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Method Article
Anisotropic Mobilities in Organic Semiconductors
Keli Han
Han's Lab, Dalian Institute of Chemical Physics, Dalian, China
Corresponding Author
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As one of the most important physical properties of the organic material, the anisotropic charge-carrier mobility directly determines device performance to a large extent. In this protocol, we mainly describe efforts in our group over the last few years to establish the quantitative relationship between angular resolution anisotropic mobilities and organic crystal packing architecture parameters (r, θ, and γ). Based on first-principles quantum mechanics (QM) calculations and Marcus-Hush theory in an effective one-dimensional diffusion equations model, the first analytical expressions of organic semiconductor crystal anisotropic mobility is proposed and applied in some typical p-/n-type organic semiconductor materials. The surprisingly agreements between our intuitive model and the available experiments indicate that the proposed anisotropic mobility analytical expressions in terms of fundamental molecular and packing properties can be applied in aiding synthetic design of organic semiconductor materials.
Keywords
Organic Semiconductors; anisotropic charge-carrier mobility; analytical expressions; p-/n-type
Figure 1
Organic semiconductors have attracted comprehensive interest among researchers all over the world, in particular as active components in organic electronic devices and molecular electronics. Compared with inorganic semiconductors, organic semiconductor materials possess advantages such as low cost, versatility of chemical synthesis, ease of processing, low weight, and flexibility. However, the performances of most current organic electronic devices are still limited by the relatively low carrier mobility of the organic material. Investigating the structure/property relationships for the ultimate design of new organic semiconductor materials with higher mobility has been a subject of great interest for many years.1-2 Nevertheless, the successful relations of microscopic molecular and structural characteristics to their macroscopic mobility properties, especially for the intrinsic anisotropic carrier mobility, are yet to be fully clarified. Only recently, with the development of single-crystal organic field-effect transistors (SCOFETs), the direct measurement of carrier mobility as an explicit function of intermolecular proximity and orientation within an organic crystal structure is allowed,3-5 which facilitate the direct comparison between theory and experiment, and provide the opportunity for theoretician to establish the quantitative relationship even the explicit analytical expression of the intrinsic anisotropic mobility of organic semiconductor crystals. For the final “functionality by design” of organic materials, a successful analytical expression of anisotropic mobility is very helpful and important since most organic crystals show the pronounced anisotropy which has to be taken into account for device design in the commercial application.
From the 1950s, significant progress has been made toward improved understanding of intrinsic charge-transport phenomena in organic materials, and several models, such as band model, tight-binding model and hopping model, have been proposed for the analysis and simulation of low-density intrinsic transport behavior in the organic crystals observed in OFET experiments.6 In most cases, the hopping model is one of the most appropriate method to describe carrier transport in organic semiconductor materials, especially at room temperature, due to the fact that organic molecules are usually aggregated by weak van der Waals forces and thus the intermolecular electronic couplings (electron transfer integral) are much weaker than the electron-vibration couplings (reorganization energy) for the majority of conjugated organic oligomers. In the hopping model, the intrinsic charge-transport rates for electron and hole transport mainly rely on two contributions. The first is the geometric relaxation of the molecule (inner reorganization energy) and its surroundings (outer reorganization energy) on movement of the charge carriers. The second is the magnitude of the intermolecular electronic coupling, which is intimately related to crystal packing. The former is mostly the energy change of a single molecule on charge addition/removal (inner reorganization energy), because contributions from the electronic and nuclear polarization/relaxation of the surrounding medium are significantly smaller.7 The latter can be approximated as nearest-neighbor contributions, as the electronic couplings fall off rapidly with intermolecular separation. In addition, electronic couplings between adjacent molecules in crystals are also highly sensitive to the molecular packing motif, such as the relative positions of the interacting molecules and intermolecular orientations.8
Another significant aspect of organic crystal transport properties is the anisotropy of charge transport on organic surfaces, which mainly originates from the sensitivity of electronic couplings to the mode of packing.9 In the last few years, the mobility anisotropy has received more and more attention as the continuous development of organic field-effect transistors (OFETs). In 2004, Sundar et al. investigated the dependence of the field-effect mobility on the orientation of the transistor channel relative to the crystallographic axes, and observed for the first time a strong anisotropy of the intrinsic hole mobility within the a-b plane of single crystals of rubrene in field-effect experiment.5 Later on, scientists found that the anisotropic field effect is common in various organic crystals, such as linear acenes and their derivatives/analogues.4, 9 These experimental results measured through single-crystal devices not only give us an opportunity to completely understand the charge transport mechanisms, but also provide references for the further theoretical study on relationships between the microscopic molecular packing and macroscopic charge transport of the materials since the crystal packing and molecular orientation are clearly fixed. On the theoretical side, there are several theoretical studies about anisotropic hole/electron mobilities and these investigations gave a detailed analysis and qualitative simulation of the anisotropy of charge transport behavior.10-12 However it should be noted that even though the Holstein–Peierls model can well describe the temperature-dependence and anisotropy of charge-carrier mobilities in organic molecular crystals, it does not give quantitatively predictive values, and in some cases the calculation results from the Holstein–Peierls model is about one to two orders of magnitude larger than that of the single-crystal experimental measurements.7 Moreover, the master equation method coupled with the Marcus–Hush electron transfer theory provides with an efficient method to numerically solve the anisotropic charge-carrier mobility from the molecular packing structure,11 nevertheless, master-equation method is always complex and does not present the inherent relationship between molecular packing architecture parameters and the mobility anisotropy in organic materials, which is very important for the design of new molecular materials and the improvement of the device performance. It will be very helpful for “design” if we can use a simpler and more intuitive model to offer clear physical insight. For this purpose, by