1
Supplementary material
In situ study of the endotaxial growth of hexagonal CoSi2
nanoplatelets in Si(001)
Daniel da Silva Costa1,Cristián Huck-Iriart2, Guinther Kellermann1, Lisandro J.
Giovanetti2, Aldo F. Craievich3, and Félix G. Requejo2
1 - Departamento de Física, Universidade Federal do Paraná, Caixa Postal 19044,
Curitiba, Paraná 81531-990, Brazil.
2 - Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA,
CONICET, Departamento de Química, Facultad de Ciencias Exactas, Universidad
Nacional de La Plata), CC/16 suc. 4, 1900 La Plata, Argentina.
3 - Instituto de Física, Universidade de São Paulo, CP 66318, CEP 05315-970, São
Paulo, Brazil.
MATERIALS AND METHODS
A. Sample preparation
The nanostructured material studied here consists of a SiO2 thin film containing dispersed
Co atoms deposited on Si (100) wafer. A rectangular and flat Si(001) wafer about 2 cm long
and 1 cm wide was used as substrate after being cleaned and dried under N2.
The silica thin film was prepared by the sol-gel process. The precursor solution is composed
of 11 µmol/g of Co nitrate and 240 µmol/g of TEOS in isopropanol. The pH of the solution
was controlled by adding HCl in order to maintain it between 2 and 3. A volume of 8 µl of
solution was deposited on the Si(001) substrate and dried during 1h at room temperature and
10 min at 100 °C. The dry sample was then held during 15 min at 500 °C and submitted to a
H2 flux of 500 sccm for reduction of Co oxide 9.
The structural transformations occurring in the studied sample - a Si wafer on which a Codoped SiO2 thin film was deposited - were investigated at the nanometer scale by in situ
GISAXS with the sample subjected to an isothermal treatment at 700 oC.
1
2
B. GISAXS setup and high temperature chamber
In situ GISAXS measurements were conducted by placing the sample inside a high
temperature chamber operating under He flux of 50 sccm. During the heating period the sample
was kept inside a pre-chamber connected to the main chamber where the isothermal treatment
at 700 ºC takes place. The main chamber for GISAXS measurements has two Kapton®
windows for the entrance of the primary monochromatic X-ray beam and exit of the scattered
photons at small and wide angles.
The high temperature chamber was mounted on a four axes Huber diffractometer at the
XRD2 beam line of the Brazilian Synchrotron Light Laboratory (LNLS), Brazil, which allows
for precise sample alignment. The X-ray wavelength was  = 0.1612 nm and the sample-todetector distance was 369 mm. The incidence angle αi was kept equal to 0.3° in order to
maximize the scattering intensity. The relevant angles and basic geometry of GISAXS
experiments are shown in Fig. S1.
A 2D Pilatus (PILATUS 100K) detector was used for recording the scattered photons. In
order to account for the continuous decrease of the intensity of the synchrotron source, a
scintillation detector was employed for continuous monitoring of the primary beam. GISAXS
patterns were recorded every 2 min during thermal treatment at 700 ºC, over a total period of
~ 180 min. Since the cross-section of the primary X-ray beam and the pixel size of the Pilatus
detector were both small enough, the obtained GISAXS patterns were assumed to be free from
significant geometrical smearing effects.
FIG. S1. Schematic description of the GISAXS setup.
2
3
C. GISAXS data analysis
The left column of Figure 1 displays 2D GISAXS patterns associated to the studied sample
submitted to an isothermal annealing during increasing periods of time at 700 ºC, after
subtracting the parasitic scattering produced by slits. GISAXS patterns shown in Figure 1a,
corresponding to 8 min of isothermal treatment, only exhibits an essentially isotropic scattering
intensity extending up to rather high q values.
GISAXS patterns corresponding to longer periods of time (Figures 1c, 1e, 1g and 1i)
evidence the additional presence of two streaks pointing along directions making an angle equal
to 54.3 degrees with respect to Si[001] crystallographic direction. As described in a previous
work 9, these streaks are the expected scattering effect produced by thin CoSi2 nanoplatelets
endotaxially hosted in the Si substrate with their main surfaces parallel to Si{111}
crystallographic planes. The phase and crystallographic structure of CoSi2 nanoplatelets was
carefully determined in Ref. [9] by XEDS (x-ray energy dispersive spectroscopy) and highresolution TEM experiments. Considering the Co:Si ratio and twined interface between the
Si:CoSi2 phases, it was possible to establish that the nanoplatelets phase was CoSi2 with a cubic
CaF2- like structure.
