Effect of c-plane sapphire substrate miscut angle on indium content of MOVPE-grown N-polar InGaN

The GaN film grown on c-plane sapphire has an epitaxial relationship of [$1\bar{1}00$]GaN//[$11\bar{2}0$]Al₂O₃. In this study, sapphire substrate surfaces have a misorientation around the [$11\bar{2}0$] axis and consequently around the GaN[$1\bar{1}00$] axis. Figures 1(a)–1(c) show typical XRD-RSMs around asymmetric ($1\bar{1}0\bar{5}$) diffractions for the A, B, and C samples, respectively. The vertical axis is along GaN[$000\bar{1}$] and the horizontal axis is along GaN[$1\bar{1}00$]. Note that the direction of the analyser streaks (an upward-sloping line) around the GaN diffraction peak in Fig. 1(c), which is perpendicular to the wave vector of the scattered X-ray, is different from those in Figs. 1(a) and 1(b) because X-rays are incident from the right-hand side of Fig. 1(c) and from the left-hand side of Figs. 1(a) and 1(b). As shown in Figs. 1(b) and 1(c), the InGaN peaks of the B and C samples located at a position with the same in-plane lattice constant as that of the underlying GaN, indicating coherent growth on the GaN template. On the other hand, from the RSM of the A samples, the peak seems to have broadened toward the horizontal direction, as shown in Fig. 1(a), indicating that the InGaN layer has partially relaxed. The relationship between the In content of the InGaN estimated from the RSM and the nominal substrate miscut angle is summarized in Fig. 2. It is found that the In contents of the B and C samples monotonically increase with the substrate miscut angle, while the In content of the A samples is almost independent of nominal substrate miscut angle.

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Figure 3 show plan-view SEM images of InGaN films of A, B, and C samples on the sapphire substrate with a miscut angle of 0.9°. Since the A samples were at a higher NH₃ flow rate and a lower temperature, as shown in Table II, it is expected that both factors will suppress the desorption of In adatoms. These growth conditions may have induced rough surfaces with a characteristic island growth mode observed in the A samples, as shown in Fig. 3(a), and also the In content increases owing to the inefficient In desorption and the simultaneous relaxation of the compressive strain.^14,15) It is reasonable to think that the substrate miscut angle had no effect on the In incorporation, once the growth mode became an island growth at the early stage of InGaN growth, since well-defined step-and-terrace structures were buried within islands, obscuring the substrate miscut angle effects. Therefore, later in this paper, detailed discussion of the A samples will not be made. The In contents of the B and C samples were kept low enough to realize coherent growth and thus the apparent dependences of In content on the miscut angle of the substrate were successfully observed, since a lower NH₃ flow rate and a higher growth temperature were adopted, which are advantageous for suppressing the island growth mode.

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It is found here that the effect of the substrate miscut angle for the coherently grown B and C samples is completely different from that for the group-III-polar grown InGaN, in which the In content monotonically decreased with increasing miscut angle.^4–6) Prior to the discussion of this In incorporation issue, firstly the microscopic step structures on the GaN template are discussed here. As mentioned before, sapphire substrate surfaces have a misorientation around the [$11\bar{2}0$] axis. Accordingly, the GaN layers have a misorientation around the [$1\bar{1}00$] axis and the surfaces should incline toward the [$11\bar{2}0$] axis. However, a closer look at the GaN template II surface morphologies in Fig. 4 shows local atomic steps that run perpendicular to the [$10\bar{1}0$] and [$01\bar{1}0$] directions on average, i.e., two sixfold $\langle 1\bar{1}00\rangle$ directions, instead of the [$11\bar{2}0$] direction. Actually, these orientations are consistent with the frequently observed step directions around hexagonal hillocks shown in Fig. 3(c) and those described in Ref. 16. Therefore, it is expected that each step will form a zigzag shape on a larger scale, where steps perpendicular to the [$10\bar{1}0$] and [$01\bar{1}0$] directions appear alternately, as observed on left-hand side of Fig. 4(c), with the resulting macroscopic surface inclination being toward the [$11\bar{2}0$] axis, which is consistent with the ideal step orientation introduced by the miscut of the substrates. If the step height is assumed to be identical to the lattice constant c of the wurtzite structure,¹⁶⁾ the mean distance along the [$11\bar{2}0$] direction between neighboring steps is estimated to be 74, 37, 33, and 27 nm when the miscut angles are 0.4, 0.8, 0.9, and 1.1°, respectively. These distances are in fairly good agreement with the observed distances in Fig. 4. This shows that the miscut angle of the substrate definitely has considerable effects on the atomic steps of the GaN template surface, on which evenly spaced atomic steps are observed, as shown in Fig. 4. Also, the above discussion holds true for both templates I and II even in the presence of step bunching, since it is also expected that the observed macrostep also will consist of a bunch of the above zigzag atomic steps distributed with quite a small interval.

