- Email: [email protected]
The effect of temperature gradient on the morphology of YBCO bulk superconductors by melt texture growth processing
Journal of Alloys and Compounds 415 (2006) 276–279
The effect of temperature gradient on the morphology of YBCO bulk superconductors by melt texture growth processing W.M. Yang a,∗ , L. Zhou b , Y. Feng b , P.X. Zhang b , C.P. Zhang b a b
Department of Physics, Shaanxi Normal University, Xi’an 710062, Shaanxi, PR China Northwest Institute for Nonferrous Metal Research, Xi’an, Shaanxi 710016, PR China
Received 26 June 2005; received in revised form 31 July 2005; accepted 4 August 2005 Available online 19 September 2005
Abstract The effects of lateral temperature gradient (TG) on the macrostructure and levitation force of YBCO bulk superconductors have been investigated. The results indicate that a positive lateral TG is more effective to depress the randomly nucleation of Y123 grain number. The levitation force of samples fabricated in this kind of furnace is about 2.5 times higher than that of samples fabricated in furnace without a positive lateral TG. A single domain YBCO bulk (30 mm) with levitation force of 94 N has been fabricated. © 2005 Elsevier B.V. All rights reserved. Keywords: YBCO superconductors; Melt textured; Temperature gradient; Levitation force
1. Introduction Since the discovery of high Tc temperature superconductors, great progress has been made in both fundamental research and practical applications. Well-textured YBCO [1–4] is one of the most important and practical high temperature superconductors due to its high Tc and high Jc in magnetic field, especially the high levitation force, which makes it possible for various applications, such as in magnetic bearing [5,6], motors [7], as trapped flux magnets (magnetic separation, etc.) [8,9] and no contact magnetic levitation transport system [10], etc. The applications are based on high quality superconductors, melt processing technique is one of the most effective way to fabricate YBCO bulk superconductors with high levitation force and stronger trapped flux density. In order to achieve high levitation forces, single domain or large domain size of YBCO bulk sample is necessary. One way for increasing the domain size of a sample is to use seeding technique, but the seeding method is not sufficient to ensure a single nucleation site in the sample during the melt ∗
Corresponding author. Tel.: +86 29 623 1079; fax: +86 29 623 1103. E-mail address: [email protected] (W.M. Yang).
0925-8388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2005.08.007
growth processing. In this paper our experiments indicated that using the seeding technique and a positive lateral TG, single domain YBCO bulk samples can be fabricated.
2. Experiment X-ray pure YBa2 Cu3 Oy , Y2 BaCuO5 powders and CeO2 were weighed and mixed in the weight ratio of 79.5:20:0.5. The well-mixed powders were uniaxially pressed into pellets by a steel mould. All the precursor pellets are with the same composition and the same size of 35 mm × 14 mm. The Sm2 O3 powder and a Nd1+x Ba2−x Cu3 Oy single crystal [11] were used as seeds in this study. Both samples #1 and #2 were fabricated with Sm2 O3 powder as seeds. Sample #1 was fabricated in furnace #1 with a positive lateral TG as shown in Fig. 1 and sample #2 was obtained in furnace #2 with a negative lateral TG as shown in Fig. 2. Sample #3 with the Nd1+x Ba2−x Cu3 Oy single crystal [11] as seed was fabricated in furnace #1. All the samples were melt processed as following: the precursor samples were heated to about 1050 ◦ C and hold for 2 h, then quickly cooled to 1020 ◦ C, and cooled to 960 ◦ C at rate of less than 1 ◦ C/h,
W.M. Yang et al. / Journal of Alloys and Compounds 415 (2006) 276–279
277
after that, the samples were cooled to room temperature. Finally the as grown samples were oxygenated in flowing O2 between 400 and 550 ◦ C for about a week to make them into superconducting state. Finally the three samples have the same dimension, 30 mm. The macrostructure of the samples was investigated by using optical microscopy. The levitation forces were measured with a home made system at liquid nitrogen temperature.
3. Results and discussion Furnaces #1 and #2 are tube furnaces and the axes of them are set in vertical direction, but furnace #1 has a poor heat preservation layer and furnace #2 has of a good heat preservation layer, which cause them to have different temperature distribution profiles. Figs. 1 and 2 shows the temperature dis-
Fig. 1. The temperature distribution along the axial direction of furnace #1, one is the temperature distribution just along the center axial line of the furnace, the other is measured along the axial line but near the inside wall of the tube furnace; a negative TG of −2.5 ◦ C/cm in axial direction and a positive lateral TG of 2 ◦ C/cm in the range where the ample located.
