Crystal Structure Theory and Applications, 2012, 1, 35-39 Published Online December 2012 (
Characterization of Thin Films by Low Incidence X-Ray
Mirtat Bouroushian*, Tatjana Kosanovic
General Chemistry Laboratory, School of Chemical Engineering, National Technical University of Athens, Athens, Greece
Email: *
Received September 20, 2012; revised October 22, 2012; accepted November 3, 2012
Glancing Angle X-ray Diffraction (GAXRD) is introduced as a direct, non-destructive, surface-sensitive technique for
analysis of thin films. The method was applied to polycrystalline thin films (namely, titanium oxide, zinc selenide,
cadmium selenide and combinations thereof) obtained by electrochemical growth, in order to determine the composition
of ultra-thin surface layers, to estimate film thickness, and perform depth profiling of multilayered heterostructures. The
experimental data are treated on the basis of a simple absorption-diffraction model involving the glancing angle of
X-ray incidence.
Keywords: Glancing Angle X-Ray Diffraction; Thin Films; Titanium Oxides; Metal Chalcogenides; Electrodeposition
1. Introduction
X-ray techniques hold a leading role as a tool for mate-
rial characterization. In this connection, X-ray powder
diffraction (XRD) generally employs the conventional θ -
2θ (or Bragg-Brentano) “reflection” geometry, in which
the incidence angle equals the angle of the diffracted
beam with respect to the inspected sample surface (Fig-
ure 1(a)). The device configuration ensures that a high
intensity beam diffracted from any particular set of crys-
talline planes of the sample will be focused onto a slit in
front of the rotating detector. However, X-rays with large
glancing angles of incidence will go through a few to
several hundred micrometers inside the material under
investigation, depending on its “radiation” density, so
that when it comes to thin film analysis the beam pene-
tration depth may be much greater than the sample thick-
ness. Hence, conventional XRD is rather not suitable for
detailed study of sub-micrometric layers in thin film
specimens. For instance, in the case of a multilayer elec-
trodeposited film, conventional XRD would only allow
for tracing the complete structure after deposition, while
the large number of overlapping peaks indicating the dif-
ferent crystallographic phases would make the spectrum
interpretation difficult.
Grazing incidence configurations have been developed
to overcome such limitations, e.g., to render the XRD
measurement more sensitive to the near surface region of
the sample and minimize the substrate contribution on
the diffraction response. In the glancing angle X-ray dif-
Figure 1. Schematic diagrams of (a) symmetric θ - 2θ, and
(b) asymmetric glancing angle XRD geometry.
fraction (GAXRD) technique, the Bragg-Brentano ge-
ometry is modified to provide an “asymmetric” diffrac-
tion result, which allows access to small depths in the
sample by varying the incidence angle. A parallel mono-
chromatic X-ray beam falls on the sample surface at a
fixed, low glancing angle, α (larger than the critical angle
for total reflection, αc, but usually smaller than 10˚) and
the diffraction profile is recorded by detector-scan only
(Figure 1(b); non-rotating sample). GAXRD makes pos-
*Corresponding author.
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sible the use of X-rays for the characterization of sur-
faces, buried interfaces, and ultra thin films. By means of
this technique, valuable information can be obtained re-
garding the thickness and phase crystallography of the
sample [1-3], the change of its composition with depth
[4], and its microstructure (stress, preferred orientation,
etc.) [5].
In the present work, the GAXRD method is applied as
a depth-profiling tool for the identification of surface
oxide layers, the estimation of film thickness, and phase
characterization in multilayer deposits. Practice and theory
behind the evaluation is briefly discussed.
2. Experimental
An X-ray Siemens D5000 powder diffractometer with a
Soller collimator, a flat monochromator, and a fixed
CuΚα radiation (λ = 154.06 pm) was employed for film
characterization. The primary beam divergence was suf-
ficiently small to allow for the required resolution of low
glancing angles of incidence. The instrument was ope-
rated in a step-scan mode in increments of 0.02˚ 2θ, and
counts were accumulated for 1 s at each step. The angle
of incidence α was set to different values (0.2˚ - 10˚) in
order to vary the interaction length in each depth region
with scanning of the exit angle.
