Here the theory described in the last section is used to calculate the pre-logarithmic coefficient K for dislocations in AlN, GaN and InN bulk. The procedure has been introduced by Holec [24] to evaluate the dislocation configuration in GaN bulk.
Three different types of dislocations are present in hexagonal structures: c-type
dislocation with Burgers vector b = , a-type with Burgers vector b = 1∕3
, and
(a + c)-type with Burgers vector b = 1∕3
. The coefficients K of these three types of
dislocations are calculated for different directions of the dislocation line using the Steeds
treatment [72]. This is done by rotating the elastic tensor according to the direction line.
The calculations are performed numerically using the software Wolfram Mathematica.
Hexagonal symmetry requires two angles, α and β, for the description of the direction
of the dislocation line (see Figure. 3.4). As a consequence, the pre-logarithmic
coefficient for one particular direction of the dislocation line is a function of the two
angles α and β. The coefficients are shown in Figure 3.5 for AlN, GaN, and InN.
Figure 3.4: | In the hexagonal (and more generally, in non-isotropic crystal) two angles, α and β, are needed for description of the dislocation line direction. |
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Figure 3.5: | Pre-logarithmic coefficient K calculated as a function of the angles α and
β for c-type dislocations (Burgers vector b = ![]() ![]() ![]() |