Abstract: A compound semiconductor substrate having at least one compound semiconductor layer epitaxially grown on a silicon single crystal substrate, wherein the silicon single crystal substrate has a surface on which the compound semiconductor layer is epitaxially grown, the surface being inclined at an off angle of not more than 1 deg to a (100) plane of silicon crystal; and the compound semiconductor layer has a free or top surface having a roughness of 3 nm or less in terms of a mean square roughness, Rms, determined by an atomic force microscopic measurement in a view field area of 10 .mu.m.times.10 .mu.m or a roughness of 10.5 nm or less in terms of a maximum height difference, Ry.