Titanium oxide films produced by anodization of me-
tallic titanium electrodes at various voltages in 1 M sul-
furic acid bath, as well as single and multi-layered thin
films of zinc and cadmium selenides, electrodeposited on
titanium and nickel electrodes from acidic aqueous solu-
tions [6,7], were used for the glancing angle XRD char-
3. Results and Discussion
3.1. Identification of Thin Surface Layers
Thin titanium oxide films were formed by soft anodiza-
tion of titanium metal for few minutes at low oxidation
potential, and the electrode specimens were characterized
by conventional and grazing angle XRD. No oxide could
be detected by conventional XRD, since the strong con-
tribution from the Ti metal substrate overshadowed the
response from the upper oxide layer (Figure 2). By con-
trast, identification of the formed oxides down to very
thin surface layers could be achieved by reducing the
angle of incidence according to the GAXRD protocol, so
that titanium sub-oxides such as Ti2O, Ti2O3 were readily
detected (Figure 2).
3.2. Depth Profiling of Surface Oxide Films
Monitoring the distribution of the oxide phases along the
perpendicular, to the substrate, direction would be indis-
pensable in following the evolution of the anodic film
through the successive stages of electrolytic growth. In
this regard, results from grazing incidence experiments
as shown in Figure 3, for a sample obtained by anodiza-
tion of titanium metal at a voltage of 100 V for 2 h, per-
mit a semi-quantitative analysis of the composition pro-
file of the oxide layer. The depicted GAXRD sequence
yields information about the proportions of the oxide
phases at various depths in the sample, on the basis of the
recorded intensities of the main diffraction peaks. By
contrast, conventional XRD (not shown in figure, but
similar to the spectrum at α = 10˚) only indicates the
formation of both the common oxide (TiO2) phases,
namely rutile and anatase [6].
3.3. Estimation of Thin Film Thickness
The method we use, according to Nauer et al. [1], in order
Figure 2. Conventional and glancing angle XRD patterns of
Ti anodized at 5 V for 15 min. JCPDS #10 - 0063 and #11 -
0218 were used for Ti2O and Ti2O3 identification.
Figure 3. GAXRD diagrams of an oxide layer obtained by
anodization of Ti at 100 V for 2 h. Anatase, rutile, and Ti
substrate reflections are indicated. Note that the diffraction
signals from the substrate get weaker and disappear by
lowering α. Shallow angles give information about layers
closer to the sample surface.
Copyright © 2012 SciRes. CSTA
to estimate the thin film thickness is based on the fol-
lowing assumptions: 1) at any low angle of incidence a
the attenuation of X-rays in the material (due to absorp-
tion, multiple scattering, etc.) follows the exponential
variation predicted by the Beer-Lambert law; and 2) the
whole of non-interacted radiation will be recorded at the
detector as a diffraction signal at the exit angle 2θ. In
Equation (1) (cf. [1]), f designates the intensity of inter-
acted radiation (lost for the detector at 2θ), normalized to
unity for complete attenuation when the transversed
depth x goes to infinity; d is the pursued thickness of the
film (= xsinα), and μ the linear absorption coefficient of
the target material.
This expression is used to provide simulation curves
for variable α angle, having the thickness d as the unde-
termined parameter (μ-values are needed here for CuKα
radiation). Concurrently, diffraction peaks are recorded
at certain glancing angles of X-ray incidence for a spe-
cific crystallographic hkl plane of the investigated mate-
rial corresponding to the selected 2θ Bragg reflection,
e.g., anatase (101). The observed peak intensity values
(Iexp) are corrected for decreasing incident radiation due
to the lowering of angle a, and normalized to the maxi-
mum corrected intensity, which corresponds to near total
external reflection conditions (i.e., for α close to the
critical angle αc). Finally, a working experimental value
is obtained, as given by Equation (2).
max sin
The above procedure applies preferably for a charac-
teristic intense diffraction peak and can be repeated for
more than one such peaks of the spectrum, if present. It is
expected that fitting of the If values to the simulation
curves drawn by Equation (1) will give a measure of the
thickness of the examined film. In Figure 4, the results
of the above procedure are depicted for an anodic oxide
film on titanium, which is assumed to consist entirely
either of anatase or rutile phase. In fact, the oxide film
comprises a mixture of varying stoichiometry; however,
the absorption coefficients of the constituent phases do
not differ appreciably, thereby this approximation is not
critical for the result.
Statistical fitting of the experimental points to the
simulation curves indicates that according to this model
the thickness of the film lies in the range 300 ± 50 nm.
The accuracy of the estimation, although not verified
here by an independent measurement, corresponds to an
anodic growth rate of 3 ± 0.5 nm·V–1, which is fairly
consistent to the rate of 2.5 nm·V–1 reported for anodic
titanium oxide films grown potentiostatically at similar
conditions [8].
