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AC conductivity, dielectric relaxation and modulus behavior of Sb2S2O new kermesite alloy for optoelectronic applications
Materials Science in Semiconductor Processing 40 (2015) 596–601
Contents lists available at ScienceDirect
Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/matsci
AC conductivity, dielectric relaxation and modulus behavior of Sb2S2O new kermesite alloy for optoelectronic applications M. Haj Lakhdar n, T. Larbi, B. Ouni, M. Amlouk Unité de physique des dispositifs a semi-conducteurs, Faculté des sciences deTunis, Tunis El Manar University, 2092 Tunis, Tunisia
art ic l e i nf o
a b s t r a c t
Article history: Received 13 March 2015 Received in revised form 8 June 2015 Accepted 9 July 2015
In this work, we present some physical properties of Sb2S2O thin films obtained through heat treatment of Sb2S3 thin films under an atmospheric pressure at 350 °C. The electrical conductivity, dielectric properties and relaxation model of these thin films were studied using impedance spectroscopy technique in the frequency range from 5 Hz to 13 MHz at various temperatures from 350 °C to 425 °C. Besides, the frequency and temperature dependence of the complex impedance, AC conductivity and complex electric modulus has been investigated. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Thin films Kermesite AC conductivity Dielectric constants Complex electric modulus
1. Introduction Metal oxysulfides compounds have been recognized for their promising applications in various fields based on the electronic, magnetic, optical, and chemical characteristics oxysulfides are attractive materials due to their chemical and thermal stability which makes them very promising in various fields such as Field emission display [1], photocatalysts [2], up conversion luminescence efficiency [3]. Commonly, the oxysulfides could be synthesized using several methods as r.f. magnetron sputtering [4], hydrothermal method [5], solid state reaction [6], and melting technique [7] or with direct sulfidation of oxides by sulfur-based gases [8]. Antimony oxysulfide (Sb2S2O) has a triclinic structure which is derived from the Sb2S3 by replacing one of the sulfur atoms with a oxygen atom. On the other hand, when sulfur atoms partially substitutes oxygen atom in oxysulfides, the band gap generally expands. Indeed, the modulation in band gap from 1.8 eV (Sb2S3) [9] to 3.93 eV (Sb2O4) [10] was reported with an intermediate band gap of 3 eV (Sb2S2O) [11] which makes them as a potential material for optoelectronic and solar cell applications. Ahn et al. reported that Zinc oxysulfide, which is a solid solution of ZnO and ZnS may be suitable in the area of heterojunction thin film solar cells [12]. Besides, the temperature and frequency dependence on AC conductivity, dielectric property, relaxation mode of semiconductors materials have been extensively studied to n
Corresponding author. E-mail address: [email protected] (M. Haj Lakhdar).
http://dx.doi.org/10.1016/j.mssp.2015.07.019 1369-8001/& 2015 Elsevier Ltd. All rights reserved.
understand transport mechanism of charge carriers, which play a crucial role in optoelectronic field. Here, Sb2S2O was investigated as a new oxysulfide in order to achieve the electrical and dielectrical properties. Since no physical properties of this material have been reported yet, we investigated the frequency and temperature dependence of the complex impedance, AC conductivity and complex electric modulus in order to identify conduction mechanism in this paper.
2. Experimental details 2.1. Sb2S2O thin films Sb2S2O thin films are deposited on glass substrates on three stages. Firstly, antimony thin films have been prepared by thermal evaporation under vacuum (10 4–10 5 Pa) The antimony was deposited on glass substrates raised to the temperature 100 °C. Then, Sb thin films are heated at 300 °C during 6 h under sulfur atmosphere [9]. Finally, Sb2S3 thin films thus obtained are oxidized in air during 6 h at 350 °C to form thin layers of Sb2S2O [11]. We estimate that the value of the thickness of Sb2S2O thin film is in the same order of magnitude as that of Sb2S3 (E 600 nm) [9]. 2.2. Characterization technique The measurements were carried out in the temperature range of 623–698 K by using a tube furnace (Vecstar FURNACES) and the
M. Haj Lakhdar et al. / Materials Science in Semiconductor Processing 40 (2015) 596–601
electrical conductivity was measured by HP4192A impedance for high frequency and Autolab PGSTAT30 for low frequency. Both devices are controlled by programs that allow received and safeguard measures. The electrical measurement was conducted using two shaped electrodes of band painted on either end of the sample by using the silver paste. AC conductivity was obtained from experimental impedance data using the relation: sAC ¼d/Z′S, where Z′ is the real components of complex impedance, d is the distance between electrodes and S is the cross-sectional area.
