Self-consistent solution of Schrodinger's and Poisson's equations in carrier confining heterostructures
Bibliographic record
Abstract
A self-consistent solution of the Schrdinger and Poisson equations is developed to calculate the energy levels and energy band offsets of a carrier confining heterostructure which is of finite extent bound by either vacuum/air or metallic contacts.The Schrdinger equation is solved in the Haftree approximation in which the band edge is the superposition of a 'bulk' band potential and a potential resulting from the presence of ionized donor (or acceptor) atoms and charge carriers distributed throughout the device.Our self-consistent method involves decoupling the Schrdinger and Poisson equations by developing an approximate expression for the dependence of the electron density on the potential energy.The finite element method (FEM), employing Hermite polynomial basis functions, is used to solve the Schrdinger and poisson equations, We present a simple integration by pafts method to derive the required finite element equations' Multiple well structures at different temperatures and donor densities are used as examples.ii pursue this thesis topic and putting up with my disappearing for periods of time as the priorities of my full time job demanded my attention.
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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".