.
For our calculations of the critical thickness hc according to the Matthews-Blakeslee model, we make use of the equations given in [8] and, for the Peierls force, in [9].
The force Fmisfit due to the misfit is given as
|
.
| (2) |
GInGaN is the bulk modulus and 
is Poisson's number of the
InGaN layer, respectively. f is the misfit at the InGaN/GaN interface,
b is the length of the Burgers vector, and l is the length of the
threading segment in the heteroepitaxial layer. The Schmid factor S is
dependent on the angle 
between the Burgers vector and a
vector i, and on the angle 
between the normal of the
slip plane and the vector i. The vector i lies in the
interfacial plane, perpendicular to the line of intersection of the interfacial
plane and the slip plane.
The force Fline tension due to the line tension of the misfit segment is given as
 .
| (3) |
GGaN is the bulk modulus of the thick GaN layer, serving as a
substrate. h represents the thickness of the InGaN layer, and 
is the angle between the Burgers vector and the line direction of the misfit
segment.
The Peierls force FPeierls is given as
 .
| (4) |
d is the spacing of the slip plane and 
the angle between the
Burgers vector and the line direction of the threading segment. 
is
a material constant given as
 .
| (5) |
The number of atoms per unit cell is represented by n, the volume of the unit cell by V. T is the growth temperature of the InGaN layer in absolute degrees, k is Boltzmann's constant.
For the calculations, we neglect differences between the bulk moduli of the InGaN layer and GaN layer and use a value of 200 GPa for both, and take Poisson's number for InGaN as 0.6 [11].
© 1998 The Materials Research Society
