有机磁电阻的理论研究
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摘要
有机固体材料是一个新型交叉研究领域,既包括与化学相关的各种有机材料的合成与加工,也包括与物理相关的电、磁、光等性质的研究和有机功能器件的开发与应用。有机固体材料在很长一段时间内都被认为是绝缘体,并没有引起人们太多的注意。直到上世纪七十年代,MacDiarmid等人发现掺杂聚乙炔的导电率有很大程度的提高,有机材料的才逐渐被人们认识与利用,从而开扁了有机材料的时代。随后有机材料的导电性与发光性得到了深入研究,并取得了很大的进展。有机发光二极管、有机场效应管与有机太阳能电池等新型有机功能器件也逐渐走进了人们的生活。对有机材料的研究与应用做出开拓性贡献的MacDiarmid等人也因此获得2000年诺贝尔化学奖。
进入新世纪以来,有机材料的一个重大进展是其在自旋电子学方面的应用。高极化率的自旋注入和自旋信号的长时间保持是实现高性能自旋器件的必要条件。有机材料具有较弱的自旋-轨道耦合作用和超精细相互作用,载流子的自旋弛豫时间比较长,因而是理想的实现自旋极化注入候选材料。由于有机材料的“软特性”,有机材料中的载流子不再是传统的电子与空穴,而是与晶格耦合在一起的自陷束缚态,它们具有更复杂的电荷自旋关系,使有机自旋电子学器件具有更丰富的特性。因此将有机材料应用到自旋电子学中,探究与自旋相关的物理过程和开发基于有机材料的自旋器件,成为近年来研究的热点,这形成了一门新的学科—有机自旋电子学。有机功能材料及其相关器件中的自旋产生、输运、存储及探测等新物理现象和其独特的物理机理是有机自旋电子学研究的主要内容。探讨有机材料在自旋电子学领域的应用具有重要的基础研究价值和潜在的应用背景,这也是当前国际上许多课题组密切关注的一个研究方向。
通过近几十年的研究,人们已经对有机材料有了比较深入的认识,深入研究了各种激发态的性质。另一方面,通过优化有机材料的结构和性能,人们已开发出有机场效应晶体管、有机太阳能电池、有机发光二极管等各种有机功能器件。2002年Dediu等人更是首次实现了有机材料内的自旋极化注入,实验中采用具有半金属性质的磁性电极作为自旋极化电子的来源。随后人们不断改进器件的性能,力争实现室温下的自旋极化注入,达到实用化的要求。2004年Francis在另一类不含有任何磁性元素的有机器件中,发现通过施加弱磁场(100mT),有机器件室温下可出现10%以上的磁电阻,磁电阻的大小和正负与有机层的厚度以及外加偏压有关。器件中采用的为普通金属电极,不存在仟何自旋极化的注入,因此磁场下器件电阻的变化应该是有机材料本征的性质,被人们称为有机磁电阻(Organic magnetoresistance, OMAR)。随后人们在包括有机聚合物和有机小分子在内的多种有机材料内均发现了有机磁电阻,表明这是有机材料的一种共性。但另-方面,不同材料内电阻对磁场的响应又是不同的,而且与温度和偏压的关系也是多变和复杂的。由于该现象在无机器件中很难出现,有机磁电阻(OMAR)很快受到物理、化学、材料和电子学界的广泛关注。几年来的研究初步发现,OMAR不仅有重大的潜在应用价值,而且内容丰富,机理复杂。有机器件不仅存在磁电阻,而且其光致发光(PL)、电致发光(EL)和光电流(PC)等都存在不同程度的强磁响应现象,我们将其统称为有机磁效应(Organic magnetic field effect, OMFE),这成为当前有机功能材料和器件研究的一个重要热点,对其弱磁场强响应机理的探索更是吸引了物理学工作者的兴趣。对有机磁效应的研究有助于帮助人们理解有机材料内各种微观过程,促进有机功能器件的发展。
目前为止虽然实验方面人们对有机磁效应进行了大量的深入研究,但理论上对其内在机制并没有统一的解释。目前主要存在三种有机磁效应机制：极化子对机制、激子-极化子淬灭机制和双极化子机制。这三种机制都是基于载流子的自旋对外磁场和(或)氢核产生的超精细场的敏感性,但遗憾的是,都没能定量地给出有机磁效应的解释。最近基于磁场对运动π电子产生的洛伦兹作用,王等人提出“磁致跃迁”机制,认为电荷在分子间的跃迁受磁场的调控,定性地给出了有机磁效应产生的物理机制。目前的理论工作中并没有明确体现出有机的特点,因此不能解释为什么弱磁场下只有有机器件中才能出现明显的磁效应。这种独特性应当是由有机材料特有的性质决定的。此外,实验测量中有机磁效应与有机材料种类和外部条件均相关,但目前的模型中并没有体现出这一点。本论文以有机磁电阻的计算来分析有机磁效应产生的物理机制,分别从塞曼相互作用和洛伦兹相互作用出发,强调了有机材料中特有的强电子-声子相互作用,给出有机磁电阻的定量计算结果。本文中我们还研究了有机磁电阻与材料的电子跃迁积分和外加偏压的关系,解释有机磁效应的多样性和复杂性。本论文研究内容和结果如下：
