Crystal Growth and Design of Sapphire: Experimental and Calculation

Apr 11, 2014 - Crystal Growth and Design of Sapphire: Experimental and Calculation Studies of Anisotropic Crystal Growth upon Pulling Directions. Cong...
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Crystal Growth and Design of Sapphire: Experimental and Calculation Studies of Anisotropic Crystal Growth upon Pulling Directions Congting Sun and Dongfeng Xue* State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China S Supporting Information *

ABSTRACT: The anisotropic growth of large-size sapphire single crystals along different pulling directions was studied on the basis of the chemical bonding theory of single crystal growth and practical Czochralski growth. The projection of thermodynamic morphology of sapphire single crystal respectively along [210], [110], [001], and [001] rotated 57.62° directions can be used to confirm the growth directions of surfaces that are preferred to be exposed thermodynamically in Czochralski growth. Starting from these thermodynamically preferred directions, the possible radial directions that are normal to the four typical pulling directions by kinetic controls have been identified by anisotropic chemical bonding distributions of sapphire single crystal. Chemical bonding calculations demonstrate that the lower pulling rate should be designed when Raxial/Rradial > 1, whereas the higher pulling rate should be designed when Raxial/Rradial < 1. The anisotropic chemical bonding conditions demonstrate the lowest chemical bonding density along the radial directions of sapphire single crystal when it grows along the [001] pulling direction. Taking [001] as the pulling direction in practical growth, a ϕ 2″ sapphire single crystal was grown via the Czochralski method with a growth rate of 2−3 mm/h. Our present work shows the effect of anisotropy on the Czochralski growth of large-size single crystals, which can provide a theoretical guide in practical growth from both thermodynamic and kinetic viewpoints. optical systems,1 which require large-size sapphire crystals.7 Attempts were made to scale up the Czochralski (Cz), Bridgman, horizontal directional crystallization, Kyropoulos, edge-defined film-fed growth and heat exchange methods to grow large sapphire single crystals.8−11 Table S1, Supporting Information summarizes the crystal size, weight, and growth directions of sapphire single crystals by different growth methods. To date, by using the heat exchange method, large sapphire boules ϕ 15″ in diameter and 84 kg in weight have been produced successfully.1 The Cz technique is the major industrial growth method for virtually all semiconductor materials that melt congruently as well as a variety of oxide crystals. The main advantages of the Cz method are growing single crystals in defined crystallographic orientations with different sizes and shapes which are mainly limited by a design of crystal puller.12 The Cz process on the other hand readily lends itself to precise growth rate control.13 Growing sapphire crystals along the pulling direction that is perpendicular to the desirable crystallographic surface can avoid a large area of the grown single crystals to become useless. The low material utilization and the high energy consumption of the growth process can add to the cost of the substrates.13 Therefore, it is

1. INTRODUCTION Sapphire (α-Al2O3) has good optical properties in the 3−5 μm wavelength range, the best resistance to erosion by rain and sand, and excellent thermal shock resistance.1 Owing to the combination of excellent optical and mechanical properties, sapphire single crystals have been in continuous production for over 130 years.2 In the 1960s, requirements for large size sapphire were for transparent armor applications because of sapphire’s high hardness and toughness.3 Since 2006, siliconon-sapphire devices production is ramping up, and commercial products are available.4 Recently, the largest volume of sapphire production is expected as the substrates for high brightness LED devices because of its low reactivity and appropriate unit cell parameters.2 The recent market study indicates that the demand for epi-ready sapphire substrates is expected to rise exponentially throughout the next decade.5 Moreover, the rapid development of electronics, electro-optical devices, and precise mechanics accompanied by widening applications of sapphire in consumer mobile devices dictates sapphire single crystals with high quality and consequently the improvement of current technologies for the fabrication of sapphire crystals.6 In order to grow single crystals with high quality, both thermodynamic and kinetic factors have to be optimized in the field of crystal growth science and technology. Large aperture sapphire optical windows have been identified as a key element of new and/or upgraded airborne electro© 2014 American Chemical Society

Received: December 14, 2013 Revised: April 7, 2014 Published: April 11, 2014 2282

