Kinetic Wulff Plots Research Articles

Analogy between growth of crystals and ferroelectric domains. Application of Wulff construction

In this article we applied a concept of kinetic Wulff plot (v-plot), which was proposed originally for understanding and control of the crystal growth, for characterization of the domain wall motion anisotropy in uniaxial ferroelectrics. Only the minima of v-plot can be obtained by the observation of the convex growth of isolated domains, whereas we can get insight of the v-plot maxima considering the concave growth during shape transformation after domain coalescence. Within this approach we reconstructed experimentally the compete v-plot for lithium niobate and potassium titanyl phosphate crystals. The giant effect of the domain wall velocity dependence on its orientation has been revealed. The effect results in fast restoration of the convex faceted domain shape with the slowest walls after merging. The proposed approach can be used for understanding and control of domain growth during electric field poling by patterned electrodes.

Elimination of Stacking Faults in Semipolar GaN and Light-Emitting Diodes Grown on Sapphire.

We report a novel approach to eliminate stacking faults (SFs) and prepare large-area, SF-free semipolar gallium nitride (GaN) on sapphire substrates. A root cause of the formation of basal-plane SFs is the emergence of N-polar (0001̅) facets during semipolar and nonpolar heteroepitaxies. Invoking the concept of kinetic Wulff plot, we succeeded in suppressing the occurrence of N-polar GaN (0001̅) facets and, consequently, in eliminating the stacking faults generated in (0001̅) basal planes. Furthermore, InGaN light-emitting diodes with promising characteristics have been produced on the SF-free semipolar (202̅1) GaN on sapphire substrates. Our work opens up a new insight into the heteroepitaxial growth of nonpolar/semipolar GaN and provides an approach of producing SF-free nonpolar/semipolar GaN material over large-area wafers, which will create new opportunities in GaN optoelectronic and microelectronic research.

Superfast domain wall motion in lithium niobate single crystals. Analogy with crystal growth

In this paper, we studied the superfast domain walls that appear after domain merging during polarization reversal in congruent lithium niobate single crystals by in situ optical visualization with a high temporal resolution. The superfast domain walls were observed during the fast transformation of the domain shape from concave polygonal that appears after merging to the convex polygonal one with slow domain walls only. Orientations and velocities of superfast domain walls were measured during transformation of an artificial polygonal X-shaped domain (with all concave angles appearing after merging) to a hexagonal one. The “convex” growth of isolated hexagonal domains was governed by the slowest domain walls, while the “concave” growth after domain merging—by the superfast walls with three orders of magnitude higher velocity. We reconstructed experimentally the v-plot (kinetic Wulff plot) for domain wall motion by analysis of both convex and concave domain growth. The slowest walls (Y-walls) correspond to the v-plot deep cusps having six-fold symmetry, whereas the superfast walls correspond to the v-plot maxima having three-fold symmetry with a difference between Y+ and Y− crystallographic directions. The field dependences of the velocities of the superfast domain walls followed the activation law, taking into account the existence of the bias field.

Seed-Initiated Anisotropic Growth of Unidirectional Armchair Graphene Nanoribbon Arrays on Germanium.

It was recently discovered that the chemical vapor deposition (CVD) of CH4 on Ge(001) can directly yield long, narrow, semiconducting nanoribbons of graphene with smooth armchair edges. These nanoribbons have exceptional charge transport properties compared with nanoribbons grown by other methods. However, the nanoribbons nucleate at random locations and at random times, problematically giving rise to width and bandgap polydispersity, and the mechanisms that drive the anisotropic crystal growth that produces the nanoribbons are not understood. Here, we study and engineer the seed-initiated growth of graphene nanoribbons on Ge(001). The use of seeds decouples nucleation and growth, controls where growth occurs, and allows graphene to grow with lattice orientations that do not spontaneously form without seeds. We discover that when the armchair direction (i.e., parallel to C-C bonds) of the seeds is aligned with the Ge⟨110⟩ family of directions, the growth anisotropy is maximized, resulting in the formation of nanoribbons with high-aspect ratios. In contrast, increasing misorientation from Ge⟨110⟩ yields decreasingly anisotropic crystals. Measured growth rate data are used to generate a construction analogous to a kinetic Wulff plot that quantitatively predicts the shape of graphene crystals on Ge(001). This knowledge is employed to fabricate regularly spaced, unidirectional arrays of nanoribbons and to significantly improve their uniformity. These results show that seed-initiated graphene synthesis on Ge(001) will be a viable route for creating wafer-scale arrays of narrow, semiconducting, armchair nanoribbons with rationally controlled placement and alignment for a wide range of semiconductor electronics technologies, provided that dense arrays of sub-10 nm seeds can be uniformly fabricated in the future.

