Ab-Initio Calculations for the Electronic Spectra of Cubic and Hexagonal Boron Nitride
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Ab-Initio Calculations for the Electronic Spectra of Cubic and Hexagonal Boron Nitride Guido Satta1 , Giancarlo Cappellini1 , Valerio Olevano2 , Lucia Reining2 1 INFM–-SLACS and Dipartimento di Fisica, Universit`a di Cagliari, Strada Provinciale Monserrato–Sestu Km 0.700, I–09042 Monserrato (Ca), Italy 2 ´ CNRES-CEA–Laboratoire des Solides Irradi´es UMR 7642, Ecole Polytechnique, F-91128 Palaiseau, France ABSTRACT We present state of the art fist-principles calculations for the optical spectra and the loss functions of bulk boron nitride in the cubic (c-BN) and in the hexagonal (h-BN) phases. We start from a DFT-LDA density functional KhonSham bandstructure to investigate the influence of many-body effects beyond the Random Phase Approximation (RPA) on the optical spectra through the inclusion of self-energy and excitonic effects by a GW calculation and the solution of the Bethe-Salpeter equation. For the loss function we only perform RPA calculations. We show to which extent the description of many-body effects is important for a meaningiful comparison with experiment, and when they can be neglected. INTRODUCTION The properties of boron nitride (BN) have motivated detailed theoretical and experimental studies since long time. Many advanced technologies rely on boron nitride and on materials based on it, due to the wide spectrum of properties offered by its polymorphic modifications, two graphitelike and two dense ones. BN is known for its peculiar electronic and mechanical properties. Cubic boron nitride (c-BN) has the diamond crystal structure and a similar lattice constant. Its physical properties, such as extreme hardness, wide energy band gap, low dielectric constant, and high thermal conductivity, are also near to those of diamond. Hexagonal BN (h-BN), is a promising material for compact ultraviolet laser devices [1]. It has a layered crystal structure similar to graphite and is the underlying structure of BN nanotubes, which are systems of growing interest.
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AIM AND THEORETICAL METHODS The minimum experimental band gap is direct in the case of h-BN, and indirect in the case of c-BN. For h-BN a direct band gap of 5.2 ± 0.2 eV associated to the transition H3v -H2c has been estimated[2], while a value of 6.4 ± 0.5 eV for the indirect minimum band gap in c-BN has been inferred from experiment [3], and associated to the Γ15v -X1c transition [4]. However, the value of 6.4 ± 0.5 eV has also often been associated with the optical absorption onset; in fact experimental spectra like transmission [3] or absorption (obtained from reflectance via a Kramers Kronig transformation) [5] show structure starting roughly at that energy. For example, Miyata et al.[6] presented, on the basis of reflectance and transmission measurements, the complex refractive index for c-BN reporting an onset for absorption of 6.1 ± 0.5 eV, whereas Chen et al.[7], measuring samples constituted of BN films with up to 88% of cubic phase, could conclude that the onset should be somewhere above 6.0 eV. The question of many-body effe
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