Abstract
Dye-sensitized solar cells have continued to receive much attention since their introduction by O’Regan and Grätzel in 1991. Modelling charge transfer during the sensitization process is one of several active research areas for the development of dye-sensitized solar cells in order to control and improve their performance and efficiency. Mathematical models for transport of electron density inside nanoporous semiconductors based on diffusion equations have been shown to give good agreement with results observed experimentally. However, the process of charge transfer in dye-sensitized solar cells is complicated and many issues are in need of further investigation, such as the effect of the porous structure of the semiconductor and the recombination of electrons at the interfaces between the semiconductor and electrolyte couple. This paper proposes a new model for electron transport inside the conduction band of a dye-sensitized solar cell comprising of as its nanoporous semiconductor. This model is based on fractional diffusion equations, taking into consideration the random walk network of . Finally, the paper presents numerical solutions of the fractional diffusion model to demonstrate the effect of the fractal geometry of on the fundamental performance parameters of dye-sensitized solar cells, such as the short-circuit current density, open-circuit voltage and efficiency.
Highlights
IntroductionDye-sensitized solar cells (DSSCs) were first introduced by O‘Regan and Grätzel in their fundamental 1991 paper [1], providing a viable low-cost alternative for renewable solar energy
Dye-sensitized solar cells (DSSCs) were first introduced by O‘Regan and Grätzel in their fundamental 1991 paper [1], providing a viable low-cost alternative for renewable solar energy.Functionally, DSSCs operate by a photosensitive dye using absorbed sunlight to inject excited electrons into a nanoporous semiconductor
We note the special case γ = 1 is equivalent to the standard diffusion equation without fractional derivatives, and the efficiency η = 7.03% is in agreement with expected efficiencies for DSSCs [8]
Summary
Dye-sensitized solar cells (DSSCs) were first introduced by O‘Regan and Grätzel in their fundamental 1991 paper [1], providing a viable low-cost alternative for renewable solar energy. DSSCs operate by a photosensitive dye using absorbed sunlight to inject excited electrons into a nanoporous semiconductor This approach relives DSSCs of the need for a costly and high purity semiconductor as opposed to the predominant silicon solar cells that have been at the forefront of solar energy since 1954 [2]. In 2000, Henry and Wearne [14] developed the standard fractional diffusion equation based on continuous-time random-walk (CTRW) models. Henry and Wearne’s model [14], together with the CTRW simulation of TiO2 by Nelson [15], provides motivation for this paper to model DSSCs using fractional partial differential equations. We find that problem is alleviated by the use of a time-fractional derivative on the diffusion term of our equation. The presence of spatially dependent source terms and the combination of Dirichlet and Neumann boundary conditions enjoy a greater level of compatibility with the Caputo fractional derivative [21]
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