磁场作用下有机小分子中极化子输运的动力学研究
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摘要
作为一种新型的功能材料,有机半导体一直是物理、化学、材料科学等交叉学科的研究热点。它具有大的π共轭结构和优良的载流子传输性能。由于有机半导体中载流子的迁移率与掺入某些杂质的浓度有很大关系,通常可以利用杂质掺杂的办法,对其导电性能进行调节。在过去的几十年间,人们利用有机半导体材料研制了各种光电器件,如有机太阳能电池、有机发光二极管和有机场效应晶体管等。
有机太阳能电池,通常也被称为有机光伏电池(Organic Photovoltaic cell, OPV),是继无机硅太阳能电池后,又一种新能源器件。传统的无机硅太阳能电池的生产工艺复杂,在制作工程中容易产生有毒物质,且转换效率已经达到理论上的极限。相比较而言,基于有机半导体材料的太阳能电池对太阳光的吸收系数较高,可以实现更高的光电转换效率。这是由于有机半导体材料的分子种类多,而且分子结构可调。通过对有机分子的结构进行调整和修饰,可以调节其带隙的大小,从而获得对太阳光照尽可能多的吸收。由于有机太阳能电池的制备成本低,制作过程中耗能少,使其在过去的几十年中得到了飞速发展,现已成为光电转换器件的主流。
有机发光二极管(Organic Light Emitting Diode, OLED)是一种新型的显示器件,其基本原理是利用了有机半导体分子的电致发光特性。关于有机固体具有发光性能的报道最早可追溯到上世纪六十年代。1963年,Pope等人用单晶蒽制备了有机电致发光器件。1979年,美国柯达公司的邓青云博士在实验中发现,有机蓄电池能够发光。自此,关于有机发光二极管的研究正式拉开了序幕。与无机半导体发光二极管(Light Emitting Diode, LED)相比,有机半导体材料的分子结构可调,因此发光范围更广,可以实现从红光到蓝光的全色彩显示。此外,由于它具有结构上的“软”性,通常可以用来制成大面积的柔性显示器件,如软屏幕、电子纸。
最早关于有机场效应晶体管(Organic Field Effect Transistor, OFET)的制作是Gamier等人在1989年提出的。这类器件所采用的有机半导体材料通常为并芳烃化合物(如并五苯)和低聚物(如六聚噻吩)。多年来,随着有机电子学的发展,有机场效应晶体管作为一种重要的电子学器件,各项性能正在逐步地完善。
有机半导体中载流子的性质与无机材料相比存在很大差异。其中,一个突出的不同体现在载流子迁移率上。通常情况下,无机材料中载流子的迁移率比有机半导体大几个数量级。由此说明,两种材料中的载流子具有不同的传输机制。目前,在众多的有机半导体材料中,并五苯能够表现出较高的载流子迁移率。从1992年到2000年近十年中,并五苯的迁移率提高了将近4个数量级。到2004年,Jurchescu等人在高纯无缺陷的并五苯晶体中发现其迁移率已经可以达到35～38cm2/(V·s)。
从微观角度看,有机半导体根据分子量的大小通常可以分为两类：有机高分子聚合物(如聚乙炔、聚噻吩、聚对苯撑和聚吡咯)和有机小分子(如Alq3、红荧烯和并五苯)。聚合物一般是指分子量在一万以上,由大量原子通过共价键聚合而成的化合物。例如,在聚乙炔中,相邻碳原子之间通过共价键σ键连接,具有准一维的结构特征。每个碳原子提供一个π电子。离域的π电子能够在相邻碳原子之间跃迁。与传统的无机材料相比,有机高分子聚合物中存在强的电子-晶格耦合相互作用。通过注入或光激发产生的额外电子和空穴,将不再以扩展态的形式出现,而是形成局域的电子-晶格耦合态。因此,聚合物中的载流子也不再是传统意义上的电子和空穴,而是孤子(只存在于基态简并的聚合物中)、极化子和双极化子等自陷束缚的元激发。孤子根据其所带的电荷量,通常分为中性孤子、负电孤子和正电孤子。极化子带个单位的正电荷或负电荷,并携带1/2自旋。双极化子带两个单位的正电荷或负电荷,不携带自旋。此外,当处于基态的聚合物分子吸收一个光子,将一个电子从价带顶或最高占据分子轨道(the Highest Occupied Molecular Orbital, HOMO)激发到导带底或最低非占据分子轨道(the Lowest Unoccupied Molecular Orbital, LUMO)后,系统中会弛豫形成一个自陷束缚的激子。若增加光激发强度使两个电子同时受激,从价带顶或HOMO能级跃迁到导带底或LUMO能级,则形成自陷束缚的双激子。
2000年,孙鑫等人分别研究了聚乙炔中的激子和双激子在均匀外电场作用下的静态极化行为,发现激子是正向极化的,而双激子则呈现出反向极化的特性。因此,他们提出当聚乙炔中的激子再吸收一个光子形成双激子时,极化方向会发生翻转,即光致极化翻转(Photoinduced Polarization Inversion, PIPI)。然而,聚合物中的两个电子同时受激跃迁,形成双激子的概率很低,且双激子的寿命很短。因此,双激子的反向极化特性将很难在实验上获得。基于这种考虑,2005年,高琨等人对低聚物中极化子激发态的静态极化行为进行了研究。发现在外电场的作用下,该激发态同样具有反向极化的特性。然而,带电的极化子在电场中会沿着聚合物链运动,因而其反向极化特性将变得不再稳定。此外,上述工作还指出,双激子和极化子激发态的反向极化特性只能在基态简并的聚合物中得到。随着简并破缺参数的增加,两者的反向极化强度迅速减弱。然而,对于大多数聚合物(聚噻吩、聚对苯撑和聚吡咯)来说,其基态都是非简并的。鉴于此,我们有必要寻找其它的激发态,使其在这些基态非简并的聚合物中仍然能够呈现出反向极化的特性。
本论文在紧束缚近似下,采用一维扩展的Su-Schrieffer-Heeger模型,研究了聚乙炔中的另外一种激发态——高能激子的静态极化行为。该激发态是将一个电子从HOMO-1能级激发到LUMO+1能级后所弛豫形成的自陷束缚态。研究发现,在均匀外电场的作用下,高能激子呈现出反向极化的特性。通过分析高能激子定域能级上的波函数在外电场作用下的极化情况,我们得出了该激发态反向极化的起因。此外,我们还给出了不同简并破缺参数对高能激子反向极化程度的影响,发现其随简并破缺参数的增加而变化不大。因此,我们得出结论：在基态非简并的聚合物中,高能激子的反向极化特性仍然能够稳定存在。此外,我们还进一步探讨了不同电场强度作用下高能激子的反向极化。发现存在一个临界电场,当所施加的均匀外电场大于此临界电场时,高能激子将会解离,反向极化现象也随之消失。
我们知道,电子同时具有电荷和自旋两种属性。在以往的研究中,人们较多得关注于电子的电荷属性,而忽略了其自旋属性。近年来,随着自旋电子学领域的发展壮大,越来越多的科研工作者开始围绕电子的自旋属性展开研究,研究内容包括自旋注入、自旋极化和自旋输运等。在有机半导体材料中,自旋-轨道耦合和超精细相互作用比较弱,这将导致较长的自旋弛豫时间。由此说明,有机半导体材料是实现自旋极化注入的理想材料。此外,磁场对基于有机半导体材料的有机发光器件光电流、光致发光、电致发光以及电荷注入电流等性能的影响,即有机半导体材料的磁场效应(Magnetic Field Effect, MFE)也是近几年自旋电子学领域研究的热点。
在上述有机半导体材料的磁场效应中,关于磁场对电荷注入电流的影响研究得最为广泛。2004年,Francis等人探讨了室温下基于高分子聚合物PFO的有机发光器件ITO/PEDOT/PFO/Ca的电阻随外磁场的变化关系,并给出了有机磁电阻(Magnetoresistance,MR)的定义：MR=[R(B)-R(0)]/R(0),即磁场施加前后器件电阻的相对变化。发现在弱磁场下(大约20mT),聚合物PFO的磁电阻MR可以达到10%。随后,Mermer等人相继在多种高分子聚合物,如RRa-P3OT、RR-P3HT、Pt-PPE和PPE,以及有机小分子,如Alq3、Ir(ppy)3和并五苯中发现了有机磁电阻效应。通过对不同材料的MR曲线进行分析,人们发现其通常具有以下几个典型特点：(1)MR有正有负,与材料种类、温度、偏压、有机层厚度等多种因素有关；(2)MR的大小与外界偏压有关,与所施加的磁场方向无关；(3)不同材料的MR曲线通常都可以用洛伦兹型函数B2/(B2+B02)和非洛伦兹型函数B2/(|B|+B0)2这两种方程进行很好地拟合。其中,B0为拟合参数,大约为几个mT。由此说明,不同材料出现有机磁电阻效应的起因可能相同。
目前,关于有机半导体材料磁场效应的理论解释主要存在以下三种机制：(1)极化子对机制。该机制提出磁场和超精细场能够调节单/三态极化子对之间的相互转换,进而影响单/三态激子的形成比例,从而实现对器件电致发光效率的调控。(2)双极化子机制。该机制认为磁场和超精细场能够调节极化子和双极化子之间的相互转换,从而影响两者之间的浓度比例。由于两者的有效质量不同,因此迁移率不同。磁场通过影响两种载流子的浓度比,最终实现对器件电流的调控。(3)极化子-三态激子淬灭机制。该机制认为极化子在输运过程中容易与三态激子发生相互作用,极化子被三态激子散射后迁移率降低。由于磁场和超精细场能够调节单/三态激子的形成比例,进而影响极化子被三态激子散射的概率,从而实现对器件电流的调控。需要提及的是,上述三种理论机制都强调了电子自旋与氢核自旋之间的超精细相互作用对有机磁电阻的重要性。
虽然目前对有机磁电阻实验结果定性的理论解释有很多,但是关于有机磁电阻效应的定量计算,特别是能够与实验结果进行直观比较的理论工作却很少。基于这种考虑,本论文我们将采用有机小分子晶体的Troisi-Orlandi模型,同时考虑电子自旋与外磁场之间的塞曼相互作用和电子自旋与氢核自旋之间的超精细相互作用,探讨小分子中的极化子迁移率在均匀外磁场作用下的相对变化。根据有机磁电阻的定义,我们给出了有机小分子的MR曲线,并与实验结果进行比较。此外,我们还进一步探讨了超精细相互作用强度以及电子-声子耦合强度等因素对有机小分子磁电阻大小的影响。发现,一方面,随着超精细场的增强,|MR|变大,这与某些实验结果符合得很好。另一方而,随着电-声耦合的减弱,|MR|变小。当电-声耦合强度减为零时,即在无机半导体中的情形,磁电阻效应消失,从而论证了“磁场效应只存在于有机半导体材料,无机材料中没有磁场效应”这一说法。
此外,偏压效应一直是近年来有机磁电阻实验研究的重要组成部分。例如,2005年Mermer等人研究了偏压对有机小分子Alq3磁电阻的影响,指出在不同的偏压下,Alq3的磁电阻总为负值,且两者之间的依赖关系与温度有关。2007年,Bloom等人同样对Alq3的磁电阻进行了偏压效应的研究,却发现偏压可以调节其磁电阻的正负。另外,Martin等人还发现偏压对磁电阻的影响还与有机层厚度有关。由此可见,有机磁电阻的偏压效应是复杂多样的。因此,有必要对偏压效应进行理论方面的探讨,从而帮助我们更好地理解上述实验现象。
本论文将在前期工作的理论基础上,继续采用有机小分子晶体的Troisi-Orlandi模型,着重探讨偏压对其磁电阻的影响。通过计算,我们分别得到了不同偏压下有机小分子Alq3和并五苯的磁电阻随磁场的变化关系。发现,在相同的磁场作用下,偏压越大,|MR|越小。从系统的哈密顿量可以看出,随机分布的超精细场对携带自旋的极化子的作用相当于一系列无序势垒。在极化子的输运过程中,该随机势垒会对其有阻碍作用。而随着外界偏压的增大,极化子将从外界获得更多的能量而处于高能态。对于高能态极化子,随机势垒对其输运的阻碍作用将会减弱。我们的计算结果能够与某些实验数据符合得很好。另一方面,随着偏压的增大,载流子的注入效率提高,从而使得有机小分子中不携带自旋的双极化子所占的比重增大。基于此,我们又进一步探讨了不同的极化子/双极化子浓度比例下的磁电阻随磁场的变化关系。发现,在相同的磁场作用下,双极化子所占比重越大,|MR|叫越小。
综上所述,我们对有机半导体材料中的各种元激发进行了理论方面的探讨,重点关注了它们在外场(包括外电场、外磁场)作用下极化特性和导电性能的改变。通过我们的工作,可以更好地理解某些实验现象,并对实验进行指导。
As one of the new functional materials, organic semiconductors have been the research hotspot in the interdisciplinary area of physics, chemistry and materials science. They possess the big π-conjugated structure and the excellent carrier transport performance. In organic semiconductors, the carrier mobility is closely related to the doping concentration of some impurity. Then we can modulate their conductivity by using the method of the impurity doping. During the past decades, the organic semiconductor materials have been used to fabricate various optoelectronic devices, such as organic solar cells, organic light emitting diodes and organic field effect transistors.