Fig. 2. The temperature distribution along the axial direction of furnace #2, one is the temperature distribution just along the center axial line of the furnace, the other is measured along the axial line but near the inside wall of the tube furnace; a negative TG of −2.5 ◦ C/cm in axial direction and a negative lateral TG of −2 ◦ C/cm in the range where the ample located.
Fig. 3. The levitation force vs. distance curves between the magnet and the samples #1 and #2 at liquid nitrogen temperature, the magnet is of 30 mm, and B is about 0.5 T at the center of the top surface.
tribution along the axial direction, there are two curves in each figure, one is the temperature distribution just along the center axial line of the furnace, the other is measured along the axial line but near the inside wall of the tube furnace. As we can see from Figs. 1 and 2, the samples were located at a place with a negative TG (−2.5 ◦ C/cm) in axial direction for both furnaces, but with a positive lateral TG 2 ◦ C/cm for furnace #1 and a negative lateral TG −2 ◦ C/cm for furnace 2#, respectively, this is the difference. Fig. 3 shows the levitation forces versus the distance between a given magnet (30 mm) and the samples at 77 K. The magnetic flux density of the magnet is about 0.5 T at the center of the top surface. It can be seen from this figure that the maximum levitation force of sample #1 is 52 N, about 2.5 times higher than that of sample #2 (21 N). As we know, for superconductors with similar dimensions, the levitation force mainly depends on the critical current density (Jc ), and the radius (r) of the induced current loop in the superconductor, the larger the r and Jc values, the higher the levitation force [12]. Because the magnet used in this experimental is the same for all the measurement, so the difference of the levitation force between samples #1 and #2 is only dependent on the difference between the samples. Fig. 4 shows the polished top surface morphology of the two samples, it is easy to see that domain size of the sample #1 is larger than that of sample #2 and the number of domains of sample #1 is less than that of sample #2. This exactly confirms that the value of r is larger in sample #1, the results is in agreement with reference [12]. In addition, the magnetized Jc measured by VSM is almost the same in each domain of the two samples; therefore the higher levitation force is obtained in sample #1. As we can see from Fig. 4, The sample #1 has a few fanshaped large YBCO domains, and the sample #2 has a number of randomly oriented YBCO domains. The morphology difference of samples is mainly dependent on the lateral TG of the furnace in which the samples are fabricated. In furnace #2, the temperature along the axial line but near inside wall
278
W.M. Yang et al. / Journal of Alloys and Compounds 415 (2006) 276–279
Fig. 5. The levitation force vs. distance curves between the magnet and the samples #3 at liquid nitrogen temperature, the magnet is of 30 mm, and B is about 0.5 T at the center of the top surface.
Fig. 4. The optical macrostructure of the samples, all the three samples are of the same 30 mm: sample #1 (a) fabricated in furnace #1 with a positive lateral TG and a Sm2 O3 seed; sample #2 (b) fabricated in furnace #2 with a negative lateral TG and a Sm2 O3 seed; sample #3 (c) fabricated in furnace #1 with a positive lateral TG and a NdBCO single crystal seed.
is always lower than that along the center axial line in the regime where the samples are located. The longitudinal TG is −2.5 ◦ C/cm and the lateral TG is −2 ◦ C/cm. When the samples are slowly cooled through the peritectic temperature, the temperature at edges will be lower than that of the center on the top surface of the sample, so the YBCO grains will be easy to nucleate at the edges and grow. No matter
what the TG changes, Sm2 O3 powder is still a nucleation site for Y123 phase, but it cannot prevent the YBCO grains from nucleating at the edges. So the Sm2 O3 powder is not the only nucleating site for YBCO grain, the random YBCO grain nucleation and growth lead to grains impinging and finally result in small grain domains. In furnace #1, the temperature near the inside wall is always higher than that along the center axial in the regime where the sample is located. The longitudinal TG is −2.5 ◦ C/cm, and the lateral TG is about 2 ◦ C/cm. The positive lateral TG and the negative longitudinal TG will ensure the YBCO grain to nucleate at the center where the Sm2 O3 powder is placed, and grows toward the edges of the sample, this agrees with the results reported by Salama and co-workers [13]. According to the experiments above, it tells us that Sm2 O3 powder can be used as a seed to obtain larger domain YBCO bulks, but it is not easy to obtain a good YBCO sample, because Sm2 O3 powder can only provide a nucleation site but cannot influence the orientation of the SmBCO and YBCO grains. In order to further improve the quality of YBCO bulks, a single domain YBCO bulk superconductors (sample #3, 30 mm) has been fabricated in furnace #1 by using a single NdBCO crystal as seed, as shown in Fig. 4, the levitation force is shown in Fig. 5, the maximum levitation force is about 94 N obtained at a gap of 0.5 mm between the two near surface of the magnet and YBCO bulk at 77 K.
