Smoluchowski ripening and random percolation in epitaxial<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Si</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mi>−</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ge</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>/</mml:mo><mml:mi mathvariant="normal">Si</mml:mi><mml:mn/><mml:mo>(</mml:mo><mml:mn>001</mml:mn><mml:mo>)</mml:mo><mml:mn/></mml:math>islands
Bibliographic record
Abstract
Island size distributions of ripened ${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}/\mathrm{Si}(001)$ $(x=0.3\ensuremath{-}0.7)$ islands exhibit a slow decay at small island sizes and an asymmetric bell-shaped distribution peaked at a large size. We explain the ripening process in ${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}/\mathrm{Si}(001)$ islands by proposing a model based on random percolation and Smoluchowski ripening. Drawing an analogy with percolation theory, we use a shifted average height to represent the time variable, which is also applicable in the Smoluchowski ripening model; this shifted average height is used to analyze size distributions and correlation functions. Critical exponents derived from the site percolation model at $d=3$ agree with our measurements. Island diffusion $D\ensuremath{\propto}{s}^{\ensuremath{-}\ensuremath{\alpha}}$ leading to coalescence events, shows a weak dependence on size s: \ensuremath{\alpha}=0.28\ifmmode\pm\else\textpm\fi{}0.20, attributable to the inverse process of sequential incorporation of atoms at step edges due to the high stress concentration at island terrace perimeters. While random percolation dominates for small sizes regime, Smoluchowski ripening controls the distribution peak at large island sizes. Good agreement is obtained between the model and the measured island size distributions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.009 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".