Band gap bowings of ternary REN (RE = Sc, Y, La, and Lu) alloys
Introduction
Semiconductor alloys of group III nitrides exhibit strong band gap () bowings [[1], [2], [3]]. This phenomenon is related to characteristic modifications of structural and electronic properties of a host material, caused by a presence of disorder, e.g., relatively bigger indium ions in aluminum nitride. Resulting alloys exhibit which are significantly lower than the predictions based on the simple linear Vegard’s law.
Another family of nitride semiconductors are REN materials, where RE = Sc, Y, La, and Lu, which adopt the cubic rock salt phase. According to the recent experimental and theoretical investigations, indirect of 0.9–1.3 eV are expected in (Sc; Y;Lu)N [[4], [5], [6], [7], [8], [9]], whereas the direct X–X type of a narrower band gap of 0.6 eV was revealed in theoretical investigations for LaN [[9], [10], [11]].
Several experimental studies reported that solid solutions of group III nitrides with ScN/YN, i.e., Al1−xScxN, Ga1−xScxN, and Al1−xYxN materials [[12], [13], [14], [15], [16], [17]], exhibit rather linear dependences of on Sc/Y contents. However, the band gap of ternary alloys of rare-earth element nitrides was theoretically predicted only for Sc1−xYxN [18,19].
Solid solutions of REN semiconductors may be considered as a new family of promising materials for applications in optoelectronics, in view of their cubic structure and the range of comparable with those available in zinc blende group III arsenides and antimonides [20]. Therefore, some lattice matched heterostructures formed by REN systems and zinc blende group III nitrides may be futher considered.
In this work, the structural and electronic properties of ternary REN alloys, where RE = Sc, Y, La, and Lu, are predicted with the density functional theory (DFT) methods. The local density approximation (LDA) [21] was employed for structural relaxations, whereas the modified Becke–Johnson approach (MBJLDA) [22] was used for the investigations of fully relativistic band structures of materials studied. The discussion of the results is particularly focused on possible bowings in REN alloys and a range of possible to obtain in such novel semiconductor systems.
Section snippets
Computational methods
Structural properties of REN materials have been studied with the use of the Abinit package [23,24], i.e., the equilibrium geometries of the rock salt 222 supercells of ternary REN alloys were found via stresses/forces relaxation. The PAW atomic datasets taken from the JTH table [27] with the Perdew-Wang [21] (LDA) parameterization of the exchange-correlation energy were employed for this task. Next, the Wien2k package [25] was used for calculations of fully relativistic MBJLDA [22] band
Results and discussion
The cubic lattice parameters of parent REN compounds, a = 4.427, 4.822, 5.226, and 4.714 Å calculated here for ScN, YN, LaN, and LuN, respectively, are in accordance with the results reported in previous LDA-based studies [5,9,11,[28], [29], [30]]. It is worth recalling that the experimental lattice parameters are bigger by 1.5% [[31], [32], [33], [34]], which may be expected considering the well-known correspondence between the LDA predictions and the properties of real materials.
Ternary REN
Conclusions
Theoretical investigations based on DFT predicted approximately linear dependences of lattice parameters on compositions of ternary solid solutions of ScN, YN, LaN, and LuN. Very strong bowings predicted for these systems enables design of materials with significantly lower than those of parent REN compounds. The most complex band structures and rapid changes of are expected in La-doped materials. In particular, Sc1−xLaxN systems may exhibit very narrow or even completely closed .
CRediT authorship contribution statement
Maciej J. Winiarski: Conceptualization, Methodology, Investigation, Writing - review & editing. Dorota A. Kowalska: Writing - review & editing.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was supported by the National Science Centre (Poland) under research Grant no. 2017/26/D/ST3/00447. Calculations were performed in Wroclaw Center for Networking and Supercomputing (Project nos. 158 and 175).
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