Supplementary material: Atom insertion into grain boundaries and
stress generation in physically vapor deposited films
D. Magnfält1,a, G. Abadias2, and K. Sarakinos1
1Plasma
and Coatings Physics Division, IFM-Material Physics, Linköping University, SE-58183,
Linköping, Sweden
2Institut
P’, Département Physique et Mécanique des Matériaux, Université de Poitiers-CNRS-
ENSMA, SP2MI, Téléport 2, Bd M. et P. Curie, F-86962 Chasseneuil-Futuroscope, France
Mass spectrometry
The electrostatic lenses of the mass spectrometer (PSM003, Hiden Ltd.) were tuned
to maximize the measured flux of each specie. The most abundant isotopes were
chosen for all species (Mo+ m/q = 97.9, Mo2+ m/q = 48.95 and Ar2+ m/q = 20) except
for Ar+ where 36Ar measured in order not to saturate the detector. The transfer
functions at different mass-to-charge-ratios vary even though the spectrometer has
been tuned for each mass making comparisons between ion fluxes qualitative. The
transfer function of the spectrometer also varies with ion energy due to an energy
dependence of the acceptance angle. The result is that the measured flux of low
energy ions is being exaggerated compared to the flux of high energy ions.
X-ray reflectrometry
X-ray reflectrometry measurements were performed on films with a thicknesses
between 50 and 100 nm in a four-circle diffractometer (Panalytical) equipped with
four-crystal monochromator and triple axis analyzer using Cu K-radiation (1.5406 Å).
The data was analyzed and fitted in the X’pert Reflectivity software (Panalytical). The
recorded data and best fits for samples with a thickness of approximately 50 nm are
shown in figure S1.
Figure S1: XRR data (cirles) and best fits (lines) for the different deposition conditions
X-ray diffraction
X-ray diffraction measurements in the Bragg-Brentano geometry was performed on
approximately 150 nm thick films in a four-circle diffractometer (Panalytical) equipped
with a hybrid monochromator and a parallel plate collimator. The scan range 35-135
degrees with a step size of 0.2 degrees was chosen. Figure S2, show that the films
have a 110 out-of-plane alignment.
Figure S2: XRD data for samples deposited at different peak powers (indicated on the right
hand side). Relevant Mo Bragg reflections are indicated by arrows.
Pole figures for 110, 200 and 211 reflections were measured in the four-circle
diffractometer equipped with an x-ray lens, a parallel plate collimator and a Ni-filter to
absorb the CuK-radiation. Pole figures of the 110-pole for the samples deposited at
peak target powers of 152.9 and 4.5 kW are shown in figure S4 a) and S4 b)
respectively.
Figure S3: Pole figures of the Mo 110-pole showing a) a slight in-plane alignment for a peak
power of 152.9 kW and b) random in-plane alignment for a peak power of 4.5 kW.
The diffraction experiments show that the films have a (110)-out-of-plane orientation
and a slight in-plane orientation, most likely due to the deposition geometry as the
cathode is mounted 40 degrees off the substrate normal [1].
XRD stress measurements
The film strain/stress state was determined using the sin2-method in a four circle
diffractometer (Siefert) equipped with 1x1 mm 2 collimator and a Ni-filter to absorb the
CuK-radiation. The sin2–method uses the lattice spacing dhkl of (hkl) planes as a
strain gauge. The measured lattice strain is 𝜀𝜓,𝜙 = (𝑎𝜓,𝜙 − 𝑎0 )⁄𝑎0 along the (,)
direction where  is the angle between the surface normal and the (hkl) plane
normal,  is the azimuthal angle, a, is the lattice parameter for a given {hkl}
reflection and a0 is the stress-free lattice parameter. The strain for a (110) oriented
cubic material can be described assuming an equi-biaxial stress state biax,
𝐽
𝜀𝜓,𝜙 = 𝜎𝑏𝑖𝑎𝑥 (2𝑠12 + 2 + (
𝑠44
2
𝐽
+ 2 𝑠𝑖𝑛2 𝜙) 𝑠𝑖𝑛2 𝜓), where J= s11-s12-s44/2 is an anisotropy
factor and sij are the components of the compliance tensor. Measurement results of
the lattice parameter as a function of sin2 for samples deposited with peak powers
of 152.9 kW and 4.5 kW are shown in figure S5.
Figure S4: Evolution of the lattice parameter with sin2 for samples deposited with peak
powers of 4.5 kW and 152.9 kW (lines are guides to the eye only).
Atomic force microscopy
The surface morphology of the films was imaged by atomic force microscopy (AFM)
performed in a Vecco Dimension 3100 instrument (Vecco Instruments Inc.). The
differences in surface morphology of samples deposited with peak powers 152.9 kW
and 4.5 kW are shown in fig. S6 a) and b) respectively. The grain radii were
determined using a watershed algorithm in Gwyddion [2] to detect grains, find their
area and from that approximate the in-plane grain radius assuming circular grains.
Figure S5: The surface topography of the samples deposited with peak powers of a) 152.9
kW and b) 4.5 kW.
References
[1] S. Mahieu, P. Ghekiere, D. Depla and R. De Gryse, Thin Solid Films 515, 1229
(2006)
[2] D. Necas, and Petr Klapetek, Cent. Eur. J. Phys. 10, 181 (2012).