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Temperature dependence of Vickers hardness for Cd1−xMnxTe (0⩽x⩽0.82) single crystals
Journal of Crystal Growth 249 (2003) 391–395
Temperature dependence of Vickers hardness for Cd1xMnxTe ð0pxp0:82Þ single crystals Younghun Hwanga, Hyekyeong Kima, Sunglae Choa, Youngho Uma,*, Hyoyeol Parkb a
School of Mathematics and Applied Physics, University of Ulsan, Ulsan 680-749, South Korea b Department of Semiconductors Applications, Ulsan College, Ulsan 680-749, South Korea Received 13 September 2002; accepted 12 December 2002 Communicated by G. Muller .
Abstract The Cd1x Mnx Te ð0pxp0:82Þ single crystals were grown by the vertical Bridgman method. The Vickers hardnesses of the grown crystals were measured as a function of Mn composition and temperature for the first time. The activation energy was determined for the dislocation motion from the relation between temperature and hardness, and it was decreased as increasing x in Cd1x Mnx Te single crystals. Also, the Vickers hardness HV was decreased as increasing temperature and increased as Mn composition x: r 2002 Elsevier Science B.V. All rights reserved. PACS: 62.20; 81.10.Fq Keywords: A1. Mechanical properties; A3. Crystal growth; B2. Semiconducting materials
1. Introduction Cd1x Mnx Te belongs to a class of materials known as diluted magnetic semiconductors (DMS) in which nonmagnetic Cd cations are partially substituted by magnetic Mn ions [1–3]. The exchange interaction between the localized magnetic ions and band electrons results in a large increase in Faraday rotation, an enhancement in gfactors by as much as two orders of magnitude and a giant negative magneto-resistance. These various *Corresponding author. E-mail address: [email protected] (Y. Um).
unique characteristics of DMS make their fabrication possible into special devices such as magnetic field sensors and optical isolators [4–8]. Recently, a great deal of efforts has been devoted in the development of devices with heterostructures made of Mn-based DMS [9–11]. The mechanical properties can be changed during the processing of semiconducting materials into devices. Particularly, the introduction of dislocations during thermal processing and thin film fabrication affects the electronic and optical properties of semiconductors because dislocations can strongly modify the density, mobility, and lifetime of a charge carrier. Therefore, the information of the
0022-0248/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 0 2 ) 0 2 0 9 9 - 7
392
Y. Hwang et al. / Journal of Crystal Growth 249 (2003) 391–395
mechanical properties is important in order to control dislocation generation during crystal growth and their device processing, and also to improve the optical and electrical properties. In this study, the hardness was measured as a function of composition and temperature using a Vickers microhardness tester for Cd1x Mnx Te ð0pxp0:82Þ single crystals which is widely used in testing brittle materials. The hardness measurement is the practical way to evaluate the mechanical property. We determined the activation energy for dislocation motion from the relation between temperature and hardness in Cd1x Mnx Te ð0pxp0:82Þ single crystals. As far as we know, this is the first report on the mechanical strength of Cd1x Mnx Te not only for the Mn composition up to 0.82, but also for the temperature up to 800 K.
3. Results and discussion XRD studies were performed in order to characterize the Cd1x Mnx Te ð0pxp0:82Þ crystal structure. The y 2y XRD spectra for Cd1x Mnx Te are shown in Fig. 1. The observed XRD pattern was found to be zincblende structure as expected for all crystals with various Mn compositions. The peak positions were changed with Mn contents in Cd1x Mnx Te ð0pxp0:82Þ single crystals as shown in Fig. 1. Fig. 2 shows the change in lattice constants with Mn composition. The lattice constant decreases linearly with Mn concentration up to 82% due to the smaller Mn ( [12] compared with covalent radius ð1:326 AÞ ( Cd ð1:405 AÞ [2]. The sample with x ¼ 0:82 has a ( which is 1.82% lattice constant of a ¼ 6:364 A; ( The slope of smaller than that of CdTe (6.482 A).
