2-1 Absorption and emission
Absorption and emission characteristics of organic materials can be measured by UV/VIS photoluminescence spectroscopy. The absorption/emission characteristics are determined by the molecular orbitals. According to Pauli’s exclusion principle, each molecular orbital can only be filled with two electrons. The electrons start to fill from the lowest energy level, and then we can get the lowest-energy electron configuration.
When electrons fill up the highest occupied molecular orbitals (HOMO), the molecule is in the so-called ground state and molecules are usually in the ground state. When the excitation light absorbed by molecules, electrons can transit to a higher energy level to the excited state, but the excited electrons will quickly go back to the lowest occupied molecular orbitals (LUMO) through internal conversion and relaxation.
Fig. 2-1 The emitting principle of the fluorescence and phosphorescence[8].
7
When the molecules absorb energy, the electrons will transit to the singlet excited state (Sn). Fluorescence is the light when the electrons in the singlet excited state transit to the ground state. If the electrons at the singlet excited state transit to the lower level triplet excited state (Tn) via intersystem crossing (ISC) and go back to the ground state and emit the light, the light is called phosphorescence.
8
2-2 Singlet and triplet excited states
Organic materials have different excited states after the recombination of the electrons and the holes (Fig. 2-2). One is singlet excited state with spin symmetric excited electrons and the other is triplet excited state with spin-anti-symmetric electrons. According to theoretical speculation, the ratio of the singlet excited state to the triplet excited state caused by the recombination of the electric charge is 1 : 3.
Therefore, only 25% of the energy can be used and the remaining 75% of the energy in the triplet excited state is lost through non-emitting mechanism or non-radiative decay at the use of small molecule fluorescent materials. So it is considered that the limit of internal quantum efficiency is 25%. But if we take the generation of singlet excitons by triplet-triplet annihilation into consideration, the internal quantum efficiency may be increased to 40%.
Fig. 2-2 Excited state after the recombination of the electrons and the holes[9].
9
In Fig. 2-3, the electrons in the ground state and the singlet excited state are spin-anti-symmetry. The electrons in the triplet excited are spin-symmetry. According to Hund’s Rule, it will be more stable for the electrons in spin-symmetry, so the energy level of the triplet excited state is lower. The transition of the electron from the triplet excited to the ground state will produce a pair of electrons with the same spin orientation, so is not compatible with Pauli Exclusion Principle. The electron cannot transit smoothly to the ground state since the violation of Pauli Exclusion Principle, and then the lifetime would become longer.
Fig. 2-3 Electron spin orientation in different kinds of state.
10
2-3 Charge transfer in organic molecules
Unlike the inorganic semiconductor or crystalline materials, the organic semiconductor is amorphous and doesn’t have extended energy band. There are always delocalized π electrons in the organic semiconductor structure. These electrons in organic semiconductor are freer compared to the ones in the inorganic and crystalline materials, but they are confined in the molecule. Therefore, the hopping theory is the most commonly used for describing the charge transfer between the organic molecules[10]. When the organic semiconductor is driven by the electric field or pumped by the laser, the electrons will be excited to the LUMO level, and jump to another LUMO level as shown in Fig 2-4.
Fig. 2-4 Electron transfer in organic semiconductor[8].
11
2-4 Light emitting mechanisms
Currently, the structure of the host emitter (main material) and guest emitter (dopant) system[11, 12] is widely being used in organic material device. That is, to dope the guest emitter in the host emitter and the organic semiconductor will emit the light when the host emitter with higher energy transfers the energy to the guest emitter. We can choose the emitting color and raise the device efficiency by changing different guest emitters. There are two emitting mechanisms: (1) energy transfer (2) carrier trapping
2-4.1 Energy transfer
When the electron in the excited state gives the energy to the one in low energy level, this process is called energy-transfer. Energy transfer mechanism often happens in multi-component doping system and can be classified into radiative and non-radiative. The host emitter in high energy level can transfer energy to guest emitter in low energy level. We can change the fluorescence color by doping some guest emitter.
Radiative energy transfer is related to the energy transfer rate, the quantum efficiency of the host, the concentration of the guest etc. This mechanism causes the total fluorescence quantum efficiency drops, so it should be avoided. The other is non-radiative energy transfer. There are two ways (Fig. 2-3) of non-radiative energy transfer: (1) Förster energy transfer. It transfers energy by the interaction of long distance dipole-dipole. If the radiation of the host and the absorption of the guest can overlap, the Förster energy transfer can be done. (2) Dexter energy transfer. It transfers energy by the exchange of short distance electrons. It should follow the Wigner-Witmer[13] selection rules when the electrons are transferring, that is, the spin orientation should be the same after the transfer. So Dexter energy transfer only
12
occurs between singlet state to singlet state and triplet state to triplet state. Since Dexter energy transfer only occurs between adjoining molecules, the procedure is relatively slow. By these two energy transfer mechanism, the energy can be transferred to the singlet and triplet excited state of the guest emitter. The energy at the singlet excited state can be transferred to the triplet excited state via ISC rapidly and emit the phosphorescence. Therefore, the internal quantum efficiency is possible to nearly be 100%[14]
Fig. 2-5 Förster and Dexter energy-transfer mechanisms[14].
