Analysis of the extended defects in 3C-SiC.pdf - Nelson Mandela ...

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associated displacement field of the stacking fault to obtain a line intensity profile of
the fringes.
As discussed in Section 2.6 stacking faults are produced by a disruption of the regular
stacking sequence of a material. It can also be seen as two regions of the crystal
having been shifted relative to one another by a distance given by a displacement
vector R which may be a non-lattice translation as shown by Fig. 4.4. The
displacement vector has a component parallel to the fault plane R|| and normal to it
R . Thus the presence of this fault will introduce a phase shift α = 2πg·R which
modifies the solution to the DHW equations for the bottom section (section II) of the
crystal. If α is an integer multiple of π no defect contrast will be seen which shows
that R is a lattice translation vector and effectively no modification of the solutions to
the DHW equations result. If R is a non-lattice translation, α is not an integer multiple
of π and image contrast of the form of alternating light and dark fringes will be
formed.
Fig. 4.4. (a) Schematic illustration of a planar defect separating crystal sections I
and II; (b) inclined planar defect combined with the column approximation (from De
Graef (2003))
To simulate such an intensity profile the following procedure is used. Consider a
crystal with thickness z0 containing a stacking fault as shown in Fig. 4.4 (b). Region 1
has been shifted with respect to region II by a vector R. The top section of the crystal
(region 1) is defect free and is described by a scattering matrix Sscat(s1.z1) where z1 is
the distance from the top surface to the fault. The bottom section is shifted with
respect to the top and is described by a different scattering matrix M(s2.z2) since it lies
in a different orientation with respect to the top. The two scattering matrices are as
follows,