A method for manufacturing a semiconductor device includes the steps of:
(a) preparing a non-polar single crystal substrate; (b) epitaxially
growing an MgO layer on the non-polar single crystal substrate to a
thickness of 3 nm or thicker to have rocksalt structure at a substrate
temperature of 500.degree. C. to 800.degree. C.; (c) growing on the MgO
layer a low temperature growth layer made of ZnO group material at a
substrate temperature of 500.degree. C. or lower; (d) annealing the low
temperature growth layer above the substrate at a temperature of
700.degree. C. or higher; and (e) epitaxially growing a high temperature
growth layer of ZnO group material on the annealed low temperature growth
layer at a temperature of 600.degree. C. or higher.