Assuming
1. Introduction
The current use of lighting in buildings and streets accounts for a significant percentage of the electricity consumed in the world at present and nearly 40% of that is consumed by inefficient thermoluscent incandescent lamps, only about 15 lm/W. This has created interest in investigating more efficient electroluminescent sources of white light for use in domestic, industrial and street lighting. The total light output efficieny
where
Here
The schematic of a very simple electroluminescent device can be envisaged as a single thin film of an electroluminescent layer sandwiched between anode and cathode electrodes, as shown in Fig. 1. In this case the anode is made of a transparent conducting oxide (usually indium tin oxide (ITO) and cathode is a metal, usually Al, Ca, Ag, etc). If the electroluminescent layer is of any direct band gap inorganic semiconductor, for example, based on GaAs and InP, then the injected electrons and holes from the cathode and anode, respectively, remain free electron and hole pairs and recombine radiatively by emitting light. In inorganic semiconductors, the static dielectric constant is relatively high (12.9 for GaAs and 12.5 for InP) which to a relative extent prevents the injected free charge carriers from forming bound hydrogenic excited states, called excitons. This is easy to understand as the atractive Coulomb potential energy between e and h is given by:
where
In contrast organic semiconductors, both of small molecules and polymers, have lower dielectric constant (
However, Cao
Thus, as the formation of triplet excitons is more probable than singlet, it is very desirable to capture the full emission from triplet excitons in OLEDs. It may be noted that the mechanisms of singlet and triplet emissions are different because of their different spin configurations and therefore the emission from singlet excitons is known as electrofluorecence and that from triplet excitons as electrophosphorescence in analogy with the terms used in photoluminescence. The description presented above may raise a question in your mind why then one should make any effort in organic solids/polymers for fabricating light emitting devices if the emission from triplet excitons cannpot be harvested. This is because OLEDs have the potential of being produced by one of the very cost effective chemical technolgies.
In additon, by harvesting emissions from both singlet and triplet excitons not only the 100% internal quantum efficiency (
The performance of a WOLED can be optimised by finding optimum emitting materials, manipulating the charge carrier balances and location of the recombination zone and energy transfer. The first WOLED fabricated [6] had a single poly (N-vinylcarbazole) emission layer doped with three fluorescent dyes. To achieve higher power efficiency, a combined use of blue fluorescent and green and red phosphorescent emitters in WOLEDs has been made recently [4,7]. This concept is based on the coincidence of a physical phenomenon of formation a singlet spin configuration with probability 25% and triplet with 75% between an electron and hole injected from the opposite electrodes of a device with that of a natural phenomenon that white light consists 25% of blue light and 75% of red and green lights. Thus, the combination of fluorescent (blue singlet emission) and phosphorescent (red and green or orange triplet emission) emitters is capable of reaching 100% internal quantum efficiency of white light emission by harvesting 25% singlet emission and 75% triplet emission. Although by trial and error experimental techniques on WOLEDs the triplet radiative recombination is activated by a heavy metal atom compound (phosphor) that enhances the spin-orbit interaction and hence triplet radiative recombination, the mechanism has not been fully understood theoretically until recently [8]. This is because the well known spin-orbit interaction is a stationary operator that cannot cause transitions[8-9]. In this chapter, the radiative recombination of both singlet and triplet excitons in organic solids/polymers is reviewed. Rates of spontaneous emission from both singlet and triplet excitons are calculated in several phosphorescent materials by using the recently invented new time-dependent exciton-spin-orbit-photon interaction operator [8] and found to agree quite well with the experimental results.
