Techniques for Characterization of Charge Carrier Mobility in Organic Semiconductors

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1 Techniques for Characterization of Charge Carrier Mobility in Organic Semiconductors Akshay Kokil, 1,2 Ke Yang, 1,3 Jayant Kumar 1,3 1 Center for Advanced Materials, University of Massachusetts Lowell, Lowell, Massachusetts 2 Department of Chemistry, University of Massachusetts Lowell, Lowell, Massachusetts 3 Department of Physics, University of Massachusetts Lowell, Lowell, Massachusetts Correspondence to: J. Kumar ( jayant_kumar@uml.edu) Received 27 January 2012; accepted 24 April 2012; published online 8 June 2012 DOI: /polb ABSTRACT: The charge transport characteristics of organic semiconductors are one of the key attributes that impacts the performance of organic electronic and optoelectronic devices in which they are utilized. For improved performance in organic photovoltaic cells, light-emitting diodes, and field-effect transistors (FETs), efficient transport of the charge carriers within the organic semiconductor is especially critical. Characterization of charge transport in these organic semiconductors is important both from scientific and technological perspectives. In this review, we shall mainly discuss the techniques for measuring the charge carrier mobility and not the theoretical underpinnings of the mechanism of charge transport. Mobility measurements in organic semiconductors and particularly in conjugated polymers, using space-charge-limited current, time of flight, carrier extraction by linearly increasing voltage, double injection, FETs, and impedance spectroscopy are discussed. The relative merits, as well as limitations for each of these techniques are reviewed. VC 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 50: , 2012 KEYWORDS: charge transport; conjugated polymers; photophysics INTRODUCTION Traditionally, organic materials (both small molecules and polymers) have not been utilized in applications requiring reasonable charge transport, as the charge carrier mobilities relative to inorganic semiconductors are significantly lower. However, the possibility of commercial applications utilizing electrically semiconducting small molecules and conjugated polymers has radically changed this situation. 1 These materials are attracting considerable interest not only among the scientific community but also in the industry, as they combine the processability and mechanical properties of polymers with the readily tailored optoelectronic properties of organic molecules. 2 4 The potential use of these materials as electrical conductors, 5 in light-emitting diodes (LEDs), 6,7,8 field-effect transistors (FETs), 9 photorefractive devices, 10 and photovoltaic cells has motivated the development of numerous organic semiconducting materials with unique field-responsive properties. 5,16,17 Significant progress has been made in the last two decades, and the field has matured to the point of commercial exploitation of these organic semiconductors in LEDs, 6,7,8 field-effect sensors, 18 solar cells, 11,12 and other applications In this review, we will focus on the most commonly used techniques for the determination of charge carrier mobilities in organic semiconductors and particularly for conjugated polymers used in photovoltaic devices. CHARGE TRANSPORT IN ORGANIC SEMICONDUCTORS Organic semiconductors usually have a molecular structure that features alternating single and multiple bonds, which gives rise to overlapping p-orbitals. The optoelectronic properties of these materials are not only governed by their molecular structure but also by the intermolecular interactions. Enhanced electrical charge transport in these materials is a direct consequence of delocalization of the p-electrons. 22 There is already a considerable volume of literature describing the theoretical basis of electronic structure of these organic semiconductors, 2,3,4,5,22,23 and shall not be discussed here. In their pioneering work on polyacetylene, Shirakawa, Mac- Diarmid, and Heeger demonstrated that doping allows one to increase the electrical conductivity of conjugated polymers by many orders of magnitude so that conductivities approaching those of metals are achieved. 1 For many materials platforms, high levels of electrical conductivity can be achieved at high doping levels, which are associated with a high density of charge carriers, especially in the case of trans-polyacetylene, conductivities up to 10 8 S/cm have been observed. 24 The electrical conductivity (r c ) in a material is expressed by: r c ¼ n e l (1) VC 2012 Wiley Periodicals, Inc PART B: POLYMER PHYSICS 2012, 50,

2 REVIEW Akshay Kokil received B.E. in Polymer Engineering from University of Pune in India. He received Ph.D. in Macromolecular Science and Engineering from Case Western Reserve University. He is currently working with Dr. Jayant Kumar as a postdoctoral researcher in University of Massachusetts Lowell. His research interests include design, synthesis, and characterization of functional materials, fabrication, and characterization of optoelectronic devices. Ke Yang received B.S. in Physics from Peking University, M.S. in Theoretical Physics from Tsinghua University, M.S. in Optical Physics from the University of Massachusetts Lowell, and Ph.D. in Physics from the University of Massachusetts Lowell. He is currently an adjunct faculty in the Physics Department of the University of Massachusetts Lowell and also affiliated with Center for Advanced Materials of the University. His current research interests are optical properties and transport properties of organic semiconductors. Jayant Kumar received his Ph.D. in Physics from Rutgers University. He is a professor in the Physics Department and director of Center for Advanced Materials at the University of Massachusetts Lowell. His research interests include integrated optics, optical spectroscopy, nonlinear optics, dielectric behavior of materials, electronic transport phenomena in solids, electronic, and optical phenomena in polymeric and biomolecular systems, nanoscale materials, and novel polymeric materials. where n is the number of charge carriers (which can be controlled), e is the electronic charge, and l signifies the charge carrier mobility, which is empirically defined as: l ¼ m=e (2) where v is the drift velocity of the charge carriers and E is the applied electrical field. The charge transport characteristics of conjugated polymers and molecular semiconductors are governed by the molecular structure as well as the intermolecular interactions. The charge carrier mobility of conjugated polymers depends on intrachain charge transport and interchain interactions, mediated mainly by thermally activated hopping. 