By exploiting an intense correlation exhibited between the distribution of lattice distortions in a wafer and the distribution of the threshold voltages of field effect transistors, the distribution of the lattice distortions in the wafer is reduced, thereby to mitigate the distribution of the characteristics of the semiconductor elements in the wafer. The difference between the maximum value and minimum value of the lattice distortions of a GaAs single crystal at a normal temperature is set to at most 4×10−5 and the density of Si atoms contained in the GaAs single crystal is set to at most 1×1016 cm−3, whereby the characteristics of semiconductor elements whose parent material is the GaAs single crystal can be made uniform.