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AC conductivity and dielectric properties of thermally evaporated PbTe thin films
Solid-State Electronics 54 (2010) 58–62
Contents lists available at ScienceDirect
Solid-State Electronics journal homepage: www.elsevier.com/locate/sse
AC conductivity and dielectric properties of thermally evaporated PbTe thin films L. Kungumadevi, R. Sathyamoorthy *, A. Subbarayan PG and Research Department of Physics, Kongunadu Arts and Science College, Coimbatore 641 029, Tamil Nadu, India
a r t i c l e
i n f o
Article history: Received 2 February 2009 Received in revised form 31 July 2009 Accepted 10 September 2009 Available online 13 October 2009 The review of this paper was arranged by Dr. Y. Kuk
a b s t r a c t AC conductivity and dielectric properties of thermally evaporated lead telluride (PbTe) films have been investigated in the frequency range 30 Hz–100 kHz at various temperatures (303–483 K). The annealing process caused a stabilization of the dielectric properties due to the relief of stress and local structural rearrangement of atoms. The temperature coefficient of capacitance (TCC) and temperature coefficient of permittivity (TCP) have been estimated. The dominant conduction mechanism in the films is attributed to the hopping of thermally activated electrons under ac field. The results of variation of activation energy with frequency and thickness are discussed. Ó 2009 Elsevier Ltd. All rights reserved.
Keywords: Lead telluride (PbTe) Dielectric properties Conduction mechanism Activation energy
1. Introduction The IV–VI semiconductors PbS, PbSe and PbTe with the cubic NaCl (rock salt) structure, generally known as lead salts, have been the subject of a vast amount of theoretical and experimental work during the past decades, motivated not only by their technological applications, but also by their unusual physical properties. The unusual characteristics of lead salts such as high carrier mobilities, high dielectric constants and narrow band gaps make them unique among polar compounds and have important applications in many fields, such as infra-red detectors, light-emitting devices and more recently as infra red laser in fiber optics and thermoelectric devices [1–4]. Studies about heterostructures, films, quantum wires and quantum dots or wells of lead salts and their applications have caused much attention in the recent past [5–9]. PbTe is an intermediate thermoelectric power generator and its maximum operating temperature is 900 K. PbTe has high melting point, good chemical stability, low vapor pressure and good chemical strength in addition to high figure of merit (Z) [10]. Mandale [11] has studied resistivity, Hall constant, mobility, carrier density and thermoelectric power of vacuum deposited lead telluride films formed at room temperature and evaluated the effective hole mass from the observed thermoelectric power and correlated with transport properties. Abd El-Ati [12] has studied the electrical conductivity of PbTe thin films in which a transition of conductivity from ntype to p-type was observed. The thorough literature survey revealed that no researchers have studied the AC conduction and
* Corresponding author. Tel.: +91 422 2642095x208; fax: +91 422 2644452. E-mail address: [email protected] (R. Sathyamoorthy). 0038-1101/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.sse.2009.09.023
dielectric properties of lead telluride thin films in detail. Hence an attempt was made to study the AC and dielectric properties of vacuum evaporated lead telluride thin films and the results are presented in this paper with reasonable discussions. 2. Experimental details Pure aluminium (99.999%, Aldrich Chemicals Company) was evaporated from a tungsten filament onto pre cleaned glass substrates through suitable masks to form the base electrode. Lead telluride (99.998%, Sigma Aldrich Company, Bangalore) was then evaporated from a molybdenum boat under a pressure of 2 105 Torr to form a dielectric layer. An aluminium counter electrode was evaporated onto the dielectric to form Al/PbTe/Al (MSM) structure. Quartz–crystal thickness monitor was used to determine the thickness of the films. The capacitance and the dissipation factor for MSM structure in the frequency range from 30 Hz to 100 kHz at different temperatures (303–483 K) were measured using a Digital LCR meter (LCR-819, GW Instek, Goodwill Instrument Company Ltd., Taiwan). All the measurements were carried out under a rotary vacuum. A copper–constantan thermocouple is employed to sense the temperature of the sample during the measurements. 3. Results and discussion 3.1. Structural properties X-ray diffractogram of as-deposited and annealed film of thickness 5000 Å is shown in Fig. 1. The presence of sharp peaks in the
59
700 600
Table 2 Structural parameters of as-deposited and annealed PbTe film of thickness 5000 Å.
