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The influence of indium on the growth of GaN from solution under high pressure
Journal of Crystal Growth 312 (2010) 2593–2598
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Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
The influence of indium on the growth of GaN from solution under high pressure I. Grzegory n, M. Boc´kowski, P. Stra˛k, S. Krukowski, S. Porowski Institute of High Pressure Physics of PAS, ul. Soko!owska 29/37, 01-142 Warsaw, Poland
a r t i c l e in fo
abstract
Available online 21 April 2010
The influence of significant fraction (10–50 mole%) indium in liquid gallium on GaN crystallization from a ternary Ga–In–N solution was analyzed. Crystallization experiments of GaN on GaN-sapphire templates from Ga–In solutions, at 1350–1450 1C, with prior to the growth seed wetting at 1500 1C, and 1.0 GPa N2 pressure, without solid GaN source showed faster growth of GaN on the seed (by a factor of 1.5–2) than using pure gallium solvent. Nevertheless the new grown crystals were morphologically unstable. The instability was reduced by decrease of the wetting temperature down to 1100 1C or by omitting the wetting procedure entirely, which indicated that GaN dissolves much faster in Ga–In melt than in pure Ga and that the unstable growth was caused most likely by complete dissolution of GaN template before the growth. It was observed that the crystals grown on bulk GaN substrates did not show morphological instability observed for GaN-sapphire templates. The influence of indium on thermodynamic and thermal properties of the investigated system is discussed. & 2010 Elsevier B.V. All rights reserved.
Keywords: A2. High pressure growth from solution A2. Single crystal growth B1. Gallium nitride
1. Introduction At present, stringent efforts are undertaken to develop crystallization methods of large size, high quality GaN bulk crystals. However the final goal: perfect, large and commonly available GaN crystals is still a challenge because of extreme congruent melting conditions of this compound (2220 1C, 6 GPa) [1], making application of the melt growth techniques technically impossible. The methods, allowing use of significantly lower temperatures and pressures than these required for melting have their specific limitations, of which the most important is low rate of crystallization, especially for ammonothermal and solution growth systems. The high nitrogen pressure solution (HNPS) growth is one of the few methods giving single crystalline GaN which is successfully used for fabrication of laser diodes [2]. This is possible due to extremely low dislocation density and very high, uniform electrical conductivity of this material. In the GaN crystals, grown by the HNPS method without intentional seeding [3], threading dislocation densities (TDD), measured by defect selective etching of (0 0 0 1) Ga-polar surfaces, are lower than 100 cm 2. The crystals are heavily n-type (about 5 1019 cm 3) unintentionally doped by oxygen, making them strongly and uniformly conducting. The free electrons can be removed by compensation with magnesium acceptor added to the growth solution and, in this
n
Corresponding author. Tel.: + 48 22 632 1635; fax: + 48 22 632 4218. E-mail address: [email protected] (I. Grzegory).
0022-0248/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2010.04.018
way, semi-insulating GaN can be grown. Due to relatively low equilibrium concentration of nitrogen in the liquid gallium at the growth temperatures of 1400–1500 1C (0.1–0.3 mol% respectively) the maximum rate of stable crystallization is fairly low. For thin platelets, it is about 1 mm/h for /0 0 0 1S direction and about 100 mm/h for lateral directions. The problem of limited size of spontaneously grown high pressure GaN crystals is being solved by the use of seed crystals grown by HVPE [4]. In this way the 1–2 in (0 0 0 1) oriented pressure grown substrates, with dislocation density significantly lower than in the seed, can be obtained. The crystals are grown on one surface of the seed (horizontal configuration) or on two opposite surfaces for seeds immersed in the solution (vertical configuration). Afterwards the seeds are removed from pressure grown crystals by sawing or polishing to obtain free standing, highly conducting GaN. In the horizontal configuration, the seed crystal is placed at the bottom or at the top of the crucible, filled with liquid gallium. Temperature gradient is applied along the axis of the crucible. Typical temperature range is 1400–1500 1C at 1.0 GPa N2 pressure. In Fig. 1, the horizontal configuration is schematically shown. Crucibles with internal diameter of 18, 25 and 50 mm are used for crystallization on various substrates, including HNPS GaN crystals (small, TDDo100 cm 2), HVPE GaN crystals (TDD ¼ 106–107 cm 2) and MOVPE GaN-on-sapphire templates (TDD ¼ 108–109 cm 2). The crystals grown by the HNPS method on the substrates are usually macroscopically flat with macroscopic growth steps covering the growth surface—Fig. 2a–c. The formation of these
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Fig. 1. Horizontal configuration used for seeded HNPS growth of GaN: crucible with typical temperature distribution in the crucible wall and in the crucible bottom.
growth features is a sign of non-uniform supersaturation across the growing surface. In this work, the possible influence of indium, added to the gallium solvent in significant fraction (10–50%), on seeded GaN crystallization in horizontal configuration was investigated. The following aspects were taken into account: 1. Possible increase of equilibrium solubility of GaN in the liquid metal by dilution of gallium with indium due to decrease of the chemical potential of Ga in the liquid phase. 2. Corresponding adjustment (increase) of activity of N2 gas, necessary for the solvent in contact with the gas. 3. Possible changes in temperature distribution due to different physical properties of indium and gallium metals. 4. Higher potential barrier for dissociation of N2 molecule for gallium partially replaced by indium: it should result in reduced parasitic crystallization rates but also in slowing down of nitrogen dissolution in the metal (from gaseous source of nitrogen).
