金属/聚合物/金属结构中载流子输运动力学研究
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摘要
近年来,随着实验手段的不断提高和理论研究方法的不断成熟,对有机导电高分子材料的研究已经发展成为系统的多学科交叉的研究领域。作为一种新型的功能材料,有机聚合物既具有金属和半导体的电子特性,又具有聚合物的易加工、柔韧性、且价格低廉等优点,成为近年来的研究热点。另外,聚合物是软凝聚态物质的典型代表,它的广泛研究推动了人类对有机体和生命物质的理解。
近20年来,人们已经逐渐认识到有机聚合物丰富的功能特性,许多基于有机聚合物的光电器件已经从单纯的实验兴趣转变为新兴的实用技术。目前,人们已经研制出各种各样的有机光电子器件,如有机发光二极管,场效应管,光伏电池等。这些器件的工作原理一般都是基于电荷注入、电荷传输以及电子-空穴对复合这些物理过程。
有机聚合物具有不同于传统半导体的特性。首先,有机分子间的相互作用很弱,它们大多具有准一维结构;其次,有机材料中存在着很强的电子—声子相互作用,电子态和晶格态两者相互影响。因此,聚合物中的载流子不再是传统的电子或空穴,而是电荷的自陷元激发,如孤子、极化子、双极化子等准粒子。聚合物中的这些元激发在很大程度上决定着聚合物中的电荷输运,发光等物理性质,并有助于人们理解聚合物的特性。由于这样的准粒子包括电荷和晶格畸变两部分,在外场的作用下,电荷的运动必然拖拽晶格畸变一起运动。因此,研究聚合物材料中载流子的形成过程及其在电场下的输运性质是有机材料中光电特性研究的基础。
本论文基于紧束缚的Su-Schrieffer-Heeger(SSH)模型,对哈密顿进行了修正,利用非绝热的分子动力学方法,模拟了载流子在金属/聚噻吩/金属结构中的注入与输运,另外研究了载流子在开放的金属/共聚物结构中输运的动力学过程,最后讨论了带有相反电荷的载流子在金属/耦合聚对苯乙炔链/金属结构中的注入与输运过程。本论文具体的研究内容和主要结果如下:
1.载流子在金属/聚噻吩/金属结构中注入及输运研究
近20年来,聚噻吩(polythiophene(PT))以其独特的光电性质越来越受到人们的关注,并成为技术应用中一种重要的材料,例如发光二极管、非线形光学器件、场效应晶体管等。因此针对与实际相对应的金属/PT/金属结构的体系,研究载流子在此结构中注入及输运的动力学具有重要的意义。
1.1研究发现,通过调整施加在金属电极上的偏压、金属电极与PT间的界面耦合以及施加在PT链上的电场,电荷能够注入到PT链中。在强的电子—晶格相互作用下,注入的电荷形成波包,每个波包含有的电荷数量随注入条件的不同在0-2e之间变化。另外,当无电场或者电场较弱时,注入的电荷在PT中形成稳定的波包;在强电场下,注入的电荷快速运动到PT的右端,并喷出至右金属电极中,从而不能形成稳定的波包,即大的电场不利于波包的形成。喷出的电荷也是非整数的,与注入的情况相似。
1.2在相同的条件下,研究了双电荷在PT链中的输运情况。发现注入的双电荷在噻吩链中形成两个波包,每个波包包含的电荷量为1e,为两个单极化子,而不形成一个双极化子,这与聚合物的几何构型有关。
2.载流子在金属/共聚物结构中注入及输运研究
作为有机导电聚合物的重要组成部分之一,共聚物在有机光电器件的研究中已经引起人们越来越多的重视。并且近几年以有机小分子共聚物作为导电材料,因其良好的整流特性,在分子电子学领域也引起了研究兴趣。关于共聚物电子结构性质的研究,人们在理论和实验上开展了大量的工作。并得到了一些有价值的结论,如有机量子阱和超晶格性质,能带可调的电子性质等等,这对于共聚物的进一步研究和应用都具有一定的指导意义。本章以具有普遍意义的共聚物模型-(A_x-B_y)-z_A_x-为对象,研究了载流子在外电场作用下,在开放的金属/共聚物结构中的动力学输运性质。
2.1研究发现共聚物的结构不同,注入电荷所需要的临界偏压不同,载流子在共聚物中的运动情况也是不一样的。共聚物-(PPP)_m-(PT)_m-(PPP)_m-具有垒-阱-垒结构,注入的电荷先在垒中形成波包,波包作为载流子在链中输运,在弱场下就可以从垒中进入阱中,但只能局域在阱中;在中等强度的场强下,载流子能够越过两种均聚物的界面进入到另一势垒中。
2.2对于具有阱-垒-阱结构的共聚物-(PT)_m-(PPP)_n-(PT)_m-,注入的电荷一般局域在PT阱中,只有在强场下,载流子才能从PT阱中跃迁至PPP垒中,并最终达到动态的平衡。
3.带有相反电荷的载流子在金属/耦合聚对苯乙炔链/金属结构中输运研究
近年来,以有机聚合物如聚对苯乙炔(poly(p-phenylene vinylene)(PPV))及其衍生物为基础的多功能光电器件已经开发出。这些器件的工作原理一般都是基于电荷注入、电荷传输以及电子—空穴对复合这些物理过程。其中载流子的输运包含链内和链间跃迁,是影响器件发光效率的重要因素。对于载流子的链间跃迁来说,这个过程必然包括电荷从一条链到另一条的跃迁,从而在接收电荷的链中产生几何缺陷,在施与电荷的链中相应地产生电荷湮灭效应。因此,研究带相反电荷载流子在金属/耦合PPV链/金属结构中的注入与输运的动力学过程对于理解器件发光的微观机制是非常有帮助的。
3.1研究发现,在一定的偏压下,电子、空穴分别从左右电极注入到两条链中。弱场下,注入的电荷分别在链中形成电子、空穴波包,并沿着各自的链运动;中等强度的电场下,波包中的部分电荷将跃迁至近邻的链中,并与链中的剩余电荷发生非弹性碰撞,在链中形成包含极化子和激子的混合态;强场下,注入的电荷在链中快速运动并发生跃迁、碰撞,其中小部分电荷成为自由的电子,并能够克服界面势垒而喷出至金属电极。
3.2当链间耦合强度为零时,无论电场强度怎样变化,波包只在各自的链中输运,不会发生链间跃迁。在一定的耦合强度和重叠长度下,载流子能否发生链间跃迁关键在于电场的强弱。改变链间耦合强度和重叠区域的长短,载流子跃迁所需要的临界电场基本不变。
