Influence of V/III ratio on stress control in GaN grown on different templates by hydride vapour phase epitaxy

Abstract

GaN crystals were grown on MOCVD-GaN/Al₂O₃ templates (MGA) and MOCVD-GaN/6H–SiC templates (MGS) in a hydride vapour phase epitaxy (HVPE) process where the V/III ratio was controlled. The tensile stress that exists in MGS was controlled by an increasing V/III ratio. The compressive stress that appears in MGA was controlled by a decreasing V/III ratio. The mechanism of stress control using the V/III ratio is discussed in terms of the interrelation of the stress, the V/III ratio and the crystal growth. The stress in these two kinds of substrates causes differences in atomic mobility which may be compensated by varying the V/III ratio. It is found that a larger V/III ratio results in a higher atomic mobility. Thus, atomic mobility is retarded by compressive stress and increased by tensile stress. This method of stress control has been shown to provide worthwhile guidance for GaN growth on different templates, and under different conditions in other investigations.

---

Introduction

GaN based III/V semiconductors are recognized to be excellent materials for applications in visible and ultraviolet light emitting diodes and laser diodes.^1,2 However, the development of high-performance GaN-based devices has been limited by the mismatch caused by hetero-epitaxial growth. It is widely recognized that the growth of bulk GaN single crystals with subsequent wafer slicing is a possible solution. The HVPE method, which is accepted as one of the most successful and promising methods for obtaining high quality substrates for bulk GaN, has been widely investigated. Control of the V/III ratio is essential to obtain high quality GaN films in the HVPE process. Generally, it is necessary for the V/III ratio to be modified during the entire growth process because of stress variation due to dislocation generation, impurities, cracks, etc.^3,4 The growth mode also can be changed via V/III ratio control.^5,6 Given the current paucity of research investigating the interrelation of stress, V/III ratio and crystal growth, this paper reports our efforts to identify and understand these relationships.

In this study, GaN films were grown on MOCVD-GaN/Al₂O₃ templates (MGA) and MOCVD-GaN/6H–SiC templates (MGS) with different types of stress via different V/III ratio growth processes. Below, we discuss the key role of atom mobility in crystal growth. Data and theoretical derivations are presented, which provide evidence that the stress in these two kinds of substrates can influence atomic mobility. We then discuss how atomic mobility may be compensated by varying the V/III ratio.

Experimental

GaN layers of thickness 2–4 μm were grown on a 2-inch sapphire substrate and a 2-inch SiC substrate by metal–organic chemical vapor deposition. Both the MGA and MGS were employed in subsequent HVPE growth. The home-built, PLC-controlled, vertical HVPE reactor consisted of two zones with different temperatures, with the source zone designated at the bottom and the deposition zone at the top. GaCl as the source material of Ga, is formed by the reaction between metallic Ga and HCl in the source zone when heated to about 850 °C. GaN is formed in the deposition zone as a result of the reaction between GaCl and NH₃ at the elevated temperature of 1050 °C. During the entire process, both the carrier and push flows were provided by N₂.

In order to obtain a mirror smooth GaN layer, growth parameters must be varied with time due to the difficulty of reducing surface roughness by maintaining a constant V/III ratio. In our study, respective MGA and MGS growth parameters were kept constant, with the exception of the V/III ratio. The V/III ratio was controlled by varying the ratio of the NH₃ and HCl flow rates with the other gas flow rates held constant. The HCl flow was held in the range of 10–30 mL min⁻¹, while the NH₃ flow was typically 500–2200 mL min⁻¹. The growth process of GaN grown on MGS was performed using an increasing V/III ratio, while GaN prepared on MGA was controlled using a decreasing V/III ratio. The thickness of GaN films grown on the MGS and MGA templates was 10–20 μm.

Crystal quality was determined by high-resolution X-ray diffraction (HR-XRD, PANalytical X'PERT PRO). Photoluminescence (PL) measurements were carried out at room temperature in order to characterize the optical properties using a 325 nm He–Cd laser as the excitation source. Surface morphology was confirmed by atomic force microscopy (AFM, Digital Instrument Dimension 3100). Slow positron beam Doppler broadening of annihilation radiation was performed to obtain information on native vacancies in GaN layers. Raman spectroscopy was carried out on a Horiba Jobin Yvon LabRAM HR system at room temperature using a 532 nm solid state laser as the excitation source. Transmission electron microscopy (TEM, JEOL-200CX) was employed to study dislocation characteristics.