Notice that in order to record the streaks produced by the CoSi2 nanoplatelets in the detector
plane, the azimuthal angle  should be properly selected. Looking at the GISAXS patterns
shown in Figure 1 (left column) for increasing periods of time, we could verify that the streaks
associated to the endotaxial growth of CoSi2 nanoplatelets in Si(001) progressively become
relatively more intense and better defined. Asymmetry between the left and right streaks in the
GISAXS patterns shown in Figure 1 is due to a small deviation of the Si[110] direction (~ 3 o)
with respect to the direction corresponding to the projection of primary beam on the sample
surface 9.
In order to derive quantitative information about the time dependences of density number
and sizes of Co nanoparticles and CoSi2 nanoplatelets, we have proposed a structural model
that assumes the simultaneous transformations related to (i) a dilute set of spherical Co
nanoparticles embedded in the SiO2 thin film and (ii) an also dilute set of hexagonal thin
nanoplatelets endotaxially grown inside the Si(001) substrate having all of them their large flat
surface parallel to one of the four planes of the Si{111} crystallographic form. In this model
we also assumed that the spherical Co nanoparticles exhibit a radius distribution and all
hexagonal CoSi2 nanoplatelets are of equal sizes.
3
4
Taking into account the effects of refraction of primary and scattered beams our data
analysis was performed according the (Distorted Wave Born approximation) distorted wave
Born approximation (DWBA)25-27. In this approximation and considering the reasonable
assumption that the Co nanoparticles embedded in the SiO2 film and the CoSi2 nanoplatelets
are spatially located at random, i.e. without spatial correlation, the 2D GISAXS patterns can
be written as9
2
2
2
𝐼 ∝ |𝑡(𝛼𝑖 )|2 |𝑡(𝛼𝑓 )| (𝑁ℎ𝑒𝑥 ∆𝜌ℎ𝑒𝑥
∑|𝐴ℎ𝑒𝑥(ℎ𝑘𝑙) (𝛼, 𝜙, 𝑞𝑥 , 𝑞𝑦 , 𝑞̃,
𝑧, 𝐿, 𝑇)| +
ℎ𝑘𝑙
2
2
+ Δ𝜌𝑠𝑝ℎ
∫|𝐴𝑠𝑝ℎ (𝑞𝑥 , 𝑞𝑦 , 𝑞̃,
𝑧, 𝑅)| 𝑁𝑠𝑝ℎ (𝑅)𝑑𝑅),
(1-SM)
where αi an αf are the incidence and exit angles of the primary and scattered beams,
respectively, with respect to the external surface of the Si(001) wafer, Nhex and Nsph(R) the
number density of the CoSi2 nanoplatelets and the radius distribution of the spherical Co
nanoparticles, respectively,
~ , R) the
Asph (qx , q y , q
z
scattering amplitude of a spherical particle
with a radius R and Ahex ( hkl ) ( ,  , q x , q y , q~z , L, T ) the scattering amplitude of a regular hexagon
with thickness T and lateral side L,  the azimuthal angle, qx and qy the components of the
scattering vector in x and y directions, respectively, and q~z the component of the scattering
vector in z direction inside the sample. t ( i ) and t ( f ) are the effective Fresnel transmission
coefficients of the primary and scattered beams, respectively. Notice that because of the small
difference of refractive indexes of SiO2 and Si, only the refraction due air/SiO2 interface was
accounted for in our model. Two Gaussian functions were used to describe the radius distribution of
the set of Co nanospheres embedded in the SiO2 film. Since in previous ex situ GISAXS and TEM
experiments it was established that the size dispersion of CoSi2 platelets is very narrow 9,10, in our
present modeling of GISAXS patterns we have assumed that, at any time of isothermal annealing, all
CoSi2 nanohexagons have same lateral size and thickness.
On the other hand, for a diluted and isotropic set of homogeneous particles embedded
in an also homogeneous matrix, the total particle volume, V, is proportional to the integral of
SAXS intensity in reciprocal space, Q, i.e. 35:
∞
𝑉 ∝ 𝑄 = 4𝜋 ∫0 𝐼(𝑞) 𝑞 2 𝑑𝑞.
