Physica B 325 (2003) 272–280
Determination of layer structure in Mo/Si multilayers
using soft X-ray reflectivity
M.H. Modi, G.S. Lodha*, M. Nayak, A.K. Sinha, R.V. Nandedkar
Synchrotron Utilisation Division, Centre for Advanced Technology, Indore 452 013, India
Received 20 August 2002; accepted 19 September 2002
Abstract
The soft X-ray reflectivity characterization of Mo/Si multilayer deposited by electron beam evaporation is discussed.
The measurements are performed on Indus-1 synchrotron storage ring. The interdiffusion of two-layer materials in
multilayer leads to the formation of interlayers. To understand the influence of interlayers and interfacial roughness on
soft X-ray reflectivity profile, simulation studies are performed. The roughness parameter leads to reduction in peak
reflectivity whereas the interlayers significantly change the reflectivity profile. For fitting the angle-dependent soft X-ray
reflectivity profile, a four-layer model accounts for the interlayers formed at the interfaces. Asymmetry at the two
interfaces, viz. Si-on-Mo and Mo-on-Si needs to be considered for a good model fitting of the soft X-ray reflected
profile. The mechanism, which could lead to the formation of interlayers in Mo/Si multilayer is discussed.
r 2002 Elsevier Science B.V. All rights reserved.
PACS: 81.15.Ef; 41.50.+h; 68.65.Ac; 68.35.Fx; 68.35.Ct
Keywords: Multilayer; X-ray reflectivity; Interdiffusion; Soft X-ray; Synchrotron radiation
1. Introduction
Realization of normal incidence optical devices
for imaging applications in soft X-ray, extreme
ultra-violet (EUV) region have become feasible
with the advent of multilayer optical elements
[1,2]. It fulfills the requirement of high-reflected
intensity and gives moderate spectral resolution at
near normal incidence. Since the amplitude of
reflected radiations add in phase upon reflection
from successive interfaces, the intensity of reflected
*Corresponding author. Tel.: +91-731-488002; fax: +91731-488000.
E-mail address: [email protected] (G.S. Lodha).
light becomes N 2 times, where N is the number of
periods in the multilayer [3]. Period length ‘d’ can
be tailored according to the wavelength of interest
depending upon application.
The efficiency of any optical devices, i.e.
reflectance and resolution, is most sensitive to
coating parameters [4]. The structural morphology, interface quality, interdiffusion and chemical
reactivity significantly affect the performance in
the soft X-ray region. Structural parameters of Xray multilayers are mostly obtained using X-ray
reflectivity, X-ray diffuse scattering and crosssectional transmission electron microscopy [5–8].
Complete model fitting of soft X-ray reflectivity
profiles for structural determination are scarce.
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 1 5 3 9 - 9
M.H. Modi et al. / Physica B 325 (2003) 272–280
Most of the authors only report the reflectivity
performance evaluations in soft X-ray region
[9–11]. Ravet et al. [12] used soft X-ray radiation
( for the analysis of B/Si multilayers.
ðl ¼ 126 AÞ
They have compared the results with X-ray
( Values of thickness
measurements at l ¼ 1:54 A:
and roughness obtained from both measurements
are in good agreement. Here, we report a
detailed interface analysis of Mo/Si multilayer
( The
using soft X-ray reflectivity at l ¼ 80 A:
complete angle-dependent reflectivity profile is
fitted.
Mo/Si multilayer is one of the most efficient
(
mirrors in the soft X-ray region of 130–300 A
[7,11]. Due to its technological applications in
soft X-ray projection lithography, it has extensively been studied. Various studies are carried out
to understand the interface behaviors [13–15].
Different groups have investigated thermally
induced structural modification [15–18]. Studies
on sputter-deposited Mo/Si multilayers show
that Mo layers are crystalline and textured, the
Si layers are amorphous, and that the pure layers
are separated by asymmetric interlayers composed
of an amorphous mixture of Mo and Si [19].
Yakshin et al. [14] report the formation of
interlayer in electron beam evaporated Mo/Si
multilayer using hard X-ray reflectivity measurements. In spite of the importance of Mo/Si system
in soft X-ray projection lithography, no detailed
characterization using soft X-ray radiation is
reported.
In this paper, the possibilities of structural
analysis in soft X-ray region has been discussed
by presenting a detail simulation study and a
representative measurement for one Mo/Si multi( The soft X-ray
layer sample measured at l ¼ 80 A:
measurements are carried out on Indus-1 synchrotron source using reflectivity beamline. For a
model fitting of the experimental data a four-layer
model is considered to take into account the
interlayers formed at the interfaces. Model fitting
of the reflected profile in soft X-ray region suggests
asymmetry in two different interfaces, viz. Si-onMo and Mo-on-Si. This asymmetry at the two
interfaces is in good agreement in comparison with
previous studies on Mo/Si multilayers using highresolution transmission electron microscopy [15].