Organic solar cells, which are also known as organic photovoltaic cells (OPV for short), have been another new energy devices after the inorganic silicon solar cells. For the traditional inorganic silicon solar cells, the production technology is complex, and the poisonous substances may be formed during their fabrication processes. In addition, the photoelectric conversion efficiency of the inorganic solar cells has reached the theory limit. In comparison, the organic semiconductor materials based solar cells can realize the higher photoelectric conversion efficiency as their high absorption coefficient from the sunlight. The reason is that the species of the organic semiconductor materials are rich, and their molecule structure can be modulated. By modifying the molecular structure of the organic semiconductors, and then the band gap, we can obtain the sunlight absorption as much as possible. Due to the advantages of low cost and low energy consumption during the fabrication process, the organic solar cells have been developed rapidly in the past decades. Today, organic solar cells have been the mainstream among the photoelectric conversion devices.
Organic light emitting diodes (OLED for short) are the new display devices. Their basic principle is the electroluminescence process in organic semiconductor molecules. The earliest report about the organic solid emitting can be traced back to1960s. In1963, Pope et al. fabricated the organic electroluminescence device by using the single crystal anthracene. In1979, Deng et al. of Kodak found that the organic battery can emit light during their experiment. From then on, the researchers began to focus on the organic light emitting diodes. Compared with the inorganic light emitting diodes (LED for short), the variety of the organic semiconductor molecules is rich, which induces a wide range of the light emitting. Therefore, the full color display from red to blue can be obtained. In addition, they possess the "soft" property in structure, which can be used to fabricate the large-area flexible display devices, such as the soft screen and the electronic paper.
In1989, Gamier et al. first fabricated the organic field effect transistor (OFET for short). The organic semiconductor materials which are usually used for these devices are aromatic hydrocarbon (such as pentacene) and oligomer (such as the hexamer of thiophene). With the development of the organic electronics over the years, the performance of the organic field effect transistors have been gradually improved and become the important electronic devices.
The property of carrier in organic semiconductors is very different from that in the inorganic materials, e.g., the carrier mobility. In general, the carrier mobility of inorganic semiconductors is several orders of magnitude larger than that of organic semiconductors. It indicates that the carrier in these two materials possesses different transport mechanism. At present, among the numerous organic semiconductor materials, pentacene exhibits a higher mobility. From1992to2000, the mobility of pentacene has been increased four orders of magnitude. In2004, Jurchescu et al. reported that in the high purity and no defect pentacene crystals, the mobility can reach35～38cm2/(V·s).
According to the size of the molecular weight, organic semiconductors can usually been divided into two groups:organic polymers (such as polyacetylene, polythiophene, polyparaphenylene and polypyrrole) and organic small molecules (such as Alq3, rubrene and pentacene). For polymers, their molecular weight is over ten thousand. In general, the polymer refers to the compound that is polymerized by a large number of atoms with covalent bond. For example, in polyacetylene, the two adjacent carbon atoms are connected by the covalent bond, σ bond to form a quasi-one-dimensional structure. Every carbon atom provides a π electron. This delocalized π electron can transfer between the adjacent carbon atoms. In contrast to the conventional inorganic materials, organic polymers possess strong electron-phonon (e-ph for short) interaction. The extra electron or hole produced by injection or photoexcitation will be trapped by the lattice structure to form the localized electron-lattice coupled state, rather than the expanded state. Therefore, the carriers in polymers are not the traditional electron and hole, but the self-trapped elementary excitation, such as soliton (only in polymers with the degenerate ground state), polaron and bipolaron. According to the number of the charge, soliton can be divided into the neutral solution, the negative soliton and the positive soliton. Polaron has one positive or negative charge with1/2spin. Bipolaron has two positive or negative charges with no spin. In addition, when the polymers in the ground state absorb a photon, the electron will be excited from the top of the valence band or the highest occupied molecular orbital (HOMO for short) to the bottom of the conduction band or the lowest unoccupied molecular orbital (LUMO for short), and then a self-trapped exciton is formed. If the strength of the photoexcitation is increased, two electrons will be excited simultaneously to transit from HOMO to LUMO, and then a self-trapped biexciton is formed.
In2000, Sun et al. investigated the static polarization behaviors of exciton and biexciton in polyacetylene, respectively, under a uniform external electric field. It is found that, the exciton is normally polarized while the biexciton is reversely polarized. Then they projected that when the polyacetylene with an exciton absorbs a photon to form a biexciton, the polarization of the molecule will be reversed, i.e., photoinduced polarization inversion (PIPI). However, the probability of the double-photon absorption in polymers to form a biexciton is very low, and the lifetime of biexciton is very short. Therefore, it is difficult to obtain the reverse polarization of the biexciton in experiment. With this consideration, in2005, Gao et al. investigated the static polarization behavior of the excited polaron in oligomer. It is found that this excited state also possesses the reverse polarization property. However, it is still unstable as the charged polaron will move along the polymer chain under the electric field.In addition, the above researches indicated that the reverse polarization of the biexciton and the excited polaron are obtained only in non-degenerate polymers. With the increase of the confinement constant, the strength of their reverse polarization decreases rapidly. However, for most polymers, such as polythiophene, polyparaphenylene and polypyrrole, their ground state is non-degenerate. Therefore, it is necessary for us to look for other excited states that can be reversely polarized also in non-degenerate polymers.
In this paper, we use the one-dimensional extended Su-Schrieffer-Heeger model under the tight-binding approximation, to investigate the static polarization behavior of another excited state, the high-energy exciton. This excited state is the self-trapped state induced by the single electron transition from HOMO-T to LUMO+1. We find that the high-energy exciton is reversely polarized under the uniform external electric field. By analyzing the polarization of the wave functions corresponding to the deep energy levels, we point out the origin of this reverse polarization behavior. We also show the effect of the non-degenerate confinement on the reverse polarization of the high-energy exciton, and find that with the increase of the confinement constant, the strength of the reverse polarization is little changed. Therefore, we conclude that the reverse polarization of the high-energy exciton is stable in non-degenerate polymers. In addition, we further explore the strength of reverse polarization under different electric fields. It is found that there exists a critical electric field, over which the high-energy exciton will dissociate and the reverse polarization will correspondingly vanish.
As we all know, the electron possesses both the charge and spin properties. In the past researches, more attentions have been paid on the charge property of electron, while the spin property is ignored. In recent years, with the development of the spintronics, more and more researchers have begun to focus on the study about electron spin, which contains the spin injection, spin polarization, spin transport, and so on. In organic semiconductor materials, the spin-orbit coupling and the hyperfine interaction is weak, which can induce a long spin relaxation time. Thus it can be seen that the organic semiconductor materials are the ideal materials for the spin polarized injection. In addition, the magnetic field effect (MFE) on photocurrent, photoluminescence, electroluminescence and charge-injection current of the organic semiconductor materials based organic light emitting devices has been the research hotspot in spintronics during the past years.
Among the above magnetic field effect of the organic semiconductor materials, the effect of the magnetic field on the charge-injection current is most studied. In2004, Francis et al. explored the dependence of the resistance in the PFO based organic light emitting device ITO/PEDOT/PFO/Ca at room temperature on the applied magnetic field, and gave the definition of the organic magnetoresistance (MR for short):the relative change of the device resistance R before and after the applying of the magnetic field B, as is described by the formula:MR=[R(B)-R(0)]/R(0). It is found that, under a weak magnetic field (about20mT), the MR of polymer PFO is up to10%. Later on, Mermer et al. successively observed the organic magnetoresistance effect in various polymers, such as RRa-P3OT, RR-P3HT, Pt-PPE and PPE, as well as the small molecules, such as Alq3, Ir(ppy)3and pentacene. By analyzing the MR curves of different materials, it is found that they generally have the following typical features:(1) MR can be positive or negative, depending on many factors, such as the variety of materials, temperature, voltage and the thickness of organic layer.(2) The magnitude of MR is related on the voltage, but is independent on the direction of the applied magnetic field.(3) The MR curves of different materials can be well fitted with the Lorentzian function B2/(B2+B02) or the non-Lorentzian function B2/(|B|+B0)2. Here, B0(about several mT) is the fitting parameter. It is indicated that the different organic semiconductor materials may share a common origin of the organic magnetoresistance effect.
Up to now, the theoretical explanation on MFE of organic semiconductor materials mainly contains the following three mechanisms:(1) Polaron-pair model. In this model, it is presented that the magnetic field and the hyperfine field affect the interconversion between the singlet and triplet polaron pairs, and then the formation ratio between the singlet and triplet exciton, so as to affect the light emitting efficiency of the devices.(2) Bipolaron model. This model proposes that the magnetic field and the hyperfine field can modulate the intercrossing between polaron and bipolaron, and then the concentration ratio between them. As they have different effective mass, the mobility of them is then different. By tuning the concentration ratio between polaron and bipolaron, the magnetic field ultimately affects the device current.(3) Polaron-triplet exciton quenching model. This model suggests that the polaron interacts with the triplet exciton during its transport. The mobility of polaron is decreased when it is scattered by triplet exciton. As the magnetic field and the hyperfine field can modulate the formation ratio between the singlet and the triplet exciton, and then the probability that the polaron is scattered by the triplet exaction, the magnetic field effect on device current is therefore realized. It should be mentioned that, all the above theoretical mechanisms seem to stress the importance of the hyperfine interaction between the electron spin and the hydrogen spin to the organic magnetoresistance.
Although there have been many qualitative theoretical explanations on the experimental results of the organic magnetoresistance, the quantitative calculations, especially the direct comparison with the experimental data of the organic magnetoresistance is little. With this consideration, in this paper we use the Troisi-Orlandi model of small molecular crystals, and take into account both the Zeeman interaction between the electron spin and the external magnetic field and the hyperfine interaction between the electron spin and the hydrogen spin, to explore the relative change of polaron mobility in small molecule under the magnetic field. According to the definition of organic magnetoresistance, we give the MR curve of the small molecule-pentacene, and make a direct comparison with the experimental data. In addition, we further explore the effect of the hyperfine interaction strength and the e-ph coupling interaction strength on MR. It is found that, for one thing, with the increase of the hyperfine field, the magnitude of MR,|MR|increases. The results show a good agreement with the experimental data. For another thing, with the decrease of the e-ph coupling,|MR|decreases. If the e-ph coupling is reduced to zero,i.e. the case in inorganic semiconductors,|MR|is reduced to zero too. Thus it demonstrates that the magnetic field effect is the characteristic of organic semiconductors.
In addition, the voltage effect is an important part in the experimental researches on organic magnetoresistance. For example, in2005, Mermer et al. explored the effect of the voltage on the magnetoresistance of small molecule Alq3. It is presented that the MR of Alq3is always negative at all different voltages, and the dependence between them is temperature-dependent. In2007, Bloom et al. also studied the voltage effect on MR in Alq3, while it is found that the voltage can tune the sign of MR. In addition, Martin et al.'s results show that the effect of voltage on MR is dependent on the thickness of the organic layer. Thus it can be seen that the voltage effect on magnetoresistance is complex. Therefore, it is necessary for us to undertake the theoretical investigation on this voltage effect, so as to better understand the above experimental phenomena.
