The role of local potential minima on charge transport in thin organic semiconductor layers

Organic Electronics 42 (2017) 221e227

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Organic Electronics journal homepage: www.elsevier.com/locate/orgel

The role of local potential minima on charge transport in thin organic semiconductor layers Egon Pavlica, Raveendra Babu Penumala, Gvido Bratina* Laboratory of Organic Matter Physics, University of Nova Gorica, Vipavska 13, SI-5000 Nova Gorica, Slovenia

a r t i c l e i n f o

a b s t r a c t

Article history: Received 22 August 2016 Accepted 20 December 2016 Available online 22 December 2016

We have performed a systematic study of dependence of time-resolved photocurrent on the point of charge excitation within the organic semiconductor channel formed by two coplanar metal electrodes. The results confirm that spatial variation of electric field between the electrodes crucially determines transport of photogenerated charge carriers through the organic layer. Time-of-flight measurements of photocurrent demonstrate that the transit time of photogenerated charge carrier packets drifting between the two electrodes decreases with increasing travelling distance. Such counterintuitive result cannot be reconciled with the spatial distribution of electric field between coplanar electrodes, alone. It is also in contrast to expected role of space-charge screening of external electric field. Supported by Monte Carlo simulations of hopping transport in disordered organic semiconductor layer, we submit that the space-charge screens the external electric field and captures slower charge carriers from the photogenerated charge carrier packet. The remaining faster carriers, exhibit velocity distribution with significantly higher mean value and shorter transit time. © 2016 Elsevier B.V. All rights reserved.

Keywords: Charge transport Organic semiconductors Time of flight Mobility Traps

1. Introduction Photoconductivity of organic semiconductors (OSs) is characterized by relatively high photon-to-charge conversion efficiency and low charge carrier mobility [1]. As a result, the photogenerated charge carriers accumulate within the OS layer as a space-charge, which effectively screens externally applied electric field. Consequently, effective charge carrier velocity and therefore their current through the layer, is reduced. Theoretical description of this phenomenon is known as the space-charge-limited current (SCLC) model [1,2]. At the core of the SCLC model is the concept of the distribution of localized states, which trap the carriers during charge transport. Based on the SCLC model, several experimental methods were developed in order to investigate space-charge effects on the charge transport [3]. Most of them focus on bulk materials, where space-charge screens externally applied electric field between a pair of parallel electrodes. Typically, in such configuration space-charge accumulates near the injecting electrode due to the low charge-injection barrier. For a recent review of studies of space-charge effects in OS thin layers embedded between two

* Corresponding author. E-mail address: [email protected] (G. Bratina). http://dx.doi.org/10.1016/j.orgel.2016.12.038 1566-1199/© 2016 Elsevier B.V. All rights reserved.

coplanar electrodes see for example Ref. [3]. Charge transport in thin OS layers is hindered by charge carriers, which accumulate near the low-barrier electrode [4,5]. Consequently, mobility of the injected charge carriers through the OS layer is reduced and their effect on local electric field is only minor [6]. In contrast, photogenerated charge, which is not injectionlimited, represents a significant transient perturbation of the local electric field [1]. Ligthart et al. recently demonstrated that spacecharge is the reason for relatively long relaxation time of organic photodiodes [7]. Pivrikas et al. studied photocurrent generation in conjugated polymers as a function of light intensity [8,9]. Their findings confirm that photogenerated carriers alter electric field in the polymer layer. Danielson et al. used the photoconductivity measurements in thin OS layers to probe the charge transport and recombination in bulk-heterojunction layers, used as a part of organic solar cells [10]. In this work we used photoconductivity measurement to study space-charge effects on charge carrier transport in thin OS layers. We used time-of-flight (TOF) photoconductivity method due to its extreme sensitivity to charge transport perturbations, as previously demonstrated on reduced graphene oxide layers [11]. TOF measurements yield information on charge carrier transport in semiconducting as well as in insulating materials [12]. They are selective for different charge polarity, changes in density of states [13], and

