20
3 Properties and Testing of Group III-Nitride LED Materials
12 atoms, of which 6 are Ga atoms and 6 are N atoms. The wurtzite structure is
a thermodynamically stable structure of the nitride semiconductor material. It has
two lattice constants, an in-plane lattice constant and an out-plane lattice constant
c. The hexagonal system usually uses a four-axis coordinate system to describe the
crystal orientation and crystal plane of the crystal lattice. On the bottom surface,
the three axes a 1 , a 2 , and a 3 form an angle of 120° with each other, and the unit
of measurement is a lattice constant of a. The c-axis is perpendicular to the bottom
surface, and the unit of measurement is the lattice constant c. The crystal orientation
and the crystal plane are expressed as [uvtw] and (hkil), respectively, and there are
only three independent parameters in the four coordinates, satisfying u + v = −t
and h + k = −i, and sometimes the third coordinate can be omitted and expressed
as [uvw] and (hkl).
Both structures of the nitride semiconductor are bonded to four N atoms or Group
III atoms nearest to each other to form a tetrahedral structure. The difference is in
the stacking order. The stacking order of wurtzite along the c-axis <0001> direction is ABABAB…, and the stacking order of sphalerite in the <111> direction
is ABCABC…. The physical properties of the materials with two different crystal
structure are also very different, as shown in Table 3.1. Due to the difficulty in
material preparation and the quality of the crystal, the wurtzite structure of nitride
semiconductor is the mostly investigated and widely used. The material properties
and devices involved in this book are based on this structure.
The wurtzite structure GaN, AlN, InN compound semiconductors can be alloyed
with each other to form a solid solution in different proportions. In this case, the lattice
structure is unchanged, but the lattice parameters change with the composition. Their
alloys can be expressed as Al x In y Ga 1-x-y N (0 < x + y < 1), where x and y are the
contents of Al and In, respectively. The lattice constant of an alloy can be calculated
by the following formula:
Table 3.1 Structural parameters of GaN material (300 K)
Wurtzite structure
Sphalerite structure
Lattice constant (nm)
a = 0.3189 c = 0.5185 [2]
a = 0.452
Band gap (eV)
3.39 [3]
3.2
Effective mass of electron (m 0 )
0.20
0.13
Effective DOS of the conductive band
Nc/cm −3
2.3 × 10 18
1.2 × 10 18
Effective DOS of the valence band
Nv/cm −3
4.6 × 10 19
4.1 × 10 19
Refractive index
2.67
2.5
Dielectric constant
ε r = 8.9 ε ∞ = 5.35
5.3
Coefficient of the thermal expansion
(10 −6 K −1 )
a a = 5.59 a c = 3.17
–
Note m 0 is the resting mass of electron
3 Properties and Testing of Group III-Nitride LED Materials
12 atoms, of which 6 are Ga atoms and 6 are N atoms. The wurtzite structure is
a thermodynamically stable structure of the nitride semiconductor material. It has
two lattice constants, an in-plane lattice constant and an out-plane lattice constant
c. The hexagonal system usually uses a four-axis coordinate system to describe the
crystal orientation and crystal plane of the crystal lattice. On the bottom surface,
the three axes a 1 , a 2 , and a 3 form an angle of 120° with each other, and the unit
of measurement is a lattice constant of a. The c-axis is perpendicular to the bottom
surface, and the unit of measurement is the lattice constant c. The crystal orientation
and the crystal plane are expressed as [uvtw] and (hkil), respectively, and there are
only three independent parameters in the four coordinates, satisfying u + v = −t
and h + k = −i, and sometimes the third coordinate can be omitted and expressed
as [uvw] and (hkl).
Both structures of the nitride semiconductor are bonded to four N atoms or Group
III atoms nearest to each other to form a tetrahedral structure. The difference is in
the stacking order. The stacking order of wurtzite along the c-axis <0001> direction is ABABAB…, and the stacking order of sphalerite in the <111> direction
is ABCABC…. The physical properties of the materials with two different crystal
structure are also very different, as shown in Table 3.1. Due to the difficulty in
material preparation and the quality of the crystal, the wurtzite structure of nitride
semiconductor is the mostly investigated and widely used. The material properties
and devices involved in this book are based on this structure.
The wurtzite structure GaN, AlN, InN compound semiconductors can be alloyed
with each other to form a solid solution in different proportions. In this case, the lattice
structure is unchanged, but the lattice parameters change with the composition. Their
alloys can be expressed as Al x In y Ga 1-x-y N (0 < x + y < 1), where x and y are the
contents of Al and In, respectively. The lattice constant of an alloy can be calculated
by the following formula:
Table 3.1 Structural parameters of GaN material (300 K)
Wurtzite structure
Sphalerite structure
Lattice constant (nm)
a = 0.3189 c = 0.5185 [2]
a = 0.452
Band gap (eV)
3.39 [3]
3.2
Effective mass of electron (m 0 )
0.20
0.13
Effective DOS of the conductive band
Nc/cm −3
2.3 × 10 18
1.2 × 10 18
Effective DOS of the valence band
Nv/cm −3
4.6 × 10 19
4.1 × 10 19
Refractive index
2.67
2.5
Dielectric constant
ε r = 8.9 ε ∞ = 5.35
5.3
Coefficient of the thermal expansion
(10 −6 K −1 )
a a = 5.59 a c = 3.17
–
Note m 0 is the resting mass of electron