Abstract: It is provided a hetero epitaxial growth method, a hetero epitaxial crystal structure, a hetero epitaxial growth apparatus and a semiconductor device, the method includes forming a buffer layer formed with the orienting film of an oxide, or the orienting film of nitride on a heterogeneous substrate; and performing crystal growth of a zinc oxide based semiconductor layer on the buffer layer using a halogenated group II metal and an oxygen material. It is provided a homo epitaxial growth method, a homo epitaxial crystal structure, a homo epitaxial growth apparatus and a semiconductor device, the homo epitaxial growth method includes introducing reactant gas mixing zinc containing gas and oxygen containing gas on a zinc oxide substrate; and performing crystal growth of a zinc oxide based semiconductor layer on the zinc oxide substrate.