Design rules for dislocation filters

The efficacy of strained layer threading dislocation filter structures in single crystal epitaxial layers is evaluated using numerical modeling for (001) face-centred cubic materials, such as GaAs or Si_1-xGe _x, and (0001) hexagonal materials such as GaN. We find that threading dislocation densities decay exponentially as a function of the strain relieved, irrespective of the fraction of threading dislocations that are mobile. Reactions between threading dislocations tend to produce a population that is a balanced mixture of mobile and sessile in (001) cubic materials. In contrast, mobile threading dislocations tend to be lost very rapidly in (0001) GaN, often with little or no reduction in the immobile dislocation density. The capture radius for threading dislocation interactions is estimated to be approximately 40 nm using cross section transmission electron microscopy of dislocation filtering structures in GaAs monolithically grown on Si. We find that the minimum threading dislocation density that can be obtained in any given structure is likely to be limited by kinetic effects to approximately 10 ⁴-10⁵cm^-2.