- Email: [email protected]
On the conduction mechanism of p-type GaSb bulk crystal
Materials Science and Engineering B 174 (2010) 285–289
Contents lists available at ScienceDirect
Materials Science and Engineering B journal homepage: www.elsevier.com/locate/mseb
On the conduction mechanism of p-type GaSb bulk crystal A.A. Ebnalwaled ∗ Physics Department, Faculty of Science, South Valley University, Qena 83523, Egypt
a r t i c l e
i n f o
Article history: Received 29 July 2009 Received in revised form 11 March 2010 Accepted 14 March 2010 Keywords: Bridgman technique Antimonides Ac conductivity Dc conductivity Power factor
a b s t r a c t Bulk crystals of gallium antimonide were grown using the vertical Bridgman techniques. The phase formation was confirmed by XRD studies. From dc and ac conductivity measurements, the conduction mechanism was investigated. The mobility ratio and the effective mass ratio were calculated to be 1.56 and 3.36 respectively. The measurements reveal higher values of power factor than the published results for the same compound. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Among the III–V semiconductors, gallium antimonide (GaSb) is an interesting material due to their applications as substrate for the development of optoelectronic devices with a band-gap emission in the range from 1.1 to 3.9 mm being useful for applications in optical fiber communication systems [1]. From the device point of view, gallium antimonide (GaSb) based structures have shown potentiality for applications in laser diodes with low threshold, photodetectors, super lattices with tailored optical and transport characteristics. Consequently, GaSb based binary and ternary alloys have turned out to be important candidates for applications in longer wavelength lasers, photodetectors for fiber optic communication and high speed duple heterojunction bipolar transistor. These have stimulated a lot of interest in GaSb for basic research as well as device fabrication [2–7]. Although GaSb crystals are widely grown by Czochralski method [8], the Bridgman method is currently widely used to produce good quality GaSb crystals [1,9–12]. Nominally, undoped GaSb is p-type due to native acceptor background impurities which can be identified at low-temperature PL spectra through transitions involving bands, and donor–acceptor pairs. These native acceptors are related to Sb deficiency (VSb ), Ga vacancies (VGa ), gain Sb sites with double ionizable nature and GaSb VGa complexes. These impurities are widely held identified as native acceptors, irrespective of the growth technique and growth conditions [13,14].
∗ Tel.: +20 10 4034633. E-mail address: kh [email protected]. 0921-5107/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2010.03.029
In this paper, I present the results of the experiments carried out to obtain low-defect GaSb crystals by the modified vertical Bridgman method. Results of the characterization studies such as XRD, EDX, electrical and thermoelectric properties of the grown crystals are also discussed.
2. Experimental 2.1. Crystal growth For preparing homogenized GaSb crystals, since the atomic weights of Ga and Sb are 69.72 and 121.75 amu respectively, the ratio by weight should be 1:1.75. High purity 99.9999% Ga, and Sb (they were obtained from Aldrich) were used as starting material. Extreme care was taken in the transfer of material to maintain the accuracy to the level of g/g of material. The materials were weighed by high sensitive rate and then transferred carefully to the ampoule, which previously was weighted empty, and then reweighing the ampoule after the development of materials to make sure the weight of the starting material. The modified vertical Bridgman technique was used to grow pure GaSb crystals. As crucibles, high quality quartz ampoules (with a proper conical tip at the bottom to facilitate nucleation for crystal growth) sealed at 10−4 Pa were used. The sealed ampoule was loaded into the sample holder and the furnace temperature was increased to 800 ◦ C and the melt was homogenized for 12 h. The growth was carried out at a rate of 3 mm h−1 in a modified [traveling solvent method (TSM)] Bridgman technique having a temperature gradient near 12 ◦ C/cm. More details about this technique can be found elsewhere [15].
