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Carrier Transport01:21

Carrier Transport

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The generation of electrical current in semiconductors is fundamentally driven by two mechanisms: drift and diffusion. These processes are essential for the functionality and performance of semiconductor-based devices.
Drift Current:
The drift of charge carriers is started by an external electric field (E). Charged particles, such as electrons and holes, experience an acceleration between collisions with lattice atoms. For electrons, this results in a drift velocity (vd) given by:
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Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model01:09

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Various dissolution theories provide insight into the factors that influence the dissolution rate. Danckwerts' Model suggests that turbulence, rather than a stagnant layer, characterizes the dissolution medium at the solid-liquid interface. In this model, the agitated solvent contains macroscopic packets that move to the interface via eddy currents, facilitating the absorption and delivery of the drug to the bulk solution. The regular replenishment of solvent packets maintains the...
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Passive Diffusion: Overview and Kinetics01:17

Passive Diffusion: Overview and Kinetics

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Passive diffusion is a critical process that allows small lipophilic drugs to cross the cell membrane along a concentration gradient. This mechanism's efficiency depends on four primary factors: the membrane's surface area, the drug's lipid-water partition coefficient, the concentration gradient, and the membrane's thickness.
When administered orally, drugs establish a substantial concentration gradient between the gastrointestinal (GI) lumen and the bloodstream, expediting...
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Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models00:57

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Physiological pharmacokinetic models, often called flow-limited or perfusion models, typically assume a swift drug distribution between tissue and venous blood, creating a rapid drug equilibrium. This premise is based on the idea that drug diffusion is extremely fast, and the cell membrane presents no barrier to drug permeation. In this scenario, where no drug binding occurs, the drug concentration in the tissue equals that of the venous blood leaving the tissue. This greatly simplifies the...
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Related Experiment Video

Updated: Dec 16, 2025

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation
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A Fractional Diffusion Model for Dye-Sensitized Solar Cells.

B Maldon1, N Thamwattana1

  • 1School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia.

Molecules (Basel, Switzerland)
|July 2, 2020
PubMed
Summary

This study introduces a new fractional diffusion model for electron transport in dye-sensitized solar cells. The model reveals how the fractal geometry of titanium dioxide (TiO2) impacts cell performance, including efficiency.

Keywords:
dye-sensitized solar cellselectron densityfractional diffusionmathematical modellingsubdiffusiontitanium dioxide

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Area of Science:

  • Materials Science
  • Renewable Energy
  • Nanotechnology

Background:

  • Dye-sensitized solar cells (DSSCs) are a key area of renewable energy research.
  • Accurate modeling of charge transfer is crucial for improving DSSC performance.
  • Existing diffusion models for electron transport in nanoporous semiconductors show limitations.

Purpose of the Study:

  • To propose a novel fractional diffusion model for electron transport in the conduction band of TiO2-based DSSCs.
  • To incorporate the random walk network and fractal geometry of TiO2 into the model.
  • To investigate the impact of TiO2's fractal nature on DSSC performance parameters.

Main Methods:

  • Development of a new mathematical model based on fractional diffusion equations.
  • Numerical solutions were employed to analyze the model.
  • Simulation of electron transport within the nanoporous TiO2 semiconductor.

Main Results:

  • The fractional diffusion model effectively simulates electron transport in TiO2.
  • Demonstrated the significant influence of TiO2's fractal geometry on electron transport dynamics.
  • Quantified the effect of fractal geometry on key performance metrics like short-circuit current density and open-circuit voltage.

Conclusions:

  • Fractional diffusion modeling provides a more accurate representation of electron transport in nanoporous TiO2.
  • The fractal characteristics of TiO2 play a critical role in determining DSSC efficiency.
  • This model offers a pathway for optimizing DSSC design and performance through control of semiconductor nanostructure.