annealed at 573 K
(220)
(200)
L. Kungumadevi et al. / Solid-State Electronics 54 (2010) 58–62
500 400
(422)
(420)
100
(400)
(111)
200
(222)
300
a
Annealing temperature (K)
Lattice constanta (Å)
Crystallite size (nm)
Strain (e) 104
Dislocation density (d) 1014 lines/m2
As-deposited 100 °C 300 °C
6.458 6.455 6.459
44 48 48
10.11 9.69 7.61
9.54 7.74 4.49
Standard ‘a’ value 6.454 Å.
0 400
indicates that the degrees of preferred orientation along with the other microstructural features are more effective.
annealed at 373 K
Intensity (cps)
300 200
3.2. Dielectric properties
100
3.2.1. Effect of cyclic annealing Vacuum deposited MSM structures were annealed at about 373 K in a rotary vacuum. An annealing cycle comprises of the gradual increasing of temperature of the capacitor in an oven to annealing temperature, i.e. 373 K during first half an hour, maintaining that temperature for about 1 h constantly and then decreasing gradually to room temperature in the next half an hour. The changes in capacitance with frequency for different annealing cycles of the PbTe film of thickness 5000 Å is shown in Fig. 2. The capacitance decreases markedly in the first annealing cycle. The amount of reduction becomes smaller in the subsequent cycle. Freshly deposited films may have many defects and impurities such as voids, grain boundaries, dislocations, residual stress, inhomogeneities, etc. Annealing in vacuum further improves the dielectric properties. The defects are gradually reduced cycle after cycle and each atom may occupy a stable position in the interior of the film until the dielectric properties attain a stable value. It may be interpreted to the change of the structure of the investigated films by annealing. From XRD also we observed that the crystallinity has enhanced when the annealing temperature increases. Similar behavior on various organic and inorganic films has been reported earlier [17–20]. Similar behavior is observed for all the thickness of the film.
0 300
As deposited
200
100
0 10
20
30
40
50
60
70
80
2θ (degrees) Fig. 1. X-ray diffractogram of as-deposited and annealed PbTe film.
diffractogram suggests the polycrystalline nature of the film. The observed ‘d’ spacing and hkl planes (Table 1) are in good agreement with the JCPDS X-ray file data (card number 78–1905) of cubic PbTe and earlier reports [13–16] conforming the rock salt (NaCl) structure of the PbTe film. From the XRD profiles, the grain size, dislocation density, micro strain and lattice constant were calculated [16]. The degree of structural order of crystalline PbTe films improves with an increase in annealing temperature. As-deposited and annealed PbTe films are essentially of the same crystalline singlephase state except for a difference in crystallite size. The estimated lattice cell parameters for as-deposited and annealed films are given in Table 2. The computed lattice constant ‘a’ is in good agreement with the JCPDS (78–1905) value and with earlier investigations [13–16]. There is an increase in crystallite size and decrease in strain as well as dislocation density as annealing temperature increases. The annealing effect on structural parameters
3.2.2. Effects of frequency and temperature on dielectric parameters The variation of capacitance with frequency at different temperatures for PbTe film is presented in Fig. 3. It is observed that the capacitance decreases with increase in frequency at all temperatures and attain a constant value at higher temperatures. The large increase in capacitance at lower frequencies may be attributed to the blocking of charge carriers at the electrodes. Because of the impedance to their motion at the electrodes, space charge and macroscopic distortion results. The capacitance was found to decrease with increasing frequency and this may be due to the increasing inability of the dipole to become oriented in a rapidly
Table 1 Standard and experimental XRD data of as-deposited and annealed PbTe thin film. Standard values JCPDS (78–1905)
Experimental values obtained from XRD data As-deposited
Annealed at 100 °C
Annealed at 300 °C
2h (°)
d (Å)
hkl
2h (°)
d (Å)
2h (°)
d (Å)
2h (°)
d (Å)
23.860 27.619 39.458 46.636 48.842 57.031 64.518 71.562
3.7262 3.2270 2.2818 1.9459 1.8631 1.6135 1.4431 1.3174
111 200 220 311 222 400 420 422
23.800 27.521 39.417 46.530 48.803 56.850 64.440 71.540
3.7356 3.2383 2.2841 1.9502 1.8645 1.6182 1.4447 1.3178
23.750 27.510 39.414 46.620 48.790 56.912 64.527 71.560
3.7433 3.2396 2.2843 1.9466 1.8650 1.6166 1.4430 1.3174
23.796 27.568 39.443 – 48.842 56.973 64.504 71.596
3.7361 3.2329 2.2826 – 1.8631 1.6150 1.4434 1.3174
60
L. Kungumadevi et al. / Solid-State Electronics 54 (2010) 58–62
90
as-grown annealed : cycle 1 annealed : cycle 2
80
Capacitance ( nF)
70 60 50 40 30 20 2.5
3.0
3.5
4.0
4.5
5.0
log F ( Hz ) Fig. 2. Annealing effect on capacitance of PbTe film.