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can be used to directly determine charge carrier velocity in OS layers [14]. TOF measurements are immune to the processes in the microscopic environment of a OS/metal interface. At the core of the technique is the electron-hole pair photoexcitation in an OS layer embedded between two coplanar electrodes, followed by the charge separation due to the externally applied electric field. The resulting drift current through the organic layer is monitored as a function of time. The velocity of photogenerated carriers is estimated from their drifted distance and the duration of induced current transient. Also other transport parameters can be estimated from the time dependence of the photocurrent, including charge carrier mobility, space-charge effects and photon-to-charge conversion efficiency [1,9e14]. TOF experiments can be performed on samples, in which the OS layer under investigation is sandwiched between two electrodes, of which one is transparent [12]. Such sample structure is not suitable for characterization of OS layers with thickness smaller than 1 mm [15]. This is because photon absorption exponentially decreases with depth of OS layer [16], and because of substantial leaking currents arising from large capacitance coupling between the electrodes [15]. An alternative to the sandwich-type samples are the samples, in which organic layer is placed between the two coplanar electrodes, similarly to the organic field-effect transistor (OFET) structures [17e21]. In contrast to sandwich-type samples, the electric field between coplanar electrodes is seldom spatially uniform [5,22]. Therefore, the interpretation of TOF photocurrent transients measured in these samples in terms of sandwich-type TOF measurements could lead to an underestimation of charge carrier mobility and misunderstanding of the charge transport mechanisms [22]. In our previous work [22], we introduced a model based on a displacement current [23], to calculate the photocurrent time dependence of a coplanar-type TOF measurement. The displacement-current theory of the coplanar-type TOF measurement describes the time dependent photocurrent (I(t)) as a phenomena, which stems from the time variation of the charge induced on the electrodes [22,24]. Charge is induced on the electrodes by the displacement field of the photogenerated holeelectron pairs. The amount of induced charge per unit of photogenerated charge is introduced as the “weighting” potential (UW), which depends on the position of the photogenerated charge and depends solely on spatial arrangement of the electrodes. As the photogenerated carriers drift in the electric field between electrodes, UW and the amount of induced charge vary. As a result, photocurrent exhibits a time transient, determined by the time derivative of the product of the photogenerated charges and corresponding UW. I(t) therefore depends on charge carrier velocity, which is determined by the spatial distribution of the electric field and a constant factor defined by the position of the selected charge carrier relative to the position of the electrodes. We have performed coplanar-type TOF measurements in a thin layer of a semiconducting polymer of poly(3-hexylthiophene-2,5diyl) (P3HT). We choose P3HT because it is a thoroughly investigated p-conjugated polymer [25], which exhibits field-effect mobility as high as 0.05 cm2/Vs in highly purified OFETs [26], and power conversion efficiency up to 6.4% in organic solar cells [27]. Due to disordered structure of P3HT layers deposited from a solution, charge carrier transport must be described with a hoppingtransport model. We developed kinetic Monte Carlo simulation based on the Gaussian disorder model and hopping charge transport [22]. The simulations are used to interpret TOF measurements in a P3HT layer between coplanar electrodes. Next, we present a systematic study of the role of illumination position on the time dependence of TOF photocurrent in P3HT layer between coplanar electrodes. For

