SOME ASPECTS OF THE ELECTRONIC DENSITY OF STATES OF AMORPHOUS SEMICONDUCTORS
Bibliographic record
Abstract
Recent progress in analysis of properties of a simple tight binding Hamiltonian, appropriate to study of role of topological disorder in determining properties of amorphous semiconductors, is reviewed. The band structure generated by such a Hamiltonian for diamond cubic structure is compared with a more realistic calculation for Ge. The generalisation that electronic properties of solids depend chiefly on nature and degree of short range order and are little affected by loss of long range order has in recent years achieved a proverbial status without being at all well understood in theoretical terms. It has of course for long been an important component of chemist's rather empirical point of view. On other hand, solid state theorists, accustomed to dealing with systems with essentially perfect long range order, have been somewhat dismayed to be reminded that this does not seem to play a very important role in most physical properties, however important it may be in facilitating their mathematics. In particular, this point has been driven home by observation of band gaps in amorphous semiconductors 1), equal to or even greater than those of corresponding crystals, despite fact that the conventional methods of band theory have not yet succeeded in calculating a density of states with a band gap 2) for such systems. The conventional methods of band theory are founded on Bloch's Theorem. Without this powerful first step in mathematics we might appear to be doomed to be cast adrift in a sea of approximations. This is however not entirely so -- as always, some elegant, exact, and quite simple mathematical truths lie behind empirical generalisation. We shall review below some exact results for a Hamiltonian which provides a somewhat idealised model of an amorphous semiconductor such as Si or Ge. The Hamiltonian is not capable of giving a really accurate description of these semiconductors. On other hand it is not so oversimplified as to be irrelevant to a qualitative consideration of their properties. Our approach is therefore complementary to that of Klima and McGill3), since we have sought exact results for a crude Hamiltonian while they have sought approximate results for a more accurate Hamiltonian.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".