1.基于塞曼相互作用的磁电阻计算
考虑分子晶体或弱无序系统,可以采用带输运机制。该理论下,材料内的输运主要由费米面处的态密度决定,即电导率σ∝ρ(EF)。本文第三章从塞曼相互作用出发,研究了磁场下系统费米面处态密度的变化和由此产生的磁电阻效应。
1.1有机材料中的磁电阻与载流子浓度密切相关。载流子浓度越小磁电阻越大,这也与实验观测到的磁电阻与器件的偏压相关性是一致的。
1.2一定的载流子浓度下,材料的跃迁积分越小,磁电阻越大。有机材料内分子间以弱的范德瓦尔斯力结合,产生的跃迁积分在meV量级,这是在弱磁场下观测到强磁效应的必要条件。
1.3有机磁电阻与材料内的电子-晶格耦合强度密切相关。电子-晶格耦合强度越大,磁电阻越明显。无机材料中不存在电子-晶格耦合,因此无法观察到磁效应。强的电子-声子耦合作用是弱磁场下仅能在有机材料中出现强磁效应的原因。
2.基于洛伦兹相互作用的磁电阻计算
之前的研究都是基于磁场改变载流子的能量,但这种改变远小于热扰动的影响,因此难以解释室温下的磁效应。我们知道磁场不仅可以通过自旋以塞曼相互作用的方式改变能量,也可以通过电荷以洛伦兹作用改变载流子的动量。相对于能量的改变,动量的改变更容易,受温度的影响更小。本文第四章即从洛伦兹作用出发,以“磁致跃迁”机制为基础,研究了磁场导致的跃迁积分的改变对有机材料内正负极化子碰撞过程的影响。
2.1磁场的加入将导致跃迁积分出现一虚部项,并因此将使组成电子态的瓦尼尔态之间产生相位差,相位差正比于跃迁积分的虚部项。
2.2载流子的迁移率与电子跃迁积分相关。加入磁场后,电子跃迁积分变大,但只有在非常强的磁场下,载流子的速度才会发生改变。在目前实验上观测到明显磁电阻的弱磁场范围内,极化子的速度几乎没有改变,不能解释有机磁电阻的出现。
2.3双极器件中,正负极化子的碰撞是不可避免的,这将改变器件内载流子的有效浓度。磁场导致的电子态中相位差的出现,使涉及两电子态叠加的正负极化子碰撞过程是磁场相关的。随磁场的变大,正负极化子的复合效率降低,有效载流子浓度增加,产生负磁电阻。此外,计算结果显示,磁电阻的大小与电声耦合相互作用强度相关。
Organic solid material is a new chiasmal area, which consists of both chemistry-dependent organic materials synthetizing and processing and the research of the physics-dependent electrical, magnetic and optical characteristic and the development and application of organic functional devices. Organic solid materials were for long time only associated with electrical insulators and could not get much attention. Until the1970s, MacDiarmid et al found that the electric conductivity of the doped polyacetylene had a much increase, and then open the times of the organic materials. Organic light emitting diodes (OLED), organic field effect transistors (OFET) and organic photovoltaic cells (OPVC) et al new organic functional devices have entered the people's lives. For the groundbreaking contributions in the research and application of organic materials, MacDiarmid et al got the Nobel Prize in Chemistry in2000.
