QM/MM calculations combined with the dimer approach on the static disorder at organic‐organic interfaces of thin‐film organic solar cells composed of small molecules

Abstract

A QM/MM approach using ωB97X-D combined with AMOEBA calculations was used to analyze the energetic disorder in the vicinity of interfaces in amorphous organic heterostructures. Distributions of ground-, excited-, and cationic-state energies as well as of ionization potentials and excitation energies, all being relevant quantities for the transport properties of thin films, were calculated. As already found for bulk amorphous organic semiconductors, local densities of states at molecular interfaces possess Gaussian-shaped profiles with a significant amount of disorder. Assuming a disorder-limited activation of exciton and charge transport, a decrease in the amount of disorder could improve the transport properties. Relating calculated disorders to molecular parameters revealed that in line with the Bässler model, especially the molecular polarity, its change upon electronic excitation, and the molecular polarizability are relevant quantities leading to energetically largely disordered films. Moreover, because of the different mechanisms of exciton and polaron delocalization, a given morphology with disordered charge-transport levels gives not necessarily rise to disordered exciton-transport levels and vice versa. | INTRODUCTIONDisorder in molecular organic semiconductors has been recognized as a key parameter limiting the semiconductor's transport properties for both charges and excitons. [1] A random distribution of the molecules in a disordered amorphous film results in considerable variations in local intermolecular interactions. This gives rise to a distribution of ionization and excitation energies, the relevant quantities for charge and exciton transport, which depend among others on these intermolecular interaction energies. [2] According to the central limit theorem, resulting densities of states (DOSs) for excitons and charges have a Gaussian shape because intermolecular interaction energies are composed of many independently varying contributions. [3] The width of the Gaussian-shaped DOSs, ie, the standard deviation of the Gaussian normal distribution σ, is referred to as the disorder parameter and characterizes the amount of site energy disorder, ie, of static disorder, in the semiconducting solid-state system. [2] Based on this Gaussian DOS, the Bässler model describes charge transport in organic semiconductors as an incoherent hopping process between the normally distributed sites. [4] The expression "disorder" can be connected with geometrical and energetical disorder. In line with the Bässler nomenclature, in the following the expression, "disorder" is always used to characterize the energetic disorder unless otherwise noted. Although experimentally detected field-and temperature-dependent charge carrier mobilities confirm the predictions of the Bässler model in principle, no direct experimental proof for the Gaussian-shaped DOS, particularly of charge carriers, in disordered molecular semiconductors † This article is published as part of a special issue to celebrate the 80 th birthday of P...

Excited-State Dynamics in Perylene-Based Organic Semiconductor Thin Films: Theory Meets Experiment

“…sites. 29,53,54 For H-aggregates, the final trapping occurs due to the relaxation from the upper to the lower Frenkel state 48,49 sometimes mediated through CT states. 50,87 The TR-SHG signals for DIP LT and PDIR-CN 2 thin films show two main differences: First, the signal of the DIP LT film arises after optical excitation with a specified, pump-energydependent delay, while the TR-SHG trace of PDIR-CN 2 increases instantaneously with the pump pulse.…”

“…For example, for perylene-based dyes, experimental studies indicate that excitons localize on dimers on a femtosecond time scale . Nevertheless, further hopping would still be possible for most sites. ,, For H-aggregates, the final trapping occurs due to the relaxation from the upper to the lower Frenkel state , sometimes mediated through CT states. , …”

“…An additional estimate is made by the utilization of perfect crystal structures. Work by Hertel and Bässler and by Brückner et al indicates that the disorder in the thin films induces an averaged broadening of 0.1 eV. − These studies also show the existence of trap states which lie 0.2–0.3 eV lower in energy than the average of states. Corresponding benchmark calculations of PDIR-CN 2 (Table S7) indicate that the vertical energies calculated on the tetramer (Table ) are blue-shifted by about 0.4–0.5 eV.…”

“…Improvements of this approach were suggested by Martínez and co-workers and Kühn and co-workers. , In the present work, we performed large scale quantum chemical calculations on the energetics and the characters of the involved states, using our dimer- or aggregate-based approach . This approach has been proven to be reliable for the investigations of the excited-state dynamics after optical excitations of DIP and other substituted perylene derivatives. − Further information about exciton diffusion processes in amorphous films is adopted from recent work on DIP films and DIP–C 60 interfaces. − Moreover, these data are combined with experimental information about the thin-film structures. − …”

Role of Intermolecular Interactions in the Excited-State Photophysics of Tetracene and 2,2′-Ditetracene

“…A theoretical description of the PL data measured on neat Tc and DTc single crystals was obtained by means of dimer and cluster calculations which we already employed successfully in other cases. − For this purpose, the intermolecular interaction was considered by choice of a suitable dimer pair within the real unit cell, and the crystalline environment was accounted for by including interactions of this dimer pair with its next-neighboring molecules (Figure S4). The calculated energy manifolds of ground state (S 0 ) and excited singlet (S 1 ) and triplet (T 1 ) states are displayed in Figure for both compounds as a function of the angular intermolecular coordinate (this angle is indicated by the red arrow in Figure and is a measure for the distortion relative to the crystal structure determined by XRD).…”