Gallium nitride (GaN) have been extensively used in optoelectronic devices^{[1, 2]}, such as blue and green light-emitting diodes (LEDs) and laser diodes (LDs)^[3−8]. In previous studies, there have been many discussions around three dimensional (3D) GaN, which facilitate the exposure of nonpolar/semipolar facets^{[9, 10]}. This 3D morphology could solve the problems existing in traditional c-plane polar GaN LEDs, such as efficiency droop under high injection current density^[11], green-yellow gap of external quantum efficiency^{[3, 12]}, and low −3 dB modulation bandwidth^[13].

There are many ways to obtain 3D GaN surface structures. Beside the top-down method by etching polar GaN bulk materials to form periodic structures^{[14, 15]}, the current mainstream scheme is the bottom-up method by selective area growth (SAG)^[16]. The first step is to grow polar GaN thin film on c-plane sapphire substrate, followed by a second step that SiO₂ or SiN_x mask is deposited and 3D regrowth of GaN is encouraged to form specific surface structures. When changing the window size and geometry of mask, various morphologies can be obtained, such as hexagonal pyramid^[17], stripe^[18] and nanorod^[19]. These structures can easily prepare LEDs with multi wavelengths, realizing single chip color-tunable LEDs or phosphor-free white LEDs, which has great potential for display and lighting.

Wang et al. developed a mask-free method to realize "WM" shaped growth of GaN on c-plane patterned sapphire substrate (PSS) directly without a regrowth process^[20]. Periodic inverted pyramid structures of GaN are formed on surface, wherein the bottom of the inverted pyramid is located exactly above the top of cone on PSS. Then, color tunable LEDs based on this GaN surface have been demonstrated^[20]. However, the mechanism of this growth is still not well understood, especially for the competition between c-plane and semipolar plane facets.

In this article, by summarizing the crystal growth competition model and exploring the influence of growth conditions, the areas of {0001} facet, {101¯1} facet and {112¯2} facet are controlled to obtain various morphology of GaN inverted pyramid surface structures. When using a higher growth temperature of 985 °C and a lower Ⅴ/Ⅲ ratio of 25, the {112¯2} facets dominate, while additional expansion of c-plane occurs. On the other hand, {112¯2} facets can be fully eliminated under a lower growth temperature of 930 °C and a higher Ⅴ/Ⅲ ratio of 100. Furthermore, by using PSS with pattern arrangement perpendicular to the substrate primary flat under such conditions can make the GaN surface have almost pure {101¯1} facets.

The samples are grown on 2-inch c-plane PSS by an Aixtron 2000HT metal organic vapor phase epitaxy (MOVPE) system, using trimethylgallium (TMGa), trimethylaluminum (TMAl), trimethylindium (TMIn), and ammonia (NH₃) as the Ga, Al, In, and N precursors, and hydrogen and nitrogen as the carrier gases. Commercial c-plane PSS has been used in this study, wherein the height, weight and period of patterns are around 2.7, 1.7, and 3.0 μm, respectively. The primary flat of the PSS is (112¯0). In the growth process of inverted pyramid surface structure, a traditional two-step method is used but the growth temperature of high-temperature GaN is reduced to below 1000 °C intentionally to promote 3D growth. The growth time of GaN bulk layer has been uniformly set to 30 min. The specific growth details have been reported in our previous studies^[20], and the growth flow chart is also shown in Fig. 1(a). The patterns on the substrate play a role in limiting the growth area of GaN. To investigate the effect of growth conditions on the morphology of GaN inverted pyramids, samples with different conditions of growth temperature and Ⅴ/Ⅲ ratio are prepared, as shown in Table. 1.

All samples in this work are prepared after the GaN bulk layer is grown. After growth, the surface morphology is characterized by ZEISS MERLIN scanning electron microscope (SEM). The cross-sectional SEM image of sample is obtained, as shown in Fig. 1(b). The bottom of each inverted pyramid corresponds spatially to the conical tip of the pattern one by one, verifying the validity of the growth mode.

Samples A−D are used to investigate the effect of growth temperature on the types and areas of semipolar facets in inverted pyramids. As shown in Fig. 2, two types of semipolar facets {101¯1} and {112¯2}, are formed, which can be identified through the crystal plane angle and arrangement direction. As the growth temperature increases from 940 to 985 °C, the dominant semipolar facets change from {101¯1} to {112¯2}. At the same time, the c-plane also expands, and the size of inverted pyramids correspondingly decreases.

