Annotation of the results obtained in 2020
At the third stage of the project, the spectroscopic criteria (descriptors) of order and charge-carrier mobility, which were proposed at the previous stages, were adjusted on the basis of the new data, and their efficiency and limits of applicability were analyzed. Two versions of the spectroscopic mobility criterion were formulated for different approximations (off-resonant and pre-resonant Raman regimes). Benchmarking of these two versions on a set of organic semiconductors (OSs) with available experimental mobilities showed a good correlation between the spectroscopically predicted and experimental mobilities: the Pearson’s correlation coefficients are 0.84 and 0.91 for the two versions of the criterion. Thus, these spectroscopic criteria can be used for the mobility prediction (estimation). It was also shown that the proposed criteria are most physically relevant for one-component OSs with one molecule in the primitive cell (Zred = 1) and with an inversion center. On the contrary, in OSs with an intense IR-active translational mode—a translation along the long axis of the molecule, the so-called “killer mode”—the spectroscopic criteria can underestimate the disorder and overestimate the charge mobility. The spectroscopic mobility criterion was also applied to organic semiconductors with unknown charge mobility. We have selected OSs with suitable molecular structure, namely two derivatives of naphthalene diimides (NDIs); representatives of this class of OSs have an extended conjugated system and often show a sufficiently high charge mobility and stability. For the powders of the OSs selected, Raman spectra were measured in the range of 10–2000 cm–1. From the obtained spectra, the spectroscopic order criterion, i.e., an estimate of the relative variance of the charge transfer integrals proposed in the Project, was calculated, as well as the spectroscopic mobility criterion. The calculated values of the spectroscopic mobility (in various approximations, see above) were 0.01–0.08 cm2V–1s–1. Then, single crystals were grown from the powders of the OSs under study, organic field-effect transistors were manufactured using them, and the charge mobilities were obtained from the current-voltage characteristics of the latter. Both OSs have shown electron transport, with the average mobilities of 0.05 and 0.03 cm2V–1s–1, which is in good agreement with the spectroscopically predicted values. This once again confirms the efficiency of the proposed spectroscopic method for assessing the charge mobility. Density functional theory (DFT) was applied to calculate the static polarizability and optical properties of molecular dimers (pairs of molecules), depending on the distance between the molecules. NDI Chex and NDI Hex were chosen as the objects of study; for these Oss, a large amount of experimental and calculated data had been obtained at the second stage of the Project. It was found that with a growing intermolecular distance, the polarizability component normal to the molecular planes decreases due to a suppressed overlap of the wave functions of the monomers. The energy of the first singlet excited state S1, on the contrary, increases with increasing the intermolecular distance. The obtained dependences were compared with a similar dependence of the charge transfer integrals, and a correlation between the polarizability and the electron transfer integrals near the equilibrium intermolecular distance was demonstrated. This observation emphasizes the adequacy of the approximations used in the formulation of the spectroscopic mobility criterion. The Raman spectra for a number of OSs crystals—BTBT, chrysene, NDT, TTA, triclinic and orthorhombic rubrene polymorphs—were calculated. For some of them, relative standard deviations of the charge transfer integrals were calculated. It was found that in all the crystals studied, librational modes have the highest Raman intensities; these modes also make the dominant contribution to dynamic disorder. Also, the energies of intermolecular interactions were calculated for a number of OSs. It was shown that, in a series of OSs with similar structure, the reciprocal interaction energy correlates with the magnitude of the dynamic disorder. In addition, the difference in energies in the