Final Report Summary - ELECTROMAT (Electronic Transport in Organic Materials)
Organic semiconductors based on conjugated polymers and small molecules are materials of great promise for the use in solar cells and other electronic and optical devices, such as transistors and light-emitting diodes. The significant advantage of many of the organic materials is that they are abundant and can be processed from solution, which is a cheap production process.
The operation of all the afore-mentioned devices is based on the process of transport of charges through the constituent material. For example, the sunlight to electricity conversion process in typical organic solar cells consists of the following steps. The photons of incident sunlight are absorbed and therefore their energy is transferred to generated electron-hole pairs (excitons). Next, the energy is transferred by exciton migration to the interface of two organic materials that constitute a solar cell. The interface is such that an exciton is separated to an electron and a hole (charge transporting carries), that end up in different materials at opposite sides of the interface. Electrons and holes then migrate through the materials towards the electrodes. The process of electron and hole transport needs to be efficient to extract these charges at the electrodes and obtain the charge current in the external circuit. In light-emitting diodes this sequence of steps is reversed. The charges injected at electrodes need to reach the active region where they will recombine and emit light. Effective charge transport is again a prerequisite for this to happen. Furthermore, in field-effect transistors, charge carrier mobility in the channel directly determines the maximal operating frequency of the device.
It is therefore essential to understand and be able to quantitatively describe the processes of charge transport through organic materials. The main research objective of this project was to develop a theoretical and computational framework that links the atomic structure of the organic material to its electrical properties. In the course of the project, we have reached this objective by:
-Establishing the nature of charge carriers in organic crystals.
We have addressed an important question about the nature of charge carriers in organic crystals - if the charge carriers are pure electrons or coupling to lattice vibrations (phonons) is strong enough, so that coupled electron-phonon entities called polarons are formed. To address this questions, we have performed a detailed study of electron-phonon coupling in prototypical organic crystals polyacenes and reached the conclusion that the charge carriers are not of polaronic nature. The calculations of electronic states, phonon modes and electron-phonon coupling were performed using atomistic ab-initio calculations.
-Simulating the electronic transport in organic crystals.
We have developed the methodology to simulate the transport in organic crystals. We first use ab-initio calculations to parametrize the Hamiltonian of interacting electrons and phonons that fully takes into account the quantum nature of both phonons and electrons. To solve the transport problem of that Hamiltonian, we use the approach based on a canonical transformation of the Hamiltonian. After the transformation, the Hamiltonian consists of the diagonal polaron and phonon parts and their interaction which is only a perturbation after the afore-mentioned minimization is made. The charge carrier mobility is then evaluated using perturbative techniques. We have applied this approach to calculate the temperature dependence of charge carrier mobility in organic crystals and found reasonably good agreement with experimental data in polyacene organic crystals. In the course of the project we realized that this approach can be applied to quantum dot solids as well. In quantum dot solids we found that the mobility decreases with increasing temperature in agreement with experimental data. Although such dependence is usually considered as a proof of band transport we showed that formation of small polarons localized to single dots takes place and that the transport mechanism is hopping of such polarons.
-Understanding the charge transport in amorphous conjugated polymers.
We have significantly enhanced the understanding of charge transport in amorphous conjugated polymers through further development of the methods for simulation of transport in these materials and by applications of these methods to several materials. In particular, we have developed a framework for simulation of AC mobility in these materials and applied it to simulate the hole mobility in APFO polymers. Our results indicate that charge carrier transport at THz frequencies is thermally activated but with a much smaller activation energy compared to the DC case. The results of these simulations were also essential to establish which charge carriers - electrons or holes - dominate the terahertz spectra of polymer-fullerene organic solar cell materials. By combining the experimental results of our collaborators from the Lund University and our simulations, we concluded that the holes from the polymer give the dominant contribution to these spectra. We have also performed a systematic comparison of the density of states and DC mobilities of several different materials in the polymer and monomer form. Our conclusions show that the chemical structure of the material determines its electrical properties mainly through: (1) the interring torsion potential that determines the shape of the main chains; (2) the atomic charges that define the strength of electrostatic disorder.
-Describing the electronic transport in ordered chains of conjugated polymers.
