A model is developed which predicts an ordering of the dislocation multiplication sources in Si1−xGex/Si heteroepitaxial systems. This ordering results in an increased probability for threading dislocations to annihilate. It is shown that, following certain selection rules for dislocation multiplication, an infinite three-dimensional network of misfit dislocations can develop throughout the compositionally graded Si1−xGexlayer. The model is consistent with existing experimental data.