Ferromagnetic (Ga,Mn)As Layers and ... - OPUS Würzburg

3.5. X-Ray Diffraction 35
1 0 7
1 0 6
G a A s
1 0 5
(G a ,M n )A s
In te n s ity [a .u .]
1 0 4
1 0 3
1 0 2
1 0 1
1 0 0
1 0 -1
3 2 .6 3 2 .8 3 3 .0 3 3 .2 3 3 .4
O m e g a [d e g .]
Figure 3.7: ω-2Θ scan of the (004) reflection of a 175 nm (Ga,Mn)As (6.3% Mn) layer on
GaAs.
sample with an incidence angle ω i relative to the lattice plains of spacing d in the
sample. According to the law of reflection, the exit angle ω e is equal to ω i . The total
angle between the incident beam and the detector is twice the incidence angle, and is
commonly referred to as 2Θ. If the incidence angle equals the Bragg angle Θ B , the
path difference for parallel x-rays diffracted in the sample is an integer multiple n of
the wavelength λ (1.5405929 Å for Cu K α ). For this case, constructive interference
between x-rays diffracted at different lattice planes is observed. This condition for
constructive interference is called the Bragg condition:
3.5.1 ω-2Θ Scans
2d sin Θ B = nλ. (3.2)
In a sample with multiple layers, an ω-2Θ scan (varying both the incident, as well as
the detector angle) over a range encompassing the Bragg angle for every layer, yields
a high intensity peak according to each lattice constant. Fig. 3.7 shows an ω-2Θ scan
of the (004) reflection of a (Ga,Mn)As layer on GaAs.
The (004) lattice planes are aligned parallel to the sample surface. The spacing of
the lattice planes d 004 is equal to 1/4 of the lattice constant, according to:
d hkl =
d 001
√
h2 + k 2 + l 2 (3.3)
A reflection is called symmetric, when the diffracting lattice plains are parallel to the
sample surface. Symmetric reflections contain only information about the vertical