1. 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

2. 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

3. 顏勝宏 2003/3/10 3 What is Vegard’s law a(x)=3.084x + 3.162(1-x) a(x)=3.084x + 3.162(1-x)-δx(1-x) δis deviation of Vegard’s law

4. 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)

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

6. 顏勝宏 2003/3/10 6 Parameter Introduction Lattice Constance AlN:a(x) = 3.084 Å c(x) = 4.948 Å GaN:a(x) = 3.162 Å c(x) = 5.142 Å Energy Band-Gap AlN: 6.457 eV GaN: 3.420 eV

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

8. 顏勝宏 2003/3/10 8 Convergence test Cutoff energy （ eV ）,AlN 150200250300350400450 Width of top valence band at Γ point （ eV ） 8.7457.5637.4847.1336.8216.8346.839 Cutoff energy （ eV ）,GaN 350400450500550600650 Width of top valence band at Γ point （ eV ） 7.9967.6827.3827.4247.3497.3357.324

9. 顏勝宏 2003/3/10 9 Comparison the lattice constants obtained by this work and other present (1) a (Å) c (Å) AlNThis work3.0764.935 PWPP 16) 3.1294.988 FP- LMTO 24) 3.0734.904 MBPP 18) 3.1445.046 PWPP 20) 3.0844.948 NLCC 21) 3.082 NLCC 23) 3.105.01 EXPT. 25) 3.1104.980

10. 顏勝宏 2003/3/10 10 Comparison the lattice constants obtained by this work and other present (2) GaNThis work3.1835.178 PWPP 17) 3.1265.119 MBPP 18) 3.1465.125 PWPP 19) 3.1625.142 NLCC 22) 3.143 NLCC 23) 3.205.22 EXPT. 25) 3.195.189

11. 顏勝宏 2003/3/10 11 Lattice constants of Al x Ga 1-x N. Materiala (Å) c (Å) GaN3.1835.178 Al 0.125 Ga 0.875 N3.1705.165 Al 0.25 Ga 0.75 N3.1695.151 Al 0375 Ga 0.625 N3.1515.112 Al 0.50 Ga 0.50 N3.1425.075 Al 0.625 Ga 0.375 N3.1255.055 Al 0.75 Ga 0.25 N3.1135.027 Al 0.875 Ga 0.125 N3.0874.975 AlN3.0764.935

12. 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 GaN7.4797.3353.420 Al 0.125 Ga 0.875 N7.4057.2743.7833.746 Al 0.25 Ga 0.75 N7.3227.1454.1354.017 Al 0375 Ga 0.625 N7.2047.0874.5404.447 Al 0.50 Ga 0.50 N7.0956.9714.8684.717 Al 0.625 Ga 0.375 N7.0126.9275.2445.144 Al 0.75 Ga 0.25 N6.9016.8285.6275.530 Al 0.875 Ga 0.125 N6.7926.8146.0366.031 AlN6.6436.6856.457

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

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

15. 顏勝宏 2003/3/10 15 Conclusion (1) δis -0.042±0.007 Å for a lattice constant δ is -0.123±0.013 Å for c lattice constant

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

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

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

19. 顏勝宏 2003/3/10 19