Impedance spectroscopy for high resolution ...

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Jun 14, 2013 - chose TFB as an organic semiconductor is that TFB has a structured localized-state distribution and is a good example for the present purpose.
Thin Solid Films 554 (2014) 218–221

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Impedance spectroscopy for high resolution measurements of energetic distributions of localized states in organic semiconductors Hiroyuki Hase, Takayuki Okachi, Shingo Ishihara, Takashi Nagase, Takashi Kobayashi, Hiroyoshi Naito ⁎ Department of Physics and Electronics, Osaka Prefecture University, Osaka, Japan

a r t i c l e

i n f o

Available online 14 June 2013 Keywords: Impedance spectroscopy Organic semiconductor Localized states Polyfluorene derivative

a b s t r a c t A method has been proposed for the determination of energetic distributions of localized states in organic semiconductors by the analysis of the impedance spectra (T. Okachi, T. Nagase, T. Kobayashi, and H. Naito, Appl. Phys. Lett. 94 (2009) 043301). High energetic resolution of the method is demonstrated experimentally in organic semiconductor diodes using a polyfluorene derivative, poly(9,9-dioctyl-fluorene-co-N-(4-butylphenyl)diphenylamine), by detecting a structured localized-state distribution. The method is a powerful tool for the determination of energetic distributions of localized states with high energetic resolution in organic thin film devices such as organic light-emitting diodes and organic solar cells. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Detailed information on localized-state distributions has been required for understanding electronic properties of organic semiconductors and for optimizing performance of organic devices such as organic light-emitting diodes (OLEDs) and organic solar cells. Impedance spectroscopy (IS) has been proven to be a powerful technique for studying relaxation and transport in various electronic devices based on organic materials [1–13]. IS measurements enable us to determine equivalent circuits of devices and physical quantities governing OLED operation, such as charge-carrier mobility and recombination lifetime. In this paper, we experimentally examine the differences between two analytical expressions relating an impedance spectrum to a localizedstate distribution that we have reported [11], and show that high energetic resolution measurements in organic semiconductors are possible using the analytical expression including differentiation with respect to frequency [11]. For the demonstration of high resolution measurements, we fabricated organic diodes using a light emitting polymer, poly(9,9-dioctyl-fluorene-co-N-(4-butylphenyl)-diphenylamine) (TFB) [14] whose chemical structure is shown in Fig. 1. The reason that we chose TFB as an organic semiconductor is that TFB has a structured localized-state distribution and is a good example for the present purpose. 2. Theoretical background The theoretical basis of IS measurements for determining localizedstate distributions is a single-injection space-charge-limited current

⁎ Corresponding author. Tel./fax: +81 72 254 9266. E-mail address: [email protected] (H. Naito). 0040-6090/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tsf.2013.05.159

(SCLC). In order to determine localized-state distributions below the conduction band and above the valence band separately in an organic semiconductor, IS measurements should be applied to both electrononly devices and hole-only devices (HODs). We consider hole transport in the following, but the same results can be obtained for electron transport. The impedance of single injection SCLC diodes in the presence of a localized-state distribution is represented by the expression [15] Z ¼ 6ψRi

 k 1 Γ ðψ þ 1Þ ψ k ð−iΩÞ ; k þ 3 Γ ð ψ þ k þ 2 Þ δ k¼0

∞ X

ð1Þ

where Γ is the Euler gamma function, Ω (=ωtt) is the transit angle, ω is the angular frequency, tt [=(4d2) / (3μ0Vdc)] [16] is the transit time of charge carriers in the absence of localized states, μ0 is the microscopic mobility of charge carriers, and Vdc is the applied dc voltage. Here, Ri is the low-frequency incremental resistance of the diode, which is given by 3

Ri ¼

4 d ; 9 εδμ 0 V dc S

ð2Þ

where ε is the dielectric constant of the semiconductor, S is the active area, and d is the thickness of an organic semiconductor. The trapping parameters δ and Ψ are respectively given by δ¼

 −1 E γ ðEÞ 1 þ ∫Ecv c dE ; γt ðEÞ

ψðωÞ ¼

 E 1 þ ∫Ecv

 γ c ðEÞ dE δ; γ t ðEÞ þ iω

ð3Þ

ð4Þ

H. Hase et al. / Thin Solid Films 554 (2014) 218–221

219

From Eqs. (6), (7), and (12), the localized-state distribution can be written as

Nt ðE0 Þ ¼

  2ω 2Ri GðωÞ−1 −δ : 2 2 St vth δkTπ ð2Ri ωC ðωÞÞ þ ð2Ri GðωÞ−1Þ

ð15Þ

Similarly, from Eqs. (6), (7), and (13), the localized-state distribution can also be written as Fig. 1. Chemical structure of poly(9,9-dioctyl-fluorene-co-N-(4-butylphenyl)-diphenylamine) (TFB).

