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

Elastic relaxation of lattice misfit strain via traction-free surface results in complex 3D strain distribution and morphological modification at the boundary of epitaxial heterostructure. While this phenomenon is extensively studied, the influence of the interface coherency constraining the strain relaxation has received little attention. Here it is shown that the interfacial shear stresses arise toward the traction free sidewall of microscale light emitting diode (LED) wires while the two complementary strained InGaN and GaN layers are relaxed to revert their bulk lattice parameters near the sidewall. The 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 is detected unambiguously in the strain maps and corroborated by finite element modeling. An analytical model is developed based on the Airy stress function, which incorporates the superposition of alternating in-plane pre-stress and the image stress to satisfy the boundary condition. The resultant complex strain fields in microscale LEDs, where surface emission is dominant, alter strain-induced piezoelectric polarization near the surface, significantly affecting electro-optical efficiency and resulting in spectral broadening and/or wavelength shifts in emitted light.