Results and discussion

Properties of GaN layers

There are three different types of dislocation in the GaN layers: a-type, c-type and a + c-type with Burgers vectors b, where:
as shown by Shao et al.⁷ (Note that in their paper the four-index notation was used to describe the directions and planes in the hexagonal system. A plane such as (hkil) is equivalent to (hkl) with i = −h−k in three-index notation adopted in this paper). In this study, for a (001) film, there are either edge threading dislocations (TDs) or screw TDs along the [001] direction. The specific TD geometry mentioned above leads to distortion only in specific crystallographic planes. Symmetric (00l) rocking curves are insensitive to the pure screw TD content in the layers. The distortion induced by the planar strain of the edge TDs is reflected in the full width at half-maximum (FWHM) of asymmetric reflections.^8–10 From the above considerations, symmetric (002) and asymmetric (102) reflections were used to determine the crystal quality of the HVPE GaN films in this study. The FWHM of the (002) peak is 359 arcsec for the HVPE GaN films grown on MGA, and 479 arcsec for those grown on MGS. The FWHM of the (102) peak is 334 and 435 arcsec for the HVPE GaN films grown on the MGA and MGS, respectively (see Fig. 1).

Fig. 1 HRXRD rocking curves (a) in (002) reflection and (b) in (102) reflection for HVPE GaN films grown on MGA and MGS templates.

Optical properties of the HVPE GaN films grown on MGA and MGS were investigated by room temperature PL spectroscopy. Band-edge emission peaks at 363 nm with MGA and 362 nm with MGS are indicated in Fig. 2. There is a small yellow luminescence band at 500–600 nm as a result of the low native defect density in the samples.¹¹

Fig. 2 PL spectra at room temperature for HVPE GaN films grown on MGA and MGS templates.

For the results given above, GaN films grown on different templates were prepared via different V/III ratio growth processes. In order to distinguish between MGA and MGS, stress can be employed as a characterization parameter. The stress in GaN grown on MGA is compressive, while on MGS it is tensile.¹² The stress in the templates that is related to generated dislocations, impurities, cracks, etc. is an adverse factor for good crystal growth. Therefore it is found that the tensile stress that exists in MGS is controlled by increasing the V/III ratio, while the compressive stress that appears in MGA is controlled by decreasing the V/III ratio.

Mechanism of stress control by V/III ratio

Adatom surface mobility is considered to be a key parameter that controls surface morphology.¹³ In general, Ga atoms will be orders of magnitude more mobile than N atoms due to the significantly larger diffusion barrier for N atoms compared to Ga atoms.¹³ N atoms reach equilibrium positions more quickly than Ga.¹⁴ It is demonstrated that N atoms on these surfaces are thermodynamically unstable, but they can be kinetically stabilized at the surface. Supposedly, there are two processes that are involved in the growth of GaN by HVPE. The first is the process by which the Ga atoms are delivered to the surface by gas-phase flow and diffusion. The second is the reaction on the surface that results in the addition of GaN to the crystal.

At the initial stage of growth, the GaN coalesces into an island, a process that is called nucleation. The ad-Ga atoms then incorporate into the existing islands, which are thermodynamically stable. Obviously, the average diffusion length of the ad-Ga atoms is decisive for influencing island coalescence, as shown schematically in Fig. 3. If the average diffusion length of the ad-Ga atoms is short compared to the island width, the ad-Ga atoms only diffuse on the surface of the island, which allows the island to dominate. The whole growth process is termed as the 3D (three-dimensional) growth mode and leads to high defect density and a rough yellow surface. Conversely, if the average diffusion length is longer than the island width, the adatoms diffuse until they incorporate into the island edges, and make the island grow in the horizontal direction to form a smooth surface. There is a high probability that defects are eliminated before the region is deeply buried by new adatom arrivals. This is the 2D growth mode. In this mode, GaN growth is controlled by adatom mobility.

Fig. 3 Schematic diagram of island coalescence. Smooth facets on an atomic scale are formed in 2D (two-dimensional) growth mode and pits are formed between expanding nuclei due to short diffusion length.

