Faceting kinetics of stepped Si(113) surfaces: Dynamic scaling and nano-scale grooves

Time-resolved synchrotron X-ray scattering studies are presented of the faceting kinetics of stepped silicon surfaces misoriented by 2.1° and 1.3° from the cubic [113] direction towards the [001] direction. Following a quench from the high-temperature one-phase region of the orientational phase diagram into the two-phase coexistence region, originally-uniformly-distributed steps rearrange to form a grooved superstructure. Time-resolved surface X-ray scattering measurements reveal the behavior of the grooved surface morphology as a function of time. For times up to several hundred seconds after a quench, the behaviors of the specular and diffuse scattering intensity support a dynamic scaling description of the surface morphology. Specifically, the surface is found to be self-similar in time, with a characteristic groove side (L) varying as a power-law versus time (t): L=L_ot^φ with a coarsening exponent of φ=0.164±0.021≃1/6. φ=1/6 is consistent with a theory which focuses on thermally fluctuating step bunches and takes their collisions as the key growth mechanism. At later times, the groove size approaches a limiting value which depends on the stepped phase misorientation angle. This is consistent with the behavior expected for faceted surfaces in the case that elastic effects are important [V.I. Marchenko, Zh. Eksp. Teor. Fiz. 81 (1981) 1141].