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Physica B 388 (2007) 118–123 www.elsevier.com/locate/physb

Impedance spectroscopy study of an organic semiconductor: Alizarin K.P. Chandraa,1, K. Prasadb,, R.N. Guptaa a

Department of Physics, D.D.U. Gorakhpur University, Gorakhpur 273 009, India University Department of Physics, T.M. Bhagalpur University, Bhagalpur 812 007, India

b

Received 19 December 2005; received in revised form 2 April 2006; accepted 11 May 2006

Abstract The electrical properties of alizarin, a p-conjugated organic semiconductor, were investigated by the complex impedance spectroscopy technique. A transition from semiconducting to conducting state has been observed and the transition temperature shifts to higher side with the increment in frequency. The dielectric relaxation was found to be of non-Debye type (polydispersive). Evidences of temperaturedependent electrical relaxation phenomena as well as negative temperature coefﬁcient of resistance (NTCR) character of the sample have also been observed. The AC conductivity obeys the power law and the dispersion in conductivity was observed in the lower frequency region. Also, the frequency-dependent AC conductivity at different temperatures indicated that the conduction process is thermally activated process. The activation energy, density of states at Fermi level and number of p-electrons per molecule has been estimated from AC conductivity–temperature data and was found, respectively, to be 0.78 eV, 1.2 1019 cm3 eV1 and 25. Modulus analysis has indicated the possibility of hopping mechanism for electrical transport processes in the system with non-exponential-type conductivity relaxation. r 2006 Elsevier B.V. All rights reserved. PACS: 72.80.Le; 77.22.Gm; 81.05.Hd Keywords: Alizarin; Organic semiconductor; Impedance; Electrical conductivity; Dielectric relaxation

1. Introduction Organic semiconductors (OSCs) have come into the prominence due to its entirely new scientiﬁc concepts and prospects for their use in molecular electronics [1]. They are promising candidate for light emitting diodes, ﬁeld effect transistors, future ﬂat panel display, etc. [2–5]. OSCs are considered to have an extended p-electron system which can be changed from a semiconducting state to a conducting state. The electrical charge transport in OSCs is of current interest as they follow different aspects of conduction mechanism. Also, they have capability to support electronic conduction. Further the p-electron cannot move according to the rapidly varying externally applied electric ﬁeld. At higher frequencies, the charge Corresponding author. Tel./fax: +91 641 2501699.

E-mail address: [email protected] (K. Prasad). Permanent address: Department of Physics, S.M. College (T.M. Bhagalpur University), Bhagalpur 812 001, India. 1

0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.05.010

carriers become localized in small regions of low energy barrier [6]. Therefore, complex impedance spectroscopy technique is considered to be an appropriate and effective tool to understand the charge transport and conduction mechanism in OSCs. The charge transport can be due to the charge displacement, dipole reorientation (charge hopping) and space charge formation. [7]. Charge transport process causes a number of different polarization mechanisms that results frequency dispersion or dielectric relaxation in the materials under an AC ﬁeld [8]. Besides, small signal impedance measurement provides valuable physical parameters of dielectric relaxation [9]. In this work, AC electrical response of p-conjugated OSC alizarin has been investigated. The conduction mechanism and dielectric relaxation have been evaluated. 2. Experimental The AR grade alizarin, whose molecular structure has been shown in Fig. 1, was obtained from NBS Biologicals,

ARTICLE IN PRESS K.P. Chandra et al. / Physica B 388 (2007) 118–123

OH

8

OH

30°C 40°C 50°C 60°C 70°C 80°C 90°C 100°C 110°C

7 6

Fig. 1. Molecular structure of alizarin.

England and was pressed into a circular disc-shaped pellets (diameter 10 mm and thickness 1.58 mm) under a uniaxial stress of 5 MPa. The pellets were then heated at 150 1C for 2 h. The electrical measurements were carried out on a symmetrical cell of type Ag|Alizarin|Ag, where Ag is a conductive paint coated on either side of the pellet. Electrical impedance (Z), phase angle (y), loss tangent (tan d) and capacitance (C) were measured as a function of frequency (0.1 kHz–1 MHz) at different temperatures (30–110 1C) using a computer-controlled LCR Hi-Tester (HIOKI 3532-50, Japan).

2.0

1kHz 1.6 1.2 0.8 0.4 20

40 60 80 100 120 Temperature (°C)

3 2 1 0 0.1

1

10 100 Frequency (kHz)

1000

Fig. 2. Frequency dependence of real part of impedance of alizarin at different temperatures. Inset: variation of Re(Z) with temperature at 1 kHz.

