Optical properties

The electronic π-π* transition is responsible for the absorption and emission in organic semiconductors. To a first approximation, the electron wavefunction in the conjugated chain can be viewed as a free electron confined in a one dimensional quantum well, where the width of the well is equal to the length of the conjugated chain. From this assumption, according to quantum mechanics, the energy gap between π orbital and π* orbital is determined by the length of the conjugated chains. The longer the conjugated chain, the narrower the energy gap between the two orbitals. Figure 2.5 gives an example of the impact of chain length,

represented by the number of the double bonds (monomer unit), on the HOMO-LUMO gap in poly(2,5 dioctyloxy p-phenylenevinylene) (DOO-PPV).

Figure 2.5. The impact of monomer units on the energy gap in DOO-PPV [3]

When an electron in the HOMO level is excited to the LUMO level by absorbing an incident photon, a positively charged hole is left in the HOMO level. The positively charged hole and negatively charged electron forms an excited state called an exciton, bound together by the Coulomb force. The binding energy of excitons in organic semiconductors is large (~0.5 eV), compared to their inorganic counterparts. Hence, these excitons are strongly bound at room temperature and show little temperature dependence[4].

Depending on the spin states, the interaction between the electron and hole can form singlet or triplet excitons, as shown in equation 2.2. A singlet exciton is created by electrons with anti-symmetric spin wavefunctions, hence the overall angular momentum is zero. On the other hand, the triplet exciton includes electrons possessing symmetric spin wavefunctions, resulting in the overall angular momentum to be one. The spin-conservation principle requires that spin must be conserved in electronic transitions. Therefore, under normal circumstance, only singlet to singlet or triplet to triplet transitions are allowed [5].

2.2.

The absorption and emission in organic semiconductors can be explained by electrical transitions, as illustrated in Figure 2.6.

Figure 2.6. Excitonic energy diagram for optical transitions

For simplicity, only two electronic states, the ground singlet state S0 and the first

excited singlet state S1, are shown in the diagram. The vibrations between the

nuclei divide each singlet state into many sub-level vibrational states. According to the Franck-Condon principle, the electronic transition happens much faster than the nuclei can respond, since the nuclei are heavier than the electrons. As a result, the nuclear framework remains constant during the electronic transition. Only vertical transitions (the solid lines) occur between the two electronic states. The vertical transition excites the molecule from the ground state to a higher vibrational state in the first excited singlet state. The excited molecule then rapidly relaxes non-radiatively from the higher vibrational state to the lowest vibrational state of S1 (the dotted lines). When it arrives at the lowest vibrational state in the

returning to the ground singlet state is larger than the energies that can be accepted by the surrounding molecules through collision. Consequently, the excited molecule remains in the lowest vibrational level in S1 for a relatively long time

until it decays to the vibrational level in the ground state via fluorescence by the Franck-Condon principle [6]. The emission spectrum is red shifted, in comparison to the absorption, due to the different energy gaps between the two transitions. The red shift, or Stokes shift, arises from the change of the nuclei positions and thus the potential between the electronic transitions. Other factors can also contribute to the red shift, such as the molecular environments. This is particularly the case for long chain conjugated polymers. The environment of disorder in polymers leads to conjugated chains with different lengths in different locations to form various localized energy states. When the sample is excited by a broadband light source, all the energy sites can be excited to their excited states. However, excitons in the higher energy localized states transfer their energies quickly to the lowest energy states through non-radiative dipole-dipole interactions. The excitons in the lowest localized exited state will finally decay back to the ground state by emitting a photon. In this manner, the red shift of the emission spectrum can be enhanced, in comparison to the case of a uniform molecular environment [7-10].

In some materials, phosphorescence from the triplet state can also contribute to the output emission, as indicated in Figure 2.7. When a molecule is excited to the first excited singlet state, if the triplet excited state shares a common geometry with the excited singlet state at the place where their potential curves intersect, intersystem crossing can occur via a spin flipping mechanism between the single and triplet state. Hence, the exciton can transfer from the excited singlet state to the excited triplet state. The transition from the triplet state to the ground singlet state is formally spin forbidden so that the molecule is trapped in the triplet state. However, with the help of the spin flipping mechanism, the transition from the triplet state to the ground single state can be eventually completed by weak phosphorescence emissions. In most organic semiconductors, phosphorescence is very inefficient process because the non-radiative decay is much faster. Efficient phosphorescence is only observed in organic semiconductors containing heavy metal atoms [11-12].