Theoretical prediction of GaN nanostructure equilibrium and nonequilibrium shapes

Jindal, V. K.

doi:10.1063/1.3253575

Cited by 99 publications

(117 citation statements)

References 15 publications

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“…3(a and b)) evolving from elongated ( Fig. 2(c)) to arrow-headed shape, similar to those reported by MOVPE [23]. The main difference is that the sample with higher^N showed the onset of the nanostructures coalescence.…”

Section: (C and D) (880 1csupporting

confidence: 79%

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Selective area growth of a- and c-plane GaN nanocolumns by molecular beam epitaxy using colloidal nanolithography

Bengoechea-Encabo

Albert

Sánchez-García

et al. 2012

Journal of Crystal Growth

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Selective area growth of a-plane GaN nanocolumns by molecular beam epitaxy was performed for the first time on a-plane GaN templates. Ti masks with 150 nm diameter nanoholes were fabricated by colloidal lithography, an easy, fast and cheap process capable to handle large areas. Even though colloidal lithography does not provide a perfect geometrical arrangement like e-beam lithography, it produces a very homogeneous mask in terms of nanohole diameter and density, and is used here for the first time for the selective area growth of GaN. Selective area growth of a-plane GaN nanocolumns is compared, in terms of anisotropic lateral and vertical growth rates, with GaN nanocolumns grown selectively on the c-plane.The main advantages of one-dimensional structures such as nanocolumns, compared to thin films, is the dislocation-and strain-free growth on different substrates. This higher crystal quality yields a better efficiency in devices such as light emitting diodes (LEDs) based on InGaN/GaN quantum disks (QDisks) [1][2][3][4].Much effort has been dedicated to the growth of self-assembled nanocolumns (NCs) by Plasma-Assisted Molecular Beam Epitaxy (PAMBE), allowing a better knowledge of the material physical properties and growth mechanisms [5][6][7][8]. However, the strong morphology dispersion, typical of a self-assembled process, hinders both the processing of nanodevices arrays and their electrical behavior (NCs merging, defect generation, current injection inhomogeneities). Indeed, arrays of self-assembled nanoLEDs show in general much lower electroluminescence efficiency than the corresponding one measured by photoluminescence (PL). In addition to that InGaN active regions embedded in self-assembled NCs of different diameters and lengths always show fluctuations in the composition, leading to multicolor emission. Arrays of nanostructures grown by selective area growth (SAG) provide a much better homogeneity in terms of morphology, electrical and optical characteristics. SAG of Ill-nitride NCs [9][10][11][12] and other nanostructures [13,14], is generally performed on very thin metal (Ti, Mo) or dielectric (Si0 2 , SiN) masks with an array of nanoholes.A relevant issue concerning optoelectronic devices based on Ill-nitrides is the presence of strong polarization fields that may reduce efficiency. This is the case in layers grown along the c-axis and, a huge effort is nowadays dedicated to the growth of high quality non-polar and semi-polar material [15], with a particular emphasis on non-polar LEDs [16].In the case of SAG of GaN NCs on c-plane GaN templates, the growth front is generally formed by semi-polar (r-planes) that yield a "pencil-like" profile [12]. This profile is then transferred to InGaN QDisks embedded within the GaN NC. Though in this structure the effects of internal fields in the active region of the device (i.e. nanoLED) may be reduced compared with polar planes, the most effective solution is to grow along non-polar directions, either by growing core-shell heterostructures on the latera...

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Section: (C and D) (880 1csupporting

confidence: 79%

“…In fact, the measured ratio between both growth rates (2.7) is in the range of the factor derived from the kinetic Wulff's plots (v-plots) calculated for GaN in Ref. [23] (factor 4).…”

Section: Introductionmentioning

confidence: 58%

Selective area growth of a- and c-plane GaN nanocolumns by molecular beam epitaxy using colloidal nanolithography

Bengoechea-Encabo

Albert

Sánchez-García

et al. 2012

Journal of Crystal Growth

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“…Selective-area MOCVD growth [16] exhibited convex {1101} and concave {1122} surfaces. In contrast, Jindal [17] observed in MOCVD growth a complete hexagonal pyramid on the (0001) plane as its equilibrium shape, and truncated hexagonal pyramids out of equilibrium, while the crystal grown on the (1120) and (1100) planes showed {1101} facets along the [0001] direction and a (0001) facet on the opposite side. In hydride vapor phase epitaxy [18], depending on the temperature and pressure, the truncation of the pyramidal shape was confirmed to be continuously varying along the [0001] direction.…”

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confidence: 96%

“…GaN readily grows in the form of nanowires (NWs) in molecular beam epitaxy (MBE) [12,13] and metal-organic chemical vapor deposition (MOCVD) [14,15]. However, different shapes are observed, depending on the growth temperature, pressure, and chemical environment [16][17][18][19][20]. Our study leads to new understanding of these GaN crystal shapes under various growth conditions.…”

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Computing Equilibrium Shapes of Wurtzite Crystals: The Example of GaN

Geelhaar

Riechert

et al. 2015

Phys. Rev. Lett.