90
303K 323K 343K 363K 383K 403K 423K 443K
Capacitance(nF)
80 70 60 50 40 30 20 10 2.5
3.0
3.5
4.0
4.5
5.0
log F (Hz) Fig. 3. Dependence of capacitance on frequency at different temperature.
varying electric field. Similar behavior of the capacitance has been reported by various workers on various semiconductors [20–24]. The0 variation of tan d with frequency for the film of thickness 5000 Å A is shown in Fig. 4. If the electric polarization in a dielectric is unable to follow the varying electric field, dielectric loss occurs. An applied field will alter this energy difference thus producing a net polarization, which lags behind the applied field because the tunneling transition rates are finite. This part of the polarization, which is not in Phase with the applied field, is termed as dielectric loss. The loss factor increases with increase of temperature at high frequencies and it is almost a constant at low frequencies. At high frequencies the loss factor increases which may be due to the effect of lead resistance. 3.2.3. Temperature coefficient of capacitance and permittivity The temperature coefficient of capacitance is expressed as cc ¼ C1 dC dT Where ‘dC’ is the change in capacitance for a change of temperature ‘dT’. Since the permittivity of the dielectric between the two plates is proportional to the capacitance, it is possible to relate TCC to the temperature coefficient of permittivity TCP (cc)
cc ¼ cp þ a where a is the linear expansion coefficient of the dielectric and cp is de . given by the expression, cp ¼ 1e dT Both TCP and TCC are expressed in parts per million (ppm) per Kelvin. The temperature dependence of the capacitance and permittivity for PbTe film at various frequencies is shown in Figs. 5 and 6. The capacitance increases with increase in temperature. This may be partly due to the expansion of the lattice and partly due to the excitation of the charge carriers, which are likely to be present inside the specimen at defect sites [21]. The value of permittivity is very large (>400) and increases with increase in temperature which can be attributed to the fact that the orientation polarization is connected with the thermal motion of molecules, so dipoles can not orient themselves at low temperatures [22]. This interesting result may lead to the realization of devices. When the temperature is increased the orientation of dipoles is facilitated and this increases the value of orientational polarization, which increases e0 . The estimated values of TCC and TCP
90
350
303K 323K 343K 363K 383K 403K 423K 443K 463K
tan δ
250 200 150
80 0.5 KHz 1 KHz 5 KHz 10 KHz 50 KHz
70
Capacitance (nF)
300
100
60 50 40 30
50
20 0 2.0
2.5
3.0
3.5
4.0
4.5
5.0
log F (Hz) Fig. 4. Dependence of tan d on frequency at different temperatures.
300
320
340
360
380
400
420
440
Temperature (K) Fig. 5. Temperature dependence of capacitance of PbTe film.