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2.2. Characterization The surface of the grown crystals was analyzed by scanning electron microscopy. Also the homogeneity of the grown crystals was investigated with the aid of melting point test and electrical conductivity measurements of many cuts of each crystal. The EDX analysis was performed by (Elemental Analyzer EDXRF, JSX3222, JEOL, Japan). The X-ray diffractograms were measured stepwise with angle/s value of 0.02◦ at ambient temperature with a model D 5000 Siemens diffractometer (Germany). For the dc electrical conductivity measurements, the sample dimension was adjusted to be 9 mm × 3 mm × 2 mm by gentle cleavage and with the aid of fine polishing papers (0.5 Leco mark, USA). I used liquid nitrogen to cool the sample under room temperature. For the ac electrical conductivity measurements, the original shape of the product crystal was utilized, that is, the cylindrical form. Only the length was adjusted by polishing processes to be 4 mm while the crystal natural diameter was 10 mm. A two-part calorimeter was used. The inner part acted as a holder where the crystal was mounted on a flat end of a copper cylinder. It was heated electrically (the flat end was insulated from the crystal by thin sheets of mica). The second part of the calorimeter acted as a jacket to keep the measurements under vacuum. For thermoelectric measurements, the values of the thermoelectric power ˛ were obtained by measuring small potential differences along the length of samples during slow and gradual increase and decrease of a small temperature gradient (the largest temperature difference between both ends of sample being about 5 K). The temperature difference (T) was controlled in a differential mode with temperature controller (type elcont and eliwell). A very sensitive potentiometer (UJ33-E Mark) was used to measure the potential difference between both ends. The silver conducting paste contacts were soldered on the GaSb to carry out the electrical conductivity and thermoelectric measurements. We put a small point of silver paste on each contact area of a polished GaSb. The contacts were let to dry off in air and after that the specimen was annealed in evacuated atmosphere at 100 ◦ C. The ohmic nature of the contacts was verified by recording the current–voltage characteristics for forward and reverse directions. From the current–voltage characteristics, the ohmicity coefficient has the nearest value to 1. So the silver conducting paste was successfully employed as a contact. In this work, three different cuts from the virgin ingot (near the region corresponding to the beginning of the solidification process, the centre and the region corresponding to the final stages of the growth process) were prepared for both electrical and thermoelectric power measurements. No main differences were detected in the results and the general behavior.
Fig. 1. EDX spectrum of GaSb.
indexed with the Joint Committee on Powder Diffraction Standards (JCPDS) file 7–215 [16]. The lattice parameter for the obtained crystals is 6.092 Å, where the lattice parameter for the standard GaSb is 6.095 Å [16]. This result verifies the identity between the grown crystals and the standard one. Crystallite size (D) of the obtained GaSb crystals was calculated to be 69.8 nm from the Debye Scherrer’s formula [17]. 3.2. Dc conductivity studies The dc conductivity measured in the temperature range 253–420 K exhibits semiconducting behavior, with conductivity growing from 5.9 × 10−3 to 8.69 × 10−3 −1 cm−1 at room temperature (Fig. 3).
3. Results and discussion 3.1. Structural characterization The EDX analysis was made at five different places of the sample and it was found that the composition was uniform throughout the sample. From the corresponding EDX spectrum of GaSb, the Ga/Sb ratio (at.%) was found to be 0.99 (Fig. 1). The X-ray diffraction (XRD) pattern obtained at room temperature for the grown GaSb sample is shown in Fig. 2. Indexing and refinement of XRD pattern indicate the presence of a single-phase crystalline structure for the synthesized materials. The X-ray pattern confirms the existence of face centered cubic (FCC) structure with the reflection arising from 1 1 1, 2 0 0, 2 2 0, 3 1 1, 4 0 0, 3 3 1 and 4 2 2 planes. The grown sample has good crystallinity and can be
Fig. 2. XRD spectra of GaSb crystals.
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287
Fig. 4. log dc vs. T−1/4 for GaSb crystals.