2. Experimental procedures and results Basic experimental configuration used for this study was the one shown schematically in Fig. 1. The 3 mm thick GaN-onsapphire substrates grown by MOVPE were placed on the bottom of the graphite crucible, filled with gallium and indium mixture. Prior to the growth, the system was overheated above GaN–Ga– N2 equilibrium conditions to assure a good wetting of the substrate with liquid metal. The first experiment was carried out at the following conditions: Procedure 1 Substrate: GaN-on-sapphire, (0 0 0 1) Solvent: 50 mol% Ga + 50 mol% In Wetting: 1500 1C, 2 min Axial DT: 1350–1450 1C measured in crucible wall along 15 mm high metal sample Radial DT: 1300–1350 1C measured along 10 mm radius of the crucible bottom
Fig. 2. GaN crystals, grown on GaN sapphire substrates, at the conditions specified in the text: a,b,c — general view, surface morphology and cross section, respectively, of the crystal grown from solution in pure gallium in 80 h process with high temperature wetting of the template, d, e, f—general view, surface morphology and cross section, respectively, of the crystal grown from solution in 50 mol% Ga +50 mol% In with high temperature wetting of the template, g, h, I — the same as ‘‘d, e, f’’ but with low temperature wetting. In ‘‘a, d g’’ the distance between grid lines is 1 mm.
N2 pressure: 10 kbar Duration: 25 h. The reference experiments with pure gallium solvent and at otherwise, identical conditions [3], resulted in transparent, newly grown GaN crystals (layers) with macroscopically flat surfaces,
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covered with macroscopic growth steps. The as grown GaN(0 0 0 1) surface was usually contaminated with some microcrystallites growing during final cooling of the system. The rate of growth in the reference configuration did not exceed 1 mm/h. The reference results are collected in Fig. 2a–c. The experiment with Ga–In solvent resulted in non-transparent new grown GaN crystal with apparently rough surface (Fig. 2d) patterned in a very regular way (Fig. 2e). The growth was three dimensional (Fig. 2f), like that observed earlier [5] on bare sapphire substrates. The rate of growth deduced from the mass of the new grown crystal was 2.6 mm/h. From this observation it was concluded that the thin GaN layer, on the initial substrate was dissolved in the liquid metal before the growth in temperature gradient started. This was not a case for the growth form pure gallium solvent at the same experimental conditions, including the high temperature wetting procedure. Therefore, the experiment with Ga–In solvent was repeated with modification of the wetting conditions. Both the temperature and pressure of this procedure were reduced down to 1100 1C and 30 bar, respectively. The results of such experiments as well as the ones where the back melting stage was omitted, are represented in Fig. 2g–i. The growth surface was partially stabilized, which is reflected by areas of continuous GaN layer. However, even for processes where the system was not overheated above GaN–Ga–N2 equilibrium conditions [6] for wetting, the areas of unstable morphology due to complete dissolution of the template were observed. These observations indicated that thin GaN layers, deposited on sapphire, are not acceptable as templates for GaN growth from Ga–In solutions due to enhanced dissolution of GaN in the metal, even for heating the system at the N2 pressure assuring stability of the nitride with respect to its constituents. Consequently, the bulk GaN substrates, grown by HVPE, were applied for the continuation of this study. The experiments on GaN substrates were carried out at the following conditions: Procedure 2 Substrate: HVPE GaN (0 0 0 1), polished and reactive ion etched
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Solvent: 50 mol% Ga +50 mol% In Wetting: no Axial DT: 1350–1400 1C measured in crucible wall along 7 mm high metal sample N2 pressure: 10 kbar Duration: 50 h. Fig. 3 shows the results of the growth on HVPE-GaN substrates. As it was already mentioned, the growth on the GaN-on-sapphire substrate without the wetting stage, resulted in the new grown GaN having partially stable surface morphology, including coalesced, flat islands and rough areas. The layers, grown on bulk GaN substrates (without back melting stage), were much more homogeneous in terms of their flatness and surface morphology as it is shown in Fig. 3. Growth rate in these experimental conditions approached 2 mm/h, which was over twice higher than for pure gallium solvent at otherwise the same growth conditions. The experiments with GaN substrates were repeated with 10 and 20 at% of indium in the solution in order to check the coupling of the GaN substrates to the metal with no wetting procedure. The quality of the new grown crystals, in terms of surface morphology and quality of cleavage, was as good as these obtained for 50 at% indium content. There was no significant change in the rate of crystallization in these processes. In all experiments, no GaN polycrystalline film, covering surface of the liquid metal, was observed, in contrast to the pure gallium solvent. Taking into account the fast dissolution of GaN and no surface synthesis observed for processes with gaseous N2 source, the experiments with solid source of nitrogen (GaN feed crystal) and both GaN-sapphire and bulk GaN substrates were carried out. The experiment with GaN/sapphire substrate was carried out at the conditions very similar to the ones specified as Procedure 1: Procedure 3 Substrate: GaN-on-sapphire Solvent: 50 mol% Ga +50 mol% In N-source GaN feed crystal on the top of solution Wetting: no
Fig. 3. GaN crystal, grown on HVPE-GaN substrate, at the conditions specified in the text: a, b, c — general view, surface morphology and cross section respectively, of the crystal grown from solution in 50 mol% Ga + 50 mol% In with no back melting of the substrate.