ignoring diffusion pathways interaction in the one-dimensional diffusion equations, we developed a first-principles-based simulation model predicting anisotropic hole/electron mobility of organic crystals with only crystal structures needed.13 The model leads to the first analytical expression for predicting angular resolution anisotropic mobility in the organic crystal, and the mobility orientation function µΦ explicitly shows how the hole/electron mobility correlates with the molecular packing and the underlying atomistic electronic properties, which is very useful in aiding synthetic design of organic semiconductors. In spite of the approximations and the simple one-dimensional diffusion model, the analytical expression of our angular resolution anisotropic mobility function made surprising good predictions for the anisotropic mobility distributions in many organic molecular semiconductors such as linear acene, acene derivates, perylene bisimide derivatives, and oligothiophenes as well as their derivatives/analogues. Recently, it has been more and more widely used in the description of charge transfer behaviour and provides a guideline for “tailoring” new organic compounds for organic electronics.13-28
In this procotol, we mainly describe efforts in our team over the past few years to propose a theoretical model to establish the quantitative relationship between angular resolution anisotropic mobilities and molecular packing architecture parameters (r, θ, and γ) as well as underlying electronic properties of organic materials, and to simulate the anisotropic hole/electron mobilities of typical p-/n-type organic semiconductor materials. In Section II, we briefly describe our simulation model based on quantum chemical approaches to compute the molecular parameters that govern the intermolecular charge transfer process, followed by our proposed mobility orientation function μΦ(V, λ, r, θ, γ; Φ) that describes the mobility in a specific conducting direction on a specific surface in the organic crystal. Section III and Section IV focus on the applications of our simulation model to the p-type and n-type organic semiconductor materials, respectively. The conduction mechanism and the resistances at the TTF-TCNQ organic hetero-interface, based on our calculations, are discussed in Section V. A summary and outlook are present in the last section.
Please read attachment
Based on first-principle calculations combined with the hopping description of charge mobilities, we presented an intuitive and desirable simulation model predicting anisotropic hole/electron mobility of organic crystals with only crystal structures needed. The derived analytical expression of angular resolution anisotropic mobility function provides a explicit description of how the hole/electron mobility correlates with the fundamental organic materials properties such as crystal packing (the molecular packing architecture parameters of the crystal r, θ, and γ) and the underlying atomistic electronic properties (electronic coupling V, and reorganization energies λ). On the basis of our computational model, we have systematically investigated the charge-transfer properties of various p-type and n-type organic semiconductor materials, such as oligothiophenes, oligofurans, perlene bisimide derivatives, and linear acenes as well as their derivatives. The simulation results of charge transport indicated that our computational model not only made good predictions for the anisotropic mobility distributions in the organic crystals, but also attained near quantitative agreement with experiments. In addition, we also carried out a theoretical analysis of the metallic conduction mechanism at the experimentally characterized TTF–TCNQ interface, and the calculated resistances were in good agreement with the experimental measurements, which further illustrated the validity of our simulation method. Our model supplies the analytical expression of angular resolution anisotropic mobility for the priori design and screening of new organic electronic materials, and aids the device design by aligning the conducting channel along the maximum mobility direction for highest device performance. Despite of the agreement between our model and experiment, we should consider the approximations and the errors cancellation effects in the model. Important approximations, such as weak-coupling limit, Marcus−Hush ET theory in classical forms, tunnelling effects, the neglected influences of lattice vibration on the electronic coupling, the outer reorganization energy, the interactions between hopping pathways, the large electric-field modulation effects, should be investigated carefully and detailed in the future, which is vital to find the source of the errors cancellations and improve the current model for a more concise analytical expression of mobility anisotropy.
Furthermore, it should also be noted that because conventional first-principles methods fail to describe weak intermolecular interactions such as accurate van der Waals, most theoretical calculations and analysis are based on the experimental single-crystal structures.7-8 The dependence of theoretical predictions for the intrinsic charge mobility on experimental crystal structures makes computations impractical for new molecules where there is no knowledge of the crystal molecular packing structure. Although there has been some recent success for the prediction of crystal structures of small organic rigid molecules when the contents of the asymmetric unit is known, the success of such predictions rely on highly accurate dispersion-corrected Density Functional Theory (DFT) methods that are precluded for the large extended π-conjugated molecules.47 Therefore, accurate prediction of the molecular packing within the solid has always been an important subject of the future theoretical design of organic materials. Recently, some groups have gained important progress for the accurate and affordable local and global optimization of molecular crystal.48-50 Moreover, the mechanism of charge transport in organic materials is still controversial from experimental and theoretical perspectives, and the current understanding is still limited. Despite various models, such as the band model and hopping model, being proposed and widely used in the description of charge transport in organic semiconductors, a systematic approach for predicting charge-transfer rates that is valid for arbitrary strengths of electronic coupling and local electron-phonon interactions and over the full range of temperatures has remained a challenging task confronted by theoreticians. The development of a better theoretical method that is universally applicable still is one of hot spots in present researches. Therefore, while significant progress has been made, there is still a long way to go for the full understanding of charge-transfer mechanisms and the true realization of the computationally led design of organic semiconductor materials.
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Boran Han
commented on 26 August, 2013
Hi, very impressive work on building the 1d diffusion equations model. What's the physical picture behind it? Does it mean that anisotropic mobilities are essentially biased stochastic process?
Wenliang Li
commented on 27 August, 2013
Excellent work.
Qian Xu
commented on 27 August, 2013
I like this paper, which is really helpful for our research.
Yi Ma
commented on 27 August, 2013
Quite interesting!
Wang Junhua
commented on 27 August, 2013
Good.
zhao han
commented on 27 August, 2013
It is really good paper. I like it.