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important to uncover the intrinsic relationship between growth parameters and pulling direction in Cz growth. The anisotropic growth of sapphire single crystal is important to provide wafers with different exposed surfaces, which can increase the types of sapphire substrate materials. For example, ZnO films have been deposited onto the (110), (001), and (102) faces of sapphire single crystals.14 Therefore, the study of sapphire single crystal growth along anisotropic directions can provide more theoretic guides in practical growth from the viewpoint of both thermodynamic and kinetic controls.15,16 For sapphire and YAG single crystals grown in the Cz system respectively along the [001] and [111] directions, the crystal/ metal interface configuration has been investigated on the basis of anisotropic chemical bonding conditions.17,18 However, for sapphire single crystal, it is still facing the challenge of clarifying its growth behaviors in the Cz growth system along different pulling directions. On the basis of anisotropic chemical bonding distributions, we can study the growth behaviors of sapphire single crystal when it grows along the [210], [110], [001], and [001] rotated 57.62° pulling directions, respectively. In this work, we applied the chemical bonding theory of single crystal growth to the study of bulk sapphire single crystals along four anisotropic pulling directions in the Cz system, i.e., [210], [110], [001], and [001] rotated 57.62° directions. On the basis of the thermodynamic morphology and anisotropic chemical bonding distributions, we can study the growth behaviors of sapphire single crystal grown via the Cz method along different pulling directions. Experimentally, a ϕ 2″ sapphire single crystal was grown along the [001] pulling direction with a designed growth rate in the Cz system. Our calculated results from the chemical bonding viewpoint agree well with experimental observations.

2. CALCULATION METHODOLOGY Thermodynamically, the anisotropic crystal morphology depends on the anisotropic chemical bonding conditions.19−22 On the basis of the chemical bonding theory of single crystal growth, the linear growth velocity along the [uvw] direction of single crystal can be expressed as23−27 R uvw = K

bond Euvw Aduvw

Figure 1. (a) Crystallographic structure of sapphire single crystal. Sapphire crystallizes in the trigonal R3̅c space group with a = b = 4.75 Å, c = 12.99 Å. In the sapphire structure, Al is coordinated with six O atoms, whereas O is coordinated with four Al atoms. Al atoms are highlighted in gray spheres, and O atoms are highlighted in red spheres. (b) Relationship between anisotropic growth directions of sapphire single crystal. The [210] direction is perpendicular to the (100) crystal plane, the [110] direction is perpendicular to the (110) crystal plane, the [001] direction is perpendicular to the (001) crystal plane, and [001] rotated 57.62° is perpendicular to the (012) crystal plane. (c) Thermodynamic morphology of sapphire single crystals calculated by the chemical bonding theory of single crystal growth.

(1)

where Ebond uvw is the chemical bonding energy along the [uvw] direction, duvw is the step height on the (hkl) surface perpendicular to the [uvw] direction, and A is the projection area of structural framework along the [uvw] direction. From eq 1, it can also be deduced that the specific growth rate along the [uvw] direction is proportional to direction-dependent chemical bonding energy per unit cell volume. On the basis of the chemical bonding conditions along the particular [uvw] direction, the thermodynamic morphology of sapphire single crystal can be calculated (as shown in Figure 1).

upward sapphire seed slowly from the melt surface. The growth of bulk sapphire was designed with a growth rate of 2−3 mm/h. In the Cz growth process, the sapphire single crystal grew with the phase transition at the melt/crystal interface when it was pulled out of the melt vertically. As shown in Figure S1, Supporting Information, the whole growth process was controlled by an automatic growth system. The variation of crystal mass was in situ detected by the electric balance, and then the mass signal was input into the computer. By comparing with the designed value, the computer controls the high frequency inductive heat power to modify the practical frequency, which can be used to adjust growth rate of sapphire single crystal.

