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Self-assembly of steps and vacancy lines during the early stages of heteroepitaxy
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Image of FIG. 1.
FIG. 1.

(Color online) Surface unit cells for the stretch (a) and squeeze (b) configurations reported in Ref. 3. The Ge film is shown in black, and the Si substrate in gray. The island size is and the distance between an step and a VL is . Configuration (b) requires another parameter to denote the distance between the two VLs of the unit cell. The periods along the [110] direction are and for models (a) and (b), respectively. The periodic length of the cells in the direction is . The horizontal arrows schematically show the force monopoles and dipoles at the steps and VLs, respectively.

Image of FIG. 2.
FIG. 2.

(Color online) Interaction energy of steps and VLs obtained from atomistic simulations in the stretch configuration [(a), triangles up] and in the squeeze pattern [(b), triangles down], along with the fitting curves given by Eq. (5) and Eq. (8), respectively. The dashed curves show the interaction energy between VLs [refer to Eqs. (2) and (7)] in the two configurations. The island size is in both cases, and the -VL distance in case (b) is .

Image of FIG. 3.
FIG. 3.

(Color online) Surface energy contributions (at ) and (at , ) corresponding to the arrays of line defects shown in Figs. 1(a) and 1(b), respectively. The case of free VLs (i.e., without steps) is also plotted for comparison. In the stretch and free configurations, the VL-VL distance is simply the period along [110], . For the squeeze case, the VL-VL separation is , as shown in Fig. 1(b). The curves correspond to the analytical expressions given in Eqs. (2), (4), and (6), while the data points are calculated from atomistic simulations. The optimum VL separations determined from STM experiments (expt.) (see Ref. 3) are shown along with error estimates.


Generic image for table
Table I.

Defect formation energies and interaction strength parameters computed using the Tersoff interatomic potential (see Ref. 4).


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Self-assembly of steps and vacancy lines during the early stages of Ge∕Si(001) heteroepitaxy