A simple formulation of the saturation current density in heavily doped emitters
Bibliographic record
Abstract
In a non-uniformly and heavily doped emitter region of a bipolar transistor, the continuity equation and the minority-current equation cannot be solved exactly in closed form. This paper shows that the calculation of minority-carrier current density can be calculated by a simple approach. This approach is based on the average value of the equilibrium hole density p 0 , diffusion constant D p , and lifetime τ p of minority carriers and leads to two coupled differential equations of the first order. These equations can be solved easily and can give a simple expression for the current density. Three definitions of the average values of p 0 , D p , and τ p are used and lead to three expressions for the emitter current density. The latter is identical to the one established by Rinaldi using another mathematical analysis and gives very accurate results for a shallow emitter (W < 1 µm), irrespective of the range peak doping level N(W) and surface-recombination velocity S. On the other hand, the other two expressions lead also to accurate results for the current density depending on the value of the surface-recombination velocity, but cannot be used when N(W) is greater than 10 20 cm 3 and W is superior to 0.1 µm. PACS Nos.: 72.10.d, 72.20.i
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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".