Piezoelectric potential in axial (In,Ga)N/GaN nanowire heterostructures

We derive analytic expressions for the built-in electrostatic potential arising from piezo- and pyroelectricity in a cylindrical axial In_xGa${}_{1-x}$N/GaN nanowire (NW) heterostructure. Our simulations show that, for sufficiently thin NWs, a significant reduction of the built-in potential is reached in comparison to the planar heterostructure of the same In content, thickness, and orientation. This specific feature of axial NW heterostructures makes the aspect ratio of the embedded In_xGa${}_{1-x}$N disks an important additional degree of freedom to control the recombination energies. We furthermore show that the magnitude of the polarization potential decreases again above a certain value of the aspect ratio and that the extrema of the potential move from the central axis of the NW towards the side facets when the thickness of the disk is increased. (paper)