In recent years,with the improvement of experimental instruments and the development of theoretical methods,the research on organic conducting polymers has been developed into a systematic and multidisciplinary field.As a new kind of functional material,conjugated polymers or small oligomers have been the focus of the research work both because of the processing and performance advantages for low-cost and large-area application.The unique electric,magnetic and optical properties that occur in these materials have been realized and utilized.On the other hand,conjugated polymers have common characteristics of the soft condensed matters and can serve as a medium to understand other organic and even biological molecules.
In the past twenty years,the abundant function characteristics of conjugated polymers have been cognized.Many photoelectric devices based on conjugated polymers have offered promise for use in applications from experiment.Numerous high-performance photoelectric devices fabricated from organic polymers have been made including light-emitting diodes(LEDs),field effect transistors(FETs), photovoltaic cells,etc..The work principle of these devices is mainly based on physical processes involving the charge injection,the charge transport and the combination of electron-hole pairs.
Contrast to the traditional semiconductor,organic material has its unique properties.First,most of the conjugated polymers have the qusi-one-dimensional structure due to the weak interaction force between the organic molecules.Second, owning to its soft properties,there are strong electron-phonon couplings in organic systems,the lattice defect and energy band structure interact each other.It is generally believed that these self-trapping excitations,such as solitons(only in trans-polyacetylene),polarons and bipolarons,are related to the charge carriers in conjugated polymers.These elementary excitations are of fundamental importance for charge transport and photoluminescence of conjugated polymers system.Under the driven of the external electric field,the charge gets energy and moves firstly,and at the same time it will drag the lattice atoms to move.Studies on the dynamical processes of these excitations are elements to understand the optoelectronics for the organic materials.
Within the tight-binding Su-Schrieffer-Heeger(SSH) model and a nonadiabatic dynamic evolution method,we simulate the injection and transport of charge carrier in metal/polythiophene(PT)/metal structure.In addition,we have also explored the dynamic process of charge carriers in metal/eopolymer structure.Finally,we discuss the dynamics of oppositely charged carriers in a metal/coupled poly(p-phenylene vinylene(PPV) chains/metal structure.The detailed study and main results are given below.