5,9,11,16,17 Both factors depend on a number of variables; the former is mostly based on the polymer s chemical structure, the number and nature of defect sites, conformation of the polymer backbone, and the molecular weight, while the latter strongly depends on the supramolecular architecture, that is, order and orientation Significant progress has been made in enhancing the charge carrier mobility in organic semiconductors with high molecular order and/or orientation as well as in crosslinked systems One of the key parameters that affects the efficacy of the electronic and optoelectronic devices mentioned above, for example, FETs, LEDs, organic photovoltaic cells, is the charge carrier mobility of the active material. For example, in FETs, the rate of switching of the device depends on the mobility of the charge carriers, and in the case of LEDs, lower turn on voltages become feasible if the materials have high charge carrier mobilities. 37 For obtaining improved performance in organic photovoltaic cells, the efficient transport of the separated charge carriers within the phase separated domains of the donor (which transport holes) and the acceptor (which transport electrons) molecules is especially critical. 38 In the case of materials with low charge carrier mobilities, a very thin active layer is utilized which then has a detrimental effect on the light harvesting capability of the photovoltaic cell. On the other hand for improved light harvesting, a relatively thicker active layer is desired which then concomitantly requires the utilization of conjugated polymers with high charge carrier mobilities. Hence, the characterization of charge transport in these organic semiconductors is vital. DIFFERENT METHODS OF MOBILITY MEASUREMENTS The undoped conjugated polymers are typically semiconductors with high resistance. These polymers are also relatively wide band-gap semiconductors, which contain a small amount of thermally generated charge carriers and thus most carriers come from an external source, such as through injection of carriers or photogeneration of carriers with photons of suitable energy. They also display relatively low charge carrier mobilities when compared with the inorganic semiconductors. Hence, alternative techniques are utilized for the characterization of charge transport in organic semiconductors, such as, space-charge-limited current (SCLC), PART B: POLYMER PHYSICS 2012, 50,

3 FIGURE 1 Schematic of the sample utilized for DI measurements (a) and the ideal energy levels required for measuring hole mobility in hole transport materials (b) and electron mobility in electron transport materials (c). time of flight (TOF), carrier extraction by linearly increasing voltage (CELIV), photogenerated charges in CELIV (photo- CELIV), double injection (DoI), FETs, and impedance spectroscopy (IS). The relative merits as well as specific requirements for the location of energy levels are described in the following sections. For example, SCLC requires one charge injection (ohmic) contact and one injection blocking contact. TOF and CELIV require both injection-blocking contacts, or one injection-blocking contact and one ohmic contact. DoI requires both charge injection contacts. FET requires both ohmic contacts. Generally, FETs are used to measure the charge carrier mobility in the film plane, whereas SCLC, TOF, CELIV, DoI, and IS are used to measure the charge carrier mobility perpendicular to the film plane. Not all these methods are suitable for a particular sample and the choice of the method depends on the details, such as sample thickness, nature of the electrodes, and the energy levels of the materials. Detailed description of each mobility measurement method is discussed in the following sections. Pulse-radiolysis time-resolved microwave conductivity is another technique used for determination of charge carrier mobility. As the transport properties characterized using this technique are on a very local spatial scale (i.e., along a single polymer chain), this technique will not be discussed in the review. SPACE-CHARGE-LIMITED CURRENT: DARK INJECTION SCLC AND TRAP-FREE SCLC The sample utilized for characterization of charge transport by dark injection (DI) SCLC technique normally consists of a thin organic semiconductor (200 nm 2 lm in thickness) sandwiched between two electrodes [Fig. 1(a)]. This technique requires one charge injection contact and one injection-blocking contact. Theoretical calculation and experimental evidence indicate that the injection barrier should not exceed 0.3 ev for SCLC experiments Hence, to improve the hole injection, a thin (50 nm) layer of poly(ethylenedioxythiophene)/polystyrene-sulfonic acid (PEDOT PSS) is coated on the charge injection contact before the application of the conjugated polymer film In dark injection (DI), a step function voltage is applied to the injection contact of the sandwiched sample, as shown in Figure 1(b) for hole mobility measurement in hole transporting materials and Figure 1(c) for electron mobility measurement in electrontransporting materials. The typical observed current transient (Fig. 2) shows a peak at s DI, which relates to the freecarrier transit time t tr by 45 s DI ¼ 0:787t tr (3) The t tr calculated using the above given equation can then be utilized to determine the charge carrier mobility through l ¼ m E ¼ d=t tr V=d ¼ d2 Vt tr (4) where V is the step function voltage, d is the sample thickness. An increase in the current to a maximum value is observed as the leading front of the charge carriers is transported through the organic semiconductor film. Under the applied field, the leading front of space charge will advance through the film with time. As the charges advance through the film, the gap between the counter electrode and the leading front decreases and causes an increase in the electric field. This results in a faster transit time compared with the space charge-free transit time. Consequently, the current density at the peak is slightly higher than the equilibrium SCLC density. For longer duration, the charge distribution reaches a dynamic equilibrium and the equilibrium SCLC density is reached PART B: POLYMER PHYSICS 2012, 50,