In this paper, based on the previous theoretical work, we also use the Troisi-Orlandi model of small molecules to mainly investigate the voltage effect on their magnetoresistance. By calculation, we obtain the dependence of MR in small molecules Alq3and pentacene, respectively, on the magnetic field at different voltages. It is found that, under the same magnetic field, with the increase of the voltage the magnetoresistance decreases. The reason is as follows. From the Hamilton of the system we can see that, for the polaron with1/2spin, the random distributed hyperfine fields equal to a series of disordered potential barriers, which can block the polaron transport. The increase of the voltage induces that the carrier gets more energy. In this case, the blocking effect of the disordered potential barriers produced by the random distributed hyperfine fields on the polaron transport is weakened, and then the magnetoresistance effect is weakened too. Our calculation results agree well with some experimental data. In addition, with the increase of the voltage, the injection efficiency increases. In this case, the proportion of the bipolaron in small molecule increases. With this consideration, we further explore the magnetoresistance under different polaron/bipolaron density ratio, and find that the more the bipolaron is, the smaller the magnetoresistance is.
To sum up, in this paper we will give the theoretical investigations on various kinds of elementary excitations in organic semiconductor materials, especially on the change of their polarization behavior and the conductivity under the external field, including the electric field and the magnetic field. I hope that through our work, we can better understand the experimental phenomena and guide the experiments.
有机太阳能电池,通常也被称为有机光伏电池(Organic Photovoltaic cell, OPV),是继无机硅太阳能电池后,又一种新能源器件。传统的无机硅太阳能电池的生产工艺复杂,在制作工程中容易产生有毒物质,且转换效率已经达到理论上的极限。相比较而言,基于有机半导体材料的太阳能电池对太阳光的吸收系数较高,可以实现更高的光电转换效率。这是由于有机半导体材料的分子种类多,而且分子结构可调。通过对有机分子的结构进行调整和修饰,可以调节其带隙的大小,从而获得对太阳光照尽可能多的吸收。由于有机太阳能电池的制备成本低,制作过程中耗能少,使其在过去的几十年中得到了飞速发展,现已成为光电转换器件的主流。
有机发光二极管(Organic Light Emitting Diode, OLED)是一种新型的显示器件,其基本原理是利用了有机半导体分子的电致发光特性。关于有机固体具有发光性能的报道最早可追溯到上世纪六十年代。1963年,Pope等人用单晶蒽制备了有机电致发光器件。1979年,美国柯达公司的邓青云博士在实验中发现,有机蓄电池能够发光。自此,关于有机发光二极管的研究正式拉开了序幕。与无机半导体发光二极管(Light Emitting Diode, LED)相比,有机半导体材料的分子结构可调,因此发光范围更广,可以实现从红光到蓝光的全色彩显示。此外,由于它具有结构上的“软”性,通常可以用来制成大面积的柔性显示器件,如软屏幕、电子纸。
最早关于有机场效应晶体管(Organic Field Effect Transistor, OFET)的制作是Gamier等人在1989年提出的。这类器件所采用的有机半导体材料通常为并芳烃化合物(如并五苯)和低聚物(如六聚噻吩)。多年来,随着有机电子学的发展,有机场效应晶体管作为一种重要的电子学器件,各项性能正在逐步地完善。
有机半导体中载流子的性质与无机材料相比存在很大差异。其中,一个突出的不同体现在载流子迁移率上。通常情况下,无机材料中载流子的迁移率比有机半导体大几个数量级。由此说明,两种材料中的载流子具有不同的传输机制。目前,在众多的有机半导体材料中,并五苯能够表现出较高的载流子迁移率。从1992年到2000年近十年中,并五苯的迁移率提高了将近4个数量级。到2004年,Jurchescu等人在高纯无缺陷的并五苯晶体中发现其迁移率已经可以达到35～38cm2/(V·s)。
从微观角度看,有机半导体根据分子量的大小通常可以分为两类：有机高分子聚合物(如聚乙炔、聚噻吩、聚对苯撑和聚吡咯)和有机小分子(如Alq3、红荧烯和并五苯)。聚合物一般是指分子量在一万以上,由大量原子通过共价键聚合而成的化合物。例如,在聚乙炔中,相邻碳原子之间通过共价键σ键连接,具有准一维的结构特征。每个碳原子提供一个π电子。离域的π电子能够在相邻碳原子之间跃迁。与传统的无机材料相比,有机高分子聚合物中存在强的电子-晶格耦合相互作用。通过注入或光激发产生的额外电子和空穴,将不再以扩展态的形式出现,而是形成局域的电子-晶格耦合态。因此,聚合物中的载流子也不再是传统意义上的电子和空穴,而是孤子(只存在于基态简并的聚合物中)、极化子和双极化子等自陷束缚的元激发。孤子根据其所带的电荷量,通常分为中性孤子、负电孤子和正电孤子。极化子带个单位的正电荷或负电荷,并携带1/2自旋。双极化子带两个单位的正电荷或负电荷,不携带自旋。此外,当处于基态的聚合物分子吸收一个光子,将一个电子从价带顶或最高占据分子轨道(the Highest Occupied Molecular Orbital, HOMO)激发到导带底或最低非占据分子轨道(the Lowest Unoccupied Molecular Orbital, LUMO)后,系统中会弛豫形成一个自陷束缚的激子。若增加光激发强度使两个电子同时受激,从价带顶或HOMO能级跃迁到导带底或LUMO能级,则形成自陷束缚的双激子。
2000年,孙鑫等人分别研究了聚乙炔中的激子和双激子在均匀外电场作用下的静态极化行为,发现激子是正向极化的,而双激子则呈现出反向极化的特性。因此,他们提出当聚乙炔中的激子再吸收一个光子形成双激子时,极化方向会发生翻转,即光致极化翻转(Photoinduced Polarization Inversion, PIPI)。然而,聚合物中的两个电子同时受激跃迁,形成双激子的概率很低,且双激子的寿命很短。因此,双激子的反向极化特性将很难在实验上获得。基于这种考虑,2005年,高琨等人对低聚物中极化子激发态的静态极化行为进行了研究。发现在外电场的作用下,该激发态同样具有反向极化的特性。然而,带电的极化子在电场中会沿着聚合物链运动,因而其反向极化特性将变得不再稳定。此外,上述工作还指出,双激子和极化子激发态的反向极化特性只能在基态简并的聚合物中得到。随着简并破缺参数的增加,两者的反向极化强度迅速减弱。然而,对于大多数聚合物(聚噻吩、聚对苯撑和聚吡咯)来说,其基态都是非简并的。鉴于此,我们有必要寻找其它的激发态,使其在这些基态非简并的聚合物中仍然能够呈现出反向极化的特性。
本论文在紧束缚近似下,采用一维扩展的Su-Schrieffer-Heeger模型,研究了聚乙炔中的另外一种激发态——高能激子的静态极化行为。该激发态是将一个电子从HOMO-1能级激发到LUMO+1能级后所弛豫形成的自陷束缚态。研究发现,在均匀外电场的作用下,高能激子呈现出反向极化的特性。通过分析高能激子定域能级上的波函数在外电场作用下的极化情况,我们得出了该激发态反向极化的起因。此外,我们还给出了不同简并破缺参数对高能激子反向极化程度的影响,发现其随简并破缺参数的增加而变化不大。因此,我们得出结论：在基态非简并的聚合物中,高能激子的反向极化特性仍然能够稳定存在。此外,我们还进一步探讨了不同电场强度作用下高能激子的反向极化。发现存在一个临界电场,当所施加的均匀外电场大于此临界电场时,高能激子将会解离,反向极化现象也随之消失。
我们知道,电子同时具有电荷和自旋两种属性。在以往的研究中,人们较多得关注于电子的电荷属性,而忽略了其自旋属性。近年来,随着自旋电子学领域的发展壮大,越来越多的科研工作者开始围绕电子的自旋属性展开研究,研究内容包括自旋注入、自旋极化和自旋输运等。在有机半导体材料中,自旋-轨道耦合和超精细相互作用比较弱,这将导致较长的自旋弛豫时间。由此说明,有机半导体材料是实现自旋极化注入的理想材料。此外,磁场对基于有机半导体材料的有机发光器件光电流、光致发光、电致发光以及电荷注入电流等性能的影响,即有机半导体材料的磁场效应(Magnetic Field Effect, MFE)也是近几年自旋电子学领域研究的热点。
在上述有机半导体材料的磁场效应中,关于磁场对电荷注入电流的影响研究得最为广泛。2004年,Francis等人探讨了室温下基于高分子聚合物PFO的有机发光器件ITO/PEDOT/PFO/Ca的电阻随外磁场的变化关系,并给出了有机磁电阻(Magnetoresistance,MR)的定义：MR=[R(B)-R(0)]/R(0),即磁场施加前后器件电阻的相对变化。发现在弱磁场下(大约20mT),聚合物PFO的磁电阻MR可以达到10%。随后,Mermer等人相继在多种高分子聚合物,如RRa-P3OT、RR-P3HT、Pt-PPE和PPE,以及有机小分子,如Alq3、Ir(ppy)3和并五苯中发现了有机磁电阻效应。通过对不同材料的MR曲线进行分析,人们发现其通常具有以下几个典型特点：(1)MR有正有负,与材料种类、温度、偏压、有机层厚度等多种因素有关；(2)MR的大小与外界偏压有关,与所施加的磁场方向无关；(3)不同材料的MR曲线通常都可以用洛伦兹型函数B2/(B2+B02)和非洛伦兹型函数B2/(|B|+B0)2这两种方程进行很好地拟合。其中,B0为拟合参数,大约为几个mT。由此说明,不同材料出现有机磁电阻效应的起因可能相同。
目前,关于有机半导体材料磁场效应的理论解释主要存在以下三种机制：(1)极化子对机制。该机制提出磁场和超精细场能够调节单/三态极化子对之间的相互转换,进而影响单/三态激子的形成比例,从而实现对器件电致发光效率的调控。(2)双极化子机制。该机制认为磁场和超精细场能够调节极化子和双极化子之间的相互转换,从而影响两者之间的浓度比例。由于两者的有效质量不同,因此迁移率不同。磁场通过影响两种载流子的浓度比,最终实现对器件电流的调控。(3)极化子-三态激子淬灭机制。该机制认为极化子在输运过程中容易与三态激子发生相互作用,极化子被三态激子散射后迁移率降低。由于磁场和超精细场能够调节单/三态激子的形成比例,进而影响极化子被三态激子散射的概率,从而实现对器件电流的调控。需要提及的是,上述三种理论机制都强调了电子自旋与氢核自旋之间的超精细相互作用对有机磁电阻的重要性。
虽然目前对有机磁电阻实验结果定性的理论解释有很多,但是关于有机磁电阻效应的定量计算,特别是能够与实验结果进行直观比较的理论工作却很少。基于这种考虑,本论文我们将采用有机小分子晶体的Troisi-Orlandi模型,同时考虑电子自旋与外磁场之间的塞曼相互作用和电子自旋与氢核自旋之间的超精细相互作用,探讨小分子中的极化子迁移率在均匀外磁场作用下的相对变化。根据有机磁电阻的定义,我们给出了有机小分子的MR曲线,并与实验结果进行比较。此外,我们还进一步探讨了超精细相互作用强度以及电子-声子耦合强度等因素对有机小分子磁电阻大小的影响。发现,一方面,随着超精细场的增强,|MR|变大,这与某些实验结果符合得很好。另一方而,随着电-声耦合的减弱,|MR|变小。当电-声耦合强度减为零时,即在无机半导体中的情形,磁电阻效应消失,从而论证了“磁场效应只存在于有机半导体材料,无机材料中没有磁场效应”这一说法。
此外,偏压效应一直是近年来有机磁电阻实验研究的重要组成部分。例如,2005年Mermer等人研究了偏压对有机小分子Alq3磁电阻的影响,指出在不同的偏压下,Alq3的磁电阻总为负值,且两者之间的依赖关系与温度有关。2007年,Bloom等人同样对Alq3的磁电阻进行了偏压效应的研究,却发现偏压可以调节其磁电阻的正负。另外,Martin等人还发现偏压对磁电阻的影响还与有机层厚度有关。由此可见,有机磁电阻的偏压效应是复杂多样的。因此,有必要对偏压效应进行理论方面的探讨,从而帮助我们更好地理解上述实验现象。
本论文将在前期工作的理论基础上,继续采用有机小分子晶体的Troisi-Orlandi模型,着重探讨偏压对其磁电阻的影响。通过计算,我们分别得到了不同偏压下有机小分子Alq3和并五苯的磁电阻随磁场的变化关系。发现,在相同的磁场作用下,偏压越大,|MR|越小。从系统的哈密顿量可以看出,随机分布的超精细场对携带自旋的极化子的作用相当于一系列无序势垒。在极化子的输运过程中,该随机势垒会对其有阻碍作用。而随着外界偏压的增大,极化子将从外界获得更多的能量而处于高能态。对于高能态极化子,随机势垒对其输运的阻碍作用将会减弱。我们的计算结果能够与某些实验数据符合得很好。另一方面,随着偏压的增大,载流子的注入效率提高,从而使得有机小分子中不携带自旋的双极化子所占的比重增大。基于此,我们又进一步探讨了不同的极化子/双极化子浓度比例下的磁电阻随磁场的变化关系。发现,在相同的磁场作用下,双极化子所占比重越大,|MR|叫越小。
综上所述,我们对有机半导体材料中的各种元激发进行了理论方面的探讨,重点关注了它们在外场(包括外电场、外磁场)作用下极化特性和导电性能的改变。通过我们的工作,可以更好地理解某些实验现象,并对实验进行指导。
As one of the new functional materials, organic semiconductors have been the research hotspot in the interdisciplinary area of physics, chemistry and materials science. They possess the big π-conjugated structure and the excellent carrier transport performance. In organic semiconductors, the carrier mobility is closely related to the doping concentration of some impurity. Then we can modulate their conductivity by using the method of the impurity doping. During the past decades, the organic semiconductor materials have been used to fabricate various optoelectronic devices, such as organic solar cells, organic light emitting diodes and organic field effect transistors.
