Electron transport with the McKelvey–Shockley flux method: The effect of electric field and electron–phonon scattering
Bibliographic record
Abstract
The McKelvey–Shockley (McK–S) flux method is a semi-classical transport theory that captures ballistic and non-equilibrium effects and can treat carrier flow from the nano-scale to the macro-scale. This work introduces a revised formulation of the McK–S flux equations for electron transport, in order to resolve the energy dependence of the fluxes, capture the effect of electric field, and include acoustic/optical phonon scattering. This updated McK–S formalism is validated by simulating electron transport across a finite-length semiconductor under the influence of a constant electric field under varying conditions, from ballistic to diffusive and from near-equilibrium to non-equilibrium, and benchmarked against solutions of the Boltzmann transport equation (BTE). The McK–S results display good agreement with those of the BTE, including the directed fluxes and heating profiles, with the electron density showing larger differences when far from equilibrium. Compared to other more rigorous techniques, the McK–S flux method is physically intuitive and computationally efficient and, thus, well suited to treat systems that are complex and/or span multiple length scales.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 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".