where γt(E) [=νexp{−( E − Ev) / kT}] is the release rate from the localized state located at the energy E, γc(E)dE [≅Nt(E)St(E)vthdE] is the capture rate of the localized state at the energy E, and kT is the thermal energy. Here, Ec is the conduction-band mobility edge, Ev is the valence-band mobility edge, ν [=NvSt(E)vth] is the attempt-to-escape frequency, Nt(E) is the energetic distribution of the localized-state density, Nv is the effective density of states in the valence band, St(E) is the capture cross-section, and vth is the hole thermal velocity. At sufficiently low frequencies (Ω ≪ 1), the first term in Eq. (1) is dominant, thus the impedance of the diode becomes [17] Z ¼ Ri

2ψ : 1þψ

ð5Þ

As a result, the conductance and the capacitance [1/Z = G + iωC, Ψ = (1 + A − iB)δ] in the low frequency region are respectively given by GðωÞ ¼

  1 1þA −δ ; 2 2 2Ri δ ð1 þ AÞ þ B

ð6Þ

C ðωÞ ¼

1 B : 2Ri δω ð1 þ AÞ2 þ B2

ð7Þ

In Eqs. (6) and (7), A and B are defined by E

A ¼ ∫Ecv Nt ðEÞSt vth hA ðω; EÞdE; E

B ¼ ω∫Ecv N t ðEÞSt vth hB ðω; EÞdE;

ð8Þ ð9Þ

where hA ðω; EÞ ¼

γt ðEÞ ; γt ðEÞ2 þ ω2

hB ðω; EÞ ¼

γ t ðEÞ γ t ðEÞ2 þ ω2

ð10Þ !2 ð11Þ

These functions, hA(ω,E) and hB(ω,E), can be approximated by a delta function, thus we have kTπ A ¼ Nt ðE0 ÞSt vth ; 2ω

ð12Þ

∂ωB kT ¼ N t ðE0 ÞSt vth ; ω ∂ω

ð13Þ

where E0 −Ev ¼ kT lnðν=ωÞ:

ð14Þ

Nt ðE0 Þ ¼

( ) 2Ri ω ∂ ω2 C ðωÞ : St vth δkT ∂ω ð2Ri ωC ðωÞÞ2 þ ð2Ri GðωÞ−1Þ2

ð16Þ

Thus, the localized-state distributions in SCLC diodes can be determined from the frequency dependences of conductance and capacitance using Eqs. (14) and (15) or Eqs. (14) and (16) [11]. In the case of determining localized-state distributions using Eq. (16), the numerical differentiation with respect to ω is necessary and the analysis using Eq. (16) is slightly time-consuming than that using Eq. (15). Localized-state distributions are obtained by plotting Eq. (16) or Eq. (15) as a function of the logarithmic function of ω, which can be converted into the energy axis using Eq. (14) with the value of ν. In general, the value of ν can be determined by measuring the temperature dependence ofγt(E) at a structured localized state. The numerical calculation using Eq. (1) shows that the calculated localized-state distributions by Eqs. (15) and (16) are respectively spread out by 2.64kT and 1.76kT in full width at half maximum of the distributions in the case of a discrete localized state. The broadening is a result of the delta-function approximations mentioned above and the narrower width of the distribution calculated by Eq. (16) is an indication of higher energetic resolution of Eq. (16) [11]. 3. Experiment To demonstrate high energy resolution of Eq. (16) in the measurement of localized-state distribution, we fabricated TFB SCLC diodes. The sample structure was ITO/PEDOT:PSS/TFB/Au (HOD), where ITO is indium-tin-oxide and PEDOT:PSS is poly(3,4-ethylenedioxythiophene)/ polystyrenesulphonic acid. The HOD was prepared according to the following procedure: The ITO-coated glass substrate was first cleaned with detergent, ultrasonicated in acetone and isopropyl alcohol, and dried in vacuum. PEDOT:PSS (Baytron P) was deposited by spin coating from aqueous solution, and the substrate was dried in air. TFB was deposited by spin coating from a xylene solution to film thickness of ~450 nm on the surface of the PEDOT:PSS layer, and then moved into a glove-box and dried for 120 min at 100 °C in vacuum. Subsequently, the HOD was pumped down in vacuum, and a ~50-nm thick Au film was deposited on the surface of the TFB layer. After the fabrication of the HOD, the devices were encapsulated without exposing them to air. The active area of the HOD was 2 × 2 mm2. IS measurements were carried out using a Solartron 1260 impedance analyzer with a 1296 dielectric interface in the frequency sweep range from 100 mHz to 10 MHz at different measurement temperatures. 4. Results Fig. 2(a) and (b) show the frequency dependences of capacitance and conductance of the HOD at different measurement temperatures obtained by spectroscopic impedance measurements, respectively. The increase in capacitance and the decrease in conductance with decreasing frequency have been observed in Fig. 2(a) and (b), respectively. Those frequency dependences are due to the presence of distributed localized states [10]. The increase in capacitance similar to Fig. 2(a) has been observed in organic SCLC diodes based on such as

