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顏勝宏 2003/3/10 1 Vegard’s law deviation in band gap and bowing parameter of ternary Al x Ga 1-x N compound semiconductors Speaker : Sheng-Horng Yen Bo-Ting Liou, and Yen-Kuang Kuo 2003/3/10

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顏勝宏 2003/3/10 2 Simulation items Vegard’s law deviation of wurtzite Al x Ga 1-x N Bowing parameters of linear and nonlinear Influence of Vegard’s law or not in bowing parameter

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顏勝宏 2003/3/10 3 What is Vegard’s law a(x)=3.084x (1-x) a(x)=3.084x (1-x)-δx(1-x) δis deviation of Vegard’s law

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顏勝宏 2003/3/10 4 What is bowing parameter E g (x) = x · E g,AlN + (1-x) ·E g,GaN - b · x · (1-x)

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顏勝宏 2003/3/10 5 Wurtzite Al x Ga 1-x N 六方晶系的 wurtzite 結構

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顏勝宏 2003/3/10 6 Parameter Introduction Lattice Constance AlN:a(x) = Å c(x) = Å GaN:a(x) = Å c(x) = Å Energy Band-Gap AlN: eV GaN: eV

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顏勝宏 2003/3/10 7 Numerical simulation tool CASTEP ()

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顏勝宏 2003/3/10 8 Convergence test Cutoff energy （ eV ）,AlN Width of top valence band at Γ point （ eV ） Cutoff energy （ eV ）,GaN Width of top valence band at Γ point （ eV ）

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顏勝宏 2003/3/10 9 Comparison the lattice constants obtained by this work and other present (1) a (Å) c (Å) AlNThis work PWPP 16) FP- LMTO 24) MBPP 18) PWPP 20) NLCC 21) NLCC 23) EXPT. 25)

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顏勝宏 2003/3/10 10 Comparison the lattice constants obtained by this work and other present (2) GaNThis work PWPP 17) MBPP 18) PWPP 19) NLCC 22) NLCC 23) EXPT. 25)

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顏勝宏 2003/3/10 11 Lattice constants of Al x Ga 1-x N. Materiala (Å) c (Å) GaN Al Ga N Al 0.25 Ga 0.75 N Al 0375 Ga N Al 0.50 Ga 0.50 N Al Ga N Al 0.75 Ga 0.25 N Al Ga N AlN

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顏勝宏 2003/3/10 12 Comparison Valence and Band-Gap of linear and nonlinear MaterialWidth of top valence band at Γ point （ eV ） Band-gap energy （ eV ） LinearNonlinearLinearNonlinear GaN Al Ga N Al 0.25 Ga 0.75 N Al 0375 Ga N Al 0.50 Ga 0.50 N Al Ga N Al 0.75 Ga 0.25 N Al Ga N AlN

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顏勝宏 2003/3/10 13 Nonlinear lattice constance a(x)

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顏勝宏 2003/3/10 14 Nonlinear lattice constance c(x)

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顏勝宏 2003/3/10 15 Conclusion (1) δis ±0.007 Å for a lattice constant δ is ±0.013 Å for c lattice constant

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顏勝宏 2003/3/10 16 Energy Band-Gap of linear and nonlinear

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顏勝宏 2003/3/10 17 Indirect Energy Band-Gap of linear and nonlinear

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顏勝宏 2003/3/10 18 Conclusion (2) linearnonlinear direct indirect

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顏勝宏 2003/3/10 19

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