Growth mechanism of InGaN nanodots on three‐dimensional GaN structures

In this study, we investigated the growth mechanism of indium gallium nitride (InGaN) nanodots (NDs) and an InGaN layer, which were simultaneously formed on a three‐dimensional (3D) gallium nitride (GaN) structure, having (0001) polar, (11‐22) semi‐polar, and (11‐20) nonpolar facets. We observed the difference in the morphological and compositional properties of the InGaN structures. From the high resolution transmission electron microscopy (HR‐TEM) images, it can be seen that the InGaN NDs were formed only on the polar and nonpolar facets, whereas an InGaN layer was formed on the semi‐polar facet. The indium composition variation in all the InGaN structures was observed using scanning transmission electron microscopy (STEM) and the energy dispersive X‐ray spectroscopy (EDS). The different growth mechanism can be explained by two reasons: (i) The difference in the diffusivities of indium and gallium adatoms at each facet of 3D GaN structure; and (ii) the difference in the kinetic Wulff plots of polar, semi‐polar, and nonpolar GaN planes.

Quasiequilibrium crystal shape and kinetic Wulff plot for GaN grown by trihalide vapor phase epitaxy using GaCl3

We demonstrated the selective‐area growth (SAG) of the nonpolar m‐plane and the polar −c‐plane substrates to determine the quasiequilibrium crystal shape (quasi‐ECS) by trihalide vapor phase epitaxy (THVPE). The results were compared with those by hydride vapor phase epitaxy (HVPE). The polar N‐face and the nonpolar m‐planes were consistently stable with the semipolar planes emerging only at high temperature for the quasi‐ECS grown by THVPE. The clear facets of the polar Ga‐face (0001) and Ga‐face sense semipolar planes such as did not appear. The kinetic Wulff plots for THVPE were constructed using the growth velocities for each emerging facet of the SAG.Bird's‐eye view SEM images of the selective‐area GaN crystals grown on the m‐plane and –c‐plane for THVPE.

Mechanism of preferential nucleation of [\bf 1{\overline 1}0{\overline 3}]-oriented GaN twins on an SiO2-patternedm-plane sapphire substrate

The mechanism of preferential nucleation of [1{\overline 1}0{\overline 3}]-oriented GaN faceted twins on an SiO2-patternedm-plane sapphire substrate was investigated. Each variant of twins, which were enclosed byc- andm-facets, was observed to be preferentially nucleated over the opposite sides of an SiO2pattern. It was hypothesized, from the fact that the same method of Legendre transformation is applied to a Wulff plot and a kinetic Wulff plot to determine the growth morphology of a crystalline domain, that theeffectivesurface energy ofc- andm-facets would be proportional to the growth rate of the respective facet. On the basis of this hypothesis, minimization of the effective surface energy of a nucleated domain was proposed as a mechanism of preferential nucleation. This proposed mechanism successfully explained the preferential nucleation behaviour.

Quasi-equilibrium crystal shapes and kinetic Wulff plots for gallium nitride grown by hydride vapor phase epitaxy

In this paper we demonstrate work on developing the kinetic Wulff plots and quasi-equilibrium crystal shapes of GaN by hydride vapor phase epitaxy to understand the stable polar, semipolar, and nonpolar planes that emerge naturally from the GaN crystal. High quality bulk m-plane GaN substrates were masked with circular openings to perform selective area growth studies. Growths were performed by hydride vapor phase epitaxy over a range of temperatures, pressures and carrier gases. The quasi-equilibrium crystal shapes were shown to have clear m-plane {11¯00} facets and a sharp and flat (0001¯) N-face or c− face. The (0001) Ga-face or c+ face became faceted with {101¯1} planes emerging with reduced pressures and temperatures. Based on the stable facets, kinetic Wulff plots were constructed.