W.M. Yang et al. / Journal of Alloys and Compounds 415 (2006) 276–279
4. Conclusion It is found that a positive lateral TG is more effective for the fabrication of large domain-sized YBCO pellets compared to a negative lateral TG during the fabrication of YBCO bulks. Large domains of fan-shaped YBCO pellets have been fabricated using Sm2 O3 powder as seed, the levitation force of these samples is about 2–3 times higher than that of samples fabricated in furnace with a negative lateral TG. A single domain YBCO bulk has been fabricated by using a single NdBCO crystal as seed, the maximum levitation force is about 94 N at liquid nitrogen temperature.
Acknowledgment This work was supported by the key science and technology project of Chinese ministry of education, No. 105154.
References [1] S. Jin, T.H. Teifel, R.C. Sherwood, E.M. Gyorgy, T.H. Tiefel, R.B. van Dover, S. Nakahala, L.F. Schneemeyer, R.A. Fastnacht, M.E. Davis, Appl. Phys. Lett. 54 (1989) 584.
279
[2] S.K. Selvamaickanov, L. Gao, K. Sun, Appl. Phys. Lett. 54 (1989) 2352. [3] M. Murakami, M. Morita, N. Koyama, Jpn. J. Appl. Phys. 28 (1989) L1125. [4] Zhou Lian, Zhang Pingxiang, Ji Ping, Wang Keguang, Wang Jingrong, Wu Xiaozu, Supercond. Sci. Technol. 10 (1990) 490. [5] John R. Hull, Shaul Hanany, Tomotake Matsumura, Bradley Johnson, Terry Jones, Supercond. Sci. Technol. 18 (2005) S1. [6] F.N. Werfel, U. Floegel-Delor, R. Rothfeld, B. Goebel, D. Wippich, T. Riedel, Supercond. Sci. Technol. 18 (2005) S19. [7] B. Oswald, K.-J. Best, M. Setzer, M. S¨oll, W. Gawalek, A. Gutt, L. Kovalev, G. Krabbes, L. Fisher, H.C. Freyhardt, Supercond. Sci. Technol. 18 (2005) S24. [8] S. Gruss, G. Fuchs, G. Krabbes, P. Verges, G. St¨overs, K.H. M¨oller, J. Fink, L. Schultz, Appl. Phys. Lett. 79 (2001) 3131. [9] M. Tomita, M. Murakami, Nature 421 (2003) 517. [10] Jiasu Wang, Suyu Wang, Youwen Zeng, Haiyu Huang, Fang Luo, Zhipei Xu, Qixue Tang, Guobin Lin, Cuifang Zhang, Zhongyou Ren, Guomin Zhao, Degui Zhu, Shaohua Wang, He Jiang, Min Zhu, Changyan Deng, Pengfei Hu, Chaoyong Li, Fang Liu, Jisan Lian, Xiaorong Wang, Lianghui Wang, Xuming Shen, Xiaogang Dong, Physica C 378–381 (2002) 809. [11] W.M. Yang, L. Zhou, Y. Feng, P.X. Zhang, C.P. Zhang, Z.M. Yu, Physica C 337 (2000) 115. [12] M. Murakami, T. Oyama, H. Fujimoto, T. Taguchi, S. Gotoh, Y. Shiohara, N. Koshizuka, S. Tanaka, Jpn. J. Appl. Phys. 29 (1990) L1991. [13] D.F. Lee, C.S. Partsinevelos, R.G. Presswood Jr., K. Salama, J. Appl. Phys. 76 (1994) 603.