Jian Ma
commented on 27 August, 2013
I find this topic quite interesting.
shuhao wen
commented on 27 August, 2013
Anisotropic charge-carrier mobility is an interesting and important topic of organic semiconductor materials. With the research and development of single crystal OFET, mobility anisotropy attracts more and more attention. Pioneering works of John A. Rogers in 2004, and the good research from Bao z' lab in Stanford are typical experimental research. Theoretical work needs to keep space with experiments, and many groups are doing research to build the model of anisotropic mobility for organic semiconductors materials. The advantages of our model are using a intuitional way to consider the effects from all different electronic couplings in the crystal structures on every conducting channel, and in this way to incorporate important transport parameters such as electronic coupling, reorganization energy, and the materials crystal geometry (not only the packing but also the lattice). The error cancellations still exist in current model. Any comments are appreciated about the model.
Jing Guan
commented on 27 August, 2013
The protocol promotes the development of high-performance organic semiconductor materials. DFT computations combined with experimental data shed new light on anisotropic charge transport characteristics.
Rui Yu
commented on 29 August, 2013
The research on anisotropic mobility in organic semiconductors would be very interesting.
Ruifeng Lu
commented on 29 August, 2013
In Han's series of works, the accurate quantum descriptions and predictions of anisotropic mobilities in organic semiconductors provides very helpful guidance for relevant experiments. Good jobs!
Xian-Fang Yue
commented on 31 August, 2013
This protocol provides me an exciting and useful result about the the anisotropic charge-carrier mobility. Especially, the anisotropic mobility analytical expressions are very helpful for me to carriy out the studies on synthetic design of organic semiconductor materials.
Tianshu Chu
commented on 31 August, 2013
I think this is a very useful protocol. The idea of establishing the relationship between anisotropic charge transfer mobility and the organic crystal material is very exciting and useful for studying and developing organic semiconductors. The successful application of the proposed method in various types of organic semiconductors should make the protocol attractive and valuable to a wide range of researchers (both experimentalists and theoreticians) in the relevant area. It is a seriously impressive piece of work.
Xiaohu Li
commented on 01 September, 2013
I read this paper with interest. Apparently, with an joint efforts of work for several years, an interesting and useful model that give the quantitative relationship between angular resolution anisotropic mobilities and organic crystal packing architecture parameters is now proposed and was proved to be able to achieve good agreements with experiments. true, it will be very helpful for "design" when we can use a simpler an more intuitive model to offer clear physical insight. I was wondering, this model was established by ignoring diffusion pathways interaction in the one-dimensional diffusion equations, is there any influence of this assumption to the capabilities of the model?
peng song
commented on 02 September, 2013
Recently, we have studied the electron transfer rate of the organic material based on Marcus theory. After I read your interesting paper entitled "Anisotropic Mobilities in Organic Semiconductors", some results about the anisotropic charge-carrier mobility inspire us for deeply understanding the physical properties of the organic material. The quantitative relationship between angular resolution anisotropic mobilities and organic crystal packing architecture parameters (r, θ, and γ) provides a useful method for predicting anisotropic mobilities in organic semiconducting materials. Especially, the theoretical investigations have an important enlightenment function to analyze the ultrafast dynamics in semiconductor and the charge transfer process across the interfaces.
Xiaohu Li
commented on 03 September, 2013
Thanks, it is a very good paper.
oliver yang
commented on 04 September, 2013
it's an outstanding work!
Mingjun Yang
commented on 04 September, 2013
The quantitative relationship between anisotropic charge transfer mobility and the organic crystal architecture parameters is attractive and useful in understanding and design of new semiconductor material. Additionally, the prediction can be made from the quantum chemistry calculations which is really amazing work.
Ying Shi
commented on 07 September, 2013
I think this is a excellent work
oliver yang
commented on 07 September, 2013
Yang Di said: I think it's an outstanding work!
Xianghua Zhang
commented on 09 September, 2013
This work provides an explicit strategy to theoretically explore anisotropic electron transfer mechanisms in organic semiconductor. This work will be beneficial for the development of vast fields based on organic semiconductors including organic electrochemistry, organic photovoltaic cell, etc.
yang hou
commented on 09 September, 2013
important work.
Keli Han
commented on 10 September, 2013
Reply to Boran Han: In fact, the charge hopping direction is stochastic, and in our model, Pi = Wi/ΣiWi represents the hopping probability of the ith hopping pathway. However, the charge hopping rate between adjacent organic molecules is quite different, which is mainly related to the difference between the intermolecular electronic couplings. Our simulation model reflects the relationship between the anisotropic mobilities and organic crystal packing architecture parameters as well as the intermolecular electronic couplings depended on crystal packing architecture.Rely to Xiaohu Li: true, there is no interaction between diffusion pathways, and our assumption has little influence to the capabilities of the model.
Guochun Yang
commented on 07 October, 2013
A fundamental understanding of relationship between intermolecular interactions and transport properties in organic semiconducting materials for potential applications as electronic device element is significant. In this work, Han et al established the quantitative relationship between angular resolution anisotropic mobilities and organic crystal packing architecture parameters (r, θ, and γ), which will be very useful for understanding and reorganization of anisotropic mobility in organic semiconducting materials.
Deepak Sharma
commented on 27 June, 2018
Nice article..
Boran Han
commented on 26 August, 2013
Hi, very impressive work on building the 1d diffusion equations model. What's the physical picture behind it? Does it mean that anisotropic mobilities are essentially biased stochastic process?
Wenliang Li
commented on 27 August, 2013
Excellent work.
Qian Xu
commented on 27 August, 2013
I like this paper, which is really helpful for our research.
Yi Ma
commented on 27 August, 2013
Quite interesting!
Wang Junhua
commented on 27 August, 2013
Good.
zhao han
commented on 27 August, 2013
It is really good paper. I like it.
