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 102 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 JM–G using a f(Ts, Es, ϕ0) function using work function values ϕ0 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(Ts, Es, ϕ0) functions computed for each value of ϕ0 and for Es > 1.2 × 109 V m−1.
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How this classification was reachedexpand
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 | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".