597
Table 1 Cole–Cole values fitting parameters. Temperature (K)
R (Ω)
C (10 13 F)
α
623 648 673 698
1628460 1107325 505797 311710
7.84 7.96 7.51 7.46
0.908 0.844 0.899 0.901
16 14
350 °C 375 °C 400 °C 425 °C
3. Results and discussion Shown in Fig. 1 are the complex impedance spectra of Sb2S2O thin films at different temperatures. It is clearly observed from this plot that the semicircles are depressed and their centers are shifted down to the real axis indicating non-Debye type relaxation processes in the material [13,14]. The experimental impedance data can be modeled by an equivalent circuit consisting by a parallel combination of a constant phase element (CPE) and a resistance (R). Indeed, the variation of the real part Z′ with the imaginary part of impedance Z″ (Nyquist plots) can be described by the Cole–Cole model [15,16], which is given by:
10 8 6 4 2 0 11
12
13
14
15
16
17
Ln(ω) Fig. 2. Frequency dependence of Z′ at different temperatures.
8
R [1 + (jωτ )α ]
7
5
5
- Z '' (10 Ω )
Where ω is angular frequency, τ ¼ RC is the relaxation time and α is a parameter which characterizes the distribution of relaxation times. The values of the equivalent circuit element have been listed in Table 1. Fig. 2 shows the experimental values of Z′ versus frequency at different temperatures. As seen in Fig. 2, Z′ magnitude decreases with increasing frequency as well as temperature, which indicates a semiconductor behavior. The variation of imaginary part Z″ with frequency at different temperatures is plotted in Fig. 3. It is clearly observed from this plot that the imaginary part Z″ increase with frequency reaching a ‵‵ then decrease. Furthermore, the relaxation maximum peak Zmax peak position shifts to higher frequencies when the temperature ‵‵ values decrease with temperaincreases, we also note that Zmax ture. The imaginary impedance spectra can be employed to evaluate the relaxation time τ of the electrical phenomena in the material. The relaxation time has been evaluated from the following equation: ωmτ = 1 The temperature variation of the relaxation frequency at maximum of Z″ is shown in Fig. 4, which satisfies the Arrhenius law [17] given by:
350 °C 375 °C 400 °C 425 °C
6
4 3 2 1 0 11
12
13
14
15
16
17
Ln(ω) Fig. 3. Frequency dependence of Z″ at different temperatures. 15,6 15,3
Linear fit
15,0
Ln(fz max )
Z=
Z ' (105Ω )
12
EaZ = 0.86 eV
14,7 14,4 14,1 13,8 13,5
12 13,2
350 °C 375 °C 400 °C 425 °C
5
- Z'' (10 Ω )
10 8
1,40
1,44
1,48
1,52
1,56
1,60
1,64
1000/T Fig. 4. Temperature dependence of relaxation frequency for Z″.
6
⎛ E ⎞ fmax = f0 exp⎜ − a ⎟ ⎝ kBT ⎠
4 2 0 0
2
4
6
8
10
12
14
16
Z' (10 Ω ) 5
Fig. 1. Complex impedance spectra at different temperatures.
Where f0 is the pre-exponential factor, Ea is the activation energy, T is the measuring temperature and kB is the Boltzmann constant. The activation energies are calculated from straight line fit (Fig. 4) and is found to be Ea ¼0. 86 eV. This value supports the idea that the conduction mechanism for Sb2S2O is due to charge carriers hopping [18,19].
598
M. Haj Lakhdar et al. / Materials Science in Semiconductor Processing 40 (2015) 596–601
0,920
1,0
350 °C 375 °C 400 °C 425 °C
0,915
0,910
0,6
S(T)
Z ''/Z ''max
0,8
0,4
0,905
0,2
0,900
0,0
0,895
-5
-4
-3
-2
-1
0
1
2
3
4
5
620 630 640 650 660 670 680 690 700
Ln(ω /ωmax )
T (K)
Fig. 5. Variation of Z″/Zmax ‵‵ with Ln (ω/ωmax ) at different temperature.
Fig. 7. Temperature dependence of the parameters. -10,5
-10,4
Ln( ω)= 11.25 Ln( ω )= 11.75 Ln( ω)= 12.25 Ln( ω)= 12.75 Ln( ω)= 13.25 Ln( ω)= 13.50
-10,8 -11,1
-11,2
-11,4
-11,6
350 °C 375 °C 400 °C 425 °C
-12,0 -12,4
Ln(σAC )
Ln(σAC )
-10,8
-11,7 -12,0 -12,3
Arrhenius Fit
-12,6 -12,9 1,41
-12,8 11,0 11,5 12,0 12,5 13,0 13,5 14,0 14,5 15,0
1,44
1,47
σAC = σDC + Aωs where ω is the angular frequency, A is a constant, σDC is the DC conductivity due to band conduction, and (s) is an exponent lower or equal to 1. In order to give an idea about the conduction mechanism in this material, we present the variation of the exponent (s) in function of the temperature Fig. 7. The (s) value was determined from the slope of the linear part of ln(σAC ) versus ω curve at high frequencies Fig. 7. As shown in Fig. 7, S(T) decreases with increasing temperature. Such behavior suggests that the correlated barrier hopping (CBH) model may be suitable to explain the conduction mechanism in Sb2S2O thin film. In such model, the charge carriers are assumed to hop between the sites over a potential barrier separating them. Fig. 8 shows the variation of ln(σAC ) as a function of the reciprocal of absolute temperature, measured at different frequencies. As seen from the figure, σAC increases linearly with the reciprocal of absolute temperature indicating that the AC conductivity is a thermally activated process from different localized
1,56
1,59
1,62
Fig. 8. Temperature dependence of AC conductivity at different frequency.
