Trap-Controlled Dispersive Hopping Transport

Pfister, G.; Grammatica, S.; Mort, J.

doi:10.1103/physrevlett.37.1360

Cited by 100 publications

(28 citation statements)

References 7 publications

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“…The linear decrease and crossover was observed experimentally in ref. 3. The linear decrease was not obvious from the usual drift mobility expression derived for the band case.…”

Section: ]mentioning

confidence: 81%

“…Recent studies (3,4) have probed some additional interesting features of carrier hopping motion in the presence of traps. There are several aspects of this trapping process that are distinct from the more familiar case involving band motion besides the additional mechanism for release-time dispersion.…”

mentioning

confidence: 99%

“…Thus, it can serve as a model system for the transport mode discussed above. In the experiment ofPfister et al (3), the hopping transport of holes is established with an appropriate concentration of one molecule. The transport was trap-modulated by the addition ofanother molecule (with lower ionization energy).…”

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confidence: 99%

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Random walk theory of a trap-controlled hopping transport process

Scher

1981

Proc. Natl. Acad. Sci. U.S.A.

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A random walk theory of hopping motion in the presence of a periodic distribution of traps is presented. The solution of the continuous-time random walk equations is exact and valid for arbitrary intersite interactions and trap concentration. The treatment is shown to be equivalent to an exact solution ofthe master equation for this trapping problem. These interactions can be a general function of electric field and are not restricted to nearest neighbors. In particular, with the inclusion oftrap-to-trap interactions, as well as trap-to-host interactions, an exact treatment ofthe change from one hopping channel to another has been obtained. The trap-modulated propagator has been derived in terms of a type of Green's function that is introduced. The results are specialized-to spatial moments of the propagator, from which .expressions for the drift velocity and diffusion coefficient are obtained. Numerical results for the drift velocity are presented-and shown to account for the change in hopping channels in recent transport measurements in mixed molecularly doped polymers.A transport model (1, 2) for the hole mobility in amorphous As2Se3 has been advanced that accounts for the dispersive nature of the transient current as well as the mobility activation energy. The model is trap-controlled (or trap-limited) hopping.One envisions a carrier hopping through a set of localized states-e.g., band tail states-with a spatial density Nh and also interacting with a deeper set of levels with a density N. If we assume Nh >> Nt, then the carrier undergoes stochastic hopping with an activation energy Ah among the random array of sites (h) and hops occasionally into the deeper level site (t), where it awaits release with an additional activation energy At.Variations in A can cause a variation in the release time in the usual way. In addition, even for a fixed value of At, variations in the intersite separation between t and h sites can also cause release-time dispersion. This latter feature is unique to trap-controlled hopping.Recent studies (3, 4) have probed some additional interesting features of carrier hopping motion in the presence of traps. There are several aspects of this trapping process that are distinct from the more familiar case involving band motion besides the additional mechanism for release-time dispersion. The mean free path for the hopping carrier is usually comparable to or smaller than the radius ofthe trapping cross section; the trapping process is more of the diffusion-limited kind. The temperature (T) and electric field (E) dependence ofthe trapping. time is typically different for the hopping carrier. Spatial correlation plays a larger role in the hopping, case. When a carrier is released from a trap it could simply 'back transfer into the trap again. With multiple back transfer the effective trap residence time could be much larger. This type of correlation is not considered important in the band case. The electric field affects both this back transfer and the asymmetry of the hopping motion...

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“…The linear decrease and crossover was observed experimentally in ref. 3. The linear decrease was not obvious from the usual drift mobility expression derived for the band case.…”

Section: ]mentioning

confidence: 81%

mentioning

confidence: 99%

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Random walk theory of a trap-controlled hopping transport process

Scher

1981

Proc. Natl. Acad. Sci. U.S.A.

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“…This has been observed in a solid solution of N-isopropylcarbazole ͑NIPC͒ in polycarbonate when adding low concentrations of N,NЈ-diphenyl-N,NЈ-bis͑3-methylphenyl͒-͓1,1Ј-biphenyl͔-4,4Ј-diamine ͑TPD͒. 4 Holes, which is the mobile species in all photorefractive polymers that have been reported until today, are expected to become trapped at impurities accidentally present in the polymer, 5 defects of the polymer backbone ͑such as chain ends͒, 6,7 sensitizer 8 and chromophore 7 molecules, etc. Apart from its fundamental interest, control of charge trapping has great technological importance: optimization of charge trapping might be the route towards long storage time and high diffraction efficiency required for optical data storage applications.…”

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confidence: 84%

Control of charge trapping in a photorefractive polymer

Malliaras

Krasnikov

Bolink

et al. 1995

Applied Physics Letters

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“…13 Table III lists the results of doping on hole drift mobility. The mobility in an IPCz-PSt film was reduced remarkably with the addition of a slight amount of TPA.…”

Section: Doping Effects On Hole Drift Mobilitymentioning

confidence: 99%

Hole Transport in Amorphous Films of Poly(N-vinylcarbazole), Copolymers of N-Vinylcarbazole with Styrene, Polystyrene Molecularly-Doped with N-Isopropylcarbazole, and 1,3-Di(N-carbazolyl)propane

Itaya

Okamoto

Kusabayashi

1985

Polym J

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ABSTRACT:The hole drift mobility in amorphous films of poly(N-vinylcarbazole) prepared by the radical and cationic polymerizations (abbreviated as PVCz(r) and PVCz(c), respectively), copolymers of N-vinylcarbazole with styrene (VCz-St), polystyrene molecularly-doped with Nisopropylcarbazole (IPCz-PSt). and 1,3-di(N-carbazolyl)propane (DCzP(a)) was investigated by the time-of-flight method. The electric field and temperature dependence of the mobility of all the materials fitted the Gill's empirical equation. The mobility of PVCz(r) was larger than that of PVCz(c) by a factor of ca.By heat-treatment at a temperature above the glass transition temperature, PVCz(r) film was crystallized and its mobility increased by a factor of ca. 5. The thermal-crystallization of PVCz(c) film was much more difficult than that of PVCz(r) film and the mobility of PVCz(c) film hardly changed with heat-treatment. These significant differences between PVCz(r) and PVCz(c) seem to be attributable to the difference in their tacticity. The mobility of PVCz(r) increased about twice as much with an increase in the sequence length of VCz chain from 20 to 200, while the mobility ofPVCz(c) was independent of it. This may be qualitatively explained by the existence of the chain-end vinyl group in PVCz(r). Under usual conditions (T=296 K, E= 1.6 x 10 5 V em -•). the mobility of low molecular-weight compounds (DCzP(a) and IPCz-PSt) was larger than that of polymeric compounds (PVCz and VCz-St). Using the results of a comparison of the values of parameters in the Gill's equation for these films, this was explained by a negative polymer effect due to the higher value of T0 .

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Trap-Controlled Dispersive Hopping Transport

Cited by 100 publications

References 7 publications

Random walk theory of a trap-controlled hopping transport process

Random walk theory of a trap-controlled hopping transport process

Control of charge trapping in a photorefractive polymer

Hole Transport in Amorphous Films of Poly(N-vinylcarbazole), Copolymers of N-Vinylcarbazole with Styrene, Polystyrene Molecularly-Doped with N-Isopropylcarbazole, and 1,3-Di(N-carbazolyl)propane

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