Fig. 3. Typical variations of the dc electrical conductivity as a function of inverse temperature for GaSb crystals.
the ac conductivity follows the power law behavior [27]: As grown GaSb crystals were found to be p-type semiconductor, this result is in good agreement with published data [13,14]. The dc conductivity behavior can be explained using the following Arrhenius relations [18]: = 0 exp
−E a
2KB T
(Extrinsic conduction [253 K < T > 313 K])
= 0 exp
−Eg 2KB T
(1)
(Intrinsic conduction [379 K < T > 420 K])
(2)
where is the conductivity, 0 is a constant, KB is the Boltzmann constant, Ea is the impurity ionization energy, Eg is the energy gap width and T is the absolute temperature. From the above relationships Ea is deduced to be 0.13 eV while Eg is 0.71 eV. The obtained values for Ea and Eg are in good agreement with reported values by other authors [19–23]. The increase of dc in the intrinsic region (above 379 K) is regarded as a result of excitation of the carriers from the valence band to the conduction band. In the low-temperature region, the conduction may follow the variable range hopping (VRH) model [24,25]. According to VRH model, the dc conductivity is proportional to exp(−T0 /T)1/4 , T0 being the characteristic temperature. Fig. 4 shows the variation of log dc vs. T−1/4 which fits linearly indicating the validity of variable range hopping mechanism. For more study of conduction mechanism in GaSb crystals, I extend my work to study the behavior of ac conductivity with frequency and with temperature.
ac (ω) = Aωs
(3)
where A is temperature dependent constant and s is the frequency exponent and ω is angular frequency. Always (s ≤ 1) but in our case as indicated from Fig. 5 the value of s is greater than 1 in the high temperature range indicates that the conduction in this region is a thermally activated process [28,29], and the value of s is 0 in the low-temperature region indicates that the conduction is due to hopping in this region [30]. Fig. 6 shows the ac conductivity as a function of the reciprocal temperature at different frequencies for GaSb crystals. It is clear from the figure that ( ac ) increasing with decreasing the reciprocal of absolute temperature. This suggested that the ac conductivity is a thermally activated process from different localized states in the gap or its tails [31]. The activation energy of conduction E (ω) is calculated at different frequencies using the well-known equation: ac = 0 exp
E(ω) KB T
The frequency dependence of ac activation energy for the investigated sample is shown in Fig. 7. The obtained activation energy at any frequency is higher than the dc activation energy.
3.3. Ac conductivity studies The ac conductivity ( ac ) was studied over a frequency range of 102 to 105 Hz, for temperature varying from 290 to 420 K. Fig. 5 shows the typical ac conductivity behavior of GaSb crystals at different temperatures. The sample exhibits the high frequency dispersion and a frequency-independent conductivity at low frequencies, but at high frequencies ac increases with increasing frequency. The switch over from the frequency-independent region to frequency-dependent region is the signature of on set of conductivity relaxation [26]. For semiconductors and disordered systems
(4)
Fig. 5. The plot of log ac vs. log ω.
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Fig. 6. Temperature dependence of ac (ω) for GaSb crystals.
It is clear that E (ω) decreases with increasing frequency. Such a decrease can be attributed to that, the increase of the applied field enhances the charge carrier’s jumps between the localized states, consequently the activation energy E (ω) decreases with increasing frequency [32]. The smaller values of the ac activation energy and the decrease of E (ω) with frequency confirm that the hopping conduction is the dominant mechanism [31–33]. The obtained results from ac conductivity measurements confirm the obtained results from dc conductivity studies. 3.4. Seebeck coefficient measurements Shown in Fig. 8, the as-measured Seebeck coefficient of the obtained GaSb crystals. The Seebeck coefficient measurements show that the semiconducting character of GaSb crystals is p-type, since the Seebeck coefficient is positive. The value measured for the Seebeck coefficient at room temperature is 0.065 mV/K. It is clear from the graph that with increasing temperature in the extrinsic region, the Seebeck coefficient increases up from 0.0385 mV/K to a maximum value 0.097 mV/K occurring at about 322 K, after that a rapid decrease of the Seebeck coefficient is observed. As pointed
Fig. 7. Frequency dependence of the ac activation energy for GaSb crystals.
