Elastic Variation of Quasi-One-Dimensional Cubic-Phase GaN at Nanoscale

Abstract

The elastic properties of the cubic (c-) phase GaN confined in a nanoscale one-dimensional (1D) v-grooved Si(001) substrate are investigated. Along a ∼900 nm-wide v-groove formed with two facing Si(111)-type facets, submicrometer-wide c-GaN is achieved by the hexagonal-to c-phase (h−c) transition from the h-GaN which plays the role of an interlayer in its epitaxy on Si. The resulting nonplanar stack of c-GaN/h-GaN on Si has complicated stress distribution. This work focuses on the elastic properties the c-GaN, which are critically affected by its low dimensionality, and presents experimental evidence for it with an analytical stress modeling. A reciprocal lattice map reveals that the c-GaN in each groove consists of several micrometer-long single crystals which are microscopically tilted from each other in their serial coalescence, as its unit structures. The corresponding micrometer-scale lateral correlation length, d c , results from the h−c transition that is interrupted by the groove imperfections generated in fabrication and the stress fluctuation in the misoriented h-GaN interlayer. The modeling suggests that d c is long enough to induce the tensile stress, dominating with the longitudinal strain parallel to the groove which is ∼2.5× the transverse strain, and the c-GaN can be regarded as a serial array of a quasi-1D unit structures which retain such anisotropic stress resulting from their geometrical shape. The Poisson ratio of the c-GaN in <110> is ∼0.21, close to 0.26 from a theoretical prediction. The variation of the c-phase bandgap under the given tensile stress is addressed.