Depending on processing conditions, conjugated polymers can exhibit different morphologies, from fully disordered (amorphous) to semicrystalline. The highest mobilities in conjugated polymer materials so far have been obtained in ordered chains of polymers that form a two dimensional lamela. To understand the electronic transport mechanism in ordered chains of conjugated polymers at room temperature, we have performed electronic structure calculations for realistic atomic structure of the material that includes the effects of thermal disorder that arise due to atomic motion at finite temperature. The results show that disorder in main chains has a strong effect on the electronic structure and leads to the localisation of the wave functions of the highest states in the valence band, similar to localisation that occurs in amorphous polymers. The presence of such states leads to thermally activated electrical transport in ordered polymers at room temperature.
-Identifying the influence of grain boundaries in organic crystals on charge transport.
Realistic small molecule-based organic materials are polycrystalline. Within each grain, they can be considered as single crystals with efficient charge transport. The mobility of charge carriers through the material is then limited by grain boundaries, where carriers can be trapped or scattered. To investigate the effect of grain boundaries on material properties, we constructed the atomic structure of the grain boundary by joining two missoriented crystals together and relaxing the energy of the structure using configuration Monte Carlo approach. We found that grain boundaries in organic crystals introduce trap states within the band gap of the material. Our results showed that the spatial positions and energies of trap states can be predicted solely from geometrical arrangement of molecules near the boundary. Wave functions of these states are localized on closely spaced pairs of molecules from opposite sides of the boundary. The energies of trap states are strongly correlated
with the distances between the molecules in the pair.
-Establishing the role of the interface between ordered and disordered regions in polymers.
Since realistic conjugated polymer materials exhibit complex structure with interlaced crystalline and amorphous domains, it is very important to understand what happens at the interface between these domains. We investigated the electronic structure of the interface between crystalline and amorphous domains in P3HT. Two types of the interface were considered: sharp interface and interface composed of extended chains. We have found that HOMO states of both interface types belong to the crystalline domains. States belonging to both domains were not found. Importantly, we find that there is no formation of trap states at the investigated interfaces, which is a quite different scenario to the one occurring in small molecule based organic crystals. Regardless of the interface type, amorphous domains present high barriers for charge carriers, which lead to charge transport through crystalline domains.
The developments from the project open the way to the researchers to predict the charge transport properties of the material (such as for example the electron or hole mobility) based on the chemical formula of the polymer or molecule. This largely contributes to shifting the research in the area of organic electronic materials from the trial-and-error approach to the rational design approach. While the development of organic electronic devices was not within the objectives of this project, the results of this project have indirectly helped in the development of the devices such as solar cells and polymer - Li ion car batteries which may have a big socio-economic impact.
Project website: www.scl.rs/electromat
The operation of all the afore-mentioned devices is based on the process of transport of charges through the constituent material. For example, the sunlight to electricity conversion process in typical organic solar cells consists of the following steps. The photons of incident sunlight are absorbed and therefore their energy is transferred to generated electron-hole pairs (excitons). Next, the energy is transferred by exciton migration to the interface of two organic materials that constitute a solar cell. The interface is such that an exciton is separated to an electron and a hole (charge transporting carries), that end up in different materials at opposite sides of the interface. Electrons and holes then migrate through the materials towards the electrodes. The process of electron and hole transport needs to be efficient to extract these charges at the electrodes and obtain the charge current in the external circuit. In light-emitting diodes this sequence of steps is reversed. The charges injected at electrodes need to reach the active region where they will recombine and emit light. Effective charge transport is again a prerequisite for this to happen. Furthermore, in field-effect transistors, charge carrier mobility in the channel directly determines the maximal operating frequency of the device.
It is therefore essential to understand and be able to quantitatively describe the processes of charge transport through organic materials. The main research objective of this project was to develop a theoretical and computational framework that links the atomic structure of the organic material to its electrical properties. In the course of the project, we have reached this objective by:
-Establishing the nature of charge carriers in organic crystals.
We have addressed an important question about the nature of charge carriers in organic crystals - if the charge carriers are pure electrons or coupling to lattice vibrations (phonons) is strong enough, so that coupled electron-phonon entities called polarons are formed. To address this questions, we have performed a detailed study of electron-phonon coupling in prototypical organic crystals polyacenes and reached the conclusion that the charge carriers are not of polaronic nature. The calculations of electronic states, phonon modes and electron-phonon coupling were performed using atomistic ab-initio calculations.
-Simulating the electronic transport in organic crystals.