that purpose, we have measured I(t) by varying the illumination position from biased electrode to the opposite electrode for both positive and negative bias voltages. Finally, we compare MC simulations with experimental data and discuss the effect of spacecharge on the I(t) dependence. 2. Experimental 20 nm-thick P3HT layers were prepared by spin-coating a 4 mg/ ml chloroform solution at 3000 rpm for 1 min on glass substrates. Two 100 nm-thick Al coplanar electrodes were deposited by vacuum evaporation through a shadow mask. The interelectrode separation (L) was 125 mm. We will use the OTFT nomenclature and refer to the interelectrode region as “the channel”. Samples were thermally annealed at 150
C for 5 min before characterization. TOF measurements of I(t) were performed using 4 GHz probe tips and 2.5 GHz oscilloscope as schematically presented in Fig. 1a. A constant bias voltage Vb was applied to the left electrode, from now on referred-to as the “biased” electrode. The opposite electrode labeled “sensing” electrode, was connected to a resistor (R) of 100 kU. I(t) of the photoexcited carriers was measured as a voltage drop over R. The selected value of R was a minimum, which allowed detection of the photocurrent, while maintaining the electric field between the electrodes unchanged. The charge carriers were excited by a pulsed laser with pulse duration of 3 ns, and a repetition rate of 3 Hz. Full-width at half-maximum intensity of the laser line was 20 mm, as measured with a commercial camera sensor (Fig. 1b). We selected photon energy of 2.34 eV, which corresponds to the maximum light absorption in P3HT. The incoming laser beam was focused perpendicularly onto the polymer layer surface with a cylindrical convex lens (Fig. 1a). The lens focused laser light into a narrow line, which was aligned along the electrode edge at a varying distance (xi) from the biased electrode. The width of the illuminated area was approximately five times smaller than L. Two distinct laser pulse light intensities were used to illuminate the polymer. The number of photons per pulse was estimated by comparing the maximum of the measured I(t), and I(t) obtained by the Monte Carlo simulations (see below). The corresponding numbers of photons per pulse were 7.2$107 for low intensity and 1.6$108 for high intensity. 3. Results and discussion Photogenerated charge carriers moving in a P3HT layer embedded between two coplanar electrodes (Fig. 1a), which are at different potentials due to the applied bias voltage Vb, induce variation of charge and current on the electrodes [23,24,28]. Time evolution of charge and current, therefore reflects dynamics of the charge carriers drifting in the inter-electrode electric field. The potential difference of the two electrodes, determines the direction of velocity of the holes and the electrons. This allows us to discriminate the contributions of the holes and electrons to I(t). For positive Vb, electrons drift to the biased electrode and for small values of xi contribute only a fraction of current in to the I(t) curve, while holes drift away from the biased electrode, and contribute to I(t) during their travel through the channel. For negative values of Vb holes drift to the biased electrode and electrons drift to the sensing electrode. As we have shown previously by numerically solving Poisson equation for biased coplanar-electrode structures [22], the corresponding electric field (E(x)) inside the channel de1 creases rapidly with the distance from the electrode (zðx=LÞ2 within 10 mm). Further into the channel the decrease with the distance is considerably slower. The carriers that are generated near the biased electrode initially exhibit high acceleration due to high E(x). This is manifested in the I(t) line shape as an initial surge. As

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Fig. 1. (a) Schematic representation of time-of-flight photoconductivity measurement of an organic semiconductor (OS) layer (red) between coplanar metal electrodes. Bias voltage Vb is applied to the left electrode. Cylindrical convex lens is used to focus incident laser light into the semiconductor layer at distance xi from the biased electrode. Time-dependence of a photocurrent is measured as a voltage drop on the right electrode, which is grounded by a resistor R. (b) Spatial distribution of incident light intensity at the surface of the OS layer. The intensity was acquired with a camera sensor, which was placed at the same position as the OS layer (filled circles). The measured light profile was modeled with a Gaussian curve (dashed line) of width s ¼ 8±0:03 mm. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

the carriers enter the low-field region within the channel, their velocity starts decreasing, which is reflected in the I(t) line shape as a monotonic decrease. Upon arrival to the sensing electrode the fastest carriers enter a region of high E(x). In ordered materials, this is manifested in the I(t) curve obtained as a cusp [22], followed by a rapid decrease in current due to the collection of the carriers by the electrode. The time of the cusp is an estimate of the transit time (ttr) of the 10% of the fastest carriers [22]. In disordered materials, however the cusp degenerates into a relatively broad change in slope of I(t). In this case ttr can be obtained as an intersection of the two asymptotes on both sides of the change of slope [22]. In Fig. 2a we present a typical I(t) measurement in a P3HT layer between coplanar electrodes obtained using three different values of Vb. Dashed lines are the asymptotes, which intersection is considered as ttr [29]. Under this polarity of Vb, I(t) corresponds to transport of holes across the P3HT layer. The arrows indicate ttr, which consistently moves to shorter times with increasing Vb. In an ideal case, when a single carrier is drifting with a constant velocity, its velocity (v) can be directly calculated as a ratio between the drifted distance and a time-span of photocurrent [12]. Electric field between the electrodes is assumed to be constant and given by the usual expression E ¼ Vb =L. Under these assumptions, charge mobility is given by

mTOF ¼

v L2 ¼ E Vb ttr

(1)

