Temperature and electric field dependent hole mobility in a polyfluorene copolymer

Synthetic Metals 161 (2011) 794–798

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Temperature and electric field dependent hole mobility in a polyfluorene copolymer Francesca Tinti a , Siraye E. Debebe b , Wendimagegn Mammo b , Teketel Yohannes b , Nadia Camaioni a,∗ a b

Istituto per la Sintesi Organica e la Fotoreattività, Consiglio Nazionale delle Ricerche, via P. Gobetti 101, I-40129 Bologna, Italy Department of Chemistry, Addis Ababa University, P.O. Box 1176, Addis Ababa, Ethiopia

a r t i c l e

i n f o

Article history: Received 17 November 2010 Accepted 31 January 2011 Available online 26 February 2011 Keywords: Hole mobility Transport properties Conjugated polymers Polyfluorene Admittance spectroscopy

a b s t r a c t Transport of holes in thin films of a low-bandgap alternating polyfluorene copolymer, APFO-Green5, was investigated by means of admittance spectroscopy as a function of field and temperature. The values of hole mobility were evaluated from the position of the maxima in the plots of the negative differential susceptance as a function of frequency. Hole mobility was found to be strongly field- and temperature-dependent. The charge transport parameters were extracted by analyzing the mobility data by the uncorrelated and the correlated Gaussian Disorder Models. © 2011 Elsevier B.V. All rights reserved.

1. Introduction In the last two decades, an intensive research activity on ␲conjugated polymers has been stimulated by the prospect for low-cost fabrication of plastic electronic devices with reasonable stability and performance. In addition to the easy processability and good mechanical properties of ␲-conjugated polymers, their electronic properties can be easily tailored to suit a specific application. For example, the energy gap in these systems can be easily tuned by subtle modification of the chemical structure [1]. Charge carrier mobility of conjugated polymers is one of the key parameters of interest, both for the realization of polymer devices with improved performance, and for understanding the underlying mechanisms for charge transport in such complex materials. Indeed, mobility in conjugated polymers is relevant to the operation of a wide range of electronic devices such as field-effect transistors [2], light-emitting diodes [3] and solar cells [4]. Concerning this last application, conjugated polymers are used as electron-donor component in bulk-heterojunction (BHJ) polymer/fullerene solar cells [5], with the role of transporting photo-generated positive carriers to the anode contact, other than acting as the main solar light absorbers, given the poor optical absorption of fullerene in the visible range. It has been shown that optimum and balanced charge carrier mobilities for the polymer and the fullerene phase of a BHJ solar cell are required to avoid

∗ Corresponding author. Tel.: +39 051 6399779; fax: +39 051 6399844. E-mail address: [email protected] (N. Camaioni). 0379-6779/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.synthmet.2011.01.032

space charge effects [6], as well as for an effective charge extraction, both limiting device efficiency. The conjugated polymer investigated in this study, namely APFO-Green5 [7], belongs to a large family of alternating fluorene copolymers (APFOs) [8]. Due to the alternating electron-rich and electron-poor units in its molecular structure (Fig. 1), APFO-Green5 exhibits an energy gap of 1.6 eV, making it suitable for absorbing long-wavelength photons. It has already been used as electrondonor component in polymer/fullerene BHJ solar cells, showing a photoresponse extended up to 800 nm [7]. In this paper, the results of an investigation of the mobility of positive carriers in thin films of APFO-Green5 are reported. A powerful technique for the study of bulk transport properties of high resistive materials, admittance spectroscopy (AS) [9], was used. In an admittance experiment, the charge relaxation driven by a small harmonic voltage modulation vac is probed. The amplitude and the phase difference of the ac current iac are monitored as a function of frequency f, and the admittance Y is given by Y (ω) =

iac (ω)

vac (ω)

= G(ω) + iωC(ω)

where G is the conductance, C the capacitance, i is the imaginary unit, and ω = 2f, the angular frequency. By superimposing a forward dc bias Vbias to the harmonic voltage modulation, free carriers can be injected into a sample having a diode structure and, in case of injection, the transit time ( tr ) of carriers determines the frequency dependence of admittance. In the ideal case, the capacitance makes a step around the frequency of  tr −1 , C tending at higher frequencies to the dielectric or geometrical capacitance of the sample,

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Fig. 1. Molecular structure of APFO-Green5 and energy level diagram of the investigated devices.

Cg , and decreasing to a lower value towards lower frequencies [9]. However, in real cases the capacitance spectra are often affected at low-frequencies by trap contribution and the effect of carriers transit time results in minimum regions of C at intermediate frequencies [10–12]. Charge transport in most conjugated polymers, and in general in disordered systems, usually occurs as a series of hops between localized states, leading to a strong dependence of mobility on temperature and electric field [13], thus the investigation of mobility with temperature and field provides insight into the mechanisms of charge transport in these materials. In this paper the dependence of hole mobility in thin films of APFO-Green5 on both temperature and electric field is described.

