We have grown stepwise equilibrated graded GexSi1−x(x≤0.20) buffers with threading dislocation densities between 102and 103cm−2in their unstrained cap layers. The Ge content of the buffer was increased stepwise. The equilibrating treatment was performed as aninsituannealing in hydrogen at 1050 °C after each and every layer of the buffer. Subsequently, the buffer was grown relaxed layer by relaxed layer. The extreme low threading dislocation density was present on the whole area of 4 in. wafers. ©1995 American Institute of Physics.