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Fig. 4. Arrhenius plot of γt(E) versus 1/T. The value of γt(E) is equal to ω at the bump of the localized-state distribution in Fig. 3, and the value of ν is determined to be 1012 Hz.

Fig. 2. Frequency dependences of (a) capacitance and (b) conductance of TFB HOD by IS with different measurement temperatures.

polyfluorene derivatives, poly(p-phenylene vinylene) derivatives, tris (8-hydroxyquinolinato)aluminum and 4,4′,4″-tris[N,-(3-methylphenyl)N-phenylamino]-triphenylamine [1,2,4,10,11,13]. The localized-state distributions above Ev calculated from the frequency dependences of capacitance and conductance of HOD shown in Fig. 2 at different measurement temperatures from 293 K to 338 K using Eqs. (14) and (15), and Eqs. (14) and (16) are shown in Fig. 3. We assumed here that St is independent of the energy, and the value of ν is determined by recording localized-state distributions at different temperatures and then by analyzing the Arrhenius plot of γt(E) versus 1/T in Fig. 4. The value of γt(E) is equal to ω at the bump in the localized-state distribution, and ω, henceγt(E), at the bump is dependent on temperature as shown in Fig. 4. The value of ν is determined to be 1012 Hz according to γt(E) = νexp{−( E − Ev) / kT}. We observe an exponential distribution of localized states,

from the analysis using Eq. (15) in the whole energy range, where N0 is the density of localized states at Ev, and T0 is the characteristic temperature. The value of T0 is 378 K. On the other hand, we observe a structured distribution of localized states, a Gaussian distribution superimposed on a continuously decaying distribution of localized states, from the analysis using Eq. (16). The Gaussian bump in the localized-state distribution in TFB appears at 0.7 eV above Ev. The structured distribution can be approximated to be an exponential distribution in the energy range between 0.47 eV and 0.55 eV and its characteristic temperature is 233 K. We find from the numerical calculation that the characteristic temperature of T/2 can be resolved using Eq. (16) at the measurement temperature of T. We note here that such a structured distribution revealed by Eq. (16) cannot be resolved by Eq. (15). We also note that the frequency corresponding to 1/tt should be located at a high frequency in order to observe a wider energetic range of localized-state distributions. This is so because Eqs. (15) and (16) are valid for Ω ≪ 1 (ω ≪ 1/tt) as mentioned above. In Fig. 2, 1/tt is located at about 104 Hz [11] and hence a relatively wide range of localized states can be mapped out as shown in Fig. 3. For this reason, one should adjust the location of 1/tt at a high frequency (for instance, 104–106 Hz in the present case) by tuning Vdc and d to observe a wide range of localized-state distribution through the analysis of the frequency dependences of conductance and capacitance using Eqs. (15) or (16). 5. Discussion

  E−Ev ; Nt ðEÞ ¼ N 0 exp − kT 0

ð17Þ

Eq. (15)

Eq. (16)

Fig. 3. Localized-state distributions from the valence-band mobility edge in TFB determined from the capacitance and conductance data in Fig. 2 using Eqs. (14) and (15), and Eqs. (14) and (16).

We carry out computer simulation to confirm high energetic resolution of localized-state distributions determined by Eq. (16). We assumed a Gaussian distribution superimposed on an exponential distribution as a structured distribution similar to the distribution in Fig. 3 and as shown in the solid line in Fig. 5. The frequency dependences of conductance and capacitance were calculated from Eq. (1) for the distribution (the solid line in Fig. 5) as the input distribution, and the localized-state distributions determined by Eqs. (15) and (16) are compared to the input distribution. The following physical quantities appropriate for disordered organic semiconductors were used in the calculation: Nv = 1020 cm−3 and Stvth = 10−8 cm3/s [18,19]. All calculations were carried out at T = 300 K, d = 450 nm, S = 4 mm2, Vdc = 10 V, and μ0 = 10−3 cm2/Vs. Fig. 5 shows the localized-state distributions determined from the calculated capacitance and conductance data using Eqs. (14) and (15), and Eqs. (14) and (16). It can be seen that the input localizedstate distribution is not reconstructed correctly when we analyze the data using Eq. (15) (the localized state-distribution determined using Eq. (15) is a single exponential distribution). On the contrary, Eq. (16) can accurately reconstruct the input distribution. We note