2. Experimental APFO-Green5 was prepared as reported elsewhere [7]. The polymer films were deposited onto ITO-glass substrates (ITO is indium tin oxide), coated with a layer of poly(3,4ethylenedioxythiophene)/polystyrene sulphonic acid (PEDOT:PSS, CLEVIOS P VP AI 4083, H.C. Starck). ITO substrates were first cleaned in detergent and water, then ultrasonicated in acetone and isopropyl alcohol for 15 min each. The layer of PEDOT:PSS (∼40 nm) was spin-coated at 4000 rpm onto the ITO substrates, then was baked in an oven at 120 ◦ C for 10 min. The APFO-Green5 layer was spin-coated at 760 rpm from a chloroform solution (10 g/l). The thickness of the polymer layer, measured with a Tencor AlphaStep profilometer, was 260 nm. Before the deposition of the top electrode the polymer films were annealed at 135 ◦ C for 25 min. The top Al electrode (70 nm) was thermally evaporated at a base pressure of 4 × 10−6 mbar through a shadow mask giving an active device area of 0.26 cm2 . The electrical characterization of the devices was carried out in a home-made chamber under dynamic vacuum (5 × 10−1 mbar). The device temperature was varied in the range 4–64 ◦ C, with a temperature step of 20 ◦ C. A Pt100 thermoresistor was used for the measurement of the temperature of the devices. The complex admittance was measured using a Solartron 1255 Frequency Response Analyzer equipped with a Solartron 1294 dielectric interface. The amplitude of the ac modulation voltage was 50 mV, the forward dc bias was varied in the range 0–10 V and a frequency sweep range of 1–106 Hz was used.

3. Results and discussion The devices used in this study were prepared in the sandwiched structure ITO/PEDOT:PSS/APFO-Green5/Al. The highest occupied molecular orbital and the lowest unoccupied molecular orbital levels of APFO-Green5, as determined by cyclic voltammetry, are at −5.0 eV and at −3.4 eV [7], respectively, thus PEDOT:PSS (work function 5.0–5.2 eV) is expected to form an ohmic contact for efficient hole injection, while Al (work function 4.2 eV) should act as a blocking contact for electrons under forward bias (ITO positively bias), the energy barrier for electron injection al the Al/APFOGreen5 interface being around 0.8 eV (Fig. 1). For each temperature, the conductance increased by orders of magnitudes with the dc bias, as a consequence of hole injection (not shown here). Fig. 2 shows the conductance as a function of the modulation frequency, measured on an ITO/PEDOT:PSS/APFOGreen5/Al hole-only device, for different values of temperature and at the forward bias of 6 V. As expected, conductance was also greatly enhanced by increasing the temperature, changing by more than one order of magnitude in the temperature range 4–64 ◦ C, indicating a strongly thermally activated charge carrier mobility. In the intermediate frequency range 104 –105 Hz, the conductance spectra show very small dips (Fig. 2), moving towards higher frequencies

Fig. 2. Frequency dependence of conductance for an ITO/PEDOT:PSS/APFOGreen5/Al device at different temperatures and for a dc bias of 6 V.

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Fig. 4. Square-root field dependence of the average hole mobility for an ITO/PEDOT:PSS/APFO-Green5/Al device at different temperatures. The lines represent the linear fits to the experimental data.

Fig. 3. Intermediate-frequency spectra of capacitance (a) and negative differential susceptance (b) for an ITO/PEDOT:PSS/APFO-Green5/Al device at different temperatures and for a dc bias of 6 V. In the bottom figure, the lines are shown to guide the eye.

for higher temperatures. Those dips are an indication of charge injection, indeed, in the same frequency range, the typical minima in the capacitance spectra were observed (Fig. 3a), allowing the construction of the plots of the negative differential susceptance, −B, shown in Fig. 3b for Vbias = 6 V. The average transit time of carriers was inferred from the frequencies, fmax , at which −B plots show their maxima [14]. Indeed,  tr can be evaluated from −1 the position of the maximum in −B plot through fmax = ktr , where k is an empirical coefficient. The peaks increase and shift towards higher frequencies as temperature increases, other than with increasing the dc bias (not shown here). From the average transit time of carriers, here calculated by assuming a value for k of 0.54 [15], the average mobility was obtained using the well-known expression =

d2 Etr

(1)

where E is the electric field applied to the sample and d the thickness. In the analysis of the admittance data the device built-in potential (Vbi ) has to be taken into account, given that electrodes with different work-functions were used. It is approximately equal to the difference of the work-functions and reduces the externally applied voltage. The effect of Vbi is that there exists a non-vanishing electric field in the organic layers, already for zero applied bias, which has to be overcome for the injection of carriers. So, in the case of a non-negligible built-in potential, the applied voltage Vbias must