mentioned series was explained by the difference in the electrostatic potential: the presence of sulfur atoms with a lone pair of electrons instead of a pair of carbon and hydrogen atoms changes the pattern of interactions between neighboring molecules. This observation is extremely useful for the design of OS, and based on it, for the first time, a strategy for reducing disorder by enhancing electrostatic interactions was proposed. A code package was developed to optimize the OPLS AA force field, and with its use, the torsion constants for the popular OS molecules, TCNQ and F2-TCNQ, were optimized. Using the optimized force fields, a molecular dynamics simulation of the crystals of these OSs was performed, and transfer integrals and their standard deviations were calculated from a molecular-dynamics sampled geometries of pairs of neighboring molecules. The relative standard deviation of the transfer integrals turned out to be two times smaller for F2-TCNQ than for TCNQ, which was quite expected, being in agreement with the spectroscopic data and the calculations of the spectroscopic order parameter previously performed within the Project. Novel methods for modeling the charge transport in OSs were developed, which take into account a nontrivial interplay of the local and nonlocal electron-phonon interaction. Namely, the corresponding theory was formulated for the first time and, on its basis, a program code was developed that is able to account for the effect of the local electron/hole interaction with the intramolecular high-frequency vibrational modes on the dynamic disorder (associated primarily with nonlocal interaction with the intermolecular low-frequency modes). The developed method for the first time coherently describes the motion of a charge carrier between the molecular sites of a crystalline OS, combining this description with that of polaron screening (band narrowing). Using the developed methods and code, model systems and real OSs—three naphthalene diimide derivatives NDI-Chex, NDI-Hex, NDI-But—were studied. It was demonstrated for the first time that the influence of high-frequency modes on the low-frequency disorder leads to an enhancement of the “band” character of the temperature dependence of the mobility and may even lead to an improvement of the mobility characteristics due to suppression of dynamic disorder by polaron screening. This result is important both from a fundamental and from a practical standpoint, since it virtually suggests a new strategy for design of high-mobility OSs via suppression of the local electron-phonon interaction with intermolecular modes and "damping" of dynamic disorder using the polaron screening effect. Finally, the possibility of extending the spectroscopic method for assessing the mobility to semiconductors of other classes was evaluated. Raman spectra for a number of inorganic and hybrid semiconductors have been measured: zinc selenide (ZnSe), silver thiogallate (AgGaS2), zinc sulfide (ZnS), titanium (IV) oxide (TiO2), copper iodide (CuI), perovskites FaPbBr3, CsPbBr3, MaPbBr3, as well as a transition metal dichalcogenide WS2. It was shown that the spectra of perovskites exhibit broad intense Raman bands in the low-frequency region and a depleted spectrum in the high-frequency region. On the contrary, the WS2 spectrum has a weak Raman intensity in the low-frequency range in comparison both with perovskites and the studied OSs, which corresponds to a lower dynamic disorder and a higher (compared to OSs) experimental charge mobility. The data obtained indirectly indicate the fundamental possibility of using Raman scattering for assessing the dynamic disorder and charge mobility for inorganic and hybrid materials. However, due to the absence of intense bands in the high-frequency region, as well as the difference between the mechanism of charge transport in the mentioned materials and the charge transport in OSs, it is necessary to reformulate the spectroscopic criterion of charge mobility for them. The results obtained have been published in four articles in the peer-reviewed scientific journals referenced in Web of Science and Scopus (Adv. Electron. Mater; Int. J. Mol. Sci.; RSC Advances; J. Chem. Phys.) and corresponding to the Q1 quartile. An oral talk was presented at an international conference.

