Vegards law deviation in band gap and bowing

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

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

What is Vegard’s law a(x)=3. 084 x + 3. 162(1 -x)-δx(1 -x) δis deviation of Vegard’s law 顏勝宏 2003/3/10 3

What is bowing parameter Eg(x) = x · Eg, Al. N + (1 -x) ·Eg, Ga. N - b · x · (1 -x) 顏勝宏 2003/3/10 4

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

Parameter Introduction Lattice Constance Al. N: a(x) = 3. 084 Å c(x) = 4. 948 Å Ga. N: a(x) = 3. 162 Å c(x) = 5. 142 Å Energy Band-Gap Al. N: 6. 457 e. V Ga. N: 3. 420 e. V 顏勝宏 2003/3/10 6

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

Convergence test Cutoff energy（e. V）, Al. N 150 200 250 300 350 400 450 Width of top valence band at Γ point （e. V） 8. 745 7. 563 7. 484 7. 133 6. 821 6. 834 6. 839 Cutoff energy（e. V）, Ga. N 350 400 450 500 550 600 650 Width of top valence band at Γ point （e. V） 7. 996 7. 682 7. 382 7. 424 7. 349 7. 335 7. 324 顏勝宏 2003/3/10 8

Comparison the lattice constants obtained by this work and other present (1) a (Å) c (Å) Al. N This work 3. 076 4. 935 PWPP 16) 3. 129 4. 988 FPLMTO 24) 3. 073 4. 904 MBPP 18) 3. 144 5. 046 PWPP 20) 3. 084 4. 948 NLCC 21) 3. 082 NLCC 23) 3. 10 5. 01 EXPT. 25) 3. 110 4. 980 顏勝宏 2003/3/10 9

Comparison the lattice constants obtained by this work and other present (2) Ga. N This work 3. 183 5. 178 PWPP 17) 3. 126 5. 119 MBPP 18) 3. 146 5. 125 PWPP 19) 3. 162 5. 142 NLCC 22) 3. 143 NLCC 23) 3. 20 5. 22 EXPT. 25) 3. 19 5. 189 顏勝宏 2003/3/10 10

Lattice constants of Alx. Ga 1 -x. N. Material a (Å) c (Å) Ga. N 3. 183 5. 178 Al 0. 125 Ga 0. 875 N 3. 170 5. 165 Al 0. 25 Ga 0. 75 N 3. 169 5. 151 Al 0375 Ga 0. 625 N 3. 151 5. 112 Al 0. 50 Ga 0. 50 N 3. 142 5. 075 Al 0. 625 Ga 0. 375 N 3. 125 5. 055 Al 0. 75 Ga 0. 25 N 3. 113 5. 027 Al 0. 875 Ga 0. 125 N 3. 087 4. 975 Al. N 3. 076 4. 935 顏勝宏 2003/3/10 11

Comparison Valence and Band-Gap of linear and nonlinear Material Width of top valence band at Γ point（e. V） Band-gap energy（e. V） Linear Nonlinear Ga. N 7. 479 7. 335 3. 420 Al 0. 125 Ga 0. 875 N 7. 405 7. 274 3. 783 3. 746 Al 0. 25 Ga 0. 75 N 7. 322 7. 145 4. 135 4. 017 Al 0375 Ga 0. 625 N 7. 204 7. 087 4. 540 4. 447 Al 0. 50 Ga 0. 50 N 7. 095 6. 971 4. 868 4. 717 Al 0. 625 Ga 0. 375 N 7. 012 6. 927 5. 244 5. 144 Al 0. 75 Ga 0. 25 N 6. 901 6. 828 5. 627 5. 530 Al 0. 875 Ga 0. 125 N 6. 792 6. 814 6. 036 6. 031 Al. N 6. 643 6. 685 6. 457 顏勝宏 2003/3/10 12

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

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

Conclusion (1) δis -0. 042± 0. 007 Å for a lattice constant δis -0. 123± 0. 013 Å for c lattice constant 顏勝宏 2003/3/10 15

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

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

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

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