2. Experimental procedure The Cd1x Mnx Te single crystals were grown by double furnace of vertical Bridgman method from the Cd(6N), Te(6N), and Mn(4N) elements. The elements were put into the ampoule which had a capillary bottom in order to grow only one seed after the inside wall of the quartz ampoule was coated with carbon. Then, the ampoule was evacuated and sealed under a pressure of 106 Torr and placed in the furnace. The reaction temperature was slowly raised from 6001C to 12501C: The ampoule was held at 12501C for 3 h to homogenize the melt and lowered at a rate of 1.44 mm/h. The solidification gradient in the furnace was 22:51C=cm: The crystal obtained was a cylindrical form of about 10 mm in diameter and 20 mm in length. The mole fraction x was determined by Electron Probe Microanalyzer (EPMA-1400, SHIMADZU) and X-ray diffraction (XRD) measurements. The sample used in the experiment was mechanically polished with 0.05mm alumina powder to a thickness of 1 mm. The measurement of the microhardness was carried out using the Vickers indenter (MSA-1, USA) with a load of 25 g for 10 s, and the temperature of the sample was slowly raised to the desired value and kept for a fixed time.
Fig. 1. y 2y X-ray diffraction spectra of Cd1x Mnx Te ð0pxp0:82Þ:
Y. Hwang et al. / Journal of Crystal Growth 249 (2003) 391–395
Fig. 2. Lattice constants as a function of Mn mole fraction x:
( agrees satisfacthe fitting line of 6.485–0.146x(A) torily with the previous studies [13]. The decrease in the lattice constant with Mn concentration strongly shows that Mn ions are incorporated into the host Cd sites substitutionally. The microhardness of material was defined as its resistance to the formation of indentations. It represents the work done to indent a unit volume of material caused by the movement of dislocations. Vickers hardness HV has the relation [14] HV ¼
1:8544P ðkg=mm2 Þ; l2
ð1Þ
where P is the load and l is the length of indentation. Fig. 3 shows that the hardness HV versus x for Cd1x Mnx Te ð0pxp0:82Þ: As increasing x; the hardness HV of Cd1x Mnx Te is increased and the value of the hardness is varied from 49 to 60 kg=mm2 at 300 K. According to Sher et al. [15], the hardness HV of tetrahedrally coordinated semiconductor material has the approximate relation HV B
V23 d 5 ðV22 þ V32 Þ3=2
B d 5B11 ;
ð2Þ
393
Fig. 3. Vickers’ hardness of Cd1x Mnx Te ð0pxp0:82Þ as a function of Mn composition x at various temperatures.
where V2 is a covalent energy, V3 is an ionic energy, and d is a bond length. Therefore, we may conclude that the increase in the hardness for Cd1x Mnx Te with increasing x results from the decrease in the bond length with x: Fig. 4 shows the hardness HV as a function of temperature for Cd1x Mnx Te ð0pxp0:82Þ: The magnitude of the hardness becomes larger with Mn mole fraction x: The hardness of Cd1x Mnx Te increases exponentially with decreasing temperature for Tp600 K and it is temperature independent for TX700 K: The temperature-dependent behavior of the hardness can be understood as follows. The velocity of dislocation in covalent crystals increases exponentially with temperature [16] and the length of dislocation grows in accordance with movement, thereby, the density of dislocation increases, resulting in that the hardness decreases with temperature [17]. An Arrehnius plot showing the lnðHV Þ as a function of inverse temperature is shown in Fig. 5. The activation energy for the dislocation motion can be determined from an expression, U HV ¼ A exp ; ð3Þ kT
394
Y. Hwang et al. / Journal of Crystal Growth 249 (2003) 391–395
Fig. 4. Vickers’ hardness of Cd1x Mnx Te ð0pxp0:82Þ as a function of temperature.
Fig. 6. Activation energy for the dislocation motion of Cd1x Mnx Te as a function of Mn mole fraction x:
where k is the Boltzmann constant, A is a constant, and U is the activation energy for the dislocation motion. The activation energy is determined from the slope of lnðHV Þ between 350 and 620 K, as presented in Fig. 6. The activation energy for CdTe (x ¼ 0) is 0.0407 eV, which is in good agreement with the result reported by Barbot et al. [18]. The activation energy for the dislocation motion decreases as increasing Mn composition x: Note that the hardness increases with increasing x; as shown in Fig. 3. The relation between the dislocation length (o) and the hardness, HV BexpðoÞ [19], indicates that the dislocation length decreases with x: Resultantly, the shorter the dislocation length is, the smaller the activation energy for the dislocation motion is, and leads that the activation energy decreases with increasing x:
4. Conclusions
Fig. 5. lnðHV Þ of Cd1x Mnx Te ð0pxp0:82Þ as a function of inverse temperature.