460
61
L. Kungumadevi et al. / Solid-State Electronics 54 (2010) 58–62
0.0
1400
5KHz 100KHz
1200 -1.0
l KHz 5 KHz 10 KHz 50 KHz 100 KHz
1000
800
log σ
Dielectric Constant (ε)
-0.5
-1.5
-2.0
600 -2.5
400 2.2
300
320
340
360
380
400
420
440
460
480
for the film of thickness 5000 Å at 1 kHz for 340 K are 4032 ppm/ K and 3100 ppm/K. 3.3. AC conduction The AC conductivity ðr ¼ xC p tan dðd=AÞÞ of PbTe films has been calculated at various temperatures from the measured values of capacitance, Cp, dissipation factor and area of the capacitor, A and thickness, d. The frequency dependence of the AC conductivity of PbTe is shown in Fig. 7. The curves are seen to exhibit two dispersive regions one below 10 kHz and the other above 10 kHz. The AC conductivity is observed to be proportional to xn, where ‘n’ is seen to vary depending on the frequency and temperature range studied. At high frequencies, the curves approximate to square-law dependence on frequency and show relatively little dependence on temperature. At lower frequencies the curve shows straight line, but the slopes are now slightly greater than one [n = 1.051.23] and are temperature sensitive [21,25]. Fig. 8 shows the temperature dependence of AC conductivity of PbTe film at different frequencies. It is observed that the conductivity increases with temperature. The activation energies have
-2
log σ
-3
2.6
2.8
3.0
3.2
3.4
-1
1000/T (K )
Temperature (K) Fig. 6. Temperature dependence of permittivity of PbTe film.
2.4
Fig. 8. Temperature dependence of AC conductivity of PbTe film.
been determined from the slopes of these curves at different frequencies and are observed to decrease with increase of frequency. The calculated values of activation energy for the film of thickness 0 5000 Å A at 5 kHz and 100 kHz are 0.05267 and 0.0395 eV, respectively. This may be due to the increase of the applied field frequency enhances the electronic jumps between the localized states. The similar trend has been reported for various semiconductors [20,25–27]. Thus as frequency increases, the activation energy decreases to a small value, is a characteristic of thermally activated hopping. The low value of the activation energies in this film along with the frequency dependence of conductivity shows that the conduction mechanism may be due to the hopping of electrons, which is in accordance with earlier investigations on semiconducting films [25–27]. 4. Conclusion The X-ray analysis of thermally evaporated PbTe film shows that the film possesses polycrystalline nature having cubic structure. Annealing of the film in vacuum improves the dielectric properties. The capacitance and dielectric loss seems likely to be both frequency and temperature dependent. The value of dielectric constant varies from 349 to 1069. The large value of TCC and TCP indicates that the material is suitable for capacitor applications. Regarding the small value of activation energy along with the frequency dependence of conductivity, the conduction mechanism was suggested to be hopping conduction. References
303 K 323 K 343 K 363 K 383 K 403 K 423K
-4
-5
-6 2.5
3.0
3.5
4.0
4.5
5.0
log F (Hz) Fig. 7. Frequency dependence of AC conductivity at different temperature of PbTe film.
[1] Chao IN, McCann PJ, Yuan Wl, O’Rear EA, Yuan S. Thin Solid Films 1998;323:126–35. [2] Samoylov AM, Sharov MK, Buchnev SA, Khoviv AM, Dolgopolova EA. J Cryst Growth 2002;240:340–6. [3] Orozco RA, Sotelo-Lerma M, Ramirez-Bon R, Quevedo-Lopez MA, MendozaGonzalez O, et al. Thin Solid Films 1999;343–344:587–90. [4] Pop I, Nascu C, Ionescu V, Indrea E, Bratu I. Thin Solid Films 1997;307:240–4. [5] Tung YW, Cohen ML. Phys Rev 1969;180:823–6. [6] Rogacheva EI, Lyubchenko SG, Dresselhaus MD. Thin Solid Films 2005;476:391–5. [7] Rogacheva EI, Nashchekina ON, Tavrina TV, Us M, Dresselhaus MS, Cronin SB, et al. Physica E 2003;17:313–5. [8] Rodriguez E, Jimenez E, Jacob GJ, Neves AAR, Cesar CL, Barbosa CL. Physica E Low-dim Syst Nanostruct 2005;26:361–5. [9] Lach-hab M, Keegan M, Papaconstantopoulos DA, Mehl MJ. J Phys Chem Solids 2000;61:1639–45. [10] Dughaish ZH. Physica B 2002;322:205–23. [11] Mandale AB. Thin Solid Films 1991;195:15–21.
