80
5 InGaN/GaN Multiple Quantum Wells Materials …
Table 5.1 Fundamental
constants of nitride materials
[6]
Parameters
Material type
GaN
InN
AlN
P sp (c/m 2 )
−0.034
−0.042
−0.090
e 33 (cm 2 )
0.73
0.97
1.46
e 13 (cm 2 )
−0.49
−0.57
−0.60
c 13 (GPa)
10.8
92
12
c 33 (GPa)
39.9
224
39.5
a 0 (nm)
3.189
3.545
3.11
where e 31 and e 33 are piezoelectric constants and ε z is the in-plane strain which can
be calculated by using formula
ε z = (c − c 0 )/c 0
(5.4)
where c is the in-plane lattice constant of nitride, and c 0 is the lattice constant after
relaxation.
Lattice constants of wurtzite group III-V nitrides have the following relationship:
c − c 0
c 0
= −2
c 13
c 33
a − a 0
a 0
(5.5)
where c 13 and c 33 are elastic coefficients.
P pe = 2
a − a 0
a 0
e 31 − e 33
c 13
c 33
(5.6)
According to the theoretical calculation results of Fiorentini et al. [7], the relationship between piezoelectric polarization intensity and components of multicomponent
nitrides can be expressed as follows:
P pz
Al x I n y Ga 1−x−y N
= P pz (Al N )x + P pz (Al N )x + P pz (I nN )y
+ P pz (Ga N )(1 − x − y)
(5.7)
where
P pz (Al N ) = −1.808ε + 5.624ε
2
, when ε < 0,
(5.8)
P pz (Al N ) = −1.808ε − 7.888ε
2
, when ε > 0,
(5.9)
P pz (Ga N ) = −0.918ε + 9.541ε
2
(5.10)