5.2 Polarization Effects in InGaN/GaN Multiple Quantum Wells Materials
79
P
sp
I n x Ga 1−x N = −0.042x − 0.034(1 − x) + 0.037x(1 − x)
(5.1)
P
S P
Al x Ga 1−x N = 0.09x − 0.034(1 − x) + 0.019x(1 − x)
(5.2)
When the Group III nitride undergoes lattice distortion from biaxial stress from the
outside, piezoelectric polarization effects are also produced in the material [8–11].
In the nitride crystal of the Ga polar plane, when the epitaxial material is subjected
to biaxial tensile stress, the bond angle θ between the metal cation and the three
nitrogen atoms becomes large in the structural unit cell of the material, in which
P 1 > P 2 exists in the entire structural units because the resultant polarization vector P 2
between the metal cation and the three nitrogen atoms gets smaller, thereby generating
a piezoelectric polarization along [000-1] direction in the material. When the material
is subjected to biaxial compressive stress, the bond angle θ becomes smaller so that
the resultant polarization vector P 2 increases. In this case, P 1 < P 2 , a piezoelectric
polarization along the [0001] direction is generated in the material. The magnitude
of the piezoelectric polarization in the nitride material can be calculated from the
piezoelectric coefficient and the strain of the material. In nitrides, the heterojunction
materials composed of GaN, InN, and AlN or their alloy materials have a certain
stress due to their different lattice constants, and piezoelectric polarization occurs in
the material [12].
In 2002, Bernardini et al. [7] proposed a nonlinear polarization model of III-nitride
materials through experimental tests and theoretical simulations. In the nonlinear
polarization model, the polarization surface charge density at the heterojunction
interface is a second order function of the material composition. Later, Yu et al.
[13] studied the correctness and validity of the nonlinear polarization model. In
InGaN/GaN quantum wells, the polarization effect causes spatial separation of the
wave functions of electrons and holes in the quantum well, reducing the luminous
efficiency of the quantum well. The strongly polarized electric field also causes the
LED emission wavelength to red-shift.
The macroscopic polarization is strong in the wurtzite nitride heterostructure. The
polarization includes (1) piezoelectric polarization caused by lattice mismatch strain
and (2) spontaneous polarization caused by charge accumulation at the heterojunction
interface. In a typical nitride heterostructure grown along (0001) plane, there is a large
piezoelectric polarization due to the large piezoelectric constant (see Table 5.1).
Piezoelectric polarization causes an internal electric field to be generated in the
[0001] growth direction.
Piezoelectric polarization is caused by lattice mismatch between heterojunctions.
For nitride materials, when the material is grown along the [0001] direction and the
material is subjected to biaxial stress, its piezoelectric polarization can be expressed
as:
P pz = 2
e 33 ε z + e 31
ε x + ε y
(5.3)
79
P
sp
I n x Ga 1−x N = −0.042x − 0.034(1 − x) + 0.037x(1 − x)
(5.1)
P
S P
Al x Ga 1−x N = 0.09x − 0.034(1 − x) + 0.019x(1 − x)
(5.2)
When the Group III nitride undergoes lattice distortion from biaxial stress from the
outside, piezoelectric polarization effects are also produced in the material [8–11].
In the nitride crystal of the Ga polar plane, when the epitaxial material is subjected
to biaxial tensile stress, the bond angle θ between the metal cation and the three
nitrogen atoms becomes large in the structural unit cell of the material, in which
P 1 > P 2 exists in the entire structural units because the resultant polarization vector P 2
between the metal cation and the three nitrogen atoms gets smaller, thereby generating
a piezoelectric polarization along [000-1] direction in the material. When the material
is subjected to biaxial compressive stress, the bond angle θ becomes smaller so that
the resultant polarization vector P 2 increases. In this case, P 1 < P 2 , a piezoelectric
polarization along the [0001] direction is generated in the material. The magnitude
of the piezoelectric polarization in the nitride material can be calculated from the
piezoelectric coefficient and the strain of the material. In nitrides, the heterojunction
materials composed of GaN, InN, and AlN or their alloy materials have a certain
stress due to their different lattice constants, and piezoelectric polarization occurs in
the material [12].
In 2002, Bernardini et al. [7] proposed a nonlinear polarization model of III-nitride
materials through experimental tests and theoretical simulations. In the nonlinear
polarization model, the polarization surface charge density at the heterojunction
interface is a second order function of the material composition. Later, Yu et al.
[13] studied the correctness and validity of the nonlinear polarization model. In
InGaN/GaN quantum wells, the polarization effect causes spatial separation of the
wave functions of electrons and holes in the quantum well, reducing the luminous
efficiency of the quantum well. The strongly polarized electric field also causes the
LED emission wavelength to red-shift.
The macroscopic polarization is strong in the wurtzite nitride heterostructure. The
polarization includes (1) piezoelectric polarization caused by lattice mismatch strain
and (2) spontaneous polarization caused by charge accumulation at the heterojunction
interface. In a typical nitride heterostructure grown along (0001) plane, there is a large
piezoelectric polarization due to the large piezoelectric constant (see Table 5.1).
Piezoelectric polarization causes an internal electric field to be generated in the
[0001] growth direction.
Piezoelectric polarization is caused by lattice mismatch between heterojunctions.
For nitride materials, when the material is grown along the [0001] direction and the
material is subjected to biaxial stress, its piezoelectric polarization can be expressed
as:
P pz = 2
e 33 ε z + e 31
ε x + ε y
(5.3)