1.
Introduction

High-quality AlN template is essential to fabricate high-efficiency deep-ultraviolet light-emitting diodes (LEDs) and laser diodes (LDs), which can be widely used in sterilization, water purification, medicine, and biochemistry. Sapphire is one of the most suitable substrates for high-quality AlN template, thanks to its mature processing technique and high transparency in UV-light range^[1]. However, the heteroepitaxy of AlN template in sapphire substrate leads to high threading dislocation density (TDD), typically in the order of 10⁹–10¹⁰ cm^–2, and deteriorates internal quantum efficiency (IQE) of the devices. Epitaxial lateral overgrowth (ELOG) on patterned sapphire substrate (PSS) or AlN/sapphire template has been proven to be an effective technique to obtain low TDD and crack-free AlN template since part of the threading dislocations would bend and get annihilated^{[2, 3]}. Many groups used those techniques to obtain high-performance device which was benefited from high internal quantum efficiency due to the improvement of crystal quality^[4–6].



Various patterns are selected to serve for the ELOG, such as stripe^{[3, 4, 7–17]}, concave cone^{[5, 18–20]} or convex cone^[21]. As for the stripe pattern, realizing coalescence of AlN has been a crucial issue. Many groups discussed the influence of stripe direction^{[3, 8, 9, 13]}, and found that if the stripe is along ${leftlangle {11bar 20}
ight
angle} _{{{
m{AlN}}}}$, the coalescence is very difficult. The other growth conditions, such as growth temperature^{[3, 8, 9, 12]}, V/III ratio^{[12, 16]} were also optimized to obtain flat AlN. Some groups combined the ELOG with migration enhanced technique^{[7, 11]}, which is useful to accelerate the coalescence. For the convex cone pattern, which is widely used for commercial blue LED, none report has been heard that AlN can coalesce like GaN by MOCVD. However, Hagedorn et al.^[21] realized coalescence of AlN grown on the top of the truncated cone, which is more like the coalescence of AlN rods^{[6, 22]}.



ELOG on concave patterned sapphire substrate can bring significant improvements for the crystal quality and device performance, which has reported by Dong et al.^{[5, 18]}. Wang et al.^[20] and Zhang et al.^[19] further explored the V/III radio and pattern’s size to reduce the TDD. However, the morphology evolution and coalescence mechanism of AlN grown on the concave patterned sapphire substrate has been rarely reported. In fact, coalescence mechanism of the AlN differs greatly from the GaN. The $left{ {11bar 22}
ight}$ facet which typically exists in the process of ELOG of GaN is almost invisible in the ELOG of AlN, unless modulating the growth temperature, which would be shown later. And purely modulating the V/III ratio could not obtain the stabilized growth of $left{ {11bar 22}
ight}$ facet.



It should be noted that evolution of the facets might affect the evolution of the dislocation. For instance, with reference to the ELOG of GaN, the inclined facets arising in the process of coalescence play an important role in reducing the dislocation, as the threading dislocations which terminate at the inclined facets will bend in the basal plane during the lateral growth. Consequently, two steps ELOG of GaN including both 3D process which makes the surface contain as large inclined facets as possible and 2D recovery process was mentioned to improve crystal quality, which is called facet-controlled epitaxial lateral overgrowth (FACELO)^[23–26]. To our knowledge, such concept has been rarely studied in the ELOG of AlN. However, as for ELOG of AlN, high-density threading dislocations might still exist above the mesa region^{[9, 10]}.



In this paper, morphology evolution of AlN growth on NPSS under different growth conditions was detailly discussed and the growth habit of the $left{ {11bar 22}
ight}$ facet of AlN was reported. For the common growth conditions (high temperature and appropriate V/III ratio), the AlN has 2D growth mode. The $left{ {11bar 21}
ight}$ facets arise and then vanish in the process, thus leading to coalescence. And when decreasing the temperature, the $left{ {11bar 22}
ight}$ facets arise, leading to 3D growth mode. Keeping growth at the lower temperature, the (0001) c-plane facet vanishes and growth front entirely consists of $left{ {11bar 22}
ight}$ facets, appearing to inverse pyramid AlN structure.

2.
Experiment

In this research, the NPSS was fabricated by nano-imprint lithography. As shown in Fig. 1, the opening diameter of circular hole is about 350 nm, and the period of the pattern is about 500 nm. A home-made low-pressure metal–organic chemical vapor deposition (LP–MOCVD) system with a vertical shower-head reactor was used to process epitaxial growth. Trimethylaluminum (TMAl) and ammonia (NH₃) were used as precursors for Al and N, respectively. High-purity hydrogen (H₂ )was used as the carrier gas. The reaction pressure was set as 50 Torr. Two samples with different structures were fabricated, as shown in Fig. 2, which manifested as different growth modes. The sample I contained the HT-AlN layers purely, which were grown at 1200 °C as normal growth temperature. The growth time for the HT-AlN in sample I was two hours, leading to near coalescence of the AlN epilayer. And the growth process of sample I was divided into three stages, which were labeled as S1 (0~40 min), S2 (40–60 min) and S3 (60–120 min), to investigate the evolution of the surface morphology. For sample II, an MT-AlN layer was grown based on the HT-AlN layer at 1130 °C. The growth time for the both HT-AlN layer and MT-AlN layer in sample II was 40 min. In addition, the V/III ratios of the HT-AlN and MT-AlN were 578 and 1156, respectively. Both samples were grown based on low-temperature buffer layer at 790 °C. The growth rate of HT-AlN and MT-AlN under the abovementioned growth condition was about 1.2 μm/h. After growth, scanning electron microscopy (SEM) and atomic force microscope (AFM) were used to study the surface morphology of the AlN.