Using this expression and the values for ttr we obtained the values for mTOF, which are summarized in the inset of Fig. 2a (solid circles). Dashed curve ispaffiffiffi least-squares fit to the Poole-Frenkel expression: m ¼ m0 expðb E Þ, assuming constant electric field. The resulting values for the zero-field mobility m0pand the parameter b ffiffiffiffiffiffiffiffiffiffiffiffi are 2:9±0:2$104 cm2 =Vs and 5:8±0:3$103 cm=V , respectively. These results agree well with those reports, which suggest that P3HT is a hole-conductor [25]. In order to get deeper insight in the behavior of electric field with the position inside the channel, we have investigated the dependence of the amount of extracted electric charge on the illumination position xi . Total extracted charge produced by each incident laser pulse comprising Nph photons is given by R Q ¼ IðtÞdt. In Fig. 3 we present Q ðxi Þ extracted from I(t) as a function of xi for positive Vb (circles) and for negative Vb (squares). Note that Q ðxi Þ can be less or equal to the amount of total photogenerated charge ðQph ðxi ÞÞ, depending on the efficiency of the charge extraction process. Charge generation by a laser pulse proceeds through creation of excitons and their subsequent dissociation [30]. Since the exciton binding energy is relatively high for the

most of the polymers (about 0.5 eV), thermally-assisted dissociation is unlikely at room temperature [31]. Therefore, the majority of photogenerated carriers result from the electrical-field-assisted exciton dissociation [32]. Qph ðxi Þ is a convolution of the exciton decay rate and the spatial distribution of incident photons ðnph ðxÞÞ; which can be extracted from the measured light pulse intensity (Fig. 1b) as a Gaussian function of the width s and centered at xi : expððx  xi Þ2 =2s2 Þ. The exciton decayprate ffiffiffiffiffiffiffiffiffi in polymers [33] follows Poole-Frenkel behavior ½a$expðb EðxÞ Þ  11, and EðxÞ can be approximated with the following equation [22]:

V EðxÞ ¼ b pL

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi 1 x=L 1  x=L

0
(2)

Approximation in Eq. (2) is valid as long as Q(xi) is negligible compared to the charge on the electrodes, which equals to CVb , where C is the capacitance of coplanar electrodes [34]. This condition is met as long as both, photogenerated charge and injected charge from the electrodes are sufficiently low. Charge injection is controlled by the proper choice of electrode material, and the amount of photogenerated charge is controlled by the selection of light intensity. Using Eq. (2) we obtain the equation for total photogenerated charge as a function of illumination position:

  Qph xi ¼ g

ZL

h   i1 pffiffiffiffiffiffiffiffiffi . 2 2 eðxxi Þ =2s a$exp  b EðxÞ kB T  1 dx

0

(3) where a, b and g are material parameters. g comprises also the intensity of the incident light. The values of these parameters are determined by minimizing the difference between measured Q ðxi Þ and calculated Qph ðxi Þ (dashed line in Fig. 3). The calculated values of Qph ðxi Þ were compared to the values measured at distances from the biased electrode xi  60 mm, for positive Vb, and at distances xi  60mm for negative Vb. The resulting calculated line shape Qph ðxi Þ agrees well with the measured values. We note that the calculation overestimates measured values at xi > 60 mm, Vb > 0 V and at xi < 60 mm, Vb < 0 V. This deviation is symmetric in Vb and in the distance from the center of the channel. This mismatch is likely to be a result of incomplete charge extraction due to transit times shorter than electronic response time. 3.1. Transit time as a function of illumination position In Fig. 2b we present measurements of I(t) as a function of

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(a)

1.5 V >0 V <0

Q/e × 10

8

0.9

-3

× 10 cm2/Vs

1

0.7

log(I) (a.u.)

μ

TOF

0.8

1

model

0.5

300

400

500

Vb (V)

0

0

20

40

60

80

100

120

140

xi (μm) Fig. 3. Total extracted charge (Q) as a function of illuminating position (xi) on a P3HT layer between coplanar electrodes. Red circles represent Q at positive bias voltage Vb. Blue squares represent Q at negative Vb. Vertical dash-dotted lines represent the edges of the P3HT layer. Q is collected also when xi is beyond the polymer edges, which agrees with the theoretical model (dashed line) of Eq. (3). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Vb (V) 500 400 300

10-4

10-3 t (s)

(b)

10-2

log(I) (a.u.)

xi (μm) 115 106 97 88 78 69 60 50 41 32 27 23 18 13 9 4 -1 -5 -10 -15

10−4

10−3 t (s)

