Onsager Theory Of Geminate Recombination Research Articles

Radiation-induced conductivity in polystyrene, a common insulating polymer with a hopping conduction

Radiation-induced conductivity (RIC) of polystyrene has been studied experimentally and numerically mostly in a small-signal regime in a broad time range from some nanoseconds to seconds. It has been established that hole transport is dispersive with a low value of the dispersion parameter α = 0.35. We have suggested a direct method of determination of the frequency factor of the Rose–Fowler–Vaisberg model, which has been parameterized using computer simulations by the trial and error method. The main outstanding concern is the application of the Onsager theory of geminate recombination concerning the field dependence of the free carrier yield and the possible frequency factor increase at high electric fields. The effect of hopping transport on the RIC in this common insulating polymer is still to be understood.

Exciton quenching in emitter blends for organic light emitting devices probed by electric field–dependent time-resolved luminescence

We investigate quenching mechanisms of excited states in emitter layers for organic light emitting diodes (LEDs). An extensive study of a strong electric field-induced modulation (over 50%) of the time-resolved luminescence in a diamine derivative (TPD): polycarbonate blend films doped with an organic complex of europium are presented as a typical example of an important class of emitters for organic monochromatic LEDs. Using this method allowed us to identify the quenched species as the excited ligand precursors of the emissive europium ion states. Manipulating the electrode materials and their electrical bias, the electric field-enhanced dissociation, and interaction with injected charge could be separated and found as principal quenching mechanisms. We show the first one to follow the three-dimensional Onsager theory of geminate recombination, and the second one raised by their interaction with the TPD-transported holes. The interaction rate constant is found to be underlain by the three-dimensional diffusion of excited ligand singlets, combining the exciton diffusion coefficient and long-range (Forster type) energy transfer parameters. The dynamic parameters of the hole-precursor excitons interactions, extracted from the experimental data, allow us to establish the criteria for identifying useful ligands and matrices in the optimized design of electrophosphorescent, linelike emitting molecules, and device structure for organic LEDs.

Charge generation and trapping in bisphenol-A-polycarbonate/N-isopropylcarbazole mixture: A study by electron bombardment-induced conductivity

Electron bombardment-induced conductivity measurements were carried out on cast films of N-isopropylcarbazole (NIPC) dispersed into an amorphous matrix of bisphenol-A-polycarbonate. The charge generation was studied by estimating the hole yield (g), the fraction of charge escaping recombination, as a function of electric field and concentration of NIPC at room temperature. The hole yield, besides increasing by increasing the content of NIPC, was observed to increase with the electric field in the manner predicted by the Onsager theory of geminate recombination. Deep trapping levels were studied by filling under electron bombardment and observing transients. The deep traps were neutral in nature with a concentration on the order of 8.0×1014 cm−3, which was low enough not to degrade transport under normal conditions.

Photophysics of an electrophosphorescent platinum (II) porphyrin in solid films

We examine electronic processes in platinum (II) octaethyl porphyrin (PtOEP) embedded in an organic solid state matrix and in the form of vacuum-evaporated neat films in conjunction with potential applications of this compound to organic photovoltaic and electrophosphorescent devices. Absorption, photoexcitation, and luminescence spectra indicate the excitonic dimers to be dominant excited states, and their dissociation underlies the charge photogeneration process. Different charge separation distance (1.5 nm and 2.6 nm) in opposite charge carrier pairs preceding dissociation can be distinguished based on the fit of the three-dimensional Onsager theory of geminate recombination to electromodulated luminescence and photoconduction measurements. The near-positive electrode concentrated triplet dimer excitons, produced by strongly 370 nm absorbed light in neat PtOEP films, are efficiently quenched by electron transfer to the metal (Al), generating the positive charge with an efficiency eta+ exceeding 0.15 at high electric fields and dominating the measured photocurrent. Their dissociation efficiency in the bulk, eta- (negatively biased illuminated electrode), is more than one order of magnitude lower than eta+. The dissociation of singlet dimer states dominates the bulk photogeneration process induced by the weakly-absorbed light at 450 nm, with comparable eta+ and eta-. The "hot excited state" underlying the temperature-increasing emission at 540 nm has been attributed to the upper excitonic component Q+ of the first absorption band Q consistent with the exciton concept applied successfully to the interpretation of all dimer-underlain spectroscopic features of PtOEP samples studied.

Polysilylenes: charge carrier transport and photogeneration

Charge carrier transport and photogeneration in polysilylenes, specifically in poly[methyl(phenyl)silylene], are discussed. Electronic properties are influenced by electron delocalization along the silicon backbone. A model of disordered polarons seems to be adequate to describe the charge carrier transport properties. Dissociation of ion pairs in external electric field, which can be described in terms of the Onsager theory of geminate recombination, seems to be the main mechanism of the free charge carrier photogeneration. Polar additives or polar side groups attached to the polymer backbone locally modify the ionization energy of the polymer segments and energies of electrostatic interactions of charge carriers and the dipoles. These changes result in the creation of local states for charge carriers and in the formation of a potential well structure. If the side groups are photochromic species changing their dipole moments upon illumination, then a light-driven molecular switch can be proposed.