1.Dynamics of charge carrier injection and transport in a metal/PT/metal structure
In the past twenty years,with the unique photoelectric properties,PT has been attached importance to technological applications,so it is important and significative to study the dynamic processes of injection and transport of the charge carriers in metal/PT/metal sandwich structure.
1.1 The dynamical formation of the wave packet sensitively depends on the strength of applied voltage,the electric feid,and the contact between PT and the electrode.Each wave packet contains charges 0-2e depending upon the injection condition.On the other hand,we obtained that the wave packet is formed in the absence of the electric field and under weak or moderate electric fields.For a stronger electric field,the wave packet can be still formed while it moves rapidly to the right PT/metal interface,and the electronic charge can be ejected from PT into the right metal electrode.Furthermore,we compared the effect of the applied different electric fields on the charge ejection,and obtained that the strong electric field is in favor of the charges ejection,and the quantity of ejected charge also is uninteger.
1.2 We have studied the injection and transport of two charges in metal/PT/metal system.The injected two charges form two wave packets in PT chain,the quantity of charge in each wave packet is 1e.The two wave packets are two single polarons,but not a bipolaron.
2.Study on transport of charge carrier in metal/eopolymer structure
Increasing attention has been paid to the research on organic optoelectronic devices based on copolymers,which is one kind of the most important polymers. Great deals of studies on the electronic structures of copolymers have been performed both theoretically and experimentally,and some valuable results,e.g.,the properties of organic quantum well and superlattice,the tunable band structures,etc.,have been obtained,which is significant for the further studies and applications of copolymers. For this reason,we systematically studied the dynamical transport properties of charge carriers driven by external electric fields in a metal/copolymer structure.
2.1 With the different configuration of copolymer,the critical voltage that makes charges inject into copolymer is different,and the motion of charge carriers in copolymer is different too.The copolymer -(PPP)_m-(PT)_n-(PPP)_m-has barrier-well-barrier structure,the injected charges form wave packet in barrier and transport in chain.For weak electric field,the wave packet can transfer from barrier into well,but only localizes in well;for moderate electric fields,the wave packet gets through interface of two polymer and enters another barrier.
2.2 For the copolymer-(PT)_m-(PPP)_n-(PT)_m- with well-barrier-well configuration, the injected charge localizes in PT well.Only under the stronger electric field,can the charge carrier jump over PT well and enter PPP chain.
3.Dynamics of oppositely charged carriers in a metal/coupled PPV chains/metal structure
Recent years,conjugated polymers including PPV and its derivant have been widely applied in optoelectronic devices.The conjugated polymers are used as the light-emitting and charge-transporting layers,in which electrons and/or holes are injected from the metal electrode and driven by the external field.In addition,the efficiency of LEDs also depends crucially on both intra- and interchain transport processes of the charge carriers.For the charge carrier picture to hold even for interchain charge transport,this process must involve hopping of charge from one chain to another followed by the creation of a geometrical defect in the charge accepting chain,and a corresponding annihilation of thus defect on the charge donating chain.To study the dynamics of injection and transport of the oppositely charged carriers is helpful to understand the microcosmic mechanism of luminescent device.
3.1 It is shown that the oppositely charged carriers can be injected into PPV chains by adjusting the voltage biases of two metal electrodes.The behavior of the injected charge carriers depends closely on the electric field.For weak fields,the injected oppositely charged carriers form wave packets and move along different chains.For moderate electric fields,part quantity of charges of the two wave packets jumps over respectively to the neighboring chain and collides with the residual charge remained in the chain.The mixed state with excitons and polarons on each chain can be finally created due to the collision.For stronger electric fields,the injected oppositely charged carriers move too rapid to form stable wave packets.The extended carriers jump over respectively to the neighboring chains,collide and induce a lot of small lattice vibrations.Finally,the charges get across the interface of polymer/metal and ejected into the metal electrodes.
