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Simultaneous and direct measurement of carrier diffusion constant and mobility in organic.

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RAPID COMMUNICATIONS

PHYSICAL REVIEW B 84, 041201(R) (2011)


Simultaneous and direct measurement of carrier diffusion constant and mobility in organic
semiconductors and deviation from standard Einstein relation

Awnish K. Tripathi,1,2 Durgesh C. Tripathi,1,2 and Y. N. Mohapatra1,2,3
1
Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208 016, India
2
Samtel Center for Display Technologies, Indian Institute of Technology Kanpur, Kanpur 208 016, India
3
Materials Science Programme, Indian Institute of Technology Kanpur, Kanpur 208 016, India
(Received 27 January 2011; published 1 July 2011)
We show that the shape of electroluminescence transients in organic semiconductors can be conveniently
used to obtain the diffusion constant D of injected charge carriers, enabling the study of generalized Einstein
relationship under nonequilibrium conditions as a function of the electric field. The appearance of peak at the onset
of transient is shown to be the signature of diffusive regime of transport. We demonstrate it for two representative
materials, Alq3 and polymer poly [2-methoxy-5-(2 -ethyl-hexyloxy)-1,4-phenylene vinylene], with the focus on
the role of hot carriers in transport and their diffusivity.

DOI: 10.1103/PhysRevB.84.041201 PACS number(s): 81.05.Fb, 73.61.Ph, 72.20.Ee, 66.30.−h

The emergence of organic and polymeric semiconductors1 mobility typically lower by several orders.18 The onset of
as electronic materials has brought to focus the need for a electroluminescence (EL) is normally observed to be broad4,9
deeper understanding of the carrier drift-diffusion equations.2,3 and has been attributed to dispersive transport in which carriers
In most applications of organic semiconductors, the carrier relax in energy during transit giving rise to a broad velocity
statistics are considered as degenerate4 from this perspective distribution. However, despite some attempts, a satisfactory
and hence, the need to invoke the generalized Einstein model of the broadening, which can be used to obtain transport
relationship D/μ = χ (kB T /q), where the factor χ is a ther- parameters of interest, does not exist. Nikitenko et al. have
modynamic factor and is defined as χ = (n/kB T )(∂η/∂n), suggested that the broadening of onset in ELT is due to
where n is the carrier concentration and η is the chemical field-induced dispersion.9 In this work, we focus on a more
potential. The thermodynamic factor χ is thus a measure of the intriguing feature of ELT in which a distinct peak occurs at the
extent of deviation from the standard nondegenerate Einstein switch-on edge. Though this phenomenon has been reported
relation.2,4–7 The theoretical motivation to understand abnor- by several authors,19–21 it has not been explained cogently and
mal diffusivity in hopping controlled regimes has traditionally quantitatively, and is considered as a challenge to modeling.22
come from the anomalous broadening of time-of-flight (TOF) In this study we show that the appearance of the peak is
signals2,8 despite the occurrence of well-defined plateaus, and due to a combined effect of drift and diffusion of a packet
more recently, a broadening in switch-on electroluminescence of carriers. This is reminiscent of the way minority carriers
transients (ELT),9 and ideality factors of organic junction in inorganic semiconductors were studied in the well-known
diodes.10,11 This has led to a quest for a deeper understanding Haynes-Shockley experiment.23
of transport in disordered solids, in general, as provoked by the We use two well-characterized organic luminescent semi-
early studies of Richert et al.2 and their current resurgence.12–14 conductors viz. small molecule tris(8-hydroxyquinolinolato)
There have been attempts to measure χ in organic solids using aluminum (III) (Alq3 ) and polymer poly [2-methoxy-5-
techniques such as photoelectromotive force measurements15 (2 -ethyl-hexyloxy)-1,4-phenylene vinylene] (MEH-PPV), re-
and Kelvin force measurements.16 However, these techniques spectively, in a sandwich device configuration. The RCA
do not measure the diffusion constant D for the study of cleaned indium tin oxide (ITO as anode) substrates were
deviation from the standard Einstein relationship. Traditionally pretreated under oxygen-argon plasma prior to active layer
D is sought to be derived from TOF experiments,17 however, deposition. The small molecule device fabrication was
the procedures seem to be indirect and require specific carried out in a state-of-the art automated multichamber
samples and conditions. In this Rapid Communication we vacuum-deposition system. A hole injecting layer of 4,4 ,4 -
show that for typical injection conditions and high fields used tris[N-(3-methylphenyl)-N-phenylamino] triphenylamine (m-
in applications, the transport of carriers displays a diffusive MTDATA) doped with tetrafluoro-tetracyano-quinodimethane
regime during transport enabling the direct measurement of (F4 -TCNQ) is deposited followed by the Alq3 layer result-
D and mobility μ, and we demonstrate it for two prototypical ing in a device structure ITO/m-MTADTA/Alq3 /LiF/Al.
organic materials. The single layer MEH-PPV diode (ITO/PEDOT:PSS/MEH-
We use the ELT technique in which a voltage pulse injects PPV/cathode) is fabricated with two different cathodes
a bunch of carriers which move toward the opposite electrode (calcium and aluminum) for comparison. MEH-PPV was
to meet the carriers from the other electrode to recombine and spin cast in a nitrogen glovebox from solution prepared in
give out luminescence. The measured time difference between xylene:chloroform (50:50). The thickness of the active layer
the application of the voltage step and the appearance of light was determined using a profilometer (Tencor alpha–Step 500).
is the duration of the drift of carriers under a known average For ELT measurement, a 50 MHz HP 81101A pulse generator
applied electric field, and hence allows the determination (rise time 10 ns) was used to apply rectangular voltage pulses
of μ. The mobility of the fast carriers is usually measured of different magnitudes across the device. A photomultiplier
in such an experiment since the slower of the carriers has tube (S100 response with time resolution <1 ns), facing the

1098-0121/2011/84(4)/041201(4) 041201-1 ©2011 American Physical Society

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