Fig. 8. Variation of the Seebeck coefficient as a function of temperature for GaSb crystals.
out earlier, the Seebeck coefficient continuously decreased as the hole concentration increased from underdoped to an overdoped state [34]. The expression for the Seebeck coefficient at high temperature was given by [35]: ˛=
KB e
n − p n + p
Eg 3 +2 + ln 2KB T 4
m∗n m∗p
(5)
Thus we constructed Fig. 9 to show the relationship between ˛ and 103 /T. From the figure the mobility ratio
(n /p ) was calculated to be 1.56, where the effective mass ratio m∗n /m∗p was calculated to be 3.36. The power factor, ˛2 , for thermoelectric conversion was calculated for GaSb crystals. The result is displayed in Fig. 10. As can be seen, the power factor of the sample reaches the maximum value at 322 K, about 8.82 × 10−5 mW/cm K2 . The obtained value is better than the published one for the same crystals as will as other crystals [36,37], also it is appropriate compared with published results for other crystals [38].
Fig. 9. The relationship between ˛ and 103 /T for GaSb crystals.
A.A. Ebnalwaled / Materials Science and Engineering B 174 (2010) 285–289
Fig. 10. The variation of the power factor with temperature for GaSb crystals.
4. Conclusion 1. GaSb was synthesized by modified vertical Bridgman technique from stochiometric melts. 2. The lattice parameter for the obtained crystals is 6.092 Å, and the crystallite size (D) was calculated to be 69.8 nm from the Debye Scherrer’s formula. 3. The conduction mechanism in the extrinsic region was found to be due to hopping conduction, but in the intrinsic region it was due to thermal activated process. 4. The dispersion of ac conductivity has been estimated in terms of frequency exponent s, which varies with temperature and is explained using CBH model. References [1] J.L. Plaza, P. Hidalgo, B. Mendez, J. Piqueras, J.L. Castano, E. Dieguez, Mater. Sci. Eng. B81 (2001) 157. [2] N. Bouarissa, Mater. Sci. Eng. B100 (2003) 280.
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[3] K. Zaima, R. Hashimoto, M. Ezaki, M. Nishioka, Y. Arakawa, J. Cryst. Growth 310 (2008) 4843. [4] N.K. Udayashankar, H.L. Bhat, Bull. Mater. Sci. 24 (5) (2001) 445. [5] Ch.B. Lioutas, G. Zoulis, S. Konidaris, E.K. Polychroniadis, D. Stroz, Micron 40 (2009) 6. [6] R. Wiersma, J.A.H. Stotz, O.J. Pitts, C.X. Wang, M.L.W. Thewalt, S.P. Watkins, J. Electron. Mater. 