Materials for Organic Solar Cells
The quest for clean and sustainable energy sources drives the development of solar cell technology. Organic photovoltaics (OPV), in which sunlight is harvested by organic species, have several appealing advantages: they are made of earth-abundant elements; they can be manufactured cheaply over large areas via solution deposition and printing techniques; they may be deposited on oddly shaped and/or flexible surfaces; they are lightweight; and most importantly, their electronic properties may be tuned over a broad and almost continuous range through chemical and structural modification. However, the relatively low efficiency of OPV compared to inorganic solar cells, leaves much to be desired.
In a typical organic solar cell, the absorption of a photon promotes an electron into an unoccupied state, leaving a positively charged hole in the valence band. This electron-hole pair, bound by electrostatic attraction, is called an exciton. In order to generate free charge carriers, which can conduct electrical current, the excitons must be separated. Charge separation is driven by the potential energy difference at an interface between donor and acceptor species.
The efficiency of organic solar cells may be significantly enhanced by harnessing singlet fission (SF), a quantum mechanical process, whereby one photogenerated singlet (opposite spin) exciton splits into two triplet (same-spin) excitons. This process enables the generation of two free carriers from one photon. Conversely, triplet-triplet annihilation, the reverse process of SF, may be harnessed to improve the efficiency of solar cells by enabling the absorption of photons with energies below the band gap, which would otherwise be lost. Presently, very few materials are known to exhibit SF or TTA. Our goal is to discover new SF and TTA materials to advance the realization of more efficient organic solar cells.
In order for SF to be thermodynamically favorable the singlet exciton energy must be larger than the energy of two triplet excitons (Es > 2Et). In addition, to facilitate intermolecular SF in molecular crystals it is considered desirable for the singlet exciton to have a charge transfer character, where the electron and hole probability densities are concentrated on different molecules. Both the thermodynamic driving force for SF and the exciton character depend not only on the single molecule’s properties, but also on the crystal structure.
To calculate excited-state properties we use many-body perturbation theory within the GW approximation and the Bethe-Salpeter equation (GW+BSE). To determine the degree of charge transfer character (%CT) of an exciton wave-function produced from a GW+BSE calculation, we have developed the double-Bader analysis method. We then formulated a two-dimensional descriptor that correlates with SF efficiency. Based on this descriptor, quaterrylene is a promising SF candidate and both polymorphs of perylene are promising for TTA.
SF has been observed in the orthorhombic form of rubrene. We examined two lesser known monoclinic and triclinic polymorphs of rubrene and found that their crystal packing induces significantly different coupling between neighboring molecules, which modifies the fundamental band gap and band dispersion. This further affects the character of the singlet exciton wave-function. In particular, monoclinic rubrene has a charge transfer singlet exciton, considered favorable for SF, whereas in the orthorhombic form the singlet exciton has a mixed charge transfer and Frenkel character with some of the electron probability density (yellow) concentrated around the hole (red). In terms of the thermodynamic driving force for SF, monoclinic rubrene is very close to pentacene, the quintessential SF material.