Although standard GaN device structures used for FETs, light emitters, and detectors have been investigated extensively, device structures relying on the particulars of current transport over barriers in this material system have not received as much attention, to a large extent due to the insufficient quality of the layers. Unless special measures are taken, the defects present in the barrier material induce current conduction paths that preclude any possibility of observing the fundamental current conduction mechanisms. To overcome this impediment, high quality GaN layers, followed by vertical single barrier heterostructures, have been grown on sapphire substrates using epitaxial lateral overgrowth in a metal organic chemical vapor deposition system. With these templates, n-GaN/i-AlxGa1-xN/n-GaN structures with varying barrier width and height have been prepared and tested for their I-V characteristics. The rectification behavior observed is consistent with the barrier design. Since the energy bands are affected by polarization charge, which can be influenced by pressure, I-V measurements under hydrostatic pressure have also been recorded. In this presentation, the details of the measurements and analyses, as well as the pertinent aspects of growth related issues will be discussed.