Supplementary information:
S1. TEM results
Figure S1. TEM images corresponding to different specimen orientations.
S2. GISAXS experiments
Figure S2. Scheme of the orientations of the hexagonal nanoplatelets, with respect to
the silicon crystallographic directions.
S1. TEM results
A first glance analysis of Figure 1a (see text) may suggest that the buried objects are
highly anisotropic rod-shaped nanostructures. However, this conclusion may be a
misinterpretation, because TEM images are 2D projections of the 3D structures. In order
to properly infer the 3D shape of the observed nano-objects, several TEM images for
different sample orientations were analyzed. We have obtained a sequence of TEM
images for increasing sample tilt conditions (FigureS1). The images shown in Figure
S1a, b and c corresponding to sample tilting of 0, 15 and 30° (with respect to the Si
[110] zone axis), respectively, evidence an increase in the nano-object projected width
for increasing tilting angles. This effect indicates that the observed objects, initially
presented as rod-shaped are in fact thin plate-like nanostructures in a side-view. In
addition, Figure S1d shows a front-view of another plate-like nanostructure, clearly
indicating a hexagonal shape. This front-view image was recorded with the sample
slightly misaligned from the Si zone axis to improve the object contrast.
Figure S1. TEM images corresponding to different specimen orientations. a) Image
with two different nanoplatelets oriented at Si[110] zone axis (tilting angle = 0°), b)
same specimen tilted 15° around the [100] direction, c) same specimen surface tilted
30° around the [100] direction and d) same specimen oriented along the large faces
normal to the electron beam showing a projection of the hexagonal nanoplatelet onto de
Si(110) plane.
S2. GISAXS experiments
In order to determine the GISAXS intensity produced by the studied material - i.e. a
SiO2 thin film containing Co nanoparticles deposited on a flat Si(001) wafer -, the
scattering produced by a similar sample prepared under the same conditions but without
addition of Co nanoparticles was also measured. The results for the sample without Co
nanoparticles showed a weak and approximately constant scattering intensity except at
very small angles, for which a slight contribution from the totally reflected beam was
noticed. This weak contribution was subtracted from the total intensity produced by the
sample to be studied here.
A Huber four-circle diffractometer was used for the procedure of sample
alignment and adjustment of the incidence, tilting and azimuthal angles. The angular
divergences of the X-ray beam along the vertical and horizontal directions were 0.005°
and 0.2°, respectively.
Measurements were performed for a sample-to-detector distance equal to 538
mm allowing us to access q values within the 0.15-3.6 nm-1 range. The resolutions in
reciprocal space for this configuration -determined by the point spread function of the
direct beam on the 2D detector- were
qz = 0.02 nm-1  q y = 0.2 nm-1.
A schematic representation of the geometry used in our GISAXS experiment is
displayed in Figure 3.g (see text). The GISAXS pattern was determined as a function of
the photon momentum transfer given by:
 cos 2 cos  f  cos  i 
q 

  x  2 
 
q  k f  ki   q y  
sin 2 cos  f


(1)



q 
 z
 sin  i  sin  f



where  is the wavelength of the X-rays, k i and k f are the wave vectors of the
incidence and scattered X-ray photons;  i and  f are the angles between the surface of
the sample and the incidence and scattered X-ray beams, respectively, and 2 is the


angle between the k i and k f wave-vectors projected onto the multilayer surface.1
In order to keep the incidence angle constant during the whole experiment the
sample was pre-aligned using a laser in such a way that the sample surface was always
normal the diffractometer rotation axis responsible for azimuthal orientation of the
sample.
Modeling for GISAXS intensity
The model for the calculation of the total GISAXS intensity was assumed to be
composed of additive contributions from the X-ray scattering produced by (i) spatially
uncorrelated spherical nanoparticles embedded in the about 100 nm thick Co-doped
SiO2 film, and (ii) spatially uncorrelated and hexagonally-shaped nanoplatelets inserted
in the Si(001) crystalline wafer with their faces parallel to the four different orientations
of the {111} crystallographic form of the Si single crystals.