Quenching effects in organic electrophosphorescence

We examine various electronic processes that underlie the quenching of the emission from highly efficient phosphorescent and electrophosphorescent organic solid-state molecular systems. As an example, we study the luminescent efficiencies from the phosphorescent iridium (III) complex, fac tris (2-phenylpyridine) iridium $[\mathrm{Ir}{(\mathrm{ppy})}_{3}]$ doped into a diamine derivative doped polycarbonate hole-transporting matrix and in the form of vacuum-evaporated films, as a function of electric field. We demonstrate that the observed decrease in electrophosphorescence efficiencies at high electric fields, and electric-field-induced quenching of phosphorescence from neat $[\mathrm{Ir}{(\mathrm{ppy})}_{3}]$ solid films is due to the field-assisted dissociation of Coulombically correlated electron-hole (e-h) pairs. They are formed in a bimolecular recombination process prior to the formation of emissive triplet excitons, or are charge-transfer (CT) states originating from the localized electronic excited states as a result of the initial charge separation upon photoexcitation, respectively. It is found that the high-field dependence of the quenching efficiency in both cases follows the three-dimensional Onsager theory of geminate recombination, the fit yielding the initial intercarrier distance ${(r}_{0})$ of the carrier pairs. We find ${r}_{e\ensuremath{-}h}>~3.5\mathrm{nm}$ for the triplet exciton precursor pairs in the bimolecular recombination, and ${r}_{\mathrm{CT}}=1.8\ifmmode\pm\else\textpm\fi{}0.1\mathrm{nm}$ for the initial carrier separation from the photo-excited electronic states. Triplet-triplet and triplet-charge carrier annihilation processes are shown to play major roles in the decrease of the electrophosphorescence efficiency within the lower-field regime at lower current densities. Summarizing the results allows us to point out some emitter features important for identifying phosphors useful for practical electroluminescent devices.

Electric field-assisted dissociation of singlet excitons in tris-(8-hydroxyquinolinato) aluminum (III)

Results based on the electric-field dependence of electro-modulated fluorescence and steady-state photoconduction in films of tris-(8-hydroxyquinolinato) aluminum (III) (Alq3) are consistent with a model where singlet excitons dissociate into electron–hole pairs through charge transfer state. Dissociation into free carriers or predominantly geminate recombination results from this intermediate state. The quantum efficiency of charge separation is in agreement with predictions based on a model using the three-dimensional Onsager theory of geminate recombination combined with volume (bimolecular) recombination of the photogenerated space charge. This model is used to account for the decrease in the electroluminescence quantum efficiency of Alq3-based organic light-emitting diodes at high electric fields.

Poly(silyens)s: Charge Carrier Photogeneration and Transport: S. Nešpůrek, A. Eckhardt Polym. Adv. Technol.12, 427–440 (2001)

AbstractThe original article to which this Erratum refers was published in Polym. Adv. Technol. 12, 427–440 (2001)In the following paragraph, ‘µ’ was inserted instead of ‘γ’.The paragraph should have read: Xerographic DischargeThe electric field (F) dependences of photogeneration efficiency as measured by the xerographic discharge method are shown in Figure 4 for PMPSi and PBMSi. The electric field and temperature (T) dependences of the photogeneration efficiency can be described using Onsager theory of geminate recombination (full lines). This theory can be used to describe one step in the photogeneration process, the thermal dissociation of ion‐pairs formed by light into free charge carriers in the external electric field. Under the assumption that the distribution of bound pairs is spherically symmetrical, the overall photogeneration efficiency ν is expressed as $\eta\,(r,F,T)=\eta_0\,\,{\textstyle\int}\,4\pi r^2f(r,F,T)g(r)dr$ where ϵ0 is the voltage and temperature independent primary quantum yield (fraction of the ion‐pair generated per photon), g(r) is the spatial distribution of the pairs, and r is the pair separation distance. Function f(r,F,T) represents the Onsager dissociation probability [9] of the ion‐pair. The best theoretical fits of the experimental data given in Figure 4 were found using the Onsager theory with the Gaussian distribution of radii [17] $g(r)=(\pi^{-3/2}$­$\gamma^{-3})$ exp (−r2/γ2) using parameters: γ = 1.3 nm, η0 = 0.45 and γ = 1.6 nm, η0 = 0.85 for PMPSi and PBMSi, respectively. According to Eq. 2 the photogeneration quantum efficiency η is also temperature dependent. The activation energy was determined as Eη = 0.05 eV for PMPSi (inset in Figure 4) and 0.04 eV for PBMSi. The temperature dependence of the photogeneration efficiency is also in good agreement with the Onsager dissociation theory (full line in inset of Figure 4).