In order to study the influence of the V/III ratios on the mobility of atoms, GaN layers were deposited on MGA using different V/III ratios. The HCl flow was held at 20, 50, and 100 mL min⁻¹, respectively, while the NH₃ flow was typically 1000 mL min⁻¹ with the other gas flow rates held constant. AFM was used to investigate the surface morphology of the GaN films. The crystal quality of the GaN films was characterized by high-resolution X-ray diffraction (HRXRD) using symmetrical (002) and asymmetrical (102) reflections. In this study, the mode of GaN growth was fixed. Dislocations in the substrates with a vertical orientation thread to the subsequent HVPE epilayer appeared only intermittently. Consequently, the FWHM is similar to the substrates of MOCVD-GaN. The root-mean-square (RMS) roughness, and the full width at half maximum (FWHM) values of the (002) peak and (102) peak all decrease monotonically with the increase of the V/III ratio, as shown in Fig. 4. The results indicate that the films with a smooth surface and reduced density of TDs were grown using a large V/III ratio. Based on our analysis of the interrelation between atomic mobility, surface morphology and film quality, a large V/III ratio results in high mobility and growth in a horizontal direction to form a smooth surface. On the other hand, a low V/III ratio leads to an increase of TD density as a result of incomplete coalescence due to the short diffusion length with a 3D growth mode.

Fig. 4 Properties of GaN films deposited on MGA with different V/III ratios. FWHM values of HRXRD rocking curves (a) in (102) reflection; (b) in (002) reflection; (c) surface roughness (root mean square, RMS).

Fig. 5 shows Raman spectra of GaN films grown via different V/III ratios. The E₂ (high) phonon is used to characterize the in-plane strain state of the GaN epilayer. The stress may be calculated by the following equation,¹⁵

where σ is the biaxial stress and Δω is the E₂ phonon peak shift. The E₂ (high) phonon of stress-free GaN is believed to be 567.1 ± 0.1 cm⁻¹. Hence, the film stress values for different V/III ratios can be obtained.¹⁶ The E₂ (high) phonon values for different V/III ratios as indicated are shown in Fig. 5. According to the equation, it is clear that the stress for different V/III ratios increases monotonically with an increase in the V/III ratio. It is commonly accepted that residual stress in the films results from the large difference in the thermal expansion coefficients between GaN and substrate. Lower V/III ratios lead to a coarser surface (due to the short diffusion length with a 3D growth mode), which is beneficial for the release of thermal stress while cooling. This is consistent with the morphologies and quality characterization depicted in Fig. 4.

Fig. 5 Raman spectra of GaN films grown via different V/III ratios.

These results provide some evidence regarding the influence of different V/III ratios on atomic mobility. We also used positron annihilation technology (PAT) to obtain information on native vacancies in GaN. Positrons become trapped at neutral and negative vacancies due to the missing positive charge of the ion cores. In this study, the GaN layers were investigated with slow positron beam Doppler broadening experiments at room temperature, and described using the conventional low and high electron-momentum parameters S and W. When positrons annihilate at vacancies, the S parameter increases and the W parameter decreases because a larger fraction of annihilations occur with the valence electrons that have lower momentum. Consequently, the lower the S parameter, the lower the concentration of vacancies.¹⁷

Fig. 6 shows the electron-momentum parameters S and W in the GaN films. The data for all GaN layers form a straight line in the (S, W) plane, indicating that the same defect (Ga vacancy) is found in all samples.¹⁸

Fig. 6 The electron-momentum parameters S and W in GaN films of different V/III ratios.

The S parameter is a clear sign of Ga vacancy present in the GaN samples mentioned above. Fig. 7 shows the S parameter as a function of the positron incident energy. The S parameters increase with the reduction of V/III ratios. These results show that the increase of Ga vacancy in the GaN samples is related to the reduction of V/III ratios. There is a balance between the diffusion process and the interfacial energy related to the mobility of atoms, which might be affected by the V/III ratio in the films. As V/III ratio decreases, the Ga atoms are less mobile, and the growth layer is not able to fully achieve free energy while the Ga atoms are in equilibrium; therefore, the Ga vacancy increases. Ga atoms with low mobility cannot reach the site lattice, and this results in the creation of Ga vacancies. We conclude that a small V/III ratio results in correlation between low atom mobility and the creation of Ga vacancies; this conforms to the data presented in Fig. 4.

Fig. 7 S parameter measured as a function of the positron incident energy for GaN films of different V/III ratios.