4 REVIEW where J is the current density, V is the applied voltage, l is the mobility, e is the dielectric constant, and e 0 is the vacuum permittivity. For materials that display field dependence of mobility, often the equation is modified to, J ¼ 9 8 ee 0l 0 e 0:89c ðþ V 1 2 V 2 d d 3 (6) FIGURE 2 A representative schematic for an ideal DI current transient. Dramatically different current transients can be obtained for DI SCLC measurements with different electrical contacts; hence, an ohmic contact is necessary for these measurements. DI SCLC experiments also require a much smaller RC time constant of the utilized experimental circuit when compared with the measured s DI so that the s DI can be correctly determined. If the obtained s DI is close to the RC time constant, it is very possible that the RC effect has significant contribution on s DI, and the RC time constant needs to be reduced until RC < s DI. Temperature and field dependence of the mobility can be obtained using the DI SCLC technique. As thin films of small molecules can be easily fabricated, this method has been successfully used to measure hole mobility for small molecule organic semiconductors such as 2,2 0,7,7 0 - tetrakis-(n,n-di-p-methoxyphenylamine) 9,9 0 -spirobifluorene (spiro-meotad, l h ¼ cm 2 V 1 s 1 ). 46 It was reported that for thin films of spiro-meotad the RC time constant became comparable to the transit time. Hence, the authors successfully utilized a bridge circuit (Fig. 3), 47 which consisted of a differential amplifier to subtract the capacitive response of the circuit. Using a similar bridge circuit, the hole mobilities of 4,4 0 -bis[n-(1-naphthyl)-n-phenylamino]-biphenyl (l h ¼ cm 2 V 1 s 1 ) were recently reported. 48 DI SCLC technique has also been utilized to determine the hole mobilities of polyfluorene copolymers The authors also reported that pretreatment of Indium tin oxide (ITO) and PEDOT PSS with O 2 plasma aided in obtaining the desired DI current transients. TF SCLC technique requires similar sample geometry and electrode Fermi levels as described above in the DI SCLC technique (Fig. 1). 46 For the trap-free (TF) case with both ohmic contacts and ignoring surface potential jumps, the J V relation is given by Mott-Gurney equation: 52 J ¼ 9 8 lee V 2 0 d 3 (5) where l 0 is the zero field mobility and c describes the field activation, that is, the field dependence of mobility as a function of temperature. Using TOF technique (discussed in the following section) on molecularly doped polyvinylcarbazoles, Gill proposed the temperature dependence of c using the following equation: 56 1 c ¼ B k B T 1 k B T 0 where k B is the Boltzmann constant, B ¼ ev (m/ V) 1/2 and T 0 ¼ 600 K. The values for B and T 0 are similar for a large class of disordered organic semiconductors and that the variation in parameters describing this behavior is less than a factor of two. 57 Using the temperature dependence of dc mobility with applied field as a parameter plot 58 and the mobility as a function of E 1/2 plot, 58 these constants can also be independently determined. In the case of materials containing traps, the effect of localization of charge carriers on the obtained mobility values has also been investigated. The influence of the charge carrier trapping on the J V characteristics in the SCLC technique has also been studied. 59 As the charge carrier mobility in bulk can be determined using TF SCLC, it has been widely utilized for characterizing charge transport in conjugated polymers utilized for Bulk Heterojunction Solar Cells (BHJSCs). Blom et al. have utilized this technique for determining hole mobilities in substituted derivatives of poly(p-phenylene vinylene)s (PPV). 55,58,60 By using electrodes with carefully chosen work functions, the authors reported hole and electron mobility measurements FIGURE 3 DI current transient for measurement of hole mobility in spiro-meotad. (Reprinted from Ref. 46, with permission from American Institute of Physics.) (7) PART B: POLYMER PHYSICS 2012, 50,

5 FIGURE 4 Energy levels of the electrodes used for electron only and hole only device (left) and the SCLC J V curves for determination of electron (a) and hole (b) mobility in PPV PCBM blend films (right). (Reprinted from Ref. 61, with permission from Wiley- VCH Verlag.) in blends of donor (PPV) and acceptor (6,6-phenyl C61-butyric acid methyl ester, PCBM), respectively (Fig. 4). 61,62 Yang et al. have utilized SCLC to determine the effect of growth rate of phases in a BHJSC active layer on the mobilities of its components, namely, poly(3-hexylthiophene) (P3HT) and PCBM. 63 They reported that for fast growth rates the electron mobility (l e ) and hole mobility (l h ) were and cm 2 V 1 s 1, respectively. A two orders of magnitude increase in the hole mobility was reported for active layers with slow growth rates with l e ¼ cm 2 V 1 s 1 and l h ¼ cm 2 V 1 s 1. McGehee et al. have also reported hole mobilities of the order of cm 2 V 1 s 1 in a blend film of poly(2,5-bis(3-tetradecyllthiophen-2-yl)thieno[3,2-b]thiophene) and PCBM. 64 As the required thickness of the sample is similar to that used for the active layer in BHJSCs, many researchers use this technique for charge-carrier mobility measurements However, a charge injection contact is critical for SCLC. These techniques cannot be used to measure hole mobility for organic semiconductors with very low HOMO level, or measure electron mobility with very high LUMO level. For those cases, TOF and CELIV methods should be used. TIME OF FLIGHT TOF is a widely used technique for determination of charge carrier mobilities in organic semiconductors. 68 Similar sample geometry is utilized for the TOF samples as stated above, with the exception of the charge injection layer. In addition, much thicker films (>1 lm) of the organic semiconductor are required. As photogenerated charge carriers are required in TOF, transparent or semitransparent electrodes are also necessary. As shown in Figure 5(a), injection-blocking contacts are required for this technique. If this condition is not fulfilled, the injection of carriers occurs under the strong applied electric fields leading to SCLC, which can significantly affect the applied electric field, making the electric field extremely nonuniform. Typically, in TOF measurements, a thin sheet of charge carriers is created in the organic semiconductor using a short laser pulse incident on the sample through the transparent/semitransparent electrode [Fig. 5(b)]. Depending on the polarity of the applied uniform DC electric field (E) either electrons or holes are transported across the sample. In general, before utilizing the ToF technique, following parameters should