The effect of temperature gradient on the morphology of YBCO bulk superconductors by melt texture growth processing W.M. Yang a,∗ , L. Zhou b , Y. Feng b , P.X. Zhang b , C.P. Zhang b a b
Department of Physics, Shaanxi Normal University, Xi’an 710062, Shaanxi, PR China Northwest Institute for Nonferrous Metal Research, Xi’an, Shaanxi 710016, PR China
Received 26 June 2005; received in revised form 31 July 2005; accepted 4 August 2005 Available online 19 September 2005
Abstract The effects of lateral temperature gradient (TG) on the macrostructure and levitation force of YBCO bulk superconductors have been investigated. The results indicate that a positive lateral TG is more effective to depress the randomly nucleation of Y123 grain number. The levitation force of samples fabricated in this kind of furnace is about 2.5 times higher than that of samples fabricated in furnace without a positive lateral TG. A single domain YBCO bulk (30 mm) with levitation force of 94 N has been fabricated. © 2005 Elsevier B.V. All rights reserved. Keywords: YBCO superconductors; Melt textured; Temperature gradient; Levitation force
1. Introduction Since the discovery of high Tc temperature superconductors, great progress has been made in both fundamental research and practical applications. Well-textured YBCO [1–4] is one of the most important and practical high temperature superconductors due to its high Tc and high Jc in magnetic field, especially the high levitation force, which makes it possible for various applications, such as in magnetic bearing [5,6], motors [7], as trapped flux magnets (magnetic separation, etc.) [8,9] and no contact magnetic levitation transport system [10], etc. The applications are based on high quality superconductors, melt processing technique is one of the most effective way to fabricate YBCO bulk superconductors with high levitation force and stronger trapped flux density. In order to achieve high levitation forces, single domain or large domain size of YBCO bulk sample is necessary. One way for increasing the domain size of a sample is to use seeding technique, but the seeding method is not sufficient to ensure a single nucleation site in the sample during the melt ∗
Corresponding author. Tel.: +86 29 623 1079; fax: +86 29 623 1103. E-mail address: [email protected] (W.M. Yang).
0925-8388/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2005.08.007
growth processing. In this paper our experiments indicated that using the seeding technique and a positive lateral TG, single domain YBCO bulk samples can be fabricated.
2. Experiment X-ray pure YBa2 Cu3 Oy , Y2 BaCuO5 powders and CeO2 were weighed and mixed in the weight ratio of 79.5:20:0.5. The well-mixed powders were uniaxially pressed into pellets by a steel mould. All the precursor pellets are with the same composition and the same size of 35 mm × 14 mm. The Sm2 O3 powder and a Nd1+x Ba2−x Cu3 Oy single crystal [11] were used as seeds in this study. Both samples #1 and #2 were fabricated with Sm2 O3 powder as seeds. Sample #1 was fabricated in furnace #1 with a positive lateral TG as shown in Fig. 1 and sample #2 was obtained in furnace #2 with a negative lateral TG as shown in Fig. 2. Sample #3 with the Nd1+x Ba2−x Cu3 Oy single crystal [11] as seed was fabricated in furnace #1. All the samples were melt processed as following: the precursor samples were heated to about 1050 ◦ C and hold for 2 h, then quickly cooled to 1020 ◦ C, and cooled to 960 ◦ C at rate of less than 1 ◦ C/h,
W.M. Yang et al. / Journal of Alloys and Compounds 415 (2006) 276–279
277
after that, the samples were cooled to room temperature. Finally the as grown samples were oxygenated in flowing O2 between 400 and 550 ◦ C for about a week to make them into superconducting state. Finally the three samples have the same dimension, 30 mm. The macrostructure of the samples was investigated by using optical microscopy. The levitation forces were measured with a home made system at liquid nitrogen temperature.
3. Results and discussion Furnaces #1 and #2 are tube furnaces and the axes of them are set in vertical direction, but furnace #1 has a poor heat preservation layer and furnace #2 has of a good heat preservation layer, which cause them to have different temperature distribution profiles. Figs. 1 and 2 shows the temperature dis-
Fig. 1. The temperature distribution along the axial direction of furnace #1, one is the temperature distribution just along the center axial line of the furnace, the other is measured along the axial line but near the inside wall of the tube furnace; a negative TG of −2.5 ◦ C/cm in axial direction and a positive lateral TG of 2 ◦ C/cm in the range where the ample located.
