scholarly journals Applicability of the High Field Model: A Preliminary Numerical Study

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 275-282 ◽  
Author(s):  
Carlo Cercignani ◽  
Irene M. Gamba ◽  
Joseph W. Jerome ◽  
Chi-Wang Shu
Keyword(s):  
High Field ◽  
Field Model ◽  
Numerical Study ◽  
Macroscopic Model ◽  
Kinetic Regime ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
New Model ◽  
The One ◽  
Transition Kinetic

In a companion presentation, we have discussed the theory of a mesoscopic/ macroscopic model, which can be viewed as an augmented drift-diffusion model. Here, we describe how that model is used. The device we consider for this presentation is the one dimensional GaAs n+−n−n+ structure of length 0.8μm. First, a full Hydro- Dynamic (HD) model, proven reliable when compared with Monte Carlo simulations, is used to simulate the device via the ENO finite difference method. As applied to the full device, the new model is not necessarily superior to traditional Drift-Diffusion (DD). Indeed, when we plot the quantity η= μ0E/kT0/m, where μ0 is the mobility constant and E=−ϕ′ is the electric field, we verify that the high field assumption η › 1, required for the high field model, is satisfied only in an interval given approximately by [0.2, 0.5]. When we run both the DD model and the new high field model in this restricted interval, with boundary conditions of concentration n and potential ϕ provided by the HD results, we demonstrate that the new model outperforms the DD model. This indicates that the high field and DD models should be used only in parts of the device, connected by a transition kinetic regime. This will be a domain decomposition issue involving interface conditions and adequate numerical methods.

scholarly journals Applicability of the High Field Model: An Analytical Study Via Asymptotic Parameters Defining Domain Decomposition

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 135-141 ◽  
Author(s):  
Carlo Cercignani ◽  
Irene M. Gamba ◽  
Joseph W. Jerome ◽  
Chi-Wang Shu
Keyword(s):  
Electric Fields ◽  
High Field ◽  
Field Model ◽  
Debye Length ◽  
Mean Free Path ◽  
Field Approximation ◽  
Macroscopic Model ◽  
Boltzmann Transport ◽  
Kinetic Transition ◽  
Macroscopic States

In this paper, we present a mesoscopic-macroscopic model of self-consistent charge transport. It is based upon an asymptotic expansion of solutions of the Boltzmann Transport Equation (BTE). We identify three dimensionless parameters from the BTE. These parameters are, respectively, the quotient of reference scales for drift and thermal velocities, the scaled mean free path, and the scaled Debye length. Such parameters induce domain dependent macroscopic approximations. Particular focus is placed upon the so-called high field model, defined by the regime where drift velocity dominates thermal velocity. This model incorporates kinetic transition layers, linking mesoscopic to macroscopic states. Reference scalings are defined by the background doping levels and distinct, experimentally measured mobility expressions, as well as locally determined ranges for the electric fields. The mobilities reflect a coarse substitute for reference scales of scattering mechanisms. See [9] for elaboration.The high field approximation is a formally derived modification of the augmented drift-diffusion model originally introduced by Thornber some fifteen years ago [25]. We are able to compare our approach with the earlier kinetic approach of Baranger and Wilkins [5] and the macroscopic approach of Kan, Ravaioli and Kerkhoven [20].

Getting Over Athens

2018 ◽  
Author(s):  
Nicolas Wiater
Keyword(s):  
Roman Empire ◽  
The Other ◽  
The Political ◽  
New Model ◽  
Dionysius Of Halicarnassus ◽  
The One

This chapter examines the ambivalent image of Classical Athens in Dionysius of Halicarnassus’ Roman Antiquities. This image reflects a deep-seated ambiguity of Dionysius’ Classicist ideology: on the one hand, there is no question for Dionysius that Athenocentric Hellenicity failed, and that the Roman empire has superseded Athens’ role once and for all as the political and cultural centre of the oikoumene. On the other, Dionysius accepted Rome’s supremacy as legitimate partly because he believed (and wanted his readers to believe) her to be the legitimate heir of Classical Athens and Classical Athenian civic ideology. As a result, Dionysius develops a new model of Hellenicity for Roman Greeks loyal to the new political and cultural centre of Rome. This new model of Greek identity incorporates and builds on Classical Athenian ideals, institutions, and culture, but also supersedes them.

scholarly journals Flexible categorization in perceptual decision making

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Genís Prat-Ortega ◽  
Klaus Wimmer ◽  
Alex Roxin ◽  
Jaime de la Rocha
Keyword(s):  
Decision Making ◽  
Network Models ◽  
Drift Diffusion Model ◽  
Perceptual Decision Making ◽  
Drift Diffusion ◽  
Perceptual Decision ◽  
Attractor Dynamics ◽  
Attractor Model ◽  
Sensory Evidence ◽  
Winner Take All

AbstractPerceptual decisions rely on accumulating sensory evidence. This computation has been studied using either drift diffusion models or neurobiological network models exhibiting winner-take-all attractor dynamics. Although both models can account for a large amount of data, it remains unclear whether their dynamics are qualitatively equivalent. Here we show that in the attractor model, but not in the drift diffusion model, an increase in the stimulus fluctuations or the stimulus duration promotes transitions between decision states. The increase in the number of transitions leads to a crossover between weighting mostly early evidence (primacy) to weighting late evidence (recency), a prediction we validate with psychophysical data. Between these two limiting cases, we found a novel flexible categorization regime, in which fluctuations can reverse initially-incorrect categorizations. This reversal asymmetry results in a non-monotonic psychometric curve, a distinctive feature of the attractor model. Our findings point to correcting decision reversals as an important feature of perceptual decision making.

scholarly journals Informing cognitive abstractions through neuroimaging: The neural drift diffusion model.

2015 ◽  
Vol 122 (2) ◽  
pp. 312-336 ◽  
Author(s):  
Brandon M. Turner ◽  
Leendert van Maanen ◽  
Birte U. Forstmann
Keyword(s):  
Diffusion Model ◽  
Drift Diffusion Model ◽  
Drift Diffusion

Incorporating photon recycling into the analytical drift-diffusion model of high efficiency solar cells

2014 ◽  
Vol 116 (19) ◽  
pp. 194504 ◽  
Author(s):  
Matthew P. Lumb ◽  
Myles A. Steiner ◽  
John F. Geisz ◽  
Robert J. Walters
Keyword(s):  
Solar Cells ◽  
Diffusion Model ◽  
High Efficiency ◽  
Drift Diffusion Model ◽  
Drift Diffusion ◽  
High Efficiency Solar Cells ◽  
Photon Recycling
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