Fig. 8 shows cross-sectional TEM images of GaN films grown with V/III ratios of 50 and 10, respectively. A number of stacking faults were found in Fig. 8(a). The presence of stacking faults may prevent the propagation of threading dislocations. In contrast with Fig. 8(a), we observed more threading dislocations penetrating to the surface in Fig. 8(b). This is consistent with our obtained FWHM values of HRXRD rocking curves.

Fig. 8 Cross-sectional TEM images for the GaN films grown (a) with a V/III ratio of 50 and (b) with a V/III ratio of 10.

All the results above provide evidence of the influence of the V/III ratio on atomic mobility. Decreasing mobility is caused by a decreasing V/III ratio. By contrast, an increasing V/III ratio results in an increasing mobility.

Choosing the appropriate mobility is important for quality crystal growth. As described above, GaN films grown on templates with different stress were prepared via different V/III ratio growth processes. It is assumed that stress existing in the MGA and MGS could have an impact on atom mobility, and would be offset by the V/III ratio during growth. According to Einstein's relation, the atomic diffusion length is proportional to the average atomic lifetime, τ and the diffusion coefficient, D, which can be expressed in the form of the Arrhenius reaction velocity equation commonly used for the rate of a thermally activated process.^19,20

D = D₀ exp(−Q/k_BT) (3)

where Q is the surface diffusion activation energy connected to the diffusion barrier, k_B is the Boltzmann constant, T is the growth temperature, and D₀ is the frequency factor.

It is difficult to observe atomic migration in crystalline samples. Therefore, it becomes important to connect the diffusion process to atomic mechanisms. Vacancy-assisted diffusion is known as an atomistic mechanism. The consequence of the theory is the relation for the activation energy barrier of diffusion (Q), which is the sum of the formation energy barrier (E_f) and the migration energy barrier (E_m).²¹

Q = E_f + E_m (4)

The highest free energy state along the minimum energy diffusion path is called the saddle point. E_m is the difference in free energy between the saddle point and when the atom is at equilibrium. The change in the atomic free energy under stress is closely related to the strain.²² In general, E_m is hardly changed by the slight lattice distortion caused by hydrostatic stress.²³ Consequently, the vacancy migration energy barrier remains almost constant in MGS and MGA.

The formation energy barrier E_f, which is the excess free energy of a crystal with a vacancy compared to a perfect crystal, is sensitive to the vacancy concentration. The vacancy concentration can be attributed to the change in formation enthalpy, which is stress-dependent. Jang et al. have discussed the hydrostatic pressure dependence associated with the formation enthalpy.²³ It is demonstrated that E_f increases with increasing pressure.

According to eqn (4), stress that exists in the MGA and MGS has an impact on atomic mobility. This is a result of the distinction between the activation energy barrier present compared with the stress-free state. The Q value of compressive stress is greater than that of the stress-free state; conversely, the Q value of tensile stress is less than that of the stress-free state. It may be concluded that atomic mobility is retarded by compressive stress and promoted by tensile stress.

In summary, it is clear that stress controlled by the V/III ratio affects atomic diffusion. The compressive stress in GaN grown on an MGA sample has a higher activation energy barrier. Initially a large V/III ratio is required to promote the mobility of the adatoms for a 2D growth mode. As the growth proceeds, the compressive stress gradually decreases as the activation energy barrier is reduced. At this point, a decreasing V/III ratio is necessary for growth with the appropriate atomic mobility. In the case of the MGS template, in order to control the decreasing tensile stress with increasing activation energy barrier, an increasing V/III ratio is introduced in order to stabilize the atomic mobility.

Conclusions

Here, we have discussed how GaN films grown on MGA and MGS templates were prepared using different V/III ratios in the growth process. Subsequently, the interrelation between stress, V/III ratio and atomic mobility was investigated. Atomic mobility is an issue of crucial importance for optimal crystal growth. It is found that a large V/III ratio improves atom mobility. Diffusion is retarded by compressive stress that appears in the MGA template, and promoted by tensile stress in the MGS template. Therefore, it is true to say that the tensile stress existing in the MGS template is controlled by increasing V/III ratio, while the compressive stress that appears in the MGA temples is controlled by decreasing V/III ratio. This method of stress control is performed accurately not only with the two different templates examined in this study, but also in the case of templates with different types of stress cited in our previous work.^24,25

Acknowledgements

This work was supported by National Basic Research Program of China (2011CB301904), NSFC (Contract no. 51321091) and IIFSDU.

