Field emission of electrons from spherical conducting carbon nanotube tip including the effect of image force
Bibliographic record
Abstract
An expression for the potential energy and field emission current density function of spherical conducting carbon nanotubes (CNTs), including the effect of image force, corresponding to the expression for the electron transmission coefficient obtained from the solution of the time-independent Schrödinger equation, has been derived. Numerical calculations of the potential energy, transmission coefficient, and the current density function have been carried out for the typical set of CNT parameters. It is found that the potential energy decreases with radial distance when image force is ignored. When image force is incorporated, it increases with radial distance in the beginning and then decreases. The transmission probability and the current density function increase, both with the normalized radial energy and normalized Fermi energy, but both the transmission probability and the current density function are larger in the presence of the image force for given values of the normalized radial energy and the normalized Fermi energy. In addition, the image force decreases the applied value of the field. The field emission current density function of emitted electrons decreases with the spherical CNT tip radius. Some of our theoretical results are in accordance with existing experimental observations.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".