In this study, the Cd1x Mnx Te single crystals were grown up to x ¼ 0:82 by the vertical Bridgman method. It was shown from the results of XRD measurements that the structure of all of the grown Cd1x Mnx Te crystals with various Mn
Y. Hwang et al. / Journal of Crystal Growth 249 (2003) 391–395
compositions was zincblende. We measured the Vickers hardness of Cd1x Mnx Te ð0pxp0:82Þ single crystal as a function of Mn composition and temperature ð300B800 KÞ: The hardness of the Cd1x Mnx Te crystal was increased with Mn composition x and decreased as increasing temperature. The activation energy for the dislocation motion was decreased as increasing Mn composition x: The present data will provide a useful information on material strength of Cd1x Mnx Te crystals at various temperatures.
Acknowledgements This research was supported by the Research Fund of 2001, University of Ulsan.
References [1] N.B. Brandt, V.V. Moshchkalov, Adv. Phys. 33 (1984) 193. [2] W. Giriat, J.K. Furdyna, in: J.K. Furdyna, J. Kossut (Eds.), Diluted Magnetic Semiconductors, Semiconductors and Semimetals, Vol. 25, Academic, Boston, 1988 (Chapter 1). [3] J.K. Furdyna, J. Appl. Phys. 64 (1988) R29. [4] N. Kullendorff, B. Hok, Appl. Phys. Lett. 46 (1985) 1016.
395
[5] J.K. Furdyna, N. Samarth, J. Appl. Phys. 61 (1987) 3526. [6] D.A. Aksionov, V.I. Konov, P.I. Nikitin, A.M. Prokhorov, A.I. Savchuk, A.V. Savitski, K.S. Ulyanitski, Sensors and Actuators A21–A23 (1990) 875. [7] N. Mikami, C. Nagao, T. Sawada, H. Takahashi, Y. Furukawa, E. Aikawa, J. Appl. Phys. 69 (1991) 433. [8] W. Zaets, K. Ando, Appl. Phys. Lett. 77 (2000) 1593. [9] L. Chen, P.J. Klar, W. Heimbrodt, F. Brieler, M. Froba, Appl. Phys. Lett. 76 (2000) 3531. [10] S.A. Crooker, N. Samarth, D.D. Awschalom, Phys. Rev. B 61 (2000) 1736. [11] W. Maslana, W. Mac, J.A. Gaj, P. Kossacki, A. Golnik, J. Cibert, S. Tatarenko, T. Wojtowicz, G. Karczewski, J. Kossut, Phys. Rev. B 63 (2001) 165318. [12] D.R. Yoder-Short, U. Debska, J.K. Furdyna, J. Appl. Phys. 58 (1985) 4056. [13] N. Bottka, J. Stankiewicz, W. Giriat, J. Appl. Phys. 52 (1981) 4189. [14] N.A. Goryunova, A.S. Borshchevskii, P.N. Tretiakov, Semiconductor and Semimetal, Vol. 4, Academic press, New York, 1968, pp. 6. [15] A. Sher, A.-B. Chen, W.E. Spicer, Appl. Phys. Lett. 46 (1985) 54. [16] P. Hassen, H.A. Alexander, Solid State Phys. 22 (1968) 27. [17] C.R. Barrett, W.D. Nix, A.S. Tetelman, The Principles of Engineering Materials, Prentice-Hall, Englewood Cliffs, NJ, 1973. [18] J.F. Barbot, G. Rivaud, H. Garem, C. Blanchard, J.C. Desoyer, D. Le-Scoul, J.L. Dessus, A. Durand, J. Mater. Sci. 25 (1990) 1877. [19] B. Henderson, Defects in Crystalline Solids, Crane, Russak Company Inc., 1972, pp. 162.