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Figure1.
Plan-view SEM image of the NPSS.






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Figure2.
(Color online) Schematic diagrams of two samples with different structures.

3.
Results and discussion

Fig. 3 presents the morphology of three distinguishing stages of Sample I. The corresponding growth time was 40, 60, and 120 min, respectively. At the initial stage, locally continuous AlN film with circular holes was gradually formed above un-etched mesa zones of the substrate after hundreds-nanometer growth. Then the outer contour of the holes turned into a hexagon shape when thickness of the AlN is around 800 nm, as shown in Fig. 3(a). Six inclined $left{ {11bar 2x}
ight}$ facets were exposed, due to the lateral growth of the AlN. The angle θ between the $left{ {11bar 2x}
ight}$ facets and the (0001) facet (c-plane) is determined by following equation






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Figure3.
(a–c) Plan-view SEM images of surface morphology of sample I at end of the three growth stages. (d–f) The corresponding cross-sectional SEM images for (a), (b) and (c). The black dashed line in (a) indicates direction of the cross-sectional view as (d), (e) and (f). All images use the same scale bar as (a).

$theta = { m{ta}}{{ m{n}}^{ - 1}}left( {frac{{2 c}}{{x a}}} ight).$

As shown in Fig. 3(d), the value of θ is around 72°, thus the value of x is deduced to be ~1. According to the Wulff growth theory^[27], the facets dominating the growth morphology have the max growth rate, for the inward growing (concave) situation.



As shown in Figs. 3(b) and 3(e), the sidewall of the holes became vertical and the outer contour of the holes evolved to trapezium or triangle after totally 60 min growth. It illustrates that the six inclined facets are unstable. In addition, some misoriented AlN grew in the holes of sapphire substrate, as marked in the red dotted line circle in Figs. 3(a) and 3(d). Nevertheless, the misoriented AlN appearing in Fig. 3(a) is invisible in Fig. 3(b), deducing that continued growth of the misoriented AlN had been hindered when the inclined facets turned into vertical. As shown in Figs. 3(c) and 3(f), invert V-shaped air gap had been formed when the entire AlN film was nearly coalescent. The reason for the formation of the invert V-shaped air gap might be that the reactant which flowed into the holes was not sufficient for the growth of the lower part of the holes when the opening was small.



This process is quite different from GaN growth on the PSS. As for GaN^[28], the entire process of coalescence keeps the symmetrical hexagonal morphology which consisted of the six $left{ {11bar 22}
ight}$ facets. On the contrary, hexagonal symmetry only existed in the first stage of ELOG-AlN, as mentioned above. One of the possible reasons might be low surface migration of the Al atoms, which means the morphology was influenced mainly by reactant flow rather than surface energy. Also, we believe that the $left{ {11bar 22}
ight}$ facet was crucial for the symmetrical growth, and it will be discussed later.



Fig. 4 shows the evolution of facets for sample II. The typical morphology with six hexagonal inclined facets after HT-AlN growth for 40 min can be seen in Fig. 4(a). Continuing to react at the condition as HT-AlN will obtain the flat film, thus it can be called the 2D growth mode of the AlN. Conversely, the MT-AlN grown based on HT-AlN reveals no tendency of coalescence, as shown in Fig. 4(b). Growth front of the MT-AlN film is dominated by inclined facets, as the (0001) facet shrinks and even disappears. Thus the MT-AlN epilayer has 3D growth mode.






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Figure4.
Plan-view SEM images of surface morphology of Sample II.




