model for the layer chemical potential per atom has been proposed by Markov as: where is the bulk chemical potential of the adsorbate material, is the desorption energy of an adsorbate atom from a wetting layer of the same material, the desorption energy of an adsorbate atom from the substrate, is the per atom misfit dislocation energy, and the per atom homogeneous strain energy. In general, the values of , , , and depend in a complex way on the thickness of the growing layers and lattice misfit between the substrate and adsorbate film. In the limit of small strains, , the criterion for a film growth mode is dependent on . VW growth: (adatom cohesive force is stronger than surface adhesive force) FM growth: (surface adhesive force is stronger than adatom cohesive force) SK growth can be described by both of these inequalities. While initial film growth follows an FM mechanism, i.e. positive differential μ, nontrivial amounts of strain energy accumulate in the deposited layers. At a critical thickness, this strain induces a sign reversal in the chemical potential, i.e. negative differential μ, leading to a switch in the growth mode. At this point it is energetically favorable to nucleate islands and further growth occurs by a VW type mechanism. A thermodynamic criterion for layer growth similar to the one presented above can be obtained using a force balance of surface tensions and contact angle. Since the formation of wetting layers occurs in a commensurate fashion at a crystal surface, there is often an associated misfit between the film and the substrate due to the different lattice parameters of each material. Attachment of the thinner film to the thicker substrate induces a misfit strain at the interface given by . Here and are the film and substrate lattice constants, respectively. As the wetting layer thickens, the associated strain energy increases rapidly. In order to relieve the strain, island formation can occur in either a dislocated or coherent fashion. In dislocated islands, strain relief arises by forming interfacial misfit dislocations. The reduction in strain energy accommodated by introducing a dislocation is generally greater than the concomitant cost of increased surface energy associated with creating the clusters. The thickness of the wetting layer at which island nucleation initiates, called the critical thickness , is strongly dependent on the lattice mismatch between the film and substrate, with a greater mismatch leading to