Fig. 2. Time dependence of photocurrent I(t) measured by time-of-flight method in P3HT layer in double-logarithmic plot as a function of bias voltage Vb (a), and as a function of illumination position xi (b). Arrows represent the transit time ttr, which corresponds to the intersection of asymptotes to I(t) (dashed lines). I(t) curves are vertically shifted for clarity. Inset in (a): charge mobility as a function of Vb calculated 2 =t V . Dashed line represents m calculated by Poole-Frenkel from ttr using equation tr b pLffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffi equation m ¼ m0 expðb Vb =L Þ, using m0 ¼ 2:9$104 cm2 =Vs and b ¼ 5:8$103 cm=V .

illumination position xi in a P3HT layer between the electrodes at Vb ¼ 400 V. The adjacent curves were obtained at distances approximately 10 mm apart. We note that cusps are clearly visible in curves obtained at xi  30 mm. For larger values of xi the cusp degenerates to a broad monotonic change in slope of I(t). As a result,

the uncertainty of ttr is raised, which precludes reliable determination of charge carrier mobility. From the I(t)s illustrated in Fig. 2b we determined the transit time of photogenerated carriers using the intersection of two asymptotes. The results are shown in Fig. 4 were the transit time is presented as a function of illumination position for low and high light intensity as represented by squares and circles, respectively. For low light intensity the transit time increases for positions up to 30 mm away from the biased electrode, where it reaches a maximum value. As the distance from the electrode increases beyond xmax ¼ xi z 30 mm transit time starts decreasing. Qualitatively, we expect a decrease of transit time with increasing distance from the electrode, if we assume that the mobility of the charge carriers is constant and that the position-dependent electric field is given by Eq. (2). The values of transit time calculated under these assumptions are shown in Fig. 4 by a dashed line. For high light intensity transit time exhibits qualitatively similar behavior as for low light intensity, albeit with somewhat broader maximum. Lower intensity illumination results in longer transit times below xmax, the behavior reverses above xmax and photoexcitation by low light intensity results in faster charge carriers. This behavior was further investigated by comparing the I(t) time dependence at the xi of 10 mm from the electrode and two different illumination intensities. In Fig. 5 we show I(t)s obtained at high and low light intensity, filled squares and filled circles, respectively. Solid and dashed curves represent the results of Monte Carlo simulation of I(t) curves, and will be discussed later. The low-photon-intensity curve exhibits a cusp at approximately 0.6 ms. At high light intensity, the magnitude of I(t) is increased, but the cusp is less distinct, which increases the uncertainty in determination of the transit time. Nevertheless, we see that the transit time decreases with increasing light intensity. Results presented in Figs. 4 and 5 argue for an important role of the light intensity in determination of the transit time from the I(t) line shape. 3.2. Monte-Carlo simulations To precisely determine the role of light intensity on the I(t) line shape we performed a Monte Carlo simulation of I(t). The simulations are based on the assumption of charge carrier hopping in the manifold of localized states [35]. This approach is justified from the comparison of the results presented in Figs. 2 and 3 and corresponding theoretical description in Eq. (3). The value of b in Eq. (3) pffiffiffiffiffiffiffiffiffiffiffiffi was 4:44±0:02$103 cm=V , which is compellingly similar to the

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7.2 × 10 Simulation

1 ttr (ms)

Approximation

0.5

0

0

20

40

60

80

100

120

xi (μ m) Fig. 4. Transit time (ttr) as a function of illumination position xi at Vb of 400 V. Symbols represent ttr estimated from measurements at two different illumination intensities. Solid curve represents ttr estimated from I(t) curves obtained by the Monte Carlo simulations. Dashed curve represents ttr calculated by assuming constant charge mobility and spatially varying electric field given by Eq. (2). Vertical dash-dotted lines represent the edges of polymer layer.

I (A)

10-8

N ( x = 10 μ m ) -9

10

1.6 × 10 7.2 × 10 -3

10-4

10 t (s)

Fig. 5. Time dependence of photocurrent I(t) measured by time-of-flight method in P3HT layer in double-logarithmic plot at Vb ¼ 400V obtained at two different photon fluxes at constant illumination position xi ¼ 10 mm. The symbols represent measured I(t)s, while the curves represent simulated I(t)s. Solid curves represent simulated I(t)s using hopping time unit of 8.2$1015 s, energetic disorder of 90 meV, hopping distance of 30 nm, overlap parameter of 0.017 Å1, and positional disorder of 14%. The dashed I(t) curve was obtained by simulation using same parameters as solid curves except the hopping time unit is reduced by 30%. Consequently, the corresponding transit time as indicated by the change in slope of I(t) is also reduced.

