Origins of Stokes Shift in PbS Nanocrystals
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Bibliographic record
Abstract
Stokes shift, an energy difference between the excitonic absorption and emission, is a property of colloidal quantum dots (CQDs) typically ascribed to splitting between dark and bright excitons. In some materials, e.g., PbS, CuInS 2, and CdHgTe, a Stokes shift of up to 200 meV is observed, substantially larger than the estimates of dark–bright state splitting or vibronic relaxations. The shift origin remains highly debated because contradictory signatures of both surface and bulk character were reported for the Stokes-shifted electronic state. Here, we show that the energy transfer among CQDs in a polydispersed ensemble in solution suffices to explain the excess Stokes shift. This energy transfer is primarily due to CQD aggregation and can be substantially eliminated by extreme dilution, higher-viscosity solvent, or better-dispersed colloids. Our findings highlight that ensemble polydispersity remains the primary source of the Stokes shift in CQDs in solution, propagating into the Stokes shift in films and the open-circuit voltage deficit in CQD solar cells. Improved synthetic control can bring notable advancements in CQD photovoltaics, and the Stokes shift continues to provide a sensitive and significant metric to monitor ensemble size distribution.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 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 it