be considered: dielectric relaxation time (s r ) should be larger than the transit time (t tr ), sample thickness should be significantly larger than the inverse of the absorption coefficient (i.e., d > 1/a), the RC time constant should be much smaller than t tr (differential ToF technique) and the integral ToF technique should be used when RC time constant is much larger than t tr. In the following part of this section, these requirements are discussed in detail. In the most commonly used low light intensity mode of the TOF technique, the absorption depth of the utilized laser pulse should be short enough such that the photogenerated carriers are concentrated in a thin layer with well-defined position, compared to the sample thickness d. This requirement can be written as: d n10 a where a is the absorption coefficient of the material. About 90% of the photo generated carriers are concentrated in a thin layer with the width of n10 a. The requirement can also be expressed as: A k ¼ (8) ad n10 1 (9) 1134 PART B: POLYMER PHYSICS 2012, 50,

6 REVIEW FIGURE 5 Ideal energy levels required for determination of charge carrier mobilities using TOF (a) and a representative schematic of TOF setup, the laser pulse can be illuminated through ITO electrode as well as a semitransparent metal electrode (b). where A k is the absorbance (or optical density) of the sample at the excitation laser wavelength k. Under the presence of the electric field, the thin layer of charge carriers travels from the front electrode to the back electrode. The duration of the light pulse should be short as compared to the transit time of the charge carriers. As the sheet of charges reaches the back electrode, a drop in the photocurrent is observed and a characteristic plateau and knee at the transit time t tr is observed in the photocurrent transient, especially for materials displaying nondispersive charge transport. The charge transport in disordered organic semiconductors can also be dispersive in nature. This is due to the existence of a distribution of charge trapping sites with different depths. In the photocurrent transient, the characteristic plateau region is not observed for materials displaying dispersive charge transport. In this case, the photocurrent transient is plotted in a double-logarithmic format and the t tr is determined from the inflection point. 69 The charge carrier mobility can be determined using the following equation: l ¼ d2 t tr V where V is the applied voltage. (10) If the organic semiconductor does not have enough absorption or thickness to satisfy the condition expressed in eq 9, a charge generation layer with strong absorption at the laser wavelength can be added between the sample and the front electrode. By using a very thin-charge generation layer of perylene diimide (10 nm) hole mobilities in relatively thin spincoated films of conjugated polymers as well as dendrimers (1.6 lm) were reported by TOF technique N-type silicon (Si) wafer has been successfully used as both cathode and as charge generation material for a 400-nm tris(8-hydroxyquinolato)aluminum (Alq) layer deposited on top of it. 73 It was reported that the laser pulses passed through the semitransparent front electrode (thin Au film) and the Alq layer (no absorption) and were then absorbed by the Si substrate. The photogenerated electrons were injected by the applied electric field from the Si substrate into the Alq layer and passed through the Alq layer. The obtained photocurrent transient was then used for determination of electron mobility. An important requirement of the TOF technique is that the transit time t tr should be shorter than the dielectric relaxation time s r, which is defined as the time for the photogenerated charges to relax back to the original state. 45 The dielectric relaxation time is defined as, PART B: POLYMER PHYSICS 2012, 50,

7 cm 2 V 1 s 1 in region-regular and region-random P3HT PCBM blend films. 86 They also concluded that the change in charge carrier mobility did not affect the power conversion efficiencies upon annealing. CARRIER EXTRACTION BY LINEARLY INCREASING VOLTAGE AND PHOTO-CELIV FIGURE 6 Comparison of the calculated electric field dependences of the apparent mobility (solid line) and true mobility (dotted line) at two different temperatures (T 2 > T 1 ). (Reprinted [Fig. 2] from Ref. 74, with permission from American Physical Society.) s r ¼ ee 0 r (11) where r is the conductivity of the material. In TOF measurements, the length of the region where charge depletion occurs should be greater than the sample thickness. 74 Significant overestimation of the true mobility can occur if this condition is not satisfied, leading to a false-negative field dependence at low field, as shown in Figure 6. RC time constant is also an important factor in TOF measurements. The conventional TOF experiments require that RC < t tr such that the transit time t tr can be correctly obtained. In the case of RC > t tr, the conventional TOF method cannot be used to determine the transit time t tr and the mobility. The integral mode of TOF needs to be used to measure t tr, and thus, the mobility for RC > t tr. 75 In these cases, the obtained current represents the accumulated charge on the capacitor plates. The total accumulated charge Q t is obtained when time approaches to infinity. The time for accumulation of half of the total charge (Q t /2), is equal to half of the transit time, t tr /2. 75,79,77,78 Therefore, t tr can be determined, and the mobility can be obtained through eq 10. The determination of transit time t tr for a region-random P3HT film using integral mode TOF is shown in Figure 7. For the case in which RC is close to t tr, or for the case in which RC < t tr and the double logarithmic plot does not yield t tr, integration of the photocurrent transient can be used to obtain the collected charge Q t as a function of time, and the aforementioned method can be used to determine the transit time t tr and the charge carrier mobility. An advantage of the TOF technique is that mobility of both electron and hole can be obtained from the same sample. Electron and hole mobilities of organic and organometallic molecules, 73,79,80 conjugated polymers, 67,81 84 and conjugated polymer networks 35,85 have been successfully obtained by TOF experiments. In an interesting study, Laquai et al. reported hole and electron mobilities of the order of 10 5 CELIV is a mobility measurement technique, which has been more recently applied for the characterization of charge transport in organic semiconductors The sample geometry and the required energy levels are similar to the one used in TOF technique. However, in contrast to TOF measurements, CELIV technique can be used for relatively thin samples. Spin-coated films with thickness of a few hundred nanometers are usually acceptable for CELIV measurements. The other advantage associated with this technique is that it allows the measurement of charge carrier mobilities in materials with high bulk conductivity and complete charge depletion from the sample is not necessary. Consequently, much weaker electric fields can be applied when compared with TOF measurements. The experimental setup for CELIV is similar to that utilized in TOF, except that a linearly increasing voltage (ramp) pulse with slope, A ¼ U/t pulse (where t pulse is the duration of the ramp), is applied to the sample (Fig. 8). 