Ionic screening of charged impurities in electrolytically gated graphene: A partially linearized Poisson-Boltzmann model
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Bibliographic record
Abstract
We present a model describing the electrostatic interactions across a structure that consists of a single layer of graphene with large area, lying above an oxide substrate of finite thickness, with its surface exposed to a thick layer of liquid electrolyte containing salt ions. Our goal is to analyze the co-operative screening of the potential fluctuation in a doped graphene due to randomness in the positions of fixed charged impurities in the oxide by the charge carriers in graphene and by the mobile ions in the diffuse layer of the electrolyte. In order to account for a possibly large potential drop in the diffuse later that may arise in an electrolytically gated graphene, we use a partially linearized Poisson-Boltzmann (PB) model of the electrolyte, in which we solve a fully nonlinear PB equation for the surface average of the potential in one dimension, whereas the lateral fluctuations of the potential in graphene are tackled by linearizing the PB equation about the average potential. In this way, we are able to describe the regime of equilibrium doping of graphene to large densities for arbitrary values of the ion concentration without restrictions to the potential drop in the electrolyte. We evaluate the electrostatic Green's function for the partially linearized PB model, which is used to express the screening contributions of the graphene layer and the nearby electrolyte by means of an effective dielectric function. We find that, while the screened potential of a single charged impurity at large in-graphene distances exhibits a strong dependence on the ion concentration in the electrolyte and on the doping density in graphene, in the case of a spatially correlated two-dimensional ensemble of impurities, this dependence is largely suppressed in the autocovariance of the fluctuating potential.
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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 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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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