Organic solar cells, which are also known as organic photovoltaic cells (OPV for short), have been another new energy devices after the inorganic silicon solar cells. For the traditional inorganic silicon solar cells, the production technology is complex, and the poisonous substances may be formed during their fabrication processes. In addition, the photoelectric conversion efficiency of the inorganic solar cells has reached the theory limit. In comparison, the organic semiconductor materials based solar cells can realize the higher photoelectric conversion efficiency as their high absorption coefficient from the sunlight. The reason is that the species of the organic semiconductor materials are rich, and their molecule structure can be modulated. By modifying the molecular structure of the organic semiconductors, and then the band gap, we can obtain the sunlight absorption as much as possible. Due to the advantages of low cost and low energy consumption during the fabrication process, the organic solar cells have been developed rapidly in the past decades. Today, organic solar cells have been the mainstream among the photoelectric conversion devices.
Organic light emitting diodes (OLED for short) are the new display devices. Their basic principle is the electroluminescence process in organic semiconductor molecules. The earliest report about the organic solid emitting can be traced back to1960s. In1963, Pope et al. fabricated the organic electroluminescence device by using the single crystal anthracene. In1979, Deng et al. of Kodak found that the organic battery can emit light during their experiment. From then on, the researchers began to focus on the organic light emitting diodes. Compared with the inorganic light emitting diodes (LED for short), the variety of the organic semiconductor molecules is rich, which induces a wide range of the light emitting. Therefore, the full color display from red to blue can be obtained. In addition, they possess the "soft" property in structure, which can be used to fabricate the large-area flexible display devices, such as the soft screen and the electronic paper.
In1989, Gamier et al. first fabricated the organic field effect transistor (OFET for short). The organic semiconductor materials which are usually used for these devices are aromatic hydrocarbon (such as pentacene) and oligomer (such as the hexamer of thiophene). With the development of the organic electronics over the years, the performance of the organic field effect transistors have been gradually improved and become the important electronic devices.
The property of carrier in organic semiconductors is very different from that in the inorganic materials, e.g., the carrier mobility. In general, the carrier mobility of inorganic semiconductors is several orders of magnitude larger than that of organic semiconductors. It indicates that the carrier in these two materials possesses different transport mechanism. At present, among the numerous organic semiconductor materials, pentacene exhibits a higher mobility. From1992to2000, the mobility of pentacene has been increased four orders of magnitude. In2004, Jurchescu et al. reported that in the high purity and no defect pentacene crystals, the mobility can reach35～38cm2/(V·s).
According to the size of the molecular weight, organic semiconductors can usually been divided into two groups:organic polymers (such as polyacetylene, polythiophene, polyparaphenylene and polypyrrole) and organic small molecules (such as Alq3, rubrene and pentacene). For polymers, their molecular weight is over ten thousand. In general, the polymer refers to the compound that is polymerized by a large number of atoms with covalent bond. For example, in polyacetylene, the two adjacent carbon atoms are connected by the covalent bond, σ bond to form a quasi-one-dimensional structure. Every carbon atom provides a π electron. This delocalized π electron can transfer between the adjacent carbon atoms. In contrast to the conventional inorganic materials, organic polymers possess strong electron-phonon (e-ph for short) interaction. The extra electron or hole produced by injection or photoexcitation will be trapped by the lattice structure to form the localized electron-lattice coupled state, rather than the expanded state. Therefore, the carriers in polymers are not the traditional electron and hole, but the self-trapped elementary excitation, such as soliton (only in polymers with the degenerate ground state), polaron and bipolaron. According to the number of the charge, soliton can be divided into the neutral solution, the negative soliton and the positive soliton. Polaron has one positive or negative charge with1/2spin. Bipolaron has two positive or negative charges with no spin. In addition, when the polymers in the ground state absorb a photon, the electron will be excited from the top of the valence band or the highest occupied molecular orbital (HOMO for short) to the bottom of the conduction band or the lowest unoccupied molecular orbital (LUMO for short), and then a self-trapped exciton is formed. If the strength of the photoexcitation is increased, two electrons will be excited simultaneously to transit from HOMO to LUMO, and then a self-trapped biexciton is formed.
In2000, Sun et al. investigated the static polarization behaviors of exciton and biexciton in polyacetylene, respectively, under a uniform external electric field. It is found that, the exciton is normally polarized while the biexciton is reversely polarized. Then they projected that when the polyacetylene with an exciton absorbs a photon to form a biexciton, the polarization of the molecule will be reversed, i.e., photoinduced polarization inversion (PIPI). However, the probability of the double-photon absorption in polymers to form a biexciton is very low, and the lifetime of biexciton is very short. Therefore, it is difficult to obtain the reverse polarization of the biexciton in experiment. With this consideration, in2005, Gao et al. investigated the static polarization behavior of the excited polaron in oligomer. It is found that this excited state also possesses the reverse polarization property. However, it is still unstable as the charged polaron will move along the polymer chain under the electric field.In addition, the above researches indicated that the reverse polarization of the biexciton and the excited polaron are obtained only in non-degenerate polymers. With the increase of the confinement constant, the strength of their reverse polarization decreases rapidly. However, for most polymers, such as polythiophene, polyparaphenylene and polypyrrole, their ground state is non-degenerate. Therefore, it is necessary for us to look for other excited states that can be reversely polarized also in non-degenerate polymers.
In this paper, we use the one-dimensional extended Su-Schrieffer-Heeger model under the tight-binding approximation, to investigate the static polarization behavior of another excited state, the high-energy exciton. This excited state is the self-trapped state induced by the single electron transition from HOMO-T to LUMO+1. We find that the high-energy exciton is reversely polarized under the uniform external electric field. By analyzing the polarization of the wave functions corresponding to the deep energy levels, we point out the origin of this reverse polarization behavior. We also show the effect of the non-degenerate confinement on the reverse polarization of the high-energy exciton, and find that with the increase of the confinement constant, the strength of the reverse polarization is little changed. Therefore, we conclude that the reverse polarization of the high-energy exciton is stable in non-degenerate polymers. In addition, we further explore the strength of reverse polarization under different electric fields. It is found that there exists a critical electric field, over which the high-energy exciton will dissociate and the reverse polarization will correspondingly vanish.
As we all know, the electron possesses both the charge and spin properties. In the past researches, more attentions have been paid on the charge property of electron, while the spin property is ignored. In recent years, with the development of the spintronics, more and more researchers have begun to focus on the study about electron spin, which contains the spin injection, spin polarization, spin transport, and so on. In organic semiconductor materials, the spin-orbit coupling and the hyperfine interaction is weak, which can induce a long spin relaxation time. Thus it can be seen that the organic semiconductor materials are the ideal materials for the spin polarized injection. In addition, the magnetic field effect (MFE) on photocurrent, photoluminescence, electroluminescence and charge-injection current of the organic semiconductor materials based organic light emitting devices has been the research hotspot in spintronics during the past years.
Among the above magnetic field effect of the organic semiconductor materials, the effect of the magnetic field on the charge-injection current is most studied. In2004, Francis et al. explored the dependence of the resistance in the PFO based organic light emitting device ITO/PEDOT/PFO/Ca at room temperature on the applied magnetic field, and gave the definition of the organic magnetoresistance (MR for short):the relative change of the device resistance R before and after the applying of the magnetic field B, as is described by the formula:MR=[R(B)-R(0)]/R(0). It is found that, under a weak magnetic field (about20mT), the MR of polymer PFO is up to10%. Later on, Mermer et al. successively observed the organic magnetoresistance effect in various polymers, such as RRa-P3OT, RR-P3HT, Pt-PPE and PPE, as well as the small molecules, such as Alq3, Ir(ppy)3and pentacene. By analyzing the MR curves of different materials, it is found that they generally have the following typical features:(1) MR can be positive or negative, depending on many factors, such as the variety of materials, temperature, voltage and the thickness of organic layer.(2) The magnitude of MR is related on the voltage, but is independent on the direction of the applied magnetic field.(3) The MR curves of different materials can be well fitted with the Lorentzian function B2/(B2+B02) or the non-Lorentzian function B2/(|B|+B0)2. Here, B0(about several mT) is the fitting parameter. It is indicated that the different organic semiconductor materials may share a common origin of the organic magnetoresistance effect.
Up to now, the theoretical explanation on MFE of organic semiconductor materials mainly contains the following three mechanisms:(1) Polaron-pair model. In this model, it is presented that the magnetic field and the hyperfine field affect the interconversion between the singlet and triplet polaron pairs, and then the formation ratio between the singlet and triplet exciton, so as to affect the light emitting efficiency of the devices.(2) Bipolaron model. This model proposes that the magnetic field and the hyperfine field can modulate the intercrossing between polaron and bipolaron, and then the concentration ratio between them. As they have different effective mass, the mobility of them is then different. By tuning the concentration ratio between polaron and bipolaron, the magnetic field ultimately affects the device current.(3) Polaron-triplet exciton quenching model. This model suggests that the polaron interacts with the triplet exciton during its transport. The mobility of polaron is decreased when it is scattered by triplet exciton. As the magnetic field and the hyperfine field can modulate the formation ratio between the singlet and the triplet exciton, and then the probability that the polaron is scattered by the triplet exaction, the magnetic field effect on device current is therefore realized. It should be mentioned that, all the above theoretical mechanisms seem to stress the importance of the hyperfine interaction between the electron spin and the hydrogen spin to the organic magnetoresistance.
Although there have been many qualitative theoretical explanations on the experimental results of the organic magnetoresistance, the quantitative calculations, especially the direct comparison with the experimental data of the organic magnetoresistance is little. With this consideration, in this paper we use the Troisi-Orlandi model of small molecular crystals, and take into account both the Zeeman interaction between the electron spin and the external magnetic field and the hyperfine interaction between the electron spin and the hydrogen spin, to explore the relative change of polaron mobility in small molecule under the magnetic field. According to the definition of organic magnetoresistance, we give the MR curve of the small molecule-pentacene, and make a direct comparison with the experimental data. In addition, we further explore the effect of the hyperfine interaction strength and the e-ph coupling interaction strength on MR. It is found that, for one thing, with the increase of the hyperfine field, the magnitude of MR,|MR|increases. The results show a good agreement with the experimental data. For another thing, with the decrease of the e-ph coupling,|MR|decreases. If the e-ph coupling is reduced to zero,i.e. the case in inorganic semiconductors,|MR|is reduced to zero too. Thus it demonstrates that the magnetic field effect is the characteristic of organic semiconductors.