Jian Ma
commented on 27 August, 2013
I find this topic quite interesting.
shuhao wen
commented on 27 August, 2013
Anisotropic charge-carrier mobility is an interesting and important topic of organic semiconductor materials. With the research and development of single crystal OFET, mobility anisotropy attracts more and more attention. Pioneering works of John A. Rogers in 2004, and the good research from Bao z' lab in Stanford are typical experimental research. Theoretical work needs to keep space with experiments, and many groups are doing research to build the model of anisotropic mobility for organic semiconductors materials. The advantages of our model are using a intuitional way to consider the effects from all different electronic couplings in the crystal structures on every conducting channel, and in this way to incorporate important transport parameters such as electronic coupling, reorganization energy, and the materials crystal geometry (not only the packing but also the lattice). The error cancellations still exist in current model. Any comments are appreciated about the model.
Jing Guan
commented on 27 August, 2013
The protocol promotes the development of high-performance organic semiconductor materials. DFT computations combined with experimental data shed new light on anisotropic charge transport characteristics.
Rui Yu
commented on 29 August, 2013
The research on anisotropic mobility in organic semiconductors would be very interesting.
Ruifeng Lu
commented on 29 August, 2013
In Han's series of works, the accurate quantum descriptions and predictions of anisotropic mobilities in organic semiconductors provides very helpful guidance for relevant experiments. Good jobs!
Xian-Fang Yue
commented on 31 August, 2013
This protocol provides me an exciting and useful result about the the anisotropic charge-carrier mobility. Especially, the anisotropic mobility analytical expressions are very helpful for me to carriy out the studies on synthetic design of organic semiconductor materials.
Tianshu Chu
commented on 31 August, 2013
I think this is a very useful protocol. The idea of establishing the relationship between anisotropic charge transfer mobility and the organic crystal material is very exciting and useful for studying and developing organic semiconductors. The successful application of the proposed method in various types of organic semiconductors should make the protocol attractive and valuable to a wide range of researchers (both experimentalists and theoreticians) in the relevant area. It is a seriously impressive piece of work.
Xiaohu Li
commented on 01 September, 2013
I read this paper with interest. Apparently, with an joint efforts of work for several years, an interesting and useful model that give the quantitative relationship between angular resolution anisotropic mobilities and organic crystal packing architecture parameters is now proposed and was proved to be able to achieve good agreements with experiments. true, it will be very helpful for "design" when we can use a simpler an more intuitive model to offer clear physical insight. I was wondering, this model was established by ignoring diffusion pathways interaction in the one-dimensional diffusion equations, is there any influence of this assumption to the capabilities of the model?
peng song
commented on 02 September, 2013
Recently, we have studied the electron transfer rate of the organic material based on Marcus theory. After I read your interesting paper entitled "Anisotropic Mobilities in Organic Semiconductors", some results about the anisotropic charge-carrier mobility inspire us for deeply understanding the physical properties of the organic material. The quantitative relationship between angular resolution anisotropic mobilities and organic crystal packing architecture parameters (r, θ, and γ) provides a useful method for predicting anisotropic mobilities in organic semiconducting materials. Especially, the theoretical investigations have an important enlightenment function to analyze the ultrafast dynamics in semiconductor and the charge transfer process across the interfaces.
Xiaohu Li
commented on 03 September, 2013
Thanks, it is a very good paper.
oliver yang
commented on 04 September, 2013
it's an outstanding work!
Mingjun Yang
commented on 04 September, 2013
The quantitative relationship between anisotropic charge transfer mobility and the organic crystal architecture parameters is attractive and useful in understanding and design of new semiconductor material. Additionally, the prediction can be made from the quantum chemistry calculations which is really amazing work.
Ying Shi
commented on 07 September, 2013
I think this is a excellent work
oliver yang
commented on 07 September, 2013
Yang Di said: I think it's an outstanding work!
Xianghua Zhang
commented on 09 September, 2013
This work provides an explicit strategy to theoretically explore anisotropic electron transfer mechanisms in organic semiconductor. This work will be beneficial for the development of vast fields based on organic semiconductors including organic electrochemistry, organic photovoltaic cell, etc.
yang hou
commented on 09 September, 2013
important work.
Keli Han
commented on 10 September, 2013
Reply to Boran Han: In fact, the charge hopping direction is stochastic, and in our model, Pi = Wi/ΣiWi represents the hopping probability of the ith hopping pathway. However, the charge hopping rate between adjacent organic molecules is quite different, which is mainly related to the difference between the intermolecular electronic couplings. Our simulation model reflects the relationship between the anisotropic mobilities and organic crystal packing architecture parameters as well as the intermolecular electronic couplings depended on crystal packing architecture.Rely to Xiaohu Li: true, there is no interaction between diffusion pathways, and our assumption has little influence to the capabilities of the model.
Guochun Yang
commented on 07 October, 2013
A fundamental understanding of relationship between intermolecular interactions and transport properties in organic semiconducting materials for potential applications as electronic device element is significant. In this work, Han et al established the quantitative relationship between angular resolution anisotropic mobilities and organic crystal packing architecture parameters (r, θ, and γ), which will be very useful for understanding and reorganization of anisotropic mobility in organic semiconducting materials.
Deepak Sharma
commented on 27 June, 2018
Nice article..
