A procedure for the fabrication of two‐dimensional carrier (electron and hole) gases in modulation doped GeSi/Si heterostructures is presented. The best 4.2 K mobilities measured for the two‐dimensional electron and hole gases are 180 000 cm2/V s and 18 000 cm2/V s, respectively. Recently, two‐dimensional hole gases with mobilities as high as 55 000 cm2/V s have been obtained. The carrier gases are fabricated on top of relaxed, compositionally graded GexSi1−xbuffer layers with low threading dislocation densities (≊106cm−2). Experimental evidence indicates that the function of the graded buffer is to promote dislocation propagation while suppressing nucleation. A comparative analysis is carried out for two dimensional electron gases in GeSi/Si/GeSi and in AlGaAs/GaAs structures. Although molecular beam epitaxy is used to grow the samples, the principle discussed here is independent of growth technique.