In addition, the voltage effect is an important part in the experimental researches on organic magnetoresistance. For example, in2005, Mermer et al. explored the effect of the voltage on the magnetoresistance of small molecule Alq3. It is presented that the MR of Alq3is always negative at all different voltages, and the dependence between them is temperature-dependent. In2007, Bloom et al. also studied the voltage effect on MR in Alq3, while it is found that the voltage can tune the sign of MR. In addition, Martin et al.'s results show that the effect of voltage on MR is dependent on the thickness of the organic layer. Thus it can be seen that the voltage effect on magnetoresistance is complex. Therefore, it is necessary for us to undertake the theoretical investigation on this voltage effect, so as to better understand the above experimental phenomena.
In this paper, based on the previous theoretical work, we also use the Troisi-Orlandi model of small molecules to mainly investigate the voltage effect on their magnetoresistance. By calculation, we obtain the dependence of MR in small molecules Alq3and pentacene, respectively, on the magnetic field at different voltages. It is found that, under the same magnetic field, with the increase of the voltage the magnetoresistance decreases. The reason is as follows. From the Hamilton of the system we can see that, for the polaron with1/2spin, the random distributed hyperfine fields equal to a series of disordered potential barriers, which can block the polaron transport. The increase of the voltage induces that the carrier gets more energy. In this case, the blocking effect of the disordered potential barriers produced by the random distributed hyperfine fields on the polaron transport is weakened, and then the magnetoresistance effect is weakened too. Our calculation results agree well with some experimental data. In addition, with the increase of the voltage, the injection efficiency increases. In this case, the proportion of the bipolaron in small molecule increases. With this consideration, we further explore the magnetoresistance under different polaron/bipolaron density ratio, and find that the more the bipolaron is, the smaller the magnetoresistance is.
To sum up, in this paper we will give the theoretical investigations on various kinds of elementary excitations in organic semiconductor materials, especially on the change of their polarization behavior and the conductivity under the external field, including the electric field and the magnetic field. I hope that through our work, we can better understand the experimental phenomena and guide the experiments.
引文
[1]吴世康,汪鹏飞,有机电子学概论,化学工业出版社,北京(2010)
[2]解士杰,尹笋,高琨,有机固体物理,科学出版社,北京(2012)
[3]孙鑫,高聚物中的孤子和极化子,四川教育出版社,成都(1987)
[4]H. Kakuta, T. Hirahara. I. Matsuda, T. Nagao, S. Hasegawa, N. Ueno and K. Sakamoto, Phys. Rev. Lett 98 247601:1-4 (2007)
[5]T.-C. Chung, F. Moraes. J.D. Flood and A.J. Heeger, Phys. Rev. B 29 2341-2343 (1984)
[6]W.P. Su, J.R. Schrieffer and A.J. Heeger, Phys. Rev. Lett.42 1698-1701 (1979)
[7]W.P. Su, J.R. Schrieffer and A.J. Heeger, Phys. Rev. B 22 2099-2111 (1980)
[8]A.J. Heeger, S. Kivelson, J.R. Schrieffer and W.P. Su, Rev. Mod. Phys.60781-850 (1988)
[9]C.W. Tang and S.A. VanSlyke, Appl. Phys. Lett.51913-915 (1987)
[10]J.H. Burroughes, D.D.C. Bradley, A.R. Brown, R.N. Marks, K. Mackay, R.H. Friend, P. L. Burns and A.B. Holmes, Nature 347 539-541 (1990)
[11]Z. An, B. Di, H. Zhao and C.Q. Wu, Eur. Phys. J. B 63 71-77 (2008)
[12]V. Dediu, M. Murgia, F.C. Matacotta, C. Taliani and S. Barbanera, Solid State Commun.122 181-184(2002)
[13]Z.H. Xiong, D. Wu, Z.V. Vardeny and J. Shi, Nature 427 821-824 (2004)
[14]B. Hu, L. Yan and M. Shao, Adv. Mater.21 1500-1516 (2009)
[15]O. Mermer, G. Veeraraghavan, T.L. Francis, Y. Sheng, D.T. Nguyen, M. Wohlgenannt, A. Kohler. M.K. Al-Suti and M.S. Khan, Phys. Rev. B 72 205202:1-12 (2005)
[16]E. Frankevich and A. Zakhidov, Phys. Rev. B 53 4498-4508 (1996)
[17]J. Kalinowski, M. Cocchi, D. Virgili, P.D. Marco and V. Fattori, Chem. Phys. Lett. 380710-715(2003)
[18]T.L. Francis, O. Mermer, G. Veeraraghavan and M. Wohlgenannt, New J. Phys.6 185:1-8(2004)
[19]O. Mermer, G. Veeraraghavan, T.L. Francis and M. Wohlgenannt, Solid State Commun.134631-636 (2005)
[20]Y. Sheng, T.D. Nguyen, G. Veeraraghavan, O. Mermer, M. Wohlgenannt, S. Qiu and U. Scherf, Phys. Rev. B 74 045213:1-9 (2006)
[21]Y. Sheng, T.D. Nguyen, G. Veeraraghavan, O. Mermer and M. Wohlgenannt, Phys. Rev. B 75 035202:1-6 (2007)
[22]G. Veeraraghavan, T.D. Nguyen, Y. Sheng,O. Mermer and M. Wohlgenannt, J. Phys.: Condens. Matter 19 036209:1-13 (2007)
[23]T.D. Nguyen, Y. Sheng, M. Wohlgenannt and T.D. Anthopoulos, Synth. Met.157 930-934 (2007)
[24]T.D. Nguyen, Y. Sheng, J. Rybicki and M. Wohlgenannt, Phys. Rev. B 77 235209:1-5 (2008)
[25]T.D. Nguyen, Y. Sheng, J. Rybicki, G. Veeraraghavan and M. Wohlgenannt, Synth. Met.160 320-324(2010)
[26]W. Wagemans and B. Koopmans, Phys. Status Solidi B 248 1029-1041 (2011)
[27]V.N. Prigodin, J.D. Bergeson, D.M. Lincoln and A.J. Epstein, Synth. Met.156 757-761 (2006)
[28]P.A. Bobbert, T.D. Nguyen, F.W.A. van Oost, B. Koopmans and M. Wohlgenannt, Phys. Rev. Lett.99 216801:1-4 (2007)
[29]P.A. Bobbert, T.D. Nguyen, W. Wagemans, F.W.A. van Oost, B. Koopmans and M. Wohlgenannt, Synth. Met.160 223-229 (2010)
[30]P. Desai, P. Shakya, T. Kreouzis and W.P. Gillin, Phys. Rev. B 75 094423:1-5 (2007)
[31]Z. Sun, D.S. Liu, S. Stafstrom and Z. An, J. Chem. Phys.134 044906:1-5 (2011)
[32]X.R. Wang and S.J. Xie, Eur. Phys. Lett.9257013:1-4 (2010)
[33]Y. Yao, W. Si and C.Q. Wu, Synth. Met.161632-636 (2011)
[34]解士杰,高琨,低维量子物理,山东科学技术出版社,济南(2009)
[35]M.I.迪阿科诺夫,姬扬,半导体中的自旋物理学,科学出版社,北京(2010)
[36]杨福家,原子物理学(第三版),高等教育出版社,北京(2000)
[37]X. Sun, R.L. Fu, K. Yonemitsu and K. Nasu, Phys. Rev. Lett.84 2830-2832 (2000)
[38]X. Sun, R.L. Fu, K. Yonemitsu and K. Nasu, Phys. Rev. A 64 032504:1-7 (2001)
[39]K. Gao, X.J. Liu, D.S. Liu and S.J. Xie, J. Chem. Phys.123 234702:1-5 (2005)
[40]高琨,刘晓静,刘德胜,解士杰,物理学报54 5324-5328(2005)
[41]K. Gao, X.J. Liu, D.S. Liu and S.J. Xie, J. Phys.:Conf. Ser. 29 45-49 (2006)
[42]G. Iucci, K. Xing, M. Logdlund, M. Fahlman and W.R. Salaneck, Chem. Phys. Lett. 244 139-144(1995)
[43]M.P. Lima, G.M. e Silva, Phys. Rev. B 74 224304:1-6 (2006)
[1]W.P. Su, J.R. Schrieffer and A.J. Heeger. Phys. Rev. Lett.42 1698-1701 (1979)
[2]W.P. Su, J.R. Schrieffer and A.J. Heeger, Phys. Rev. B 22 2099-2111 (1980)
[3]A.J. Heeger, S. Kivelson, J.R. Schrieffer and W.P. Su, Rev. Mod. Phys.60781-850 (1988)
[4]S. Stafstrom and K.A. Chao, Phys. Rev. B 29 7010-7011 (1984)
[5]H.W. Streitwolf, Phys. Rev. B 58 14356-14363 (1998)
[6]A. Johansson and S. Stafstrom, Phys. Rev. Lett.86 3602-3605 (2001)
[7]A.A. Johansson and S. Stafstrom, Phys. Rev. B 69 235205 (2004)
[8]M. Hultell and S. Stafstrom, Phys. Rev. B 75104304:1-7 (2007)
[9]X.J. Liu, K. Gao, J.Y. Fu, Y. Li, J.H. Wei and S.J Xie, Phys. Rev. B 74 172301:1-4 (2006)
[10]K. Gao, X.J. Liu, D.S. Liu and S.J Xie, Phys. Rev. B 75 205412:1-6 (2007)
[11]Z. Sun, Y. Li, S.J Xie, Z. An and D.S. Liu Phys. Rev. B 79 201310:1-4 (2009)
[12]Z. An, C.Q. Wu and X. Sun, Phys. Rev. Lett.93 216407:1-4 (2004)
[13]Z. An, B. Di, H. Zhao and C.Q. Wu Eur. Phys. J. B 6371-77 (2008)
[14]Y. Meng, X.J. Xiu, B. Di and Z. An, J. Chem. Phys.131 244502 (2009)
[15]Y. Ono and A. Terai, J. Phys. Soc. Jpn.59 2893-2904 (1990)
[16]M. Kuwabara, Y. Ono and A. Terai, J. Phys. Soc. Jpn.60 1286-1293 (1991)
[17]Y. Ono, M. Kuwabara and A. Terai, J. Phys. Soc. Jpn.6031 20-3129 (1991)
[18]M. Kuwabara, Y. Ono and A. Terai, J. Phys. Soc. Jpn.612412-2418 (1992)
[19]Y. Arikabe, M. Kuwabara and Y. Ono J. Phys. Soc. Jpn.65 1317-1324 (1996)
