Reconciling Nano- and Micro-Scale VLS Growth by Including Multi-Scale Supersaturation: A Growth Model Applied to Lateral Ge Films on Si
Bibliographic record
Abstract
Extensive work on metal-catalyst-assisted vapor-liquid-solid (VLS) growth has been focused on nanometer-scale wires (nanowires) and there have been several studies modelling the effect of diameter, growth time, surface diffusion, etc. on these nanowires. In this context of nanowires, since the catalyst is so small, one could and researchers have ignored the effect of the requirement to supersaturate the catalyst. In this work, an analytical growth model is presented to explain the effect of supersaturation on the size of micrometer-scale catalysts and resulting films grown via the VLS mechanism by chemical vapor deposition by introducing the idea of “multi-scale” supersaturation (supersaturation as a function of catalyst size). The proposed model is derived from a materials balance relation which reduces to the nanowire equation (without the need for considering catalyst supersaturation) for sufficiently small radii. By including the supersaturation term, the model predicts the existence of the maximum size range of film at certain growth conditions which is not present in the pre-existing models. The model could also explain the “induction time” required for the catalyst to reach a supersaturation state to begin VLS growth. More importantly, it agrees with the available experimental data of VLS lateral heteroepitaxy of micrometer-scale Ge films on Si substrate which suggests that 0.0379 mol/cm3of Ge atoms are required to supersaturate the Au catalyst at the growth conditions studied (375 °C). This new perspective on the multi-scale supersaturation effect unravels the role of the supersaturation term that had been hidden for more than half a century.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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".