3. EXPERIMENTAL SECTION The Cz method is one of the most important techniques for the growth of bulk sapphire single crystals. We utilize the Cz method to grow sapphire single crystals along the [001] pulling direction. Before crystal growth, α-Al2O3 polycrystalline materials of high purity was filled in the Ir crucible. Then, the Ir crucible within the Cu loop was heated via high frequency inductive heat power. When α-Al2O3 polycrystalline was melted and a thermal equilibrium was built, a single-crystal sapphire seed was lowered to the surface of the melt. Thereafter, the growth of sapphire single crystal proceeded by pulling

4. RESULTS AND DISCUSSION Crystallographically, sapphire crystallizes in the trigonal R3̅c space group with a = b = 4.75 Å, and c = 12.99 Å.28 As shown in 2283

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the [001] pulling direction in the Cz system thermodynamically. However, in practical growth, higher chemical bonding energy density at the intersection of two adjacent {110} surfaces leads to the appearance of surfaces that are perpendicular to ⟨210⟩ directions kinetically. Figure 3 shows

Figure 1a, Al is coordinated with six O atoms, whereas O is coordinated with four Al atoms in the sapphire structure. On the basis of chemical bonding theory of single crystal growth, the chemical bonding density along the normal direction of {012} planes is the lowest, which leads to the lowest growth rate along this direction and the exposure of {012} surfaces. Consequently, the thermodynamic morphology of sapphire single crystal exhibits a rhombohedral polyhedron bounded by six crystallographically equivalent {012} planes (Figure 1c). Previous studies show that large-size sapphire single crystals have been grown along the [210], [110], [001], [001] rotated 57.62° directions.2,3,8 In order to illustrate the effect of anisotropy on the Cz growth of sapphire, we selected [210] (perpendicular to (100) crystal plane), [110] (perpendicular to (110) crystal plane), [001] (perpendicular to (001) crystal plane), and [001] rotated 57.62° directions (perpendicular to the (012) crystal plane) as pulling directions. Figure 1b shows the relationship between these four anisotropic growth directions of sapphire single crystal. The angle between [100] and [210] is 30°, the angle between [210] and [110] is 30°, [001] is perpendicular to [210] and [110], and the rotation of [001] toward the [010] direction with the angle of 57.62° is [001] rotated 57.62° direction (i.e., r-axis). According to eq 1, the relative growth rate between different growth directions can be calculated, R(001)/R(110) = 1.50, R(100)/R(116) = 0.44, R(110)/ R(116) = 0.67, and R(012)/R(1,8,18) = 0.12 (herein, the growth direction is the normal direction of the (hkl) crystal plane). Thermodynamically, anisotropic crystallographic structure directs the anisotropic growth of single crystal. In the Cz growth process, the thermodynamically preferred radial directions can therefore be ascertained by both pulling direction and thermodynamic morphology. As shown in Figure 2, the projection of thermodynamic morphology of sapphire

Figure 3. Anisotropic chemical bonding distributions of sapphire single crystal along the ⟨210⟩ and ⟨110⟩ directions. Thermodynamic growth directions, i.e., ⟨110⟩ directions, that are perpendicular to the [001] direction are identified on the basis of thermodynamic morphology of sapphire. In practical growth, higher chemical bonding density at the intersection of two adjacent {110} surfaces leads to the appearance of surfaces that are perpendicular to ⟨210⟩ directions kinetically.

the anisotropic chemical bonding distributions of sapphire single crystal respectively along the ⟨210⟩ and ⟨110⟩ directions. Further, the surfaces that are parallel to {h10} facets will be exposed in order to further decrease the high chemical bonding energy at the intersection between adjacent surfaces respectively perpendicular to ⟨210⟩ and ⟨110⟩ directions. Finally, sapphire single crystal prefers to exhibit a round shape viewed down the [001] growth direction in the Cz system. Crystallographically, the (100) plane is perpendicular to the [210] direction in the trigonal sapphire structure. Crystal wafers exposed to the surface parallel to (100) can be obtained via growing sapphire single crystal along the [210] pulling direction. Figure 4 shows the geometry of thermodynamic morphology of sapphire single crystal viewed down along the [210] direction. On the basis of thermodynamic morphology of sapphire single crystal, normal directions of (120̅ ), (21̅ 0), (21̅6), (2̅16), (2̅16̅), and (21̅6̅) planes can be identified as thermodynamically preferred growth directions that are perpendicular to the [210] pulling direction in Cz growth. According to the anisotropic chemical bonding distributions, higher chemical bonding density at the intersection of two adjacent thermodynamically preferred surfaces leads to the appearance of surfaces that are parallel to {12̅0}, {21̅6}, {001}, and {12h̅ } in practical growth (Figure 5). Consequently, sapphire single crystal prefers to exhibit an ellipse shape viewed down the [210] growth direction in the Cz system. The geometry of thermodynamic morphology of sapphire single crystal viewed down the [110] direction can be used to identify the radial growth directions of sapphire in thermodynamics, i.e., the normal directions of (11̅2), (1̅12̅), (1̅14), and (11̅4̅) planes, respectively (Figure 6). On the basis of