88 A typical current transient from a CELIV measurement is also displayed in Figure 8. The initial step increase in the current is due to the capacitance of the sample, given by: jð0þ ¼ ee 0A d (12) where d is the film thickness. 87 The increase in current after j(0) is caused by the extraction of the dominant charge carrier present in the sample. The time required to reach the maximum in the extraction current (t max ) is utilized for calculating the charge carrier mobility. FIGURE 7 Photocurrent transient of a Regiorandom poly(3-hexylthiophene) film using integral mode TOF. The estimation of total collected charge Q t and transit time t tr is shown. The inset shows the fast carrier charge component Q f at T ¼ 305 K (solid line) and T ¼ 275 K (dashed line). Reprinted from Ref. 75, with permission from Elsevier Science B.V.) 1136 PART B: POLYMER PHYSICS 2012, 50,

8 REVIEW FIGURE 8 A representative schematic for an ideal current transient obtained in CELIV for the applied voltage ramp. The mobility is obtained from measured current by the following expression: l ¼ 2d2 3At 2 max 1 þ 0:36 Dj 1 (13) jð0þ where A is the rate of increase of the applied voltage, Dj is the difference between the maximum current and j(0), as shown in Figure 9. The above equation is valid when Dj/j(0) is less than or close to one. In the case where Dj/j(0) 7, numerical solutions to the equations describing the current transient yields a more precise expression for mobility given by: 90 h i l ¼ 2d2 Atmax 2 0:329e 0:180Dj=jð0Þ þ 0:005e 0:253Dj=jð0Þ (14) Figure 9 compares the mobility obtained from different expressions with the actual mobility of a modeled material. 90 We can see from the figure that eq 14 gives mobility closer to the correct value than the original expression does. Typically, in organic semiconductors, the equilibrium charge carriers are present due to low-level doping or impurities. In the case of materials that do not contain these equilibrium charge carriers, irradiation of sample with a short laser pulse can be utilized to obtain photogenerated charge carriers, which after a certain delay can then be extracted from the film. This modified technique is usually referred to as photo-celiv and the charge carrier mobility can be determined using equations used for CELIV measurements. 91 There are some reports in which charge transport in conjugated polymers has been characterized using CELIV. 92,93 In the first report, Juska et al. demonstrated the determination of charge carrier mobilities in regioregular P3HT, PPV, and polyazomethine by CELIV. 88 Mozer et al. reported the charge carrier mobilities in P3HT using TOF and CELIV. 94 They reported that the mobilities obtained by using these two independent techniques were mutually consistent except at low temperatures (<130 K) (Fig. 10). Photo-CELIV has also been utilized for determination of mobilities in the active layers of BHJSCs. In the photo-celiv technique, long photo pulse and constant illumination could also be used. For photo-celiv, the distribution of the photogenerated charge carriers and their recombination effects has also been investigated. These effects may give significant errors under certain conditions. 90 Dennler et al. reported the determination of hole mobilities in blend films of PCBM and a PPV derivative. 95 It was reported that the hole mobility increased with increasing PCBM concentration, with l hole ¼ cm 2 V 1 s 1 for the PPV derivative and l hole ¼ cm 2 V 1 s 1 for the 1:4 blend film of PPV derivative and PCBM. They also reported that the dispersive character of the transient decreased with increasing PCBM content in blend films. Using an electron-blocking layer of N,N 0 -bis(3- methylphenyl)-n,n 0 -diphenyl-[1,1 0 -biphenyl]-4,4 0 -diamine (a well-known electron-blocking material in small molecule solar cells), Yang et al. reported the determination of hole transport in polyalkylthiophene PCBM blend films. 96 The nature of the transient peaks was correlated with the fill factor of the BHJSCs, and it was reported that for the blend films with balanced hole and electron mobilities highest fill factors were obtained. Tolbert et al. utilized photo-celiv technique for determining the cause of a S -shaped current voltage (J V) behavior usually observed in low-performance BHJSCs. 97 They reported that the S-curve results from an imperfect contact between PCBM from the active layer and the device cathode. They also displayed that this behavior can be corrected by spin-coating an additional PCBM film on the active layer before the deposition of the cathode. In a recent report, Pivrikas et al. reported a comparison in the electron mobility for C60 in bulk and at the interface using photo-celiv and FETs, respectively. 98 Because of the lower charge carrier concentration in diodes (used in photo-celiv), lower electron mobilities were reported when compared with the transistors. Based on the temperature dependence of electron mobility, the authors also concluded a disordered nature of FIGURE 9 Results of the calculation of correction factor v as a function of Dj/j(0) from the numerical solution governing the CELIV process (symbols), compared to fit II (eq 14) as well as the parameterization used by Juška et al. (eq 13). Reprinted (Fig. 1) from Ref. 90, with permission American Physical Society. PART B: POLYMER PHYSICS 2012, 50,