3.2 In addition,the intensity of interchain coupling and the overlap length of the two PPV chains have important effect on the transfer of oppositely charged carriers. In the absence of interchain coupling,no matter how change the electric field,the formed wave packet transports only in each chain.For certain coupling intensity and overlap length of interchain,the key of interchain hopping of the oppositely charged carriers is the electric field strength.Even if the coupling intensity and overlap length are changed,the critical electric field that makes the oppositely charged carriers jump over to another chain remains is steady.
近20年来,人们已经逐渐认识到有机聚合物丰富的功能特性,许多基于有机聚合物的光电器件已经从单纯的实验兴趣转变为新兴的实用技术。目前,人们已经研制出各种各样的有机光电子器件,如有机发光二极管,场效应管,光伏电池等。这些器件的工作原理一般都是基于电荷注入、电荷传输以及电子-空穴对复合这些物理过程。
有机聚合物具有不同于传统半导体的特性。首先,有机分子间的相互作用很弱,它们大多具有准一维结构;其次,有机材料中存在着很强的电子—声子相互作用,电子态和晶格态两者相互影响。因此,聚合物中的载流子不再是传统的电子或空穴,而是电荷的自陷元激发,如孤子、极化子、双极化子等准粒子。聚合物中的这些元激发在很大程度上决定着聚合物中的电荷输运,发光等物理性质,并有助于人们理解聚合物的特性。由于这样的准粒子包括电荷和晶格畸变两部分,在外场的作用下,电荷的运动必然拖拽晶格畸变一起运动。因此,研究聚合物材料中载流子的形成过程及其在电场下的输运性质是有机材料中光电特性研究的基础。
本论文基于紧束缚的Su-Schrieffer-Heeger(SSH)模型,对哈密顿进行了修正,利用非绝热的分子动力学方法,模拟了载流子在金属/聚噻吩/金属结构中的注入与输运,另外研究了载流子在开放的金属/共聚物结构中输运的动力学过程,最后讨论了带有相反电荷的载流子在金属/耦合聚对苯乙炔链/金属结构中的注入与输运过程。本论文具体的研究内容和主要结果如下:
1.载流子在金属/聚噻吩/金属结构中注入及输运研究
近20年来,聚噻吩(polythiophene(PT))以其独特的光电性质越来越受到人们的关注,并成为技术应用中一种重要的材料,例如发光二极管、非线形光学器件、场效应晶体管等。因此针对与实际相对应的金属/PT/金属结构的体系,研究载流子在此结构中注入及输运的动力学具有重要的意义。
1.1研究发现,通过调整施加在金属电极上的偏压、金属电极与PT间的界面耦合以及施加在PT链上的电场,电荷能够注入到PT链中。在强的电子—晶格相互作用下,注入的电荷形成波包,每个波包含有的电荷数量随注入条件的不同在0-2e之间变化。另外,当无电场或者电场较弱时,注入的电荷在PT中形成稳定的波包;在强电场下,注入的电荷快速运动到PT的右端,并喷出至右金属电极中,从而不能形成稳定的波包,即大的电场不利于波包的形成。喷出的电荷也是非整数的,与注入的情况相似。
1.2在相同的条件下,研究了双电荷在PT链中的输运情况。发现注入的双电荷在噻吩链中形成两个波包,每个波包包含的电荷量为1e,为两个单极化子,而不形成一个双极化子,这与聚合物的几何构型有关。
2.载流子在金属/共聚物结构中注入及输运研究
作为有机导电聚合物的重要组成部分之一,共聚物在有机光电器件的研究中已经引起人们越来越多的重视。并且近几年以有机小分子共聚物作为导电材料,因其良好的整流特性,在分子电子学领域也引起了研究兴趣。关于共聚物电子结构性质的研究,人们在理论和实验上开展了大量的工作。并得到了一些有价值的结论,如有机量子阱和超晶格性质,能带可调的电子性质等等,这对于共聚物的进一步研究和应用都具有一定的指导意义。本章以具有普遍意义的共聚物模型-(A_x-B_y)-z_A_x-为对象,研究了载流子在外电场作用下,在开放的金属/共聚物结构中的动力学输运性质。
2.1研究发现共聚物的结构不同,注入电荷所需要的临界偏压不同,载流子在共聚物中的运动情况也是不一样的。共聚物-(PPP)_m-(PT)_m-(PPP)_m-具有垒-阱-垒结构,注入的电荷先在垒中形成波包,波包作为载流子在链中输运,在弱场下就可以从垒中进入阱中,但只能局域在阱中;在中等强度的场强下,载流子能够越过两种均聚物的界面进入到另一势垒中。
2.2对于具有阱-垒-阱结构的共聚物-(PT)_m-(PPP)_n-(PT)_m-,注入的电荷一般局域在PT阱中,只有在强场下,载流子才能从PT阱中跃迁至PPP垒中,并最终达到动态的平衡。
3.带有相反电荷的载流子在金属/耦合聚对苯乙炔链/金属结构中输运研究
近年来,以有机聚合物如聚对苯乙炔(poly(p-phenylene vinylene)(PPV))及其衍生物为基础的多功能光电器件已经开发出。这些器件的工作原理一般都是基于电荷注入、电荷传输以及电子—空穴对复合这些物理过程。其中载流子的输运包含链内和链间跃迁,是影响器件发光效率的重要因素。对于载流子的链间跃迁来说,这个过程必然包括电荷从一条链到另一条的跃迁,从而在接收电荷的链中产生几何缺陷,在施与电荷的链中相应地产生电荷湮灭效应。因此,研究带相反电荷载流子在金属/耦合PPV链/金属结构中的注入与输运的动力学过程对于理解器件发光的微观机制是非常有帮助的。
3.1研究发现,在一定的偏压下,电子、空穴分别从左右电极注入到两条链中。弱场下,注入的电荷分别在链中形成电子、空穴波包,并沿着各自的链运动;中等强度的电场下,波包中的部分电荷将跃迁至近邻的链中,并与链中的剩余电荷发生非弹性碰撞,在链中形成包含极化子和激子的混合态;强场下,注入的电荷在链中快速运动并发生跃迁、碰撞,其中小部分电荷成为自由的电子,并能够克服界面势垒而喷出至金属电极。