0,80 0,75 0,70
Ea (eV)
Fig. 5 shows the variation of imaginary impedance Z″ with frequency at different temperatures, where Z″ axis is normalized ‵‵ and frequency axis by ωmax . The perfect overlap of curves by Zmax at different temperatures into a single master curve indicates that the dynamical processes occurring at different frequencies are independent of temperature or it has the same thermal energy. Fig. 6 depicts the plot of ln(sac) versus frequency at various temperatures for Sb2S2O. It is remarkable from these plots that the conductivity is substantially constant at low frequencies while at higher frequencies it increases rapidly. On the other hand, the conductivity shows dispersion which shifts to higher frequency side with the increase of temperature. The variation of conductivity with angular frequency at different temperatures is described by the Jonscher law [20] as:
1,53
1000/T
Ln(ω) Fig. 6. Frequency dependence of AC conductivity at different temperature.
1,50
0,65 0,60 0,55 0,50 0,45 11,0
11,5
12,0
12,5
13,0
13,5
14,0
Ln(ω) Fig. 9. Frequency dependence of ac activation energy.
states in the gap [21,22]. Therefore, we can conclude that the ac conductivity versus temperature, at different frequencies, obeys the Arrhenius law given by:
⎛ E ⎞ σAC = σAC0exp⎜ − AC ⎟ ⎝ kBT ⎠ Frequency dependence of AC activation energy is plotted in Fig. 9. It is still remarkable that the activation energy decreases with increasing frequency. the decrease of activation energy can be explained by the given that the increase in frequency (decrease of period) does not allow time to charge carries to return to their fundamental states, thus the charge carriers see a low barrier to cross [23]. As shown in Fig. 10, The DC conductivity follows the Arrhenius law which can be written as:
M. Haj Lakhdar et al. / Materials Science in Semiconductor Processing 40 (2015) 596–601
-10,5
Linear fit
-10,8
EaDC = 0.87 eV
ln(σDC)
-11,1 -11,4 -11,7 -12,0 -12,3 -12,6 -12,9 1,40
1,44
1,48
1,52
1,56
1,60
1,64
1000/T Fig. 10. Temperature dependence of DC conductivity.
⎛ E ⎞ σDC = σDC0exp⎜ − DC ⎟ ⎝ kBT ⎠ where, σDC0 is the pre-exponential factor, and EDC is the activation energy for DC conduction. We note a value of activation energy of about 0.87 eV which is almost identical to the activation energy obtained from the angular relaxation frequency. The study of dielectric properties is another important source of information on the conduction process. This study can be used to explain the origin of dielectric losses, electrical and dipolar relaxation time. Firstly, at constant temperature, the dielectric constant decreases by increasing frequency of the applied field (Fig. 11a). This behavior can be explained by the fact that at low frequencies, several kinds of polarizations contributes in the dielectric constant value, as deformational polarization (electronic, ionic) as well as relaxation (orientational and interfacial). When the frequency becomes higher, the electric dipoles can no longer follow the variation of the electric field, which leads to a reduction of 180 170 160
350 °C 375 °C 400 °C 425 °C
ε'
150 140 130 120 110 100 90 0,0
2,0x10
4,0x10
6,0x10
8,0x10
1,0x10
ω (rad.s ) 30
orientational polarization. At high frequency, ε′ reached a constant value due to interfacial polarization. Secondly, at constant frequency, the dielectric constant increases by increasing temperature (Fig. 11a). This behavior can be explained by the fact that the dipoles cannot orient themselves at low temperatures. However, when the temperature rises, the orientation of dipole becomes easier (following thermal movements), which tends to increase the value of the dielectric constant. The dependence of the dielectric loss on the frequency at different temperatures of Sb2S2O thin films is illustrated in Fig. 11b. The dielectric loss increases by increasing temperature at constant frequency (Fig. 11b). This behavior can be explained by the fact that at low temperatures, the conduction loss is minimal, when the temperature increases the conduction loss increases due to the increase in conductivity [24,25]. This increases the value of dielectric loss with increasing temperature. The impedance spectrum does not provide information at high and low frequencies. Another approach to study electrical relaxation of material is the complex electrical modulus Mn [26,27]. The real (M′) and imaginary (M″) parts of electric modulus were calculated from the impedance data using the relation:
