• Title, Summary, Keyword: h-stability

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Stability of H2O2 as an Oxidizer for Cu CMP

  • Lee, Do-Won;Kim, Tae-Gun;Kim, Nam-Hoon;Kim, Sang-Yong;Chang, Eui-Goo
    • Transactions on Electrical and Electronic Materials
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    • v.6 no.1
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    • pp.29-32
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    • 2005
  • Chemical mechanical polishing is an essential process in the production of copper-based chips. On this work, the stability of hydrogen peroxide ($H_{2}O_{2}$) as an oxidizer of copper CMP slurry has been investigated. $H_{2}O_{2}$ is known as the most common oxidizer in copper CMP slurry. But $H_{2}O_{2}$ is so unstable that its stabilization is needed using as an oxidizer. As adding KOH as a pH buffering agent, stability of $H_{2}O_{2}$ decreased. However, $H_{2}O_{2}$ stability in slurry went up with putting in small amount of BTA as a film forming agent. There was no difference of $H_{2}O_{2}$ stability between pH buffering agents KOH and TMAH at similar pH value. Addition of $H_{2}O_{2}$ in slurry in advance of bead milling led to better stability than adding after bead milling. Adding phosphoric acid resulted in the higher stability. Using alumina C as an abrasive was good at stabilizing for $H_{2}O_{2}$.

Stability of Oxidizer $H_2O_2$ for Copper CMP Slurry (구리 CMP 슬러리를 위한 산화제 $H_2O_2$의 안정성)

  • Lee, Do-Won;Kim, In-Pyo;Kim, Nam-Hoon;Kim, Sang-Yong;Seo, Yong-Jin;Chang, Eui-Goo
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • pp.382-385
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    • 2003
  • Chemical mechanical polishing(CMP) is an essential process in the production of copper-based chips. On this work, the stability of Hydrogen Peroxide($H_2O_2$) as oxidizer of Cu CMP slurry has been investigated. $H_2O_2$ is known as the most common oxidizer in Cu CMP slurry. Copper slowly dissolves in $H_2O_2$ solutions and the interaction of $H_2O_2$ with copper surface had been studied in the literature. Because hydrogen peroxide is a weak acid in aqueous solutions, a passivation-type slurry chemistry could be achieved only with pH buffered solution.[1] Moreover, $H_2O_2$ is so unstable that its stabilization is needed using as oxidizer. As adding KOH as pH buffering agent, stability of $H_2O_2$ decreased. However, stability went up with putting in small amount of BTA as film forming agent. There was no difference of $H_2O_2$ stability between KOH and TMAH at same pH. On the other hand, $H_2O_2$ dispersion of TMAH is lower than that of KOH. Furthermore, adding $H_2O_2$ in slurry in advance of bead milling lead to better stability than adding after bead milling. Generally, various solutions of phosphoric acids result in a higher stability. Using Alumina C as abrasive was good at stabilizing for $H_2O_2$; moreover, better stability was gotten by adding $H_3PO_4$.

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LYAPUNOV FUNCTIONS FOR NONLINEAR DIFFERENCE EQUATIONS

  • Choi, Sung Kyu;Cui, Yinhua;Koo, Namjip
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.4
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    • pp.883-893
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    • 2011
  • In this paper we study h-stability of the solutions of nonlinear difference system via the notion of $n_{\infty}$-summable similarity between its variational systems. Also, we show that two concepts of h-stability and h-stability in variation for nonlinear difference systems are equivalent. Furthermore, we characterize h-stability for nonlinear difference systems by using Lyapunov functions.

h-Stability of differential systems via $t_{\infty}$-similarity

  • Park, Sung-Kyu;Koo, Nam-Jip
    • Bulletin of the Korean Mathematical Society
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    • v.34 no.3
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    • pp.371-383
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    • 1997
  • In recent years M. Pinto introduced the notion of h-stability. He extended the study of exponential stability to a variety of reasonable systems called h-systems. We investigate h-stability for the nonlinear differential systems using the notions of $t_\infty$-similarity and Liapunov functions.