3.2当链间耦合强度为零时,无论电场强度怎样变化,波包只在各自的链中输运,不会发生链间跃迁。在一定的耦合强度和重叠长度下,载流子能否发生链间跃迁关键在于电场的强弱。改变链间耦合强度和重叠区域的长短,载流子跃迁所需要的临界电场基本不变。
In recent years,with the improvement of experimental instruments and the development of theoretical methods,the research on organic conducting polymers has been developed into a systematic and multidisciplinary field.As a new kind of functional material,conjugated polymers or small oligomers have been the focus of the research work both because of the processing and performance advantages for low-cost and large-area application.The unique electric,magnetic and optical properties that occur in these materials have been realized and utilized.On the other hand,conjugated polymers have common characteristics of the soft condensed matters and can serve as a medium to understand other organic and even biological molecules.
In the past twenty years,the abundant function characteristics of conjugated polymers have been cognized.Many photoelectric devices based on conjugated polymers have offered promise for use in applications from experiment.Numerous high-performance photoelectric devices fabricated from organic polymers have been made including light-emitting diodes(LEDs),field effect transistors(FETs), photovoltaic cells,etc..The work principle of these devices is mainly based on physical processes involving the charge injection,the charge transport and the combination of electron-hole pairs.
Contrast to the traditional semiconductor,organic material has its unique properties.First,most of the conjugated polymers have the qusi-one-dimensional structure due to the weak interaction force between the organic molecules.Second, owning to its soft properties,there are strong electron-phonon couplings in organic systems,the lattice defect and energy band structure interact each other.It is generally believed that these self-trapping excitations,such as solitons(only in trans-polyacetylene),polarons and bipolarons,are related to the charge carriers in conjugated polymers.These elementary excitations are of fundamental importance for charge transport and photoluminescence of conjugated polymers system.Under the driven of the external electric field,the charge gets energy and moves firstly,and at the same time it will drag the lattice atoms to move.Studies on the dynamical processes of these excitations are elements to understand the optoelectronics for the organic materials.
Within the tight-binding Su-Schrieffer-Heeger(SSH) model and a nonadiabatic dynamic evolution method,we simulate the injection and transport of charge carrier in metal/polythiophene(PT)/metal structure.In addition,we have also explored the dynamic process of charge carriers in metal/eopolymer structure.Finally,we discuss the dynamics of oppositely charged carriers in a metal/coupled poly(p-phenylene vinylene(PPV) chains/metal structure.The detailed study and main results are given below.
