Direct determination of the step-edge formation energies of the energetically stable and unstable double-layer step edges of Si(001).

Scanning tunneling microscopy images of 4.5° misoriented double B stepped Si͑001͒ have been analyzed to determine the double-layer step-edge formation energies of the energetically stable double step (B-type͒ as well as the energetically unstable double step (A-type͒. The ordering of the various single-and double-layer step-edge formation energies is in accordance with semiempirical tight-binding-based total-energy calculations performed by Chadi ͓Phys. Rev. Lett. 59, 1691 ͑1987͔͒. Finally, the miscut angle at which the transition between the single-and double-layer stepped surface occurs as calculated using the experimentally obtained step-edge formation energies is in agreement with the experiments. One of the most intriguing and frequently studied surfaces is without any doubt Si͑001͒. The Si͑001͒ surface reconstructs to form rows of dimerized atoms. A rich variety of step structures have been reported in the literature over the past years. Among them are the transition from a hilly single-layer stepped surface to a surface containing coexist-ing areas with wavy single-layer steps and straight single-layer steps, 1 the transition from wavy and straight single-layer steps to straight single-layer steps only 2 and finally the transition from single-layer steps to double-layer steps. 3 Because of the symmetry of the diamond lattice, dimer rows are oriented in two perpendicular directions. Two types of single-and double-layer steps can be discriminated. Single-͑double-͒ layer step edges are denoted S A (D A) when the dimer rows of the upper terrace run parallel to the step edge, whereas they are denoted S B (D B) when the dimer rows run perpendicular to the step edge. From a technological point of view double-layer steps on Si͑001͒ are particularly interesting , because the growth of, e.g., GaAs on single-layer stepped Si͑001͒ gives rise to disorder in the overlayer, whereas double-layer steps allow the growth of coherent Ga and As layers. The first real-space images of double-layer steps on Si͑001͒ were reported by Wierenga, Kubby, and Griffith. 3 Their high-resolution scanning tunneling micros-copy images have confirmed the rebonded geometry as proposed by Chadi. 4 Besides the atomic structure of the various types of step edges of Si͑001͒ Chadi also calculated their formation energies using a semiempirical tight-binding-based total-energy calculation. The S A step edge turns out to have the lowest formation energy because it is the only step edge that does not lead to large strains or to extra dangling bonds. The D A step edge has the highest formation energy. Scanning tunneling microscopy images of …