273
The sensitivity of soft X-ray reflectivity technique
to structural characterization, particularly to the
four-layer model, is demonstrated by systematic
simulation study. The reflectivity formulation is
presented which has not been explored in the
literature for soft X-ray study. The simulation
study shows that the effect of interlayer is very
different compared to statistical RMS roughness
parameters. The interlayer, which takes into
account the formation of compound on interfaces,
causes the redistribution of reflectivity pattern
whereas the roughness parameters reduce the
reflected intensity.
2. Model calculation
The reflection and refraction taking place at
the interfaces is basically governed by optical
index contrast. The reflectance of multilayer
system, consisting of N layers can be calculated
using recursive formalism given by Parratt [20].
Let nj be the refractive index of the jth layer
defined as
nj ¼ 1 dj ibj ;
ð1Þ
where dj and bj are the real and imaginary parts of
refractive index, also referred as optical constants.
These optical constants for the jth layer consisting
of Nj number of atoms per unit volume are
defined as
dj ¼
r e l2
Nj ðZj þ Df 0 Þ;
2p
ð2Þ
bj ¼
r e l2
Nj Df 00 ;
2p
ð3Þ
where re is the electron classical radius, Df 0 and
Df 00 are the resonance and absorption correction
terms to atomic scattering factor arising from
anomalous dispersion. For s-polarized radiation
where the electric field vector is perpendicular to
the plane of incidence, the Fresnel coefficient for
reflection from the interface between j and j þ 1
layer is given by
Fj;jþ1 ¼
EjR
Ej
¼
kj;z kjþ1;z
kj;z þ kjþ1;z
ð4Þ
274
M.H. Modi et al. / Physica B 325 (2003) 272–280
with
2p 2
ðn cos2 yÞ1=2 ;
l j
where Ej and EjR are the amplitude of electric
vector of incident and reflected waves on the
interface j and j þ 1 and in medium j: Recursion
relation for reflection can be obtained with the
boundary condition that tangential component of
electric vector is continuous:
Rjþ1;jþ2 þ Fj;jþ1
Rj;jþ1 ¼ a2j
;
ð5Þ
1 þ Rjþ1;jþ2 Fj;jþ1
kj;z ¼
where aj ¼ expðikj;z dj Þ is the amplitude factor for
half the perpendicular distance dj ; the thickness of
jth layer. The final reflectivity from multilayer
system, the ratio of reflected intensity to incident
intensity can be written as
2
IR E1R jR1;2 j2 ¼
¼ :
ð6Þ
I0
E1
The recursion method starts from bottom layer
with the assumption that RN;Nþ1 ¼ 0; since there is
no reflection from infinite thick substrate.
If a continuous refractive index profile is
assumed between layers j and j þ 1 with error
function, then Eq. (5) is to be multiplied with the
factor [21]
Sj ¼ expð2kj;z kjþ1;z s2j Þ;
ð7Þ
where sj is the root mean square deviation of
interface atoms with respect to a smooth interface.
Using this formalism reflectivity pattern is simulated for a given multilayer system. The fitting
of the measured data yields the information
about layer thickness, interface roughness and
composition.
In any real multilayer system the interfaces are
imperfect due to interdiffusion and reactivity of
materials. Because of these imperfections the
reflectivity pattern gets modified. Imperfect interfaces can be dealt either by statistical approach or
multiple layer model with the incorporation of
interlayers between the two-layer system. In
statistical approach, the Fresnel reflection coefficient is multiplied by a factor given in Eq. (7). In
this case, the composition gradient at the interfaces is usually modeled using either sinusoidal,
linear, step profile, or error function [22]. In the
Fig. 1. Schematic of four-layer model assumed for Mo/Si
multilayer is shown. The interlayers formed due to intermixing
of Mo and Si at the imperfect boundaries are presented by
crossed region.
case when a compound material is formed at the
interface, multiple layer model gives a better model
fitting of the reflected profile than the model based
on statistical approach. In this paper, we show that
a four-layer model gives better experimental fit to
the soft X-ray reflectivity data on Mo/Si multilayer
than a statistical model. In Fig. 1 the model of the
four-layer system is shown to describe the formation of interlayers at the imperfect boundaries due
to interdiffusion. The thickness of the interlayers
separating the layers of materials ‘1’ and ‘2’ at two
different interfaces are d12 and d21 : Hence, the
period of the multilayer is d ¼ d1 þ d12 þ d21 þ d2 :
The thickness of the interlayers d12 and d21 may or
may not be same. If it is not the same, then this
asymmetry significantly modifies the reflectivity
profile. We now discuss the presence of interlayers
and the effect of asymmetry on the soft X-ray
reflectivity pattern.
