Vegard’s law deviation in band gap and
bowing parameter of ternary AlxGa1-xN
compound semiconductors
Speaker : Sheng-Horng Yen
Bo-Ting Liou, and Yen-Kuang Kuo
2003/3/10
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Simulation items
Vegard’s law deviation of wurtzite
AlxGa1-xN
Bowing parameters of linear and
nonlinear
Influence of Vegard’s law or not in
bowing parameter
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What is Vegard’s law
a(x)=3.084x + 3.162(1-x)
AlxGa1-x N
Al(x)
a(x)
0
3.162
0.25
3.1425
0.5
3.123
0.75
3.1035
1
3.084
a(x)=3.084x + 3.162(1-x)-δx(1-x)
δis deviation of Vegard’s law
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What is bowing parameter
Eg(x) = x · Eg,AlN + (1-x) ·Eg,GaN - b · x · (1-x)
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Wurtzite AlxGa1-xN
六方晶系的wurtzite結構
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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
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Numerical simulation tool
CASTEP ()
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Convergence test
Cutoff energy（eV）,AlN
150
200
250
300
350
400
450
Width of top valence band at Γ point
（eV）
8.745
7.563
7.484
7.133
6.821
6.834
6.839
Cutoff energy（eV）,GaN
350
400
450
500
550
600
650
Width of top valence band at Γ point
（eV）
7.996
7.682
7.382
7.424
7.349
7.335
7.324
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Comparison the lattice constants obtained by
this work and other present (1)
AlN
a
(Å)
c
(Å)
This work
3.076
4.935
PWPP16)
3.129
4.988
FPLMTO24)
3.073
4.904
MBPP18)
3.144
5.046
PWPP20)
3.084
4.948
NLCC21)
3.082
NLCC23)
3.10
5.01
EXPT. 25)
3.110
4.980
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Comparison the lattice constants obtained by
this work and other present (2)
GaN
This work
3.183
5.178
PWPP17)
3.126
5.119
MBPP18)
3.146
5.125
PWPP19)
3.162
5.142
NLCC22)
3.143
NLCC23)
3.20
5.22
EXPT. 25)
3.19
5.189
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Lattice constants of AlxGa1-xN.
Material
a
(Å)
c
(Å)
GaN
3.183
5.178
Al0.125Ga0.875N
3.170
5.165
Al0.25Ga0.75N
3.169
5.151
Al0375Ga0.625N
3.151
5.112
Al0.50Ga0.50N
3.142
5.075
Al0.625Ga0.375N
3.125
5.055
Al0.75Ga0.25N
3.113
5.027
Al0.875Ga0.125N
3.087
4.975
AlN
3.076
4.935
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Comparison Valence and Band-Gap of linear
and nonlinear
Material
Width of top valence band at Γ
point（eV）
Band-gap energy（eV）
Linear
Nonlinear
Linear
Nonlinear
GaN
7.479
7.335
3.420
3.420
Al0.125Ga0.875N
7.405
7.274
3.783
3.746
Al0.25Ga0.75N
7.322
7.145
4.135
4.017
Al0375Ga0.625N
7.204
7.087
4.540
4.447
Al0.50Ga0.50N
7.095
6.971
4.868
4.717
Al0.625Ga0.375N
7.012
6.927
5.244
5.144
Al0.75Ga0.25N
6.901
6.828
5.627
5.530
Al0.875Ga0.125N
6.792
6.814
6.036
6.031
AlN
6.643
6.685
6.457
6.457
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Lattice Constant (Angstrom)
Nonlinear lattice constance a(x)
3.20
3.18
3.16
3.14
3.12
3.10
3.08
3.06
0.0
0.2
0.4
0.6
0.8
1.0
Aluminum Composition x
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Lattice Constant (Angstrom)
Nonlinear lattice constance c(x)
5.20
5.15
5.10
5.05
5.00
4.95
4.90
0.0
0.2
0.4
0.6
0.8
1.0
Aluminum Composition x
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Conclusion (1)
δis -0.042±0.007 Å for a lattice
constant
δis -0.123±0.013 Å for c lattice
constant
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Energy Band-Gap (eV)
Energy Band-Gap of linear and
nonlinear
6.5
Nonlinear
Linear
6.0
5.5
5.0
4.5
4.0
3.5
3.0
0.0
0.2
0.4
0.6
0.8
1.0
Aluminum Composition x
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Energy Band-Gap (eV)
Indirect Energy Band-Gap of linear
and nonlinear
7.5
Nonlinear
Linear
7.0
6.5
6.0
5.5
5.0
0.0
0.2
0.4
0.6
0.8
1.0
Aluminum Composition x
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Conclusion (2)
linear
nonlinear
direct
indirect
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