| 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. |
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