Poly(silylene)s: charge carrier photogeneration and transport

AbstractAn Erratum has been published for this article in Polymers for Advanced Technologies 12(10)2001, 603.Poly(diorganylsilylene)s can be excited within the framework of Si bonds in the polymer backbone as well as within a side group skeleton. An electron transfer from the main chain to a side group or an interchain electron transfer is necessary to form a quasi‐stable ion‐pair. Dissociation of the ion‐pair in the external electric field can be described in terms of the Onsager theory of geminate recombination. The charge carrier transport proceeds predominantly along σ‐delocalized Si backbone with participation of interchain hopping and polaron formation. A model of disordered polarons seems to be adequate to describe the charge carrier transport properties. Copyright © 2001 John Wiley & Sons, Ltd.

Free Charge Carrier Formation in Polymers under Illumination

In addition to many extrinsic processes, free charge carriers in polymers can be photogenerated intrinsically via an intermediate stage of bound ion-pairs formed in consequence of band-to-band transitions or exciton autoionization. The excitation can be realized within the framework of (i) a chemical bond in the polymer backbone or (ii) a side group skeleton. An electron—hole pair with a short separation distance created by light on the same polymer chain or on the same side group usually recombines geminately very fast and does not contribute to the photocurrent. An inter- or intrachain charge transfer or transfer of the electron from the main chain to a side group is necessary to form a more stable ion-pair. Dissociation of the ion-pairs by Brownian motion subjected to a combination of Coulomb and applied electrical field, into free charge carriers, can be described in terms of the Onsager theory of geminate recombination. The photogeneration yield can be improved by an electron acceptor doping or by an electron accepting groups attached to side chains.

Free Charge Carrier Formation in Polymers under Illumination

In addition to many extrinsic processes, free charge carriers in polymers can be photogenerated intrinsically via an intermediate stage of bound ion-pairs formed in consequence of band-to-band transitions or exciton autoionization. The excitation can be realized within the framework of (i) a chemical bond in the polymer backbone or (ii) a side group skeleton. An electron—hole pair with a short separation distance created by light on the same polymer chain or on the same side group usually recombines geminately very fast and does not contribute to the photocurrent. An inter- or intrachain charge transfer or transfer of the electron from the main chain to a side group is necessary to form a more stable ion-pair. Dissociation of the ion-pairs by Brownian motion subjected to a combination of Coulomb and applied electrical field, into free charge carriers, can be described in terms of the Onsager theory of geminate recombination. The photogeneration yield can be improved by an electron acceptor doping or by an electron accepting groups attached to side chains.

Charge carrier photogeneration and transport in poly(methyl‐phenylsilylene)

AbstractOptical excitations in poly(methyl‐phenylsilylene) can be realized within the framework of a chemical bond in the polymer backbone or a side group skeleton. A charge transfer of the electron from the main chain to a side group is necessary to form stable ion‐pairs. Dissociation of the ion‐pairs can be described in terms of the Onsager theory of geminate recombination. The photogeneration efficiency can be improved by an electron acceptor doping. The charge carrier transport is influenced by two factors: delocalized movement inside the conjugated domains and intra‐ and interchain hopping. The electrostatic interactions of polar additives with polarons influence the polaron binding energy and the charge hopping.

Simultaneous measurements of thermoluminescence and thermally stimulated currents in poly(N-vinylcarbazole)/polycarbonate blends

Photoconducting model systems: poly(N-vinylcarbazole)/polycarbonate (PVK/PC) blends were investigated by simultaneous measurements of thermally stimulated currents (TSC) and thermoluminescence (TL). It was found that with increasing applied electric field, the TSC maximum increases and shifts towards lower temperatures, but the TL maximum decreases and its position on temperature scale remains unchanged. Moreover, the TSC maximum shifts also towards lower temperatures with increasing PVK content and with decreasing sample thickness and its position depends on the applied electric field polarity in a case when the sample is excited at low temperatures with a strongly absorbed light. The position of the TL maximum is unaffected by these factors. It is concluded that the field dependent TSC maximum cannot be interpreted in terms of the Poole-Frenkel effect, but it is the so-called ‘‘transport peak,’’ determined by transport and trapping phenomena, and can be regarded as thermally stimulated time-of-flight signal. Spectral analysis of TL indicates that it is characteristic of PVK phosphorescence. It results from recombination of charge carriers thermally liberated from neutral traps under the influence of a charged recombination center, and it can be described by a model based on the Onsager theory of geminate recombination. The detrapping is probably stimulated by the so called ‘‘wet dog’’ effect, related to molecular γ-relaxation in PVK.