In order to understand the area competition among the different crystal planes, the Wulff construction is used to explain the relation between the growth rate and the final retained crystal plane^[21]. As shown in Fig. 3(a), when the angle between two crystal planes is greater than 180°, the crystal plane with a relatively faster growth rate will gradually shrink as the growth progresses. On the other hand, when the angle between crystal planes is less than 180°, the crystal plane with a relative faster growth will gradually expand, as shown in Fig. 3(b). For the GaN inverted pyramids prepared in this work, the angle between semipolar facets and c-planes is greater than 180°, while that between {101¯1} facets and {112¯2} facets is less than 180°, corresponding to the former and latter cases, respectively.

According to the analysis of Hiramatsu et al.^[22], there is a significant difference in the growth rate of {101¯1} facet, {112¯2} facet and c-plane as temperature increases. A surface growth competition model has been established, as shown in Fig. 3(c). Under a lower growth temperature, the growth of {112¯2} facet is slower than that of {101¯1} facet, so the latter dominates. Meanwhile, the growth of the c-plane is faster at low temperatures, and its area is fully suppressed, which is consistent with the morphologies of samples A and B. As the growth temperature increases, growth rates of three crystal facets intersect in the growth competition model. The growth rate of {112¯2} facet begins to exceed that of {101¯1} facet and gradually expands in the inverted pyramids. As the temperature increases, the area of c-plane gradually increases, which is consistent with the morphologies of samples A−D.

In order to ensure that the {112¯2} facet dominates but suppressing the expansion of c-plane under high temperature, the growth rate of c-plane must be increased. By reducing the NH₃ flow rate to 1000 sccm (the Ⅴ/Ⅲ ratio is reduced to 25) while keeping the growth temperature constant at 985 °C, an increase in c-plane growth rate can be achieved, as shown in Fig. 4. When NH₃ flowrate is 4000 sccm, the growth rate of c-plane is relatively low, resulting in the expansion of c-plane in sample D, as shown in Fig. 4(a). As the NH₃ flowrate decreases, the c-plane area shrinks, while the area of {112¯2} facet remains basically unchanged (Fig. 4(c)). When NH₃ flowrate further decreases, the growth rate of {112¯2} facet with more dangling bonds on the surface increases rapidly, leading to an expansion of {112¯2} facet in inverted pyramids. However, as the growth rates of c-plane and {112¯2} facet both increase, the growth competition between c-plane and {112¯2} facet could lead to an additional expansion of c-plane located between the inverted pyramids, which also leads to an irregular shape of inverted pyramids, as shown in Figs. 4(e)−4(g).

On the other hand, the growth method to extend {101¯1} facets is studied. According to Fig. 4(c), reducing the growth temperature is expected to achieve sufficient suppression of c-plane while ensuring that {101¯1} facet in inverted pyramids is dominant. Sample H decreases the growth temperature to 930 °C with other growth conditions unchanged compared to sample D as shown in Fig. 5(b). The uniform inverted pyramids arrange neatly on the surface with pure six {101¯1} facets on their sidewall, as shown in Fig. 5(a). Besides, triangular c-plane regions remain among the inverted pyramids. These results are completely consistent with the growth competition model that a lower growth temperature means a larger difference in growth rate between c-plane and semipolar facets, as well as between {101¯1} facet and {112¯2} facet.

Furthermore, the arrangement of the patterns of PSS will directly affect the morphology of inverted pyramid GaN. Because the GaN bulk layer is rotated by 30° with respect to the sapphire^[23], the inverted pyramids are arranged along the direction of GaN <101¯0>, regardless of whether the arrangement of patterns on the substrate rotates or not. Thus, by changing the pattern arrangement on PSS from parallel to perpendicular to the primary flat of substrate (rotating by 90°), the c-plane region can be fully eliminated and almost pure {101¯1} facets are obtained, as shown in Fig. 5(c).

In summary, the GaN inverted pyramid structure is grown directly on c-plane PSS. The influences of growth temperature and the Ⅴ/Ⅲ ratio on the proportion of c-plane, {112¯2}, and {101¯1} facets have been systematically studied. A growth rate competition model has been established to explain the different surface morphologies based on the Wulff construction. A higher growth temperature of 985 °C and a lower Ⅴ/Ⅲ ratio of 25 can expand the {112¯2} facets, but will cause an irregular shape of inverted pyramids due to the expansion of c-plane. On the other hand, {112¯2} facets can be fully eliminated under a lower growth temperature of 930 °C and a higher Ⅴ/Ⅲ ratio of 100. Furthermore, by using PSS with pattern arrangement perpendicular to the substrate primary flat under such conditions can make the GaN surface has almost pure {101¯1} facets.