Fig. 5(a) shows the tilted-view SEM image of surface morphology after the growth of the MT-AlN, which has been already exhibited in Fig. 4(b). It reveals that the nanoholes with inverse pyramid morphology are well-arrayed. Each hole has nearly closed bottom and six inclined facets. From the cross-sectional SEM image, as shown in the inset of Fig. 5(a), the inclination angle of the facets was measured to be 58°, implying that the facets are $left{ {11bar 22}
ight}$ type. As mentioned above, the inclined facets are $left{ {11bar 21}
ight}$ type for the first stage of the HT-AlN. Thus the $left{ {11bar 22}
ight}$ facets were “induced” by decreasing the growth temperature based on $left{ {11bar 21}
ight}$ facets. The phenomenon is related to the surface atom of the facets^[29]. As shown in Fig. 5(c), the semi-polar $left{ {11bar 22}
ight}$ facet has the possibilities to be N-terminated or Al-terminated. The N-terminated surface will be passivated with N–H bonds in the growth ambiance of hydrogen^[30–32] and hardly accommodate Al adatom, especially for the low growth temperature and N-rich condition (high V/III). Thus the $left{ {11bar 22}
ight}$ facets with N-polarity which have a low growth rate are stabilized in such growth condition. While for $left{ {11bar 21}
ight}$ facet, dangling bonds of Al atoms and N atoms both exist in the surface, which is not stabilized, as shown in Fig. 5(d). Stably and slowly growth of the semi-polar $left{ {11bar 22}
ight}$ facets leads to the inverse pyramid morphology, which can be illustrated in a plain geometrical relationship. Fig. 5(b) is a schematic diagram of the cross section of the hole. v_h represents the vertical growth rate of c-plane, and v_s represents the growth rate of the sloped facet. If the point A arrives at the position A’ after a period of growth, the contour lines of the hole evolve from the solid lines to the broken lines. In this case, the relationship of growth rates v_h and v_s needs to satisfy






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Figure5.
(a) 25° tilted-view SEM image of surface morphology of for as-grown MT-AlN. The inset shows cross-sectional view with the direction indicated by the black dashed line. (b) Schematic diagram of AlN growth keeping the 3D morphology. (c) and (d) Schematic of the AlN atomic structure.

${{{nu }}_{ m s}} = {{{nu }}_{ m h}} { m{cos}}theta .$

Thus if the growth rate of the sloped gets smaller, point A will move left and top facet will shrink. So, the growth velocity of the $left{ {11bar 22}
ight}$ facets should be below 0.63 μm/h at the growth condition as MT-AlN. Such inverse pyramid structure also can be used for three-dimensional semi-polar LED^{[33, 34]}, which is beneficial to reduce the quantum confined stark effect (QCSE) and the efficiency droop, and enhance the LED performance.



In addition, we also tried to realize 2D growth based on MT-AlN. The growth temperature was 1270 °C and the V/III ratio was 578. Flat surface had been obtained after the growth for 2 hours. As shown in Fig. 6(a), the total coalescence thickness was around 2.5 μm. Fig. 6(b) presents a 2 × 2 μm² atomic force microscopy (AFM) image of the surface morphology of the sample II after 2D growth. AlN had a flat surface with a step-flow growth mode and a root-mean-square (RMS) roughness of 0.17 nm.






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Figure6.
(Color online) (a) Cross-sectional SEM image and (b) AFM image (2 × 2 μm²) of the Sample II after 2D growth.




Another characteristic of the 2D growth based on MT-AlN is that two rows of air gaps in the coalescence region, as shown in Fig. 6(a). The phenomenon is different with typical ELOG of AlN as sample I, which was caused by the behavior of the $left{ {11bar 21}
ight}$ facets and the $left{ {11bar 22}
ight}$ facets when grew the MT-AlN. Fig. 7 displays the morphology evolution of the two samples and illustrates the process of forming the air gaps in sample II. As mentioned above, the HT-AlN at the first stage has the inclined facets in $left{ {11bar 21}
ight}$ type, whereas the as-grown MT-AlN which based on HT-AlN consists of $left{ {11bar 22}
ight}$ facets. It’s necessary to figure out the process how the $left{ {11bar 21}
ight}$ facets “transform” to $left{ {11bar 22}
ight}$ facets. As shown in Fig. 7, the $left{ {11bar 22}
ight}$ facets induced by low temperature in sample II derived from the upper part of $left{ {11bar 21}
ight}$ facets. The $left{ {11bar 22}
ight}$ facets become larger after subsequent growth due to the slow growth rate of themselves. In the meantime the other part of the $left{ {11bar 21}
ight}$ facets had the same behavior as the sample I, hence a row of air gaps was formed closed to the substrate. After HT-AlN growth, the 3D structure transformed to 2D smooth surface, another row of air gaps would be formed above the first.






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Figure7.
(Color online) Schematic diagram of the facet evolution of both samples.

4.
Conclusion

We analyzed the morphology evolution of AlN grown on NPSS. We found the process that the $left{ {11bar 21}
ight}$ type facets emerge and vanish at the relatively high temperature, which illustrates instability of such type facets. And we decreased the growth temperature, inducing the growth of $left{ {11bar 22}
ight}$ facets and making the growth mode transforms from the initial 2D growth mode to 3D growth mode. In this growth mode, the growth front would get rid of the {0001} type facet. Purely inverse pyramid structure was formed. Also, we implemented the high-temperature growth to transform such inverse pyramid structure to the flat surface, demonstrating temperature plays an important role in the coalescence of AlN. However, the morphology evolution related to the misfit dislocation needs to be further explored.

Acknowledgments

This work was supported by the National Key R&D Program of China (No. 2016YFB0400800), the National Natural Sciences Foundation of China (Grant Nos. 61875187, 61527814, 61674147, U1505253), Beijing Nova Program Z181100006218007 and Youth Innovation Promotion Association CAS 2017157.