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The B and C InGaN layers grown on the GaN templates are presumably affected by the substrate miscut angle, at least in the initial stage of their growth before hillocks and/or irregularities are formed. Therefore, to explain the difference in the miscut angle dependence of In incorporation between the N- and group-III-polar InGaN layers, here we show a cross-sectional schematic illustration of the step-and-terrace structures for each polarity in Fig. 5. In Fig. 5, group-III atoms without bonds indicate possible incorporation sites. It is reported that the step height of a N-polar surface is c, while that of a group-III-polar surface is c/2.¹⁶⁾ The atomic structures are drawn using VESTA.¹⁷⁾

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Under our growth conditions, the growth rate is limited by the total concentration of group-III precursors.¹⁸⁾ In other words, there are sufficient N-precursors in ambient that are not adsorbed or incorporated into a crystal. Therefore, the NH_n (n = 1, 2, 3) radical, after the attachment of group-III atoms immediately covers, the growth surface, and it is probable that a model with a nitrogen-stabilized-growth surface can be adopted in the case we will discuss below.¹⁹⁾ In the case of InGaN growth, the bond strength between In and N is weaker than that between Ga and N, as expected from a higher nitrogen-equilibrium vapour pressure of InN than of GaN.²⁰⁾ Therefore, what determines the In incorporation efficiency in InGaN growth is the rate of replacement of In atoms by Ga atoms on the growth surface. To prevent the In atom replacement, a site with the higher number of bonds from the surrounding N atoms has distinct advantage because a higher number of bonds can hold In atoms tightly and prevent their detachment.

In the case of the N-polar surface, it is predicted by theoretical calculations that 3/4 of the surface N atoms are terminated by H and 1/4 of the surface N atoms have a lone pair of electrons on the terrace under MOVPE atmosphere,²¹⁾ while the group-III atoms at the step edge adsorb NH_n, where n is varied to satisfy the electron counting rule. Then the next incoming group-III adatoms can be caught between this adsorbate and the surface N below it instead of H atoms, as shown in Fig. 5(a). Therefore, group-III atoms are incorporated mainly at step edges, not on the terrace of the N-polar surface. This is consistent with the fact that the MOVPE growth rate on N-polar surfaces is much lower than that on group-III polar surfaces, unless hillocks are formed.¹⁶⁾ When the growth rate increases with the step density, the In incorporation efficiency also increases because In can be covered by N atoms rapidly before they are replaced by Ga atoms.

On the other hand, in the case of group-III-polar growth, it is predicted by the theoretical calculations that 3/4 of the surface Ga atoms will be terminated by NH₂ and 1/4 of the Ga atoms will be terminated by NH₃ on the terrace under MOVPE atmosphere,²²⁾ while the step edge is being terminated by NH_n. Therefore, each of the group-III atoms can be caught by three N adatoms on the terrace and the nucleation of two-dimensional islands is possible, as shown in Fig. 5(b). It is therefore considered that the effects of the step density and substrate miscut on group-III incorporation are smaller on group-III polar surfaces than on their N-polar counterparts.

Finally, to confirm the validity of the above models, it is necessary to know the initial surface morphology of the underlayers just before the InGaN growth. In this study, we have observed both the macroscopic and microscopic surface morphologies of GaN templates by OM and AFM. Figure 6 shows OM images of GaN templates I and II. Note here that GaN templates without hexagonal hillocks were obtained owing to the introduction of the vicinal substrate.⁹⁾ However, giant or macroscopic steps due to surface step bunching become pronounced in the higher-miscut-angle region, as shown in Figs. 6(b) and 6(c), and 6(f) and 6(g), respectively. Therefore, we considered these macroscopic steps as the origin of the enhanced In incorporation, and estimated the average distance between neighboring macroscopic step edges by AFM. Figure 7 shows the In content of InGaN plotted as a function of the average interval of macrostep edges. It was found that the In content increased with increasing macroscopic step density, which is the inverse of the macrostep period. Note that the tendency was only observed in the series of the B and C samples grown coherently on the GaN template. This result is in good agreement with the model shown in Fig. 5(a).

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