A MODEL OF ORGANIC THIN FILM ELECTROLUMINESCENCE

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1 Journal o Optoelectronics and Advanced Materials, Vol. 4, No., September, p A MODEL OF ORGANIC THIN FILM ELECTROLUMINESCENCE Institute o Molecular and Atomic Physics, F. Skaryna ave. 7, Minsk, 7, Belarus A simple model or thin ilm organic electroluminescence in single layered one-dimensional cell is developed, assuming direct excitation o luminophor molecules by electron impact. The values and behaviour o calculated curves or brightness and eiciencies correlate with experimental data. For high eiciency, low work unction, and high Fermi energy cathodes, and relatively low electric ields should be used. (Received July, ; accepted July, ) Keywords: Organic thin ilm, Electroluminescence, Electron impact. Introduction Organic solid thin ilm structures are very promising materials or the development o maniold optoelectronic devices. However, undamental physical processes in such structures and mechanisms o luminophor excited states ormation are not clear yet. Many authors assume that organic luminophor excited states appear due to an electron-hole recombination. But luminophor molecules can also be excited by direct hot electron impact [], especially at high electric ields. I we understand all the mechanisms o organic electroluminescence, we can solve their main problems, such as eiciency and durability. The theoretical modeling can essentially clear this question. Some authors tried to solve this problem (see, or example [, ]). In this paper a model o processes in organic thin ilm electroluminescent cell is developed, assuming direct excitation o luminophor molecules by electron impact into singlet, triplet, and ion states and electron-ion recombination.. Background and model description Electroluminescent studies o organic substances were earlier held in the gas phase [4]. The molecules in the gas discharge are conclusively excited by an electron impact, because the shape o luminescence spectrum o ree molecules strongly depends on the average electron energy, which can be changed by applied voltage [5] or by addition o another gas with dierent excitation potential [6]. As it is known rom the gas discharge physics [7], the condition or electron-ion recombination at high electric ield is very bad, because electrons and positive ions are divided spatially and continue to divorce by a ield. Thermal electrons only take part in the recombination process. A rise o electric ield strength increases electron energy and makes recombination process diicult. The conditions o electric excitation in an organic electroluminescent cell and in a gas discharge tube are similar. A value E/n= -4 V cm determining the average electron energy is the same both in neon and organic gas discharge (E= V/cm, n= 6 cm - [7, 8]) and in organic electroluminescent cell (E 6-7 V/cm [9], n= cm - ). Particularly, many amorphous organic thin ilms conserve their properties in monomolecular state. It is known that electrons are ejected rom the cathode as a result o tunneling in a high electric ield, where they are also accelerated. The ejected electrons energy approximately equals the Fermi energy. The real energy received by electron rom electric ield between inelastic collisions in this ield equals to eed=ee/nσ and can reach ev (here n is about cm -, and σ is the cross section o inelastic collisions (about -6 cm ), d= nm is the thickness o the cell). But the excitation threshold o molecules is about - ev. Note that the way between two inelastic

2 576 collisions d=/nσ is about nm, i.e. one inelastic collision occurs in the thickness o electroluminescent cell, and we can consider the excitation only near surace region. The above presented data show that we have to take into consideration the process o direct excitation by hot electrons. It is interesting to describe the organic electroluminescence on the basis o this process. Though, charge transport in the bulk o amorphous organic materials is widely described as a hopping process with low mobilities, it can strong dier in thin near interace ilms due to dipole layer. It should be also noted that with only recombination description o organic electroluminescence the calculated electroluminescent intensity is around one order o magnitude higher than experimental [,], the recombination cross section much exceeds geometrical one [], recombination zone is supposed to be near cathode surace [], near the anode surace [], at the interace [], or in the volume []. The typical electroluminescent cell consists o three organic layers sandwiched between two electrodes. They are so called electron transporting, emitting, and hole transporting. However, the real role o the additional transporting layers is not clear yet. It is known that diamine based antioxidants gives the possibility or organic electroluminescent devices to work in contact with oxygen and air, at rising in temperature and radiation level, in contacts with metals, etc., as well as to reduce molecular aggregation increasing luminescence quantum yield. Such substances can accept charge or energy and prevent destruction o molecules due to dissociation or chemical reaction. This is possibly one o the unctions o additional organic charge transporting layer. On the other hand, it is well known [4] that a thin dielectric ilm o electronegative substance placed on the cathode surace results in decreasing o the cathode work unction. Thus, the additional layers are the part o electrodes. The very low drop o potential on additional layer [5] corroborates this conclusion. As a result, the real thickness o electroluminescent cell consists o the thickness o radiating layer. Moreover, we can consider the reduced work unction o the cathode metal. As a rule, on the cathode surace there always are microscopic edges o h height and r radius, and electric ield strength is h/r times more than a mean value in the space between electrodes. The ield increase can be times and more, as it was earnestly shown in the gas discharge [4]. Note, that tunnelling process is very inertial [6] due to charge accumulation at the interace [7]. It really determines the electroluminescence response. Taking into account the above assumptions, or single layered electroluminescent cell the rate o excitation o organic molecules with the x coordinate F(x) was calculated using the standard expression j( px, py, pz ) F( x) = σ ( px, py, pz) dpxdp ydpz = e mh π σ ( p, ρ, α) D( p, E) pρdpd ρdα () where σ(p x,p y,p z ) is the excitation cross section, j(p x,p y,p z ) is the current density, D(p,E) is the tunneling probability. The right part is written in cylindrical coordinates. In the one-dimensional approximation the tunneling probability or a triangular barrier is: / p ( ψ + E - ) 8π m D( p, E) = exp[ m θ( y)] () h e E where Ψ is the work unction, E is the Fermi energy (chemical potential) o the metal, E is the electric ield strength, and θ(y) is the Schottky unction. Then the excitation rate is: m E m E p 4π 8π m F( x) = ( p, )exp[ mh σ ρ h p / ( ψ + E - ) m θ ( y)] pρdpd ρdα () e E