In the new century, a significant breakthrough in organic materials is the application in Spintronics. Due to the weak spin-orbital coupling and hyperfine interaction, the carriers in organic materials have a relative long spin relaxation time, so it is a good candidate for spin injection and transport. Different from the carriers in traditional semiconductors, the carriers in organic materials is soliton, polaron and bipolarons, which have a more complicate charge-spin relation, and make organic electronics has more abundant properties. Combined the organic electronics with the Spintronics, exploring the spin-dependent applications in organic materials, then forming a new subject-Organic Spintronics. In recent years, the generation, transport, storage and detection of spin et al., new physical phenomenons and underlying mechanisms in organic functional materials and devices are the main contents in Organic Spintronics. There is important basic research value and potential application in the application of organic material in spintronics, which is also a hot subject among some international research groups.
People have gotten a deep cognition for organic materials and the excited states through a thorough research for decades. On the other hand, people have developed several organic functional devices, such as organic field effect transistors, organic solar cells and organic light emitting diodes. In2002, Dediu et al. realized the spin polarized injection into organic materials, a ferromagnetic electrode was adopted as the source. Then, the performance of the device is improved to achieve the spin polarized injection at room temperature. In2004, Francis et al found that with the application of a weak magnetic field (≤100mT), the magnetoresistance of the device ITO/PEDOT/polyfluorene/Ca can be up to10%at room temperature, the magnitude and the sign is also dependent on the thickness and the bias. The electrode adopted in the device is normal metal without any spin polarized carriers, the corresponding magnetoresistance is the intrinsic property of organic materials, which is dubbed Organic magnetoresistance (OMAR). OMAR has been found in many organic materials containing conjugated polymers and small molecules. However, the organic magnetoresistance is complex, and the dependence on temperature and bias is complicated. As this phenomenon is very unusual in inorganic device, organic magnetoresistance (OMAR) obtained much attention from physics, chemistry, material and electronics. From the investigation in the last few years, there are many significant applications in OMAR, and it is rich in content and is very complicated. There are not only magnetoresistance, but also large magnetic field effect in photoluminescence (PL), electroluminescence (EL) and photocurrent (PC) in organic semiconductor (device), we can call all of them organic magnetic field effect (Organic magnetic field effect, OMFE). This is a hot issue in the current research on organic functional materials and devices, even more the exploration of its mechanism attracted the interest of the physics workers. The investigation on organic magnetic field effect is helpful for the understanding of microscopic process in organic materials and the development of organic functional devices.
UP to now, although people have carried a deep research on organic magnetic field effect experimentally, the mechanism governing OMFE is highly debated and the origin has not been achieved with one voice. There are mainly three models to explore the origin of the OMFE:the electron-hole model, the triple exciton-polaron quenching model and the bipolaron model. All these models are based on an assumption that the carriers are spin sensitive to the external magnetic field and the internal hyperfine field of the hydrogen nucleus. Recently, based on the Lorentz force caused by magnetic field, Wang et al. put forward the "magnetic field caused hopping" mechanism, which believes that the electron hopping between molecules is dependent on the magnetic field. However, the peculiar properties of organic materials are not reflected, it is hard to explain why the corresponding magnetic field effect can not be found in its inorganic counterparts. In addition, the diversity of the organic materials and the dependence on temperature and bias are also not reflected. In this paper, we take the calculation of organic magnetoresistance for example, emphasized the peculiar electron-phonon interaction, to illustrate the mechanism of organic magnetic field effect. Based on the Zeeman interaction and Lorentz interaction separately, we give the quantitative calculation on the OMAR. Additionally, the dependence of organic magnetoresistance on electron transfer integral and bias are also investigated. The detailed research and main results are given below:
1. Calculation on OMAR based on Zeeman interaction
Considering the crystalline structure of organic small molecule, the band transport mechanism is applicable. Under this mechanism, the conductance of the material is mainly dependent on the density of states near the Fermi level, i.e. σ∞ρ(EF). In the third chapter of this paper, we calculate the change of the density of the states near the Fermi level caused by the magnetic field based on the Zeeman interaction. And then OMAR is obtained.
