Theoretical Prediction of the Impact of Phosphorus Doping on the Elastic Constants of Silicon
Bibliographic record
Abstract
Accurately controlling the mechanical properties of silicon is essential for developing high-performance micro-devices and systems. In this study, we investigate the influence of phosphorus doping on the elastic constants of silicon across a wide temperature range using a combination of tight-binding simulations and deformation potential theory. The mechanical properties were derived using Keyes’s framework integrated with Fermi–Dirac statistics. The Goodwin–Skinner–Pettifor functional form was applied to estimate dopant-induced stress potentials and their effect on lattice stiffness. In particular, we investigated the change in elastic constants and their temperature dependence under ultra-high doping concentrations. The results show a monotonic decrease in c11 and a non-monotonic increase in c12 with both temperature and doping, while c44 remains relatively unaffected, consistent with experimental and theoretical studies. These changes are attributed to anisotropic carrier redistribution among conduction band valleys and strain-modulated interactions between valleys. The novelty of this work lies in the explicit, atomistically informed calculation of deformation potential constants using tight-binding parameters specific to phosphorus doping in silicon, enabling the accurate prediction of temperature-dependent elastic constants and anisotropic mechanical behaviour in emerging microsystem applications.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 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".