Fig. 2. The temperature distribution along the axial direction of furnace #2, one is the temperature distribution just along the center axial line of the furnace, the other is measured along the axial line but near the inside wall of the tube furnace; a negative TG of −2.5 ◦ C/cm in axial direction and a negative lateral TG of −2 ◦ C/cm in the range where the ample located.
Fig. 3. The levitation force vs. distance curves between the magnet and the samples #1 and #2 at liquid nitrogen temperature, the magnet is of 30 mm, and B is about 0.5 T at the center of the top surface.
tribution along the axial direction, there are two curves in each figure, one is the temperature distribution just along the center axial line of the furnace, the other is measured along the axial line but near the inside wall of the tube furnace. As we can see from Figs. 1 and 2, the samples were located at a place with a negative TG (−2.5 ◦ C/cm) in axial direction for both furnaces, but with a positive lateral TG 2 ◦ C/cm for furnace #1 and a negative lateral TG −2 ◦ C/cm for furnace 2#, respectively, this is the difference. Fig. 3 shows the levitation forces versus the distance between a given magnet (30 mm) and the samples at 77 K. The magnetic flux density of the magnet is about 0.5 T at the center of the top surface. It can be seen from this figure that the maximum levitation force of sample #1 is 52 N, about 2.5 times higher than that of sample #2 (21 N). As we know, for superconductors with similar dimensions, the levitation force mainly depends on the critical current density (Jc ), and the radius (r) of the induced current loop in the superconductor, the larger the r and Jc values, the higher the levitation force [12]. Because the magnet used in this experimental is the same for all the measurement, so the difference of the levitation force between samples #1 and #2 is only dependent on the difference between the samples. Fig. 4 shows the polished top surface morphology of the two samples, it is easy to see that domain size of the sample #1 is larger than that of sample #2 and the number of domains of sample #1 is less than that of sample #2. This exactly confirms that the value of r is larger in sample #1, the results is in agreement with reference [12]. In addition, the magnetized Jc measured by VSM is almost the same in each domain of the two samples; therefore the higher levitation force is obtained in sample #1. As we can see from Fig. 4, The sample #1 has a few fanshaped large YBCO domains, and the sample #2 has a number of randomly oriented YBCO domains. The morphology difference of samples is mainly dependent on the lateral TG of the furnace in which the samples are fabricated. In furnace #2, the temperature along the axial line but near inside wall
278
W.M. Yang et al. / Journal of Alloys and Compounds 415 (2006) 276–279
Fig. 5. The levitation force vs. distance curves between the magnet and the samples #3 at liquid nitrogen temperature, the magnet is of 30 mm, and B is about 0.5 T at the center of the top surface.
Fig. 4. The optical macrostructure of the samples, all the three samples are of the same 30 mm: sample #1 (a) fabricated in furnace #1 with a positive lateral TG and a Sm2 O3 seed; sample #2 (b) fabricated in furnace #2 with a negative lateral TG and a Sm2 O3 seed; sample #3 (c) fabricated in furnace #1 with a positive lateral TG and a NdBCO single crystal seed.
is always lower than that along the center axial line in the regime where the samples are located. The longitudinal TG is −2.5 ◦ C/cm and the lateral TG is −2 ◦ C/cm. When the samples are slowly cooled through the peritectic temperature, the temperature at edges will be lower than that of the center on the top surface of the sample, so the YBCO grains will be easy to nucleate at the edges and grow. No matter
what the TG changes, Sm2 O3 powder is still a nucleation site for Y123 phase, but it cannot prevent the YBCO grains from nucleating at the edges. So the Sm2 O3 powder is not the only nucleating site for YBCO grain, the random YBCO grain nucleation and growth lead to grains impinging and finally result in small grain domains. In furnace #1, the temperature near the inside wall is always higher than that along the center axial in the regime where the sample is located. The longitudinal TG is −2.5 ◦ C/cm, and the lateral TG is about 2 ◦ C/cm. The positive lateral TG and the negative longitudinal TG will ensure the YBCO grain to nucleate at the center where the Sm2 O3 powder is placed, and grows toward the edges of the sample, this agrees with the results reported by Salama and co-workers [13]. According to the experiments above, it tells us that Sm2 O3 powder can be used as a seed to obtain larger domain YBCO bulks, but it is not easy to obtain a good YBCO sample, because Sm2 O3 powder can only provide a nucleation site but cannot influence the orientation of the SmBCO and YBCO grains. In order to further improve the quality of YBCO bulks, a single domain YBCO bulk superconductors (sample #3, 30 mm) has been fabricated in furnace #1 by using a single NdBCO crystal as seed, as shown in Fig. 4, the levitation force is shown in Fig. 5, the maximum levitation force is about 94 N obtained at a gap of 0.5 mm between the two near surface of the magnet and YBCO bulk at 77 K.