 

Publications

---

Annotation of the results obtained in 2018
The aim of the project is the formulation, justification, and experimental verification of the spectroscopic method for investigation of electron-phonon interaction in organic semiconductors (OS) and rapid estimation of charge mobility in them. As a spectroscopic criterion for charge carrier mobility, we have proposed a ratio of the Raman intensity in the high-frequency range (>600 cm-1) to that in the low-frequency range (LF, <200 cm-1). The physical content of the criterion comes from the fact that the low-frequency Raman scattering is related to dynamic disorder — fluctuations of intermolecular transfer integrals — which, according to the current view, leads to the transient localization of charge carriers that limiting their mobility. The work on the project includes, on one hand, experimental investigation of Raman spectra for various Oss, calculation of the spectroscopic criterion from them and establishment of the correlation between the spectroscopic criterion and charge mobility, and on the other hand, theoretical studies of charge transport, electron-phonon interaction, charge delocalization and Raman spectra, as well as the relationship between these characteristics. Raman spectra have been measured for a number of OSs, which show high charge mobility according to the literature data. Notably, for some of these spectra, the low-frequency part has been measured for the first time. From the Raman spectra, the spectroscopic criterion was calculated. It was found that the spectroscopic criterion does correlate with the charge mobility for the studied OSs: the larger its value, the higher the mobility. We have also studied the temperature dependencies of the Raman spectra, which revealed a considerable suppression of the low-frequency part of the spectra as the temperature decreases. This reduction in the low-frequency Raman intensities for lower temperatures leads to an enhancement of the spectroscopic criterion, which, in fact, correlates with the observed mobility enhancement in the studied OSs. Thus, the obtained experimental results justify the efficiency of the spectroscopic criterion. These results are novel, since the relationship between the Raman intensity and the charge carrier mobility has not been studied before; moreover, our results are important from both the fundamental and the practical point of view. On one hand, they justify the connection between the charge-transport and the optical properties of OSs, while on the other hand, they provide an opportunity for carrier mobility estimation before its measuring it in an actual device. The theoretical part of the work included computation of vibrational spectra of isolated molecules and crystals, a study of the connection between the Raman spectra and electron-phonon couplings, as well as analysis of charge delocalization and charge mobility estimation within the polaron model. For isolated molecules, it was demonstrated that in the high-frequency range, the highest Raman intensity is observed for the vibrational modes that considerably contribute to the electron-phonon interaction. These vibrations typically have frequencies in the 1400–1700 cm-1 range and constitute bond-length alternation modes significantly changing the conjugation length of the molecule. At the same time, spectra of some OSs contain several vibrations having low Raman intensities but contributing noticeably to the electron-phonon interaction, and vice versa. A possible source of this discrepancy is the static polarizability approximation used in the Raman intensity calculations, which does not allow for accounting for a (pre-)resonance character of Raman scattering that can be the case in experiment and assumes a straight relationship between the Raman spectrum and electron-phonon couplings. Thus, during the 2nd year of the project implementation, we plan to calculate also the resonant Raman spectra and compare them with the non-resonant ones, as well as with the electron-phonon couplings. Vibrations of Oss crystals were addressed by means of DFT with periodic boundary conditions. Vibrational modes were calculated for several crystalline OSs — naphthalene, stilbene, and a series of alkyl-substituted naphthalenediimide (NDI) derivatives. As a result, for the first time, theoretical Raman spectrum that agrees