value obtained from the m(Vb) dependence presented in Fig. 2a. This indicates that the charge-pair separation process, which determines the Q/e ratio, was influenced by electric field in the same manner as m, and can be described by Poole-Frenkel formalism, which describes charge trapping by localized states [36]. In order to exit this state, the charge carrier requires additional energy, which is normally obtained from thermal vibrations. In the presence of the electric field, the energy required to leave the site is reduced, which directly increases m and indirectly Q/e ratio. At the core of our kinetic Monte-Carlo simulations is the MillerAbrahams formalism [37], which is used to describe the hopping rate of electric charge carriers within the framework of localized states with different energies [35]. The energetic disorder was simulated by assuming a Gaussian energy distribution of hopping states, with the width of s. The positional disorder ðDgÞ was simulated by varying the overlap parameter g. The average overlap parameter was set to 2ga ¼ 10, with the inter site hopping distance a set to 30 nm. This value corresponds to the grain size of spincoated P3HT layers [22]. Temperature T was fixed to 300 K. The polymer layer was described as a cubic array of 41667 sites along x direction, which equals to electrode separation of 125 mm. In y direction the array size was selected as 3 sites, which corresponds to the polymer layer thickness of 60 nm. Periodic boundary conditions

were used in the z direction, which was considered to be perpendicular to x and y directions. Electric field was introduced through the potential energy of the hopping sites (U(x)). We have numerically calculated U(x) and E(x) in the polymer layer on a glass substrate between coplanar electrodes by solving Poisson equation εDU ¼ r and E ¼ VU, where the charge density ðrÞ in polymer was assumed to be zero. In our calculations we used dielectric constants ðεÞ of 1 and 7 for the polymer and the glass substrate, respectively. The results of the numerical calculation are presented in Fig. 6, where different curves exemplify position-dependence of U(x) at different space-charge densities, and will be discussed below. Solid curve represents U(x) calculated under the absence of spacecharge, and was used to simulate I(t). Simulated I(t) was obtained as a time-derivative of total induced charge on the sensing electrode (see Fig. 1a) by the displacement field originating from 3.4$104 simulated charge carriers, which is a minimum number necessary to yield a reproducible simulation of I(t). This number is three orders of magnitude lower than the number of charge carriers estimated from the total charge determined from the measurements (see Fig. 3), which is in the range between 107 and 108 carriers. Therefore, the simulation can be considered as the zero spacecharge I(t) response. I(t) represented by the solid line in Fig. 5 was obtained by such simulation, and corresponds to the illumination with a light pulse with a Gaussian spatial profile centered at 10 mm from the biased electrode. The best match between the measured and simulated I(t) was obtained by using s ¼ 90 meV, ðDg=gÞ ¼ 14%, hopping time unit of 8.2$1015 s and a number of photogenerated carriers of 7.2$107. The simulated I(t) exhibits a cusp, and clearly reproduces the measured I(t). The biggest difference occurs before the cusp (t < 3$104 s), when the values of simulated I(t) underestimate the measured values. This difference is even higher when we compare simulated I(t) (dashed line) with I(t) measured using high light intensity (red square symbols). As already noted, the cusp in I(t) measured at high light intensity occurs at shorter time compared to the low light intensity. This further confirms that the light intensity affects the I(t) line shape and thereby the observed transit time. In order to match simulated I(t) to measured I(t) at high light intensity, the hopping time unit of simulated I(t) was reduced by approximately 30% compared to the hopping time unit used to simulate I(t) at low light intensity. The

N ( t = 9 μs ) 0 10 10 6 × 10

4

400 300 200

U (V)

1.6 × 10

n (a.u.)