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Axial DT: 1350–1450 1C measured in crucible wall along 15 mm high metal sample Radial DT: 1300–1350 1C measured along 10 mm radius of the crucible bottom N2 pressure: 10 kbar Duration: 20 h. This experiment resulted in the highest observed growth rate of 3.12 mm/h for the applied conditions of the process. Dissolution rate of the feed crystal estimated from the change of the crystal mass corresponded to 2.8 mm/h.
3. Discussion The idea of using indium for dilution of gallium solvent in solution growth of GaN was proposed by Angus et al. [7], who applied nitrogen plasma as an active nitrogen source for synthesis of III–V nitrides. It was suggested that equilibrium concentration of nitrogen in the liquid metal can be increased significantly by dilution of the liquid gallium by a third component, which does not incorporate into the growing crystal. Indeed at dilution, the chemical potential of liquid gallium decreases whereas the chemical potential of GaN does not change. Therefore, in new equilibrium between the crystal and the liquid, the chemical potential of N in the liquid (solution) should increase to fulfill equilibrium condition for the constituents:
mlGa þ mlN ¼ msGaN
ð1Þ
where the indices ‘‘l’’ and ‘‘s’’ denote liquid and solid, respectively. On the other hand, if the solution has a direct contact with N2 gas, the increased concentration of N in the liquid requires a compensation by adequate increase of N2 activity, which is a function of pressure and temperature following N2 equation of state [8]. Activity of N2 gas increases with pressure and decreases with temperature as it is illustrated in Fig. 4. The black arrow in the figure shows approximately the pressure and temperature range of high pressure solution growth of GaN. It can be noticed that no significant change of N2 activity can be achieved by varying pressure between 5 and 10 kbar at high temperatures. Moreover, the activity of nitrogen, dissolved in the metal (or equivalently concentration, for ideal solution) is proportional to the square root of the activity of N2 gas. Therefore, for compensation of two-fold increase of N activity (concentration) in the liquid, four-fold increase of activity of N2 gas is required. At 1450 1C, the equilibrium N2 pressure over GaN and its
1.0x105 T = 1000K T = 373K
activity
8.0x104
T = 1500K
constituents is about 8 kbar, corresponding to the N2 activity of 41.2 kbar. When the pressure increased to 10 kbar, the N2 activity increases to 83 kbar, which indicates a possibility to compensate an increase of nitrogen solubility in the liquid metal by factor smaller than 2 (approximately, square root of 2). The above considerations suggest that the mechanism of increasing of nitrogen concentration in the liquid gallium by dilution of the gallium by a third component can be applied for high pressure crystallization of GaN in quite a limited extent, if the solution has direct contact with the N2 gas. On the other hand, this mechanism could be responsible for the observed limited increase of the crystallization rate of GaN from Ga–In solutions in comparison to the crystallization from pure gallium solvent. The dilution of gallium with indium can modify distribution of temperature in the crucible containing liquid metal which in particular, means that both axial and radial temperature gradients in the metal can be changed. That can influence mass transport in the solution, both convection and diffusion. The relevance of this phenomenon was evaluated for the purpose of this study, by computerized fluid dynamics (CFD) simulations of the temperature field in the liquid gallium and indium for the same border conditions, determined by both axial and radial temperature gradients, measured along the wall and across the bottom of graphite crucible respectively as it is shown in Fig. 1. The simulation was made using commercial Fluent 6 package provided by ANSYS Inc., allowing solution of Navier–Stokes equations using the finite element method (FEM). The details of similar calculations were already described [4]. Physical properties of gallium and indium [9], used as input parameters in the modeling, are listed in Table 1, whereas the results are shown in Fig. 5. The plotted diagrams of temperature distribution in the liquid metals indicate that both axial and radial temperature gradients are apparently larger in indium than in gallium. Therefore, an enhanced mass transport could be expected at high indium content in the liquid phase. It can obviously lead to an increase of GaN crystallization rate providing that a sufficient rate of nitrogen dissolution in the metal is attained. In case when the source of nitrogen is N2 gas, it is not so obvious that dissolution of atomic N in the metal will be fast enough because, as it was shown by Density Functional Theory (DFT) modeling [10], the energy barrier for dissociation of N2 molecule on the metal surface is higher for indium than for gallium. This can explain experimental observation that the surface of gallium, alloyed with significant amount (equal or more than 10 at%) of indium, was never covered by the GaN film, which is commonly observed for the pure gallium solvent. The lack of the surface film can also explain the observed good wetting of GaN substrates by indium containing solvent and dissolution of GaN even at heating of the system at high N2 overpressure (referred to the GaN–Ga–N2 equilibrium curve [6]). It follows from above considerations that the optimum configuration of the experiment with In-rich solvent should include the following elements:
T = 500K
6.0x104
1. bulk GaN substrate (thin GaN layers on foreign substrates will be dissolved)
4.0x104 T= 2000K 2.0x104
Table 1 Physical properties of liquid indium and gallium, used in the calculations [9].
