A two-stage cryocooler includes an ambient temperature portion, a first-stage temperature portion, and a second-stage temperature portion. 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. establishing the amplification of the repeater as a function of the frequency in a frequency band, and observing the magnitude of wave-like variations in the established frequency response, this magnitude constituting a measure of the stability margin such that an increasing magnitude corresponds to a decreasing stability margin.