A new approach to study organic solar cell using Lambert W-function

doi:10.1016/j.solmat.2004.07.004

Solar Energy Materials and Solar Cells

Volume 86, Issue 2, 1 March 2005, Pages 197-205

https://doi.org/10.1016/j.solmat.2004.07.004 Get rights and content

Abstract

Organic photovoltaic solar cells bear an important potential of development in the search for low-cost modules for the production of domestic electricity. One of the main differences between inorganic and organic solar cells is that photo-excitation in these materials does not automatically lead to the generation of free charge carriers, but to bind electron–hole pairs (exciton) with a binding energy of about 0.4 eV. Till now various numerical methods using approximations have been reported to study different aspects of organic solar cells. For the first time an accurate method using Lambert W-function is presented to study different parameters of organic solar cells.

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: $V = I_{R sh} R_{sh} + I R_{S},$ $I = - I ph + I_{R sh} + I_{d},$ $I_{d} = I_{o} e^{((V - i R_{s}) V_{th} / n)} .$

We are assuming $i = I .$

Solving the above equation we get $\ln (\frac{i + I_{ph}}{I o} - \frac{V - i R_{s}}{I o R_{sh}} + 1) = \frac{V - i R_{s}}{n V_{th}},$ where i and V are terminal current and voltages, respectively, $I_{0}$ , $R_{s}$ , $R_{sh}$ , n and $V_{th}$ 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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A new approach to study organic solar cell using Lambert W-function

Abstract

Introduction

Section snippets

Theory

Conclusion

Chem. Phys. Lett.

Sol. Energy Mater. Sol. Cells

Appl. Phys. Lett.

Sol. Energy Mater. Sol. Cells

Phys. Rev. Lett.

Am. Phys. Soc.-Rap. Comm.

J.Phys.Condens. Matter