Ideal gas
0.0 0
5000 pressure [bar]
10000
Fig. 4. Activity of N2 gas as function of pressure and temperature [8].
Density Specific heat Thermal conductivity Viscosity Thermal expansion
Indium
Gallium
Unit
6097 270 25.33 1.0355 19.62 10 5
5360 374 87–93 0.55–0.56 11 10 5
(kg/m3) (J/kg m) (W/m K) (mPa s) (1/k)
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Fig. 5. Distribution of temperature in the crucible with liquid metal for experimental configuration used in Procedure 1: (a) vertical temperature profiles in liquid gallium, corresponding positions in the crucible are indicated, (b) vertical temperature profiles in liquid indium, (c) vertical temperature profiles in gallium and indium at the center of the crucible, (d) vertical temperature profiles in gallium and indium at the crucible wall.
2. solid source of nitrogen (GaN feed crystal), since the N2 source can be inefficient 3. large temperature gradient along crucible of small height: large thermal gradient perpendicular to the substrate should stabilize the growth surface whereas the small height of the solution should assure low supersaturation necessary for stable growth at smaller equilibrium concentrations.
4. Conclusions It was shown that process of crystallization of GaN from solution in gallium at high N2 pressure is influenced by indium added into the gallium solvent in significant amount (10–50%). This influence is demonstrated by the following experimental observations: 1. No GaN synthesis surface reaction is observed. 2. Very good wetting of GaN by Ga–In solvent, with no initial overheating required. 3. Fast dissolution of GaN in Ga–In metal, even at high N2 overpressure with respect to the condition of equilibrium between GaN and its constituents.
4. GaN crystallization rate on the substrates is higher by factor of about 2 than that from pure Ga solvent, most probably it is due to Ga dilution and/or bigger temperature gradients in the liquid, caused by the presence of indium; further increase (over 3 mm/h) can be achieved using solid N source (GaN feed crystal). Therefore, experimental configuration containing GaN substrate and solid nitrogen source (GaN feed crystal) in large temperature gradient on relatively small distance (Ga–In solvent height) is proposed as optimum configuration for more efficient crystallization of GaN at high N2 pressure. Acknowledgements The research was partially supported by the European Union within European Regional Development Fund, through grant Innovative Economy (POIG.01.01.02-00-008/08). References [1] W. Utsumi, H. Saitoh, H. Kaneko, T. Watanuki, K. Aoki, O. Shimomura, Nat. Mater. 2 (2003) 735.
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[2] P. Perlin, M. Leszczyn´ski, P. Prystawko, R. Czernecki, P. Wis´niewski, J.L. Weyher, G. Nowak, J. Borysiuk, L. GorczycaT. S´wietlik, G. Franssen, A. Bering, C. Skierbiszewski, I. Grzegory, T. Suski and S. Porowski, , in: Proceedings of Photonics West 2004, San Jose, CA, USA. [3] I. Grzegory, M. Boc´kowski, S. Porowski, in: P. Capper (Ed.), Bulk Crystal Growth of Electronic, Optical & Optoelectronic Materials, UK, 2005, pp. 173–207 (chapter 6). [4] M. Bockowski, P. Stra˛k, I. Grzegory, B. Łucznik, S. Porowski, J. Cryst Growth 310 (2008) 3924. [5] M. Bockowski, I. Grzegory, S. Krukowski, B. Łucznik, M. Wro´blewski, G. Kamler, J. Borysiuk, P. Kwiatkowski, K. Jasik, S. Porowski, J. Cryst. Growth 270 (2004) 419.
[6] J. Karpinski, J. Jun, S. Porowski, J. Cryst. Growth 66 (1984) 1. [7] B.D. Schultz, A. Argoitia, C.C. Hayman, J.C. Angus, J.S. Dyck, K. Kash and Nan Yang, in: Proceedings of the Electrochemical Society, vol. 98-18, p. 108. [8] P. Strak, S. Krukowski, J. Chem. Phys. 126 (2007) 194510. [9] M.V. Peralta-Martinez, W.A. Wakeham, Int. J. Thermophys. 22 (2001) 395. [10] S. Krukowski, Z. Romanowski, I. Grzegory, S. Porowski, J. Cryst. Growth 189/ 190 (1999) 159.
