such as gan algan alingan or other iii v group compounds or cdte zno zns or other ii vi group compounds as shown in fig1 the epitaxial substrate 1 according to the invention includes a crystalline substrate 10 the crystalline substrate 10 has an epitaxial surface 102 different from the prior arts the epitaxial surface 102 of the crystalline substrate 10 is nano rugged and non patterned it is noted that similar to the epitaxial substrates with patterned surfaces of the prior arts the epitaxial substrate 1 according to the invention can also benefit the compound semiconductor material in lateral epitaxy in one embodiment the epitaxial surface 102 of the crystalline substrate 10 has an average surface roughness ra in a range from 100 nm to 400 nm in one embodiment the epitaxial surface 102 of the crystalline substrate 10 has a mean peak to valley height rz in a range from 50 nm to 350 nm in practical application the crystalline substrate 10 can be formed of sapphire sic gan gaas zno si scalmgo 4 srcu 2 o 2 ysz yttria stabilized zirconia lialo 2 ligao 2 li 2 sio 3 ligeo 3 naalo 2 nagao 2 na 2 geo 3 na 2 sio 3 li 3 po 4 li 3 asa 4 li 3 vo 4 li 2 mggeo 4 li 2 zngeo 4 li 2 cdgeo 4 li 2 mgsio 4 li 2 znsio 4 li 2 cdsio 4 na 2 mggeo 4 na 2 zngeo 4 na 2 znsio 4 or other commercial materials provided for epitaxy referring to fig2 a through 2c and.