be corrected by Vbi and, if a spatially homogeneous electric field is assumed within the device it is given by E = (Vbias − Vbi )/d. The value of the built-in potential for the ITO/PEDOT:PSS/APFOGreen5/Al structure has been already determined from the current–voltage curve recorded at room temperature. By fitting the current data to the Murgatroyd formula [16] in the space-charge limited current regime, and by assuming a value of 3 for the polymer relative permittivity, a Vbi of 0.7 V was found [17]. Given the limited range of the investigated temperatures in this study, we assume a non meaningful variation of the built-in potential, though a weak dependence of Vbi with temperature has been reported for organic devices [18]. The average hole mobility () values obtained at the considered temperatures are reported in the semi-logarithmic plot of Fig. 4 as a function of the square root of the electric field. A good linear trend of the experimental data was obtained, very common for disordered organic materials and indicating that mobility in APFOGreen5 obeys, in the investigated range of field and temperature, a Poole–Frenkel behavior [19,20] √ (E) = 0 exp(ˇ E) (2) where 0 denotes the mobility at zero field and ˇ is the parameter describing how strong is the dependence on the electric field. The data of Fig. 4 can be analyzed within the disorder formalisms for hopping transport in disordered organic solids. According to the well-known Gaussian Disorder Model (GDM) [21] for the hopping conduction of charge carriers among localized sites with a Gaussian profile of the density of states, mobility can be expressed in the following semi-empirical equation: GDM = inf exp

   2 2 −

3kT

+ C0

 2  kT

−

2 √

E

(3)

where inf is the mobility at infinity (the high-temperature limit of 0 ), k is the Boltzmann constant, T the absolute temperature, , the width of the Gaussian distribution of the energy states, a parameter describing the energetic disorder, C0 is a constant and ˙ describes the degree of positional disorder. The behavior with temperature of the zero-field mobility, obtained for each temperature from the fits of the experimental data of Fig. 4 to Eq. (2), is reported in Fig. 5, showing an exponential decreasing trend with 1/T2 , as predicted by the GDM model. The slope of the plot of 0 versus 1/T2 yielded  = 0.14 eV and its value was used to build the plot of Fig. 6a, in which the parameter ˇ is reported as a function of (/kT)2 . Again, ˇ was derived, for each temperature, from the fits of the mobility data shown in Fig. 4 to

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Table 1 Values of the charge transport parameters obtained by fitting the mobility data using the GDM and CDM models. Model

GDM CDM

Parameter inf (cm2 V−1 s−1 )

 (eV)

C0 (V cm−1 )−1/2

˙

a (nm)

0.15 0.15

0.14 0.16

4.8 × 10−4 –

3.86 –

– 4.1

on their simulations, mobility can be expressed as:



CDM = inf exp

Fig. 5. Zero-field mobility as a function of 1/T2 . The line represents the linear fits to the experimental data.

Eq. (2). According to Eq. (3), the x intercept of the plot of Fig. 6a gave ˙ = 3.86. The rather high value obtained for ˙ was expected, given the trend of the data shown in Fig. 4. Indeed, an increase of the slope of the field-dependent mobility by decreasing temperature is typical of materials with large positional disorder. The values determined for the other parameters are inf = 0.15 cm2 V−1 s−1 and C0 = 4.8 × 10−4 (V cm−1 )−1/2 . Novikok et al. proposed the so-called Correlated Gaussian Disorder Model (CDM) [22] for the description of charge transport in disordered organic materials, taking into consideration the spatial correlations between sites due to charge-dipole interactions. Based

 3 2

−

5kT

+ 0.78

 3/2  kT



−2

qaE 

(4)

where q is the electronic charge and a the inter-site spacing. The main difference between Eqs. (3) and (4) is the different temperatures dependence of parameter ˇ, apart a slightly higher values for the energetic disorder , with respect to the GDM model (0.16 eV was calculated for  from the fit of data of Fig. 5 to Eq. (4)). The values of ˇ were plotted against (/kT)3/2 (Fig. 6b) and an extremely high value for the average site separation, a = 4.1 nm, was extracted from the linear fit according to Eq. (4). This could indicate that the CDM model is less appropriate to describe the field- and temperature-dependent mobility of APFO-Green5 thin films. The values of the charge transport parameters obtained by fitting the mobility data using the GDM and CDM models are summarized in Table 1. All the parameters are rather high, justifying the moderate transport properties of the investigated polymer films. 4. Conclusions The electric field dependence of hole mobility in thin films of APFO-Green5 has been investigated with temperature by admittance spectroscopy. Mobilities of the order of 10−6 –10−5 cm2 V−1 s−1 were calculated at room temperature from the peak positions of the negative differential susceptance. Transport of positive charges carriers is strongly field and thermally activated. In the investigated field range, the mobility is enhanced by roughly one order of magnitude by increasing the temperature from 4 ◦ C to 64 ◦ C. Using the GDM formalism, a value of 0.14 eV was found for the with of the Gaussian distribution of energy states and 3.86 for the positional disorder. The parameters extracted by fitting the mobility data according to the disorder formalism indicate that charge transport in spin-coated thin films of APFO-Green5 is greatly affected by high energetic and positional disorder, justifying the moderate mobility values. Acknowledgements S.E. Debebe acknowledges the “Programme for Training and Research in Italian Laboratories (TRIL)”, The Abdus Salam International Centre for Theoretical Physics (ICTP), for financial support (budget code 421.FITU.21.G). This work was partially supported by ENI S.p.A. References

Fig. 6. Poole–Frenkel ˇ parameter as a function of: (a) (/kT)2 and (b) (/kT)3/2 . The lines represent the linear fits to the experimental data.

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