Temperature dependence of Vickers hardness for Cd1xMnxTe ð0pxp0:82Þ single crystals Younghun Hwanga, Hyekyeong Kima, Sunglae Choa, Youngho Uma,*, Hyoyeol Parkb a
School of Mathematics and Applied Physics, University of Ulsan, Ulsan 680-749, South Korea b Department of Semiconductors Applications, Ulsan College, Ulsan 680-749, South Korea Received 13 September 2002; accepted 12 December 2002 Communicated by G. Muller .
Abstract The Cd1x Mnx Te ð0pxp0:82Þ single crystals were grown by the vertical Bridgman method. The Vickers hardnesses of the grown crystals were measured as a function of Mn composition and temperature for the first time. The activation energy was determined for the dislocation motion from the relation between temperature and hardness, and it was decreased as increasing x in Cd1x Mnx Te single crystals. Also, the Vickers hardness HV was decreased as increasing temperature and increased as Mn composition x: r 2002 Elsevier Science B.V. All rights reserved. PACS: 62.20; 81.10.Fq Keywords: A1. Mechanical properties; A3. Crystal growth; B2. Semiconducting materials
1. Introduction Cd1x Mnx Te belongs to a class of materials known as diluted magnetic semiconductors (DMS) in which nonmagnetic Cd cations are partially substituted by magnetic Mn ions [1–3]. The exchange interaction between the localized magnetic ions and band electrons results in a large increase in Faraday rotation, an enhancement in gfactors by as much as two orders of magnitude and a giant negative magneto-resistance. These various *Corresponding author. E-mail address: [email protected] (Y. Um).
unique characteristics of DMS make their fabrication possible into special devices such as magnetic field sensors and optical isolators [4–8]. Recently, a great deal of efforts has been devoted in the development of devices with heterostructures made of Mn-based DMS [9–11]. The mechanical properties can be changed during the processing of semiconducting materials into devices. Particularly, the introduction of dislocations during thermal processing and thin film fabrication affects the electronic and optical properties of semiconductors because dislocations can strongly modify the density, mobility, and lifetime of a charge carrier. Therefore, the information of the
0022-0248/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 0 2 ) 0 2 0 9 9 - 7
392
Y. Hwang et al. / Journal of Crystal Growth 249 (2003) 391–395
mechanical properties is important in order to control dislocation generation during crystal growth and their device processing, and also to improve the optical and electrical properties. In this study, the hardness was measured as a function of composition and temperature using a Vickers microhardness tester for Cd1x Mnx Te ð0pxp0:82Þ single crystals which is widely used in testing brittle materials. The hardness measurement is the practical way to evaluate the mechanical property. We determined the activation energy for dislocation motion from the relation between temperature and hardness in Cd1x Mnx Te ð0pxp0:82Þ single crystals. As far as we know, this is the first report on the mechanical strength of Cd1x Mnx Te not only for the Mn composition up to 0.82, but also for the temperature up to 800 K.
3. Results and discussion XRD studies were performed in order to characterize the Cd1x Mnx Te ð0pxp0:82Þ crystal structure. The y 2y XRD spectra for Cd1x Mnx Te are shown in Fig. 1. The observed XRD pattern was found to be zincblende structure as expected for all crystals with various Mn compositions. The peak positions were changed with Mn contents in Cd1x Mnx Te ð0pxp0:82Þ single crystals as shown in Fig. 1. Fig. 2 shows the change in lattice constants with Mn composition. The lattice constant decreases linearly with Mn concentration up to 82% due to the smaller Mn ( [12] compared with covalent radius ð1:326 AÞ ( Cd ð1:405 AÞ [2]. The sample with x ¼ 0:82 has a ( which is 1.82% lattice constant of a ¼ 6:364 A; ( The slope of smaller than that of CdTe (6.482 A).