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has been observed by the analysis using Eq. (16) while an exponential distribution of localized states is deduced from the analysis using Eq. (15). Numerical simulation confirms that the structured distribution obtained by Eq. (16) reflects the true distribution of localized states in TFB. We show that the energetic resolution of Eq. (16) is higher than that of Eq. (15) by probing structures in the localized-state distribution of TFB and thus Eq. (16) is suitable to probe localized-state distribution on which fine structures are superimposed. Acknowledgments

Fig. 5. Localized-state distributions from the valence-band mobility edge calculated from computer-generated capacitance and conductance data using Eqs. (14) and (15), and Eqs. (14) and (16). The capacitance and the conductance data are calculated from Eq. (1) using the solid line as the input distribution of localized states.

from these results that the structured distribution obtained using Eq. (16) in Fig. 3 reflects the true distribution of localized states in TFB. We stress that higher energetic resolution of Eq. (16) can be shown both experimentally and numerically in comparison with that of Eq. (15). The control of localized-state distribution is an extremely important issue and to do this, we should study the origins of localized states in organic semiconductors. In general, localized states originate in intrinsic contribution (e.g., structural randomness and defects) and in extrinsic contribution (e.g., impurities from organic solvent). Unfortunately, the origin of the structured distribution in Fig. 3 is not known and is beyond the scope of the present paper. However, influence of purification and thermal annealing on the localized-state distribution in TFB would give us clues for origins of the distribution. 6. Conclusions Two analytical expressions, Eqs. (15) and (16), relating impedance spectrum to a localized-state distribution have been derived on the basis of a single-injection SCLC model. We have determined the localized-state distribution in TFB by IS measurements to demonstrate higher energetic resolution of Eq. (16). Continuously decaying localized-state distribution with the bump at 0.7 eV above Ev in TFB

This research is granted by the Japan Society for the Promotion of Science (JSPS) through the “Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program)” initiated by the Council for Science and Technology Policy (CSTP). This research is partly supported by a Grant-in-Aid for Scientific Research (B) (No. 23360140) and by a Grant-in-Aid for Scientific Research on Innovative Areas “New Polymeric Materials Based on Element-Blocks (No. 2401)” (No. 24102011) of the Ministry of Education, Culture, Sports, Science, and Technology, Japan. References [1] H.C.F. Martens, J.N. Huiberts, P.W.M. Blom, Appl. Phys. Lett. 77 (2000) 1852. [2] S. Berleb, W. Brutting, Phys. Rev. Lett. 89 (2002) 286601. [3] H. Azuma, T. Okachi, N. Watanabe, T. Kobayashi, H. Naito, Proc. 12th Int. Display Workshops in Conjunction with Asia Display, 2005, p. 757. [4] D. Poplavskyy, F. So, J. Appl. Phys. 99 (2006) 033707. [5] T. Okachi, H. Azuma, T. Nagase, T. Kobayashi, H. Naito, Proc. 13th Int. Display Workshops, 2006, p. 1323. [6] S.W. Tsang, S.K. So, J.B. Xu, J. Appl. Phys. 99 (2006) 013706. [7] T. Okachi, T. Nagase, T. Kobayashi, H. Naito, Proc. 14th Int. Display Workshops, 2007, p. 1129. [8] T. Okachi, T. Nagase, T. Kobayashi, H. Naito, Thin Solid Films 517 (2008) 1327. [9] T. Okachi, T. Nagase, T. Kobayashi, H. Naito, Thin Solid Films 517 (2008) 1331. [10] T. Okachi, T. Nagase, T. Kobayashi, H. Naito, Jpn. J. Appl. Phys. 47 (2008) 8965. [11] T. Okachi, T. Nagase, T. Kobayashi, H. Naito, Appl. Phys. Lett. 94 (2009) 043301. [12] S. Ishihara, T. Okachi, H. Naito, Thin Solid Films 518 (2009) 452. [13] S. Ishihara, H. Hase, T. Okachi, H. Naito, J. Appl. Phys. 110 (2011) 036104. [14] H. Takahashi, H. Naito, Thin Solid Films 477 (2005) 53. [15] D. Dascalu, Int. J. Electron. 21 (1966) 183. [16] M.A. Lampert, P. Mark, Current Injection in Solids, Academic, New York, 1970. [17] D. Dascalu, Solid State Electron. 11 (1961) 491. [18] M. Pope, C.E. Swenberg, Electronic Processes in Organic Crystals and Polymers, Oxford University Press, New York, 1999. 616. [19] T. Nagase, K. Kishimoto, H. Naito, J. Appl. Phys. 86 (1999) 5026.