with experiment not only in the frequencies, but also in the intensities both in low- and the high-frequency parts was obtained for a crystalline OS (stilbene). This result is of key importance for the project, as well as for the organic electronics in general: first, it indicates a correct reproduction of the electronic and vibrational structures of an OS crystal, and, second, enables prediction of the spectroscopic criterion for the charge carrier mobility. For a naphthalene crystal, we have demonstrated that nonlocal electron-phonon interaction is mainly associated with the Raman-active vibrational modes, and the low-frequency Raman spectrum correlates with the contributions of various vibrations to the former. For NDI derivatives, calculation of the low-frequency vibrational structure has been performed for the first time. The calculation has revealed a specific feature of Raman spectra of these crystals: the frequency of the lowest Raman-active vibration decreases monotonically with the increase of the alkyl substituent length. Unlike naphthalene, a majority of low-frequency vibrational modes in these crystals are intramolecular. Moreover, electron-phonon interaction is mostly caused by IR-active vibrations, while the Raman-active modes make smaller contributions into it. A considerable contribution of intramolecular vibrations into nonlocal electron-phonon interaction and hence significant impact of them on charge transport has not been discussed in literature before, which indicates the novelty and importance of the results obtained. The theoretical study of charge carrier mobility in OSs has been done with a state-of-the-art framework of charge transport, the polaron theory. Within the small polaron theory for the Holstein–Peierls model parameterized by the results of ab initio simulations of crystalline naphthalene and F2–TCNQ, we have evaluated the charge mobility tensor, which exhibits a considerable agreement with experimental data and earlier estimations. The temperature dependence of the mobility, as expected, is of the ‘bandlike’ type, i.e., the mobility increases when the temperature decreases. Within the same polaron framework, for the first time, an analytical expression has been derived describing the time dynamics of delocalization of a charge carrier interacting with quantum phonons; it turned out that this expression also leads to the so-called transient localization that was known before within the quasiclassical approach (Ehrenfest dynamics). Thus, it was demonstrated that two intrinsically different frameworks — the polaron theory and the Ehrenfest dynamics — lead to similar results, at least for model systems representing the studied OS crystals. The results obtained are of key importance for the project, as well as for theoretical description of charge transport in OSs in general, since they (a) indicate applicability of the polaron theory to the analysis of the transient localization and mobility estimations in OS crystals of interest; (b) enables estimation of the (de)localization length for a charge carrier. The impact of charge delocalization on electron-phonon interaction was performed using a hybrid quantum mechanics/molecular mechanics method (QM/MM). It has been demonstrated that charge delocalization leads to suppression of both the local and nonlocal electron-phonon interaction. The delocalization effect is most pronounced in those OSs, where the electron-phonon interaction is the strongest. Estimations of the nonlocal electron-phonon interaction using QM/MM and investigation of the effect of delocalization on it have been obtained here for the first time. To conclude, during the reporting period, a number of new world-level experimental and theoretical results have been obtained, including several not initially planned. The results are of fundamental and practical importance for the field of organic electronics. On the basis of these results, two papers have been published in Physica status solidi – rapid research letters and Phys. Chem. Chem. Phys. journals (Q1 quartile). In addition, a chapter has been published in book that is indexed in Scopus. Another paper is submitted to J. Phys. Chem. Lett. (Q1). The results of the work on the project were presented at the international conferences, one of them (ICOE-2019) being a keynote meeting for the organic electronics community.

