# Effect of uniaxial stress on the polarization of light emitted from GaN AlN quantum dots grown on Si(111) Academic Article

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### abstract

• Cathodoluminescence (CL) measurements of the ground-state excitonic transition of vertically stacked $\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}$ quantum dots (QDs) exhibited an in-plane linear polarization anisotropy in close proximity to microcracks. Microcracks form as a result of a mismatch of the thermal expansion coefficient between the $\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}$ layers and the Si(111) substrate. In close proximity to the cracks, the layers are found to be under uniaxial tensile stress, whereas the film is under biaxial tensile stress for distances greater than $\ensuremath{\sim}3\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ from the cracks. The microcracks serve as an excellent stressor through which the strain tensor of the $\mathrm{Ga}\mathrm{N}∕\mathrm{Al}\mathrm{N}$ QDs can be reproducibly modified for studies of strain-induced changes in the optical and electronic properties by using a spatially resolved probe, such as with CL. Changes in the optical properties of the QDs are attributed to stress-dependent variations of the band edges and the electric field along [0001], which is caused by charge polarization. Such changes in the field will subsequently affect the oscillator strength between electrons and holes. Three-dimensional $6\ifmmode\times\else\texttimes\fi{}6$ $\mathbit{k}\ensuremath{\cdot}\mathbit{p}$ calculations of the QD electron and hole wave functions and eigenstates were performed to examine the influence of biaxial and uniaxial tensile stresses on the polarization-dependent momentum matrix element in varying proximity to the microcracks. The model reveals that a change from biaxial to uniaxial stress alters the admixture of ${p}_{x}$ and ${p}_{y}$ characters of the band edges and the ground-state hole wave function, changes the shape and direction of elongation of the hole isosurfaces, and accounts well for the subsequent anisotropy in the polarization dependent optical transitions.

### publication date

• January 1, 2008