| Summary: | Lattice parameters and electronic properties of <inline-formula><math display="inline"><semantics><mrow><mi>R</mi><msub><mi>E</mi><mrow><mn>1</mn><mo>−</mo><mi>x</mi></mrow></msub><msub><mi>A</mi><mi>x</mi></msub></mrow></semantics></math></inline-formula>N alloys, where <i>RE</i> = Sc, Y, Lu and <i>A</i> = Al, Ga, and In, have been derived from first principles. The materials are expected to exhibit a linear decrease in cubic lattice parameters and a tendency to a linear increase in band gaps as a function of composition. These effects are connected with a strong mismatch between ionic radii of the <i>RE</i> and group III elements, which leads to chemical pressure in the mixed <i>RE</i> and group III nitrides. The electronic structures of such systems are complex, i.e., some contributions of the <i>d</i>- and <i>p</i>-type states, coming from <i>RE</i> and <i>A</i> ions, respectively, are present in their valence band regions. The findings discussed in this work may encourage further experimental efforts of band gap engineering in <i>RE</i>-based nitrides via doping with group III elements.
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