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Associated Publications
Ultra-low resistance at TTF–TCNQ organic interfaces
by Shuhao Wen, Wei-Qiao Deng, and Ke-Li Han
Chemical Communications (21 August, 2013)
First-Principles Investigation of Anistropic Hole Mobilities in Organic Semiconductors
by Shu-Hao Wen, An Li, Junling Song, +3
Revealing quantitative structure–activity relationships of transport properties in acene and acene derivative organic materials
by Shu-Hao Wen, Wei-Qiao Deng, and Ke-Li Han
Simulation of Hole Mobility in α-Oligofuran Crystals
by Jin-Dou Huang, Shu-Hao Wen, Wei-Qiao Deng, +1
Method Article
Anisotropic Mobilities in Organic Semiconductors
Keli Han
Han's Lab, Dalian Institute of Chemical Physics, Dalian, China
Corresponding Author
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As one of the most important physical properties of the organic material, the anisotropic charge-carrier mobility directly determines device performance to a large extent. In this protocol, we mainly describe efforts in our group over the last few years to establish the quantitative relationship between angular resolution anisotropic mobilities and organic crystal packing architecture parameters (r, θ, and γ). Based on first-principles quantum mechanics (QM) calculations and Marcus-Hush theory in an effective one-dimensional diffusion equations model, the first analytical expressions of organic semiconductor crystal anisotropic mobility is proposed and applied in some typical p-/n-type organic semiconductor materials. The surprisingly agreements between our intuitive model and the available experiments indicate that the proposed anisotropic mobility analytical expressions in terms of fundamental molecular and packing properties can be applied in aiding synthetic design of organic semiconductor materials.
Figure 1
Organic semiconductors have attracted comprehensive interest among researchers all over the world, in particular as active components in organic electronic devices and molecular electronics. Compared with inorganic semiconductors, organic semiconductor materials possess advantages such as low cost, versatility of chemical synthesis, ease of processing, low weight, and flexibility. However, the performances of most current organic electronic devices are still limited by the relatively low carrier mobility of the organic material. Investigating the structure/property relationships for the ultimate design of new organic semiconductor materials with higher mobility has been a subject of great interest for many years.1-2 Nevertheless, the successful relations of microscopic molecular and structural characteristics to their macroscopic mobility properties, especially for the intrinsic anisotropic carrier mobility, are yet to be fully clarified. Only recently, with the development of single-crystal organic field-effect transistors (SCOFETs), the direct measurement of carrier mobility as an explicit function of intermolecular proximity and orientation within an organic crystal structure is allowed,3-5 which facilitate the direct comparison between theory and experiment, and provide the opportunity for theoretician to establish the quantitative relationship even the explicit analytical expression of the intrinsic anisotropic mobility of organic semiconductor crystals. For the final “functionality by design” of organic materials, a successful analytical expression of anisotropic mobility is very helpful and important since most organic crystals show the pronounced anisotropy which has to be taken into account for device design in the commercial application.
From the 1950s, significant progress has been made toward improved understanding of intrinsic charge-transport phenomena in organic materials, and several models, such as band model, tight-binding model and hopping model, have been proposed for the analysis and simulation of low-density intrinsic transport behavior in the organic crystals observed in OFET experiments.6 In most cases, the hopping model is one of the most appropriate method to describe carrier transport in organic semiconductor materials, especially at room temperature, due to the fact that organic molecules are usually aggregated by weak van der Waals forces and thus the intermolecular electronic couplings (electron transfer integral) are much weaker than the electron-vibration couplings (reorganization energy) for the majority of conjugated organic oligomers. In the hopping model, the intrinsic charge-transport rates for electron and hole transport mainly rely on two contributions. The first is the geometric relaxation of the molecule (inner reorganization energy) and its surroundings (outer reorganization energy) on movement of the charge carriers. The second is the magnitude of the intermolecular electronic coupling, which is intimately related to crystal packing. The former is mostly the energy change of a single molecule on charge addition/removal (inner reorganization energy), because contributions from the electronic and nuclear polarization/relaxation of the surrounding medium are significantly smaller.7 The latter can be approximated as nearest-neighbor contributions, as the electronic couplings fall off rapidly with intermolecular separation. In addition, electronic couplings between adjacent molecules in crystals are also highly sensitive to the molecular packing motif, such as the relative positions of the interacting molecules and intermolecular orientations.8
Another significant aspect of organic crystal transport properties is the anisotropy of charge transport on organic surfaces, which mainly originates from the sensitivity of electronic couplings to the mode of packing.9 In the last few years, the mobility anisotropy has received more and more attention as the continuous development of organic field-effect transistors (OFETs). In 2004, Sundar et al. investigated the dependence of the field-effect mobility on the orientation of the transistor channel relative to the crystallographic axes, and observed for the first time a strong anisotropy of the intrinsic hole mobility within the a-b plane of single crystals of rubrene in field-effect experiment.5 Later on, scientists found that the anisotropic field effect is common in various organic crystals, such as linear acenes and their derivatives/analogues.4, 9 These experimental results measured through single-crystal devices not only give us an opportunity to completely understand the charge transport mechanisms, but also provide references for the further theoretical study on relationships between the microscopic molecular packing and macroscopic charge transport of the materials since the crystal packing and molecular orientation are clearly fixed. On the theoretical side, there are several theoretical studies about anisotropic hole/electron mobilities and these investigations gave a detailed analysis and qualitative simulation of the anisotropy of charge transport behavior.10-12 However it should be noted that even though the Holstein–Peierls model can well describe the temperature-dependence and anisotropy of charge-carrier mobilities in organic molecular crystals, it does not give quantitatively predictive values, and in some cases the calculation results from the Holstein–Peierls model is about one to two orders of magnitude larger than that of the single-crystal experimental measurements.7 Moreover, the master equation method coupled with the Marcus–Hush electron transfer theory provides with an efficient method to numerically solve the anisotropic charge-carrier mobility from the molecular packing structure,11 nevertheless, master-equation method is always complex and does not present the inherent relationship between molecular packing architecture parameters and the mobility anisotropy in organic materials, which is very important for the design of new molecular materials and the improvement of the device performance. It will be very helpful for “design” if we can use a simpler and more intuitive model to offer clear physical insight. For this purpose, by ignoring diffusion pathways interaction in the one-dimensional diffusion equations, we developed a first-principles-based simulation model predicting anisotropic hole/electron mobility of organic crystals with only crystal structures needed.13 The model leads to the first analytical expression for predicting angular resolution anisotropic mobility in the organic crystal, and the mobility orientation function µΦ explicitly shows how the hole/electron mobility correlates with the molecular packing and the underlying atomistic electronic properties, which is very useful in aiding synthetic design of organic semiconductors. In spite of the approximations and the simple one-dimensional diffusion model, the analytical expression of our angular resolution anisotropic mobility function made surprising good predictions for the anisotropic mobility distributions in many organic molecular semiconductors such as linear acene, acene derivates, perylene bisimide derivatives, and oligothiophenes as well as their derivatives/analogues. Recently, it has been more and more widely used in the description of charge transfer behaviour and provides a guideline for “tailoring” new organic compounds for organic electronics.13-28
In this procotol, we mainly describe efforts in our team over the past few years to propose a theoretical model to establish the quantitative relationship between angular resolution anisotropic mobilities and molecular packing architecture parameters (r, θ, and γ) as well as underlying electronic properties of organic materials, and to simulate the anisotropic hole/electron mobilities of typical p-/n-type organic semiconductor materials. In Section II, we briefly describe our simulation model based on quantum chemical approaches to compute the molecular parameters that govern the intermolecular charge transfer process, followed by our proposed mobility orientation function μΦ(V, λ, r, θ, γ; Φ) that describes the mobility in a specific conducting direction on a specific surface in the organic crystal. Section III and Section IV focus on the applications of our simulation model to the p-type and n-type organic semiconductor materials, respectively. The conduction mechanism and the resistances at the TTF-TCNQ organic hetero-interface, based on our calculations, are discussed in Section V. A summary and outlook are present in the last section.