1.1The magnetoresistance in organic materials is much dependent on the density of the carriers. With the decrease of density, the magnitude of magnetoresistance increases. This is consistent with the dependence on the bias that obtained in experiments.
1.2For a fixed density of carriers, with the decrease of electron integral, the magnitude of magnetoresistance also increases. The organic molecules are usually bonded by weak Van der Waals force, the corresponding electron transfer integral is in the scale of mT, and this is the prerequisite for the obvious magnetic field effect.
1.3The magnetoresistance in organic materials is much dependent on the electron-phonon interaction constant. For a stronger electron-phonon interaction, the magnetoresistance is more obvious. There is no electron-phonon interaction in inorganic materials, so one can not observe any magnetic field effect.
2. Calculation on OMAR based on Zeeman interaction
The previous researches are all based on the change of energy caused by magnetic field, but this change is much less than the thermal perturbation, it is difficult to explain this effect at room temperature. As we all know, apart from the Zeeman interaction, there is also Lorentz interaction between the charge and the magnetic field, and this effect can also influence the performance of the device. Compared to the energy, the change of momentum is easier and less dependent on the temperature. In the fourth chapter of this paper, based on the magnetic field-induced hopping mechanism, we investigate the collision process between two oppositely charged polarons under the magnetic field.
2.1An imaginary part of electron transfer integral will be induced by the magnetic field. The series Wannier states that compose the electronic state will have a phase difference which is dependent on the imaginary part of electron transfer integral.
2.2The mobility of the carrier is related with the electron transfer integral. With the application of magnetic field, the electron transfer integral increases. However, only under a very strong magnetic field, the increase of the velocity of polaron is obvious, and that is not consistent to the observation in experiments.
2.3In bipolar device, the combination process between two oppositely charged polarons is inevitable, and this will change the effective density of the carrier. The phase difference caused by the magnetic field make the collision process which is related with superposition between two electron states is magnetic field dependent. With the increase of the magnetic field, the combination probability decreases, and then the effective density of the carrier increases, a negative magnetoresistance is naturally obtained. In addition, it is shown that the magnetoresistance is also dependent on t electron-phonon interaction.
进入新世纪以来,有机材料的一个重大进展是其在自旋电子学方面的应用。高极化率的自旋注入和自旋信号的长时间保持是实现高性能自旋器件的必要条件。有机材料具有较弱的自旋-轨道耦合作用和超精细相互作用,载流子的自旋弛豫时间比较长,因而是理想的实现自旋极化注入候选材料。由于有机材料的“软特性”,有机材料中的载流子不再是传统的电子与空穴,而是与晶格耦合在一起的自陷束缚态,它们具有更复杂的电荷自旋关系,使有机自旋电子学器件具有更丰富的特性。因此将有机材料应用到自旋电子学中,探究与自旋相关的物理过程和开发基于有机材料的自旋器件,成为近年来研究的热点,这形成了一门新的学科—有机自旋电子学。有机功能材料及其相关器件中的自旋产生、输运、存储及探测等新物理现象和其独特的物理机理是有机自旋电子学研究的主要内容。探讨有机材料在自旋电子学领域的应用具有重要的基础研究价值和潜在的应用背景,这也是当前国际上许多课题组密切关注的一个研究方向。