3. Results and discussion

4.0 3.5 3.0 Im(Z) (MΩ)

Data from complex impedance spectroscopy can be analysed using four different complex formalisms [7], each of which consists of real as well as imaginary components viz., complex impedance, Z ðoÞ ¼ Z 0 jZ 00 ¼ Rs j=oC s ; complex admittance, Y ðoÞ ¼ Y 0 jY 00 ¼ 1=Rp þ joC p ; complex permittivity, ðoÞ ¼ 0 j00 and complex modulus, M ðoÞ ¼ M 0 þ jM 00 . These formalisms are interrelated as M ¼ 1= ¼ joC 0 Z ¼ joC 0 ð1=Y Þ and the loss tangent, tan d ¼ Z 0 =Z 00 ¼ 00 =0 ¼ M 00 =M 0 , where Rs, Cs are the series resistance and capacitance; Rp, Cp are the parallel resistance and capacitance. Here, primed and double primed parameters denote, respectively, the real and imaginary components; o ¼ 2pf , f is the appliedpﬃﬃﬃﬃﬃﬃ fre-ﬃ quency; C0 is the empty cell capacitance and j ¼ 1. These data can also be presented as a complex plain plot, i.e., the imaginary versus real component with variable frequency or as a spectroscopic plot, i.e., real and/or imaginary components as a function of logf. Fig. 2 shows the variation of the real part of impedance (Z0 ) with frequency at several temperatures. It is observed that the magnitude of Z0 decreases on increasing frequency. Inset Fig. 2 displays that the value of Z0 decreases with temperature up to 80 1C in the semiconducting region and afterwards it increases (conducting region). The Z0 values for all temperatures merge above 50 kHz. The curves also display an increase in AC conductivity with the increase in temperature (up to 80 1C) and frequency. This result may be related to the release of space charge as a result of reduction in the barrier properties of material with the rise in temperature and may be a responsible factor for the enhancement of AC conductivity of material with temperature at higher frequencies. Further, the Z0 values

4

Im(Z) (MΩ) Ω)

O

Re(Z) (MΩ)

5

2.4

Re(Z) (MΩ) Ω)

O

119

3.0

30°C

2.5

40°C 50°C

1kHz

2.0

60°C

1.5

70°C

1.0

80°C

0.5

2.5

0.0 20

2.0

90°C 40

60 80 100 Temperature (°C)

120

100°C 110°C

1.5 1.0 0.5 0.0 0.1

1

10 100 Frequency (kHz)

1000

Fig. 3. Frequency dependence of imaginary part of impedance of alizarin at different temperatures. Inset: variation of Im(Z) with temperature at 1 kHz.

decrease with rise in temperature show negative temperature coefﬁcient of resistance (NTCR) type behaviour of alizarin. Fig. 3 shows the variation of the imaginary part of impedance (Z00 ) with frequency at different temperatures as loss spectrum. The loss spectrum is characterized by some important features in the pattern, such as (i) a decrease in Z00 without any peak in the investigated frequency range at high temperatures (X60 1C), (ii) appearance of small peak (Z00 max) in the loss spectrum, (iii) asymmetric peak broadening and (iv) the values of Z00 max decrease and shift to higher frequencies with the increasing temperature. The

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120

temperatures, suggesting the dielectric relaxation to be of polydispersive non-Debye type. This may happen due to the presence of distributed elements in the material– electrode system [7] that results in the deviation from the pure semicircle in complex impedance plots. Further, the curves do not coincide with the origin and hence there should be a series resistance for the LCR circuit representation of the sample (inset Fig. 4). The value of Rb could directly be obtained from the intercept of semicircle on the Z0 -axis. The capacitance (Cb) can be estimated using the relation

8 8 0.20

Im(Z) (MΩ)

Rb (MΩ)

6

Cb

4

Rb

2

5

CS

0.15 0.10

Cb

0.05

0

4

RS Cb (nF)

7 6

Rb

0.00

20

40 60 80 100 Temperature (°C)

3

30°C 50°C 100°C

1 0

omax tb ¼ 2pf max Rb C b ¼ 1,

ωοτb=1

2

0

1

2

3

4 5 Re(Z) (MΩ)

6

7

8

Fig. 4. Complex impedance plots of alizarin at different temperatures. Inset 1: variation of bulk resistance and bulk capacitance with temperature. Inset 2: appropriate LCR circuit.