W.M. Yang et al. / Journal of Alloys and Compounds 415 (2006) 276–279
4. Conclusion It is found that a positive lateral TG is more effective for the fabrication of large domain-sized YBCO pellets compared to a negative lateral TG during the fabrication of YBCO bulks. Large domains of fan-shaped YBCO pellets have been fabricated using Sm2 O3 powder as seed, the levitation force of these samples is about 2–3 times higher than that of samples fabricated in furnace with a negative lateral TG. A single domain YBCO bulk has been fabricated by using a single NdBCO crystal as seed, the maximum levitation force is about 94 N at liquid nitrogen temperature.
Acknowledgment This work was supported by the key science and technology project of Chinese ministry of education, No. 105154.
References [1] S. Jin, T.H. Teifel, R.C. Sherwood, E.M. Gyorgy, T.H. Tiefel, R.B. van Dover, S. Nakahala, L.F. Schneemeyer, R.A. Fastnacht, M.E. Davis, Appl. Phys. Lett. 54 (1989) 584.
279
[2] S.K. Selvamaickanov, L. Gao, K. Sun, Appl. Phys. Lett. 54 (1989) 2352. [3] M. Murakami, M. Morita, N. Koyama, Jpn. J. Appl. Phys. 28 (1989) L1125. [4] Zhou Lian, Zhang Pingxiang, Ji Ping, Wang Keguang, Wang Jingrong, Wu Xiaozu, Supercond. Sci. Technol. 10 (1990) 490. [5] John R. Hull, Shaul Hanany, Tomotake Matsumura, Bradley Johnson, Terry Jones, Supercond. Sci. Technol. 18 (2005) S1. [6] F.N. Werfel, U. Floegel-Delor, R. Rothfeld, B. Goebel, D. Wippich, T. Riedel, Supercond. Sci. Technol. 18 (2005) S19. [7] B. Oswald, K.-J. Best, M. Setzer, M. S¨oll, W. Gawalek, A. Gutt, L. Kovalev, G. Krabbes, L. Fisher, H.C. Freyhardt, Supercond. Sci. Technol. 18 (2005) S24. [8] S. Gruss, G. Fuchs, G. Krabbes, P. Verges, G. St¨overs, K.H. M¨oller, J. Fink, L. Schultz, Appl. Phys. Lett. 79 (2001) 3131. [9] M. Tomita, M. Murakami, Nature 421 (2003) 517. [10] Jiasu Wang, Suyu Wang, Youwen Zeng, Haiyu Huang, Fang Luo, Zhipei Xu, Qixue Tang, Guobin Lin, Cuifang Zhang, Zhongyou Ren, Guomin Zhao, Degui Zhu, Shaohua Wang, He Jiang, Min Zhu, Changyan Deng, Pengfei Hu, Chaoyong Li, Fang Liu, Jisan Lian, Xiaorong Wang, Lianghui Wang, Xuming Shen, Xiaogang Dong, Physica C 378–381 (2002) 809. [11] W.M. Yang, L. Zhou, Y. Feng, P.X. Zhang, C.P. Zhang, Z.M. Yu, Physica C 337 (2000) 115. [12] M. Murakami, T. Oyama, H. Fujimoto, T. Taguchi, S. Gotoh, Y. Shiohara, N. Koshizuka, S. Tanaka, Jpn. J. Appl. Phys. 29 (1990) L1991. [13] D.F. Lee, C.S. Partsinevelos, R.G. Presswood Jr., K. Salama, J. Appl. Phys. 76 (1994) 603.