30 (11) (2001) 1429. [7] C.R. Bolognesi, S.P. Watkins, Compound Semiconductor 6 (94) (2000). [8] F. Moravec, J. Cryst. Growth 128 (1993) 457. [9] J.L. Plaza, P. Hidalgo, B. Méndez, J. Piqueras, E. Diéguez, J. Cryst. Growth 241 (3) (2002) 283. [10] Carmen Stelian, Thierry Duffar, J. Cryst. Growth 266 (1–3) (2004) 190. [11] Yu.A. Serebryakov, I.A. Prokhorov, V.N. Vlasov, E.N. Korobeynikova, B.G. Zakharov, I.L. Shul’pina, M.P. Marchenko, I.V. Fryazinov, J. Cryst. Growth 304 (1) (2007) 11. [12] J.A. Wei, L.L. Zheng, H. Zhang, Int. J. Heat Mass Transfer 52 (15–16) (2009) 3747. [13] I. Vurgaftman, J. Appl. Phys. 89 (2001) 5815. [14] L. Tirado-Mejıa, J.A. Villada, M. de los Rıos, J.A. Penafiel, G. Fonthal, D.G. Espinosa-Arbelaez, H. Ariza-Calderon, M.E. Rodrıguez-Garcı, Physica B 403 (2008) 4027. [15] G.A. Gamal, M. Abou Zied, A.A. Ebnalwaled, J. Alloys Compd. 431 (2007) 32. [16] Natl. Bur. Stand. (U.S.), Circ. 539, 6 (1956) 30. [17] V. Senthilkumar, M. Thamilselvan, K. PremNazeer, Sa.K. Narayandass, D. Mangalaraj, B. Karunagaran, K. Kim, J. Yi, Vacuum 79 (2005) 163. [18] M.T. Chang, L.J. Chou, C.H. Hsieh, Y.L. Chueh, Z.L. Wang, Y. Murakami, D. Shindo, Adv. Mater. 19 (2007) 2290. [19] S. Iyer, L. Small, S.M. Hedge, K.K. Bajaj, A. Abul-Fadl, J. Appl. Phys. 77 (1995) 5902. [20] D. Labrie, J.O. Brien, R.F. Redden, N. Audet, B. Lent, W.F. Micklethwaite, J. Vac. Technol. A18 (2007) 701. [21] S. Iyer, S. Hedge, K.K. Bajaj, Ali Abul-Fadl, W. Mitchel, J. Appl. Phys. 73 (1993) 3958. [22] A. Kuczkowski, S. Schulz, W. Assenmacher, J. Mater. Chem. 11 (2001) 3241. [23] S. Abroug, F. Saadallah, N. Yacoubi, J. Alloys Compd. 484 (2009) 772. [24] M. Viret, L. Ranno, J.M.D. Coey, Phys. Rev. B 55 (1997) 8067. [25] K. De, R. Ray, R.N. Panda, S. Giri, H. Nakamura, T. Kohara, J. Magn. Magn. Mater. 288 (2005) 339. [26] R. Murugaraj, G. Govindaraj, D. George, Mater. Lett. 57 (2003) 1656. [27] A.K. Jonscher, J. Mater. Sci. 16 (1981) 2037. [28] K. Funke, Prog. Solid State Chem. 22 (1993) 111. [29] P.V.B. Rao, E.V. Ramana, T.B. Sankaram, J. Alloys Compd. 467 (2009) 293. [30] N.E. Rajeevan, R. Kumar, D.K. Shukla, P.P. Pradyumnan, S.K. Arora, I.V. Shvets, Mater. Sci. Eng. B 163 (2009) 48. [31] I.G. Austin, N.F. Mott, Adv. Phys. 18 (1969) 41. [32] A.E. Bekheet, Physica B 403 (2008) 4342. [33] N.A. Hegab, M.A. Afifi, H.E. Atyia, A.S. Farid, J. Alloys Compd. 477 (2009) 925. [34] M.C. Sekhar, S.V. Suryanarayana, Physica C 415 (2004) 209. [35] V.A. Jonson, K.L. Horovitz, Phys. Rev. 92 (1953) 226. [36] K. Lu, Q. Wang, C. Li, Y. Wang, X. Chen, J. Non-Cryst. Solids 312–314 (2002) 34. [37] H.-J. Gau, J.-L. Yu, C.-C. Wu, Y.-K. Kuo, C.-H. Ho, J. Alloys Compd. 480 (2009) 73. [38] T. Souma, G. Nakamoto, M. Kurisu, J. Alloys Compd. 340 (2002) 275.