One can substantially simplify the above procedure by
assuming that the observed vanishing of the diffraction
response of the substrate (Ti metal) for a certain X-ray
grazing incidence practically occurs when the radiation
intensity penetrating the material becomes 1/e of its ini-
tial value. Then, according to the absorption law (Equa-
tion (1)) for the corresponding shallow incidence α, gi-
ven that the incoming radiation has interacted only with
the oxide upper layer, the interface between the latter and
the substrate can be considered as lying at a depth:
Assuming that the entire oxide layer consists of the
anatase phase, one has μ = 488 cm–1 (CuKα), and from
detailed spectra similar to Figure 3 the as-obtained layer
Figure 4. Solid lines: relative intensity (f) of radiation vs.
angle of incidence (α) as obtained by Equation (1), for dif-
ferent layer thicknesses of anatase and rutile. Black squares:
normalized experimental intensities of GAXRD signals for
anatase (101) at 2θ = 25.3˚, and rutile (110) at 2θ = 27.5˚, for
varying α.
Copyright © 2012 SciRes. CSTA
thickness is estimated as 180 nm. This value deviates
from the above calculated, certainly as expected from the
simplistic argument we used, and can be trusted only as
an order-of-magnitude calculation. In any case, accurate
assignment of the α-angle marking the disappearance of
the substrate is essential for the calculation. Note also
that factors related to material density and surface rough-
ness account for limited accuracy as to the thickness
evaluation of the present anodic films. Actually, the up-
per values of the above estimation should be preferred
since the effective density of the anodic oxide layer is
less than the bulk value, due to a porous structure [6].
Clearly, independent measurements should be used in
order to verify the reliability of the presented procedure,
and possibly standardize a correction or scaling factor for
a range of thickness values. Along this line, our GAXRD
results for cadmium selenide (CdSe) films of sub micro-
metric thickness (electrodeposited on Ti or Ni electrodes
by various electrolysis charges) were found to be in fair
agreement with stylus profilometry measurements, namely,
within an accuracy of 50 nm (unpublished results). Else-
where also [1], application of the above model has been
shown to give results in consistence with other mea-
suring techniques.
3.4. Analysis of Multilayer Heterostructures
The present GAXRD protocol was employed for per-
forming analysis of a multilayer heterostructure, namely
the two-layer ZnSe/CdSe/Ni system, prepared by se-
quential cathodic electrodeposition of polycrystalline ZnSe
and CdSe on Ni substrate. The (111) reflection of the
upper ZnSe layer (2θ = 27.3˚) along with the CdSe(111)
(2θ = 25.3˚) were used for the estimation (Figure 5). The
GAXRD patterns of the system as given in Figure 5 re-
veal the layer sequence and the depth profile of the
stratified film. Note that upon decreasing the angle of
incidence the signals from the lowest lying phase (Ni
substrate; not shown in the figure) disappear first, follow-
ed by the complete vanishing of signals from the interme-
diate CdSe layer. Eventually, only the response from the
ZnSe layer remains, and no other phases are detected. It
can be concluded thus that appreciable intermixing of the
various phases can be excluded, that is, the electroche-
mical deposition sequence yields the intended stratified
structure with abrupt transition at the interfaces. In other
words, the very existence of a barrier-type upper layer
(ZnSe) is observed by the disappearance of the CdSe(111)
reflection at a certain low incidence angle (Figure 5: line
at 0.6˚).
The estimation of the thickness of the ZnSe layer is
demonstrated in Figure 6, where corrected and norma-
lized ZnSe(111) diffraction intensities obtained for X-ray
incidence angles of 0.2˚ - 4˚ are shown fitted to the rele-
vant simulation curves. By this graph, a thickness of
Figure 5. GAXRD diagrams of a ZnSe/CdSe bilayer elec-
trodeposited on Ni from acidic electrolyte [7]. ZnSe(111)
and CdSe(111) reflections are indicated.
Figure 6. Solid lines: relative intensity (f) of radiation vs.
angle of incidence (α) as obtained by Equation (1), for dif-
ferent layer thicknesses of ZnSe. Black squares: norma-
lized experimental intensities of GAXRD signals for
ZnSe(111) at 2θ = 27.3˚.
250 ± 50 nm could be ascribed to the ZnSe layer under
examination. At the same time, the application of the
simple formula of Equation (3) led to the quite consistent
result of 290 nm. It is believed that the better agreement
between these two values compared to the case of anodic
oxide layers of the preceding paragraph is due to the ex-
istence of a better defined interface in the present he-
terostructure between the epilayer and the substrate.
4. Conclusion
On the basis of the presented results, the low-glancing
angle incidence X-ray technique (GAXRD) has been
demonstrated to provide a simple and innovative tool for
studying the microstructure of polycrystalline films; in
particular for: 1) identification of crystalline surface
phases; 2) estimation of the thickness of crystalline thin
layers/films; and 3) depth profiling of multilayer struc-
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