Lattice mismatched epitaxy and methods for lattice mismatched epitaxy are provided. The method includes providing a growth substrate and forming a plurality of quantum dots, such as, for example, AlSb quantum dots, on the growth substrate. The method further includes forming a crystallographic nucleation layer by growth and coalescence of the plurality of quantum dots, wherein the nucleation layer is essentially free from vertically propagating defects. The method using quantum dots can be used to overcome the restraints of critical thickness in lattice mismatched epitaxy to allow effective integration of various existing substrate technologies with device technologies.