通过近几十年的研究,人们已经对有机材料有了比较深入的认识,深入研究了各种激发态的性质。另一方面,通过优化有机材料的结构和性能,人们已开发出有机场效应晶体管、有机太阳能电池、有机发光二极管等各种有机功能器件。2002年Dediu等人更是首次实现了有机材料内的自旋极化注入,实验中采用具有半金属性质的磁性电极作为自旋极化电子的来源。随后人们不断改进器件的性能,力争实现室温下的自旋极化注入,达到实用化的要求。2004年Francis在另一类不含有任何磁性元素的有机器件中,发现通过施加弱磁场(100mT),有机器件室温下可出现10%以上的磁电阻,磁电阻的大小和正负与有机层的厚度以及外加偏压有关。器件中采用的为普通金属电极,不存在仟何自旋极化的注入,因此磁场下器件电阻的变化应该是有机材料本征的性质,被人们称为有机磁电阻(Organic magnetoresistance, OMAR)。随后人们在包括有机聚合物和有机小分子在内的多种有机材料内均发现了有机磁电阻,表明这是有机材料的一种共性。但另-方面,不同材料内电阻对磁场的响应又是不同的,而且与温度和偏压的关系也是多变和复杂的。由于该现象在无机器件中很难出现,有机磁电阻(OMAR)很快受到物理、化学、材料和电子学界的广泛关注。几年来的研究初步发现,OMAR不仅有重大的潜在应用价值,而且内容丰富,机理复杂。有机器件不仅存在磁电阻,而且其光致发光(PL)、电致发光(EL)和光电流(PC)等都存在不同程度的强磁响应现象,我们将其统称为有机磁效应(Organic magnetic field effect, OMFE),这成为当前有机功能材料和器件研究的一个重要热点,对其弱磁场强响应机理的探索更是吸引了物理学工作者的兴趣。对有机磁效应的研究有助于帮助人们理解有机材料内各种微观过程,促进有机功能器件的发展。
目前为止虽然实验方面人们对有机磁效应进行了大量的深入研究,但理论上对其内在机制并没有统一的解释。目前主要存在三种有机磁效应机制：极化子对机制、激子-极化子淬灭机制和双极化子机制。这三种机制都是基于载流子的自旋对外磁场和(或)氢核产生的超精细场的敏感性,但遗憾的是,都没能定量地给出有机磁效应的解释。最近基于磁场对运动π电子产生的洛伦兹作用,王等人提出“磁致跃迁”机制,认为电荷在分子间的跃迁受磁场的调控,定性地给出了有机磁效应产生的物理机制。目前的理论工作中并没有明确体现出有机的特点,因此不能解释为什么弱磁场下只有有机器件中才能出现明显的磁效应。这种独特性应当是由有机材料特有的性质决定的。此外,实验测量中有机磁效应与有机材料种类和外部条件均相关,但目前的模型中并没有体现出这一点。本论文以有机磁电阻的计算来分析有机磁效应产生的物理机制,分别从塞曼相互作用和洛伦兹相互作用出发,强调了有机材料中特有的强电子-声子相互作用,给出有机磁电阻的定量计算结果。本文中我们还研究了有机磁电阻与材料的电子跃迁积分和外加偏压的关系,解释有机磁效应的多样性和复杂性。本论文研究内容和结果如下：
1.基于塞曼相互作用的磁电阻计算
考虑分子晶体或弱无序系统,可以采用带输运机制。该理论下,材料内的输运主要由费米面处的态密度决定,即电导率σ∝ρ(EF)。本文第三章从塞曼相互作用出发,研究了磁场下系统费米面处态密度的变化和由此产生的磁电阻效应。
1.1有机材料中的磁电阻与载流子浓度密切相关。载流子浓度越小磁电阻越大,这也与实验观测到的磁电阻与器件的偏压相关性是一致的。
1.2一定的载流子浓度下,材料的跃迁积分越小,磁电阻越大。有机材料内分子间以弱的范德瓦尔斯力结合,产生的跃迁积分在meV量级,这是在弱磁场下观测到强磁效应的必要条件。
1.3有机磁电阻与材料内的电子-晶格耦合强度密切相关。电子-晶格耦合强度越大,磁电阻越明显。无机材料中不存在电子-晶格耦合,因此无法观察到磁效应。强的电子-声子耦合作用是弱磁场下仅能在有机材料中出现强磁效应的原因。
2.基于洛伦兹相互作用的磁电阻计算
之前的研究都是基于磁场改变载流子的能量,但这种改变远小于热扰动的影响,因此难以解释室温下的磁效应。我们知道磁场不仅可以通过自旋以塞曼相互作用的方式改变能量,也可以通过电荷以洛伦兹作用改变载流子的动量。相对于能量的改变,动量的改变更容易,受温度的影响更小。本文第四章即从洛伦兹作用出发,以“磁致跃迁”机制为基础,研究了磁场导致的跃迁积分的改变对有机材料内正负极化子碰撞过程的影响。
2.1磁场的加入将导致跃迁积分出现一虚部项,并因此将使组成电子态的瓦尼尔态之间产生相位差,相位差正比于跃迁积分的虚部项。
2.2载流子的迁移率与电子跃迁积分相关。加入磁场后,电子跃迁积分变大,但只有在非常强的磁场下,载流子的速度才会发生改变。在目前实验上观测到明显磁电阻的弱磁场范围内,极化子的速度几乎没有改变,不能解释有机磁电阻的出现。
2.3双极器件中,正负极化子的碰撞是不可避免的,这将改变器件内载流子的有效浓度。磁场导致的电子态中相位差的出现,使涉及两电子态叠加的正负极化子碰撞过程是磁场相关的。随磁场的变大,正负极化子的复合效率降低,有效载流子浓度增加,产生负磁电阻。此外,计算结果显示,磁电阻的大小与电声耦合相互作用强度相关。
Organic solid material is a new chiasmal area, which consists of both chemistry-dependent organic materials synthetizing and processing and the research of the physics-dependent electrical, magnetic and optical characteristic and the development and application of organic functional devices. Organic solid materials were for long time only associated with electrical insulators and could not get much attention. Until the1970s, MacDiarmid et al found that the electric conductivity of the doped polyacetylene had a much increase, and then open the times of the organic materials. Organic light emitting diodes (OLED), organic field effect transistors (OFET) and organic photovoltaic cells (OPVC) et al new organic functional devices have entered the people's lives. For the groundbreaking contributions in the research and application of organic materials, MacDiarmid et al got the Nobel Prize in Chemistry in2000.