2. Emission from singlet excitons
Let us consider an excited pair of electron and hole created such that the electron (e) is excited in the lowest unoccupied molecular orbital (LUMO) and hole (h) in the highest occupied molecular orbital (HOMO) of organic layer sandwiched between two electrodes, and then they recombine radiatively by emitting a photon. The interaction operator between a pair of excited e and h and radiation can be written as:
where
where
Using the centre of mass,
where
The field operator of an electron in LUMO can be written as:
where
Likewise the field operator of a hole excited in HOMO can be written as:
Using Eqs. (5), (7) and (8), the operator
where
We now consider a transition from an initial state
for singlets and
for triplets. We assume that there are no photons in the initial state and the final state has no excitons but only a photon in a
where
Here the energy difference between the LUMO and HOMO levels is given by
where
where
In organic solids,
3. Emission from triplet excitons
As recombination of a triplet exciton state to the ground state is spin forbidden, it cannot occur unless either the triplet goes through an intersystem crossing to a singlet or a source of flipping the spin is introduced to make such a radiative recombination possible. Unlike inorganic solids, most organic solids and polymers have significant exchange energy between singlet and triplet excitons states. Therefore the mechanism of intersystem crossing may not be very efficient without doping the solids with another material of lower singlet energy state. This is possible and usually the host material is doped with a fluorescent material but some loss of energy is inevitable due to the difference in energy [4]. A more efficient way of harvesting triplet is to dope the host material with phosphorescent compounds containing heavy metal atoms, like platinum (Pt), palladium (Pd) or iridium (Ir) [1]. Here again the energy matching needs to be carefully examined otherwise an energy loss will occur. Thus, in the fabrication of a WOLED, the host polymer is doped with a fluorophore to emit the blue emission from singlet excitons and two phosphorescent compounds to emit green and red from the triplet radiative recombination [4,7]. A most efficient such combination is the host polymer being doped with a blue fluorophore 4,4‘-bis(9-ethyl-3-carbazovinylene)-1,1‘-biphenyl (BCzVBi) 12 in a region separate from the phosphorescent dopants, which are fac-tris (2-phenylpyridine) iridium(Ir(ppy)3) for emitting green and iridium(III) bis(2-phenyl quinolyl-N,C20) acetylacetonate (PDIr) for emitting red [4]. In some cases an orange phosphorescent dopant is used in place of red and green. It is commonly well established that the transfer of singlet excitons to blue fluorophore occurs efficiently due to the Förster transfer and that of triplet excitons to phosphorescent dopants due to Dexter or diffusive transfer. However, after that how the radiative recombination occurs by the enhanced spin-orbit interaction due to the introduction of heavy metal atoms is not thoroughly explored. The problem is that the well known expression for an electron spin-orbit interaction in an atom is given by:
where
Furthermore, the interaction operator given in Eq. (18) is a stationary interaction operator, i.e., s and L are intrinsic properties of charge carriers (electrons and holes) and are always with them. These are present in all atoms all the time like the Coulomb interaction between electrons and nucleus. Such an interaction can give rise only to the stationary effects, like splitting the degeneracy of a triplet state but it cannot cause any transitions. As the splitting depends on the strength of the spin-orbit interaction, which increases with
We have recently addressed the problem [8-9] of finding a new time-dependent exciton-spin-orbit-photon interaction operator as described below.
3.1. Electron-spin-orbit-photon interaction
We consider the case of an atom of atomic number
where
where A is the vector potential of photons as used in Eq. (5) but expressed in a different form here (see Eq. (21)),
Within the dipole approximation (
where
where
The interaction operator in Eq. (20) can be further simplified by noting that within the dipole approximation we get
Even otherwise, the contribution of the term in (23b) is expected to be small and therefore will not be considered here.
Substituting Eqs. (22) and (23) in Eq. (20) the interaction operator contains only the following two non-zero terms:
where L = r
where
For an atom, the field operator for an electron in the excited state and a hole in the ground state can be respectively written as:
where
Using Eq. (27), the interaction operator in Eq. (26) can be expressed in second quantization as:
Using the property of the spin operator
It may be noted that the operator
We now consider a transition from an initial state with a triplet excitation whose spin has been flipped by the spin-orbit interaction but it has no photons to a final state with no excitation (ground state) and one photon created in a mode
where |0> and |0
Using Fermi’s golden rule and Eq. (32), the rate of spontaneous emission of a photon from the radiative recombination of a triplet exitation in an atom denoted by
where the sum over
where
The rate of spontaneous emission obtained in Eq. (34) is derived within the two level approximation may be applied to organic solids and polymers [9] where excitation gets confined on individual molecules/monomers as Frenkel excitons and also referred to as molecular excitons [19]. Until the late seventies excitons in organic solids, like naphthalene, anthracene, etc., were regarded in this category. Furthermore, the concept that an exciton consists of an excited electron and hole pair was considered to be applicable only for excitons created in onorganic solids, known as Wannier excitons or Wannier-Mott excitons. These were also known as the large radii orbital excitons because of the small binding energy the separation between electron and hole is relatively larger than that in Frenkel excitons in organic solids. However, this distinction has blurred since the development of OLEDs where electrons and holes are injected from the opposite electrodes, as described above, and form Frenkel excitons. This proves the point that Frenkel excitons also consist of the excited electron and hole pairs but they indeed form a molecular excitations because of the small overlap betwen the intermolecular electronic wavefunctions.
