Influence of Spontaneous and Piezoelectric Polarizations on the Lattice Dynamics of III-Nitride Structures
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Influence of Spontaneous and Piezoelectric Polarizations on the Lattice Dynamics of III-Nitride Structures Jérôme Gleize, Jean Frandon, Marie A. Renucci, and Friedhelm Bechstedt1 Laboratoire de Physique des Solides, UMR 5477 CNRS, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse cedex 4, France 1 Institut für Festkörpertheorie und Theoretische Optik, Friedrich Schiller Universität, D-07743 Jena, Germany. ABSTRACT The influence of pyroelectric and piezoelectric polarizations on the lattice dynamics of strained III-nitride based structures is investigated within a macroscopic framework. New relationships between stress and strain are derived, which take into account the piezoelectric fields, which appear in the strained III-nitride layers. Consequently, the strained phonon frequencies in such systems differ from those calculated within the elasticity theory framework. In the case of strained, free-standing GaN/AlN superlattices grown along the [0001] axis, the difference of the spontaneous polarizations of GaN and AlN also contributes to the change in the effective strain along the growth direction. The corresponding shift of the zone center phonon frequencies of GaN and AlN might be negligible or significant, depending on the value of the ratio of the GaN and AlN layer thickness. INTRODUCTION The III-group nitrides, such as wurtzite GaN and AlN, exhibit strong piezoelectric properties, as well as a spontaneous polarization in the absence of strains [1,2]. These effects are of primarily importance for the tailoring of the optical properties of strained III-nitride based heterostructures, such as quantum wells (QWs) and superlattices (SLs) [3,4]. The strain-induced shifts of the phonon frequencies of the constituent materials can give a quantitative insight on the strains in such structures [5,6]. However, a macroscopic description of the equilibrium configuration of such systems should take into account strain-induced piezoelectric fields. We recently addressed this issue in the case of pseudomorphic GaN/AlN SLs grown along the [0001] direction on a given substrate [7]. On the other hand, such systems are not realistic, since real SLs, which often contain a large number of periods, are in a free-standing state [8]. We apply, in this paper, the macroscopic model we developed in our previous study to the case of free-standing GaN/AlN SLs, with particular emphasis on the influence of the GaN and AlN layer thickness ratio on the strains and phonon frequencies. MODEL We consider an infinite wurtzite GaN/AlN SL grown along the [0001] direction, taken along the z direction. The SL layers are labeled with an index j (j=1 for GaN and j=2 for AlN). Due to the lattice mismatch between GaN and AlN, we expect the GaN and AlN layers to undergo a biaxial strain, inducing piezoelectric polarizations in the SL layers. Assuming that the strains do not change the symmetry of the layers, the polarization is directed along the z direction. Taking into account the permanent polarization Pz(,jsp) , the total polarization in t
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