9 FIGURE 10 Comparison in hole mobilities determined using CELIV and ToF at different sample temperatures. (Reprinted [Fig. 9] from Ref. 94, with permission from American Physical Society.) charge transport in the evaporated C60 films. CELIV and photo-celiv are being increasingly used for characterization of charge carrier mobility in blends of donors and acceptors due to the various advantages of these techniques stated above DOUBLE INJECTION TRANSIENT TECHNIQUE The DoI technique is complementary to the ToF and CELIV techniques as ambipolar charge carrier mobility and bimolecular recombination coefficient can be obtained for a given sample at the same time. This technique can also be applied for samples with injecting contacts, in which case the ToF and CELIV cannot be applied. Also, this technique does not require photoexcitation from a laser pulse. In this technique, through the selected electrodes, both electrons and holes are injected into the sample. The effect of both electric field and temperature on charge carrier mobility can be determined. The experimental setup utilized for DoI is similar to that used in ToF. In this technique, a step-function voltage is applied to the sample in the forward bias, which injects both electrons and holes in the sample, and the current transient is recorded on the oscilloscope (Fig. 11). After application of the electric field, the current transient displays an immediate RC decay followed by increase in the current due to carrier accumulation, until it reaches a saturated value (j S ) caused by charge recombination. 103 The determination of charge carrier mobility depends on the relation between s r and t tr. For high-conductivity samples, that is, when s r t tr, the saturated DoI current is given by, 103 j S ¼ 8Vee 0 9d sffiffiffiffiffiffiffiffiffiffiffiffiffi b L 1 b s r t a (15) where d is the sample thickness; b is the bimolecular recombination coefficient; b L is the Langevin recombination coefficient; and t a is the ambipolar carrier transit time. The ambipolar charge carrier mobility can be determined using t a ; however, it might not be discernible in the current transient. Hence, a derivative of the current transient is plotted, from which the obtained inflexion point (t m ) is utilized to determine the ambipolar charge carrier mobility (l a ), t a ¼ 6t m 5 ¼ d2 Vl a (16) For low conductivity samples, that is, when s r t tr, and when the recombination is Langevin type, the saturated DoI current is given by: 104 j S ¼ C ee 0 ðl e þ l h Þ V 2 d 3 (17) FIGURE 11 A representative schematic for an ideal current transient obtained in DoI for the applied step voltage. where C is very close to 1. In the case where b b L, the amount of charge carrier increases and saturates due to recombination. Here, the saturated current is given by: PART B: POLYMER PHYSICS 2012, 50,

10 REVIEW sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi j S ¼ ee 0 2b L b l V 2 el h d 3 (18) In this case, the mobility of both the fast and slow carrier can be determined from the cusp seen in the current transient and from the maximum observed at the longer time scale in the time derivative of the current transient. The bimolecular recombination coefficient can also be determined from the DoI transients for the case where the (non- Langevin) bimolecular recombination is small. The ratio of the bimolecular recombination coefficient with Langevin recombination coefficient is given by: 103 b ¼ ln 3 ee 0 V 1 b L 2 d t 1=2 Dj (19) FIGURE 12 Schematic of the typical organic FET architectures. where t 1/2 is the time when the current is half of its saturated value (starting from t m ) and Dj is the difference between the saturated current and the current at the time t m. Using this technique, the ambipolar charge carrier mobility and the charge carrier recombination was investigated in a variety of conjugated polymer PCBM (donor acceptor) blends FIELD-EFFECT TRANSISTORS Organic FETs were first reported in the 1970s 108,109 and, since then, have attracted significant interest for applications in large area electronics, radio-frequency identification (RFID) tags,flexibleactivematrixdisplays,andsoforth. 9, Organic FETs are typically constructed similar to thin-film transistors with two possible configurations, namely, bottom-gated and top-gated architectures (Fig. 11), and can be utilized for the determination of charge carrier mobilities. The source and the drain electrodes in FETs form an ohmic contact with the conducting channel. The source electrode is grounded and all other voltages as given in relation to this electrode. The current is injected from the source electrode and collected at the drain electrode. The organic semiconductor and the gate electrode are separated by a carefully selected thin dielectric layer. The gate electrode controls the flow of current in the organic semiconductor layer by capacitive coupling of the thin dielectric layer. The charge carrier mobility is determined using the characteristic output curves of the transistor, that is, the plot of drain source current (I DS ) versus drain voltage (V DS ) as a function of varying gate voltages (V GS ) (Fig. 12). The output curves can be differentiated in two regions: the linear region and the saturation region. 9 The linear region of the curve is defined as I DS ¼ W L lc s ðv GS V T Þ V DS V DS (20) 2 where W and L are the width and length of the conduction channel, respectively; l is the charge carrier mobility, C S is the capacitance per unit area for the insulating layer and V T is the threshold voltage. The slope of the transfer characteristic curve, which is a plot of I DS versus V GS at a constant V DS, can be utilized to determine the charge carrier mobility using the following GS ¼ W L lc SV DS (21) However, the above given equation can be utilized only when V DS < (V GS V T ). The saturation region (V DS > V GS V T ) of the output curve is defined as: I DS ¼ W 2L lc sðv GS V T Þ 2 (22) For the saturation region, the slope of the transfer characteristic (I 1=2 DS vs. V GS at constant V DS ) can also be utilized for calculating the charge carrier mobility. 9 The above given equations are valid in the case where the charge carrier mobility is assumed to be temperature and field independent. Most organic semiconductors display field as well as temperature-dependant charge carrier mobilities; to account for these effects, Horowitz et al. further refined the model. 113,114 However, an estimation of the charge carrier mobilities can be obtained. The interface between the materials used in fabricating an FET governs the output curves obtained, and hence, care has to be taken while selecting them. 115 The dielectric layer utilized is also important, and it can have a significant effect on the performance of the FET. 116 Especially for measuring electron mobilities, the hydroxyl groups present at the dielectric surface can act as electrochemical traps; 117 hence hydroxylfree dielectric materials, such as divinyltetramethysiloxane- (bis benzyl cyclobutene) have been utilized. FETs have been utilized for measuring charge carrier mobilities for a variety of conjugated polymers and organic molecules. 110,111,112, Recently, FETs have been utilized for determining charge carrier mobilities in donor acceptor PART B: POLYMER PHYSICS 2012, 50,

