Unifying description of the wurtzite-to-rocksalt phase transition in wide-gap semiconductors: The effect ofdelectrons on the elastic constants

Abstract

The mechanism responsible for the wurtzite-to-rocksalt structural phase transition in zinc oxide has been studied through the ab initio calculations of the full phonon properties. We derive a new and general path of the transformation from the parent to the daughter phase which involves an intermediate tetragonal phase. This hypothesis has been tested through analogous calculations on other wide-gap semiconductors, and confirmed in GaN and InN, but not in AlN and SiC. As a consequence of these results, we formulate a general prediction on the effect of d-electrons on the structural and elastic properties of wurtzite semiconductors under pressure.

Phonon pressure coefficients and deformation potentials of wurtzite AlN determined by uniaxial pressure-dependent Raman measurements

“…Similar to the case of C 44 , the C 66 constant is indeed not softening in AlN on the application of hydrostatic pressure up to four times the corresponding wurtzite-to-rocksalt transition pressure, while both elastic constants are indeed softening in GaN and even more rapidly diminishing in ZnO. This scaling behavior directly mirrors the lack of d-electrons in AlN, whose presence in GaN and ZnO is discussed as the origin of the C 44 and C 66 softening [48]. Hence, despite the rather similar absolute values of the elastic constants in GaN and AlN [32,49], the E low 2 mode directly reveals fundamental differences between the nature of the bonds for both material systems, which is also related to a particular effect regarding their phase transition mechanisms [22,48].…”

“…However, the correspondingã values scale from 0.77(3) for ZnO, over 0.55(5) for GaN [11], towards 0.34(3) cm −1 /GPa for AlN, providing a strong motivation for calculating the uniaxial pressure dependence of the related shear elastic constants. This directly measured scaling behavior does not only nicely match the order of the hydrostatic pressure dependencies of the shear elastic constants in ZnO, GaN, and AlN [48] but also their absolute values that scale from e.g. 40, over 123, towards 131 GPa for C 66 [32,49,50].…”

“…This scaling behavior directly mirrors the lack of d-electrons in AlN, whose presence in GaN and ZnO is discussed as the origin of the C 44 and C 66 softening [48]. Hence, despite the rather similar absolute values of the elastic constants in GaN and AlN [32,49], the E low 2 mode directly reveals fundamental differences between the nature of the bonds for both material systems, which is also related to a particular effect regarding their phase transition mechanisms [22,48].…”

“…For ZnO and GaN the E low 2 is softening under the application of hydrostatic pressure in clear contrast to the case of AlN. Calculations reported by Saitta et al [48] allow a better understanding of this context based on the pressure dependence of the shear elastic constant C 66 that strongly affects the E low 2 mode due to its bond-bending nature [22]. Similar to the case of C 44 , the C 66 constant is indeed not softening in AlN on the application of hydrostatic pressure up to four times the corresponding wurtzite-to-rocksalt transition pressure, while both elastic constants are indeed softening in GaN and even more rapidly diminishing in ZnO.…”

Aspect Ratio Dependence of the Elastic Properties of ZnO Nanobelts

“…[23][24][25] Considering a maximum load F of 200 nN used in our experiments, E* ) 75 GPa, a tip radius of 60 nm, eq 3 would give a contact radius of 5 nm, and thus a maximum pressure of only 3 GPa. Indeed, no hysteresis or sudden force variations have been observed in our experiments when the tip is approaching or retracting during the indentation process.…”