Figure 2. Geometrics of thermodynamic morphology of sapphire single crystal viewed down along the [001] direction. The thermodynamic morphology of sapphire single crystal was calculated on the basis of chemical bonding theory of single crystal growth. Thermodynamically, [100], [110], [010], [10̅ 0], [11̅ 0̅ ], and [010̅ ] are six crystallographic-equivalent directions that are perpendicular to the [001] direction.

single crystals along the [001] direction exhibits a hexagonal configuration. Thermodynamically, [100], [110], [010], [1̅00], [11̅ 0̅ ], and [010̅ ] are six crystallographic-equivalent directions that are perpendicular to the [001] direction. This means that the surfaces respectively perpendicular to these six directions prefer to be exposed when sapphire single crystal grows along 2284

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Figure 4. Geometrics of thermodynamic morphology of sapphire single crystal viewed down along the [210] direction. Thermodynamically, directions that are respectively perpendicular to (12̅0), (1̅20), (21̅6), (2̅16), (2̅16̅), and (21̅6̅) planes can be identified on the basis of thermodynamic morphology of sapphire single crystal.

Figure 6. Geometrics of thermodynamic morphology of sapphire single crystal viewed down along the [110] direction. On the basis of thermodynamic morphology of sapphire single crystal, thermodynamic growth directions that are respectively perpendicular to (11̅2), (1̅12̅), (1̅14), and (11̅4̅) planes can be identified, which are normal to the [110] direction.

Figure 5. Anisotropic chemical bonding distributions of sapphire single crystal growing along the [210] direction. On the basis of thermodynamic morphology of sapphire, thermodynamic growth directions normal to the [210] direction can be identified, which are respectively perpendicular to the (12̅0), (1̅20), (21̅6), (2̅16), (2̅16̅), and (21̅6̅) planes. In practical growth, higher chemical bonding density at the intersection of two adjacent thermodynamically preferred surfaces leads to the appearance of surfaces that are parallel to {12̅0}, {21̅6}, {001}, and {12̅h}, respectively.

Figure 7. Anisotropic chemical bonding distributions of sapphire single crystal growing along the [110] direction. On the basis of thermodynamic morphology of sapphire, thermodynamic growth directions normal to the [110] direction can be identified, which are respectively perpendicular to (11̅2), (1̅12̅), (1̅14), and (11̅4̅) planes. In practical growth, higher chemical bonding density at the intersection of adjacent thermodynamically preferred surfaces leads to the appearance of surfaces that are parallel to (11̅0), (1̅10), (001), and (001̅), respectively.

anisotropic chemical bonding distributions of sapphire single crystal, the chemical bonding density at the intersection of two adjacent thermodynamically preferred surfaces are high along the [110] directions (Figure 7). This can result in the appearance of surfaces that are parallel to (11̅0), (1̅10), (001), and (001)̅ , respectively. Consequently, sapphire single crystal prefers to exhibit an ellipse shape viewed down the [110] growth direction in the practical Cz growth system. The thermodynamic morphology of sapphire single crystal is exposed with {012} surfaces. The normal direction of the (012) crystal plane is [001] rotated 57.62°. As shown in Figure 8, we can identify the normal directions of (110), (1̅1̅0) (8,1,1̅8̅), (1,8,18), (8̅,1̅,1̅8̅) and (1̅,8̅,18) planes as thermodynamically

preferred growth directions parallel to the (012) plane. From the chemical bonding viewpoint, the anisotropic chemical bonding distributions that are normal to the pulling direction can be used to further identify the possible radial growth direction in practical Cz growth along the [001] rotated 57.62° direction. These anisotropic chemical bonding distributions indicate the appearance of surfaces that are parallel to {110}, {1̅1̅0}, (1̅15), and (11̅5) owing to the higher chemical bonding density at the intersection of two adjacent thermodynamically preferred surfaces. Likewise, an ellipse shape is exhibited by sapphire when it pulled along the [001] rotated 57.62° growth direction in the Cz growth system. On the basis of our current 2285