62 [12] [13] [14] [15] [16]
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Abd El-Ati MI. Phys Solid State 1997;39:68–71. Kumar S, Khan ZH, Majeed Khan MA, Husain M. Curr Appl Phys 2005;5:561–6. Baleva M, Surtchev M. Vacuum 2003;69:419–23. Jdanov A, Pelleg J, Dashevasky Z, Shneck R. Mater Sci Eng, B 2004;106:89–94. Kungumadevi L, Rajasekar K, Subbarayan A, Sathyamoorthy R. Ionics 2008;14:63–7. [17] Subbarayan A, Balasubramanian C, Narayandass SaK. Indian J Pure Appl Phys 1988;26:410–6. [18] Afifi MA, Bekheet AE, Abd Elwanhhah E, Atiya HE. Vacuum 2001;61:9–17. [19] Muruganand S, Narayandass Sa K, Mangalraj D, Vijayan TM. Polym Int 2001;50:1089–94.
[20] Dheepa J, Sathyamorthy R, Subbarayan A, Velumani S, Sebastian PJ. Sol Energy Mater Sol Cells 2005;88:187–98. [21] Balasundaram N, Mangalaraj D, Narayandass Sa K, Balasubramanian C. Phys Idus Sol Status (a) 1992;130:141–5. [22] Tsai MS, Tseng TY. Mater Chem Phys 1998;57:47–51. [23] Seyam MAM. Appl Surf Sci 2001;181:128–38. [24] Nagaraj D, Senthil K, Narayandass Sa K, Mangalraj D. Crys Res Technol 1997;34:867–72. [25] Argall F, Jonscher AK. Thin Solid Films 1968;2:185–210. [26] Jonscher AK. J Non-Cryst Solids 1972;8:293–315. [27] Walley PA. Thin Solid Films 1968;2:327–36.
Contents lists available at ScienceDirect
Solid-State Electronics journal homepage: www.elsevier.com/locate/sse
AC conductivity and dielectric properties of thermally evaporated PbTe thin films L. Kungumadevi, R. Sathyamoorthy *, A. Subbarayan PG and Research Department of Physics, Kongunadu Arts and Science College, Coimbatore 641 029, Tamil Nadu, India
a r t i c l e
i n f o
Article history: Received 2 February 2009 Received in revised form 31 July 2009 Accepted 10 September 2009 Available online 13 October 2009 The review of this paper was arranged by Dr. Y. Kuk
a b s t r a c t AC conductivity and dielectric properties of thermally evaporated lead telluride (PbTe) films have been investigated in the frequency range 30 Hz–100 kHz at various temperatures (303–483 K). The annealing process caused a stabilization of the dielectric properties due to the relief of stress and local structural rearrangement of atoms. The temperature coefficient of capacitance (TCC) and temperature coefficient of permittivity (TCP) have been estimated. The dominant conduction mechanism in the films is attributed to the hopping of thermally activated electrons under ac field. The results of variation of activation energy with frequency and thickness are discussed. Ó 2009 Elsevier Ltd. All rights reserved.
Keywords: Lead telluride (PbTe) Dielectric properties Conduction mechanism Activation energy
1. Introduction The IV–VI semiconductors PbS, PbSe and PbTe with the cubic NaCl (rock salt) structure, generally known as lead salts, have been the subject of a vast amount of theoretical and experimental work during the past decades, motivated not only by their technological applications, but also by their unusual physical properties. The unusual characteristics of lead salts such as high carrier mobilities, high dielectric constants and narrow band gaps make them unique among polar compounds and have important applications in many fields, such as infra-red detectors, light-emitting devices and more recently as infra red laser in fiber optics and thermoelectric devices [1–4]. Studies about heterostructures, films, quantum wires and quantum dots or wells of lead salts and their applications have caused much attention in the recent past [5–9]. PbTe is an intermediate thermoelectric power generator and its maximum operating temperature is 900 K. PbTe has high melting point, good chemical stability, low vapor pressure and good chemical strength in addition to high figure of merit (Z) [10]. Mandale [11] has studied resistivity, Hall constant, mobility, carrier density and thermoelectric power of vacuum deposited lead telluride films formed at room temperature and evaluated the effective hole mass from the observed thermoelectric power and correlated with transport properties. Abd El-Ati [12] has studied the electrical conductivity of PbTe thin films in which a transition of conductivity from ntype to p-type was observed. The thorough literature survey revealed that no researchers have studied the AC conduction and
