Study On The Magnetic Field Effect In Organic Devices Based On Hopping Theory

The electron possesses two properties, including the charge and spin properties. Most attentions have been paid on the charge property of the electron in the past investigations, but its spin property is ignored. With the progress of spintronics, in recent years, researchers have started to focus on investigations on the spin property. And the most studied work contain spin polarization, spin injection and spin transport.The basic configuration of ferromagnetic/interlayer/ferromagnetic sandwich structure is used to study the spin polarized injection and transport. The interlayer made of nonmagnetic material can be superconductor, metal, conventional semiconductor, and organic material, et al. When the interlayer is a superconductor in which the carriers are spinless Cooper pairs, it is impossible to realize spin transport. In metals, although carriers are extended electrons with 1/2 spin, the signals can not be amplified in such devices. In semiconductors where the carrier is the electron or hole carrying 1/2 spin, since the existence of the bandgap, semiconductors become most suitable in carrying spin as well as amplifying the signal. As the existence of semiconducting properties, organic polymers should be another option. In addition, the polymer also possesses its own characteristics. For example, due to the "soft" atomic configuration, it can easily form a well contacted interface or an adjustable injection barrier.Organic semiconductors (OSCs) are widely used, including small molecules and polymers devices. These materials could possess high carrier mobility and shows apparent functional properties. Polymers has the strong electron-lattice coupling, so its carriers are not electrons or holes (they are extended) but the self-trapped elementary excitations. The elementary excitations in conjugated polymers such as solitons, polarons or bipolarons behave the characteristic of "quasi-particles" and complete localization, stability, and integrality. It was also indicated that, in some small molecule crystals, as the molecular fluctuation around the equilibrium position, one extra electron (hole) can also form a self-trapped state, which is similar to the charged excitation of polymers. In OSCs, these excitations show the especially charge-spin relation. For example, a soliton possesses a reverse charge-spin relation. This is quite different from the conventional electron or hole, i.e., the charged soliton S± is spinless, while the neutral one S0 has a ±h/2 spin. For a charged polaron, it carries spin ±h/2. A bipolaron binds two electrons or holes, and it is spinless. Thus only charged polarons or neutral solitons can serve as spin carriers.The organic small molecule and polymer behave abundant electronic, magnetic and even optical properties. Besides, as OSCs show weak spin-orbit coupling, the electron spin diffusion length is quite long than that of usual inorganic materials. Therefore, these properties make them suitable for the spin polarized injection as well as the transport application. The organic materials have been applicated in various optoelectronic devices during the past decades, such as the organic solar cell, the organic light emitting diode and the organic field effect transistor.In organic spintronics, another tempting phenomenon which is called organic magnetic field effect (OMFE) was found, and it has been experienced explosive investigations. OMFE shows that at room temperature there are substantial responses of electrical as well as optical properties of nonmagnetic OSCs to a very low magnetic field (usually in the scale of mT), even on the absence of any magnetic contact. As one aspect of OMFE, the organic magnetoresistance (OMAR) or organic magnetoconductance (OMC, the inverse of OMAR) behaviors show universal line shapes which can be fitted by the empirical Lorentzian function B2/(B2+B20), non-Lorentzian form [B/(|B|+B0)]2 or their combinations. Some results can also be fitted by the power law Bn,f1/B2+f2/B4 or d1B2+d2B4. Usually, values of OMAR around 0～15% have been found in a number of OSCs. A MR value over 300% has also been observed in some cases.In OSCs, there has been a proliferation of models for spin-related electronic processes. The interactions include the spin-Zeeman interaction and also the charge-Lorentzian one when a magnetic field is applied. In addition, spin hyperfine interaction (HFI) of the hydrogen nuclear can also be very important. For example, Yu et al. presented a job and showed a systematic study of HFI as well as its role on organic spintronic applications. Three mechanisms are proposed for OMFE up to now: (1) Polaron-pair model. In the model, the magnetic field as well as the hyperfine field influence the interconversion between singlet and triplet polaron pairs. Then it affects the ratio of the singlet and the triplet excitons, so the light emitting efficiency is influenced. (2) Bipolaron model. The magnetic field as well as the hyperfine field can change the intercrossing between bipolarons and polarons. Then the concentration ratio between them is changed. The mobilities of them are different as they have different effective mass. Thus the magnetic field change the concentration ratio between bipolarons and polarons and then influences the device’s current. (3) Exciton quenching model. The polaron interacts with the triplet exciton (during the polaron’s transport). When it is scattered by the triplet exciton, the mobility of the polaron is decreased. The magnetic field and the hyperfine field change the ratio of singlet and triplet excitons. Therefore, the probability that the polaron is scattered by triplet excitons is changed and the magnetic field effect on device’s current is realized. These theoretical mechanisms show HFI is important to OMFE.The charge-mobility relationship J= nev shows that the current J is not only dependent on the density of the carrier, but also on its velocity. The experimental sdudies seem to reveal both the carrier density