Abstract
Ionization potentials (IPs) and electron affinities (EAs) are important quantities input into most models for calculating the open-circuit voltage (Voc) of organic solar cells. We assess the semi-empirical density-functional tight-binding (DFTB) method with the third-order self-consistent charge (SCC) correction and the 3ob parameter set (the third-order DFTB (DFTB3) organic and biochemistry parameter set) against experiments (for smaller molecules) and against first-principles GW (Green’s function, G, times the screened potential, W) calculations (for larger molecules of interest in organic electronics) for the calculation of IPs and EAs. Since GW calculations are relatively new for molecules of this size, we have also taken care to validate these calculations against experiments. As expected, DFTB is found to behave very much like density-functional theory (DFT), but with some loss of accuracy in predicting IPs and EAs. For small molecules, the best results were found with ΔSCF (Δ self-consistent field) SCC-DFTB calculations for first IPs (good to ± 0.649 eV). When considering several IPs of the same molecule, it is convenient to use the negative of the orbital energies (which we refer to as Koopmans’ theorem (KT) IPs) as an indication of trends. Linear regression analysis shows that KT SCC-DFTB IPs are nearly as accurate as ΔSCF SCC-DFTB eigenvalues (± 0.852 eV for first IPs, but ± 0.706 eV for all of the IPs considered here) for small molecules. For larger molecules, SCC-DFTB was also the ideal choice with IP/EA errors of ± 0.489/0.740 eV from ΔSCF calculations and of ± 0.326/0.458 eV from (KT) orbital energies. Interestingly, the linear least squares fit for the KT IPs of the larger molecules also proves to have good predictive value for the lower energy KT IPs of smaller molecules, with significant deviations appearing only for IPs of 15–20 eV or larger. We believe that this quantitative analysis of errors in SCC-DFTB IPs and EAs may be of interest to other researchers interested in DFTB investigation of large and complex problems, such as those encountered in organic electronics.
Highlights
Organic electronics is a rapidly-growing alternative to silicon-based electronics
For example, by the Shockley diode model presented in the Appendix and perhaps even better by the Shockley-like model developed in [5] for organic solar cells, it is important to be able to understand the underlying phenomenology of organic photovoltaics at the atomistic level
These are complex systems that can benefit from both molecular and solid-state theory and that are likely to require hybrid approaches, which are somewhere between what is standard for molecules and what is standard for inorganic solids
Summary
Organic electronics is a rapidly-growing alternative to silicon-based electronics. In contrast to the latter, which is well enough understood [1], that fabless manufacturing may be used for circuit design using modeling software, such as SPICE [2], and be outsourced to a semiconductor foundry for actual fabrication, organic electronics is a rapidly growing, but much less well understood [3,4,5,6,7,8]. Given the size and complexity of minimum-sized cluster models or unit cells of periodic models for a reasonable description of organic solar cells, it is clear that we need a highly efficient method This is especially clear for such things as charge diffusion lengths and the size of depletion zones. This gives us a useful first indication of how DFTB might work for the case that really interests us, namely for larger molecules of interest in organic electronics.
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