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
The influence of indium on the growth of GaN from solution under high pressure I. Grzegory n, M. Boc´kowski, P. Stra˛k, S. Krukowski, S. Porowski Institute of High Pressure Physics of PAS, ul. Soko!owska 29/37, 01-142 Warsaw, Poland
a r t i c l e in fo
abstract
Available online 21 April 2010
The influence of significant fraction (10–50 mole%) indium in liquid gallium on GaN crystallization from a ternary Ga–In–N solution was analyzed. Crystallization experiments of GaN on GaN-sapphire templates from Ga–In solutions, at 1350–1450 1C, with prior to the growth seed wetting at 1500 1C, and 1.0 GPa N2 pressure, without solid GaN source showed faster growth of GaN on the seed (by a factor of 1.5–2) than using pure gallium solvent. Nevertheless the new grown crystals were morphologically unstable. The instability was reduced by decrease of the wetting temperature down to 1100 1C or by omitting the wetting procedure entirely, which indicated that GaN dissolves much faster in Ga–In melt than in pure Ga and that the unstable growth was caused most likely by complete dissolution of GaN template before the growth. It was observed that the crystals grown on bulk GaN substrates did not show morphological instability observed for GaN-sapphire templates. The influence of indium on thermodynamic and thermal properties of the investigated system is discussed. & 2010 Elsevier B.V. All rights reserved.
Keywords: A2. High pressure growth from solution A2. Single crystal growth B1. Gallium nitride
1. Introduction At present, stringent efforts are undertaken to develop crystallization methods of large size, high quality GaN bulk crystals. However the final goal: perfect, large and commonly available GaN crystals is still a challenge because of extreme congruent melting conditions of this compound (2220 1C, 6 GPa) [1], making application of the melt growth techniques technically impossible. The methods, allowing use of significantly lower temperatures and pressures than these required for melting have their specific limitations, of which the most important is low rate of crystallization, especially for ammonothermal and solution growth systems. The high nitrogen pressure solution (HNPS) growth is one of the few methods giving single crystalline GaN which is successfully used for fabrication of laser diodes [2]. This is possible due to extremely low dislocation density and very high, uniform electrical conductivity of this material. In the GaN crystals, grown by the HNPS method without intentional seeding [3], threading dislocation densities (TDD), measured by defect selective etching of (0 0 0 1) Ga-polar surfaces, are lower than 100 cm 2. The crystals are heavily n-type (about 5 1019 cm 3) unintentionally doped by oxygen, making them strongly and uniformly conducting. The free electrons can be removed by compensation with magnesium acceptor added to the growth solution and, in this
n
Corresponding author. Tel.: + 48 22 632 1635; fax: + 48 22 632 4218. E-mail address: [email protected] (I. Grzegory).
0022-0248/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2010.04.018
way, semi-insulating GaN can be grown. Due to relatively low equilibrium concentration of nitrogen in the liquid gallium at the growth temperatures of 1400–1500 1C (0.1–0.3 mol% respectively) the maximum rate of stable crystallization is fairly low. For thin platelets, it is about 1 mm/h for /0 0 0 1S direction and about 100 mm/h for lateral directions. The problem of limited size of spontaneously grown high pressure GaN crystals is being solved by the use of seed crystals grown by HVPE [4]. In this way the 1–2 in (0 0 0 1) oriented pressure grown substrates, with dislocation density significantly lower than in the seed, can be obtained. The crystals are grown on one surface of the seed (horizontal configuration) or on two opposite surfaces for seeds immersed in the solution (vertical configuration). Afterwards the seeds are removed from pressure grown crystals by sawing or polishing to obtain free standing, highly conducting GaN. In the horizontal configuration, the seed crystal is placed at the bottom or at the top of the crucible, filled with liquid gallium. Temperature gradient is applied along the axis of the crucible. Typical temperature range is 1400–1500 1C at 1.0 GPa N2 pressure. In Fig. 1, the horizontal configuration is schematically shown. Crucibles with internal diameter of 18, 25 and 50 mm are used for crystallization on various substrates, including HNPS GaN crystals (small, TDDo100 cm 2), HVPE GaN crystals (TDD ¼ 106–107 cm 2) and MOVPE GaN-on-sapphire templates (TDD ¼ 108–109 cm 2). The crystals grown by the HNPS method on the substrates are usually macroscopically flat with macroscopic growth steps covering the growth surface—Fig. 2a–c. The formation of these
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Fig. 1. Horizontal configuration used for seeded HNPS growth of GaN: crucible with typical temperature distribution in the crucible wall and in the crucible bottom.
growth features is a sign of non-uniform supersaturation across the growing surface. In this work, the possible influence of indium, added to the gallium solvent in significant fraction (10–50%), on seeded GaN crystallization in horizontal configuration was investigated. The following aspects were taken into account: 1. Possible increase of equilibrium solubility of GaN in the liquid metal by dilution of gallium with indium due to decrease of the chemical potential of Ga in the liquid phase. 2. Corresponding adjustment (increase) of activity of N2 gas, necessary for the solvent in contact with the gas. 3. Possible changes in temperature distribution due to different physical properties of indium and gallium metals. 4. Higher potential barrier for dissociation of N2 molecule for gallium partially replaced by indium: it should result in reduced parasitic crystallization rates but also in slowing down of nitrogen dissolution in the metal (from gaseous source of nitrogen).