Please read attachment
Based on first-principle calculations combined with the hopping description of charge mobilities, we presented an intuitive and desirable simulation model predicting anisotropic hole/electron mobility of organic crystals with only crystal structures needed. The derived analytical expression of angular resolution anisotropic mobility function provides a explicit description of how the hole/electron mobility correlates with the fundamental organic materials properties such as crystal packing (the molecular packing architecture parameters of the crystal r, θ, and γ) and the underlying atomistic electronic properties (electronic coupling V, and reorganization energies λ). On the basis of our computational model, we have systematically investigated the charge-transfer properties of various p-type and n-type organic semiconductor materials, such as oligothiophenes, oligofurans, perlene bisimide derivatives, and linear acenes as well as their derivatives. The simulation results of charge transport indicated that our computational model not only made good predictions for the anisotropic mobility distributions in the organic crystals, but also attained near quantitative agreement with experiments. In addition, we also carried out a theoretical analysis of the metallic conduction mechanism at the experimentally characterized TTF–TCNQ interface, and the calculated resistances were in good agreement with the experimental measurements, which further illustrated the validity of our simulation method. Our model supplies the analytical expression of angular resolution anisotropic mobility for the priori design and screening of new organic electronic materials, and aids the device design by aligning the conducting channel along the maximum mobility direction for highest device performance. Despite of the agreement between our model and experiment, we should consider the approximations and the errors cancellation effects in the model. Important approximations, such as weak-coupling limit, Marcus−Hush ET theory in classical forms, tunnelling effects, the neglected influences of lattice vibration on the electronic coupling, the outer reorganization energy, the interactions between hopping pathways, the large electric-field modulation effects, should be investigated carefully and detailed in the future, which is vital to find the source of the errors cancellations and improve the current model for a more concise analytical expression of mobility anisotropy.
Furthermore, it should also be noted that because conventional first-principles methods fail to describe weak intermolecular interactions such as accurate van der Waals, most theoretical calculations and analysis are based on the experimental single-crystal structures.7-8 The dependence of theoretical predictions for the intrinsic charge mobility on experimental crystal structures makes computations impractical for new molecules where there is no knowledge of the crystal molecular packing structure. Although there has been some recent success for the prediction of crystal structures of small organic rigid molecules when the contents of the asymmetric unit is known, the success of such predictions rely on highly accurate dispersion-corrected Density Functional Theory (DFT) methods that are precluded for the large extended π-conjugated molecules.47 Therefore, accurate prediction of the molecular packing within the solid has always been an important subject of the future theoretical design of organic materials. Recently, some groups have gained important progress for the accurate and affordable local and global optimization of molecular crystal.48-50 Moreover, the mechanism of charge transport in organic materials is still controversial from experimental and theoretical perspectives, and the current understanding is still limited. Despite various models, such as the band model and hopping model, being proposed and widely used in the description of charge transport in organic semiconductors, a systematic approach for predicting charge-transfer rates that is valid for arbitrary strengths of electronic coupling and local electron-phonon interactions and over the full range of temperatures has remained a challenging task confronted by theoreticians. The development of a better theoretical method that is universally applicable still is one of hot spots in present researches. Therefore, while significant progress has been made, there is still a long way to go for the full understanding of charge-transfer mechanisms and the true realization of the computationally led design of organic semiconductor materials.
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Boran Han
commented on 26 August, 2013
Hi, very impressive work on building the 1d diffusion equations model. What's the physical picture behind it? Does it mean that anisotropic mobilities are essentially biased stochastic process?
Wenliang Li
commented on 27 August, 2013
Excellent work.
Qian Xu
commented on 27 August, 2013
I like this paper, which is really helpful for our research.
Yi Ma
commented on 27 August, 2013
Quite interesting!
Wang Junhua
commented on 27 August, 2013
Good.
zhao han
commented on 27 August, 2013
It is really good paper. I like it.