In the kinematic approximation the scattering amplitude A ( q ) produced by a
single nanoparticle having a homogeneous electron density embedded in an also
homogeneous medium is given by the Fourier transform of the difference in electron
density between the nanoparticle and the matrix over the whole volume occupied by the
particle. Except for centre-symmetric particles, A ( q ) depends of the relative orientation

of the nanoparticle with respect to k i . The X-ray scattering intensity produced by the




nanoparticles is given by I (q )  A(q ) * A(q ) , where A(q )* is the complex conjugate of

the A ( q ) function.
The X-ray scattering amplitude
produced by hexagonal shaped
Ahex(111)
nanoplatelets having a lateral dimension equal to  and a thickness t , oriented in such a
way that the incidence X-ray beam coincides with the Si[110] direction (Figure S2a) is
given by
Ahex (111) 
(  hex -  Si )
,
y
q q ,x (q ,2y - 3q ,2z )
{i exp[-i(2 q ,y + 3q ,z + q ,x t)/2](-1 + exp[iq ,x t])[-2 3exp[i 3q ,z /2 ]q ,y
- 2 3exp[i (4q ,y + 3q ,z )/2]q ,y + exp[3i q ,y /2]( 3q ,y - 3q ,z ) + exp[i (q ,y + 2 3q ,z )/2]( 3q ,y - 3q ,z )
,
y
,
y
,
z
,
y
,
z
,
y
(2)
,
z
+ Exp[i q /2]( 3q + 3q ) + exp[i (3q + 2 3q )/2]( 3q + 3q )]}
where:
 q,   q cos   q sin  
z
 x  x

 q,y   
qy
,
 , 

 qz   qx sin   qz cos  

  
(qx,  0, q,y  0)
(3)
 = 35.3° being the angle between the Si[111] and Si[110] directions.  hex and  Si are
the electron density of the hexagonal platelets and of Si, respectively.
The rotation of an object in real space generates the same rotation in reciprocal
space. As a consequence the equations for the scattering amplitudes produced by
nanohexagons oriented according to Figs. S2b, S2c and S2d, Ahex(1 1 1) , Ahex( 1 1 1) and
Ahex( 1 11) , respectively, are obtained by applying the mathematical transformations
associated to a rotation around the q z axis
 qx,   cos  sin  0  qx 
  
 
 q ,y    sin  cos 0  q y 
 ,  
 
0
1  qz 
 qz   0
(4)
for  = 90°, 180° and 270°, respectively.
On the other hand, to achieve an adequate X-ray penetration depth, the sample has
to be rotated around y´ axis in such a way the incidence angle  i between the incoming
wave-vector and sample surface be higher than the critical angle for total X-ray
reflection. An additional rotation around the z´ axis accounts for the  angle between

the Si[110] direction and the component of ki along the Si(001) plane (azimuthal
angle). These combined rotations are achieved by applying the transformation
 q x,   cu z  2(1 - c)u 2x u z
  
 q ,y   
su z
 ,  
q
cu

(
1
c)
(u x u 2z  u 3x )
x
 z 
cu x  2(1 - c)u x u 2z  q x 
 
 q y 
- su x
 
cu z  (1 - c)(u 2x u z  u 3z )  q z 
s( u 2x - u 2z )
c
0
(5)
where c = cos , s = sin  , u x   sin  and u z  cos  ,  being the angle between the