2. Experimental procedures and results Basic experimental configuration used for this study was the one shown schematically in Fig. 1. The 3 mm thick GaN-onsapphire substrates grown by MOVPE were placed on the bottom of the graphite crucible, filled with gallium and indium mixture. Prior to the growth, the system was overheated above GaN–Ga– N2 equilibrium conditions to assure a good wetting of the substrate with liquid metal. The first experiment was carried out at the following conditions: Procedure 1 Substrate: GaN-on-sapphire, (0 0 0 1) Solvent: 50 mol% Ga + 50 mol% In Wetting: 1500 1C, 2 min Axial DT: 1350–1450 1C measured in crucible wall along 15 mm high metal sample Radial DT: 1300–1350 1C measured along 10 mm radius of the crucible bottom
Fig. 2. GaN crystals, grown on GaN sapphire substrates, at the conditions specified in the text: a,b,c — general view, surface morphology and cross section, respectively, of the crystal grown from solution in pure gallium in 80 h process with high temperature wetting of the template, d, e, f—general view, surface morphology and cross section, respectively, of the crystal grown from solution in 50 mol% Ga +50 mol% In with high temperature wetting of the template, g, h, I — the same as ‘‘d, e, f’’ but with low temperature wetting. In ‘‘a, d g’’ the distance between grid lines is 1 mm.
N2 pressure: 10 kbar Duration: 25 h. The reference experiments with pure gallium solvent and at otherwise, identical conditions [3], resulted in transparent, newly grown GaN crystals (layers) with macroscopically flat surfaces,
I. Grzegory et al. / Journal of Crystal Growth 312 (2010) 2593–2598
covered with macroscopic growth steps. The as grown GaN(0 0 0 1) surface was usually contaminated with some microcrystallites growing during final cooling of the system. The rate of growth in the reference configuration did not exceed 1 mm/h. The reference results are collected in Fig. 2a–c. The experiment with Ga–In solvent resulted in non-transparent new grown GaN crystal with apparently rough surface (Fig. 2d) patterned in a very regular way (Fig. 2e). The growth was three dimensional (Fig. 2f), like that observed earlier [5] on bare sapphire substrates. The rate of growth deduced from the mass of the new grown crystal was 2.6 mm/h. From this observation it was concluded that the thin GaN layer, on the initial substrate was dissolved in the liquid metal before the growth in temperature gradient started. This was not a case for the growth form pure gallium solvent at the same experimental conditions, including the high temperature wetting procedure. Therefore, the experiment with Ga–In solvent was repeated with modification of the wetting conditions. Both the temperature and pressure of this procedure were reduced down to 1100 1C and 30 bar, respectively. The results of such experiments as well as the ones where the back melting stage was omitted, are represented in Fig. 2g–i. The growth surface was partially stabilized, which is reflected by areas of continuous GaN layer. However, even for processes where the system was not overheated above GaN–Ga–N2 equilibrium conditions [6] for wetting, the areas of unstable morphology due to complete dissolution of the template were observed. These observations indicated that thin GaN layers, deposited on sapphire, are not acceptable as templates for GaN growth from Ga–In solutions due to enhanced dissolution of GaN in the metal, even for heating the system at the N2 pressure assuring stability of the nitride with respect to its constituents. Consequently, the bulk GaN substrates, grown by HVPE, were applied for the continuation of this study. The experiments on GaN substrates were carried out at the following conditions: Procedure 2 Substrate: HVPE GaN (0 0 0 1), polished and reactive ion etched
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Solvent: 50 mol% Ga +50 mol% In Wetting: no Axial DT: 1350–1400 1C measured in crucible wall along 7 mm high metal sample N2 pressure: 10 kbar Duration: 50 h. Fig. 3 shows the results of the growth on HVPE-GaN substrates. As it was already mentioned, the growth on the GaN-on-sapphire substrate without the wetting stage, resulted in the new grown GaN having partially stable surface morphology, including coalesced, flat islands and rough areas. The layers, grown on bulk GaN substrates (without back melting stage), were much more homogeneous in terms of their flatness and surface morphology as it is shown in Fig. 3. Growth rate in these experimental conditions approached 2 mm/h, which was over twice higher than for pure gallium solvent at otherwise the same growth conditions. The experiments with GaN substrates were repeated with 10 and 20 at% of indium in the solution in order to check the coupling of the GaN substrates to the metal with no wetting procedure. The quality of the new grown crystals, in terms of surface morphology and quality of cleavage, was as good as these obtained for 50 at% indium content. There was no significant change in the rate of crystallization in these processes. In all experiments, no GaN polycrystalline film, covering surface of the liquid metal, was observed, in contrast to the pure gallium solvent. Taking into account the fast dissolution of GaN and no surface synthesis observed for processes with gaseous N2 source, the experiments with solid source of nitrogen (GaN feed crystal) and both GaN-sapphire and bulk GaN substrates were carried out. The experiment with GaN/sapphire substrate was carried out at the conditions very similar to the ones specified as Procedure 1: Procedure 3 Substrate: GaN-on-sapphire Solvent: 50 mol% Ga +50 mol% In N-source GaN feed crystal on the top of solution Wetting: no
Fig. 3. GaN crystal, grown on HVPE-GaN substrate, at the conditions specified in the text: a, b, c — general view, surface morphology and cross section respectively, of the crystal grown from solution in 50 mol% Ga + 50 mol% In with no back melting of the substrate.