Jian Ma
commented on 27 August, 2013
I find this topic quite interesting.
shuhao wen
commented on 27 August, 2013
Anisotropic charge-carrier mobility is an interesting and important topic of organic semiconductor materials. With the research and development of single crystal OFET, mobility anisotropy attracts more and more attention. Pioneering works of John A. Rogers in 2004, and the good research from Bao z' lab in Stanford are typical experimental research. Theoretical work needs to keep space with experiments, and many groups are doing research to build the model of anisotropic mobility for organic semiconductors materials. The advantages of our model are using a intuitional way to consider the effects from all different electronic couplings in the crystal structures on every conducting channel, and in this way to incorporate important transport parameters such as electronic coupling, reorganization energy, and the materials crystal geometry (not only the packing but also the lattice). The error cancellations still exist in current model. Any comments are appreciated about the model.
Jing Guan
commented on 27 August, 2013
The protocol promotes the development of high-performance organic semiconductor materials. DFT computations combined with experimental data shed new light on anisotropic charge transport characteristics.
Rui Yu
commented on 29 August, 2013
The research on anisotropic mobility in organic semiconductors would be very interesting.
Ruifeng Lu
commented on 29 August, 2013
In Han's series of works, the accurate quantum descriptions and predictions of anisotropic mobilities in organic semiconductors provides very helpful guidance for relevant experiments. Good jobs!
Xian-Fang Yue
commented on 31 August, 2013
This protocol provides me an exciting and useful result about the the anisotropic charge-carrier mobility. Especially, the anisotropic mobility analytical expressions are very helpful for me to carriy out the studies on synthetic design of organic semiconductor materials.
Tianshu Chu
commented on 31 August, 2013
I think this is a very useful protocol. The idea of establishing the relationship between anisotropic charge transfer mobility and the organic crystal material is very exciting and useful for studying and developing organic semiconductors. The successful application of the proposed method in various types of organic semiconductors should make the protocol attractive and valuable to a wide range of researchers (both experimentalists and theoreticians) in the relevant area. It is a seriously impressive piece of work.
Xiaohu Li
commented on 01 September, 2013
I read this paper with interest. Apparently, with an joint efforts of work for several years, an interesting and useful model that give the quantitative relationship between angular resolution anisotropic mobilities and organic crystal packing architecture parameters is now proposed and was proved to be able to achieve good agreements with experiments. true, it will be very helpful for "design" when we can use a simpler an more intuitive model to offer clear physical insight. I was wondering, this model was established by ignoring diffusion pathways interaction in the one-dimensional diffusion equations, is there any influence of this assumption to the capabilities of the model?
peng song
commented on 02 September, 2013
Recently, we have studied the electron transfer rate of the organic material based on Marcus theory. After I read your interesting paper entitled "Anisotropic Mobilities in Organic Semiconductors", some results about the anisotropic charge-carrier mobility inspire us for deeply understanding the physical properties of the organic material. The quantitative relationship between angular resolution anisotropic mobilities and organic crystal packing architecture parameters (r, θ, and γ) provides a useful method for predicting anisotropic mobilities in organic semiconducting materials. Especially, the theoretical investigations have an important enlightenment function to analyze the ultrafast dynamics in semiconductor and the charge transfer process across the interfaces.
Xiaohu Li
commented on 03 September, 2013
Thanks, it is a very good paper.
oliver yang
commented on 04 September, 2013
it's an outstanding work!
Mingjun Yang
commented on 04 September, 2013
The quantitative relationship between anisotropic charge transfer mobility and the organic crystal architecture parameters is attractive and useful in understanding and design of new semiconductor material. Additionally, the prediction can be made from the quantum chemistry calculations which is really amazing work.
Ying Shi
commented on 07 September, 2013
I think this is a excellent work
oliver yang
commented on 07 September, 2013
Yang Di said: I think it's an outstanding work!
Xianghua Zhang
commented on 09 September, 2013
This work provides an explicit strategy to theoretically explore anisotropic electron transfer mechanisms in organic semiconductor. This work will be beneficial for the development of vast fields based on organic semiconductors including organic electrochemistry, organic photovoltaic cell, etc.
yang hou
commented on 09 September, 2013
important work.
Keli Han
commented on 10 September, 2013
Reply to Boran Han: In fact, the charge hopping direction is stochastic, and in our model, Pi = Wi/ΣiWi represents the hopping probability of the ith hopping pathway. However, the charge hopping rate between adjacent organic molecules is quite different, which is mainly related to the difference between the intermolecular electronic couplings. Our simulation model reflects the relationship between the anisotropic mobilities and organic crystal packing architecture parameters as well as the intermolecular electronic couplings depended on crystal packing architecture.Rely to Xiaohu Li: true, there is no interaction between diffusion pathways, and our assumption has little influence to the capabilities of the model.
Guochun Yang
commented on 07 October, 2013
A fundamental understanding of relationship between intermolecular interactions and transport properties in organic semiconducting materials for potential applications as electronic device element is significant. In this work, Han et al established the quantitative relationship between angular resolution anisotropic mobilities and organic crystal packing architecture parameters (r, θ, and γ), which will be very useful for understanding and reorganization of anisotropic mobility in organic semiconducting materials.
Deepak Sharma
commented on 27 June, 2018
Nice article..
Boran Han
commented on 26 August, 2013
Hi, very impressive work on building the 1d diffusion equations model. What's the physical picture behind it? Does it mean that anisotropic mobilities are essentially biased stochastic process?
Wenliang Li
commented on 27 August, 2013
Excellent work.
Qian Xu
commented on 27 August, 2013
I like this paper, which is really helpful for our research.
Yi Ma
commented on 27 August, 2013
Quite interesting!
Wang Junhua
commented on 27 August, 2013
Good.
zhao han
commented on 27 August, 2013
It is really good paper. I like it.
