Elastic Relaxation of Coherent InGaN/GaN Interfaces at the Microwire LED Sidewall

Elastic relaxation of the misfit strain via traction-free surface results in a complex three-dimensional strain distribution and morphological modification at the boundary of epitaxial heterostructure. While this phenomenon has been extensively studied for various epitaxial heterostructures, the influence of the interface lattice coherency constraining the strain relaxation has received little attention. Here we show that the inter facial shear stresses arise towards the traction free sidewall while the two complementary strained InGaN and GaN layers in a submicron wire light emitting diode are relaxed to revert their bulk lattice parameters in the near-surface region. The alternating shear stresses with opposite signs achieve mechanical equilibrium by counterbalancing the change in the sign of the in-plane strain in each layer of the near-surface region. A unique nonmonotonic modulation of both normal and shear strain has been detected unambiguously in the experimental strain maps and further corroborated by finite element modeling. An analytical model was developed based on the Airy stress function, which incorporates the superposition of alternating in-plane prestress and the image stress to satisfy the boundary condition at traction-free sidewall. The strain distribution identified in this study is likely prevalent in various nanostructured epitaxial heterostructures with substantial free surface portions, underscoring its importance in accurately understanding surface strain distribution.