M⁎ = M′ + jM″ = jωC0Z⁎ Where C0 = ε0S /d the empty cell capacitance, with ε0 representing the permittivity of free space, d the sample thickness, and S the area of the sample. Fig. 12 shows a plot of M″ versus M′. From Fig. 12 it is remarkable that the M″ versus M′ plots at different temperatures overlap on a single arc indicating the presence of a single phase of the material. Furthermore, Fig. 12 reveal that the semicircles are depressed and their centers are shifted down to M′ axis which further confirms a distributions of relaxation time which supports the non-Debye type of relaxation in the material. Fig. 13 shows the variation of the real part of the electric modulus M′ as a function of frequency at different temperatures. As seen from Fig. 13, M′ value approaches zero for low frequency. This behavior can be interpreted by a lack of force which governs the mobility of charge carriers under the influence of an electric field [28]. Moreover, an increase in the value of M′ with increasing frequency at different temperatures has been observed. Shown in Fig. 14 is the variation of imaginary part M″ with frequency at different temperatures. On one hand, at different temperature, imaginary part M″ increase with frequency up a ‵‵ then decrease. On the other hand, the pomaximum peak Mmax sition of the relaxation peak shifts to low frequencies with decreasing temperature. M″ / M″max versus ln(ω / ωmax) at different temperatures is plotted in Fig. 15. The overlap of the curves shows that the relaxation mechanism is the same regardless of temperatures [13]. 0,012
25
350 °C 375 °C 400 °C 425 °C
20
350 °C 375 °C 400 °C 425 °C
0,009
15
M''
tan( δ )
599
10 5
0,006
0,003
0 11
12
13
14
15
16
17
Ln(ω)
0,000 0,000
0,003
0,006
0,009
0,012
0,015
0,018
M' Fig. 11. (a) Frequency dependence of dielectric constant at different temperatures. (b) Frequency dependence of dielectric loss at different temperatures.
Fig. 12. Complex modulus spectrum at different temperatures.
600
M. Haj Lakhdar et al. / Materials Science in Semiconductor Processing 40 (2015) 596–601
0,018
350 °C 375 °C 400 °C 425 °C
0,014 0,012
M'
M''/M''max Z''/Z''max
1,0
0,016
0,010
0,8
T = 375 °C
0,6
0,008 0,006
0,4
0,004 0,002
0,2
0,000 11
12
13
14
15
16
17
Ln(ω)
0,0 11
12
13
14
15
16
17
Ln(ω)
Fig. 13. Frequency dependence of M′ at different temperatures.
Fig. 17. Frequency dependence of Z″/ Zmax ‵‵ and M″/Mmax ‵‵ at T ¼618 K. 0,008 0,007 0,006 0,005
M''
It is also known that at the peaks corresponding to M″ the relaxation time τ can be deduced from the following equation: ωmτ = 1. Fig. 16 shows the temperature dependence of the relaxation time, which follows the Arrhenius law:
350 °C 375 °C 400 °C 425 °C
0,004
⎛ E ⎞ fM max = fM0 exp⎜ − Ma ⎟ ⎝ kBT ⎠
0,003 0,002 0,001 0,000 11
12
13
14
15
16
17
Ln(ω) Fig. 14. Frequency dependence of M″ at different temperatures.
1,0
350 °C 375 °C 400 °C 425 °C
M''/M''max
0,8 0,6
4. Conclusion
0,4 0,2 0,0 -5
-4
-3
-2
-1
0
1
2
3
4
5
Ln(ω/ωmax) Fig. 15. Variation of M″/Mmax ‵‵ with Ln (f/fmax ) at different temperature.
15,9
Linear fit
15,6
EaM = 0.85 eV
15,3
Ln (fM max)
where fM0 is the pre-exponent factor, EMa is the activation energy for dielectric relaxation. It can be observed that the value of EMa was found to be about 0.85 eV. ‵‵ and Z″/Zmax ‵‵ is The variation of normalized parameters M″/Mmax ‵‵ and Z″/Zmax ‵‵ plotted in Fig. 17. It is still remarkable that M″/Mmax ‵‵ peak do not overlap. The overlapping peak position of M″/Mmax ‵‵ gives an idea about relaxation (delocalized or long and Z″/Zmax ‵‵ and Z″/Zmax ‵‵ peak do not range) [29]. For Sb2S2O the M″/Mmax overlap, which proves the existence from both long range and localized relaxation. On the other hand, the broadening of the Z″ and M″ spectra represented is due to the existence of a distribution of relaxation times [30].
This paper reports some electrical properties of Sb2S2O thin films obtained through thermal treatment of Sb thin films under a sulfur atmosphere at 300 °C followed by oxidation in air during 6 h at 350 °C. Dielectric relaxation, modulus behavior and conduction mechanism of obtained Sb2S2O thin films have been investigated in terms of both temperature and frequency. It is found that the scaling behavior of imaginary impedance and imaginary electric modulus suggests that the relaxation phenomenon describes the same mechanism at various temperatures. The study of ac conductivity via frequency showed universal power law s dependence. Further studies are in progress to test this ternary compound in some electronic devices in solar cells.
15,0 14,7
References
14,4 14,1 13,8 13,5 1,40
1,44
1,48
1,52
1,56
1,60
1,64
1000/T Fig. 16. Temperature dependence of relaxation frequency for M″.