2. Experimental procedure The Cd1x Mnx Te single crystals were grown by double furnace of vertical Bridgman method from the Cd(6N), Te(6N), and Mn(4N) elements. The elements were put into the ampoule which had a capillary bottom in order to grow only one seed after the inside wall of the quartz ampoule was coated with carbon. Then, the ampoule was evacuated and sealed under a pressure of 106 Torr and placed in the furnace. The reaction temperature was slowly raised from 6001C to 12501C: The ampoule was held at 12501C for 3 h to homogenize the melt and lowered at a rate of 1.44 mm/h. The solidification gradient in the furnace was 22:51C=cm: The crystal obtained was a cylindrical form of about 10 mm in diameter and 20 mm in length. The mole fraction x was determined by Electron Probe Microanalyzer (EPMA-1400, SHIMADZU) and X-ray diffraction (XRD) measurements. The sample used in the experiment was mechanically polished with 0.05mm alumina powder to a thickness of 1 mm. The measurement of the microhardness was carried out using the Vickers indenter (MSA-1, USA) with a load of 25 g for 10 s, and the temperature of the sample was slowly raised to the desired value and kept for a fixed time.
Fig. 1. y 2y X-ray diffraction spectra of Cd1x Mnx Te ð0pxp0:82Þ:
Y. Hwang et al. / Journal of Crystal Growth 249 (2003) 391–395
Fig. 2. Lattice constants as a function of Mn mole fraction x:
( agrees satisfacthe fitting line of 6.485–0.146x(A) torily with the previous studies [13]. The decrease in the lattice constant with Mn concentration strongly shows that Mn ions are incorporated into the host Cd sites substitutionally. The microhardness of material was defined as its resistance to the formation of indentations. It represents the work done to indent a unit volume of material caused by the movement of dislocations. Vickers hardness HV has the relation [14] HV ¼
1:8544P ðkg=mm2 Þ; l2
ð1Þ
where P is the load and l is the length of indentation. Fig. 3 shows that the hardness HV versus x for Cd1x Mnx Te ð0pxp0:82Þ: As increasing x; the hardness HV of Cd1x Mnx Te is increased and the value of the hardness is varied from 49 to 60 kg=mm2 at 300 K. According to Sher et al. [15], the hardness HV of tetrahedrally coordinated semiconductor material has the approximate relation HV B
V23 d 5 ðV22 þ V32 Þ3=2
B d 5B11 ;
ð2Þ
393
Fig. 3. Vickers’ hardness of Cd1x Mnx Te ð0pxp0:82Þ as a function of Mn composition x at various temperatures.
where V2 is a covalent energy, V3 is an ionic energy, and d is a bond length. Therefore, we may conclude that the increase in the hardness for Cd1x Mnx Te with increasing x results from the decrease in the bond length with x: Fig. 4 shows the hardness HV as a function of temperature for Cd1x Mnx Te ð0pxp0:82Þ: The magnitude of the hardness becomes larger with Mn mole fraction x: The hardness of Cd1x Mnx Te increases exponentially with decreasing temperature for Tp600 K and it is temperature independent for TX700 K: The temperature-dependent behavior of the hardness can be understood as follows. The velocity of dislocation in covalent crystals increases exponentially with temperature [16] and the length of dislocation grows in accordance with movement, thereby, the density of dislocation increases, resulting in that the hardness decreases with temperature [17]. An Arrehnius plot showing the lnðHV Þ as a function of inverse temperature is shown in Fig. 5. The activation energy for the dislocation motion can be determined from an expression, U HV ¼ A exp ; ð3Þ kT
394
Y. Hwang et al. / Journal of Crystal Growth 249 (2003) 391–395
Fig. 4. Vickers’ hardness of Cd1x Mnx Te ð0pxp0:82Þ as a function of temperature.
Fig. 6. Activation energy for the dislocation motion of Cd1x Mnx Te as a function of Mn mole fraction x:
where k is the Boltzmann constant, A is a constant, and U is the activation energy for the dislocation motion. The activation energy is determined from the slope of lnðHV Þ between 350 and 620 K, as presented in Fig. 6. The activation energy for CdTe (x ¼ 0) is 0.0407 eV, which is in good agreement with the result reported by Barbot et al. [18]. The activation energy for the dislocation motion decreases as increasing Mn composition x: Note that the hardness increases with increasing x; as shown in Fig. 3. The relation between the dislocation length (o) and the hardness, HV BexpðoÞ [19], indicates that the dislocation length decreases with x: Resultantly, the shorter the dislocation length is, the smaller the activation energy for the dislocation motion is, and leads that the activation energy decreases with increasing x:
4. Conclusions
Fig. 5. lnðHV Þ of Cd1x Mnx Te ð0pxp0:82Þ as a function of inverse temperature.