3 A model o organic thin ilm electroluminescence 577 because momentum changes rom zero to me. The same ormula without cross section multiplier was used or current density calculation. The energy dependence o cross section o organic luminophor excitation into singlet states was approximated by Born ormula, which behaviour is similar to molecular luorescence excitation unction [8, 9] σ ( p, ρ) = α p ln( β p ), where p p m e E W N x = ( + ( - σ ) ) + ρ, W is the averaged energy which loses the electron ater one collision, σ is the averaged cross section o the process, α and β are the coeicients or the studied molecule. The energy dependence o triplet states excitation was calculated using ormulae σ t (E)= σ max t E th /E, where σ max t is the maximal value o cross section, E th is the threshold energy. For ionization the Born approximation with threshold at ionization energy (7.5 ev) was used. The weakening o the electron lux was taken into account by multiplying o expression in () by exp(- σ Nx), where σ is the cross section o this process. The values o excitation rates were ound by means o numerical integration. Using this value, the electroluminescence brightness can be easily calculated. Electron concentration, N e, was calculated by integration over x coordinate the expression Ne ( px, x) ( x, x) j p = (see ormula ). Maximal ( ) ev x max max values o cross sections σ t and σ I were varied rom -7 to -6 cm -. Electron-ion recombination rate K rec = -6 cm /sec, singlet and triplet excited molecules (:) are ormed ater recombination. The ull number o luminescent molecules in the volume was ound by F = ( NηV / d ) F( x) dx, where V and d is the volume and the thickness o the cell, η is the v d quantum yield o luminescence, hν is the averaged energy o luminescence quantum. The energy eiciency was deined as Φ = Fvhν /( Wk + jsu ), and quantum eiciency ϕ = Fv / js (the ratio o radiated quanta to a number o electrons), where W k is the energy o ejected electrons. We consider organic diode abricated using indeinite organic phosphor with η=.8, excited state lietime τ= -9 sec, the energy o excited state.4 ev, and the maximal value o excitation cross section to be -6 cm -. We take N= cm -, d= nm. Some calculations are made or host-guest system with eective energy transer rom host molecules to guest. The eects o space charge, polarization o luminophor layer, and electron-electron cooling are not taken into consideration, though they are very essential at high ields. The electrical ield is supposed to be homogeneous and directed along the x axis. Intramolecular processes are described by the system o standard equations in the our-level approximation.. Results and discussion In Fig. the calculated dependences o distribution o excitation rate on the cell thickness or dierent values o work unctions and Fermi energies (.8 ev or Al, and ev or Ca []) are presented. Here all the curves are normalized on the maximal values. This characteristic strongly depends on Fermi energy, which can change rom.8 ev or Al to.5 ev or Na, especially at low work unctions. It is connected with the energy dependence o excitation cross section, which rises rom threshold E th at excitation potential to a maximal value σ max at -4 E th and then decays slowly. I E is less or more than the energy o σ max or ater acceleration by electric ield, electrons are not optimal or excitation o luminophor molecules. So, or deined conditions there is an optimal thickness o emitting layer. The very intensive electroluminescence is observed in rather narrow thickness range nearby the cathode surace, in compliance with the experimental data []. I we use the real energy dependence o excitation cross section [], this range will be narrower.