11 FIGURE 13 Representative schematic of FET output curves. blend films typically used in BHJSCs. Hauff et al. reported a electron mobility of the order of 10 3 cm 2 V 1 s 1 in pure PCBM films. 122 However, upon blending with P3HT, they reported a decrease in the electron mobility by an order of magnitude, which was attributed to the unoptimized morphology of the blend film. By determining electron and hole mobilities in blend films of P3HT and PCBM, Morana et al. reported that balanced mobilities were important for obtaining improved BHJSC performance particularly high fill factors. 123 They also compared the effect of two commonly used solvents, namely, o-xylene and chlorobenzene, on the solar cell performance as well as the charge carrier mobilities. It was reported that films obtained from chlorobenzene solutions performed better than those obtained from o-xylene. In a recent report, Anthopoulos et al. utilized FETs for indirect investigating the evolution of phase-separated morphology in P3HT/PCBM blends upon thermal annealing (Fig. 13). 124 They used FET measurements on P3HT/PCBM blends annealed at different temperatures and reported that the hole and electron mobilities remain constant till the annealing temperature of 140 C. However, upon annealing above this temperature, the hole mobility increases while the electron mobility drastically decreases. The observed effect was attributed to the increased crystallization in the P3HT domains and the increased clustering of PCBM. The authors also reported in situ FET measurements where hole and electron mobilities were measured from the saturation region of the FET as a function of annealing time. It was reported that at 130 C, the mobilities remained almost unaffected over a period of 30 min. However, at a temperature of 160 C, the hole mobility slightly increased and the electron mobility drastically decreased after 10 min. This drop in electron mobility was also attributed to the increased phase separation in the blend films upon annealing them at 160 C for more than 10 min. IMPEDANCE SPECTROSCOPY IS is a technique to investigate charge transport kinetics and relaxation processes involved in solid-state devices. The sample geometry utilized to determine charge carrier mobility by this technique is similar to the diodes used in SCLC stated above. This technique is based on the specific frequency dependence displayed by the admittance (Y ¼ I ac /V ac ), which is governed by the transit of injected charge carriers. 58,125 A broad distribution of the transit time for individual charge carriers occurs due to the dispersive nature of charge transport and this can be obtained from the ac response. The sample conductance [G ¼ Re(Y)] and capacitance [C ¼ Im(Y/ x)] display a significant frequency dependence. Hence, to determine the charge carrier mobility using this technique, typically, a DC bias V dc is applied to the sample and a SCLC flow is generated. A small AC voltage (much weaker than the DC voltage) is applied to the sample at the same time. The G and C spectra are measured as a function of AC frequency. These spectra display a sharp decrease in G or increase in C at the AC frequency close to x ¼ 1/t t, where t t is the transit time given by: t t ¼ 4d2 3lV dc (23) where d is the sample thickness. Once the transit time t t is determined, the charge carrier mobility l can be calculated from above equation. Similar to SCLC, the charge carrier mobility is assumed to be independent of the electric field inside the material. It was also recently reported that the transit time t t can also be determined from the plot of negative differential susceptance [ DB ¼ x(c 1 (x) C geo )] versus the frequency of the applied AC field, where C 1 is the AC capacitance, C geo is the geometrical capacitance. 126 The first peak obtained in the plot at a frequency f max is related to the transit time by the equation f max ¼ 0.72/t t. Similarly, xdg [which is defined as FIGURE 14 Electron and hole mobilities for P3HT PCBM blend films as a function of annealing temperature and the DSC thermogram from the blend. (Reprinted from Ref. 124, with permission from Wiley-VCH Verlag.) 1140 PART B: POLYMER PHYSICS 2012, 50,

12 REVIEW TABLE 1 Summary of Requirements and Limitations of the Discussed Charge Transport Characterization Techniques Techniques Requirements and Advantages Limitations SCLC TOF CELIV DoI FET IS Film thickness: 200 nm 2 lm. One charge injection contact and one injection blocking contact. Both injection-blocking contacts. Electron and hole mobilities can be determined using the same sample. Transport of photoinduced charge carriers can be characterized. Charge transport in bulk can be characterized. Field dependence of charge carrier mobility can be characterized. Both injection-blocking contacts. Electron and hole mobilities can be determined using the same sample and can be differentiated by using photo- CELIV. Transport of photoinduced charge carriers can be characterized using photo-celiv. Charge transport in materials with high bulk conductivity can be characterized. Much weaker fields when compared with TOF can be utilized. Both charge injection contacts required. Charge transport can be measured for conducting samples. Photoexcitation not required. Ambipolar charge carrier mobility and bimolecular recombination coefficient can be investigated. Ohmic contacts required with the conducting channel. Charge carrier mobility obtained in film plane. Same as SCLC Careful selection of the electrodes required. Additional fitting parameters required for materials that display field-dependant charge carrier mobilities. For most materials, Film thickness > 1 lm. Dielectric relaxation time of the organic semiconductor should be much greater than the carrier transit time. For extraction of the equilibrium carriers, the differentiation between electron and hole mobility is difficult for materials displaying ambipolar charge transport. Numerical curve fitting is required to obtain precise charge carrier mobilities for high Dj/j(0) values. Careful selection of the electrodes required. The differentiation between electron and hole mobility is difficult. The utilized experimental conditions may significantly affect the obtained charge carrier mobilities. The utilized dielectric layer can have a significant effect on the performance of the FET. Careful selection of the electrodes required. The utilized experimental conditions may significantly affect the obtained charge carrier mobilities. Appropriate equivalent circuit model with physical meaning to the utilized device is required. x(g 1 (x) G 1 (1)), where G 1 is the AC conductance] can be plotted against the frequency of the applied AC field. The first peak obtained in the plot at a frequency f max is related to the transit time by the equation f max ¼ 0.48/t t. Using eq 23, hole mobilities in P3HT were determined. 