2.1. Influence of interlayer
The reflectivity pattern in multilayer is modulated by structure factor ðGÞ: In an ideal multilayer
it is defined as the ratio of thickness of high
refractive index material to the period of multilayer, i.e. d1 =ðd1 þ d2 Þ: The modulation of intensity
of Bragg peaks depends on G ratio. The weight
factor of interlayer d12 and d21 decides the G
ratio in the four-layer model system [14]. The
presence of interlayers significantly affects the
reflectivity patterns as shown in Fig. 2. The
reflectivity curves for Mo/Si multilayer with and
without interlayers are simulated for soft X-ray
( We consider the five periods
radiation ðl ¼ 80 AÞ:
M.H. Modi et al. / Physica B 325 (2003) 272–280
275
Fig. 2. Effect of interdiffused layer thickness upon reflectivity pattern of Mo/Si multilayer is calculated. As interdiffused layer
thickness increases the Bragg peak reflectivity decreases.
of Mo/Si coated on float glass substrate. The
thickness of Si and Mo layers are assumed to be 59
( respectively in case if there are no
and 30 A;
interlayers present. As the thickness of interlayer
increases the corresponding thickness is subtracted
from Si and Mo layer thickness to keep the period
of the multilayer constant. In addition to interlayer, which takes into account the compound
( is
formation, the interface roughness of 5.5 A
assumed for continuous composition changes. The
interlayer is assumed to be of MoSi2. The motive
behind these numbers taken for simulation is to
match these with our experimental parameters as
will be discussed later. From Fig. 2 it is seen that
as the thickness of the interlayer increases the
reflectivity of Bragg peak decreases as well as
the position shifts to the higher angle side due to
the change in refraction correction term. In Fig. 3,
for comparison, the reflectivity curves are simulated for increasing the roughness with no-interlayers. In case of increasing roughness (Fig. 3),
the reduction of reflectivity is observed without
affecting the distribution of intensities of individual peaks. It is to be noted here that the
incorporation of interlayer leads to redistribution
of peak intensity, which is not the case when
no interlayer is present and only roughness
increases.
2.2. Effect of asymmetry
The thicknesses of interlayers for two interfaces,
viz. Si-on-Mo and Mo-on-Si, may not be the same
which lead to an asymmetric behavior. The degree
of asymmetry is a sensitive parameter. In addition
to material combination, it may depend on
deposition techniques and ambient conditions.
Different authors [14–16] have reported the asymmetric nature of interlayers for Mo/Si multilayers
grown in different conditions. The interchange of
two interlayer thicknesses, i.e. dSi-on-Mo and
dMo-on-Si affects the reflectivity pattern. The effect
of interchanging the thickness of asymmetric
( wavelength, and is
interlayer is simulated at 80 A
shown in Fig. 4. Where curve A corresponds to
(
thickness dSi-on-Mo and dMo-on-Si 8 and 10 A,
respectively. Curve B corresponds to interchanging
of these thicknesses for two interlayers. This
interchange leads to change in peak reflectivity of
B20% and a steep fall in reflectivity just before
276
M.H. Modi et al. / Physica B 325 (2003) 272–280
Fig. 3. Effect of statistical roughness parameter on reflectivity pattern is simulated. The increasing roughness causes the reduction in
whole reflected intensity.
Fig. 4. The calculated spectra to see the effect of interchanging the thickness of interlayers. If the thickness of two interlayers are
interchanged then the reflectivity changes by B20%.
the Bragg peak in case B: This may be understood
by the standing wave-field intensity distribution
inside the multilayer. The position of nodes and
anti-nodes of standing wave field leads to
significant change of reflectivity [23]. These simu( suggest that the
lation results for l ¼ 80 A
interlayer formation and its asymmetric nature
can be picked up in soft X-ray measurements.
M.H. Modi et al. / Physica B 325 (2003) 272–280
3. Experimental
Mo/Si multilayers have been deposited using
an ultra-high-vacuum (UHV) electron beam
evaporation system [24] at a base pressure of
4 109 mbar. The system has three electron guns
of 3 kW power. Multilayer samples have been
deposited on good-quality float glass substrates.
