Antiband instability on vicinal Si(111) under the condition of diffusion-limited sublimation

Abstract

In this paper, we investigate the antiband instability on vicinal Si(111) surfaces with different angles of misorientation. It is known that prolonged direct current-annealing of Si(111) results in the formation of antibands; i.e., the step bunches with the opposite slope to the primary bunches. We provide a theoretical description of antiband formation via the evolution of the atomic steps' shape. We also derive a criterion for the onset of the antiband instability under the conditions of sublimation controlled by slow adatom surface diffusion. We examine this criterion experimentally by studying the initial stage of the antiband formation at a constant temperature of 1270 • C while systematically varying the applied electromigration field. The experiment strongly supports the validity of the derived theoretical criterion and indicates the importance of accounting for the factor of critical field in the theoretical modeling of step bunching or antiband instabilities. Deduced from the comparison of theory and experiment, the Si surface atoms' effective charge cannot exceed double the elementary charge, set by the lower limit of kinetic characteristic length d s = 0.3 nm. Using d s = 1.7 − 4.5 nm draws values of the effective charge in line with the values reported in earlier studies.

Real-time observation of self-interstitial reactions on an atomically smooth silicon surface

“…The decay kinetics of the isolated islands and holes was described by power law dependence with an exponent value of 0.78 [54]. The evidence of the diffusion-limited mechanism of the surface mass transport was found in studies of surface morphology transformations during sublimation [56,57] and epitaxial growth [58].…”

Revealing electromigration on dielectrics and metals through the step-bunching instability

“…The terrace marked by an arrow in Fig. 2 captures all the essential stages of crossing steps evolution driven by electromigration as seen on Si(111) [84,85]. Initially, the crossing steps are curved in a long-S shape (marked 2), and in the terrace plane, the sign of their slope remains the same along the entire length.…”

“…The shape evolution of these crossing steps gives rise to new morphologies such as antibands (marked 1 in Fig. 2), which can be described as secondary step bunches running along the terrace edges with slopes opposite to the surface global offcut direction [82][83][84]. As the terraces widen the shape of the crossing steps gradually develops in order to compensate for the gradient of the adatom concentration across terraces, via the appropriate variation of the step curvature [83][84][85].…”

“…2), which can be described as secondary step bunches running along the terrace edges with slopes opposite to the surface global offcut direction [82][83][84]. As the terraces widen the shape of the crossing steps gradually develops in order to compensate for the gradient of the adatom concentration across terraces, via the appropriate variation of the step curvature [83][84][85]. Analysis of the shape can reveal the relative rates of adatom surface diffusion and adatom exchange with the crystal phase, and thus distinguish between the diffusion and the step-kinetic limited SB dynamics [84,85].…”

“…As the terraces widen the shape of the crossing steps gradually develops in order to compensate for the gradient of the adatom concentration across terraces, via the appropriate variation of the step curvature [83][84][85]. Analysis of the shape can reveal the relative rates of adatom surface diffusion and adatom exchange with the crystal phase, and thus distinguish between the diffusion and the step-kinetic limited SB dynamics [84,85]. Notably, crossing steps on Al 2 O 3 (0001) have heights predominantly from 2.4 to 6.5 nm corresponding to 2-5 C-lattice constants (within 0.2 nm error) which is much higher than the 0.2-0.3nm typical height of monatomic steps.…”