Hierarchical Modeling of Heat Transfer in Silicon-Based Electronic Devices
Bibliographic record
Abstract
Abstract A hierarchical model of heat transfer for the thermal analysis of electronic devices is presented. The integration of participating scales (from nanoscale to macroscales) is achieved by (i) estimating the input parameters and thermal properties to solve the Boltzmann transport equation (BTE) for phonons using molecular dynamics (MD), including phonon relaxation times, dispersion relations, group velocities, and specific heat, (ii) applying quantum corrections to the MD results to make them suitable for the solution of BTE, and (iii) numerically solving the BTE in space and time subject to different boundary and initial conditions. We apply our hierarchical model to estimate the silicon out-of-plane thermal conductivity and the thermal response of an silicon on insulator (SOI) device subject to Joule heating. We have found that relative phonon contribution to the overall conductivity changes as the dimension of the domain is reduced as a result of phonon confinement. The observed reduction in the thermal conductivity is produced by the progressive transition of modes in the diffusive regime (as in the bulk) to transitional and ballistic regimes as the film thickness is decreased. In addition, we have found that relaxation time expressions for optical phonons are important to describe the transient response of SOI devices and that the characteristic transport regimes, determined with Holland and Klemens phonon models, differ significantly.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".