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Contents lists available at ScienceDirect
Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/matsci
AC conductivity, dielectric relaxation and modulus behavior of Sb2S2O new kermesite alloy for optoelectronic applications M. Haj Lakhdar n, T. Larbi, B. Ouni, M. Amlouk Unité de physique des dispositifs a semi-conducteurs, Faculté des sciences deTunis, Tunis El Manar University, 2092 Tunis, Tunisia
art ic l e i nf o
a b s t r a c t
Article history: Received 13 March 2015 Received in revised form 8 June 2015 Accepted 9 July 2015
In this work, we present some physical properties of Sb2S2O thin films obtained through heat treatment of Sb2S3 thin films under an atmospheric pressure at 350 °C. The electrical conductivity, dielectric properties and relaxation model of these thin films were studied using impedance spectroscopy technique in the frequency range from 5 Hz to 13 MHz at various temperatures from 350 °C to 425 °C. Besides, the frequency and temperature dependence of the complex impedance, AC conductivity and complex electric modulus has been investigated. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Thin films Kermesite AC conductivity Dielectric constants Complex electric modulus
1. Introduction Metal oxysulfides compounds have been recognized for their promising applications in various fields based on the electronic, magnetic, optical, and chemical characteristics oxysulfides are attractive materials due to their chemical and thermal stability which makes them very promising in various fields such as Field emission display [1], photocatalysts [2], up conversion luminescence efficiency [3]. Commonly, the oxysulfides could be synthesized using several methods as r.f. magnetron sputtering [4], hydrothermal method [5], solid state reaction [6], and melting technique [7] or with direct sulfidation of oxides by sulfur-based gases [8]. Antimony oxysulfide (Sb2S2O) has a triclinic structure which is derived from the Sb2S3 by replacing one of the sulfur atoms with a oxygen atom. On the other hand, when sulfur atoms partially substitutes oxygen atom in oxysulfides, the band gap generally expands. Indeed, the modulation in band gap from 1.8 eV (Sb2S3) [9] to 3.93 eV (Sb2O4) [10] was reported with an intermediate band gap of 3 eV (Sb2S2O) [11] which makes them as a potential material for optoelectronic and solar cell applications. Ahn et al. reported that Zinc oxysulfide, which is a solid solution of ZnO and ZnS may be suitable in the area of heterojunction thin film solar cells [12]. Besides, the temperature and frequency dependence on AC conductivity, dielectric property, relaxation mode of semiconductors materials have been extensively studied to n
Corresponding author. E-mail address: [email protected] (M. Haj Lakhdar).
http://dx.doi.org/10.1016/j.mssp.2015.07.019 1369-8001/& 2015 Elsevier Ltd. All rights reserved.
understand transport mechanism of charge carriers, which play a crucial role in optoelectronic field. Here, Sb2S2O was investigated as a new oxysulfide in order to achieve the electrical and dielectrical properties. Since no physical properties of this material have been reported yet, we investigated the frequency and temperature dependence of the complex impedance, AC conductivity and complex electric modulus in order to identify conduction mechanism in this paper.
2. Experimental details 2.1. Sb2S2O thin films Sb2S2O thin films are deposited on glass substrates on three stages. Firstly, antimony thin films have been prepared by thermal evaporation under vacuum (10 4–10 5 Pa) The antimony was deposited on glass substrates raised to the temperature 100 °C. Then, Sb thin films are heated at 300 °C during 6 h under sulfur atmosphere [9]. Finally, Sb2S3 thin films thus obtained are oxidized in air during 6 h at 350 °C to form thin layers of Sb2S2O [11]. We estimate that the value of the thickness of Sb2S2O thin film is in the same order of magnitude as that of Sb2S3 (E 600 nm) [9]. 2.2. Characterization technique The measurements were carried out in the temperature range of 623–698 K by using a tube furnace (Vecstar FURNACES) and the
M. Haj Lakhdar et al. / Materials Science in Semiconductor Processing 40 (2015) 596–601
electrical conductivity was measured by HP4192A impedance for high frequency and Autolab PGSTAT30 for low frequency. Both devices are controlled by programs that allow received and safeguard measures. The electrical measurement was conducted using two shaped electrodes of band painted on either end of the sample by using the silver paste. AC conductivity was obtained from experimental impedance data using the relation: sAC ¼d/Z′S, where Z′ is the real components of complex impedance, d is the distance between electrodes and S is the cross-sectional area.