1.Dynamics of charge carrier injection and transport in a metal/PT/metal structure
In the past twenty years,with the unique photoelectric properties,PT has been attached importance to technological applications,so it is important and significative to study the dynamic processes of injection and transport of the charge carriers in metal/PT/metal sandwich structure.
1.1 The dynamical formation of the wave packet sensitively depends on the strength of applied voltage,the electric feid,and the contact between PT and the electrode.Each wave packet contains charges 0-2e depending upon the injection condition.On the other hand,we obtained that the wave packet is formed in the absence of the electric field and under weak or moderate electric fields.For a stronger electric field,the wave packet can be still formed while it moves rapidly to the right PT/metal interface,and the electronic charge can be ejected from PT into the right metal electrode.Furthermore,we compared the effect of the applied different electric fields on the charge ejection,and obtained that the strong electric field is in favor of the charges ejection,and the quantity of ejected charge also is uninteger.
1.2 We have studied the injection and transport of two charges in metal/PT/metal system.The injected two charges form two wave packets in PT chain,the quantity of charge in each wave packet is 1e.The two wave packets are two single polarons,but not a bipolaron.
2.Study on transport of charge carrier in metal/eopolymer structure
Increasing attention has been paid to the research on organic optoelectronic devices based on copolymers,which is one kind of the most important polymers. Great deals of studies on the electronic structures of copolymers have been performed both theoretically and experimentally,and some valuable results,e.g.,the properties of organic quantum well and superlattice,the tunable band structures,etc.,have been obtained,which is significant for the further studies and applications of copolymers. For this reason,we systematically studied the dynamical transport properties of charge carriers driven by external electric fields in a metal/copolymer structure.
2.1 With the different configuration of copolymer,the critical voltage that makes charges inject into copolymer is different,and the motion of charge carriers in copolymer is different too.The copolymer -(PPP)_m-(PT)_n-(PPP)_m-has barrier-well-barrier structure,the injected charges form wave packet in barrier and transport in chain.For weak electric field,the wave packet can transfer from barrier into well,but only localizes in well;for moderate electric fields,the wave packet gets through interface of two polymer and enters another barrier.
2.2 For the copolymer-(PT)_m-(PPP)_n-(PT)_m- with well-barrier-well configuration, the injected charge localizes in PT well.Only under the stronger electric field,can the charge carrier jump over PT well and enter PPP chain.
3.Dynamics of oppositely charged carriers in a metal/coupled PPV chains/metal structure
Recent years,conjugated polymers including PPV and its derivant have been widely applied in optoelectronic devices.The conjugated polymers are used as the light-emitting and charge-transporting layers,in which electrons and/or holes are injected from the metal electrode and driven by the external field.In addition,the efficiency of LEDs also depends crucially on both intra- and interchain transport processes of the charge carriers.For the charge carrier picture to hold even for interchain charge transport,this process must involve hopping of charge from one chain to another followed by the creation of a geometrical defect in the charge accepting chain,and a corresponding annihilation of thus defect on the charge donating chain.To study the dynamics of injection and transport of the oppositely charged carriers is helpful to understand the microcosmic mechanism of luminescent device.
3.1 It is shown that the oppositely charged carriers can be injected into PPV chains by adjusting the voltage biases of two metal electrodes.The behavior of the injected charge carriers depends closely on the electric field.For weak fields,the injected oppositely charged carriers form wave packets and move along different chains.For moderate electric fields,part quantity of charges of the two wave packets jumps over respectively to the neighboring chain and collides with the residual charge remained in the chain.The mixed state with excitons and polarons on each chain can be finally created due to the collision.For stronger electric fields,the injected oppositely charged carriers move too rapid to form stable wave packets.The extended carriers jump over respectively to the neighboring chains,collide and induce a lot of small lattice vibrations.Finally,the charges get across the interface of polymer/metal and ejected into the metal electrodes.
3.2 In addition,the intensity of interchain coupling and the overlap length of the two PPV chains have important effect on the transfer of oppositely charged carriers. In the absence of interchain coupling,no matter how change the electric field,the formed wave packet transports only in each chain.For certain coupling intensity and overlap length of interchain,the key of interchain hopping of the oppositely charged carriers is the electric field strength.Even if the coupling intensity and overlap length are changed,the critical electric field that makes the oppositely charged carriers jump over to another chain remains is steady.
引文
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