White light-emitting diodes (LEDs) are becoming an alternative general light source, with huge energy savings compared to conventional lighting. However, white LEDs using phosphor(s) suffer from unavoidable Stokes energy converting losses, higher manufacturing cost, and reduced thermal stability. In this dissertation, we demonstrate electrically driven, phosphor-free, white LEDs based on three-dimensional gallium nitride structures with double concentric truncated hexagonal pyramids. Selective area growth using hole, ring and complex mask is systematically studied and we intentionally design patterns that emit white color. The electroluminescence spectra are stable with varying current. The origin of the emission wavelength is studied by cathodoluminescence and high-angle annular dark field scanning transmission electron microscopy experiments. Spatial variation of the carrier injection efficiency is also investigated by a comparative analysis between spatially resolved photoluminescence and electroluminescence. We believe that our results will open a new approach for the fabrication of phosphor-free white LEDs. We also believe that our spatially resolved photoluminescence and electroluminescence data will facilitate the design and engineering of three dimensional structure LEDs.