127 It was recently reported that the Nyquist plot [ Im(Z) vs. Re(Z)] can be utilized to determine the electron diffusion times (s d ) in donor acceptor blend films of P3HT and PCBM (Fig. 14). 128 This was then used to calculate the electron diffusion coefficient (D n ¼ L 2 /s d ). The electron mobility was then calculated using the Nernst-Einstein equation l ¼ ed n / k B T, where k B is the Boltzmann constant and T is the utilized temperature. FIELD AND TEMPERATURE DEPENDENCE OF CHARGE CARRIER MOBILITY As seen in the above sections, the charge carrier mobility in most of the organic semiconductors is dependent on the utilized field and the sample temperature. Currently, there are two expressions to formulate the field and temperature dependence of mobility. The first one is an empirical expression originated by Gill, 56 that is, FIGURE 15 Nyquist plots for P3HT PCBM blend films. Reprinted with permission from Garcia-Belmonte, G.; Munar, A.; Barea, E. M.; Bisquert, J.; Ugarte, I.; Pacios, R. Org. Electron. 2008, 9, 847. (Reprinted from Ref. 128, with permission from Copyright 2008, Elsevier Science B.V.) PART B: POLYMER PHYSICS 2012, 50,

13 h i lðt; EÞ ¼ l 0 exp E 0 be 1=2 ð1=t 1=T 0 Þ=k B (24) where T is the temperature, E is the electric field inside the material, k B is the Boltzmann constant, l 0, E 0, b, andt 0 are constants. E 0 be 1/2 is the activation energy. The second expression is the B assler model, 129 that is, ( " r 2 lðt; EÞ ¼ l 0 exp C X # 2 E 1=2 2 ) r 2 k B T 3 k B T (25) where r is the width of the density of states, R is a parameter for positional disorder, C is a constant. Both these models have been successfully applied to the charge transport in organic semiconductors. 130,131 At fixed temperature, both models give the same field dependence, 94,132 that is, the Poole- Frenkel behavior, lðeþ ¼ l 0 0 exp c p ffiffiffi E (26) where l 0 andc are constants. The Poole-Frenkel expression is typically used to study the field dependence of mobility at constant temperature. In most cases, positive field dependence (c > 0) is observed. However, in certain cases, the negative field dependence (c < 0) is also observed. At a fixed electric field, Gill and B assler models give different temperature dependence of charge carrier mobilities. Gill s expression leads to the Arrhenius-like behavior, that is, Log l / 1=T (27) While B assler model leads to a dependence which is given by, Log l / 1=T 2 (28) Both the models for the temperature dependence of charge carrier mobilities have been utilized to explain the experimental results for a variety of organic semiconductors in the used temperature range SUMMARY Charge carrier mobility is one of the important physical attributes of an organic semiconductor, and it has a critical effect on their performance in a variety of applications. In this review, we have discussed the different techniques widely used for the characterization of charge transport in these organic semiconductors. The characterization of charge transport requires a judicious selection of electrode materials as well as careful selection of the experimental conditions is required. The protocol used for sample preparation and sample storage can have a considerable effect on the measured charge carrier mobilities. It has been reported that oxygen can form a charge transfer complex with P3HT resulting in an increase in the charge carrier concentration and conductivity; on the other hand, the measured charge carrier mobilities decreased. 136 The choice of the most appropriate technique for a sample depends on the organic semiconductor utilized. Some of these considerations are summarized in Table 1. These techniques can also be utilized as the indirect means for determination of bulk morphology in the active layer of BHJSCs. ACKNOWLEDGMENTS This material is based on work supported as part of polymerbased materials for harvesting solar energy, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC REFERENCES AND NOTES 1 Shirakawa, H.; Louis, E. J.; MacDiarmid, A. G.; Chiang, C. K.; Heeger, A. J. J. Chem. Soc. Chem. Commun. 1977, Heeger, A. J. J. Phys. Chem. 2001, 105, MacDiarmid, A. G. Rev. Mod. Phys. 2001, 73, Shirakawa, H. Rev. Mod. Phys. 2001, 73, Handbook of Conducting Polymers, 2nd ed.; Skotheim, T. J.; Elsenbaumer, R. L.; Reynolds, J. R., Eds.; Dekker: New York, Kraft, A.; Grimsdale, A. C.; Holmes, A. B. Angew. Chem. Int. Ed. 1998, 37, Mitschke, U.; B auerle, P. J. Mater. Chem. 2000, 10, Greiner, A.; Weder, C. In Encyclopedia of Polymer Science and Technology, 3rd ed.; Kroschwitz, J. I., Ed.; Wiley-Interscience: New York, 2003; Vol. 3, p Horowitz, G. Adv. Mater. 1998, 10, Moerner, W. E.; Silence, S. M. Chem. Rev. 1994, 94, Brabec, C. J.; Sariciftci, N. S.; Hummelen, J. C. Adv. Funct. Mater. 2001, 11, Thompson, B. C.; Frechet, J. M. J. Angew. Chem. Int. Ed. 2008, 47, Dennler, G.; Scharber, M. C.; Brabec, C. J. Adv. Mater. 2009, 21, Venkataraman, D.; Yurt, S.; Venkatraman, B. H.; Gavvalapalli, N. J. Phys. Chem. Lett. 2010, 1, Kim, Y. G.; Walker, J.; Samuelson, L. A.; Kumar, J. Nano Lett. 2003, 3, Handbook of Organic Conductive Molecules and Polymers; Nalwa, H. S. Ed.; Wiley: New York, Physical Properties of Polymers Handbook; Mark, J. A. Ed.; American Institute of Physics: New York, Swager, T. M. Chem. Res. Toxicol. 2002, 15, Tallman, D. E.; Spinks, G.; Dominis, A.; Wallace, G. G. J. Solid State Electrochem. 2002, 6, Karg, S.; Riess, W.; Meier, M.; Schwoerer, M. Synth. Met. 1993, 55-57, Hoeben, F. J. M.; Jonkheijm, P.; Meijer, E. W.; Schenning, A. P. H. J. Chem. Rev. 2005, 105, One-Dimensional Metals, 2nd ed.; Roth, S.; Caroll, D., Eds.; Wiley-VCH: Weinheim, Peierls, R. E. Quantum Theory of Solids; Clarendon Press: Oxford, MacDiarmid, A. G. Angew. Chem. Int. Ed. 2001, 40, PART B: POLYMER PHYSICS 2012, 50,