Methods of forming ternary III-nitride materials include epitaxially growing ternary III-nitride material on a substrate in a chamber. The epitaxial growth includes providing a precursor gas mixture within the chamber that includes a relatively high ratio of a partial pressure of a nitrogen precursor to a partial pressure of one or more Group III precursors in the chamber. Due at least in part to the relatively high ratio, a layer of ternary III-nitride material may be grown to a high final thickness with small V-pit defects therein. Semiconductor structures including such ternary III-nitride material layers are fabricated using such methods.