597
Table 1 Cole–Cole values fitting parameters. Temperature (K)
R (Ω)
C (10 13 F)
α
623 648 673 698
1628460 1107325 505797 311710
7.84 7.96 7.51 7.46
0.908 0.844 0.899 0.901
16 14
350 °C 375 °C 400 °C 425 °C
3. Results and discussion Shown in Fig. 1 are the complex impedance spectra of Sb2S2O thin films at different temperatures. It is clearly observed from this plot that the semicircles are depressed and their centers are shifted down to the real axis indicating non-Debye type relaxation processes in the material [13,14]. The experimental impedance data can be modeled by an equivalent circuit consisting by a parallel combination of a constant phase element (CPE) and a resistance (R). Indeed, the variation of the real part Z′ with the imaginary part of impedance Z″ (Nyquist plots) can be described by the Cole–Cole model [15,16], which is given by:
10 8 6 4 2 0 11
12
13
14
15
16
17
Ln(ω) Fig. 2. Frequency dependence of Z′ at different temperatures.
8
R [1 + (jωτ )α ]
7
5
5
- Z '' (10 Ω )
Where ω is angular frequency, τ ¼ RC is the relaxation time and α is a parameter which characterizes the distribution of relaxation times. The values of the equivalent circuit element have been listed in Table 1. Fig. 2 shows the experimental values of Z′ versus frequency at different temperatures. As seen in Fig. 2, Z′ magnitude decreases with increasing frequency as well as temperature, which indicates a semiconductor behavior. The variation of imaginary part Z″ with frequency at different temperatures is plotted in Fig. 3. It is clearly observed from this plot that the imaginary part Z″ increase with frequency reaching a ‵‵ then decrease. Furthermore, the relaxation maximum peak Zmax peak position shifts to higher frequencies when the temperature ‵‵ values decrease with temperaincreases, we also note that Zmax ture. The imaginary impedance spectra can be employed to evaluate the relaxation time τ of the electrical phenomena in the material. The relaxation time has been evaluated from the following equation: ωmτ = 1 The temperature variation of the relaxation frequency at maximum of Z″ is shown in Fig. 4, which satisfies the Arrhenius law [17] given by:
350 °C 375 °C 400 °C 425 °C
6
4 3 2 1 0 11
12
13
14
15
16
17
Ln(ω) Fig. 3. Frequency dependence of Z″ at different temperatures. 15,6 15,3
Linear fit
15,0
Ln(fz max )
Z=
Z ' (105Ω )
12
EaZ = 0.86 eV
14,7 14,4 14,1 13,8 13,5
12 13,2
350 °C 375 °C 400 °C 425 °C
5
- Z'' (10 Ω )
10 8
1,40
1,44
1,48
1,52
1,56
1,60
1,64
1000/T Fig. 4. Temperature dependence of relaxation frequency for Z″.
6
⎛ E ⎞ fmax = f0 exp⎜ − a ⎟ ⎝ kBT ⎠
4 2 0 0
2
4
6
8
10
12
14
16
Z' (10 Ω ) 5
Fig. 1. Complex impedance spectra at different temperatures.
Where f0 is the pre-exponential factor, Ea is the activation energy, T is the measuring temperature and kB is the Boltzmann constant. The activation energies are calculated from straight line fit (Fig. 4) and is found to be Ea ¼0. 86 eV. This value supports the idea that the conduction mechanism for Sb2S2O is due to charge carriers hopping [18,19].
598
M. Haj Lakhdar et al. / Materials Science in Semiconductor Processing 40 (2015) 596–601
0,920
1,0
350 °C 375 °C 400 °C 425 °C
0,915
0,910
0,6
S(T)
Z ''/Z ''max
0,8
0,4
0,905
0,2
0,900
0,0
0,895
-5
-4
-3
-2
-1
0
1
2
3
4
5
620 630 640 650 660 670 680 690 700
Ln(ω /ωmax )
T (K)
Fig. 5. Variation of Z″/Zmax ‵‵ with Ln (ω/ωmax ) at different temperature.
Fig. 7. Temperature dependence of the parameters. -10,5
-10,4
Ln( ω)= 11.25 Ln( ω )= 11.75 Ln( ω)= 12.25 Ln( ω)= 12.75 Ln( ω)= 13.25 Ln( ω)= 13.50
-10,8 -11,1
-11,2
-11,4
-11,6
350 °C 375 °C 400 °C 425 °C
-12,0 -12,4
Ln(σAC )
Ln(σAC )
-10,8
-11,7 -12,0 -12,3
Arrhenius Fit
-12,6 -12,9 1,41
-12,8 11,0 11,5 12,0 12,5 13,0 13,5 14,0 14,5 15,0
1,44
1,47
σAC = σDC + Aωs where ω is the angular frequency, A is a constant, σDC is the DC conductivity due to band conduction, and (s) is an exponent lower or equal to 1. In order to give an idea about the conduction mechanism in this material, we present the variation of the exponent (s) in function of the temperature Fig. 7. The (s) value was determined from the slope of the linear part of ln(σAC ) versus ω curve at high frequencies Fig. 7. As shown in Fig. 7, S(T) decreases with increasing temperature. Such behavior suggests that the correlated barrier hopping (CBH) model may be suitable to explain the conduction mechanism in Sb2S2O thin film. In such model, the charge carriers are assumed to hop between the sites over a potential barrier separating them. Fig. 8 shows the variation of ln(σAC ) as a function of the reciprocal of absolute temperature, measured at different frequencies. As seen from the figure, σAC increases linearly with the reciprocal of absolute temperature indicating that the AC conductivity is a thermally activated process from different localized
1,56
1,59
1,62
Fig. 8. Temperature dependence of AC conductivity at different frequency.