and the mobility μ(μ= v/E, where E is the electric field strength) can be changed by a magnetic field. For instance, Nguyen et al. used techniques such as electroluminescence spectroscopies and charge-induced absorption spectroscopies and measured the dependence of singlet exciton, triplet exciton and the polaron density on the applied magnetic field, respectively. It is found that all of the densities increased with the applied magnetic field. However, Veeraraghavan et al. carried out a magnetoresistance (MR) measurement in polyfluorene (PFO) devices. They found that the effect of the magnetic field acted on the carrier mobility but not the carrier density. Moreover, Ding et al. showed that magnetoelectroluminescence (MEL) exhibited a close relationship with the carrier mobility from their investigations of the magnetic field effect on organic light emitting devices with a emission layer of mixed NPB:Alq3 blends.The underlying mechanism of OMFE is still needed to understand although many groups have produced different phenomenological models for OMFE. We can see that most of theoretical work just proposed a model or gave a qualitative derivation at most. OMFE should include two aspects in fact:one is the microscopic mechanism for carrier-magnetic field interactions; the other is the specific transport mechanism of carriers in organic layers. Both of them will sensitively affect OMFE. In the present work, we mainly focus on the spin-dependent Master Equation, from which we can obtain OMFE quantitatively. From the quantitative investigation, we may find some real microscopic mechanisms of OMFE.In stead of the band transport, transport takes place mainly through hopping of localized carriers between different sites (or molecules) for most of organic materials have amorphous structures. Variations of the on-site energies are usually obeyed Gaussian distribution. The model for hopping between sites has been studied by the master equation (ME) method to calculte mobilities of organic materials. The ME is proved to be an effective tool to understand the mobility observed by relative experiments and provides a framework for understanding the transport in disordered OSCs. However, the case will appear complex if the spin index is included.In this work, the hopping rate is influenced by the magnetic field and the hyperfine field. Then we employed the spin-related ME. When we calculate the mobility of polarons as well as the magnetoconductance (MC), we obtained a very large MC in a disordered OSC. The theoretical results are well consistent with the experimental observation by choosing suitable parameters. The magnetic field effect is related to the concrete organic materials as well as operating conditions. The MC reaches its saturation value slower for stronger HFI, and it reveals the specific importance of HFI on OMC. The MC becomes larger for stronger localized polarons for the carriers in OSCs are localized polarons. And this shows why the MC is much apparent in an organic material than its inorganic counterpart. Besides, we also found that the MC increases with the anisotropy of the OSC. It suggests us to employ OSCs that have high anisotropy structures to obtain a large MC.OMC appears complexity from a number of experimental studies on organic devices. Positive and negative OMAR values have been found in the OSCs, showing a transition between positive and negative depending on voltages as well as the concrete samples. A polaron’s spin is determined by the magnetic field as well as the effective hyperfine interaction when it is localized on a site. And the ground state of the polaron spin contains spin up and spin down components.Julliere’s model which is used to study the MR assumes spins are conserved (no spin reorientation/flip occurs) during transport. In addition, the electron spin diffusion length of an organic semiconductor is expected much longer than that of a usual inorganic material. Therefore, in this work we assumed that the polaron keeps its spin orientation when it hops in the system under a low carrier density.We use the ME method to calculate the system mobility and then obtain the MR. The theoretical simulation in our work is in agreement with the experimental data under suitable parameters. OMAR is dependent on specific material properties and the operating conditions. Our calculation presents that the sign of the MR changes from negative to positive when the electric field increases. Inaddition, the sign inversion of the MR also occurs when the energetic disorder widths decreases. The temperature dependence of MR agrees with that of energetic disorder parameters’dependence in our simulation. The MR will reach its saturation value slower for stronger HFI, and it exibits the importance of HFI on OMAR. In addition, for carriers in organic materials are localized polarons, the MR becomes obvious for a stronger localized polaron. It explains why apparent MR values are obtained in OSCs rather than its inorganic counterparts.The above work studied the magnetic field effect in unipolar device. In bipolar device, we consider the triplet exciton act as a trap for polaron’s transport. Under the effect of the magnetic field, hyperfine interaction, and exchange interaction of e-h pairs, we present mutual conversions among electrons, holes and e-h pairs. By constructing a group of equations, we obtain the density of the triplet e-h pairs. As e-h pairs can recombine into excitons, we get the density of the triplet exciton at last. To simulate the triplet excitons’trap effect, we assume the site (or molecule) with a triplet exciton possesses a lower on-site energy and more localized electron states. By using the method of the master equation, we get the mobility of the system and then calculate the MR. It is found that the MR value increases as the trap depth of the triplet exciton increases. In addition, if there are more e-h pairs recombine into excitons, the MR will be more obvious. Under different electric fields, our results are in good agreement with the experimental investigations.