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Axial DT: 1350–1450 1C measured in crucible wall along 15 mm high metal sample Radial DT: 1300–1350 1C measured along 10 mm radius of the crucible bottom N2 pressure: 10 kbar Duration: 20 h. This experiment resulted in the highest observed growth rate of 3.12 mm/h for the applied conditions of the process. Dissolution rate of the feed crystal estimated from the change of the crystal mass corresponded to 2.8 mm/h.
3. Discussion The idea of using indium for dilution of gallium solvent in solution growth of GaN was proposed by Angus et al. [7], who applied nitrogen plasma as an active nitrogen source for synthesis of III–V nitrides. It was suggested that equilibrium concentration of nitrogen in the liquid metal can be increased significantly by dilution of the liquid gallium by a third component, which does not incorporate into the growing crystal. Indeed at dilution, the chemical potential of liquid gallium decreases whereas the chemical potential of GaN does not change. Therefore, in new equilibrium between the crystal and the liquid, the chemical potential of N in the liquid (solution) should increase to fulfill equilibrium condition for the constituents:
mlGa þ mlN ¼ msGaN
ð1Þ
where the indices ‘‘l’’ and ‘‘s’’ denote liquid and solid, respectively. On the other hand, if the solution has a direct contact with N2 gas, the increased concentration of N in the liquid requires a compensation by adequate increase of N2 activity, which is a function of pressure and temperature following N2 equation of state [8]. Activity of N2 gas increases with pressure and decreases with temperature as it is illustrated in Fig. 4. The black arrow in the figure shows approximately the pressure and temperature range of high pressure solution growth of GaN. It can be noticed that no significant change of N2 activity can be achieved by varying pressure between 5 and 10 kbar at high temperatures. Moreover, the activity of nitrogen, dissolved in the metal (or equivalently concentration, for ideal solution) is proportional to the square root of the activity of N2 gas. Therefore, for compensation of two-fold increase of N activity (concentration) in the liquid, four-fold increase of activity of N2 gas is required. At 1450 1C, the equilibrium N2 pressure over GaN and its
1.0x105 T = 1000K T = 373K
activity
8.0x104
T = 1500K
constituents is about 8 kbar, corresponding to the N2 activity of 41.2 kbar. When the pressure increased to 10 kbar, the N2 activity increases to 83 kbar, which indicates a possibility to compensate an increase of nitrogen solubility in the liquid metal by factor smaller than 2 (approximately, square root of 2). The above considerations suggest that the mechanism of increasing of nitrogen concentration in the liquid gallium by dilution of the gallium by a third component can be applied for high pressure crystallization of GaN in quite a limited extent, if the solution has direct contact with the N2 gas. On the other hand, this mechanism could be responsible for the observed limited increase of the crystallization rate of GaN from Ga–In solutions in comparison to the crystallization from pure gallium solvent. The dilution of gallium with indium can modify distribution of temperature in the crucible containing liquid metal which in particular, means that both axial and radial temperature gradients in the metal can be changed. That can influence mass transport in the solution, both convection and diffusion. The relevance of this phenomenon was evaluated for the purpose of this study, by computerized fluid dynamics (CFD) simulations of the temperature field in the liquid gallium and indium for the same border conditions, determined by both axial and radial temperature gradients, measured along the wall and across the bottom of graphite crucible respectively as it is shown in Fig. 1. The simulation was made using commercial Fluent 6 package provided by ANSYS Inc., allowing solution of Navier–Stokes equations using the finite element method (FEM). The details of similar calculations were already described [4]. Physical properties of gallium and indium [9], used as input parameters in the modeling, are listed in Table 1, whereas the results are shown in Fig. 5. The plotted diagrams of temperature distribution in the liquid metals indicate that both axial and radial temperature gradients are apparently larger in indium than in gallium. Therefore, an enhanced mass transport could be expected at high indium content in the liquid phase. It can obviously lead to an increase of GaN crystallization rate providing that a sufficient rate of nitrogen dissolution in the metal is attained. In case when the source of nitrogen is N2 gas, it is not so obvious that dissolution of atomic N in the metal will be fast enough because, as it was shown by Density Functional Theory (DFT) modeling [10], the energy barrier for dissociation of N2 molecule on the metal surface is higher for indium than for gallium. This can explain experimental observation that the surface of gallium, alloyed with significant amount (equal or more than 10 at%) of indium, was never covered by the GaN film, which is commonly observed for the pure gallium solvent. The lack of the surface film can also explain the observed good wetting of GaN substrates by indium containing solvent and dissolution of GaN even at heating of the system at high N2 overpressure (referred to the GaN–Ga–N2 equilibrium curve [6]). It follows from above considerations that the optimum configuration of the experiment with In-rich solvent should include the following elements:
T = 500K
6.0x104
1. bulk GaN substrate (thin GaN layers on foreign substrates will be dissolved)
4.0x104 T= 2000K 2.0x104
Table 1 Physical properties of liquid indium and gallium, used in the calculations [9].