Contents lists available at ScienceDirect
Materials Science and Engineering B journal homepage: www.elsevier.com/locate/mseb
On the conduction mechanism of p-type GaSb bulk crystal A.A. Ebnalwaled ∗ Physics Department, Faculty of Science, South Valley University, Qena 83523, Egypt
a r t i c l e
i n f o
Article history: Received 29 July 2009 Received in revised form 11 March 2010 Accepted 14 March 2010 Keywords: Bridgman technique Antimonides Ac conductivity Dc conductivity Power factor
a b s t r a c t Bulk crystals of gallium antimonide were grown using the vertical Bridgman techniques. The phase formation was confirmed by XRD studies. From dc and ac conductivity measurements, the conduction mechanism was investigated. The mobility ratio and the effective mass ratio were calculated to be 1.56 and 3.36 respectively. The measurements reveal higher values of power factor than the published results for the same compound. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Among the III–V semiconductors, gallium antimonide (GaSb) is an interesting material due to their applications as substrate for the development of optoelectronic devices with a band-gap emission in the range from 1.1 to 3.9 mm being useful for applications in optical fiber communication systems [1]. From the device point of view, gallium antimonide (GaSb) based structures have shown potentiality for applications in laser diodes with low threshold, photodetectors, super lattices with tailored optical and transport characteristics. Consequently, GaSb based binary and ternary alloys have turned out to be important candidates for applications in longer wavelength lasers, photodetectors for fiber optic communication and high speed duple heterojunction bipolar transistor. These have stimulated a lot of interest in GaSb for basic research as well as device fabrication [2–7]. Although GaSb crystals are widely grown by Czochralski method [8], the Bridgman method is currently widely used to produce good quality GaSb crystals [1,9–12]. Nominally, undoped GaSb is p-type due to native acceptor background impurities which can be identified at low-temperature PL spectra through transitions involving bands, and donor–acceptor pairs. These native acceptors are related to Sb deficiency (VSb ), Ga vacancies (VGa ), gain Sb sites with double ionizable nature and GaSb VGa complexes. These impurities are widely held identified as native acceptors, irrespective of the growth technique and growth conditions [13,14].
∗ Tel.: +20 10 4034633. E-mail address: kh [email protected]. 0921-5107/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2010.03.029
In this paper, I present the results of the experiments carried out to obtain low-defect GaSb crystals by the modified vertical Bridgman method. Results of the characterization studies such as XRD, EDX, electrical and thermoelectric properties of the grown crystals are also discussed.
2. Experimental 2.1. Crystal growth For preparing homogenized GaSb crystals, since the atomic weights of Ga and Sb are 69.72 and 121.75 amu respectively, the ratio by weight should be 1:1.75. High purity 99.9999% Ga, and Sb (they were obtained from Aldrich) were used as starting material. Extreme care was taken in the transfer of material to maintain the accuracy to the level of g/g of material. The materials were weighed by high sensitive rate and then transferred carefully to the ampoule, which previously was weighted empty, and then reweighing the ampoule after the development of materials to make sure the weight of the starting material. The modified vertical Bridgman technique was used to grow pure GaSb crystals. As crucibles, high quality quartz ampoules (with a proper conical tip at the bottom to facilitate nucleation for crystal growth) sealed at 10−4 Pa were used. The sealed ampoule was loaded into the sample holder and the furnace temperature was increased to 800 ◦ C and the melt was homogenized for 12 h. The growth was carried out at a rate of 3 mm h−1 in a modified [traveling solvent method (TSM)] Bridgman technique having a temperature gradient near 12 ◦ C/cm. More details about this technique can be found elsewhere [15].
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2.2. Characterization The surface of the grown crystals was analyzed by scanning electron microscopy. Also the homogeneity of the grown crystals was investigated with the aid of melting point test and electrical conductivity measurements of many cuts of each crystal. The EDX analysis was performed by (Elemental Analyzer EDXRF, JSX3222, JEOL, Japan). The X-ray diffractograms were measured stepwise with angle/s value of 0.02◦ at ambient temperature with a model D 5000 Siemens diffractometer (Germany). For the dc electrical conductivity measurements, the sample dimension was adjusted to be 9 mm × 3 mm × 2 mm by gentle cleavage and with the aid of fine polishing papers (0.5 Leco mark, USA). I used liquid nitrogen to cool the sample under room temperature. For the ac electrical conductivity measurements, the original shape of the product crystal was utilized, that is, the cylindrical form. Only the length was adjusted by polishing processes to be 4 mm while the crystal natural diameter was 10 mm. A two-part calorimeter was used. The inner part acted as a holder where the crystal was mounted on a flat end of a copper cylinder. It was heated electrically (the flat end was insulated from the crystal by thin sheets of mica). The second part of the calorimeter acted as a jacket to keep the measurements under vacuum. For thermoelectric measurements, the values of the thermoelectric power ˛ were obtained by measuring small potential differences along the length of samples during slow and gradual increase and decrease of a small temperature gradient (the largest temperature difference between both ends of sample being about 5 K). The temperature difference (T) was controlled in a differential mode with temperature controller (type elcont and eliwell). A very sensitive potentiometer (UJ33-E Mark) was used to measure the potential difference between both ends. The silver conducting paste contacts were soldered on the GaSb to carry out the electrical conductivity and thermoelectric measurements. We put a small point of silver paste on each contact area of a polished GaSb. The contacts were let to dry off in air and after that the specimen was annealed in evacuated atmosphere at 100 ◦ C. The ohmic nature of the contacts was verified by recording the current–voltage characteristics for forward and reverse directions. From the current–voltage characteristics, the ohmicity coefficient has the nearest value to 1. So the silver conducting paste was successfully employed as a contact. In this work, three different cuts from the virgin ingot (near the region corresponding to the beginning of the solidification process, the centre and the region corresponding to the final stages of the growth process) were prepared for both electrical and thermoelectric power measurements. No main differences were detected in the results and the general behavior.