1.5

225

100 2

0

0

0

50

100 x (μ m)

Fig. 6. Electric potential (U e rightmost ordinate) as obtained by numerical solution of Poisson equation in a thin polymer layer between two coplanar electrodes on a glass substrate. The calculation of U(x) comprises space-charge due to photogenerated charge carriers 9 ms after illumination at xi ¼ 10 mm. Each curve corresponds to different number of simulated charge carriers. x is the distance from the biased electrode, which is at Vb ¼ 400 V (see shematic in Fig. 1). The sensing electrode is at 0 V. The separation between electrodes is 125 mm. The dielectric constants of the polymer layer and the glass substrate are 1 and 7, respectively. Spatial distribution of the charge carriers is obtained by kinetic Monte Carlo simulations and is represented as a filled (red) histogram for electrons, and empty histogram (blue) for holes. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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simulated I(t)s are shown in Fig. 5 by two solid lines and one dashed line, which represent the simulations with the original and reduced hopping time units, respectively. We see that the simulation with the reduced time units better reproduces the cusp in measured I(t) relative to the original time units. This indicates that I(t)s measured by using high light intensity, which results in high density of photogenerated charge carriers, exhibit a change in slope at shorter times than I(t)s measured by using low light intensity. This fact can be used to explain the complex dependence of ttr on the illumination position xi in Fig. 4. Solid curve in Fig. 4 was obtained by simulating I(t) at each xi position using parameters that were presented in Fig. 5, except that hopping unit time was adjusted to align the simulated I(t) to the measured I(t) at xi > 40 mm, since above 40 mm ttr exhibits expected dependence on the distance (dashed line in Fig. 4). ttr was determined from the simulated I(t) curves using the intersection of the two asymptotes. The simulated ttr dependence on xi exhibits similar dependence as ttr obtained by assuming a constant charge carrier mobility and spatially varying electric field given by Eq. (2) (dashed line). According to the Monte Carlo simulations, ttr is supposed to monotonously decrease with increasing xi. However, near the electrode, where higher electric field produces higher density of photogenerated carriers, measured ttr is reduced by a factor of two compared to the simulation. The amount of photogenerated carriers crucially determines the time of the cusp in I(t) curve. When the number of carriers is increased, ttr is reduced. This implies that their velocity and mobility is increased. Similar increase of charge mobility is known to occur in disordered materials when all trapping states are populated [38]. In P3HT, this occurs at the hole concentration of 1020 cm3. In our case, the number of photogenerated charge carriers equals to 108 in the illuminated volume of a 90 nm  5 mm x 20 mm. The highest carrier density is at the center of the laser beam (xi) and is lower than 1017 cm3, which is more than three orders of magnitude lower compared to the values at which the mobility starts to increase as reported in Ref. [38]. Despite the fact that carrier density is relatively low, the photogenerated carriers can act as a space-charge and screen the electric field between the electrodes. In order to quantify electric field in presence of photogenerated charge, we have used the results of a Monte Carlo simulation to determine snapshots of positions, occupied by the simulated carriers 9 ms after the laser pulse illumination. The corresponding histogram of their positions is presented at the bottom of Fig. 6. The positions of electrons (red filled histogram) were fixed at the point of photogeneration. Their histogram represents also the light intensity at time zero, which has a Gaussian shape centered at 10 mm away from the biased electrode and has standard deviation of 8 mm. In contrast, holes (blue-lined histogram) were hopping towards the opposite electrode located at 125 mm. 9 ms after the illumination, the hole histogram is shifted by 8 mm and its width is reduced by 38%. The time distributions of photogenerated electrons and holes were used to calculate U(x) by numerically solving Poisson equation for the biased coplanar-electrode structures, following a formerly described approach [22,24]. Calculated U(x) is shown in Fig. 6, where each curve corresponds to different number of total photogenerated charge. The solid curve is the electric potential in the absence of electric charges and corresponds to Eq. (2). The dashed line, corresponding to 1  106 total charge, exhibits relatively small deviation from the zero-charge-density curve. However, dash-dotted and dotted curves, corresponding to 1$107 and 6$107 total charge carriers, respectively, exhibit strong variation of U(x). The slope of U(x), which represents electric field in the x direction, is changing sign several times from the biased to the sensing electrode. Starting from the biased electrode, which is at