In the new century, a significant breakthrough in organic materials is the application in Spintronics. Due to the weak spin-orbital coupling and hyperfine interaction, the carriers in organic materials have a relative long spin relaxation time, so it is a good candidate for spin injection and transport. Different from the carriers in traditional semiconductors, the carriers in organic materials is soliton, polaron and bipolarons, which have a more complicate charge-spin relation, and make organic electronics has more abundant properties. Combined the organic electronics with the Spintronics, exploring the spin-dependent applications in organic materials, then forming a new subject-Organic Spintronics. In recent years, the generation, transport, storage and detection of spin et al., new physical phenomenons and underlying mechanisms in organic functional materials and devices are the main contents in Organic Spintronics. There is important basic research value and potential application in the application of organic material in spintronics, which is also a hot subject among some international research groups.
People have gotten a deep cognition for organic materials and the excited states through a thorough research for decades. On the other hand, people have developed several organic functional devices, such as organic field effect transistors, organic solar cells and organic light emitting diodes. In2002, Dediu et al. realized the spin polarized injection into organic materials, a ferromagnetic electrode was adopted as the source. Then, the performance of the device is improved to achieve the spin polarized injection at room temperature. In2004, Francis et al found that with the application of a weak magnetic field (≤100mT), the magnetoresistance of the device ITO/PEDOT/polyfluorene/Ca can be up to10%at room temperature, the magnitude and the sign is also dependent on the thickness and the bias. The electrode adopted in the device is normal metal without any spin polarized carriers, the corresponding magnetoresistance is the intrinsic property of organic materials, which is dubbed Organic magnetoresistance (OMAR). OMAR has been found in many organic materials containing conjugated polymers and small molecules. However, the organic magnetoresistance is complex, and the dependence on temperature and bias is complicated. As this phenomenon is very unusual in inorganic device, organic magnetoresistance (OMAR) obtained much attention from physics, chemistry, material and electronics. From the investigation in the last few years, there are many significant applications in OMAR, and it is rich in content and is very complicated. There are not only magnetoresistance, but also large magnetic field effect in photoluminescence (PL), electroluminescence (EL) and photocurrent (PC) in organic semiconductor (device), we can call all of them organic magnetic field effect (Organic magnetic field effect, OMFE). This is a hot issue in the current research on organic functional materials and devices, even more the exploration of its mechanism attracted the interest of the physics workers. The investigation on organic magnetic field effect is helpful for the understanding of microscopic process in organic materials and the development of organic functional devices.