Fig. 1. EDX spectrum of GaSb.
indexed with the Joint Committee on Powder Diffraction Standards (JCPDS) file 7–215 [16]. The lattice parameter for the obtained crystals is 6.092 Å, where the lattice parameter for the standard GaSb is 6.095 Å [16]. This result verifies the identity between the grown crystals and the standard one. Crystallite size (D) of the obtained GaSb crystals was calculated to be 69.8 nm from the Debye Scherrer’s formula [17]. 3.2. Dc conductivity studies The dc conductivity measured in the temperature range 253–420 K exhibits semiconducting behavior, with conductivity growing from 5.9 × 10−3 to 8.69 × 10−3 −1 cm−1 at room temperature (Fig. 3).
3. Results and discussion 3.1. Structural characterization The EDX analysis was made at five different places of the sample and it was found that the composition was uniform throughout the sample. From the corresponding EDX spectrum of GaSb, the Ga/Sb ratio (at.%) was found to be 0.99 (Fig. 1). The X-ray diffraction (XRD) pattern obtained at room temperature for the grown GaSb sample is shown in Fig. 2. Indexing and refinement of XRD pattern indicate the presence of a single-phase crystalline structure for the synthesized materials. The X-ray pattern confirms the existence of face centered cubic (FCC) structure with the reflection arising from 1 1 1, 2 0 0, 2 2 0, 3 1 1, 4 0 0, 3 3 1 and 4 2 2 planes. The grown sample has good crystallinity and can be
Fig. 2. XRD spectra of GaSb crystals.
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287
Fig. 4. log dc vs. T−1/4 for GaSb crystals.
Fig. 3. Typical variations of the dc electrical conductivity as a function of inverse temperature for GaSb crystals.
the ac conductivity follows the power law behavior [27]: As grown GaSb crystals were found to be p-type semiconductor, this result is in good agreement with published data [13,14]. The dc conductivity behavior can be explained using the following Arrhenius relations [18]: = 0 exp
−E a
2KB T
(Extrinsic conduction [253 K < T > 313 K])
= 0 exp
−Eg 2KB T
(1)
(Intrinsic conduction [379 K < T > 420 K])
(2)
where is the conductivity, 0 is a constant, KB is the Boltzmann constant, Ea is the impurity ionization energy, Eg is the energy gap width and T is the absolute temperature. From the above relationships Ea is deduced to be 0.13 eV while Eg is 0.71 eV. The obtained values for Ea and Eg are in good agreement with reported values by other authors [19–23]. The increase of dc in the intrinsic region (above 379 K) is regarded as a result of excitation of the carriers from the valence band to the conduction band. In the low-temperature region, the conduction may follow the variable range hopping (VRH) model [24,25]. According to VRH model, the dc conductivity is proportional to exp(−T0 /T)1/4 , T0 being the characteristic temperature. Fig. 4 shows the variation of log dc vs. T−1/4 which fits linearly indicating the validity of variable range hopping mechanism. For more study of conduction mechanism in GaSb crystals, I extend my work to study the behavior of ac conductivity with frequency and with temperature.
