A method for forming III-N structures of desired nanoscale dimensions is disclosed. The method is based on, first, providing a material to serve as a shell inside which a cavity can be formed, followed by using epitaxial growth to fill the cavity with III-N semiconductor(s). Filling a cavity of specified shape and dimensions with a III-N semiconductor results in formation of a III-N structure which has shape and dimensions defined by those of the cavity in the shell, advantageously enabling formation of III-N structures on a nanometer scale without having to rely on etching of III-N materials. Ensuring that at least a part of the III-N material in the cavity is formed by lateral epitaxial overgrowth allows obtaining high quality III-N semiconductor in that part without having to grow a thick layer. Disclosed III-N nanostructures can serve as foundation for fabricating III-N device components, e.g. III-N transistors, having non-planar architecture.