In this study, the Cd1x Mnx Te single crystals were grown up to x ¼ 0:82 by the vertical Bridgman method. It was shown from the results of XRD measurements that the structure of all of the grown Cd1x Mnx Te crystals with various Mn
Y. Hwang et al. / Journal of Crystal Growth 249 (2003) 391–395
compositions was zincblende. We measured the Vickers hardness of Cd1x Mnx Te ð0pxp0:82Þ single crystal as a function of Mn composition and temperature ð300B800 KÞ: The hardness of the Cd1x Mnx Te crystal was increased with Mn composition x and decreased as increasing temperature. The activation energy for the dislocation motion was decreased as increasing Mn composition x: The present data will provide a useful information on material strength of Cd1x Mnx Te crystals at various temperatures.
Acknowledgements This research was supported by the Research Fund of 2001, University of Ulsan.
References [1] N.B. Brandt, V.V. Moshchkalov, Adv. Phys. 33 (1984) 193. [2] W. Giriat, J.K. Furdyna, in: J.K. Furdyna, J. Kossut (Eds.), Diluted Magnetic Semiconductors, Semiconductors and Semimetals, Vol. 25, Academic, Boston, 1988 (Chapter 1). [3] J.K. Furdyna, J. Appl. Phys. 64 (1988) R29. [4] N. Kullendorff, B. Hok, Appl. Phys. Lett. 46 (1985) 1016.
395
[5] J.K. Furdyna, N. Samarth, J. Appl. Phys. 61 (1987) 3526. [6] D.A. Aksionov, V.I. Konov, P.I. Nikitin, A.M. Prokhorov, A.I. Savchuk, A.V. Savitski, K.S. Ulyanitski, Sensors and Actuators A21–A23 (1990) 875. [7] N. Mikami, C. Nagao, T. Sawada, H. Takahashi, Y. Furukawa, E. Aikawa, J. Appl. Phys. 69 (1991) 433. [8] W. Zaets, K. Ando, Appl. Phys. Lett. 77 (2000) 1593. [9] L. Chen, P.J. Klar, W. Heimbrodt, F. Brieler, M. Froba, Appl. Phys. Lett. 76 (2000) 3531. [10] S.A. Crooker, N. Samarth, D.D. Awschalom, Phys. Rev. B 61 (2000) 1736. [11] W. Maslana, W. Mac, J.A. Gaj, P. Kossacki, A. Golnik, J. Cibert, S. Tatarenko, T. Wojtowicz, G. Karczewski, J. Kossut, Phys. Rev. B 63 (2001) 165318. [12] D.R. Yoder-Short, U. Debska, J.K. Furdyna, J. Appl. Phys. 58 (1985) 4056. [13] N. Bottka, J. Stankiewicz, W. Giriat, J. Appl. Phys. 52 (1981) 4189. [14] N.A. Goryunova, A.S. Borshchevskii, P.N. Tretiakov, Semiconductor and Semimetal, Vol. 4, Academic press, New York, 1968, pp. 6. [15] A. Sher, A.-B. Chen, W.E. Spicer, Appl. Phys. Lett. 46 (1985) 54. [16] P. Hassen, H.A. Alexander, Solid State Phys. 22 (1968) 27. [17] C.R. Barrett, W.D. Nix, A.S. Tetelman, The Principles of Engineering Materials, Prentice-Hall, Englewood Cliffs, NJ, 1973. [18] J.F. Barbot, G. Rivaud, H. Garem, C. Blanchard, J.C. Desoyer, D. Le-Scoul, J.L. Dessus, A. Durand, J. Mater. Sci. 25 (1990) 1877. [19] B. Henderson, Defects in Crystalline Solids, Crane, Russak Company Inc., 1972, pp. 162.