[20]H. Okamoto and Y. Ono, J. Phys. Soc. Jpn.74 1006-1013 (2005)
[21]孙鑫,高聚物中的孤子和极化子,四川教育出版社,成都(1987)
[22]解士杰,韩圣浩,凝聚态物理,山东教育出版社,济南(2001)
[23]解士杰,高琨,低维量子物理,山东科学技术出版社,济南(2009)
[24]解士杰,尹笋,高琨,有机固体物理,科学出版社,北京(2012)
[25]A. Troisi and G. Orlandi, Phys. Rev. Lett.96 086601:1-4 (2006)
[26]D.L. Cheung and A. Troisi, Phys. Chem. Chem. Phys.10 5941-5952 (2008)
[27]A. Troisi, Adv. Polym. Sci.223 259-300 (2010)
[28]R.W. Brankin, I. Gladwell and L.F. Shampine, RKSUITE:Software for ODE IVPS, http://www.netlib.org
[1]J.H. Burroughes, D.D.C. Bradley, A.R. Brown, R.N. Marks, K. Mackay, R.H. Friend, P. L. Burns and A.B. Holmes, Nature 347 539-541 (1990)
[2]R.H. Friend, R. W. Gymer, A.B. Holmes, J.H. Burroughes, R.N. Marks, C. Taliani, D.D.C. Bradley, D.A.Dos Santos, J.L. Bredas, M. Logdlund and W.R. Salaneck, Nature 397 121-128(1999)
[3]H. Sirringhaus, N. Tessler and R.H. Friend, Science 280 1741-1744 (1998)
[4]N. Stutzmann, R.H. Friend and H. Sirringhaus, Science 299 1881-1884 (2003)
[5]W.R Su, J.R. Schrieffer and A.J. Heeger, Phys. Rev. Lett.42 1698-1701 (1979)
[6]W.R Su, J.R. Schrieffer and A.J. Heeger, Phys. Rev. B 22 2099-2111 (1980)
[7]A.J. Heeger, S. Kivelson, J.R. Schrieffer and W.R Su, Rev. Mod. Phys.60781-850 (1988)
[8]S.A. Brazovskil and N.N. Kirova, JETP Lett.334-8 (1981)
[9]傅柔励,叶红娟,李蕾,傅荣堂,缭健,孙鑫,张志林,物理学报,47 94-101(1998)
[10]李蕾,饶雪松,孙鑫,傅柔励,褚君浩,张志林,物理学报,47 1536-1541(1998)
[11]X. Sun, L. Li, R.L. Fu, T.F. George, Synth. Met.101263-264 (1999)
[12]X. Sun, R.L. Fu, K. Yonemitsu and K. Nasu, Phys. Rev. Lett.84 2830-2832 (2000)
[13]R.L. Fu, G.Y. Guo, X. Sun, Phys. Rev. B 62 15735-15744 (2000)
[14]X. Sun, R.L. Fu, K. Yonemitsu and K. Nasu, Phys. Rev. A 64 032504:1-7 (2001)
[15]L.X. Wang, D.S. Liu, J.H. Wei, S.J. Xie and S.H. Han, J. Chem. Phys.116 6760-6763 (2002)
[16]王鹿霞,刘德胜,解士杰,物理学报51 362-366(2002)
[17]高琨,付吉永,刘德胜,解士杰,物理学报54 665-668(2005)
[18]K. Gao, S.J. Xie, S. Yin, Y. Li, D.S. Liu and X. Zhao, Org. Electron.10 1601-1605 (2009)
[19]K. Gao, X.J. Liu, D.S. Liu and S.J. Xie, J. Chem. Phys.123 234702:1-5 (2005)
[20]高琨,刘晓静,刘德胜,解士杰,物理学报54 5324-5328(2005)
[21]K. Gao, X.J. Liu, D.S. Liu and S.J. Xie, J. Phys.:Conf. Ser. 29 45-49 (2006)
[22]Z. An, C.Q. Wu and X. Sun Phys. Rev. Lett.93 216407:1-4 (2004)
[23]W.P. Su, Solid State Commun.35899-901 (1980)
[24]S. Stafstrom and K.A. Chao, Phys. Rev. B 29 7010-7011 (1984)
[25]魏建华,解士杰,梅良模,物理学报46 747-755(1997)
[26]L. Lauchlan, S. Etemad, T.-C. Chung, A.J. Heeger and A.G. MacDiarmid, Phys. Rev. B 24 3701-3711 (1981)
[27]Y. Ono and A. Terai, J. Phys. Soc. Jpn.59 2893-2904 (1990)
[28]M. Kuwabara, Y. Ono and A. Terai, J. Phys. Soc. Jpn.60 1286-1293 (1991)
[1]C.W. Tang, Appl. Phys. Lett.48 183-185 (1986)
[2]J.H. Burroughes, D.D.C. Bradley, A.R. Brown, R.N. Marks, K. Mackay, R.H. Friend, P.L. Burns and A.B. Holmes, Nature 347 539-541 (1990)
[3]H. Sirringhaus, N. Tessler and R.H. Friend, Science 280 1741-1744 (1998)
[4]R.H. Friend, R.W. Gymer, A.B. Holmes, J.H. Burroughes, R.N. Marks, C. Taliani, D.D.C. Bradley, D.A.Dos Santos, J.L. Bredas, M. Logdlund and W.R. Salaneck, Nature 397 121-128 (1999)
[5]T.L. Francis, O. Mermer, G. Veeraraghavan and M. Wohlgenannt, New. J. Phys.6 185:1-8(2004)
[6]O. Mermer, G. Veeraraghavan, T.L. Francis and M. Wohlgenannt, Solid State Commun.134631-636 (2005)
[7]O. Mermer, G. Veeraraghavan, T.L. Francis, Y. Sheng, D.T. Nguyen, M. Wohlgenannt, A. Kohler, M.K. Al-Suti and M.S. Khan, Phys. Rev. B 72 205202:1-12 (2005)
[8]Y. Sheng, T.D. Nguyen, G. Veeraraghavan, O. Mermer, M. Wohlgenannt, S. Qiu and U. Scherf, Phys. Rev. B 74 045213:1-9 (2006)
[9]Y. Sheng, T.D. Nguyen, G. Veeraraghavan, O. Mermer, M. Wohlgenannt, Phys. Rev. B 75 035202:1-6 (2007)
[10]G. Veeraraghavan, T.D. Nguyen, Y. Sheng, O. Mermer and M. Wohlgenannt, J. Phys.: Condens. Matter 19 036209:1-13 (2007)
[11]T.D. Nguyen, Y. Sheng, M. Wohlgenannt and T.D. Anthopoulos, Synth. Met.157 930-934 (2007)
[12]T.D. Nguyen, Y. Sheng, J. Rybicki and M. Wohlgenannt, Phys. Rev. B 77 235209:1-5 (2008)
[13]T.D. Nguyen, Y. Sheng, J. Rybicki, G. Veeraraghavan and M. Wohlgenannt, Synth. Met.160320-324(2010)
[14]F.J. Wang, H. Bassler and Z.V. Vardeny, Phys. Rev. Lett.101 236805:1-4 (2008)
[15]T.D. Nguyen, B.R. Gautam, E. Ehrenfreund and Z.V. Vardeny, Phys. Rev. Lett.,105 166804:1-4(2010)
[16]T.D. Nguyen, G.H. Markosian, F. Wang, L. Wojcik, X.G. Li, E. Ehrenfreund and Z.V. Vardeny, Nature Mater.9 345-352 (2010)
[17]G. Ni, T.D. Nguyen and Z.V. Vardeny, Appl. Phys. Lett.98 263302 (2011)
[18]E. Ehrenfreund and Z.V. Vardeny, Isr. J. Chem.52552-562 (2012)
[19]P.A. Bobbert, T.D. Nguyen, F.W.A. van Oost, B. Koopmans and M. Wohlgenannt, Phys. Rev. Lett.99 216801:1-4 (2007)
[20]P.A. Bobbert, W. Wagemans, F.W.A. van Oost, B. Koopmans and M. Wohlgenannt, Phys. Rev. Lett.102 156604:1-4 (2009)
[21]P.A. Bobbert, T.D. Nguyen, W. Wagemans, F.W.A. van Oost, B. Koopmans and M. Wohlgenannt, Synth. Met.160 223-229 (2010)
[22]Y. Zhang, R. Liu, Y.L. Lei and Z.H. Xiong, Appl. Phys. Lett.94 083307:1-3 (2009)
[23]P. Chen, Q.L. Song, W.C.H. Choy, B.F. Ding, Y.L. Liu and Z.H. Xionga, Appl. Phys. Lett.99 143305:1-3(2011)
[24]Y. Yao, W. Si, C.Q. Wu, Synth. Met.161632-636 (2011)
[25]B. Hu and Y. Wu, Nature Mater.6 985-991 (2007)
[26]B. Hu, L. Yan and M. Shao, Adv. Mater.21 1500-1516 (2009)
[27]V.N. Prigodin, J.D. Bergeson, D.M. Lincoln and A.J. Epstein, Synth. Met.156 757-761 (2006)
[28]N.J. Rolfe, M. Heeney, P.B. Wyatt, A.J. Drew, T. Kreouzis and W.P. Gillin, Phys. Rev. B 80 241201:1-4 (2009)
[29]B.F. Ding, Y. Yao, Z.Y. Sun, C.Q. Wu, X.D. Gao, Z.J. Wang, X.M. Ding, W.C.H. Choy and X.Y Hou, Appl. Phys. Lett.97 163302:1-3 (2010)
[30]Y.H. Yan, M.J. Chen and C.Q. Wu, Chin. Phys. Lett.23 2549-2552 (2006)
[31]A. Troisi and G. Orlandi, Phys. Rev. Lett.96 086601:1-4 (2006)
[32]陈鄂生,量子力学基础教程,山东大学出版社,济南(2006)
[33]K. Schulten and P.G. Wolynes, J. Chem. Phys.68 3292-3297 (1978)
[34]解士杰,高琨,低维量子物理,山东科学技术出版社,济南(2009)
[35]R.W. Brankin, I. Gladwell and L.F. Shampine, RKSUITE:Software for ODE IVPS, http://www.netlib.org
[36]A.A. Johansson and S. Stafstrom, Phys. Rev. B 69 235205:1-7 (2004)
[1]G. Veeraraghavan, T.D. Nguyen, Y. Sheng, O. Mermer and M. Wohlgenannt, J. Phys.: Condens. Matter 19 036209:1-13 (2007)
[2]B. Hu, L. Yan and M. Shao, Adv. Mater.21 1500-1516 (2009)
[3]T.D. Nguyen, B.R. Gautam, E. Ehrenfreund and Z.V. Vardeny, Phys. Rev. Lett.105 166804:1-4(2010)
[4]T.L. Francis, O. Mermer, G. Veeraraghavan and M. Wohlgenannt, New J. Phys.6 185:1-8(2004)
[5]O. Mermer, G. Veeraraghavan, T.L. Francis and M. Wohlgenannt, Solid State Commun.134 631-636 (2005)
[6]O. Mermer, G. Veeraraghavan, T.L. Francis, Y. Sheng, D.T. Nguyen, M. Wohlgenannt, A. Kohler, M.K. Al-Suti and M.S. Khan, Phys. Rev. B 72 205202:1-12 (2005)
[7]J.L. Martin, J.D. Bergeson, V.N. Prigodin and A.J. Epstein, Synth. Met.160 291-296 (2010)
[8]P. Shakya, P. Desai, M. Somerton, G. Gannaway, T. Kreouzis and W.P. Gillin, J. Appl. Phys.1031 03715:1-5(2008)
[9]H. Kang, C.H. Park, J. Lim, C. Lee, W. Kang and C.S. Yoon, Org. Electron.13 1012-1017(2012)
[10]V.N. Prigodin, J.D. Bergeson, D.M. Lincoln and A.J. Epstein, Synth. Met.156 757-761 (2006)
[11]P.A. Bobbert, T.D. Nguyen, F.W.A. van Oost, B. Koopmans and M. Wohlgenannt, Phys. Rev. Lett.99 216801:1-4 (2007)
[12]P. Desai, P. Shakya, T. Kreouzis and W.P. Gillin, Phys. Rev. B 75 094423:1-5 (2007)
[13]Y. Sheng, T.D. Nguyen, G. Veeraraghavan, O. Mermer, M. Wohlgenannt, S. Qiu and U. Scherf, Phys. Rev. B 74 045213:1-9 (2006)
[14]Y. Sheng, T.D. Nguyen, G. Veeraraghavan, O. Mermer and M. Wohlgenannt, Phys. Rev. B 75 035202:1-6 (2007)
[15]X.F. Dong, X.X. Li and S.J Xie, Org. Electron.12 1835-1840 (2011)
[16]X.X. Li, X.F. Dong, J. Lei, S.J. Xie and A. Saxena, Appl. Phys. Lett.100 142408:1-4 (2012)
