| Among all the advanced semiconductor growth techniques, molecular beam epitaxy provides the greatest ease of growing complex semiconductor multilayered structures, with a precise control of the thickness and the composition. Here we present a three-dimensional continuum nonequilibrium theory for the epitaxial growth of an elastic film that allows for stress and diffusion within the film surface. Our approach relies on recent ideas concerning configurational forces, and is based on (i) standard (Newtonian) balance laws for forces and moments together with an independent balance for configurational forces; (ii) atomic balances, one for each species of mobile atoms, in the absence or presence of lattice constraint; (iii) a mechanical version of the second law that accounts for temporal changes in free energy, energy flows due to atomic transport, and power expended by both standard and configurational forces; and (iv) thermodynamically consistent constitutive relations for the film surface.; We derive partial differential equations that govern the evolution of the film surface. These equations serve for the investigation of initial (prior to formation of dislocations) morphological and compositional instability that occurs during the epitaxial growth of binary substitutional alloy film. The main reasons for the loss of stability are a mismatch between the lattice constants of substrate and adsorbate, a difference in size of the species atoms leading to solute strain, and different surface mobilities and chemical energy levels. These effects often interact, thus leading to a complex picture.; We perform a linear stability analysis, and consider the dependence of the growth rate of instability on the wave number. This dispersion relation is a function of many parameters that describe the elasticity and chemistry of the film and substrate. The analysis permits us to recover the classical results for Asaro-Tiller-Grinfeld instability, as well as more recent achievements predicting compositional segregation. Finally, we investigate the response of the instability towards a new chemical parameter (ratio of chemical energies of the species), and show that, under certain conditions, the instability behavior is determined by this parameter. |
