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