[17]F.L. Bloom, W. Wagemans, M. Kemerink and B. Koopmans, Phys. Rev. Lett.99 257201:1-4(2007)
[18]A. Troisi and G. Orlandi, Phys. Rev. Lett.96 086601:1-4 (2006)
[19]K. Schulten and P.G. Wolynes, J. Chem. Phys.68 3292-3297 (1978)
[20]W. Wagemans and B. Koopmans, Phys. Status Solidi B 248 1029-1041 (2011)
[21]R.W. Brankin, I. Gladwell and L.F. Shampine, RKSUITE:Software for ODE IVPS, http://www.netlib.org
[22]K.A. Nelson, D.R. Lutz and M.D. Fayer, Phys. Rev. B 24 3261-3275 (1981)
[23]R.G. Kepler, P.M. Beeson, S.J. Jacobs, R.A. Anderson, M.B. Sinclair, V.S. Valencia and P.A. Cahill, Appl. Phys. Lett.66 3618-3620 (1995)
[24]B.J. Chen, W.Y. Lai, Z.Q. Gao, C.S. Lee, S.T. Lee and W.A. Gambling, Appl. Phys. Lett.75 4010-4012(1999)
[25]Y. Olivier, V. Lemaur, J.L. Bredas and J. Cornil, J. Phys. Chem. A 110 6356-6364 (2006)
[26]S.J. Xie, Z.Y. Li and X. Sun, J. Shandong University 24 44-50 (1989)
[27]V. Mujica, A.E. Roitberg and M. Ratner, J. Chem. Phys.112 6834-6839 (2000)
[28]Y. Xue and M.A. Ratner, Phys. Rev. B 68 115406:1-18 (2003)
[29]N.J. Rolfe, M. Heeney, P.B. Wyatt, A.J. Drew, T. Kreouzis and W.P. Gillin, Phys. Rev. B 80 241201:1-4 (2009)
[30]G. Iucci, K. Xing, M. Logdlund, M. Fahlman and W.R. Salaneck, Chem. Phys. Lett. 244 139-144(1995)
[31]M.P. Lima, G.M. e Silva, Phys. Rev. B 74 224304:1-6 (2006)
[2]解士杰,尹笋,高琨,有机固体物理,科学出版社,北京(2012)
[3]孙鑫,高聚物中的孤子和极化子,四川教育出版社,成都(1987)
[4]H. Kakuta, T. Hirahara. I. Matsuda, T. Nagao, S. Hasegawa, N. Ueno and K. Sakamoto, Phys. Rev. Lett 98 247601:1-4 (2007)
[5]T.-C. Chung, F. Moraes. J.D. Flood and A.J. Heeger, Phys. Rev. B 29 2341-2343 (1984)
[6]W.P. Su, J.R. Schrieffer and A.J. Heeger, Phys. Rev. Lett.42 1698-1701 (1979)
[7]W.P. Su, J.R. Schrieffer and A.J. Heeger, Phys. Rev. B 22 2099-2111 (1980)
[8]A.J. Heeger, S. Kivelson, J.R. Schrieffer and W.P. Su, Rev. Mod. Phys.60781-850 (1988)
[9]C.W. Tang and S.A. VanSlyke, Appl. Phys. Lett.51913-915 (1987)
[10]J.H. Burroughes, D.D.C. Bradley, A.R. Brown, R.N. Marks, K. Mackay, R.H. Friend, P. L. Burns and A.B. Holmes, Nature 347 539-541 (1990)
[11]Z. An, B. Di, H. Zhao and C.Q. Wu, Eur. Phys. J. B 63 71-77 (2008)
[12]V. Dediu, M. Murgia, F.C. Matacotta, C. Taliani and S. Barbanera, Solid State Commun.122 181-184(2002)
[13]Z.H. Xiong, D. Wu, Z.V. Vardeny and J. Shi, Nature 427 821-824 (2004)
[14]B. Hu, L. Yan and M. Shao, Adv. Mater.21 1500-1516 (2009)
[15]O. Mermer, G. Veeraraghavan, T.L. Francis, Y. Sheng, D.T. Nguyen, M. Wohlgenannt, A. Kohler. M.K. Al-Suti and M.S. Khan, Phys. Rev. B 72 205202:1-12 (2005)
[16]E. Frankevich and A. Zakhidov, Phys. Rev. B 53 4498-4508 (1996)
[17]J. Kalinowski, M. Cocchi, D. Virgili, P.D. Marco and V. Fattori, Chem. Phys. Lett. 380710-715(2003)
[18]T.L. Francis, O. Mermer, G. Veeraraghavan and M. Wohlgenannt, New J. Phys.6 185:1-8(2004)
[19]O. Mermer, G. Veeraraghavan, T.L. Francis and M. Wohlgenannt, Solid State Commun.134631-636 (2005)
[20]Y. Sheng, T.D. Nguyen, G. Veeraraghavan, O. Mermer, M. Wohlgenannt, S. Qiu and U. Scherf, Phys. Rev. B 74 045213:1-9 (2006)
[21]Y. Sheng, T.D. Nguyen, G. Veeraraghavan, O. Mermer and M. Wohlgenannt, Phys. Rev. B 75 035202:1-6 (2007)
[22]G. Veeraraghavan, T.D. Nguyen, Y. Sheng,O. Mermer and M. Wohlgenannt, J. Phys.: Condens. Matter 19 036209:1-13 (2007)
[23]T.D. Nguyen, Y. Sheng, M. Wohlgenannt and T.D. Anthopoulos, Synth. Met.157 930-934 (2007)
[24]T.D. Nguyen, Y. Sheng, J. Rybicki and M. Wohlgenannt, Phys. Rev. B 77 235209:1-5 (2008)
[25]T.D. Nguyen, Y. Sheng, J. Rybicki, G. Veeraraghavan and M. Wohlgenannt, Synth. Met.160 320-324(2010)
[26]W. Wagemans and B. Koopmans, Phys. Status Solidi B 248 1029-1041 (2011)
[27]V.N. Prigodin, J.D. Bergeson, D.M. Lincoln and A.J. Epstein, Synth. Met.156 757-761 (2006)
[28]P.A. Bobbert, T.D. Nguyen, F.W.A. van Oost, B. Koopmans and M. Wohlgenannt, Phys. Rev. Lett.99 216801:1-4 (2007)
[29]P.A. Bobbert, T.D. Nguyen, W. Wagemans, F.W.A. van Oost, B. Koopmans and M. Wohlgenannt, Synth. Met.160 223-229 (2010)
[30]P. Desai, P. Shakya, T. Kreouzis and W.P. Gillin, Phys. Rev. B 75 094423:1-5 (2007)
[31]Z. Sun, D.S. Liu, S. Stafstrom and Z. An, J. Chem. Phys.134 044906:1-5 (2011)
[32]X.R. Wang and S.J. Xie, Eur. Phys. Lett.9257013:1-4 (2010)
[33]Y. Yao, W. Si and C.Q. Wu, Synth. Met.161632-636 (2011)
[34]解士杰,高琨,低维量子物理,山东科学技术出版社,济南(2009)
[35]M.I.迪阿科诺夫,姬扬,半导体中的自旋物理学,科学出版社,北京(2010)
[36]杨福家,原子物理学(第三版),高等教育出版社,北京(2000)
[37]X. Sun, R.L. Fu, K. Yonemitsu and K. Nasu, Phys. Rev. Lett.84 2830-2832 (2000)
[38]X. Sun, R.L. Fu, K. Yonemitsu and K. Nasu, Phys. Rev. A 64 032504:1-7 (2001)
[39]K. Gao, X.J. Liu, D.S. Liu and S.J. Xie, J. Chem. Phys.123 234702:1-5 (2005)
[40]高琨,刘晓静,刘德胜,解士杰,物理学报54 5324-5328(2005)
[41]K. Gao, X.J. Liu, D.S. Liu and S.J. Xie, J. Phys.:Conf. Ser. 29 45-49 (2006)
[42]G. Iucci, K. Xing, M. Logdlund, M. Fahlman and W.R. Salaneck, Chem. Phys. Lett. 244 139-144(1995)
[43]M.P. Lima, G.M. e Silva, Phys. Rev. B 74 224304:1-6 (2006)
[1]W.P. Su, J.R. Schrieffer and A.J. Heeger. Phys. Rev. Lett.42 1698-1701 (1979)
[2]W.P. Su, J.R. Schrieffer and A.J. Heeger, Phys. Rev. B 22 2099-2111 (1980)
[3]A.J. Heeger, S. Kivelson, J.R. Schrieffer and W.P. Su, Rev. Mod. Phys.60781-850 (1988)
[4]S. Stafstrom and K.A. Chao, Phys. Rev. B 29 7010-7011 (1984)
[5]H.W. Streitwolf, Phys. Rev. B 58 14356-14363 (1998)
[6]A. Johansson and S. Stafstrom, Phys. Rev. Lett.86 3602-3605 (2001)
[7]A.A. Johansson and S. Stafstrom, Phys. Rev. B 69 235205 (2004)
[8]M. Hultell and S. Stafstrom, Phys. Rev. B 75104304:1-7 (2007)
[9]X.J. Liu, K. Gao, J.Y. Fu, Y. Li, J.H. Wei and S.J Xie, Phys. Rev. B 74 172301:1-4 (2006)
[10]K. Gao, X.J. Liu, D.S. Liu and S.J Xie, Phys. Rev. B 75 205412:1-6 (2007)
[11]Z. Sun, Y. Li, S.J Xie, Z. An and D.S. Liu Phys. Rev. B 79 201310:1-4 (2009)
[12]Z. An, C.Q. Wu and X. Sun, Phys. Rev. Lett.93 216407:1-4 (2004)
[13]Z. An, B. Di, H. Zhao and C.Q. Wu Eur. Phys. J. B 6371-77 (2008)
[14]Y. Meng, X.J. Xiu, B. Di and Z. An, J. Chem. Phys.131 244502 (2009)
[15]Y. Ono and A. Terai, J. Phys. Soc. Jpn.59 2893-2904 (1990)
[16]M. Kuwabara, Y. Ono and A. Terai, J. Phys. Soc. Jpn.60 1286-1293 (1991)
[17]Y. Ono, M. Kuwabara and A. Terai, J. Phys. Soc. Jpn.6031 20-3129 (1991)
[18]M. Kuwabara, Y. Ono and A. Terai, J. Phys. Soc. Jpn.612412-2418 (1992)
[19]Y. Arikabe, M. Kuwabara and Y. Ono J. Phys. Soc. Jpn.65 1317-1324 (1996)
[20]H. Okamoto and Y. Ono, J. Phys. Soc. Jpn.74 1006-1013 (2005)
[21]孙鑫,高聚物中的孤子和极化子,四川教育出版社,成都(1987)
[22]解士杰,韩圣浩,凝聚态物理,山东教育出版社,济南(2001)
[23]解士杰,高琨,低维量子物理,山东科学技术出版社,济南(2009)
[24]解士杰,尹笋,高琨,有机固体物理,科学出版社,北京(2012)
[25]A. Troisi and G. Orlandi, Phys. Rev. Lett.96 086601:1-4 (2006)
[26]D.L. Cheung and A. Troisi, Phys. Chem. Chem. Phys.10 5941-5952 (2008)
[27]A. Troisi, Adv. Polym. Sci.223 259-300 (2010)
[28]R.W. Brankin, I. Gladwell and L.F. Shampine, RKSUITE:Software for ODE IVPS, http://www.netlib.org
[1]J.H. Burroughes, D.D.C. Bradley, A.R. Brown, R.N. Marks, K. Mackay, R.H. Friend, P. L. Burns and A.B. Holmes, Nature 347 539-541 (1990)
[2]R.H. Friend, R. W. Gymer, A.B. Holmes, J.H. Burroughes, R.N. Marks, C. Taliani, D.D.C. Bradley, D.A.Dos Santos, J.L. Bredas, M. Logdlund and W.R. Salaneck, Nature 397 121-128(1999)
[3]H. Sirringhaus, N. Tessler and R.H. Friend, Science 280 1741-1744 (1998)
[4]N. Stutzmann, R.H. Friend and H. Sirringhaus, Science 299 1881-1884 (2003)
[5]W.R Su, J.R. Schrieffer and A.J. Heeger, Phys. Rev. Lett.42 1698-1701 (1979)
[6]W.R Su, J.R. Schrieffer and A.J. Heeger, Phys. Rev. B 22 2099-2111 (1980)
[7]A.J. Heeger, S. Kivelson, J.R. Schrieffer and W.R Su, Rev. Mod. Phys.60781-850 (1988)
[8]S.A. Brazovskil and N.N. Kirova, JETP Lett.334-8 (1981)
[9]傅柔励,叶红娟,李蕾,傅荣堂,缭健,孙鑫,张志林,物理学报,47 94-101(1998)
[10]李蕾,饶雪松,孙鑫,傅柔励,褚君浩,张志林,物理学报,47 1536-1541(1998)
