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This software tool simulates the creation of excitons when light is absorbed by a semiconducting polymer film and the subsequent exciton annihilation mechanisms that can occur, as measured by pump-probe femtosecond transient absorption spectroscopy. The tool uses a cubic lattice model to calculate a theoretical prediction for the exciton concentration in the polymer film 100 fs after the pump pulse as a function of the pump pulse intensity. Of particular importance is the exciton delocalization radius parameter, which defines the size of the excitons and has a significant impact on the prevalence of exciton-exciton annihilation. This tool can be used to model experimental data and extract an estimate for the exciton delocalization radius.
The system is defined as a thin polymer film (~100 nm) deposited onto a thick transparent substrate (~1 mm) such as glass. When light is directed at the film, some photons with energy greater than the polymer bandgap are absorbed by the polymer material. Each absorbed photon creates an excited electronic state consisting of a bound electron-hole pair called an exciton. Once created, excitons in the film can undergo several different processes. The exciton can move around in the material through energy transfer. The exciton can also dissociate into an unbound electron and hole. Finally, excitons can undergo two types of annihilation mechanisms, exciton-exciton annihilation and exciton-polaron annihilation. In exciton-exciton annihilation, when two excitons are near each other the energy from one exciton is transferred to the other. The exciton which loses its energy disappears and the exciton which gains the additional energy becomes a hot exciton. This process is also sometimes called singlet fusion. Subsequently, the hot exciton can either realx back down to its lower energy state or again dissociate into an unbound electron-hole pair. In the second type of annihilation, exciton-polaron annihilation, when an exciton and a charge are near each other, the exciton transfers its energy to the charge. As a result, the exciton is removed and a hot charge is created, which quickly relaxes back to its lower energy state.
In a pump-probe experiment, the material is excited by a short laser pulse, and then the system is measured over time to determine the dynamic behavior of the system. In femtosecond transient absorption spectroscopy, the state of the system at a particular time is measured using a short pulse of multi-wavelength light covering the near infrared range. Excitons in semiconducting polymer films have a characteristic absorption region, and the near-IR absorption spectrum can be analyzed to estimate the exciton concentration at the time the spectrum is taken. This tool simulates the exciton concentration that would be measured from an near-IR absorption spectrum taken by this technique 100 fs after the pump pulse.
In typical experiments of this nature, when the pump intensity is low, very few excitons are created in the polymer film and the probability of there being excitons near each other is very small. In this regime, as the pump pulse intensity increases, more photons are absorbed and the measured exciton concentration increases in a linear fashion. However, as the pump pulse intensity increases, the probability of excitons being created near each other increases, resulting in an increase in the probability of exciton-exciton annihilation. As a result, the relationship between the exciton concentration and the pump pulse intensity becomes sub-linear at higher pump pulse intensities. The transition point from the linear to sub-linear regime has been used previously to estimate the exciton delocalization radius. In semiconducting polymers, excitons become delocalized when their wavefunctions extend either along the polymer backbone or between adjacent polymer chains. Here, as a simplification, delocalized excitons are assumed to have a spherical shape. Delocalized excitons are larger and, as a result, have an increased interaction radius. As excitons become larger, the probability of them being created created near each other increases. This tool has been developed to simulate this exciton-exciton annihilation behavior in order to model experimental femtosecond pump-probe absorption spectroscopy data and extract an estimate for the exciton delocalization radius of the material being tested.
This tool uses a simple optical model to calculate the initial absorption of the pump pulse, and then uses a cubic lattice model to simulate the subsequent exciton dissociation and exciton annihilation mechanisms that occur within 100 fs. A peer-reviewed article describing the development and application of this tool is currently under review. More details about the methodology will be provided here following publication.
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