 

Publications

---

Annotation of the results obtained in 2019
At the second stage of the project, important results were obtained that confirm the main hypothesis of the project – the relationship between the charge transport in crystalline organic semiconductors and their low-frequency Raman spectra, and the possibility of using this relationship to assess the charge mobility. These results were obtained within a combined experimental and theoretical study involving: Raman spectroscopy of single-crystal organic semiconductors (OSs) in various crystallographic directions (Raman anisotropy) and for various temperatures; calculation of resonance and off-resonance Raman spectra of OS molecules; calculation of the order parameter for OSs using molecular dynamics; development and application of new theoretical methods for mobility estimation; modification of the spectroscopic criterion of charge mobility proposed at the first stage of the project – the ratio of the Raman intensity in the high-frequency region (HF, >600 cm-1) to its intensity in the low-frequency region (LF, <200 cm–1) – in order to account for the OS electronic structure (namely, the charge transfer integrals). The key result of the second stage is the established correlation between the charge transport anisotropy and the LF Raman anisotropy, which is most pronounced for single crystals of naphthalenediimide derivatives (NDI) grown at this stage. Namely, while the highest Raman intensity in the HF region is observed for the pump radiation polarized along the long molecular axes, in the LF region high intensity is observed when the pump radiation is polarized along the directions with large intermolecular charge transfer integrals. We attribute the latter observation to the fact that LF vibrations modulate the transfer integrals and, thus, the polarizability of the material. Moreover, modulation of the transfer integrals by various LF vibrations (their contributions to the non-local electron-phonon interaction) correlate with the Raman intensities of these vibrations. At the same time, it is demonstrated for the first time that the theoretical Raman anisotropy in the LF range reasonably describes the experimental data, confirming the reliability of the calculations. Thus, it is shown that Raman spectroscopy is an efficient method for studying the impact of LF vibrations on charge transport in OSs in different directions. The second important result is that the calculated resonance Raman intensities for various HF intramolecular vibrations correlate well with the contributions of these vibrations to the reorganization energy, λi (the local electron-phonon interaction). Moreover, it is shown that if the lowest dipole-allowed electronic transition has a large dipole moment, the resonance and off-resonance Raman spectra are very similar, and, therefore, the off-resonance Raman intensities also correlate with λi. It is shown for the first time that the spectrally integrated Raman intensity is directly related to the reorganization energy. The observed correlations highlight the prospects of using HF Raman spectroscopy as a tool for studying the local electron-phonon interaction. Another important result is that molecular dynamics simulations for a number of oligoacenes revealed a correlation between the spectroscopic criterion proposed at the first stage of the project and the order parameter – the inverse variance of distances between the molecular centers. Moreover, it is demonstrated that the temperature dependence of the spectroscopic criterion correlates with both the temperature dependence of the order parameter and the temperature dependence of the charge mobility. The results obtained explain the efficiency of the spectroscopic criterion for describing charge mobility in the OSs, which was demonstrated at the first stage of the project. Important results were also obtained for description of charge transport in OSs. For the first time, the time dynamics of charge carrier delocalization was studied within the Holstein-Peierls model, with an account for nonlocal interaction of the charge carrier with quantum phonons. It turned out that in such a quantum regime, the so-called transient localization also takes place, much like it does within semiclassical approaches, where it plays an extremely important role in limiting the charge transport. Moreover, the calculation revealed for the first time that transient localization can be caused not only by non-local, but also by local electron-phonon interaction. This observation is extremely important because it allows one to consider local and non-local electron-phonon interaction on equal footing – within similar approaches. Also, a new asymptotic low-phonon-frequency expansion framework for numerical estimation of the charge carrier mobility in organic semiconductors was developed, which lets one go beyond the conventional bandlike and hopping transport regimes. Charge mobilities for NDI derivatives calculated using this approach demonstrate a good agreement with experimental data, and one can also trace the mobility properties down to the characteristics of electron-phonon interaction, which, as described above, can be estimated from the Raman data. Based on the results obtained, the spectroscopic criterion of charge mobility was modified: the electronic structure of an OS (namely, the charge transfer integrals) and not only its modulation by low-frequency vibrations was considered. Modification of the spectroscopic criterion enabled assessment of charge mobility not only in OSs with efficient charge transport, but also in low-mobility OSs. Thus, a Protocol for spectroscopic assessment of charge mobility was proposed, which will be used at the third stage of the project to predict the mobility in new OSs, where charge mobility measurements have not been carried out yet. Among the other results, it was found that the changes in the Raman spectrum with temperature for an OS single crystal is almost identical to that for an OS powder, which allows to study changes in the spectroscopic criterion with temperature for powders of different OSs without resorting to laborious and time-consuming growth of single crystals. It is shown that insertion of electronegative atoms (e.g. fluorine or nitrogen) into OS molecules leads to a decrease in the LF Raman intensity, which can be explained by a decrease in dynamic disorder due to the changes in the crystal structure. Thus, the results obtained confirm the main hypothesis of the project and allow us to use the proposed (modified) spectroscopic method for assessment of the charge mobility in OSs of different molecular and crystal structures. All the tasks planned have been completed, and the expected results have been achieved. At the last stage of the project, we will improve the theoretical justification of the spectroscopic criterion, assess its applicability limits and use it to search for new OSs with high charge mobility. We consider that a number of the obtained results correspond to the world level in the field of organic electronics. This is confirmed by the publication of six articles in journals indexed by WoS and Scopus, including ACS Appl. Mater. Interfaces (IF > 8), J.Phys. Chem. Lett. (IF > 7), and Mater. Des. (IF > 5) in this year. Four of these articles were published in Q1 journals. Thus, the publication plan is exceeded significantly.

 

Publications

---