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Crystal morphologies are important for the design and functionality of devices based on low-dimensional nanomaterials. The equilibrium crystal shape (ECS) is a key quantity in this context. It is determined by surface energies, which are hard to access experimentally but can generally be well predicted by first-principles methods. Unfortunately, this is not necessarily so for polar and semipolar surfaces of wurtzite crystals. By extending the concept of Wulff construction, we demonstrate that ECSs can nevertheless be obtained for this class of materials. For the example of GaN, we identify different crystal shapes depending on the chemical potential, shedding light on experimentally observed GaN nanostructures. 68.35.Md,68.47.Fg,81.10.Aj Low-dimensional semiconductor nanostructures have attracted a lot of interest in the past decades, largely due to their applications in low-energy consumption and energyharvesting devices [1,2]. Owing to surface effects, the performance of such devices strongly depends on the nanocrystal morphology. To achieve comprehensive understanding and control of the preferred growth morphology, one must know the material's natural shape that results from its crystallographic anisotropy. Ab initio theory can generally provide more insight into this complicated issue through the calculation of surface energies since, according to Wulff's theorem [3], the equilibrium crystal shape (ECS) of a solid can be constructed by the mere knowledge of surface energies of various crystal planes. For a crystalline solid, the surface energy γ is defined as the excess free energy required to create one unit of surface area A [4],G represents the Gibbs free energy of the system that, neglecting temperature and pressure, is replaced by the total energy. The chemical potential µ i is the free energy per atom in the system for species i, and N i denotes the number of atoms of this species. In a bulk material, the total chemical potential is known from the corresponding total energy E bulk = ∑ i n i µ i , where n i is the number of atoms of species i in the bulk. Hence, the surface energy of a nonpolar plane can be extracted from density-functional-theory (DFT) results for a slab that contains two identical surfaces well separated from each other. For some polar and semipolar planes, however, individual surface energies are difficult to access, because different facets may appear at the two surfaces of the slab. To overcome this problem, a method has been proposed [5] involving two surface types on three side faces of a triangular wedge. This approach is, however, not applicable to all surfaces and crystal structures; polar surfaces in wurtzite crystals are one example [6,7]. Consequently, not every individual surface energy of wurtzite crystals can be computed; hence, the construction of the ECS seemed impossible. Recently, neglecting the different layer-stacking sequence, the surface energy of the polar c plane was estimated from the zincblende (111) plane [10].In this Letter, we show that such an approxim...

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“…17,18 Recently, the GaN non-equilibrium shapes obtained by MOVPE have been measured or calculated for different growth conditions on polar, 19 semipolar and nonpolar 20,21 surfaces. The anisotropy of the growth rate along <0 0 0 1> coming from the crystal polarity has been pointed out without mentioning the influence of the substrate polarity.…”

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confidence: 99%

Homoepitaxial growth of catalyst-free GaN wires on N-polar substrates

Chen¹,

Perillat-Merceroz²,

Sam-Giao³

et al. 2010

Applied Physics Letters

121

129

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3 pagesInternational audienceThe shape of c-oriented GaN nanostructures is found to be directly related to the crystal polarity. As evidenced by convergent beam electron diffraction applied to GaN nanostructures grown by metal-organic vapor phase epitaxy on c-sapphire substrates: wires grown on nitridated sapphire have the N-polarity ([000math]) whereas pyramidal crystals have Ga-polarity ([0001]). In the case of homoepitaxy, the GaN wires can be directly selected using N-polar GaN freestanding substrates and exhibit good optical properties. A schematic representation of the kinetic Wulff's plot points out the effect of surface polarity

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Theoretical prediction of GaN nanostructure equilibrium and nonequilibrium shapes

Cited by 99 publications

References 15 publications

Selective area growth of a- and c-plane GaN nanocolumns by molecular beam epitaxy using colloidal nanolithography

Selective area growth of a- and c-plane GaN nanocolumns by molecular beam epitaxy using colloidal nanolithography

Computing Equilibrium Shapes of Wurtzite Crystals: The Example of GaN

Homoepitaxial growth of catalyst-free GaN wires on N-polar substrates

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