Assuming that the Frenkel excitons are molecular excitons in organic solids/polymers, the above theory has been extended to organic solids [9] and the rate of spontaneous emission is obtained as:
where
As the rate of spontaneous emission is proportional to
The rate of spontaneous emission in equation (36) is used to calculate the triplet radiative rates in several organic molecular complexes, conjugated polymers containing platinum in the polymer chain and some organic crystals [9]. For all polymers considered from ref.[20], where the effective mass of charge carriers and excitonic Bohr radius are not known, it is assumed that
Material | Eq. (3) | (s) | (s) | ||
Benzene | 3.66 [22] | 0.63 | - | 1.6 | 4-7 [22] |
Naphthalene | 2.61 [22] | 0.45 | - | 2.2 | 2.5 [22] |
Anthracene | 1.83 [22] | 0.31 | - | 3.19 | 0.1 [22] |
P1 | 2.40 [20] | 5.5x103 | (6 | 1.82x10-4 | |
P2 | 2.25 [20] | 5.1x103 | (1.8 | 1.96x10-4 | |
P3 | 2.05 [20] | 4.6x103 | (1 | 2.17x10-4 | |
Pt(OEP) | 1.91[24] | 4.9 x103 | 2. 03x10-4 | 7.00x10-4 |
3.2. Exciton -spin-orbt-photon interaction
In the above section, it is shown that a time-dependent electron-photon-spin-orbit interaction operator does exist and it can be applied for triplet state transitions. The theory is also extended to Frenkel excitons or molecular excitons without considering them as consisting of electron and hole pairs. However, the formalism presented above is relevant to an excited electron in an atom/molecule which is not consistent with the situation occurring in a WOLED, where electrons and holes are injected from the opposite electrodes and they form excitons before their radiative recombination. Thus, for WOLEDs we need a time-dependent exciton-photon-spin-orbit interaction operator. For a pair of injected carriers in a solid with
where
where the zero magnetic contribution is neglected. In analogous with Eq. (24), one gets two non-zero terms for the electron and two for the hole as:
Here
Using the field operators in Eqs. (7) and (8) and Eq. (39), the time-dependent operator of exciton-photon-spin-orbit interaction is obtained in second quantisation as [9]:
where
The other important approximation made in Eq. (40) is that the sum over sites
Using the triplet spin configuration in Eq. (12) and the property of
It is to be noted here also that the operator (
The new operator is attractive for excitons so it attracts a triplet exciton to the heaviest atom as it is proportional to the atomic number. As the magnitude of attraction in inversely proportional to the square of the average distance between an electron and nucleaus, only the nearest heavy nucleus will play the dominant role.
As soon as a triplet exciton interacts with such a spin-orbit-exciton-photon interaction, the spin gets flipped to a singlet configuration and exciton recombines radiatively by emitting a photon.
3.3. Rate of spontaneous emission from triplet excitons
We now consider a transition from an initial state
Using Fermi’s golden rule and the transition matrix element in Eq. (43), the rate of spontaneous emission of a photon from the radiative recombination of a triplet exiton in an organic solid/polymer denoted by
where the sum over
For triplet excitons using
For different phosphorescent materials only the atomic number of the heavy metal atom and the emitted energy will be different so the rate of spontaneous emission in Eq. (36) can be simplified as follows: Using
For phosphorescent materials like fac-tris (2-phenylpyridine) iridium (Ir(ppy)3) and iridium(III) bis(2-phenyl quinolyl-N,C20) acetylacetonate (PDIr), where Ir has the largest atomic number
Both rates of spontaneous emission derived in Eq. (36) on the basis of single electron excitation (atomic case) and that obtained in Eq. (45) for an electron-hole pair excitation have been applied to calculate it in organic solids and polymers [9, 27]. Apparently for platinum complexes Eq. (36) gives rates that agree better with experimental results but for iridium complexes Eq. (45) produces more favourable results.
In addition to developing the introduction of the phosphorescent materials to enhance the radiative recombination of triplet excitons, a step progression of HOMO and LUMO of the organic materials to confine the injected carriers within the emission layer has been applied [25]. This enables the injected e and h confined in a thinner space that enhances their recombination. This scheme has apparently proven to be most efficient so far.
Another approach for meeting the requirement of availing different energy levels for singlet and triplet emissions within the same layer of a WOLED is to incorporate nanostructures, particularly quantum dots (QDs), in the host polymers [28]. As the size of QDs controls their energy band gap, the emission energy can be manipulated by the QD sizes. It is found that the energy band gap of a QD depends on its size as [29]:
where
This chapter is expected to present up to date review of the state-of-the art development in the theory of capturing emissions from triplet excitons in WOLEDs.
References
- 1.