* Corresponding author. Tel.: +91 422 2642095x208; fax: +91 422 2644452. E-mail address: [email protected] (R. Sathyamoorthy). 0038-1101/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.sse.2009.09.023
dielectric properties of lead telluride thin films in detail. Hence an attempt was made to study the AC and dielectric properties of vacuum evaporated lead telluride thin films and the results are presented in this paper with reasonable discussions. 2. Experimental details Pure aluminium (99.999%, Aldrich Chemicals Company) was evaporated from a tungsten filament onto pre cleaned glass substrates through suitable masks to form the base electrode. Lead telluride (99.998%, Sigma Aldrich Company, Bangalore) was then evaporated from a molybdenum boat under a pressure of 2 105 Torr to form a dielectric layer. An aluminium counter electrode was evaporated onto the dielectric to form Al/PbTe/Al (MSM) structure. Quartz–crystal thickness monitor was used to determine the thickness of the films. The capacitance and the dissipation factor for MSM structure in the frequency range from 30 Hz to 100 kHz at different temperatures (303–483 K) were measured using a Digital LCR meter (LCR-819, GW Instek, Goodwill Instrument Company Ltd., Taiwan). All the measurements were carried out under a rotary vacuum. A copper–constantan thermocouple is employed to sense the temperature of the sample during the measurements. 3. Results and discussion 3.1. Structural properties X-ray diffractogram of as-deposited and annealed film of thickness 5000 Å is shown in Fig. 1. The presence of sharp peaks in the
59
700 600
Table 2 Structural parameters of as-deposited and annealed PbTe film of thickness 5000 Å.
annealed at 573 K
(220)
(200)
L. Kungumadevi et al. / Solid-State Electronics 54 (2010) 58–62
500 400
(422)
(420)
100
(400)
(111)
200
(222)
300
a
Annealing temperature (K)
Lattice constanta (Å)
Crystallite size (nm)
Strain (e) 104
Dislocation density (d) 1014 lines/m2
As-deposited 100 °C 300 °C
6.458 6.455 6.459
44 48 48
10.11 9.69 7.61
9.54 7.74 4.49
Standard ‘a’ value 6.454 Å.
0 400
indicates that the degrees of preferred orientation along with the other microstructural features are more effective.
annealed at 373 K
Intensity (cps)
300 200
3.2. Dielectric properties
100
3.2.1. Effect of cyclic annealing Vacuum deposited MSM structures were annealed at about 373 K in a rotary vacuum. An annealing cycle comprises of the gradual increasing of temperature of the capacitor in an oven to annealing temperature, i.e. 373 K during first half an hour, maintaining that temperature for about 1 h constantly and then decreasing gradually to room temperature in the next half an hour. The changes in capacitance with frequency for different annealing cycles of the PbTe film of thickness 5000 Å is shown in Fig. 2. The capacitance decreases markedly in the first annealing cycle. The amount of reduction becomes smaller in the subsequent cycle. Freshly deposited films may have many defects and impurities such as voids, grain boundaries, dislocations, residual stress, inhomogeneities, etc. Annealing in vacuum further improves the dielectric properties. The defects are gradually reduced cycle after cycle and each atom may occupy a stable position in the interior of the film until the dielectric properties attain a stable value. It may be interpreted to the change of the structure of the investigated films by annealing. From XRD also we observed that the crystallinity has enhanced when the annealing temperature increases. Similar behavior on various organic and inorganic films has been reported earlier [17–20]. Similar behavior is observed for all the thickness of the film.
