5.4 Properties of Electrodeposited CMAs
159
Besides the merging of the diffraction lines, the secondary periodicity of the
multilayer gives rise to new lines around the major diffraction peaks, which are
called satellite peaks. The primary periodicity is related to the distance between the
atomic planes, while the secondary periodicity is due to the composition modulation
and the concomitant, though small, lattice plane distance variation from one layer
to the other. The satellite peak positions are related to the modulation wavelength of
the multilayer (Λ) in accord with the formula below:
Λ =
λ
sin Θ i,+1 − sin Θ i,−1
(5.3)
where λ is the wavelength of the X-ray used for the diffraction experiment, i is the
order of the reflection and Θ is the angle at which the satellite peak maximum is
observed. The two terms in the denominator of Eq. 5.3 refer to nearly symmetric
peaks at higher and lower diffraction angles around the major diffraction line. For
more details, see, e.g., Sect. 4.2 of Ref. [6]. The observation of the satellite peaks
around the major diffraction line is a key tool for the assessment of the multilayer
periodicity Λ with a non-destructive method for multilayers with Λ < 10 nm. A few
examples for such satellite peak observations for electrodeposited multilayers are
shown in Fig. 5.9. It has to be noted that satellite peaks can be observed for highquality multilayers only where stacking and, consequently, the X-ray scattering of
the layers are both coherent. Multilayers either deposited on a rough substrate or
having a high undulation do not show satellite peaks.
It is commonly found that the periodicity as calculated from the satellite peak
positions of the electrodeposited multilayers is either overestimated with respect
to the nominal periodicity or it is significantly larger than that established with
another method (e.g., EQCM weight change [100]). The explanation lies in the grain
structure of the deposit. The local deposit thickness at the centre of the grains is
the largest, while the growth near the grain boundary is retarded, as it is shown in
Fig. 5.10. This results in a grain boundary grooving [101], which is peculiar for
electrodeposited samples and does not occur for physically deposited ones (either
sputtered or evaporated). Since the satellite reflection can originate only from areas
where the layers are parallel to the substrate, the overestimation of the mean layer
thickness calculated for the entire deposit can be easily understood.
Figure 5.10 also indicates the common observation that the roughness developing
during the growth of multilayer with small layer thicknesses is cumulative. This
means that within a grain, the deviation from the planar layer growth is the higher,
the larger the distance from the substrate (faceting).
When the lateral diameter of grains is large, the multilayer growth is heteroepitaxial and the bilayer thickness is below 10 nm, the multilayer structure imposes a
significant alternating stress field, which tends to relax at large sample thicknesses.
One means of reducing the total mechanical energy of the system is that the composition modulation fronts will be inclined to the plane of the substrate, as it was shown
in Fig. 5.10. This layer plane canting can be observed in the cross-sectional TEM
159
Besides the merging of the diffraction lines, the secondary periodicity of the
multilayer gives rise to new lines around the major diffraction peaks, which are
called satellite peaks. The primary periodicity is related to the distance between the
atomic planes, while the secondary periodicity is due to the composition modulation
and the concomitant, though small, lattice plane distance variation from one layer
to the other. The satellite peak positions are related to the modulation wavelength of
the multilayer (Λ) in accord with the formula below:
Λ =
λ
sin Θ i,+1 − sin Θ i,−1
(5.3)
where λ is the wavelength of the X-ray used for the diffraction experiment, i is the
order of the reflection and Θ is the angle at which the satellite peak maximum is
observed. The two terms in the denominator of Eq. 5.3 refer to nearly symmetric
peaks at higher and lower diffraction angles around the major diffraction line. For
more details, see, e.g., Sect. 4.2 of Ref. [6]. The observation of the satellite peaks
around the major diffraction line is a key tool for the assessment of the multilayer
periodicity Λ with a non-destructive method for multilayers with Λ < 10 nm. A few
examples for such satellite peak observations for electrodeposited multilayers are
shown in Fig. 5.9. It has to be noted that satellite peaks can be observed for highquality multilayers only where stacking and, consequently, the X-ray scattering of
the layers are both coherent. Multilayers either deposited on a rough substrate or
having a high undulation do not show satellite peaks.
It is commonly found that the periodicity as calculated from the satellite peak
positions of the electrodeposited multilayers is either overestimated with respect
to the nominal periodicity or it is significantly larger than that established with
another method (e.g., EQCM weight change [100]). The explanation lies in the grain
structure of the deposit. The local deposit thickness at the centre of the grains is
the largest, while the growth near the grain boundary is retarded, as it is shown in
Fig. 5.10. This results in a grain boundary grooving [101], which is peculiar for
electrodeposited samples and does not occur for physically deposited ones (either
sputtered or evaporated). Since the satellite reflection can originate only from areas
where the layers are parallel to the substrate, the overestimation of the mean layer
thickness calculated for the entire deposit can be easily understood.
Figure 5.10 also indicates the common observation that the roughness developing
during the growth of multilayer with small layer thicknesses is cumulative. This
means that within a grain, the deviation from the planar layer growth is the higher,
the larger the distance from the substrate (faceting).
When the lateral diameter of grains is large, the multilayer growth is heteroepitaxial and the bilayer thickness is below 10 nm, the multilayer structure imposes a
significant alternating stress field, which tends to relax at large sample thicknesses.
One means of reducing the total mechanical energy of the system is that the composition modulation fronts will be inclined to the plane of the substrate, as it was shown
in Fig. 5.10. This layer plane canting can be observed in the cross-sectional TEM