Prior to deposition, substrates are ultra-sonically
cleaned with acetone. Proper care has been taken
to avoid any contamination during the loading of
substrate after cleaning.
Soft X-ray reflectivity measurements are carried
out on Indus-1 synchrotron facility using reflectivity beamline [25]. The beamline delivers radiation
( with high flux and
in the range of 40–1000 A
moderate spectral resolution using a toroidal
grating monochromator. Various absorption edge
filters are provided in the beamline to suppress the
higher order contamination from the monochromator. The experimental station operates in high
vacuum environment (B5 108 mbar). To maintain UHV environment of 1 109 mbar pressure
of beamline, a differential pumping system has
been incorporated between the experimental station and the beamline.
277
The goniometer assembly of reflectometer station comprises of two rotary stages and one linear
stage. Two rotary stages are used to accomplish
the standard y22y scan for normal reflectivity
measurements. In the exiting configuration, the
theta-stage movement of the goniometer was
restricted to B451. In addition, both stages can
be moved in coupled and uncoupled modes to
carry out different modes of reflectivity, i.e.
detector scan, rocking curve scan, etc. The linear
stage is employed to bring the sample in and out of
direct beam, to facilitate the direct beam monitoring. This feature is useful for normalization of
reflectivity data with incident beam intensity.
Sample and detector can be aligned with a
precision of 0.011. Silicon XUV photodiode has
been used to monitor reflected beam intensity. The
current output of detector is recorded using
Keithley 485 Pico ammeter. All motions in
reflectometer system are computer controlled.
The data acquisition and motion control programme is written in C++ with a visual interface
for user-friendly operation.
The detail fitting of measured reflectivity data is
carried out using the Parratt formalism discussed
in Section 2. Since in soft X-ray region the optical
( (59 A
( Si/30 A
( Mo) measured at
Fig. 5. Reflectivity spectra for an Mo/Si multilayer with five bilayers and a bilayer period of 89 A
( Measured curve is represented by open circles. The dotted line ( ) shows calculated spectrum by assuming two-layer
l ¼ 80 A:
model. The best fit represented by continuous line is obtained by assuming an interdiffused layer in between pure layers of Mo and Si.
M.H. Modi et al. / Physica B 325 (2003) 272–280
278
constants vary significantly, hence along with the
thicknesses and roughnesses, the optical constants
are also taken as fitting parameters. Optical
constants from Henke’s tabulated values [26] are
taken as a starting guess for fit.
4. Results and discussions
Angle-dependent reflectivity spectrum of Mo/Si
multilayer deposited on a float glass substrate, of
( (30 A
( Mo/59 A
( Si), with five-layer
period 89 A
pairs and 0.33 G is shown in Fig. 5. Measured
spectrum is shown by circles whereas the dotted
line represents calculated spectrum assuming a
two-layer model with no interdiffused layer, and
the continuous spectrum assuming four-layer
model as discussed earlier. It is clear from the
figure that in the case of the two-layer model the
disagreement between the calculated and the
measured spectrum is quite distinct, whereas the
four-layer model gives the best fit. The best fit is
(
obtained with interlayer thicknesses of 8 and 10 A
for Si-on-Mo and Mo-on-Si interfaces, respectively. The quantitative numbers for thicknesses,
roughnesses and optical constants deduced from
the fit are given in Table 1. The values of optical
constants for silicon differ significantly from the
tabulated values whereas the optical constants for
molybdenum MoSi2 mixing layer are slightly
different from tabulated values, which can be
attributed to density change. The variation of
silicon optical constants particularly in high
absorption region has been reported earlier [27].
In Fig. 6a, the profile of the real part of optical
index is plotted, as obtained from fitting of
experimental data. The minima and maxima
Fig. 6. Optical index profile obtained after fitting of the
reflectivity data. (a) Maxima and minima correspond to layers
of pure Mo and Si, respectively. In between are the interface
region arises from the formation of silicide. (b) Expanded view
of one period in multilayer. The dashed (- - - -) line represents
actual profile used for fitting assuming interlayers with
Gaussian roughness. The dotted ( ) line represents the
profile without Gaussian roughness. Interface width for Sion-Mo and Mo-on-Si is shown with clear asymmetry on two
sides.
Table 1
(
Parameters of the fit at l ¼ 80 A
Layer
(
Thickness (A)
(
Roughness (A)
Indicesa ( 103)
Absorptiona ( 103)
Si
Si on Mo
Mo
Mo on Si
Float Glass
50
8
21
10
N
5.5
5.5
5.5
5.5
3.0
10.78 (6.34)
12.61 (14.01)
18.18 (20.21)
12.61(14.01)
10.62 (10.62)
8.4 (14.49)
15.42 (15.42)
3.69 (3.69)
15.42 (15.42)
8.13 (8.13)
a
In braces the tabulated values of optical constants from Henke et al. [26].
