Nonequilibrium Charge Transport In Conjugated Polymer

Electrode / molecular device / electrode is the basic structure of many nano electronic devices,which is a very important research object in molecular electronics.In this structure,the process of non-equilibrium occurs.In recent years,the method represented by non-equilibrium Green's function has carried out extensive theoretical research and obtained very fruitful results.Among them,the molecular device is the structure of organic molecules,namely electrode / organic molecular device / electrode,which is an important research object of organic molecular electronics rising in recent years.Ordinary organic molecules are generally insulators,conducting through the tunneling mechanism,while conjugated organic molecules may become conductors,which have a unique conductive mechanism and show unique electrical properties.Therefore,it is very important to understand the conductive mechanism in the electrode/ conjugated organic molecules / electrode,which is of great help to the design of organic devices in the future.We know that the doped electrons and holes can deform the lattice and form selftrapped elementary excitations,such as solitons,polarons and bi-polarons in conjugated polymers.In the past,people have been devoted to the study of polaron dynamics under the action of electric field in the equilibrium state.When electrons or holes are injected from the electrode,a polaron will be formed in a weak electric field.The polaron moves at a constant speed in a relatively small electric field,but a large enough electric field will decompose the polaron.It is naturally assumed that in the structure of electrode /conjugated organic molecule / electrode,local element excitations such as solitons and polarons play the same role as in equilibrium,that is,they dominate the charge transport.We consider the unreasonable of this hypothesis,and analyze the previous research.It is found that the research on this aspect is not perfect and complete,especially the lack of charge injection and transport process.In order to improve the research,we use the time-containing calculation method.Specifically,we use an effective method based on the time-dependent nonequilibrium Green's function(TDNEGF)equation of motion(HEOM)and SSH model of coupled electrode.It is found that the soliton lattice wave plays a very important role in the nonequilibrium case.The bias voltage on the electrode will excite the transient soliton lattice waves at both ends of the polymer chain.They carry opposite charges and propagate towards each other.After meeting,they will merge.If the bias is symmetric,the static soliton lattices are formed after merging,which are the same as those in the equilibrium state(except for the boundary).The soliton lattice at equilibrium is a special exciton state,which is formed by the electrons at the top of the valence band of polymer dimerization excited one by one to the bottom of the conduction band with the same number of energy levels,and then relaxed.In the non-equilibrium state,for the case of symmetrical bias,the occurrence process in the energy domain is consistent with this.The bias in the left and right electrodes is at the top of the valence band and the bottom of the conduction band,respectively.The electrode with the bias at the top of the valence band acts as the drain and absorbs electrons from the top of the valence band above the bias(one for each energy level);the electrode with bias at the bottom of the conduction band acts as the source and absorbs electrons from the bottom of the conduction band below the bias(one for each energy level).These semi-filled energy bands form semi filled soliton lattice energy levels(bands)in the center of the original dimerization gap under the effect of lattice relaxation.According to our calculation,the transmittance of these soliton lattice energy levels is 1,so they play the role of providing conductive channels,that is to say,the current flowing through the polymer chain is completely transmitted current.If the bias is asymmetric,the charge and momentum of the transient soliton lattice waves cannot be completely neutralized after merging,and finally the steady-state soliton lattice waves moving towards the side with small bias absolute value will be formed.These soliton lattice waves carry charges and accompany the soliton lattice waves in the form of charge density waves.This moving charge density wave will lead to effective current,which is more important(compared with transmission current)only when the absolute value difference between left and right bias is very large.In the process of(transient)soliton lattice(wave)formation,there is a critical state semi soliton state.Only when the bias voltage exceeds the energy level of the semi soliton state,it will form and automatically evolve into soliton lattice(wave).If there is inter chain coupling,in addition to the soliton crystal in the original chain,the soliton lattice will also be excited in the other chain.The basic principle of its conduction is similar to that of the single chain.The soliton lattice in the two chains also provides a conductive channel,but the resonance under specific coupling may lead to a sharp decrease in the transmittance peak,and the soliton lattice energy level may no longer be located in the transparent region.The peak emissivity leads to the decrease of the effect of the conductive channel.In order to verify that the nonequilibrium numerical results can indeed be called soliton lattice waves and the relationship between them and the soliton lattice states in the equilibrium state,we analytically deduce the continuous approximation of SSH model TLM model combined with nonequilibrium Green's function.Using the relationship between Green's function and eigenwave function(the definition of Green's function),we express the lattice deformation in non-equilibrium state as the eigenwave function in equilibrium state.For the solution in the original dimerization gap,the boundary condition of Green's function can be satisfied only when the soliton lattice state is actually nonlocal.From the analytical results,on the one hand,in the energy domain,the non-equilibrium soliton lattice wave can be regarded as the combination of electron like(negatively charged)and hole like(positively charged)soliton lattices caused by the left and right electrodes;on the other hand,in the energy domain,the non-equilibrium soliton lattice wave can be regarded as the linewidth function of the left and right ends(depending on the coupling between the left and right electrodes and the polymer chain and the left and right electrodes)The density of states is modulated by the equivalent electron Fermi distribution function of the equilibrium state of the soliton lattice.If they are not equal,that is to say,the left and right bias voltage is asymmetric,the combination will take place in the range of the smaller width,and finally form the band of the sandwich structure.