13
2-4.2 Carrier trapping
The energy can be transferred not only by the energy transfer from the host emitter to the guest emitter but also by carrier trapping to excite the guest emitter.
That is, the electrons and holes recombine on the guest emitter and make a form of Frenkel excitons which representing the electrons and hole are in the same molecule, and then the guest emitter will emit the light. This mechanism will take place when the bandgap of the host emitter is larger than the guest emitter and the HOMO and LUMO of the guest should be included in the ones of the host emitter. If the bandgap of the host is too large for the electrons and holes to inject into, the carriers will directly inject into the guest emitter and have a recombination to emit light[15-21]. If either the HOMO or LUMO of the guest emitter is included in the ones of the host emitter, the emitting should depend on whether the Frenkel excitons of the guest are in the lower energy state or not. If they are, the guest will emit the light, or it will be difficult to emit the light because they form an electron-hole pair between the host and the guest.
Carrier trapping and energy transfer both exist at the same time and which one will be the major emitting mechanism depends on the different situations. Generally speaking, in the high doping concentration or low current density conditions, the carrier trapping would be the major emission mechanism.
14
2-5 The Purcell factor
The enhancement of spontaneous emission rates of molecules when they are matched in a resonant cavity was first observed by Purcell 50 years ago[1]. The spontaneous emission (SE) rate of radiating dipoles depends on the environment light source. This means that using a cavity modifies the dipole-field coupling and the density of available photon modes can modify the spontaneous emission rate. This concept is now well-established due to the large quantity of research on cavity quantum electrodynamics (CQED)[22, 23], and its applications for optoelectronics has been widely used. Many kinds of microcavities which have an ability of three-dimensional photon confinement have been developed since 1990s and a lot of these microcavities are capable of generating strong spontaneous emission rate (Purcell effect). Microcavities need a good emitter which is spectrally narrower than the resonant mode of the cavities, otherwise the magnitude of the Purcell effect will be weakened.
2-5.1 The expression of the Purcell factor[24]
In this section, we will briefly derive the formula of the Purcell factor of a cavity, and describe the physical significance. First, we suppose a single localized radiating dipole which is weakly coupled to the field and placed in a monomode cavity. And we assume that the emitter is placed in a medium of refractive index n. We can suppose that the dipole sees continuous modes if the dipole emission line is narrower spectrally than the cavity resonant mode. And then, we can calculate the spontaneous emission rate by the Fermi Golden Rule. The transition rate for an electric dipole can be written as
eq. (1) where is the density of photon modes at the emitter’s angular frequency ,
15
is the electric field operator, is the location of the emitter. The emitter sees the averaging of the squared dipolar matrix element performed over the various modes.
The electric field operator for the cavity mode is
eq. (2) where h.c. is Hermitian conjugate, is the photon creation operator and is the mode spatial function. is normalized so that its norm at the antinode of the electric field is unity and it is a complex vector which follows Maxwell equations and volume of hypothetic cavity, defined by Born–Von Karman periodic boundary conditions, and would provide the same maximum field per photon as the cavity under study. The maximum field per photon is given by equation (4), for each mode, provided that is replaced by a normalization volume V.
There are three ways of changing the cavity’s spontaneous rate when inserting the radiating dipole inside the cavity: (1) The spectral density of modes. (2) The amplitude of the vacuum field. (3) The orientation with respect to the radiating dipole.
All three of the above are modified. And then, the following evaluations will depend on the resulting change of the SE rate for a cavity which supports a single-mode of angular frequency , linewidth , and quality factor . So the mode
16
density seen by the emitter is given by a normalized Lorentzian
and
eq. (4) while the “free-space” mode density can be written as
eq. (5) The ratio of the spontaneous emission rate enhancement of the cavity to the free space is random polarization of free-space modes with respect to the dipole.
However the first term ( , ) is only related to the cavity itself. The others, which are smaller than 1, are related to the emitter/mode spectral detuning, the relative field amplitude at the emitter’s location, and the orientation matching of the transition dipole and electric field. For the purpose of finding an expression for the cavity alone, the emitter can be assumed as an ideal emitter, whose properties are allowed to maximize the magnitude of the Purcell effect. So this ideal emitter has to be: (1) perfectly matched spectrally with the cavity mode, that is , (2) located at a maximum of the electric field, (3) with its dipole aligned with the local electric field. Based on the above conditions, the expression proposed by Purcell is
eq. (7)
17