M.H. Modi et al. / Physica B 325 (2003) 272–280
correspond to layers of pure Si and Mo, respectively. Interlayer region arising due to the combination of silicide interlayers and layer roughness
is shown by dashed line (- - - -) in Fig. 6b, whereas
the dotted line ( ) represents the profile
without the Gaussian roughness. The interlayer
regions as marked in Fig. 6b on two sides are
asymmetric.
Earlier Stearns et al. [15] have shown in their
high-resolution electron microscopy study that,
in sputter deposited Mo/Si multilayer, pure
layers of Mo and Si are separated by an
amorphous interlayer of Mo–Si mixture. The
work of Yakshin et al. [14] show the formation
of silicide at interfaces in electron beam ion
assisted Mo/Si multilayer. For ion-assisted
energy of 300 and 2000 eV, the interlayer width
of silicide layer at two interfaces are slightly
different. In the case of 300 eV ion energy,
(
the width of two interlayers are the same (8 A).
For 2000 eV ion energy, the two widths are 11
( for interlayers at Si-on-Mo and Moand 13 A
on-Si interfaces respectively (multilayer period
( Feigl et al. [16] also reported the
d ¼ 75:4 A).
asymmetric nature of two interlayers in sputterdeposited Mo/Si multilayer. The thickness of two
( for a multilayer
interlayers reported is 6 and 10 A
( (0.44 G). Different mechanisms
period of 65.8 A
have been proposed to explain the formation
of interlayers and its asymmetry in Mo/Si multilayer [13,28]. Liwen Wu et al. [13] have suggested a
thermally activated model by considering the
different thermal conductivities of the deposited
Mo and Si surfaces. The thermal conductivity
of Mo is higher than that of amorphous Si, so
the heat produced by the Si adatoms on Mo
surface will diffuse quickly compare to that for
depositing Mo on Si surface. This leads to a
lower local temperature in Si-on-Mo case
and hence less probability for diffusion. This
will lead to a thinner interlayer compared to
Mo-on-Si case. The ratio of two interlayer
thicknesses may also depend on the kinetic
energy of the deposited particle. Morgan et al.
[28] in their molecular beam dynamics study
have tried to explain the thickness asymmetry
of two interlayers. The different degree of
penetration and interdiffusion of the ad atoms
279
during deposition are basic factor behind the
asymmetry. Stearns et al. [15] have suggested that
the Mo atoms can get embedded more easily into
the relatively open and disordered lattice of
amorphous Si than are the Si into the more
compact crystalline Mo lattice. If the kinetic
energy model is to play a role behind the
formation of interlayers, then the results of
electron beam deposited Mo/Si multilayer should
have been different. Since, the formation of
interlayers could be found in both electron beam
deposited and sputtering deposited Mo/Si multilayers where the kinetic energy of ad atoms are
quite different. So we conclude that the thermally
activated model should be responsible for the
formation of interlayers and its asymmetric width
in Mo/Si multilayer.
It is clear from earlier data on Mo/Si multilayer that the interlayers are formed during
deposition and its asymmetric nature has been
explored by various techniques. Our present
work on soft X-ray reflectivity also confirms
the interlayer asymmetry in Mo/Si multilayer.
This gives yet another proof of invocation
of asymmetric interlayer model in Mo/Si multilayer.
5. Conclusions
( is characterized
Mo/Si multilayer of period 89 A
for structural parameters using soft X-ray radiation of Indus-1 synchrotron facility at reflectivity
beamline. The detailed analysis of reflectivity data
shows that the Mo/Si multilayer comprises an
additional interlayer of Mo–Si in addition to a
pure layer of Mo and Si. The interlayers formed at
two interfaces, viz. Mo-on-Si and Si-on-Mo, are
asymmetric. The simulation study reveals that the
effect of interlayer is very different compared to
that of statistical RMS roughness parameters. The
roughness parameter leads to reduction in peak
reflectivity only, whereas the interlayer effect
redistributes the reflectivity pattern. Our soft Xray characterization results are consistent with the
results reported on Mo/Si multilayer characterized
by hard X-ray radiation and transmission electron
microscopy.
280
M.H. Modi et al. / Physica B 325 (2003) 272–280
Acknowledgements
The authors are thankful to Dr. K.J.S. Sawhney
for helpful discussions. We acknowledge R.K.
Gupta and M.N. Singh for their contributions in
running the beamline.
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