We have studied the structural properties of single and multiple layer
s of self-organised Ge islands grown on Si. The X-ray reflection curve
s of the single layers indicate the transition from 2D to 3D growth fo
r Ge layer thicknesses of 5.33-5.67 ML, in excellent agreement with ph
otoluminescence observations. Because of the strain fields extending i
nto the surrounding Si barrier, the dots of multiple layers are strong
ly correlated in the vertical direction. A recent theoretical model al
so predicts an increasing lateral correlation of the dots with increas
ing numbers of dot layers. In reciprocal space maps we not only observ
ed such a kind of lateral ordering, but also indications for an anisot
ropy of the interdot spacing in the [100] and [110] directions.