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bonding density along the ⟨210⟩ and ⟨110⟩ directions, a lower pulling rate has been designed to grow sapphire single crystal along the [001] direction. The growth rate of bulk sapphire was 2−3 mm/h. ϕ 2″ sapphire single crystal was grown by the Cz method along the [001] direction (Figure 10). The whole

Figure 8. Geometrics of thermodynamic morphology of sapphire single crystal viewed down along the direction of [001] rotated 57.62° (r-axis). On the basis of thermodynamic morphology of sapphire single crystal, thermodynamic growth directions that are respectively perpendicular to (110), (1̅1̅0) (8,1,1̅8̅), (1,8,18), (8̅, 1̅,18), and (1̅,8̅,1̅8̅) planes can be identified, which are parallel to the (012) plane.

calculations, when sapphire grows along the [001] pulling direction, the growth rate along axial direction is larger than that along radial directions, i.e., Raxial/Rradial > 1. However, when sapphire grows along [210], [110], and [001] rotated 57.62° pulling directions, Raxial/Rradial < 1. In Cz growth, the crystal constituents incorporate into the lattice along the radial directions, resulting in the growth of sapphire with pulling the crystal upward. Consequently, the growth rate depends on the relative growth rate between radial direction and axial direction. By combining anisotropic chemical bonding distributions as shown in Figures 3, 5, 7, and 9, it can be deduced that the faster growth rate along the pulling direction for Raxial/Rradial < 1 favors growth of sapphire single crystal with high quality, while once Raxial/Rradial > 1, the slower growth rate along the pulling direction favors growth of sapphire single crystal with high quality. In recent years, c-plane (0001) sapphire substrates have been used commercially for the fabrication of GaN-based LED devices on account of their relatively good lattice match.8 Paradoxically, the Cz technique has gradually been abandoned by the major sapphire manufacturers because of the difficulty in growing crystals along the c-axis.3 According to our chemical bonding calculations, the growth behavior of sapphire single crystal along the [001] pulling direction is different from that along the other pulling directions, i.e., Raxial/Rradial > 1. Consequently, we utilized the Cz growth system to grow ϕ 2″ sapphire single crystal along the [001] pulling direction on the basis of our theoretical guides. Since the pulling direction of sapphire is selected as the [001] direction, a cylindrical sapphire crystal can be predicted on the basis of anisotropic chemical bonding distributions that are normal to the pulling direction. As shown in Figures 2 and 3, the competed appearance of crystal surfaces respectively perpendicular to the ⟨210⟩ and ⟨110⟩ directions leads to the configuration of sapphire approaching to circle shape. Further, the appearance of highindex surfaces, {h10}, can diminish the proportion of surfaces that are perpendicular to ⟨110⟩ directions in the sapphire growth interface. Decreased chemical bonding density promotes the evolution of interface configuration and round growth interface for sapphire crystal growth along the [001] direction by the Cz method. Owing to the relative low chemical

Figure 9. Anisotropic chemical bonding distributions of sapphire single crystal growing along the direction of [001] rotated 57.62° (raxis). On the basis of thermodynamic morphology of sapphire, thermodynamic growth directions parallel to the (012) plane can be identified, which are respectively perpendicular to (110), (1̅1̅0) (8,1,1̅8̅), (1,8,18), (8̅,1̅,18), and (1̅,8̅,1̅8̅) planes. In practical growth, higher chemical bonding density at the intersection of two adjacent thermodynamically preferred surfaces leads to the appearance of surfaces that are parallel to {110}, {1̅1̅0}, (1̅15), and (11̅5̅), respectively.

