• JSTS:Journal of Semiconductor Technology and Science
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• v.14 no.5
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• pp.557-565
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• 2014

We report the effect of basal-plane stacking faults (BSFs) on X-ray diffraction (XRD) of non-polar (11$\underline{2}$0) a-plane GaN films with different $SiN_x$ interlayers. Complete $SiN_x$ coverage and increased three-dimensional (3D) to two-dimensional (2D) transition stages substantially reduce BSF density. It was revealed that the Si-doping profile in the Si-doped GaN layer was unaffected by the introduction of a $SiN_x$ interlayer. The smallest in-plane anisotropy of the (11$\underline{2}$0) XRD ${\omega}$-scan widths was found in the sample with multiple $SiN_x$ layers, and this finding can be attributed to the relatively isotropic GaN mosaic resulting from the increase in the 3D-2D growth step. Williamson-Hall (WH) analysis of the (h0$\underline{h}$0) series of diffractions was employed to determine the c-axis lateral coherence length (LCL) and to estimate the mosaic tilt. The c-axis LCLs obtained from WH analyses of the present study's representative a-plane GaN samples were well correlated with the BSF-related results from both the off-axis XRD ${\omega}$-scan and transmission electron microscopy (TEM). Based on WH and TEM analyses, the trends in BSF densities were very similar, even though the BSF densities extracted from LCLs indicated that the values were reduced by a factor of about twenty.

• Bulletin of the Korean Chemical Society
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• v.33 no.12
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• pp.4161-4164
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• 2012

Density functional MO calculations for the methylsilole anion of $[C_4H_4SiMe]^-$ and methylgermole anion of $[C_4H_4SiMe]^-$ at the B3LYP (full)/6-311+$G^*$ level (GAUSSIAN 94) were carried out and characterized by frequency analysis. The ground state structure for the methylsilole anion and methylgermole anion is that the methyl group is pyramidalized with highly localized structure. The difference between the calculated $C_{\alpha}-C_{\beta}$ and $C_{\beta}-C_{\beta}$ distances are 9.4 and 11.5 pm, respectively. The E-Me vector forms an angle of $67.9^{\circ}$ and $78.2^{\circ}$ with the $C_4E$ plane, respectively. The optimized structures of the saddle point state for the methylsilole anion and methylgermole anion have been also found as a planar with highly delocalized structure. The optimized $C_{\alpha}-C_{\beta}$ and $C_{\beta}-C_{\beta}$ distances are nearly equal for both cases. The methyl group is located in the plane of $C_4E$ ring and the angle between the E-Me vector and the $C_4E$ plane for the methylsilole anion and methylgermole anion is $2.0^{\circ}$ and $2.3^{\circ}$, respectively. The energy difference between the ground state structure and the transition state structure is only 5.1 kcal $mol^{-1}$ for the methylsilole anion. However, the energy difference of the methylgermole anion is 14.9 kcal $mol^{-1}$, which is much higher than that for the corresponding methylsilole monoanion by 9.8 kcal $mol^{-1}$. Based on MO calculations, we suggest that the head-to-tail dimer compound, 4, result from [2+2] cycloaddition of silicon-carbon double bond character in the highly delocalized transition state of 1. However, the inversion barrier for the methylgermole anion is too high to dimerize.

• Proceedings of the Korean Magnestics Society Conference
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• 2007.05a
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• pp.225.2-225.2
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• 2007

• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.535-565
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• 2004

In this paper we consider the notion of ξ-invariant or (equation omitted)-invariant real hypersurfaces in a complex two-plane Grassmannian $G_2$( $C^{m+2}$) and prove that there do not exist such kinds of real hypersurfaces in $G_2$( $C^{m+2}$) with parallel second fundamental tensor on a distribution ζ defined by ζ = ξ U(equation omitted), where(equation omitted) = Span ｛ξ$_1$, ξ$_2$, ξ$_3$｝.X>｝.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.199-213
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• 2006

We compute the holomorphic derivative of the harmonic measure associated to a $C^\infty$bounded domain in the plane and show that the exact Bergman kernel function associated to a $C^\infty$ bounded domain in the plane relates the derivatives of the Ahlfors map and the Szego kernel in an explicit way. We find several formulas for the exact Bergman kernel and the Szego kernel and the harmonic measure. Finally we survey some other properties of the holomorphic derivative of the harmonic measure.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.695-704
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• 2023

Area problems for triangles and polygons whose vertices have Fibonacci numbers on a plane were presented by A. Shriki, O. Liba, and S. Edwards et al. In 2017, V. P. Johnson and C. K. Cook addressed problems of the areas of triangles and polygons whose vertices have various sequences. This paper examines the conditions of triangles and polygons whose vertices have Lucas sequences and presents a formula for their areas.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.475-482
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• 2007

In this paper, we study composition operators $C_{\varph}f=f^{\circ}{\varph}$, induced by a fixed analytic self-map of the of the upper half-plane, acting between Hardy and Bloch-type spaces of the upper half-plane.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.1113-1133
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• 2008

In this paper we give some non-existence theorems for real hypersurfaces in complex two-plane Grassmannians $G_2({\mathbb{C}}^{m+2})$ with Lie ${\xi}$-parallel normal Jacobi operator $\bar{R}_N$ and another geometric conditions.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2012.10a
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• pp.565-566
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• 2012

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1997.04a
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• pp.1-5
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• 1997

The plane surface rolling, one of the plastic working process, good surface condition due to increase of surface roughness and hardness. It is well known that mechanism of surface rolling depends upon rolling conditions such as rolling speed, contact pressure, step length of rolling, the shape of roller and mechanical properties of material. In this study, the optimal value of the above parameter on the surface roughness were investigated by using the rolling tool with NACHI 6000ZZ ball bearing outer races on machine structure carbon steel[SM45C]