We have developed the methodology to simulate the transport in organic crystals. We first use ab-initio calculations to parametrize the Hamiltonian of interacting electrons and phonons that fully takes into account the quantum nature of both phonons and electrons. To solve the transport problem of that Hamiltonian, we use the approach based on a canonical transformation of the Hamiltonian. After the transformation, the Hamiltonian consists of the diagonal polaron and phonon parts and their interaction which is only a perturbation after the afore-mentioned minimization is made. The charge carrier mobility is then evaluated using perturbative techniques. We have applied this approach to calculate the temperature dependence of charge carrier mobility in organic crystals and found reasonably good agreement with experimental data in polyacene organic crystals. In the course of the project we realized that this approach can be applied to quantum dot solids as well. In quantum dot solids we found that the mobility decreases with increasing temperature in agreement with experimental data. Although such dependence is usually considered as a proof of band transport we showed that formation of small polarons localized to single dots takes place and that the transport mechanism is hopping of such polarons.
-Understanding the charge transport in amorphous conjugated polymers.
We have significantly enhanced the understanding of charge transport in amorphous conjugated polymers through further development of the methods for simulation of transport in these materials and by applications of these methods to several materials. In particular, we have developed a framework for simulation of AC mobility in these materials and applied it to simulate the hole mobility in APFO polymers. Our results indicate that charge carrier transport at THz frequencies is thermally activated but with a much smaller activation energy compared to the DC case. The results of these simulations were also essential to establish which charge carriers - electrons or holes - dominate the terahertz spectra of polymer-fullerene organic solar cell materials. By combining the experimental results of our collaborators from the Lund University and our simulations, we concluded that the holes from the polymer give the dominant contribution to these spectra. We have also performed a systematic comparison of the density of states and DC mobilities of several different materials in the polymer and monomer form. Our conclusions show that the chemical structure of the material determines its electrical properties mainly through: (1) the interring torsion potential that determines the shape of the main chains; (2) the atomic charges that define the strength of electrostatic disorder.
-Describing the electronic transport in ordered chains of conjugated polymers.
Depending on processing conditions, conjugated polymers can exhibit different morphologies, from fully disordered (amorphous) to semicrystalline. The highest mobilities in conjugated polymer materials so far have been obtained in ordered chains of polymers that form a two dimensional lamela. To understand the electronic transport mechanism in ordered chains of conjugated polymers at room temperature, we have performed electronic structure calculations for realistic atomic structure of the material that includes the effects of thermal disorder that arise due to atomic motion at finite temperature. The results show that disorder in main chains has a strong effect on the electronic structure and leads to the localisation of the wave functions of the highest states in the valence band, similar to localisation that occurs in amorphous polymers. The presence of such states leads to thermally activated electrical transport in ordered polymers at room temperature.
-Identifying the influence of grain boundaries in organic crystals on charge transport.
Realistic small molecule-based organic materials are polycrystalline. Within each grain, they can be considered as single crystals with efficient charge transport. The mobility of charge carriers through the material is then limited by grain boundaries, where carriers can be trapped or scattered. To investigate the effect of grain boundaries on material properties, we constructed the atomic structure of the grain boundary by joining two missoriented crystals together and relaxing the energy of the structure using configuration Monte Carlo approach. We found that grain boundaries in organic crystals introduce trap states within the band gap of the material. Our results showed that the spatial positions and energies of trap states can be predicted solely from geometrical arrangement of molecules near the boundary. Wave functions of these states are localized on closely spaced pairs of molecules from opposite sides of the boundary. The energies of trap states are strongly correlated
with the distances between the molecules in the pair.
-Establishing the role of the interface between ordered and disordered regions in polymers.
Since realistic conjugated polymer materials exhibit complex structure with interlaced crystalline and amorphous domains, it is very important to understand what happens at the interface between these domains. We investigated the electronic structure of the interface between crystalline and amorphous domains in P3HT. Two types of the interface were considered: sharp interface and interface composed of extended chains. We have found that HOMO states of both interface types belong to the crystalline domains. States belonging to both domains were not found. Importantly, we find that there is no formation of trap states at the investigated interfaces, which is a quite different scenario to the one occurring in small molecule based organic crystals. Regardless of the interface type, amorphous domains present high barriers for charge carriers, which lead to charge transport through crystalline domains.
The developments from the project open the way to the researchers to predict the charge transport properties of the material (such as for example the electron or hole mobility) based on the chemical formula of the polymer or molecule. This largely contributes to shifting the research in the area of organic electronic materials from the trial-and-error approach to the rational design approach. While the development of organic electronic devices was not within the objectives of this project, the results of this project have indirectly helped in the development of the devices such as solar cells and polymer - Li ion car batteries which may have a big socio-economic impact.
Project website: www.scl.rs/electromat