C. Adachi, M. A. Baldo, M.E. Thompson, and S. E Forrest, J. Appl. Phys. 90, 5048 (2001). - 2.
Y. Cao, I.D. Parker, G. Yu, C. Zhang and A.J. Heeger, Nature 394, 414 (1999). - 3.
Z. Shuai, D. Beljonne, R.J. Silbey and J. L. Bredas, Phys. Rev. Lett. 84, 131 (2000). - 4.
G. Schwartz, S. Reineke, T. C. Rosenow, K. Walzer and K. Leo, Adv. Funct. Mat. 19, 1319 (2009). - 5.
J. Singh, Phys. Status Solidi C8, 189 (2011). - 6.
J. Kido, K. Hongawa, K.Okuyama, K Nagai, Appl. Phys. Lett. 64, 815 (1994). - 7.
Y. Sun, N. C. Giebink, H. Kannao, B. Ma, M. E. Thompson and S. R. Forest, Nature, 440, 908 (2006). - 8.
J. Singh, Phys. Rev. B76, 085205(2007) - 9.
J. Singh, H. Baessler and S. Kugler, J. Chem. Phys. 129, 041103 (2008). - 10.
J. Singh, Photoluminescence and photoinduced changes in noncrystalline condensed Matter in Optical Properties of Condensed Matter and Applications, J. Singh (Ed.) (John-Wiley, Chichester, 2006), Ch.6. - 11.
J. Singh and I.-K. Oh, J. Appl. Phys. 97, 063516 (2005). - 12.
J. Singh and K. Shimakawa, Advances in Amorphous Semiconductors (Taylor & Francis, London, 2003). - 13.
A. Köhler, J. S. Wilson, R. H. Friend, M. K. Al-Suti, M. S. Khan, A. Gerhard, and H. Baessler, J. Chem. Phys. 116, 9457 (2002). - 14.
T. Aoki, in Optical Properties of Condensed Matter and Applications, J. Singh (Eds.) ( John Wiley and Sons, Chichester, 2006), Ch.5, pp 75 and references therein. - 15.
T. Aoki, T. Shimizu, S. Komedoori, S. Kobayashi and K. Shimakawa, J. Non-Cryst. Solids 338-340, 456 (2004) and T. Aoki, J. Non-Cryst. Solids 352, 1138 (2006). - 16.
J. Singh, Physics of Semiconductors and their Hetrostructures (McGraw-Hill, Singapore, 1993). - 17.
Gasiorowicz S. Quantum Physics. 2nd Edition. . John Wiley. Sons N. Y. 1996 H. F. Hameka in The Triplet State (Cambridge University Press, Cambridge, 1967),1 - 18.
J. Singh, Excitation Energy Transfer Processes in Condensed Matter (Plenum, N.Y., 1994). - 19.
J. S. Wilson, N. Chaudhury, R.A. Al-Mandhary, M. Younus, M.S. Khan, P.R. Raithby, A. Köhler and R.H. Friend, J. Am. Chem. Soc. 123, 9412 (2001). - 20.
M.A. Baldo, D.F. O’Brien, Y. You, A. Shoustikov, S. Sibley, M.E. Thompson, and S.R. Forrest, Nature 395, 151 (1998). - 21.
J. B. Birks, Photophysics of Aromatic Molecules (John Wiley and Sons, London, 1970). - 22.
D. Beljonne, H.F. Wittman, A. Köhler, S. Graham, M. Younus, J. Lewis, P.R. Raithby, M.S. Khan, R.H. Friend and J.L. Bredas, J. Chem Phys. 105, 3868 (1996). - 23.
F. Laquai, C. Im, A. Kadashchuk and H. Baessler, Chem. Phys.Lett. 375, 286 (2003). - 24.
S.-J. Su, E. Gonmori, H. Sasabe and. Kido, Adv. Mater. 20, 4189(2008). - 25.
N. R. Evans, L. S. Devi, C. S. K. Mak, S. E. Watkins, S. I. Pascu, A. Köhler, R. H. Friend, C. K. Williams, and A. B. Holmes, J. Am. Chem. Soc. 128, 6647 (2006). - 26.
J. Singh, Phys. Status Solidi A 208, 1809 (2011). - 27.
Park, et al., Appl. Phys. Lett. 78, 2575 (2001). - 28.
Hsueh Shih Chena! and Shian Jy Jassy Wang, Appl. Phys. Lett. 86, 131905 (2005 - 29.
H.-S. Chen, C.-K. Hsu, and H.-Y. Hong, IEEE Phot. Tech. Lett. 18, 193(2006).