0 300
As deposited
200
100
0 10
20
30
40
50
60
70
80
2θ (degrees) Fig. 1. X-ray diffractogram of as-deposited and annealed PbTe film.
diffractogram suggests the polycrystalline nature of the film. The observed ‘d’ spacing and hkl planes (Table 1) are in good agreement with the JCPDS X-ray file data (card number 78–1905) of cubic PbTe and earlier reports [13–16] conforming the rock salt (NaCl) structure of the PbTe film. From the XRD profiles, the grain size, dislocation density, micro strain and lattice constant were calculated [16]. The degree of structural order of crystalline PbTe films improves with an increase in annealing temperature. As-deposited and annealed PbTe films are essentially of the same crystalline singlephase state except for a difference in crystallite size. The estimated lattice cell parameters for as-deposited and annealed films are given in Table 2. The computed lattice constant ‘a’ is in good agreement with the JCPDS (78–1905) value and with earlier investigations [13–16]. There is an increase in crystallite size and decrease in strain as well as dislocation density as annealing temperature increases. The annealing effect on structural parameters
3.2.2. Effects of frequency and temperature on dielectric parameters The variation of capacitance with frequency at different temperatures for PbTe film is presented in Fig. 3. It is observed that the capacitance decreases with increase in frequency at all temperatures and attain a constant value at higher temperatures. The large increase in capacitance at lower frequencies may be attributed to the blocking of charge carriers at the electrodes. Because of the impedance to their motion at the electrodes, space charge and macroscopic distortion results. The capacitance was found to decrease with increasing frequency and this may be due to the increasing inability of the dipole to become oriented in a rapidly
Table 1 Standard and experimental XRD data of as-deposited and annealed PbTe thin film. Standard values JCPDS (78–1905)
Experimental values obtained from XRD data As-deposited
Annealed at 100 °C
Annealed at 300 °C
2h (°)
d (Å)
hkl
2h (°)
d (Å)
2h (°)
d (Å)
2h (°)
d (Å)
23.860 27.619 39.458 46.636 48.842 57.031 64.518 71.562
3.7262 3.2270 2.2818 1.9459 1.8631 1.6135 1.4431 1.3174
111 200 220 311 222 400 420 422
23.800 27.521 39.417 46.530 48.803 56.850 64.440 71.540
3.7356 3.2383 2.2841 1.9502 1.8645 1.6182 1.4447 1.3178
23.750 27.510 39.414 46.620 48.790 56.912 64.527 71.560
3.7433 3.2396 2.2843 1.9466 1.8650 1.6166 1.4430 1.3174
23.796 27.568 39.443 – 48.842 56.973 64.504 71.596
3.7361 3.2329 2.2826 – 1.8631 1.6150 1.4434 1.3174
60
L. Kungumadevi et al. / Solid-State Electronics 54 (2010) 58–62
90
as-grown annealed : cycle 1 annealed : cycle 2
80
Capacitance ( nF)
70 60 50 40 30 20 2.5
3.0
3.5
4.0
4.5
5.0
log F ( Hz ) Fig. 2. Annealing effect on capacitance of PbTe film.
90
303K 323K 343K 363K 383K 403K 423K 443K
Capacitance(nF)
80 70 60 50 40 30 20 10 2.5
3.0
3.5
4.0
4.5
5.0
log F (Hz) Fig. 3. Dependence of capacitance on frequency at different temperature.
varying electric field. Similar behavior of the capacitance has been reported by various workers on various semiconductors [20–24]. The0 variation of tan d with frequency for the film of thickness 5000 Å A is shown in Fig. 4. If the electric polarization in a dielectric is unable to follow the varying electric field, dielectric loss occurs. An applied field will alter this energy difference thus producing a net polarization, which lags behind the applied field because the tunneling transition rates are finite. This part of the polarization, which is not in Phase with the applied field, is termed as dielectric loss. The loss factor increases with increase of temperature at high frequencies and it is almost a constant at low frequencies. At high frequencies the loss factor increases which may be due to the effect of lead resistance. 3.2.3. Temperature coefficient of capacitance and permittivity The temperature coefficient of capacitance is expressed as cc ¼ C1 dC dT Where ‘dC’ is the change in capacitance for a change of temperature ‘dT’. Since the permittivity of the dielectric between the two plates is proportional to the capacitance, it is possible to relate TCC to the temperature coefficient of permittivity TCP (cc)
cc ¼ cp þ a where a is the linear expansion coefficient of the dielectric and cp is de . given by the expression, cp ¼ 1e dT Both TCP and TCC are expressed in parts per million (ppm) per Kelvin. The temperature dependence of the capacitance and permittivity for PbTe film at various frequencies is shown in Figs. 5 and 6. The capacitance increases with increase in temperature. This may be partly due to the expansion of the lattice and partly due to the excitation of the charge carriers, which are likely to be present inside the specimen at defect sites [21]. The value of permittivity is very large (>400) and increases with increase in temperature which can be attributed to the fact that the orientation polarization is connected with the thermal motion of molecules, so dipoles can not orient themselves at low temperatures [22]. This interesting result may lead to the realization of devices. When the temperature is increased the orientation of dipoles is facilitated and this increases the value of orientational polarization, which increases e0 . The estimated values of TCC and TCP
90
350
303K 323K 343K 363K 383K 403K 423K 443K 463K
tan δ
250 200 150
80 0.5 KHz 1 KHz 5 KHz 10 KHz 50 KHz
70
Capacitance (nF)
300
100
60 50 40 30
50
20 0 2.0
2.5
3.0
3.5
4.0
4.5
5.0
log F (Hz) Fig. 4. Dependence of tan d on frequency at different temperatures.
