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Time-of-flight mobility of charge carriers in position-dependent electric field between coplanar electrodes
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Image of FIG. 1.

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FIG. 1.

(a) Schematic representation of a polymer layer between two semi-infinite coplanar electrodes on top of a dielectric substrate, with dimensions and parameters used in the calculation of electric field by solving the Poisson equation. (b) Numerical solution of the electric field () streamlines (solid lines) and electric potential (dashed lines) in a polymer film between blocking coplanar electrodes on a glass substrate. is the thickness of the polymer layer, is the distance from the left electrode, and is the distance from the substrate. Left electrode is at 0 V and the right electrode is at . is the separation between the electrodes. ratio is 1:100. The dielectric constant of a polymer layer and the glass substrate are 3 and 10, respectively.

Image of FIG. 2.

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FIG. 2.

A representative pair of time-of-flight photocurrent simulations for position-independent (dashed line) and position-dependent (solid line) electric field. The bias voltage is 500 V, the distance between electrodes is 150 m and the level of energetic disorder is 6.4. Position-independent electric field is . Position dependent electric field is given by Eq. (1) (see text). The curves are normalized to the number of simulated carriers. The histograms represent the transit time distribution of simulated carriers. The right histogram corresponds to the simulation using . The left histogram corresponds to the simulation using . The and represent the mean transit times resulting from and simulations, respectively.

Image of FIG. 3.

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FIG. 3.

A series of Monte Carlo simulations of a photocurrent as a function of energetic disorder . The simulations were performed using the position-dependent electric field given by Eq. (1) . at  = 500 V and  150 m. Each curve is normalized to the mean transit time () of the corresponding position-independent electric field ( ) simulation and to the number of simulated carriers. Arrows represent mean transit times ( ) of simulations. Inset: The ratio as a function of . The dashed line is the minimum chi-square fit of a square power law suggesting that is increasing as .

Image of FIG. 4.

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FIG. 4.

A 2×2 m atomic microscope topography scan of a 20 nm thick P3HT layer in the region between coplanar electrodes. The polymer layer was spin-coated from a dichlorobenzene solution on a glass substrate. The height range is 15 nm. The polymer structure forms a random network of spherical grains with the diameter of approximately 30 nm. Inset: A close-up topography scan of the P3HT layer.

Image of FIG. 5.

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FIG. 5.

Time-of-flight photocurrent measurement in a P3HT thin film as a function of a bias voltage in a double logarithmic scale. Solid line represents the photocurrent of a simulation using position-dependent electric field . The simulated photocurrent was used to determine the hole mobility at of 500 V. Inset: Schematic representation of the measurement. The laser pulse was focused near the biased electrode. was measured as a voltage drop on a resistor , connected to the opposite electrode. The separation of coplanar electrodes was 100 m.


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Time-of-flight measurements of the photocurrent in thin organic semiconductor layers represent an effective way to extract charge carrier mobility. A common method to interpret the time-dependence of the photocurrent in these material systems assumes a position-independent electric field between two coplanar electrodes. In this letter, we compare time-dependence of the photocurrent, measured in the samples comprising thin layers of poly-3-hexylthiophene, with the Monte Carlo simulations. In the simulations, we have used both, a position-independent and a position-dependent electric field. We obtained a favorable agreement between the simulations and the measurements only in the case of position-dependent electric field. We demonstrate that the charge carrier mobility may be underestimated by more than one order of magnitude, if a position-independent electric field is used in the calculations of the mobility.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Time-of-flight mobility of charge carriers in position-dependent electric field between coplanar electrodes