Figure 10. ϕ 2″ sapphire single crystal grown by the Cz method along the [001] pulling direction. The length of sapphire single crystal reaches 290 mm. The whole growth process can be divided into three stages, enlarging shoulder growth, equivalent diameter growth, and bottom shrinkage sections.

growth process can be divided into three stages, enlarging shoulder growth, equivalent diameter growth, and bottom shrinkage section. The length of the equivalent diameter section of sapphire single crystal reaches 210 mm. As shown in Figure 10, no visible defects, such as bubbles, cracks, and polycrystalline growth, exist. The lengths of enlarging shoulder growth, equivalent diameter growth, and bottom shrinkage sections are 40, 210, and 40 mm, respectively. Moreover, the interface of sapphire grown along the [001] direction in the Cz 2286

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(13) Brunia, F. J.; Liu, C.-M.; Stone-Sundberg, J. Acta Phys. Polym., A 2013, 124, 213−218. (14) Pin, S.; Suardelli, M.; D’Acapito, F.; Spinolo, G.; Zema, M.; Tarantino, S. C.; Ghigna, P. J. Phys. Chem. C 2013, 117, 6105−6112. (15) Sun, C.; Xue, D. Mater. Technol. 2013, 28, 286−289. (16) Komurasaki, H.; Isono, T.; Tsukamoto, T.; Ogino, T. Appl. Surf. Sci. 2012, 258, 5666−5671. (17) Sun, C.; Xue, D. Mater. Res. Innov. 2013, 17, 552−556. (18) Sun, C.; Xue, D. CrystEngComm 2014, 16, 2088−2088. (19) Sun, C.; Zhang, Y.; Song, S.; Xue, D. J. Appl. Crystallogr. 2013, 46, 1128−1136. (20) Xue, D.; Li, K.; Liu, J.; Sun, C.; Chen, K. Mater. Res. Bull. 2012, 47, 2838−2842. (21) Sun, C.; Xu, D.; Xue, D. CrystEngComm 2013, 15, 7783−7791. (22) Sun, C.; Xue, D. J. Phys. Chem. C 2013, 117, 19146−19152. (23) Xu, D.; Xue, D. J. Synth. Cryst. 2006, 35, 598−601. (24) Yan, X.; Xu, D.; Xue, D. Acta Mater. 2007, 55, 5747−5757. (25) Xu, D.; Xue, D. J. Cryst. Growth 2006, 286, 108−113. (26) Zhao, X.; Ren, X.; Sun, C.; Zhang, X.; Si, Y.; Yan, C.; Xu, J.; Xue, D. Funct. Mater. Lett. 2008, 1, 167−172. (27) Sun, C.; Xue, D. J. Phys. Chem. C 2013, 117, 5505−5511. (28) Dobrovinskaya, E. R.; Litvinov, L. A.; Pischik, V. Sapphire: Material, Manufacturing, Applications; Springer: Berlin, 2009.

system exhibits a circle, in a good agreement with our theoretical calculations.

5. CONCLUSION From both the chemical bonding theory of single crystal growth and practical growth by the Cz method, we studied the anisotropic bonding dependence of growth directions of sapphire single crystal. Both thermodynamically and kinetically preferred growth directions of sapphire in the Cz growth system along four typical pulling directions (i.e, [210], [110], [001], and [001] rotated 57.62°) have been identified on the basis of the combination of thermodynamic morphology and anisotropic chemical bonding distributions. Chemical bonding calculations demonstrate that the slower pulling rate should be designed for Cz growth of sapphire along the [001] pulling direction, whereas a faster pulling rate should be designed along the [210], [110], and [001] rotated 57.62° pulling directions. By utilizing the large-size single crystal growth system, ϕ 2″ sapphire single crystal was grown via the Cz method along the [001] pulling direction. Our present work shows the effect of anisotropy on the Cz growth of large-size single crystals, which can provide a theoretical guide in practical growth from both thermodynamic and kinetic viewpoints.

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ASSOCIATED CONTENT

S Supporting Information *

This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +86-431-85262294. Fax: +86-431-85262294. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the National Natural Science Foundation of China (Grant No. 51125009), National Natural Science Foundation for Creative Research Group (Grant No. 21221061), and the Hundred Talents Program of the Chinese Academy of Sciences is acknowledged.

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