0,80 0,75 0,70
Ea (eV)
Fig. 5 shows the variation of imaginary impedance Z″ with frequency at different temperatures, where Z″ axis is normalized ‵‵ and frequency axis by ωmax . The perfect overlap of curves by Zmax at different temperatures into a single master curve indicates that the dynamical processes occurring at different frequencies are independent of temperature or it has the same thermal energy. Fig. 6 depicts the plot of ln(sac) versus frequency at various temperatures for Sb2S2O. It is remarkable from these plots that the conductivity is substantially constant at low frequencies while at higher frequencies it increases rapidly. On the other hand, the conductivity shows dispersion which shifts to higher frequency side with the increase of temperature. The variation of conductivity with angular frequency at different temperatures is described by the Jonscher law [20] as:
1,53
1000/T
Ln(ω) Fig. 6. Frequency dependence of AC conductivity at different temperature.
1,50
0,65 0,60 0,55 0,50 0,45 11,0
11,5
12,0
12,5
13,0
13,5
14,0
Ln(ω) Fig. 9. Frequency dependence of ac activation energy.
states in the gap [21,22]. Therefore, we can conclude that the ac conductivity versus temperature, at different frequencies, obeys the Arrhenius law given by:
⎛ E ⎞ σAC = σAC0exp⎜ − AC ⎟ ⎝ kBT ⎠ Frequency dependence of AC activation energy is plotted in Fig. 9. It is still remarkable that the activation energy decreases with increasing frequency. the decrease of activation energy can be explained by the given that the increase in frequency (decrease of period) does not allow time to charge carries to return to their fundamental states, thus the charge carriers see a low barrier to cross [23]. As shown in Fig. 10, The DC conductivity follows the Arrhenius law which can be written as:
M. Haj Lakhdar et al. / Materials Science in Semiconductor Processing 40 (2015) 596–601
-10,5
Linear fit
-10,8
EaDC = 0.87 eV
ln(σDC)
-11,1 -11,4 -11,7 -12,0 -12,3 -12,6 -12,9 1,40
1,44
1,48
1,52
1,56
1,60
1,64
1000/T Fig. 10. Temperature dependence of DC conductivity.
⎛ E ⎞ σDC = σDC0exp⎜ − DC ⎟ ⎝ kBT ⎠ where, σDC0 is the pre-exponential factor, and EDC is the activation energy for DC conduction. We note a value of activation energy of about 0.87 eV which is almost identical to the activation energy obtained from the angular relaxation frequency. The study of dielectric properties is another important source of information on the conduction process. This study can be used to explain the origin of dielectric losses, electrical and dipolar relaxation time. Firstly, at constant temperature, the dielectric constant decreases by increasing frequency of the applied field (Fig. 11a). This behavior can be explained by the fact that at low frequencies, several kinds of polarizations contributes in the dielectric constant value, as deformational polarization (electronic, ionic) as well as relaxation (orientational and interfacial). When the frequency becomes higher, the electric dipoles can no longer follow the variation of the electric field, which leads to a reduction of 180 170 160
350 °C 375 °C 400 °C 425 °C
ε'
150 140 130 120 110 100 90 0,0
2,0x10
4,0x10
6,0x10
8,0x10
1,0x10
ω (rad.s ) 30
orientational polarization. At high frequency, ε′ reached a constant value due to interfacial polarization. Secondly, at constant frequency, the dielectric constant increases by increasing temperature (Fig. 11a). This behavior can be explained by the fact that the dipoles cannot orient themselves at low temperatures. However, when the temperature rises, the orientation of dipole becomes easier (following thermal movements), which tends to increase the value of the dielectric constant. The dependence of the dielectric loss on the frequency at different temperatures of Sb2S2O thin films is illustrated in Fig. 11b. The dielectric loss increases by increasing temperature at constant frequency (Fig. 11b). This behavior can be explained by the fact that at low temperatures, the conduction loss is minimal, when the temperature increases the conduction loss increases due to the increase in conductivity [24,25]. This increases the value of dielectric loss with increasing temperature. The impedance spectrum does not provide information at high and low frequencies. Another approach to study electrical relaxation of material is the complex electrical modulus Mn [26,27]. The real (M′) and imaginary (M″) parts of electric modulus were calculated from the impedance data using the relation:
M⁎ = M′ + jM″ = jωC0Z⁎ Where C0 = ε0S /d the empty cell capacitance, with ε0 representing the permittivity of free space, d the sample thickness, and S the area of the sample. Fig. 12 shows a plot of M″ versus M′. From Fig. 12 it is remarkable that the M″ versus M′ plots at different temperatures overlap on a single arc indicating the presence of a single phase of the material. Furthermore, Fig. 12 reveal that the semicircles are depressed and their centers are shifted down to M′ axis which further confirms a distributions of relaxation time which supports the non-Debye type of relaxation in the material. Fig. 13 shows the variation of the real part of the electric modulus M′ as a function of frequency at different temperatures. As seen from Fig. 13, M′ value approaches zero for low frequency. This behavior can be interpreted by a lack of force which governs the mobility of charge carriers under the influence of an electric field [28]. Moreover, an increase in the value of M′ with increasing frequency at different temperatures has been observed. Shown in Fig. 14 is the variation of imaginary part M″ with frequency at different temperatures. On one hand, at different temperature, imaginary part M″ increase with frequency up a ‵‵ then decrease. On the other hand, the pomaximum peak Mmax sition of the relaxation peak shifts to low frequencies with decreasing temperature. M″ / M″max versus ln(ω / ωmax) at different temperatures is plotted in Fig. 15. The overlap of the curves shows that the relaxation mechanism is the same regardless of temperatures [13]. 0,012
25
350 °C 375 °C 400 °C 425 °C
20
350 °C 375 °C 400 °C 425 °C
0,009
15
M''
tan( δ )
599
10 5
0,006
0,003
0 11
12
13
14
15
16
17
Ln(ω)
0,000 0,000
0,003
0,006
0,009
0,012
0,015
0,018
M' Fig. 11. (a) Frequency dependence of dielectric constant at different temperatures. (b) Frequency dependence of dielectric loss at different temperatures.
Fig. 12. Complex modulus spectrum at different temperatures.
600
M. Haj Lakhdar et al. / Materials Science in Semiconductor Processing 40 (2015) 596–601
0,018
350 °C 375 °C 400 °C 425 °C
0,014 0,012
M'
M''/M''max Z''/Z''max
1,0
0,016
0,010
0,8
T = 375 °C
0,6
0,008 0,006
0,4
0,004 0,002
0,2
0,000 11
12
13
14
15
16
17
Ln(ω)
0,0 11
12
13
14
15
16
17
Ln(ω)
Fig. 13. Frequency dependence of M′ at different temperatures.
Fig. 17. Frequency dependence of Z″/ Zmax ‵‵ and M″/Mmax ‵‵ at T ¼618 K. 0,008 0,007 0,006 0,005
M''
It is also known that at the peaks corresponding to M″ the relaxation time τ can be deduced from the following equation: ωmτ = 1. Fig. 16 shows the temperature dependence of the relaxation time, which follows the Arrhenius law:
350 °C 375 °C 400 °C 425 °C
0,004
⎛ E ⎞ fM max = fM0 exp⎜ − Ma ⎟ ⎝ kBT ⎠
0,003 0,002 0,001 0,000 11
12
13
14
15
16
17
Ln(ω) Fig. 14. Frequency dependence of M″ at different temperatures.
1,0
350 °C 375 °C 400 °C 425 °C
M''/M''max
0,8 0,6
4. Conclusion
0,4 0,2 0,0 -5
-4
-3
-2
-1
0
1
2
3
4
5
Ln(ω/ωmax) Fig. 15. Variation of M″/Mmax ‵‵ with Ln (f/fmax ) at different temperature.
15,9
Linear fit
15,6
EaM = 0.85 eV
15,3
Ln (fM max)
where fM0 is the pre-exponent factor, EMa is the activation energy for dielectric relaxation. It can be observed that the value of EMa was found to be about 0.85 eV. ‵‵ and Z″/Zmax ‵‵ is The variation of normalized parameters M″/Mmax ‵‵ and Z″/Zmax ‵‵ plotted in Fig. 17. It is still remarkable that M″/Mmax ‵‵ peak do not overlap. The overlapping peak position of M″/Mmax ‵‵ gives an idea about relaxation (delocalized or long and Z″/Zmax ‵‵ and Z″/Zmax ‵‵ peak do not range) [29]. For Sb2S2O the M″/Mmax overlap, which proves the existence from both long range and localized relaxation. On the other hand, the broadening of the Z″ and M″ spectra represented is due to the existence of a distribution of relaxation times [30].
This paper reports some electrical properties of Sb2S2O thin films obtained through thermal treatment of Sb thin films under a sulfur atmosphere at 300 °C followed by oxidation in air during 6 h at 350 °C. Dielectric relaxation, modulus behavior and conduction mechanism of obtained Sb2S2O thin films have been investigated in terms of both temperature and frequency. It is found that the scaling behavior of imaginary impedance and imaginary electric modulus suggests that the relaxation phenomenon describes the same mechanism at various temperatures. The study of ac conductivity via frequency showed universal power law s dependence. Further studies are in progress to test this ternary compound in some electronic devices in solar cells.
15,0 14,7
References
14,4 14,1 13,8 13,5 1,40
1,44
1,48
1,52
1,56
1,60
1,64
1000/T Fig. 16. Temperature dependence of relaxation frequency for M″.
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