Roles of binding energy and diffusion length of singlet and triplet excitons in organic heterojunction solar cells

Abstract

The influence of binding energy and diffusion length on the dissociation of excitons in organic solids is studied. The binding energy and excitonic Bohr radius of singlet and triplet excitons are calculated and compared using the dissociation energy of 0.3 eV, which is provided by the lowest unoccupied molecular orbital offset in heterojunction organic solar cells. A relation between the diffusion coefficient and diffusion length of singlet and triplet excitons is derived using the Förster and Dexter transfer processes and are plotted as a function of the donor‐acceptor separation. The diffusion length reduces nearly to a zero if the distance between donor and acceptor is increased to more than 1.5 nm. It is found that the donor‐acceptor separation needs to be ≤ 1.5 nm for easy dissociation on singlet excitons leading to better conversion efficiency in heterojunction organic solar cells. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A Theoretical Study on the Operation Principle of Hybrid Solar Cells

“…P3HT is a wide band gap polymer and is the most popular and studied donor material used in organic photovoltaics [25,26] and SiNWs ensure large donor-acceptor intefacial area with continous interpenetrating pathways for better charge transport to the electrodes [27]. The input parameters for calculations are as follows: axs = 4.35 nm and axt = 0.32 nm, Z = 77 for Iridium, ε = 7, μx = 1.99 × 10 −26 kg, = 0.06 eV, = 0.76 eV [4], Rda = 0.05 nm, Rf = 8 nm, τ = 2230 ps [28], L = 0.11 nm, Rd = 1 nm [29] = −3.03 eV, = −4.00 eV [30]. Using the above design and parameters, the various rates are calculated as shown in Table 1.…”

“…These rates depend on the above input parameters and therefore some uncertainty may be expected due to the uncertainties in the parameters themselves. It is not possible exactly to estimate variations in the input parameters however according to Equations (3), (4), (11) and (12), singlet and triplet Bohr radii and corresponding binding energies depend on the parameters α and μx which are estimated to be equal to 1.37 and 0.5 me, respectively [4]. The estimate of the effective mass of charge carriers in organic materials to be equal to the electronic rest mass me is regarded to be a good approximation as the HOMO and LUMO levels are electronic molecular states instead of energy bands.…”

“…An electron is excited to the lowest unoccupied molecular orbital, (ELUMO), leaving a hole in the highest occupied molecular orbital, (EHOMO), which instantly form an exciton due to strong Coulomb interaction between e and h caused by the low dielectric constant (ε = 3-4) of organic solids. As the electronic intermolecular interaction is weak in organics, the formation of such excitons is usually of Frenkel type [4,[14][15][16]. The rate of a photon absorption for a singlet excitation due to exciton-photon interaction, , and triplet excitation due to exciton-spin-orbit-photon interaction, , are derived using the transition matrix element and Fermi's Golden rule and are given as [6]:…”

“…The excitonic Bohr radius for singlet and triplet excitons axs and axt, respectively, are given as [4]: m is the Bohr radius and μ is the reduced mass of electron in a hydrogen atom.…”

“…Hybrid materials normally consist of inorganic nanoparticles as acceptor [3] and organic materials (small molecules/polymers) as donor materials. Together they form the photovoltaic active layer where photon absorption, Frenkel exciton formation [4][5][6], diffusion [4] and dissociation [7,8] take place. The free charge carriers are transported and collected at opposite electrodes [2,7,9].…”