asymmetric broadening of peaks in frequency explicit plots of Z00 suggests that there is a spread of relaxation times i.e., the existence of a temperature-dependent electrical relaxation phenomenon in the material [10]. The spreading is indicated by the width of the curves. The merger of Z00 values in the high-frequency region may possibly be an indication of the accumulation of space charge in the material. Fig. 4 shows the complex impedance spectrum (Nyquist plot) of alizarin measured at different temperatures. It is observed that with the increase in temperature the slope of the lines decreases and they bent towards real (Z0 ) axis. It can be also seen from this ﬁgure that the complex impedance data are represented by depressed semicircle (i.e., centres of semicircle lie below the abscissa axis) and at lower frequencies the values increases. The Debye’s expression is modiﬁed in such situation by introducing a factor n. This modiﬁcation leads to the Cole– Cole empirical behaviour described by the following equation [11]: Z ¼

R , 1 þ ð jo=o0 Þ1n

(1)

where n represents the magnitude of the departure of the electrical response from an ideal condition and can be determined from the location of the centre of the Cole–Cole circles. This equation shows that the centre of the semicircle obtained by data plotting in the complex plane is located below the real axis indicates the polydispersive non-Debye-type dielectric relaxation. When n goes to zero {i.e. (1n) - 1}, Eq. (1) reduces to the classical Debye’s formalism where centre of the semicircle should lie on the real Z0 -axis. Least squares ﬁtting to the complex impedance data give the value of n40 at all the

(2)

where fmax is the frequency at maxima of the semicircle. The value of mean relaxation time of bulk (tb) was obtained from complex impedance plots at different temperatures and was found to increase with increasing temperature. The value of tb at room temperature was found to be 1.87 104 s. The variation of Rb and Cb with temperature is shown in inset Fig. 4. It is observed that the value of Rb decreases while Cb increases with the rise of temperature. The decrease in the value of Rb of alizarin associated with an increase in conductivity with the rise in temperature clearly indicates the NTCR character of the alizarin. The bulk DC conductivity was calculated using the formula sDC ¼ l=A:Rb and the activation energy ( ¼ 0.61 eV) was estimated from the variation of sDC as a function of temperature (103/T) using the relation [12]: sDC ¼ s0 exp(Ea/2kBT) where Ea is the activation energy of conduction, kB is the Boltzmann constant and T is the absolute temperature. The low value of activation energy may be due to the carrier transport through hopping between localized states in disordered manner. These localized states may be the clusters of impurity ions and/or structural defects. Further, it can be noticed that the impedance data are not forming two complete semicircles. The equivalent circuit to this can be approximated by a parallel arrangement of Rb and Cb in series with Cs (inset Fig. 4). This indicates that Ag|Alizarin|Ag structure behaves as non-ideal at these temperatures and the deviation from the ideality occurs probably due to the rough Ag–alizarin interface. Frequency dependence of real (e0 ) and imaginary (e00 ) parts of dielectric constant at several temperatures are shown, respectively in Fig. 5a and b. Both e0 and e00 follow inverse dependence on frequency. The room temperature values of e0 and e00 at 1 kHz were found, respectively, to be 51 and 59. Further, both the pattern presents the dispersion in the lower frequency region while they merge above 50 kHz. Inset Fig. 5a and b shows, respectively, the variation of e0 and e00 with temperature at 1kHz and 1 MHz. It can be seen that the values of both e0 and e00 increases up to certain temperature and then decreases. Also, the transition temperature shifts to higher side with the increment in frequency. The gradual fall in the values of both e0 and e00 with temperature may possibly be due to the electrical conductivity of the materials that modiﬁes the value of the capacitance as the temperature increases.

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600

1 kHz

0.015

8 6 4 2 0

1 MHz

20

30°C 50°C 100°C

20

40 60 80 100 Temperature (°C)

120

Electric Modulus

Re(ε)

800

x10-3

250 200 150 100 50

Im(M)

1000

0.020

Re(ε)

30°C 40°C 50°C 60°C 70°C 80°C 90°C 100°C 110°C

1200

121

15

Re(M)

10

Im(M)

5 0

0.010

0.1

400

1 10 100 Frequency (kHz)

1000

0.005 200 0

0.000 0.1

1

(a)

10 100 Frequency (kHz)

1000

600

Im(ε)

500 400

180

90

1 kHz

60 54

1 MHz

52 20

40 60 80 100 Temperature (°C)

120

200 100 0 (b)

0.1

1

0.015

0.020

120

50

300

0.010 Re(M)

150

Im(ε)

30°C 40°C 50°C 60°C 70°C 80°C 90°C 100°C 110°C

0.005

Fig. 6. Complex electric modulus plots of alizarin at different temperatures. Inset: variation of Re(M) and Im(M) with frequency at various temperatures.

