Magnetic field effects in organic semiconductors : theory and simulations

Organic semiconductors are a promising class of materials, offering several advantages over inorganic semiconductors. They are light, flexible, easy and cheap to produce, and easily chemically tunable. Organic semiconductors are currently used for lighting applications and in the displays of some smartphones and televisions. Exciting magnetic field effects have been observed in the current through and light production of organic semiconductors. A magnetoconductance and magnetoelectroluminescence of up to 30% have been measured in organic semiconductor films. Recently, an even larger magnetoconductance with a magnitude of 93% was found in molecular wires. The magnetic field effects are remarkably independent of the specific material used, always having either a Lorentzian or a so-called non-Lorentzian lineshape with a width of a few millitesla. The hyperfine interaction between nuclear magnetic moments and the spins of the particles—electrons, hole, excitons, bipolarons, etc.— in an organic semiconductor can be approximated by an effective magnetic field that acts on the spins. The difference in those so-called hyperfine fields experienced by two particles leads to spin mixing that can be suppressed by applying an external magnetic field. Magnetic field effects arise because quantities like the current and light output depend on processes that are spin-dependent and are thus affected by the amount of spin mixing. The goals of this thesis are to explain experimentally observed magnetic field effects and to make predictions for obtaining even larger effects. This is done analytically using stochastic Liouville equations as well as using Monte Carlo simulations. A much-discussed question that is related to magneto-electroluminescence is whether the statistical ratio of one singlet to three triplets can be violated in exciton formation. We have studied this question using a two-site model in Chapter 3. We found that, if the singlet- and triplet-exciton formation rates differ, the statistical singlet-to-triplet exciton ratio of 1:3 is violated when hopping is slower than or comparable to the hyperfine frequency—the precession frequency of an electron spin due to the hyperfine field. Furthermore, for those hopping rates, we found a magnetic field dependence of the singlet fraction—a measure of the electroluminescence—if and only if singlet- and triplet-exciton formation rates differ. We also found that an ultra-small-magnetic-field effect that is sometimes observed can result from the increase in spin mixing when a magnetic field is applied that is comparable in magnitude to the hyperfine fields. In Chapter 4 we found that the violation of the statistical ratio and its magnetic field effect occur at hopping rates that are several orders of magnitude higher than the hyperfine frequency when Coulomb interaction and energetic disorder are present. In addition, a violation of the statistical ratio can be found even in the fast hopping limit, because electron-hole pairs can split up after which both can recombine with another electron and hole. This violation of the singlet fraction does not depend on the magnetic field. The main conclusion of Chapter 5 is that very large magnetic field effects in both the current and diffusion constant can be obtained in doped polymers. The onedimensionality of the charge transport through the polymer leads to effective spin blocking at dopant sites. This blocking occurs even in absence of an electric field and is amplified when the charge concentration is increased. A huge magnetoconductance has been measured in molecular wires embedded in a zeolite L crystal. We have modeled the conduction through those wires using a chain of sites in Chapter 6. We conclude that a similar mechanism as in the doped polymers leads to spin blocking in the wires, where trapped electrons instead of dopant sites lead to spin blocking. We suggest that the potassium ions that are present in the zeolite lead to the necessary trapping, because trapping by just the energetic disorder results in neither the right magnitude nor in the right electric field dependence of the magnetoconductance as compared to the experiment. When all effective magnetic fields are aligned, the amount of spin mixing depends on the hopping rate and the difference in magnitude of the effective magnetic fields felt by two particles on different sites. The effective magnetic fields vary from site to site due to the random nature of the hyperfine fields. However, in Chapter 7 we show that additional spin mixing happens when an external magnetic field is present that varies more strongly as a function of position than the hyperfine fields do. We conclude that the magnetoconductance that was measured in a device with a single magnetic electrode is the result of this kind of spin mixing. The magnetization of the magnetic layer changes as a function of the applied magnetic field. The resulting change in the fringe fields throughout the organic semiconductor leads to a change in spin mixing and thus in a change in the current. Finally, the main conclusions of this thesis are summarized and an outlook on the future of modeling of magnetic field effects in organic semiconductors is given in Chapter 8.