UP to now, although people have carried a deep research on organic magnetic field effect experimentally, the mechanism governing OMFE is highly debated and the origin has not been achieved with one voice. There are mainly three models to explore the origin of the OMFE:the electron-hole model, the triple exciton-polaron quenching model and the bipolaron model. All these models are based on an assumption that the carriers are spin sensitive to the external magnetic field and the internal hyperfine field of the hydrogen nucleus. Recently, based on the Lorentz force caused by magnetic field, Wang et al. put forward the "magnetic field caused hopping" mechanism, which believes that the electron hopping between molecules is dependent on the magnetic field. However, the peculiar properties of organic materials are not reflected, it is hard to explain why the corresponding magnetic field effect can not be found in its inorganic counterparts. In addition, the diversity of the organic materials and the dependence on temperature and bias are also not reflected. In this paper, we take the calculation of organic magnetoresistance for example, emphasized the peculiar electron-phonon interaction, to illustrate the mechanism of organic magnetic field effect. Based on the Zeeman interaction and Lorentz interaction separately, we give the quantitative calculation on the OMAR. Additionally, the dependence of organic magnetoresistance on electron transfer integral and bias are also investigated. The detailed research and main results are given below:
1. Calculation on OMAR based on Zeeman interaction
Considering the crystalline structure of organic small molecule, the band transport mechanism is applicable. Under this mechanism, the conductance of the material is mainly dependent on the density of states near the Fermi level, i.e. σ∞ρ(EF). In the third chapter of this paper, we calculate the change of the density of the states near the Fermi level caused by the magnetic field based on the Zeeman interaction. And then OMAR is obtained.
1.1The magnetoresistance in organic materials is much dependent on the density of the carriers. With the decrease of density, the magnitude of magnetoresistance increases. This is consistent with the dependence on the bias that obtained in experiments.
1.2For a fixed density of carriers, with the decrease of electron integral, the magnitude of magnetoresistance also increases. The organic molecules are usually bonded by weak Van der Waals force, the corresponding electron transfer integral is in the scale of mT, and this is the prerequisite for the obvious magnetic field effect.
1.3The magnetoresistance in organic materials is much dependent on the electron-phonon interaction constant. For a stronger electron-phonon interaction, the magnetoresistance is more obvious. There is no electron-phonon interaction in inorganic materials, so one can not observe any magnetic field effect.
2. Calculation on OMAR based on Zeeman interaction
The previous researches are all based on the change of energy caused by magnetic field, but this change is much less than the thermal perturbation, it is difficult to explain this effect at room temperature. As we all know, apart from the Zeeman interaction, there is also Lorentz interaction between the charge and the magnetic field, and this effect can also influence the performance of the device. Compared to the energy, the change of momentum is easier and less dependent on the temperature. In the fourth chapter of this paper, based on the magnetic field-induced hopping mechanism, we investigate the collision process between two oppositely charged polarons under the magnetic field.
2.1An imaginary part of electron transfer integral will be induced by the magnetic field. The series Wannier states that compose the electronic state will have a phase difference which is dependent on the imaginary part of electron transfer integral.
2.2The mobility of the carrier is related with the electron transfer integral. With the application of magnetic field, the electron transfer integral increases. However, only under a very strong magnetic field, the increase of the velocity of polaron is obvious, and that is not consistent to the observation in experiments.
2.3In bipolar device, the combination process between two oppositely charged polarons is inevitable, and this will change the effective density of the carrier. The phase difference caused by the magnetic field make the collision process which is related with superposition between two electron states is magnetic field dependent. With the increase of the magnetic field, the combination probability decreases, and then the effective density of the carrier increases, a negative magnetoresistance is naturally obtained. In addition, it is shown that the magnetoresistance is also dependent on t electron-phonon interaction.
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