400 V, the slope of U(x) is negative and the electric field is pointing towards sensing electrode. At x z 8 mm, electric field reverses direction towards the biased electrode. Further away, electric field reverses direction again at 16 mm. Within the channel there are two more reversals of the sign at 28 mm and 90 mm. Electric field that is a consequence of charge distribution therefore forms a Coulombic trap, which is drawing holes located between 8 mm and 16 mm towards the biased electrode and those located below 8 mm towards the sensing electrode. At high charge carrier density, electric field may form potential minima, which immobilize charge carriers for a given period of time. Eventually they escape from these minima and contribute to the total collected charge. The net effect of such internal separation of electrons and holes is in local changes of electric field within the organic layer, and this affects the observed transit time and its dependence on the light intensity. In order to understand this dependence, we must consider that the observed I(t) is a result of collective transport of charge carries whose Brownian pathways result in the distribution of their arrival times to the collecting electrode. In the case of relatively narrow distribution, I(t) exhibits a sharp change in slope. As we have shown in Ref. [22], the time of such change in slope corresponds to the transit time of only approximately 10% of the fastest carriers, while the average transit time of the whole carrier packet may be considerably longer. As the space charge alters electric field within the organic layer such discrepancy between the transit time of the fastest carriers and the average carriers may be even more pronounced due to the formation of local potential minima as illustrated in Fig. 6. The fastest carriers can drift away from such minima, while slower carriers remain trapped, which results in the transit time distribution that is skewed towards shorter times. As a result, I(t) exhibits a cusp at earlier time, compared to I(t) measured at lower carrier density. Shorter ttr extracted from the cusp in I(t), therefore indicates that the slow charge carriers are being delayed by the local potential minima within the organic layer. The increased residence time of the charge carriers within the potential minima increases also the rate of charge carrier recombination. As the oppositely charged carries are confined within the so-called Coulomb radius, which is much smaller than the hopping distance, Langevin recombination becomes an important mechanism [30] in reducing the charge carrier concentration. With lower charge density the variation of U(x) is reduced (see Fig. 6) and can be approximated with Eq. (2). Consequently, I(t) time dependence can be described with a Monte Carlo simulation of zero-chargedensity model. On the other hand, as the charge density is decreasing due to recombination, the number of carriers that contribute to I(t) is reduced. This is especially evident in Fig. 5 during initial 0.4 ms where the magnitude of I(t) is decreasing faster than predicted by the Monte Carlo simulation. We could interpret a faster decrease in I(t) than predicted by simulation, in terms of a contribution of electrons to I(t). However, we don't observe any photocurrent at negative Vb when xi < 20 mm, which implies that the electron mobility is significantly smaller than the hole mobility. Therefore, even if the electron transit time at xi ¼ 10 mm is below 0.4 ms, their contribution to the photocurrent would be less than one order of magnitude smaller compared to hole photocurrent. A fast decrease in I(t) may be a consequence of relaxation of photogenerated carriers to the lowest-energy transporting sites within several nanoseconds after the photogeneration. We reject this possibility based on the fact that the time-scale of such initial relaxation is more than three orders of magnitude shorter than the position of the cusp, and cannot be observed in the I(t) line shape. Eventually, the fast decrease in I(t) could be interpreted in terms of the Langevin recombination. The role of Langevin recombination on photocurrent transients was

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corroborated also by Pivrikas et al. [9], who attributed the observation of space-charge limited transients in polymer layers subjected to photoexcitation of carries at high light intensity to Langevin recombination. 4. Conclusions We have combined time-of-flight photocurrent measurements and Monte-Carlo simulations to examine space-charge effects on transport of charge carriers in a semiconducting polymer layer between two biased coplanar electrodes. Mobility of photogenerated charge carriers exhibits a Poole-Frenkel-type dependence on electric field, which is typically observed in hopping charge transport. When the point of photogeneration moves from the biased electrode towards the collecting electrode, the distance travelled by the charge carriers is reduced. However, in contrast to intuitively expected decrease of transit time, we observed that the transit time increases. We attribute such behavior to the role of space-charge within the polymer layer. Photogenerated charge carriers behave as a space-charge in low-mobility organic semiconductors causing emergence of local electric potential minima within the organic layer. These minima increase the local residence time of a portion of the charge carriers, which delays their transport to the collecting electrode. In contrast, some of the carriers continue with hopping unhindered and reach the collecting electrode ahead of the average of the carrier packet. The centroid of the transit time distribution of these carriers occurs at shorter times compared to the distribution of all carriers, which is reflected in the position of the change in slope of I(t) curve. The comparison of the measured I(t) with the I(t) obtained by Monte Carlo simulation suggests that the increased residence time of the charge carriers in the local potential minima increases the recombination rate, which affects the behavior of I(t) in the early period after the photogeneration. References [1] [2] [3] [4]

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