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The Study on Emulsifying and Foaming Properties of Buckwheat Protein Isolate (분리 메밀 단백질의 유화 및 기포특성에 관한 연구)

  • 손경희;최희선
    • Korean journal of food and cookery science
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    • v.9 no.1
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    • pp.43-51
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    • 1993
  • Buckwheat protein isolate was tested for the effects of pH, addition of sodium chloride and heat treatment on solubility, emulsion capacities, emulsion stability, surface hydrophobicity, foam capacities and foam stability. The solubility of buckwheat protein isolate was affected by pH and showed the lowest value at pH 4.5, the isoelectric point of buckwheat protein isolate. The solubility significantly as the pH value reached closer to either ends of the pH, i.e., pH 1.0 and 11.0. The effects of NaCl concentration on solubility were as follows; at pH 2.0, the solubility significantly decreased when NaCl was added; at pH 4.5, it increased above 0.6 M; at pH 7.0 it increased; and at pH 9.0 it decreased. The solubility increased above $80^{\circ}C$, at all pH ranges. The emulsion capacity was the lowest at pH 4.5. It significantly increased as the pH approached higher acidic or alkalic regions. At pH 2.0, when NaCl was added, the emulsion capacity decreased, but it increased at pH 4.5 and showed the maximum value at pH 7.0 and 9.0 with 0.6 M and 0.8 M NaCl concentrations. Upon heating, the emulsion capacity decreased at acidic pH's but was maximised at pH 7.0 and 9.0 on $60^{\circ}C$ heat treatment. The emulsion stability was the lowest at pH 4.5 but increased with heat treatment. At acidic pH, the emulsion stability increased with the increase in NaCl concentration but decreased at pH 7.0 and 9.0. Generally, at other pH ranges, the emulsion stability was decreased with increased heating temperature. The surface hydrophobicity showed the highest value at pH 2.0 and the lowest value at pH 11.0. As NaCl concentrationed, the surface hydrophobicity decreased at acidic pH. The NaCl concentration had no significant effects on surface hydrophobicity at pH 7.0, 9.0 except for the highest value observed at 0.8 M and 0.4 M. At all pH ranges, the surface hydrophobicity was increased, when the temperature increased. The foam capacity decreased, with increased in pH value. At acidic pH, the foam capacity was decreased with the increased in NaCl concentration. The highest value was observed upon adding 0.2 M or 0.4 M NaCl at pH 7.0 and 9.0. Heat treatments of $60^{\circ}C$ and $40^{\circ}C$ showed the highest foam capacity values at pH 2.0 and 4.5, respectively. At pH 7.0 and 9.0, the foam capacity decreased with the increased in temperature. The foam stability was not significantly related to different pH values. The addition of 0.4 M NaCl at pH 2.0, 7.0 and 9.0 showed the highest stability and the addition of 1.0 M at pH 4.5 showed the lowest. The higher the heating temperature, the lower the foam stability at pH 2.0 and 9.0. However, the foam stability increased at pH 4.5 and 7.0 before reaching $80^{\circ}C$.

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Stability of Paeoniflorin used as Anti-wrinkle Agents in Emulsions (피부 주름 개선 소재인 페오니플로린의 에멀젼 안정성)

  • Cho, Wan-Goo;Kyung, Kee-Youl;Yu, Sang-Mun
    • Journal of the Korean Applied Science and Technology
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    • v.26 no.2
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    • pp.191-198
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    • 2009
  • We have tested the stability of paeoniflorin, a new cosmetic ingredient, extracted from the roots of Paeoniae lactiflora. The stability of aqueous paeoniflorin solution at pH 3, 5 and 7 varied by adding buffer solution was tested at $0^{\circ}C,\;25^{\circ}C,\;40^{\circ}C,\;and\;65^{\circ}C$. The test was performed with or without UV light. The solution of paeoniflorin was stable at pH 3.0, however, the recovery rate of paeoniflorin was 40% at pH 7.0. The stability of paeoniflorin solution was decreased as the pH of paeoniflorin solution was increased by pH 7.0. The effect of storage temperature of paeoniflorin solution shows that the stability of paeoniflorin solution was decreased as the temperature was increased. The stability of paeoniflorin was rather good under UV light than the condition given above $40^{\circ}C$. The stability of paeoniflorin in W/O emulsions shows similar pattern to that of aqueous solution.

h-STABILITY FOR NONLINEAR PERTURBED DIFFERENCE SYSTEMS

  • Choi, Sung-Kyu;Koo, Nam-Jip;Song, Se-Mok
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.3
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    • pp.435-450
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    • 2004
  • We show that two concepts of h-stability and h-stability in variation for nonlinear difference systems are equivalent by using the concept of $n_{\infty}$-summable similarity of their associated variational systems. Also, we study h-stability for perturbed non-linear system y(n+1) =f(n,y(n)) + g(n,y(n), Sy(n)) of nonlinear difference system x(n+1) =f(n,x(n)) using the comparison principle and extended discrete Bihari-type inequality.