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Understanding and controlling heteroepitaxy with the kinetic Wulff plot: A case study with GaN
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View: Figures


Image of FIG. 1.
FIG. 1.

(Color online) (a) A plot of the total number of publication each year for Ga-polar c-plane, nonpolar, and semipolar GaN, reflecting the research activities for each orientation. The arrow indicates the most crucial breakthrough in improving heteroepitaxial GaN material quality by a two-step growth scheme in the late 1980s. (b) A photo of a 2-in. sapphire, 1-in. m-plane SiC, and nonpolar/semipolar GaN substrate with a typical size of 5 mm × 10 mm grown by hydride vapor phase epitaxy (HVPE).

Image of FIG. 2.
FIG. 2.

(Color online) A hypothetical three-dimensional (3D) Wulff plot (solid curved lines) of surface energy for a simple cubic structure predicts an equilibrium crystal shape of a cube (dashed straight lines). The characteristic features on the 3D Wulff plot, such as the cusp z, valley zmx, and apex n, correlate with the real-space crystal features, such as plane A 1 B 1 C 1 D 1, edge A 1 B 1, and corner B 1, respectively.

Image of FIG. 3.
FIG. 3.

(Color online) (a) Schematic diagram showing the principle of morphological evolution for convex (toward the upper right) and concave (toward the lower left) growth fronts. The convex growth front will be dominated by the slow-growing facets while the concave growth front by the fast-growing facets. (b) Schematic of an annular ring opening, which produces both inward concave and outward convex growth fronts. SEM images of GaN SAG mesas grown out of an annular ring opening on (c) c-plane (0001), (d) semipolar (1122), and (e) nonpolar a-plane (1120) GaN surfaces. (f) Schematic hexagonal lattice showing the c-plane (0001), nonpolar a-plane (1120), and semipolar (1122).

Image of FIG. 4.
FIG. 4.

(Color online) (a) Scheme of the cross-section of a polygonal GaN SAG mesa grown on an opening out of an inert mask (shaded region) on a GaN epilayer. v, s, and l denote the mesa dimensions from the mask edges along vertical, sloped, and lateral directions. (b) Schematic drawing of the cross-section of a GaN mesa with a Δ-SAG. Δv, Δs, and Δl denote the differential advances of the facets along the vertical, sloped, and lateral directions due to the Δ-SAG.

Image of FIG. 5.
FIG. 5.

(Color online) Kinetic Wulff plots (v-plots) for a low reactor pressure and low V/III ratio condition [(a), (b), (e)-(g)] and a high reactor pressure and high V/III ratio condition [(c), (d), (h)-(j)]. For the three dimensional (3D) v-plots, the [0001] axis is set as θ = 0°, and the m-axis as (θ, φ) = (90°, 0°). The Ga-polar hemisphere [(a) and (c)] and the N-polar hemisphere [(b) and (d)] 3D v-plots are viewed at an angle of (62°, 0°) and (150°, 0°), respectively. (e) and (h) are the two-dimensional (2D) v-plots for the prism planes mapped onto the basal c-plane; (f) and (i) the 2D v-plots for the orientations within the m-plane; (g) and (j) the 2D v-plots for the orientations within the a-plane. Note that a six-fold symmetry is assumed for all the v-plots and the symmetry reduction due to the mask effect during SAG is ignored in this paper for simplicity.

Image of FIG. 6.
FIG. 6.

(Color online) (a) A magnified portion (marked out by the dotted square) of the kinetic Wulff plot from Fig. 2(a) and a schematic presentation of the procedure in determining the emerging facet (1122) during the coalescence of two {1011} facets of two neighboring GaN SAG mesas grown on patterned a-plane GaN template. SEM images of two neighboring a-plane GaN SAG mesas right before (b) and during the coalescence (c). The two {1011} facets before the coalescence and the (1122) emerging between the two {1011} facets are marked out.

Image of FIG. 7.
FIG. 7.

(Color online) (a) SEM top view of a c-plane GaN surface with the growth stopped at the roughening and coalescing stage, showing {1122} facets due to the concave growth. (b) SEM perspective view of a typical pitted nonpolar a-plane GaN epilayer surface showing faceted surface pits and elongated striations along [0001]. (c) SEM top view of an a-plane GaN SAG mesa, with a void in the center resembling very much the faceted surface pits in (b), grown out of an annular ring opening [Fig. 1(b)]. SEM (d) top view and perspective views 60° inclined from the vertical a-axis to (e) [0001] and (f) [0001] of the intersection of a-plane GaN SAG c-axis stripes with an m-axis stripe. The faceted two sides of the intersected m-axis stripe in (d) are very similar to the two halves on the two sides of the blue dashed line in (c).

Image of FIG. 8.
FIG. 8.

(Color online) Schematic LED structures built on (a) c-plane GaN/c-plane sapphire, (b) nonpolar a-plane GaN/r-plane sapphire, (c) semipolar (1122) GaN/m-plane sapphire, and (d) semipolar (1122) GaN/patterned r-plane sapphire. Perfect threading dislocations are represented by white curvy lines. BSFs and their associated PDs are indicated by yellow and black straight lines. A simplified energy diagram is shown to the right side of InGaN MQWs (in green) for each structure.

Image of FIG. 9.
FIG. 9.

(Color online) Plan-view TEM images of the one-step grown [(a) and (b)] and the two-step grown [(c) and (d)] nonpolar a-plane GaN samples. The g vectors were 1100 for (a) and (c) and 0002 for (b) and (d) to reveal the SFs and the PDs, respectively. The Frank-Shockley PDs ( b  = 1/6<2023>) are indicated by the red arrows. The PSFs observed on the surface of the two-step grown a-plane GaN sample are circled in (c). Cross-sectional TEM images of the one-step grown [(e) and (f)] and the two-step grown samples [(g) and (h)]. (e) and (g) were taken near the [0001] axis with g = 1100. (f) and (h) were taken near the [1100] axis with g = 1120.

Image of FIG. 10.
FIG. 10.

(Color online) Schematic model of the BSF blocking and the PD bending during the two-step growth of nonpolar a-plane GaN, cross-section viewed along the c-axis [0001] (a) and the m-axis [1100] (b). The blue dashed lines represent the a-plane GaN growth fronts, and the red solid lines are the PDs. BSFs are shown as the shaded area in (a) and the straight black lines in (b). The vertical black lines overlap with the red lines in (b), indicating that most of the BSFs are bounded by PDs. SEM (c) and monochromatic (363 nm) CL image (d) of the same surface area of a-plane GaN islands with the growth intentionally stopped at the end of the first-step roughening stage. The {1012} overhanging lateral overgrowth fronts towards the [0001] circled in (c) show a good position correlation with most of the emitting regions (with a low defect density) in (d).

Image of FIG. 11.
FIG. 11.

OCE growth evolution of semipolar (1122) GaN on patterned r-plane sapphire. (a) Selective nucleation of GaN on the sapphire c-plane sidewalls. (b) GaN stripes shaping for effective blocking of the BSFs and PDs in the neighboring stripes. (c) Full coalescence of GaN stripes into a flat semipolar (1122) GaN film.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Understanding and controlling heteroepitaxy with the kinetic Wulff plot: A case study with GaN