Since Shuji Nakamura, Hiroshi Amano, and Isamu Akasaki won the 2014 Nobel prize in Physics owing to theircontributions on the invention of efficient blue GaN light emitting diodes, GaN became an even more appealingmaterial system in the research field of optoelectronics. On the other hand, quantum structures or low-dimensionalstructures with properties derived from quantum physics demonstrate superior and unique electrical and opticalproperties, providing a significant potential on novel optoelectronic applications based on the employment of quantumconfinement.   In 2012, our research team at Linköping University utilized pyramid templates, which is an established approach toform quantum structures, to successfully grow GaN pyramids with InGaN hybrid quantum structures, includingquantum wells, quantum wires, and quantum dots. This growth enabled site-controlled pyramids based on selectivearea growth (SAG). After numerous studies on the photoluminescence properties, the mature and controlled growthtechnique was proposed to be adapted for fabrication of AlGaN pyramids on which GaN hybrid quantum structurescan be hosted.   This thesis is dedicated to the subsequent problems of the growth of AlGaN pyramids. It was found that there wasan undesired deposition of a considerable thickness on top the desired AlGaN pyramid with GaN multiple quantumwells. In this thesis, two different directions are explored to find the key solution with a potential of furtheroptimization. On one hand, the growth parameters such as precursors cut-off, carrier gas during cooling, temperatureholding, cooling pressure, III/V ratio, and the possible effect of GaN surfaces are investigated. However, due to theactual inherent properties of the metal-organic chemical vapor deposition reactor used, no promising parameter tuningcan been identified. On the other hand, from post-growth point of view, a KOH aqueous etching solution exhibits apositive result toward removing the undesired deposition. This etching process is suggested to be further optimized toachieve the final goal of eliminating the undesired deposition.