Si[110] direction and the ki vector. Because of eventual small misalignments between
the direction normal to the sample surface and the Si[001] direction, the
 and  i
angles are not necessarily equal. The rotations of the sample around the y´ axis and then
around z´ axis generate an equivalent rotation of the function I (qx' , q'y , qz' ) describing the
scattering amplitude in the 3D reciprocal space.
The asymmetry in the scattering intensity along the right and left sides of the
scattering intensity pattern, negative and positive values of the q y axis, respectively, is a
consequence of the differences in the pattern generated by the intersection of the
I (qx' , q'y , qz' ) function with the q x =0 plane along which the intensity is measured.
On the other hand, the GISAXS intensity produced by a polydisperse and
isotropic set of spherical particles embedded in the silica film only depends on the
modulus q of the scattering vector and is given by
2
I sph (q, R)   Asph (q, R) N sph ( R)dR
(6)
where N sph (R ) is the radius distribution function. N sph ( R ) dR being the number of
spherical particles with radius between R and R  dR , and Asph (q, R ) is the scattering
amplitude produced by a spherical particle with radius R and electron density  sph
embedded in an also homogeneous SiO2-based matrix with an average electron density
 SiO .2 This scattering amplitude is given by
2
Asph  4 (  sph   SiO2 )
sin qR  qR cos qR
q3
(7)
Taking into account the effects of X-ray reflection and refraction on the sample
surface, the total GISAXS intensity for our nanostructure model is given by
2
2
2
2

I  T (i ) T ( f )  c A hex ( hkl ) ( ,  , qx , q y , qz , , t )   A sph (qx , q y , qz , R ) N sph ( R )dR 
 kkl

(8)
where T  i  and T  i  are the effective Fresnel transmission coefficients for an angle
of incidence i and exit angle  f , c is the ratio between the number of hexagonal and
spherical particles,  and t are the lateral size and the thickness of the nanohexagons,
respectively.
To account for the X-ray refraction at the air/SiO2 interface, the out-of-plane
component of the scattering momentum at the detection plane q z must be substituted by
2
q~z  2π [sin r (α f )  sin r (αi )] /λ ,3 where sin r    sin α  2 δ 2 iβ and 1   and  are
the real and imaginary part, respectively, of the average index of refraction
n  1    i of the silica layer. In this case, the modulus of the scattering momentum is
given by q  q x  q y  q~z .3
As it was mentioned in the previous section, our analysis of several TEM images
indicated that all nanohexagons exhibit essentially equal thickness and lateral sizes.
Therefore we have modeled the GISAXS intensity using the same lateral size  and
thickness t for all hexagonal nanoplatelets. The fractions of nanohexagons for each one
of the four different orientations were assumed to be the same.
Structural parameters derived from GISAXS results
As it can be noticed by comparing the experimental images displayed in Figure 4a and
the corresponding simulation shown in Figure 4b (see article) and also the experimental
and modelled curves plotted in Figure 4c, the modelled GISAXS intensity function and
the experimental intensity measured in this work exhibit a good agreement. Minor
discrepancies are only apparent within the small q x range, in which the contribution
from diffuse scattering produced by surface roughness is responsible for an additional
 and  i are due the miscut error between the
Si(001) plane and the surface of silicon wafer used for sample preparation. The  value
contribution. The difference between
determined from our fitting procedure was equal to 1.0 degree.
All the relevant structural parameters of the studied material were determined
from the simulated function (equation 8) that corresponds to the best fit to the
experimental results. A lognormal function was assumed for the radius distribution of
the Co nanoparticles, N sph (R ) , and the CoSi2 nanohexagons are assumed to have the
same lateral size and thickness.
[001]
[010]
[100]
_
[110]
[110]
(a)
(b)
__
[ 1 10]
_
[ 110]
(c)
(d)
Figure S2. Scheme of the orientations of the hexagonal nanoplatelets, with respect to
the silicon crystallographic directions. The hexagons form at the SiO2/Si interface and
grow along four planes of the Si{111} crystallographic form, i.e. a) Si (111) , b) (1 1 1) , c)
(1 1 1) and d) (1 11) .
References:
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2. Glatter, O.; Kratky, O., Small-angle X-ray Scattering. Academic Press: London,
1982.
3. Paniago, R.; Forrest, R.; Chow, P. C.; Moss, S. C.; Parkin, S. S. P.; Cookson, D.,
Growth mode and asymptotic smoothing of sputtered Fe/Au multilayers studied by Xray diffuse scattering. Physical Review B 1997, 56, (20), 13442.