Using the kinetic Wulff plot to design and control nonpolar and semipolar GaN heteroepitaxy

For nonpolar and semipolar orientations of GaN heteroepitaxially grown on sapphire substrates, the development of growth procedures to improve surface morphology and microstructure has been driven in a largely empirical way. This work attempts to comprehensively link the intrinsic properties of GaN faceted growth, across orientations, in order to understand, design and control growth methods for nonpolar (1 1 2 0) GaN and semipolar (1 1 2 2) GaN on foreign substrates. This is done by constructing a comprehensive series of kinetic Wulff plots (or v-plots) by monitoring the advances of convex and concave facets in selective area growth. A methodology is developed to apply the experimentally determined v-plots to the interpretation and design of evolution dynamics in nucleation and island coalescence. This methodology offers a cohesive and rational model for GaN heteroepitaxy along polar, nonpolar and semipolar orientations, and is broadly extensible to the heteroepitaxy of other materials. We demonstrate furthermore that the control of morphological evolution, based on invoking a detailed knowledge of the v-plots, holds a key to the reduction of microstructural defects through effective bending of dislocations and blocking of stacking faults. The status and outlook of semipolar and nonpolar GaN growth on sapphire substrates will be presented.

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

This work represents a comprehensive attempt to correlate the heteroepitaxial dynamics in experiments with fundamental principles in crystal growth using the kinetic Wulff plot (or v-plot). Selective area growth is employed to monitor the advances of convex and concave facets toward the construction of a comprehensive v-plot as a guidepost for GaN heteroepitaxy. A procedure is developed to apply the experimentally determined kinetic Wulff plots to the interpretation and the design of evolution dynamics in nucleation and island coalescence. This procedure offers a cohesive and rational model for GaN heteroepitaxy on polar, nonpolar, and semipolar orientations and is broadly extensible to other heteroepitaxial material systems. We demonstrate furthermore that the control of morphological evolution, based on invoking a detailed knowledge of the v-plots, holds a key to the reduction of microstructural defects through effective bending of dislocations and geometrical blocking of stacking faults, paving a way to device-quality heteroepitaxial nonpolar and semipolar GaN materials.

Morphological and microstructural evolution in the two-step growth of nonpolar a-plane GaN on r-plane sapphire

In this paper, we report a detailed study on the evolution of surface morphology and microstructure of nonpolar a-plane GaN (a-GaN) through controlled growth interruptions. Microscopy imaging shows that the two-step a-GaN growth went through a roughening-recovery process. The first-step growth (under high V/III and high pressure) produced a rough surface with tall mesas separated by voids. The second-step growth (under low V/III and low pressure) promoted the lateral growth and filled up the voids. Striations that formed during the island coalescence persisted throughout the second-step growth, but could be relieved by an additional third-step growth. The morphological evolution was explained according to the kinetic Wulff plots. The microstructure of the a-GaN films was investigated by transmission electron microscopy (TEM) and x-ray rocking curve analysis. Most of the extended defects observed in the plan-view TEM images were I1 type basal-plane stacking faults (BSFs) and their associated partial dislocations (PDs). It is found that the bending of PDs (at the inclined/vertical growth fronts) within the basal plane toward the m-axes was responsible for the substantial reduction in threading PDs and the increase in BSF dimension. Based on a careful correlation between the morphological evolution and the microstructure development, we proposed a model explaining the possible mechanisms for the great reduction in defect density during the two-step growth process.

Effect of NH 3 flow rate on m-plane GaN growth on m-plane SiC by metalorganic chemical vapor deposition

This paper reports a study of the effect of NH 3 flow rate on m-plane GaN growth on m-plane SiC with an AlN buffer layer. It is found that a reduced NH 3 flow rate during m-plane GaN growth can greatly improve the recovery of in situ optical reflectance and the surface morphology, and narrow down the on-axis (1 0 1¯ 0) X-ray rocking curve (XRC) measured along the in-plane a-axis. The surface striation along the in-plane a-axis, a result of GaN island coalescence along the in-plane c-axis, strongly depends on the NH 3 flow rate, an observation consistent with our recent study of kinetic Wulff plots. The pronounced broadening of the (1 0 1¯ 0) XRC measured along the c-axis is attributed to the limited lateral coherence length of GaN domains along the c-axis, due to the presence of a high density of basal-plane stacking faults, most of which are formed at the GaN/AlN interface, according to transmission electron microscopy.

Understanding nonpolar GaN growth through kinetic Wulff plots

In this paper we provide explanations to the complex growth phenomena of GaN heteroepitaxy on nonpolar orientations using the concept of kinetic Wulff plots (or v-plots). Quantitative mapping of kinetic Wulff plots in polar, semipolar, and nonpolar angles are achieved using a differential measurement technique from selective area growth. An accurate knowledge of the topography of kinetic Wulff plots serves as an important stepping stone toward model-based control of nonpolar GaN growth. Examples are illustrated to correlate growth dynamics based on the kinetic Wulff plots with commonly observed features, including anisotropic nucleation islands, highly striated surfaces, and pentagonal or triangular pits.