A new approach to study organic solar cell using Lambert W-function
Introduction
Organic photovoltaic (OPV) solar cells are emerging as a potential alternative to existing inorganic solar cells. The key property, which makes OPV solar cells so attractive, is the potential of reel-to-reel processing on low-cost substrates with standard coating and printing processes. Up to now main efforts have focused on the improvement of the solar conversion efficiency which has seen a significant jump from a 1% yield 17 years ago [1] to a 5% yield [2]. This opens the perspective of seeing very soon, on a typical 5 yr time scale, OPV solar cells with solar efficiencies in excess of 10%.
Most organic semiconductors are intrinsic semiconductors and the primary excitation is coulomb-bound exciton [3], [4], [5]. Photovoltaic cells made from single organic semiconductors therefore achieve tiny power conversion efficiencies and low incident photon to current or external quantum efficiency (EQE). A high EQE does not guarantee good photovoltaic conversion, but it is a prerequisite. For OPV devices comprising a single polymeric semiconductor layer, EQE are typically below 1%. A solution was only found in 1995 when several groups independently showed that the EQE could be enhanced by several orders of magnitude upon blending two materials with relative preferences for positive and negative charges [6].
Three currently existing type of OPV solar cells are: (a) dye-sensitized solar cells [7] (DSSCs), (b) planar organic semiconductor cells [8], [9], [10] and (c) high surface area or bulk heterojunction cell [11], [12], [13], [14], [15].
Major problems associated with OPV solar cells are: (a) Spectral mismatch — most of the organic semiconductors investigated today absorb in visible range, while the sun has its maximum photon density around 700 nm. (b) Certain intrinsic limited durability of organic compound — when electrons are excited to higher orbitals, antibinding states arise and the probability for decomposition of compound increases. (c) Effective light harvesting in a blended photovoltaic device demands efficient charge separation and transport.
Advantages of organic materials for photovoltaic solar cell applications include: (a) they can be processed using spin coating or doctor blade techniques (wet-processing) or evaporation through a mask (dry-processing). (b) Amount of organic materials are relatively small (100 nm thick films) and large-scale production (chemistry) is easier than for inorganic materials. (c) They can be tuned chemically in order to adjust separately band gap, valence and conduction energies, charge transport, as well as solubility and several other structural properties. (d) The vast variety of possible chemical structures and functionalities of organic materials (polymers, oligomers, dendriomers, organo-minerals, dyes, pigments, liquid crystals, etc.) favor an active research for alternative competitive materials with desired photovoltaic properties.
In the present work an equivalent circuit for organic solar cell is taken from the literature [2]. The diode current equation for that circuit is derived, which is found to be transcendental in nature. The exact explicit solutions are determined using Lambert W-function [16], [17]. Various parameters of organic solar cell are then derived using previously determined solutions.
Section snippets
Theory
The equivalent circuit diagram (ECD) for organic solar cell by Brabec [2] is given in Fig. 1. The voltage V across the cell is given by KVL and KCL equations:
We are assuming
Solving the above equation we getwhere i and V are terminal current and voltages, respectively, ,,, n and are the saturation current density, the serial and parallel resistivity, the diode ideality factor, and the temperature
Conclusion
I–V Characteristics for different parameters are plotted using Lambert W-function. When compared with those plotted in Ref. [6] they are found to be better. This indicates that studies of organic solar cells using Lambert W-function, which provides exact explicit analytical solutions, is a better alternative to study the organic solar cells.
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2021, OptikCitation Excerpt :The popular scenarios for specifying the unknown parameters are the analytical methods, nonlinear optimization algorithms, and a combination of metaheuristics and analytical methods. In the analytical method, the suitable formulation techniques estimate the unknown variables based on datasheets or polarization curves [15–17]. Also, in the nonlinear optimization methods, the solution methods depend on empirically obtained data sets to identify the unknown parameters of solar cells [18–20].