Minimum energy path for the nucleation of misfit dislocations in Ge/Si(0 0 1) heteroepitaxy

Abstract

A possible mechanism for the formation of a 90 • misfit dislocation at the Ge/Si(001) interface through homogeneous nucleation is identified from atomic scale calculations where a minimum energy path connecting the coherent epitaxial state and a final state with a 90 • misfit dislocation is found using the nudged elastic band method. The initial path is generated using a repulsive bias activation procedure in a model system including 75000 atoms. The energy along the path exhibits two maxima in the energy. The first maximum occurs as a 60 • dislocation nucleates. The intermediate minimum corresponds to an extended 60 • dislocation. The subsequent energy maximum occurs as a second 60 • dislocation nucleates in a complementary, mirror glide plane, simultaneously starting from the surface and from the first 60 • dislocation. The activation energy of the nucleation of the second dislocation is 30% lower than that of the first one showing that the formation of the second 60 • dislocation is aided by the presence of the first one. The simulations represent a step towards unraveling the formation mechanism of 90 • dislocations, an important issue in the design of growth procedures for strain released Ge overlayers on Si(100) surfaces, and more generally illustrate an approach that can be used to gain insight into the mechanism of complex nucleation paths of extended defects in solids.

Atomic Scale Formation Mechanism of Edge Dislocation Relieving Lattice Strain in a GeSi overlayer on Si(001)

“…The presence of a step on the film can significantly lower the activation energy for the nucleation of a MD. The presence of a step indeed increases the volume of the region for which some strain is released by the nucleation of a dislocation, it can also act as a stress concentrator 19 and finally, the step may be removed by the nucleation of dislocation 17 . Preliminary calculations indicate that the activation energy for the nucleation of a 60° MD can be lowered to 2 eV by the presence of a double D B step.…”

“…Previous atomistic simulation studies have predicted activation energies larger than 10 eV for the nucleation of MDs in Ge/Si 16 , 17 . Such a high barrier cannot be overcome by thermal fluctuation on a short time scale even at a temperature close to the melting temperature.…”

Global transition path search for dislocation formation in Ge on Si(001)

“…The mechanisms for the formation of 90 • MDs previously presented in the literature require as a first step the formation of a 60 • MD [17] which is usually assumed to occur through the half loop nucleation process. In a previous study of the same system and using the Stillinger-Weber potential, it was shown that the half loop nucleation of a 60 • MD has an activation energy of 54 eV [20].…”

“…The coherent Ge film is 19 layers thick with a p(2 × 1) dimer reconstruction of the surface. This film thickness corresponds to the critical thickness for the formation of a 60 • MD [20].…”

“…In early simulation work, the nucleation of a 90 • MD in a Ge/Si (001) was studied with a quasi-two-dimensional model [19]. Recently, a full threedimensional simulation was carried out for a thin Ge film using the Stilling-Weber empirical potential to describe the atomic interactions [20]. By adding a repulsive bias potential [21,22], the relaxation of a coherent thin Ge/Si(001) film led to the formation of a straight 90 • MD at the Ge/Si interface.…”