300
320
340
360
380
400
420
440
Temperature (K) Fig. 5. Temperature dependence of capacitance of PbTe film.
460
61
L. Kungumadevi et al. / Solid-State Electronics 54 (2010) 58–62
0.0
1400
5KHz 100KHz
1200 -1.0
l KHz 5 KHz 10 KHz 50 KHz 100 KHz
1000
800
log σ
Dielectric Constant (ε)
-0.5
-1.5
-2.0
600 -2.5
400 2.2
300
320
340
360
380
400
420
440
460
480
for the film of thickness 5000 Å at 1 kHz for 340 K are 4032 ppm/ K and 3100 ppm/K. 3.3. AC conduction The AC conductivity ðr ¼ xC p tan dðd=AÞÞ of PbTe films has been calculated at various temperatures from the measured values of capacitance, Cp, dissipation factor and area of the capacitor, A and thickness, d. The frequency dependence of the AC conductivity of PbTe is shown in Fig. 7. The curves are seen to exhibit two dispersive regions one below 10 kHz and the other above 10 kHz. The AC conductivity is observed to be proportional to xn, where ‘n’ is seen to vary depending on the frequency and temperature range studied. At high frequencies, the curves approximate to square-law dependence on frequency and show relatively little dependence on temperature. At lower frequencies the curve shows straight line, but the slopes are now slightly greater than one [n = 1.051.23] and are temperature sensitive [21,25]. Fig. 8 shows the temperature dependence of AC conductivity of PbTe film at different frequencies. It is observed that the conductivity increases with temperature. The activation energies have
-2
log σ
-3
2.6
2.8
3.0
3.2
3.4
-1
1000/T (K )
Temperature (K) Fig. 6. Temperature dependence of permittivity of PbTe film.
2.4
Fig. 8. Temperature dependence of AC conductivity of PbTe film.
been determined from the slopes of these curves at different frequencies and are observed to decrease with increase of frequency. The calculated values of activation energy for the film of thickness 0 5000 Å A at 5 kHz and 100 kHz are 0.05267 and 0.0395 eV, respectively. This may be due to the increase of the applied field frequency enhances the electronic jumps between the localized states. The similar trend has been reported for various semiconductors [20,25–27]. Thus as frequency increases, the activation energy decreases to a small value, is a characteristic of thermally activated hopping. The low value of the activation energies in this film along with the frequency dependence of conductivity shows that the conduction mechanism may be due to the hopping of electrons, which is in accordance with earlier investigations on semiconducting films [25–27]. 4. Conclusion The X-ray analysis of thermally evaporated PbTe film shows that the film possesses polycrystalline nature having cubic structure. Annealing of the film in vacuum improves the dielectric properties. The capacitance and dielectric loss seems likely to be both frequency and temperature dependent. The value of dielectric constant varies from 349 to 1069. The large value of TCC and TCP indicates that the material is suitable for capacitor applications. Regarding the small value of activation energy along with the frequency dependence of conductivity, the conduction mechanism was suggested to be hopping conduction. References
303 K 323 K 343 K 363 K 383 K 403 K 423K
-4
-5
-6 2.5
3.0
3.5
4.0
4.5
5.0
log F (Hz) Fig. 7. Frequency dependence of AC conductivity at different temperature of PbTe film.
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