[11]X. Sun, L. Li, R.L. Fu, T.F. George, Synth. Met.101263-264 (1999)
[12]X. Sun, R.L. Fu, K. Yonemitsu and K. Nasu, Phys. Rev. Lett.84 2830-2832 (2000)
[13]R.L. Fu, G.Y. Guo, X. Sun, Phys. Rev. B 62 15735-15744 (2000)
[14]X. Sun, R.L. Fu, K. Yonemitsu and K. Nasu, Phys. Rev. A 64 032504:1-7 (2001)
[15]L.X. Wang, D.S. Liu, J.H. Wei, S.J. Xie and S.H. Han, J. Chem. Phys.116 6760-6763 (2002)
[16]王鹿霞,刘德胜,解士杰,物理学报51 362-366(2002)
[17]高琨,付吉永,刘德胜,解士杰,物理学报54 665-668(2005)
[18]K. Gao, S.J. Xie, S. Yin, Y. Li, D.S. Liu and X. Zhao, Org. Electron.10 1601-1605 (2009)
[19]K. Gao, X.J. Liu, D.S. Liu and S.J. Xie, J. Chem. Phys.123 234702:1-5 (2005)
[20]高琨,刘晓静,刘德胜,解士杰,物理学报54 5324-5328(2005)
[21]K. Gao, X.J. Liu, D.S. Liu and S.J. Xie, J. Phys.:Conf. Ser. 29 45-49 (2006)
[22]Z. An, C.Q. Wu and X. Sun Phys. Rev. Lett.93 216407:1-4 (2004)
[23]W.P. Su, Solid State Commun.35899-901 (1980)
[24]S. Stafstrom and K.A. Chao, Phys. Rev. B 29 7010-7011 (1984)
[25]魏建华,解士杰,梅良模,物理学报46 747-755(1997)
[26]L. Lauchlan, S. Etemad, T.-C. Chung, A.J. Heeger and A.G. MacDiarmid, Phys. Rev. B 24 3701-3711 (1981)
[27]Y. Ono and A. Terai, J. Phys. Soc. Jpn.59 2893-2904 (1990)
[28]M. Kuwabara, Y. Ono and A. Terai, J. Phys. Soc. Jpn.60 1286-1293 (1991)
[1]C.W. Tang, Appl. Phys. Lett.48 183-185 (1986)
[2]J.H. Burroughes, D.D.C. Bradley, A.R. Brown, R.N. Marks, K. Mackay, R.H. Friend, P.L. Burns and A.B. Holmes, Nature 347 539-541 (1990)
[3]H. Sirringhaus, N. Tessler and R.H. Friend, Science 280 1741-1744 (1998)
[4]R.H. Friend, R.W. Gymer, A.B. Holmes, J.H. Burroughes, R.N. Marks, C. Taliani, D.D.C. Bradley, D.A.Dos Santos, J.L. Bredas, M. Logdlund and W.R. Salaneck, Nature 397 121-128 (1999)
[5]T.L. Francis, O. Mermer, G. Veeraraghavan and M. Wohlgenannt, New. J. Phys.6 185:1-8(2004)
[6]O. Mermer, G. Veeraraghavan, T.L. Francis and M. Wohlgenannt, Solid State Commun.134631-636 (2005)
[7]O. Mermer, G. Veeraraghavan, T.L. Francis, Y. Sheng, D.T. Nguyen, M. Wohlgenannt, A. Kohler, M.K. Al-Suti and M.S. Khan, Phys. Rev. B 72 205202:1-12 (2005)
[8]Y. Sheng, T.D. Nguyen, G. Veeraraghavan, O. Mermer, M. Wohlgenannt, S. Qiu and U. Scherf, Phys. Rev. B 74 045213:1-9 (2006)
[9]Y. Sheng, T.D. Nguyen, G. Veeraraghavan, O. Mermer, M. Wohlgenannt, Phys. Rev. B 75 035202:1-6 (2007)
[10]G. Veeraraghavan, T.D. Nguyen, Y. Sheng, O. Mermer and M. Wohlgenannt, J. Phys.: Condens. Matter 19 036209:1-13 (2007)
[11]T.D. Nguyen, Y. Sheng, M. Wohlgenannt and T.D. Anthopoulos, Synth. Met.157 930-934 (2007)
[12]T.D. Nguyen, Y. Sheng, J. Rybicki and M. Wohlgenannt, Phys. Rev. B 77 235209:1-5 (2008)
[13]T.D. Nguyen, Y. Sheng, J. Rybicki, G. Veeraraghavan and M. Wohlgenannt, Synth. Met.160320-324(2010)
[14]F.J. Wang, H. Bassler and Z.V. Vardeny, Phys. Rev. Lett.101 236805:1-4 (2008)
[15]T.D. Nguyen, B.R. Gautam, E. Ehrenfreund and Z.V. Vardeny, Phys. Rev. Lett.,105 166804:1-4(2010)
[16]T.D. Nguyen, G.H. Markosian, F. Wang, L. Wojcik, X.G. Li, E. Ehrenfreund and Z.V. Vardeny, Nature Mater.9 345-352 (2010)
[17]G. Ni, T.D. Nguyen and Z.V. Vardeny, Appl. Phys. Lett.98 263302 (2011)
[18]E. Ehrenfreund and Z.V. Vardeny, Isr. J. Chem.52552-562 (2012)
[19]P.A. Bobbert, T.D. Nguyen, F.W.A. van Oost, B. Koopmans and M. Wohlgenannt, Phys. Rev. Lett.99 216801:1-4 (2007)
[20]P.A. Bobbert, W. Wagemans, F.W.A. van Oost, B. Koopmans and M. Wohlgenannt, Phys. Rev. Lett.102 156604:1-4 (2009)
[21]P.A. Bobbert, T.D. Nguyen, W. Wagemans, F.W.A. van Oost, B. Koopmans and M. Wohlgenannt, Synth. Met.160 223-229 (2010)
[22]Y. Zhang, R. Liu, Y.L. Lei and Z.H. Xiong, Appl. Phys. Lett.94 083307:1-3 (2009)
[23]P. Chen, Q.L. Song, W.C.H. Choy, B.F. Ding, Y.L. Liu and Z.H. Xionga, Appl. Phys. Lett.99 143305:1-3(2011)
[24]Y. Yao, W. Si, C.Q. Wu, Synth. Met.161632-636 (2011)
[25]B. Hu and Y. Wu, Nature Mater.6 985-991 (2007)
[26]B. Hu, L. Yan and M. Shao, Adv. Mater.21 1500-1516 (2009)
[27]V.N. Prigodin, J.D. Bergeson, D.M. Lincoln and A.J. Epstein, Synth. Met.156 757-761 (2006)
[28]N.J. Rolfe, M. Heeney, P.B. Wyatt, A.J. Drew, T. Kreouzis and W.P. Gillin, Phys. Rev. B 80 241201:1-4 (2009)
[29]B.F. Ding, Y. Yao, Z.Y. Sun, C.Q. Wu, X.D. Gao, Z.J. Wang, X.M. Ding, W.C.H. Choy and X.Y Hou, Appl. Phys. Lett.97 163302:1-3 (2010)
[30]Y.H. Yan, M.J. Chen and C.Q. Wu, Chin. Phys. Lett.23 2549-2552 (2006)
[31]A. Troisi and G. Orlandi, Phys. Rev. Lett.96 086601:1-4 (2006)
[32]陈鄂生,量子力学基础教程,山东大学出版社,济南(2006)
[33]K. Schulten and P.G. Wolynes, J. Chem. Phys.68 3292-3297 (1978)
[34]解士杰,高琨,低维量子物理,山东科学技术出版社,济南(2009)
[35]R.W. Brankin, I. Gladwell and L.F. Shampine, RKSUITE:Software for ODE IVPS, http://www.netlib.org
[36]A.A. Johansson and S. Stafstrom, Phys. Rev. B 69 235205:1-7 (2004)
[1]G. Veeraraghavan, T.D. Nguyen, Y. Sheng, O. Mermer and M. Wohlgenannt, J. Phys.: Condens. Matter 19 036209:1-13 (2007)
[2]B. Hu, L. Yan and M. Shao, Adv. Mater.21 1500-1516 (2009)
[3]T.D. Nguyen, B.R. Gautam, E. Ehrenfreund and Z.V. Vardeny, Phys. Rev. Lett.105 166804:1-4(2010)
[4]T.L. Francis, O. Mermer, G. Veeraraghavan and M. Wohlgenannt, New J. Phys.6 185:1-8(2004)
[5]O. Mermer, G. Veeraraghavan, T.L. Francis and M. Wohlgenannt, Solid State Commun.134 631-636 (2005)
[6]O. Mermer, G. Veeraraghavan, T.L. Francis, Y. Sheng, D.T. Nguyen, M. Wohlgenannt, A. Kohler, M.K. Al-Suti and M.S. Khan, Phys. Rev. B 72 205202:1-12 (2005)
[7]J.L. Martin, J.D. Bergeson, V.N. Prigodin and A.J. Epstein, Synth. Met.160 291-296 (2010)
[8]P. Shakya, P. Desai, M. Somerton, G. Gannaway, T. Kreouzis and W.P. Gillin, J. Appl. Phys.1031 03715:1-5(2008)
[9]H. Kang, C.H. Park, J. Lim, C. Lee, W. Kang and C.S. Yoon, Org. Electron.13 1012-1017(2012)
[10]V.N. Prigodin, J.D. Bergeson, D.M. Lincoln and A.J. Epstein, Synth. Met.156 757-761 (2006)
[11]P.A. Bobbert, T.D. Nguyen, F.W.A. van Oost, B. Koopmans and M. Wohlgenannt, Phys. Rev. Lett.99 216801:1-4 (2007)
[12]P. Desai, P. Shakya, T. Kreouzis and W.P. Gillin, Phys. Rev. B 75 094423:1-5 (2007)
[13]Y. Sheng, T.D. Nguyen, G. Veeraraghavan, O. Mermer, M. Wohlgenannt, S. Qiu and U. Scherf, Phys. Rev. B 74 045213:1-9 (2006)
[14]Y. Sheng, T.D. Nguyen, G. Veeraraghavan, O. Mermer and M. Wohlgenannt, Phys. Rev. B 75 035202:1-6 (2007)
[15]X.F. Dong, X.X. Li and S.J Xie, Org. Electron.12 1835-1840 (2011)
[16]X.X. Li, X.F. Dong, J. Lei, S.J. Xie and A. Saxena, Appl. Phys. Lett.100 142408:1-4 (2012)
[17]F.L. Bloom, W. Wagemans, M. Kemerink and B. Koopmans, Phys. Rev. Lett.99 257201:1-4(2007)
[18]A. Troisi and G. Orlandi, Phys. Rev. Lett.96 086601:1-4 (2006)
[19]K. Schulten and P.G. Wolynes, J. Chem. Phys.68 3292-3297 (1978)
[20]W. Wagemans and B. Koopmans, Phys. Status Solidi B 248 1029-1041 (2011)
[21]R.W. Brankin, I. Gladwell and L.F. Shampine, RKSUITE:Software for ODE IVPS, http://www.netlib.org
[22]K.A. Nelson, D.R. Lutz and M.D. Fayer, Phys. Rev. B 24 3261-3275 (1981)
[23]R.G. Kepler, P.M. Beeson, S.J. Jacobs, R.A. Anderson, M.B. Sinclair, V.S. Valencia and P.A. Cahill, Appl. Phys. Lett.66 3618-3620 (1995)
[24]B.J. Chen, W.Y. Lai, Z.Q. Gao, C.S. Lee, S.T. Lee and W.A. Gambling, Appl. Phys. Lett.75 4010-4012(1999)
[25]Y. Olivier, V. Lemaur, J.L. Bredas and J. Cornil, J. Phys. Chem. A 110 6356-6364 (2006)
[26]S.J. Xie, Z.Y. Li and X. Sun, J. Shandong University 24 44-50 (1989)
[27]V. Mujica, A.E. Roitberg and M. Ratner, J. Chem. Phys.112 6834-6839 (2000)
[28]Y. Xue and M.A. Ratner, Phys. Rev. B 68 115406:1-18 (2003)
[29]N.J. Rolfe, M. Heeney, P.B. Wyatt, A.J. Drew, T. Kreouzis and W.P. Gillin, Phys. Rev. B 80 241201:1-4 (2009)
[30]G. Iucci, K. Xing, M. Logdlund, M. Fahlman and W.R. Salaneck, Chem. Phys. Lett. 244 139-144(1995)
[31]M.P. Lima, G.M. e Silva, Phys. Rev. B 74 224304:1-6 (2006)
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