Jian Ma
commented on 27 August, 2013
I find this topic quite interesting.
shuhao wen
commented on 27 August, 2013
Anisotropic charge-carrier mobility is an interesting and important topic of organic semiconductor materials. With the research and development of single crystal OFET, mobility anisotropy attracts more and more attention. Pioneering works of John A. Rogers in 2004, and the good research from Bao z' lab in Stanford are typical experimental research. Theoretical work needs to keep space with experiments, and many groups are doing research to build the model of anisotropic mobility for organic semiconductors materials. The advantages of our model are using a intuitional way to consider the effects from all different electronic couplings in the crystal structures on every conducting channel, and in this way to incorporate important transport parameters such as electronic coupling, reorganization energy, and the materials crystal geometry (not only the packing but also the lattice). The error cancellations still exist in current model. Any comments are appreciated about the model.
Jing Guan
commented on 27 August, 2013
The protocol promotes the development of high-performance organic semiconductor materials. DFT computations combined with experimental data shed new light on anisotropic charge transport characteristics.
Rui Yu
commented on 29 August, 2013
The research on anisotropic mobility in organic semiconductors would be very interesting.
Ruifeng Lu
commented on 29 August, 2013
In Han's series of works, the accurate quantum descriptions and predictions of anisotropic mobilities in organic semiconductors provides very helpful guidance for relevant experiments. Good jobs!
Xian-Fang Yue
commented on 31 August, 2013
This protocol provides me an exciting and useful result about the the anisotropic charge-carrier mobility. Especially, the anisotropic mobility analytical expressions are very helpful for me to carriy out the studies on synthetic design of organic semiconductor materials.
Tianshu Chu
commented on 31 August, 2013
I think this is a very useful protocol. The idea of establishing the relationship between anisotropic charge transfer mobility and the organic crystal material is very exciting and useful for studying and developing organic semiconductors. The successful application of the proposed method in various types of organic semiconductors should make the protocol attractive and valuable to a wide range of researchers (both experimentalists and theoreticians) in the relevant area. It is a seriously impressive piece of work.
Xiaohu Li
commented on 01 September, 2013
I read this paper with interest. Apparently, with an joint efforts of work for several years, an interesting and useful model that give the quantitative relationship between angular resolution anisotropic mobilities and organic crystal packing architecture parameters is now proposed and was proved to be able to achieve good agreements with experiments. true, it will be very helpful for "design" when we can use a simpler an more intuitive model to offer clear physical insight. I was wondering, this model was established by ignoring diffusion pathways interaction in the one-dimensional diffusion equations, is there any influence of this assumption to the capabilities of the model?
peng song
commented on 02 September, 2013
Recently, we have studied the electron transfer rate of the organic material based on Marcus theory. After I read your interesting paper entitled "Anisotropic Mobilities in Organic Semiconductors", some results about the anisotropic charge-carrier mobility inspire us for deeply understanding the physical properties of the organic material. The quantitative relationship between angular resolution anisotropic mobilities and organic crystal packing architecture parameters (r, θ, and γ) provides a useful method for predicting anisotropic mobilities in organic semiconducting materials. Especially, the theoretical investigations have an important enlightenment function to analyze the ultrafast dynamics in semiconductor and the charge transfer process across the interfaces.
Xiaohu Li
commented on 03 September, 2013
Thanks, it is a very good paper.
oliver yang
commented on 04 September, 2013
it's an outstanding work!
Mingjun Yang
commented on 04 September, 2013
The quantitative relationship between anisotropic charge transfer mobility and the organic crystal architecture parameters is attractive and useful in understanding and design of new semiconductor material. Additionally, the prediction can be made from the quantum chemistry calculations which is really amazing work.
Ying Shi
commented on 07 September, 2013
I think this is a excellent work
oliver yang
commented on 07 September, 2013
Yang Di said: I think it's an outstanding work!
Xianghua Zhang
commented on 09 September, 2013
This work provides an explicit strategy to theoretically explore anisotropic electron transfer mechanisms in organic semiconductor. This work will be beneficial for the development of vast fields based on organic semiconductors including organic electrochemistry, organic photovoltaic cell, etc.
yang hou
commented on 09 September, 2013
important work.
Keli Han
commented on 10 September, 2013
Reply to Boran Han: In fact, the charge hopping direction is stochastic, and in our model, Pi = Wi/ΣiWi represents the hopping probability of the ith hopping pathway. However, the charge hopping rate between adjacent organic molecules is quite different, which is mainly related to the difference between the intermolecular electronic couplings. Our simulation model reflects the relationship between the anisotropic mobilities and organic crystal packing architecture parameters as well as the intermolecular electronic couplings depended on crystal packing architecture.Rely to Xiaohu Li: true, there is no interaction between diffusion pathways, and our assumption has little influence to the capabilities of the model.
Guochun Yang
commented on 07 October, 2013
A fundamental understanding of relationship between intermolecular interactions and transport properties in organic semiconducting materials for potential applications as electronic device element is significant. In this work, Han et al established the quantitative relationship between angular resolution anisotropic mobilities and organic crystal packing architecture parameters (r, θ, and γ), which will be very useful for understanding and reorganization of anisotropic mobility in organic semiconducting materials.
Deepak Sharma
commented on 27 June, 2018
Nice article..
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Associated Publications
Ultra-low resistance at TTF–TCNQ organic interfaces
by Shuhao Wen, Wei-Qiao Deng, and Ke-Li Han
Chemical Communications (21 August, 2013)
First-Principles Investigation of Anistropic Hole Mobilities in Organic Semiconductors
by Shu-Hao Wen, An Li, Junling Song, +3
Revealing quantitative structure–activity relationships of transport properties in acene and acene derivative organic materials
by Shu-Hao Wen, Wei-Qiao Deng, and Ke-Li Han
Simulation of Hole Mobility in α-Oligofuran Crystals
by Jin-Dou Huang, Shu-Hao Wen, Wei-Qiao Deng, +1