Field emission calculations revisited with Murphy and Good theory: a new interpretation of the Fowler–Nordheim plot
Bibliographic record
Abstract
The Murphy and Good (M–G) theory for thermo-field emission [1] was used to calculate the emission current densities over the 300–5000 K temperature range in order to bridge the gap with the simpler zero temperature version of the Fowler–Nordheim (F–N) equation. A comparison between the two sets of data reveals that the F–N equation as it is used in the analysis of F–N plots underestimates the true current density by a factor of 10 2 for all fields known to produce significant current in the case of carbon nanotubes arrays. We propose a new equation for field emission that is consistent with experimental current densities and that can still provide the field enhancement factor β of field emitter arrays. This equation is obtained over the 300–3000 K temperature range by fitting the temperature and field dependences of J M–G using a f ( T s , E s , ϕ 0 ) function using work function values ϕ 0 of 4.5 and 2.6 eV. Our complete parametric equation for the fitted M–G current density is found to apply within a 1% error margin for f ( T s , E s , ϕ 0 ) functions computed for each value of ϕ 0 and for E s > 1.2 × 10 9 V m −1 .
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".