ac (ω) = Aωs
(3)
where A is temperature dependent constant and s is the frequency exponent and ω is angular frequency. Always (s ≤ 1) but in our case as indicated from Fig. 5 the value of s is greater than 1 in the high temperature range indicates that the conduction in this region is a thermally activated process [28,29], and the value of s is 0 in the low-temperature region indicates that the conduction is due to hopping in this region [30]. Fig. 6 shows the ac conductivity as a function of the reciprocal temperature at different frequencies for GaSb crystals. It is clear from the figure that ( ac ) increasing with decreasing the reciprocal of absolute temperature. This suggested that the ac conductivity is a thermally activated process from different localized states in the gap or its tails [31]. The activation energy of conduction E (ω) is calculated at different frequencies using the well-known equation: ac = 0 exp
E(ω) KB T
The frequency dependence of ac activation energy for the investigated sample is shown in Fig. 7. The obtained activation energy at any frequency is higher than the dc activation energy.
3.3. Ac conductivity studies The ac conductivity ( ac ) was studied over a frequency range of 102 to 105 Hz, for temperature varying from 290 to 420 K. Fig. 5 shows the typical ac conductivity behavior of GaSb crystals at different temperatures. The sample exhibits the high frequency dispersion and a frequency-independent conductivity at low frequencies, but at high frequencies ac increases with increasing frequency. The switch over from the frequency-independent region to frequency-dependent region is the signature of on set of conductivity relaxation [26]. For semiconductors and disordered systems
(4)
Fig. 5. The plot of log ac vs. log ω.
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Fig. 6. Temperature dependence of ac (ω) for GaSb crystals.
It is clear that E (ω) decreases with increasing frequency. Such a decrease can be attributed to that, the increase of the applied field enhances the charge carrier’s jumps between the localized states, consequently the activation energy E (ω) decreases with increasing frequency [32]. The smaller values of the ac activation energy and the decrease of E (ω) with frequency confirm that the hopping conduction is the dominant mechanism [31–33]. The obtained results from ac conductivity measurements confirm the obtained results from dc conductivity studies. 3.4. Seebeck coefficient measurements Shown in Fig. 8, the as-measured Seebeck coefficient of the obtained GaSb crystals. The Seebeck coefficient measurements show that the semiconducting character of GaSb crystals is p-type, since the Seebeck coefficient is positive. The value measured for the Seebeck coefficient at room temperature is 0.065 mV/K. It is clear from the graph that with increasing temperature in the extrinsic region, the Seebeck coefficient increases up from 0.0385 mV/K to a maximum value 0.097 mV/K occurring at about 322 K, after that a rapid decrease of the Seebeck coefficient is observed. As pointed
Fig. 7. Frequency dependence of the ac activation energy for GaSb crystals.
Fig. 8. Variation of the Seebeck coefficient as a function of temperature for GaSb crystals.
out earlier, the Seebeck coefficient continuously decreased as the hole concentration increased from underdoped to an overdoped state [34]. The expression for the Seebeck coefficient at high temperature was given by [35]: ˛=
KB e
n − p n + p
Eg 3 +2 + ln 2KB T 4
m∗n m∗p
(5)
Thus we constructed Fig. 9 to show the relationship between ˛ and 103 /T. From the figure the mobility ratio
(n /p ) was calculated to be 1.56, where the effective mass ratio m∗n /m∗p was calculated to be 3.36. The power factor, ˛2 , for thermoelectric conversion was calculated for GaSb crystals. The result is displayed in Fig. 10. As can be seen, the power factor of the sample reaches the maximum value at 322 K, about 8.82 × 10−5 mW/cm K2 . The obtained value is better than the published one for the same crystals as will as other crystals [36,37], also it is appropriate compared with published results for other crystals [38].
Fig. 9. The relationship between ˛ and 103 /T for GaSb crystals.
A.A. Ebnalwaled / Materials Science and Engineering B 174 (2010) 285–289
Fig. 10. The variation of the power factor with temperature for GaSb crystals.
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