Ideal gas
0.0 0
5000 pressure [bar]
10000
Fig. 4. Activity of N2 gas as function of pressure and temperature [8].
Density Specific heat Thermal conductivity Viscosity Thermal expansion
Indium
Gallium
Unit
6097 270 25.33 1.0355 19.62 10 5
5360 374 87–93 0.55–0.56 11 10 5
(kg/m3) (J/kg m) (W/m K) (mPa s) (1/k)
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Fig. 5. Distribution of temperature in the crucible with liquid metal for experimental configuration used in Procedure 1: (a) vertical temperature profiles in liquid gallium, corresponding positions in the crucible are indicated, (b) vertical temperature profiles in liquid indium, (c) vertical temperature profiles in gallium and indium at the center of the crucible, (d) vertical temperature profiles in gallium and indium at the crucible wall.
2. solid source of nitrogen (GaN feed crystal), since the N2 source can be inefficient 3. large temperature gradient along crucible of small height: large thermal gradient perpendicular to the substrate should stabilize the growth surface whereas the small height of the solution should assure low supersaturation necessary for stable growth at smaller equilibrium concentrations.
4. Conclusions It was shown that process of crystallization of GaN from solution in gallium at high N2 pressure is influenced by indium added into the gallium solvent in significant amount (10–50%). This influence is demonstrated by the following experimental observations: 1. No GaN synthesis surface reaction is observed. 2. Very good wetting of GaN by Ga–In solvent, with no initial overheating required. 3. Fast dissolution of GaN in Ga–In metal, even at high N2 overpressure with respect to the condition of equilibrium between GaN and its constituents.
4. GaN crystallization rate on the substrates is higher by factor of about 2 than that from pure Ga solvent, most probably it is due to Ga dilution and/or bigger temperature gradients in the liquid, caused by the presence of indium; further increase (over 3 mm/h) can be achieved using solid N source (GaN feed crystal). Therefore, experimental configuration containing GaN substrate and solid nitrogen source (GaN feed crystal) in large temperature gradient on relatively small distance (Ga–In solvent height) is proposed as optimum configuration for more efficient crystallization of GaN at high N2 pressure. Acknowledgements The research was partially supported by the European Union within European Regional Development Fund, through grant Innovative Economy (POIG.01.01.02-00-008/08). References [1] W. Utsumi, H. Saitoh, H. Kaneko, T. Watanuki, K. Aoki, O. Shimomura, Nat. Mater. 2 (2003) 735.
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[2] P. Perlin, M. Leszczyn´ski, P. Prystawko, R. Czernecki, P. Wis´niewski, J.L. Weyher, G. Nowak, J. Borysiuk, L. GorczycaT. S´wietlik, G. Franssen, A. Bering, C. Skierbiszewski, I. Grzegory, T. Suski and S. Porowski, , in: Proceedings of Photonics West 2004, San Jose, CA, USA. [3] I. Grzegory, M. Boc´kowski, S. Porowski, in: P. Capper (Ed.), Bulk Crystal Growth of Electronic, Optical & Optoelectronic Materials, UK, 2005, pp. 173–207 (chapter 6). [4] M. Bockowski, P. Stra˛k, I. Grzegory, B. Łucznik, S. Porowski, J. Cryst Growth 310 (2008) 3924. [5] M. Bockowski, I. Grzegory, S. Krukowski, B. Łucznik, M. Wro´blewski, G. Kamler, J. Borysiuk, P. Kwiatkowski, K. Jasik, S. Porowski, J. Cryst. Growth 270 (2004) 419.
[6] J. Karpinski, J. Jun, S. Porowski, J. Cryst. Growth 66 (1984) 1. [7] B.D. Schultz, A. Argoitia, C.C. Hayman, J.C. Angus, J.S. Dyck, K. Kash and Nan Yang, in: Proceedings of the Electrochemical Society, vol. 98-18, p. 108. [8] P. Strak, S. Krukowski, J. Chem. Phys. 126 (2007) 194510. [9] M.V. Peralta-Martinez, W.A. Wakeham, Int. J. Thermophys. 22 (2001) 395. [10] S. Krukowski, Z. Romanowski, I. Grzegory, S. Porowski, J. Cryst. Growth 189/ 190 (1999) 159.