4 578, a, b excitation rate, a.u.,8,6,4, excitation rate, a.u.,8,6,4, 6 4 5, 4 6 8, x 5 c x 5 d excitation rate, /sec x 5 x 5 excitation rate, /sec x 5 x excitation rate, /sec 8,x 5 6,x 5 4,x 5,x 5, e excitation rate, /sec ,4,5,6,7,8,9, electric ield, MV/cm Fig.. The dependences o distribution o excitation rate on the cell thickness or dierent values o work unctions and Fermi energies: a) ψ= ev (-6), E = (-),.8 ev (4-6), E= (, 4), (, 5), MV/cm (, 6), b) ψ= ev (-6), E = (-),.8 ev (4-6), E=5 (, 4), (, 5), MV/cm (, 6). Fig.c- show the relative rates o considered processes. The dependences o volume averaged rates on electric ield () and their depth distribution or luminophor molecule singlet state S F (), triplet F T () and ion F I () are presented or cathodes with dierent Fermi energies and work unctions. I E is relatively high (Fig. c), electrons excite triplet states with approximately one order lower eiciency than singlet. Both curves (, ) decrease quickly with depth (or triplets two times quicker), the curve or ions changes more slowly. Taking into consideration recombination process, at high ields recombination rate is strongly increased and excitation rates or singlets and triplets are comparable. For cathodes with low Fermi energy (Fig. d) at cathod-luminophor interace the most intensive rates are or triplet excitation, ionization process is negligible. Maximal values singlet excitation and ionization are reached at and 4 nm, correspondingly. Triplet excitation is quickly decreased. Ionization process is essential at ields higher than MV/cm (Fig. ). It occurs at depth more than 6 nm.

5 A model o organic thin ilm electroluminescence 579 energy eiciency,,8,6,4, a quantum e iciency,5,4,,, b, electric ield, MV/cm, electric ield, MV/cm Fig.. The dependence o energy (a) and quantum (b) eiciency on electric ield. ψ =- ev, E =.8 (), 7 (), ev (). Fig. illustrates the behaviour o energy and quantum eiciency with electric ield. It can be noted that the behaviour o these curves are similar. Both the energy and the quantum yield are very sensitive to the Fermi energy at relatively low electric ields. Moreover, there is an optimal ramework or electrical ield to reach the maximal eiciency. Its value decreases with the urther enhancing o electrical ield. It is also connected with the acceleration o electrons to energies exceeding the energies o maximal excitation cross section. For our molecules this energy equals to ev. The value o quantum eiciency is agreed with our estimation [7]. The value o energy eiciency and its energy behaviour are in a good accordance with the experimental data [, 8]. Thus, the best maximal energy eiciency is nowadays about 4%. We have also to take into consideration that quantum yield o luminescence in our calculations is.8, but really it is essentially lower. 4. Conclusion In conclusion, we have shown that the operation o organic electroluminescent device could be described by a simple model based on tunneling injection o electrons and direct electron impact excitation o molecules. For high eiciency, low work unction and high Fermi energy cathodes and relatively low electric ields should be used. The urther development o this model is in progress. Reerences [] J. Kalinowski, J. Phys. D, R79 (999). [] J. Kawabe, G.E. Jabbour, S.E. Shaheen, et al., Appl. Phys. Lett. 7, 9 (997). [] U. Wol, V.I. Arkhipov, H. Bassler, Phys. Rev. B59, 757 (999). [4] I. Ambrush, Sov. Chem. Usp. 6, 45 (957) (in Russian). [5] N. A. Borisevich, L. A. Barkova, V. V. Gruzinskii, et al. J. Appl. Spectrosc. 5, 68 (976). [6] V. V. Gruzinskii, L. A. Barkova, L. K. Strazkevich, et al. Izvestiya AN SSSR 4, 7 (978). [7] Yu. P. Raiser, Physics o gas discharge (in Russian), Nauka, Moscow (987). [8] N. A. Borisevich, V. V. Gruzinskii, Izvestiya AN SSSR 46, 44 (98) (in Russian). [9] S. Kawakami, M. Kitagawa, H. Kusano et al. Thin Solid Films 6, 7 (). [] M. Yoshida, A. Fujii, Y. Ohmori, K. Yoshino, Jap. J. Appl. Phys. 5, L97 (996). [] C. W. Tang, S. A. VanSlyke, C. H. Chen, J. Appl. Phys. 65, 6 (989). [] J. Pommerehne, H. Vestweber, Y. Tak, H.Bassler, Synth. Met. 76, 67 (996). [] H. Vestweber, H. Bassler, J. Gruner, R. H. Friend, Chem. Phys. Lett. 56, 7 (996). [4] G. A. Mesyats, Pulsed discharge in dielectrics (in Russian), Nauka, Moscow (985).

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