Highlighting non-parabolic bands in semiconductors
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Bibliographic record
Abstract
Abstract The parabolic approximation to the dispersion relation is a simplification that has often been adopted for the electronic band structure of most semiconductors near the edges of the fundamental bandgap. A non-parabolic approximation can be justified which will better describe the properties of semiconductors of narrow bandgaps for which a reduction to a quadratic form is not accurate enough, nor always warranted. It also stands for a better approximation in III–V compounds and for more complex thermoelectric materials. Some of the consequences of adopting non-parabolic bands will be highlighted, as well as approximate expressions for statistical properties. It is emphasized that many properties of semiconductors are not difficult to calculate with non-parabolic bands, which may have a wider range of applications in actual materials. These calculations can then be introduced in solid state physics and statistical physics courses through projects and homework problem sets. Specific examples are discussed designed to clarify basic physics concepts in semiconductors.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it