4
(2-SM)
5
Since the X-ray scattering intensity was not measured in absolute units, the integral of SAXS
intensity due Co nanospheres and thus their volume fraction Vsph, can only be determined in
relative scale.
Fittings of the theoretical scattering intensity to the 2D experimental GISAXS patterns are
often performed for a number of 1D profiles corresponding to different qz values (i.e. different
exit angles) 1-S,2-S. In this work we have developed a new routine for full-pattern fitting, which
uses the experimental counting rates corresponding to all accessible pixels. This procedure
increases data sampling thus improving the statistic quality. The code was written in python
2.7 along with Scipy, Numpy and matplotlib libraries. A non-linear least square method
(NLLS) was employed to optimize the agreement between the simulated model and
experimental data. A more detailed description of the fitting routine is given in the next section.
D. Description of routine for full-pattern fitting
In order to find the values of the selected parametric function, the functional chi-square to
be minimized is defined as:
1
𝜒 2 = 𝑁 ∑𝑖,𝑗
(𝑃𝑖,𝑗 −𝑓𝑖,𝑗 )2
2
𝜎𝑖,𝑗
,
(3-SM)
where the Pi,j values are the experimental intensities and fi,j the modeled function corresponding
to pixels i, j. The use of a cubic interpolation as smoothing routine gives rise to the statistical
uncertainties σi,j. Each pixel of a GISAXS pattern contains information associated to reciprocal
coordinates qx, qy, qz. As the number of pixels (~105) is considerably higher than the number
of parameters of the modeled function, the functional chi-square was normalized by the total
number of pixels (N).
It is known that different fitting methods are more or less susceptible to local minima than
others 3-S. Since NLLS algorithm required a good initial guess, we have developed a numerical
method based in a Gaussian-random search of non-linear parameters. The modeled function
can be written as the sum of 𝜑𝑘 functions:
𝑓(𝜐𝐿 , 𝜐𝑁𝐿 ) = ∑ 𝜐𝐿 𝜑𝑘 ( 𝜐𝑁𝐿 ),
(4-SM)
where 𝜐𝐿 and 𝜐𝑁𝐿 are linear and non-linear parameters, respectively. In our method, the nonlinear parameters are randomly perturbed with a Gaussian probability around the minimum
found so far. At each step, the linear parameters are automatically adjusted using a non5
6
negative linear least square algorithm and the normalized 𝜒 2 - chi-square functional - is
computed and compared to the value of the previous step. At the starting point, the variance of
the Gaussian distribution is high enough to explore all the range of interest. During the course
of the minimization algorithm, the Gaussian distribution width can be reduced to explore
progressively smaller regions around the minimum (similarly to the simulated thermal
annealing method).
In addition to the scalar chi-square functional as fit goodness parameter, we have computed
the map of residual pattern calculated according to
𝑃𝑖,𝑗 −𝑓𝑖,𝑗
𝑅𝑖,𝑗 = |
𝜎𝑖,𝑗
|
(5-SM)
One of the experimental 2D GISAXS patterns and the best fitted function defined by equation
1-SM are displayed in Figure S2 (a) and (b), respectively. The weakness of the residual or
difference function shown in Figure S2(c) demonstrates the validity of the proposed structural
model. Furthermore, the described fitting method has proved to be robust, reliable and
reproducible for the whole set of analyzed patterns.
FIG. S2. 2D GISAXS patterns corresponding to the sample held during 8 min at 700 oC. (a)
experimental pattern, (b) simulated 2D GISAXS function defined by Eq. (1-SM) plus
experimental parasitic scattering intensity that best fitted to the experimental pattern, and (c)
2D residual function. The sample horizon, f = 0, is indicated by the arrow in (a).
References
6
7
1-S
R. Lazzari, J. Appl. Crystallogr., 2002, 35, 406–421.
2-S
D. Babonneau, J. Appl. Crystallogr., 2010, 43, 929–936.
3-S
J. S. Pedersen, Chapter 16: Neutron, X-rays and Light. Scattering Methods Applied to Soft
Condensed Matter, North Holland, Amsterdam, 1 edition, 2002.
7