Wavy steps on Si(001)

Abstract

Using low-energy electron microscopy we have found a new phase transition on the Si(001) surface at miscut angles smaller than -0.1°. The surface phase separates into facets with -300 A terrace width, and regions with much larger, wavy terraces. This wavy phase is stabilized by a reduction of surfacestress-induced strain energy. A theoretical study by TersofT and Pehlke compares favorably with our observations.PACS numbers: 6l.14. Hg, 6l.I6.Di, 68.35.Bs, 68.35.Rh The step structure of Si (001) surfaces intentionally miscut towards (ill) has been the subject of many recent studies [1][2][3][4][5][6][7]. This lively interest was sparked by experimental observations of a double-step predominance at larger miscut angles, with a phase transition to singleheight steps at smaller miscut angles. Much less work has been done on samples cut very close to the (001) direction. Diffraction techniques and scanning tunneling microscopy (STM), used with much success on the vicinal surfaces, are not very suitable for small miscuts, due to limited coherence length in the case of diffraction, and due to the limited field of view in STM. In this study we have used low-energy electron microscopy (LEEM) to show that in addition to the double-single-height phase transition at large miscut angles, the surface undergoes another phase transition at very small miscut angles, from straight single-height steps to a coexistence of uniquely spaced straight steps and large-terrace-width wavy steps.Step waviness allows for alternation of (1x2) and (2x1) domains not only normal to, but also parallel with, the global step edges, resulting in a reduction of surface-stress-induced strain energy. These observations are in good agreement with a theoretical study by Tersoff and Pehlke [8].The Si(001) surface exhibits a (2x1) dimer reconstruction. At a single-height atomic step the dimer orientation rotates 90° from (2x1) to (1x2) or vice versa. Experiments [9] and calculations [10] have shown that the surface stress tensor is anisotropic; tensile along the dimer direction, and compressive normal to the dimer. At small miscut angles an alternation of (2x1) and (1x2) domains separated by single-height atomic steps is favorable as it reduces the net stress in the surface. Because of the strong repulsion of S A steps (dimers on the upper terrace normal to the step edge) and SB steps (dimers parallel with the step edge) at close step separation [11], double-height steps become predominant at large miscut angles, although the energy gain is reduced by buildup of a net surface stress. The temperature-miscut phase diagram has been calculated theoretically [6,7], and appears to be in general agreement with experimental results. One of the unresolved issues, however, is the prediction that surface stress will be reduced at very small miscut angles by spontaneous generation of steps, in excess of those imposed by the miscut [5]. Such an effect has not been observed experimentally, and based on our observations we argue that this prediction results from the assu...

Continuum model for the long-range elastic interaction on stepped epitaxial surfaces in2+1dimensions

“…8 with Fig. 6, we can see that by using the traditional continuum approximation m 0 ͑x , y͒, the step bunching instability always dominates and there is no transition from step bunching instability to step undulation instability as l t increases, which does not agree with the experimental observations 36 and the analytical results using discrete step dynamics models. 23,29 This comparison shows that the additional nonlinear terms in our continuum model are crucial to include the discrete features of the stepped surface.…”

“…6 for the dispersion relation for different values of l t in this case. The transition from step bunching instability to step undulation instability as l t increases has been observed in experiments 36 and is shown using discrete step dynamics models. 23,29 Finally, we compare our linear instability results with those using the traditional continuum approximation m 0 ͑x , y͒ in Eq.…”

“…35 In reality, the steps cannot keep straight and tend to meander under many effects including the elastic interactions. 1,4,23,36 The force dipole effect between curved steps on unstrained epitaxial surfaces are relatively well modeled in the frameworks of both the discrete step dynamics 37,38 and the continuum model. 32,37,[39][40][41][42] In the framework of the continuum theory, it is well known that the elastic effect on such a stepped surface of unstrained film is quite different from that on an epitaxial surface above roughening transition temperature due to the discrete structures on the stepped surface.…”

“…Tersoff and Pehlke 23 analyzed step undulation instability of stepped Si͑001͒ surface which is subject to force monopole effect at the steps and their results agree well with the experimental observations obtained by Tromp and Reuter. 36 Houchmandzadeh and Misbah 28 studied the force dipole and force monopole elastic interactions between slightly modulated steps. Kukta and Bhattacharya 43 proposed a 2 + 1 step-flow model that accounts for both the elastic effects and terrace diffusion.…”

Triangular Step Instability and 2D/3D Transition During the Growth of Strained Ge Films on Si(100)

“…These results are consistent with experimental measurements of kink energies by STM 5, and are also in agreement with recent calculations by Xie Fig. 4 Step energy vs. terrace width for SB 3 A steps and SA steps on the Si(100) surface, and a W strained Ge/Si( 100) film surface. a is the surface lattice constant.…”