the spectra are specified. The FP-LAPW metal s states and nitrogen p states play the major role in these optical transitions as initial and final states, respectively, for Mg3N2 and Be3N2. In the case of Ca3N2, where Ca has d levels lying near the Fermi level, the Ca d states are mostly final states. The effect of the spin–orbit coupling on the optical properties is also investigated, and it is found to be quite small, especially in the low energy region. The dielectric constants are calculated and compared with the available experimental results. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction In the optical frequency range, Soto et al. [12,17,18] have measured the electron energy loss spectra of Be3N2 and Mg3N2 to determine The alkaline-earth metal nitrides (M3N2, M = Be, Mg and Ca) the dielectric constant, and de la Cruz et al. [13] have measured form a very important wide band gap semiconductor with a cubic the absorption coefficient, the refractive index, and the extinction bcc structure and the space group of Ia3(206) at normal conditions coefficient of beryllium nitride. But for Mg3N2 and Ca3N2, to our [1–3]. There are two crystallographic structures of Be3N2: a-Be3N2, knowledge, there is not yet any experimental results on these quan- cubic bcc with 40 atoms per cell, and b-Be3N2, hexagonal close tities in the optical frequency range. Our calculated results could packed with 10 atoms per cell [4]. The first structure is stable be- serve as a reference for future experimental work on this compound. tween 20 °C and 1200 °C, which changes to the hexagonal form On these materials, from theoretical point of view, there exist a over 1400 °C. The calcium nitride exists in various structures, number of first principles calculations in terms of their stability, viz., a-Ca3N2 (reddish-brown) [5], b-Ca3N2 (black) [6], c-Ca3N2 and electronic as well as structural properties [4,10,11,19–25].To (yellow) [7], and the different high pressure phase (yellow) [8].It the best of our knowledge, there is no theoretical research on opti- is further known that Mg3N2 and a-Ca3N2 compounds are iso- cal properties (i.e., real and imaginary parts of dielectric functions, structure [9]. They are characterized by their wide band gap, high reflectivity, absorption and electron energy loss function). More- thermal conductivity and large bulk modulus [10,11]. These inter- over, it seems that there is a lack of both experimental and theoret- esting properties make them potential materials for the use in the ical data on the optical properties of alkaline-earth metal nitrides, development of solid state illuminations, optoelectronic applica- and no systematic research on the optical properties of these com- tions, and display and communication devices [12]. They are tech- pounds have been reported. nologically important materials, with a band gap in the ultraviolet In this work, we have investigated a full range of optical prop- region, which can be used as an alternative to the aluminum ni- erties of alkaline-earth nitride, including real and imaginary parts tride, the aluminum–gallium nitride [12], and the beryllium for of the dielectric function, the absorption coefficient, and the energy some optical applications [13]. loss function, using the full potential linearized augmented plane The available experimental studies on the optical properties of wave (FP-LAPW) method with the generalized gradient approxi- these materials are mostly limited to the optical band gap [14–16]. mation (GGA) for the exchange correlation potential, within the density functional theory. The outline is as follows: a brief description of our calculation * Corresponding author. Tel./fax: +98 661 2201335. E-mail addresses: [email protected], [email protected] (M. Dadsetani). method is given in Section 2. In Section 3, we have given the 0927-0256/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2010.05.028 M. Dadsetani, R. Beiranvand / Computational Materials Science 49 (2010) 400–406 401 detailed band structure of alkaline-earth nitrides, which is needed WIEN2K [26] implementation of the method which allows the for optical studies. Optical properties through the study of the inclusion of local orbitals in the basis, improving upon linearization imaginary and real parts of the dielectric function, the absorption, and making possible a consistent treatment of the semicore and refraction spectra, and EELS are discussed in Section 4. A brief sum- valance states in an energy window, hence ensuring proper orthog- mary and conclusions are given in Section 5. onality. The exchange correlation potential within the GGA is cal- culated using the scheme of Perdew et al. [27]. The convergence min 2. Calculation method parameter RMT Kmax (the product of the smallest of the atomic sphere radii RMT and the plane wave cutoff parameter Kmax) which The calculations presented in this work were performed using controls the size of the basis sets in these calculations, was set to 8. the FP-LAPW method. In this method no shape approximation on The maximum l quantum number for the wavefunction expansion the potential or the electronic charge density is made. The calcula- inside the atomic sphere is confined to lmax = 10. The Gmax param- À1 tions of the electronic and optical properties have been done rela- eter was taken to be 14.0 Bohr . Brillouin-zone (BZ) integrations tivistically with and without the spin–orbit coupling. We use the within self-consistency cycles were performed via a tetrahedron (a) (b) (c) 10 8 4 8 6 2 6 4 4 0 2 2 0 0 -2 -2 -2 -4 -4 -4 -6 Energy (eV) Energy -6 -8 -6 -10 -8 -8 -12 -10 -14 -10 -12 -16 -18 -14 -12 Γ Δ H N Σ Γ Λ P Γ Δ H N ΣΓ Λ P Γ Δ H N ΣΓ Λ P (d) (e) 60 Be N 50 3 2 without so 40 with so 1.0 30 0.8 Be s 20 N1 s 10 0.6 N2 s 1200 0.4 100 Mg3N2 without so 0.2 80 with so 0.01.0 60 0.8 Be p 40 N1 p 0.6 N2 p 20 DOS (State/eV) DOS (State/eV) 0.4 3000 0.2 250 Ca3N2 without so 0.0 200 with so -15 -10 -5 0 510 150 Energy (eV) 100 50 0 -15 -10 -5 0 5 10 Energy (eV) Fig. 1. The electronic band structures of Be3N2 (a), Mg3N2 (b) and Ca3N2 (c) along with the total DOS for all three compounds (d) and partial DOS for Be3N2. 402 M. Dadsetani, R. Beiranvand / Computational Materials Science 49 (2010) 400–406 method [28], using 24 K points in the irreducible BZ. For the calcu- contributions to the occupied part of the DOS come from the N lation of the optical properties however, a denser sampling of the 2p and 2s states. BZ was needed, where we used 60 K points. The muffin-tin radius The first structure in the low lying energy side of the DOS con- of alkaline-earth metal (M) and nitrogen atoms (N) were chosen as sists of a narrow peak centered on À10.64 eV for Ca3N2 and M N (RMT; RMT) = (1.6, 1.5), (1.5, 1.5) and (2.3, 2.1) a.u. for Be3N2,Mg3N2 À12.00 eV for Mg3N2, and a broad peak about À15 eV for Be3N2. and Ca3N2, respectively. All these values have been chosen in a way This structure originates from Ns states, corresponding to the low- to ensure the convergence of the results. The calculation for the est lying bands in Fig. 1. These bands are lower in energy for Be3N2 optical properties has been done with and without spin–orbit cou- and Mg3N2 than Ca3N2 by around 2.7 and 1.0 eV, respectively. The pling to ascertain if spin–orbit coupling has any dramatic influence structure of the spin–orbit splitting and its amount are not consid- on the optical properties. We find that spin–orbit interaction has a erable in this region. minor influence on the optical properties. The next structure which, in the absence of spin–orbit coupling, is separated from the first by a gap of 5.64 eV for Be3N2, 7.22 eV for Mg3N2, and 8.55 eV for Ca3N2, is a broad peak that is situated be- tween À7.5 eV and the Fermi level, corresponding, to the valence 3.