800 700

0.000

10 100 Frequency (kHz)

1000

Fig. 5. Frequency dependence (a) of real part of permittivity of alizarin at different temperatures, inset: Variation of Re(e) with temperature at 1 kHz and 1 MHz. (b) imaginary part of permittivity of alizarin at different temperatures, inset: variation of Im(e) with temperature at 1 kHz and 1 MHz.

Fig. 6 shows the complex electric modulus spectrum of the sample at different temperatures. The pattern is characterized by the presence of little asymmetric depressed semicircular arcs whose centre does not lie on M0 -axis. This supports the polydispersive non-Debye dielectric relaxation in the compound. Besides, the appearance of peak in modulus spectrum provides a clear indication of conductivity relaxation. The behaviour of modulus spectrum is suggestive of the temperature-dependent hopping type of mechanism for electric conduction (charge transport) in the system. It is known that in disordered materials, more than one relaxation process is present. This fact is applicable to the present system as it is clear form Figs. 4 and 6 which present the polydispersive nature, i.e., the centre of the semicircles lie below the real axis, indicating the presence of more than one relaxation processes. The peak frequency of the pattern gives an estimate of conduction relaxation time

(ts) in accordance with the relaxation omax ts ¼ 1. A linear least squares ﬁtting to the ts–T data, as obtained from the modulus spectrum, to the relation ts ¼ ts0 expðDE m = kB TÞ given the value of activation energy to be 0.37 eV. Inset Fig. 6 shows the variation of real (M0 ) and imaginary (M00 ) parts of electric modulus as a function of frequency over a range of temperature. It is characterized by very low value (zero) of M0 in the low-frequency region, a continuous dispersion with the increase in frequency having a tendency to saturate at a maximum asymptotic value designated as MN in the high-frequency region for all temperatures. Such observations may possibly be related to a lack of restoring force governing the mobility of charge carriers under the action of an induced electric ﬁeld. This behaviour supports long-range mobility of charge carriers. Further, a sigmoidal increase in the value of M0 with the frequency approaching ultimately to MN, may be attributed to the conduction phenomena due to short-range mobility of carriers (speciﬁcally p-electrons). The variation M00 as a function of frequency over a range of temperature is characterized by: (i) clearly resolved peaks in the pattern appearing at unique frequency at different temperatures, (ii) signiﬁcant asymmetry in the peak with their positions lying in the dispersion region of M0 versus frequency pattern and (iii) the peak positions have a tendency to shift towards higher frequency side with the rise in temperature. The low-frequency side of the M00 peak represents the range of frequencies in which charge carriers can move over a long distance, i.e., charge carriers can perform successful hopping from one site to the neighbouring site. The highfrequency side of the M00 peak represents the range of frequencies in which the charge carriers are spatially conﬁned to their potential wells and thus could be make localized motion within the well. The region where peak occurs is an indicative of the transition from long-range to short-range mobility with increase in frequency.

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-5.7

1.0

1.0

30°C 50°C 100°C

//

0.4

-5.8

10-2

0.2

0.6

10-3

0.0

50°C

0.01 0.1

1 10 100 1000 f /fmax

0.4

0.2

σ (S/m)

Scaled parameter

0.8

0.6

//

M /Mmax

0.8

lnσ (S/m)

122

1 MHz

-5.9 -6.0 -11

1 kHz

-12 2.4

2.6

2.8

3.0

3.2

3.4

1000/T (K-1)

10-4

10-5 tanδ/tanδmax

0.0

// M///Mmax

0.1

1

10 100 Frequency (kHz)

10-6

1000

0.1

1

10 100 Frequency (kHz)

30°C 40°C 50°C 60°C 70°C 80°C 90°C 100°C 110°C

1000

Fig. 7. Normalized tan d, normalized Im(M) as a function of frequency for alizarin at 50 1C. Inset: Scaling behaviour of Im(M) at various temperatures for alizarin.

Fig. 8. Variation of AC conductivity of alizarin with frequency at different temperatures. Inset: temperature dependence of AC conductivity of alizarin at 1 kHz and 1 MHz.