References

1. S. Nakamura, T. Mukai and M. Senoh, Appl. Phys. Lett., 1994, 64, 1687.
2. S. Nakamura, M. Senoh, S.-i. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku and Y. Sugimoto, Jpn. J. Appl. Phys., Part 2, 1996, 35, L74–L76.
3. H. Ashraf, R. Kudrawiec, J. L. Weyher, J. Serafinczuk, J. Misiewicz and P. R. Hageman, J. Cryst. Growth, 2010, 312, 2398–2403.
4. J. Napierala, D. Martin, N. Grandjean and M. Ilegems, J. Cryst. Growth, 2006, 289, 445–449.
5. O. Chelda-Gourmala, A. Trassoudaine, Y. Andre, S. Bouchoule, E. Gil, J. Tourret, D. Castelluci and R. Cadoret, J. Cryst. Growth, 2010, 312, 1899–1907.
6. S. Kim, J. Oh, J. Kang, D. Kim, J. Won, J. W. Kim and H. K. Cho, J. Cryst. Growth, 2004, 262, 7–13.
7. Y. Shao, L. Zhang, X. Hao, Y. Wu, X. Chen, S. Qu, X. Xu and M. Jiang, J. Alloys Compd., 2011, 509, 6212–6216.
8. H. Heinke, V. Kirchner, S. Einfeldt and D. Hommel, Appl. Phys. Lett., 2000, 77, 2145–2147.
9. V. Srikant, J. Speck and D. Clarke, J. Appl. Phys., 1997, 82, 4286–4295.
10. B. Heying, X. Wu, S. Keller, Y. Li, D. Kapolnek, B. Keller, S. P. DenBaars and J. Speck, Appl. Phys. Lett., 1996, 68, 643–645.
11. D. Oh, S. Lee, H. Goto, S. Park, I. Im, T. Hanada, M. Cho and T. Yao, Appl. Phys. Lett., 2007, 91, 132112.
12. C. Kisielowski, J. Krüger, S. Ruvimov, T. Suski, J. Ager III, E. Jones, Z. Liliental-Weber, M. Rubin, E. Weber and M. Bremser, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 17745.
13. T. Zywietz, J. Neugebauer and M. Scheffler, Appl. Phys. Lett., 1998, 73, 487–489.
14. Z. Chen, Z. Yu, P. Lu and Y. Liu, Phys. B, 2009, 404, 4211–4215.
15. S. Tripathy, S. J. Chua, P. Chen and Z. L. Miao, J. Appl. Phys., 2002, 92, 3503–3510.
16. L. Zhang, Y. Shao, X. Hao, Y. Wu, S. Qu, X. Chen and X. Xu, J. Cryst. Growth, 2011, 334, 62–66.
17. K. Saarinen, T. Laine, S. Kuisma, J. Nissilä, P. Hautojärvi, L. Dobrzynski, J. M. Baranowski, K. Pakula, R. Stepniewski, M. Wojdak, A. Wysmolek, T. Suski, M. Leszczynski, I. Grzegory and S. Porowski, Phys. Rev. Lett., 1997, 79, 3030–3033.
18. G. Koblmuller, F. Reurings, F. Tuomisto and J. Speck, Appl. Phys. Lett., 2010, 97, 191915.
19. S. Ploch, T. Wernicke, D. V. Dinh, M. Pristovsek and M. Kneissl, J. Appl. Phys., 2012, 111, 033526.
20. L. Lymperakis and J. Neugebauer, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 79, 241308.
21. M. Bouville, arXiv preprint cond-mat/0509532, 2005.
22. A. Nazarov and A. Mikheev, J. Phys.: Condens. Matter, 2008, 20, 485203.
23. J.-W. Jang, J. Kwon and B.-J. Lee, Scr. Mater., 2010, 63, 39–42.
24. H. Zhang, Y. Shao, L. Zhang, X. Hao, Y. Wu, X. Liu, Y. Dai and Y. Tian, CrystEngComm, 2012, 14, 4777–4780.
25. L. Zhang, Y. Shao, X. Hao, Y. Wu, H. Zhang, S. Qu, X. Chen and X. Xu, CrystEngComm, 2011, 13, 5001–5004.

---