3.5  Pre-logarithmic coefficients

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.

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(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 = ) in AlN , in GaN , in InN , for a-type dislocations (Burgers vector b = 1∕3) in AlN , in GaN , in InN , for (a + c) -type dislocations (Burgers vector b = 1∕3) in AlN , in GaN , in InN .