X-ray photogeneration in amorphous selenium: Geminate versus columnar recombination.

Amorphous selenium (a-Se) is a photoconductor used for both optical and x-ray imaging. Its optical photogeneration efficiency has been understood in terms of the Onsager theory of geminate recombination. However, x-ray photogeneration in a-Se has not been understood well. A previous argument has dismissed the Onsager theory of geminate recombination in the context of carrier generation in a-Se by high-energy radiation. Instead, columnar recombination has been proposed. In this paper we examine this argument and the predictions of the two recombination mechanisms. We find that the argument which dismissed the Onsager theory of geminate recombination is unwarranted, and that the Onsager theory is generally consistent with available experimental data. On the other hand, the columnar recombination theory is inconsistent with experiment. We have extended the Onsager theory in a form appropriate for x-ray photogeneration in a-Se to reflect that there should be a broad distribution of electron-hole separations.

Onsager theory of geminate recombination: A single series expansion

The Onsager theory of geminate recombination has been widely applied to low-mobility materials such as anthracene and amorphous selenium. The photogeneration efficiency in this theory is usually expressed as a triple series expansion. A single series expansion has been previously derived, but it makes use of nonexplicit functions. Here we derive a single series expansion that allows rapid and accurate computation of the photogeneration efficiency, and eliminates the need for nonexplicit functions.

Photoconduction in a polydiacetylene film

Steady state photoconductivity, optical absorption and dark conductivity measurements in thin films of polydiacetylene ((8-butoxycarbonyl)methylurethanyl)-1-(5-pyrimidyl)octa-1, 3-diyne (PDA-BPOD) are reported. Steady state photoconductivity results are discussed within the framework of the one-dimensional Onsager theory of geminate recombination. The photoconductivity action spectrum shows a peak at 1.9 eV and a direct band to band transition above 2.4 eV. The absorption spectrum at 50 K is red shifted with respect to the 300 K spectrum. Dark conductivity studies show that the dominant conduction at high fields is due to Schottky emission with a barrier of 0.65 eV.

Steady-state photoconductivity in a novel solution-cast polydiacetylene film

Steady-state photoconductivity in solution-cast thin films of a polydiacetylene, ((8-butoxy carbonyl)methyl urethanyl)-1-(5-pyrimidyl)-octa-1,3-diyne (PDA-BPOD), has been investigated as a function of light intensity, applied electric field, incident wavelength and temperature. This newly synthesized polydiacetylene is characterized by a conjugating aromatic side group which is expected to play a role in the electronic properties of the system. The results are interpreted within the framework of one-dimensional Onsager theory of geminate recombination. The photoconductivity action spectrum shows a peak at 1.9 eV and direct band-to-band transition above 2.4 eV.

Photocarrier generation and transport in a partially polymerized polydiacetylene

Steady-state and transient photoconductivities have been investigated as a function of electric field, light intensity and temperature in single crystals of partially polymerized polydiacetylene, 1,4-bis(3-quinol)-1,3-butadiyne, with conjugating side groups. The polarization dependence of the steady-state photocurrent was also investigated. The one-dimensional Onsager theory of geminate recombination qualitatively accounts for the experimental results. Deviation from the theory is observed in the temperature dependence of the transient peak photocurrent at temperatures below 100 K.

Charge carrier photogeneration in poly(methylphenylsilylene) and its derivatives with π-conjugated side groups

The photogeneration of charge carriers in thin films of poly(methylphenylsilylene) (PMPSi) and its derivatives with attached pendant π-conjugated chromophores was investigated as a function of the electric field and temperature by the photoinduced discharge current method. Six new substituted polysilylenes were used in this study. The electric field dependence of photogeneration efficiency suggests that the Onsager theory of geminate recombination is a suitable model for the description of the electron-hole pair dissociation during the photogeneration process in these polymers. The most effective separation distances of electron-hole pairs participating in the photogeneration process were found to be 1.8–3.5 nm and 0.9–1.75 nm for low and high electric fields, respectively.

Slope to intercept ratio of low-field photogeneration efficiency in β-metal-free phthalocyanine

Using the delayed collection field technique we measured the slope to intercept ratio of the photogeneration quantum efficiency in β-metal-free phthalocyanine. At short delay times between pulsed laser illumination and the application of the collection field slope to intercept ratio is significantly smaller than the value predicted by the Onsager theory of geminate recombination. At longer delay times, exceeding about 200 ms, the slope to intercept ratio reaches the theoretical value indicating that the time evolution of geminate recombination is significantly slowed down by traps. At higher fields the carrier generation is dominated by the field modulated yield of the geminate pairs.