Fig. 7 shows the variation of scaled parameters (M00 /M00 max and tan d/tan dmax) with frequency at 50 1C. It can be seen that the peaks are not occurring at the same frequency (f tan d of M 0 ). The magnitude of mismatch between the peaks of both parameters represents a change in the apparent polarization. The overlapping of peaks is an evidence of long-range conductivity, whereas the difference is an indicative of short-range conductivity (via hopping type of mechanism) [13]. If M00 (o,T) data are plotted in scaled coordinates, i.e., M00 /M00 max versus log(f/fmax), where fmax corresponds to the peak frequency of the M00 versus logf plots, the entire M00 -data can be coalesced into one master curve, as shown in the inset Fig. 7. The value of full-width at half-maximum (FWHM) is found to be 41.14 decades. These observations indicate that the distribution function for relaxation times is nearly temperature independent with non-exponential conductivity relaxation. This phenomenon is well-deﬁned by a nonDebye-type (polydispersive) relaxation governed by the relation

onset at every temperature and the onset frequency shifts towards higher side with the rise in temperature. Further, the plots show two different straight lines (regions I and II) with positive slopes indicating that sAC increases with frequency. The total AC conductivity of the compound can be written as sAC ¼ sI ðoÞ þ sII ðoÞ. These are due to two different conduction mechanisms, described by sI (prevailing in region I) and sII (prevailing in region II). The frequency variation of sAC involves a power exponent (sAC p os, s is the exponent and can assume a value o1 and o is the frequency of applied AC ﬁeld) in both the regions. We ﬁnd the value of s to increase (0.362 at 30 1C, 0.364 at 50 1C and 0.368 at 80 1C in region I and 0.922 at 30 1C, 0.959 at 50 1C and 0.992 at 80 1C in region II) with the increasing temperature in both the regions. This indicates that the conduction process is a thermally activated process. The AC conductivity data have been used to evaluate the density of states at Fermi level N(Ef) using the relation [14]

fðtÞ ¼ exp½ðt=tm Þb ;

sAC ðoÞ ¼

ð0obo1Þ,

(3)

where f(t) stands for time evaluation of electric ﬁeld within sample, tm the conductivity relaxation time, b is the Kohlrausch exponent. The smaller the value of b larger the deviation of relaxation with respect to Debye-type relaxation (b ¼ 1). A non-exponential type conductivity relaxation governed by Eq. (3) suggests the possibility of ion migration that takes place via hopping accompanied by a consequential time-dependent mobility of other charge carriers of the same type in the vicinity occurs. The variation of bulk AC conductivity, sAC of alizarin as a function of frequency at different temperatures is shown in Fig. 8. The plot clearly shows that the conductivity is strongly dependent on frequency. Also, the plots show an

4 p 2 f q okB TfNðE f Þg2 a5 ln 0 , 3 o

(4)

where q is the electronic charge, f0 the photon frequency and a is the localized wave function. Assuming f0 ¼ 1013 Hz, a ¼ 1010 m1 and using the value of sAC ðoÞ ¼ 2:98 104 S=m at 100 kHz at 303 K, the value of N(Ef) comes to be 1.2 1019 cm3 eV1, which is in good agreement with the values obtained for several organic compounds [14–16]. In continuation, inset Fig. 8 also evidences that the AC conductivity is strongly frequency dependent. Further, it is clear that the transition temperature from the semiconducting region to the conducting region shift to higher side with the increment in frequency. The nature of variation is almost linear in the

ARTICLE IN PRESS K.P. Chandra et al. / Physica B 388 (2007) 118–123

semiconducting region. The conductivity of an OSC is expressed as [12] sAC ¼ s0 expðE a =kB TÞ.

(5)

The value Ea ¼ 0.78 eV obtained by least squares ﬁtting of the data below 80 1C. The low value of activation energy could be attributed to the inﬂuence of electronic contribution to the conductivity. The number of p-electrons per molecule (N) has been estimated from the following relation [17]: N þ1 . N2 The value of N comes to be 25.

E a ¼ 19:2

(6)

4. Conclusion This work reports the results of our investigation on the electrical properties of alizarin, a p-conjugated OSC, using complex impedance spectroscopy technique. The experimental results indicate that alizarin exhibits (i) the NTCR character, (ii) a transition from semiconducting to conducting state and the transition temperature shifts to higher side with the increment in frequency, (iii) temperaturedependent relaxation phenomena, and (iv) polydispersive non-Debye type dielectric relaxation. The AC conductivity obeys the power law and the dispersion in conductivity was observed in the lower frequency region. Also, the frequency-dependent AC conductivity at different temperatures indicated that the conduction process is thermally activated process. The activation energy, density of states at Fermi level and number of p-electrons per molecule have been estimated from AC conductivity– temperature data and was found, respectively, to be 0.78 eV, 1.2 1019 cm3 eV1 and 25. Modulus analysis

123

has indicated the possibility of hopping mechanism for electrical transport processes in the system with nonexponential-type conductivity relaxation.

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