An apparatus includes a crystalline substrate, a layer of a first group III-nitride located on a planar surface of the substrate, and a layer of a second group III-nitride located over the layer of the first group III-nitride. The first and second group III-nitrides have different alloy compositions. The layer of second group III-nitride may have a pattern of columnar holes or trenches therein. The apparatus may include a plurality of pyramidal field-emitters that include the second group III-nitride.