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Diffuse X-ray scattering of amorphous multilayers
T. Salditt, T. Metzger, J. Peisl, X. Jiang
To cite this version:
T. Salditt, T. Metzger, J. Peisl, X. Jiang. Diffuse X-ray scattering of amorphous multilayers. Journal de Physique III, EDP Sciences, 1994, 4 (9), pp.1573-1580. �10.1051/jp3:1994224�. �jpa-00249207�
Classification Physics Abstracts
61.10
Diffuse X-ray scattering of amorphous multilayers
T. Salditt, T. H. Metzger, J. Peisl, and X. Jiang (")
Sektion Physik der Ludwig-Maximilians-Universitit Miinchen, Geschwister-Scholl-Platz 1, 80539 Miinchen, Germany
(Received 19 November 1993, accepted 21 February 1994)
Abstract. We present a new method to measure the difuse scattering of amorphous mul-
tilayers. In contrast to conventional scans, that all take place in the plane of reflection, in this
out-of-plane scattering geometry the accessible range in parallel momentum transfer Qi is not limited by the sample surface. We
can therefore record data continuously from very small Qi
up to Qjj ci 2x/1, holding Qi constant at the same time. We thereby obtain a scattering
factor S(Q) of our sample, that can easily be attributed to diffuse scattering at rough inter-
faces or amorphous bulk, respectively. In the case of the W/C amorphous multilayer studied
here, the data show that the contribution of amorphous scattering is less than 2% up to about Qjj = 0.I i~~, and becomes dominant only in the wide angle region. This allows to draw the
conclusion, that the Bragg sheets observed in the vicinity of the specular condition are mainly
due to conformal roughness of the multilayer interfaces.
1. Introduction.
During recent years, much interest has been placed in the investigation of diffuse X-ray scatter-
ing of single and multilayer interfaces. To record the diffuse scattering, the detector has to be moved out of the specular position. Let the sample surface lie in the xv-plane with its normal along the z-axis, parameterized by the single valued height function z(x, y), and let the plane of reflection be the xz-plane. The specular condition is then given by Qx
= Q~ = 0,Qz > 0,
and diffuse intensity is measured with a parallel momentum transfer component Qjj, that can
be Qx,Qy, or a superposition of both. In contrast to specular reflectivity, from which the av- erage electron density profile along the interface normal can be deduced, the diffuse intensity contains information on the lateral structure of rough interfaces. It has been shown [1], that within the first Born approximation the structure factor of a rough interface is given by
s<nterface " ~i~
/~
dR R ~~~l~ol~(R)/21 J0(QiiR), (~) (")Synchrotron Radiation Laboratory, Inst. of High Energy Physics, Chinese Academy of Science, Beijing, China.1574 JOURNAL DE PHYSIQUE III N°9
Qz
Ox
Fig. 1. A Q~QV-cross section in the reciprocal space of a multilayer. The Bragg sheets are indicated in the region accessible with cv; > 0 and af > 0.
I~
'spec
f I
substrai
Fig. 2. A sketch of the scattering geometry.
with
g(~/(xi x)2 + (vi v)2) .=< iz(xi,vi) z(x,v)12 >
However, roughness is not the only source of diffusively scattered radiation. As known, amor- phous structures lead to isotropical scattering, that can be described by a structure factor
SbuIk(Q), reflecting the atomic correlation of the amorphous material. Sbuik(Q) rests finite
over the whole Q-range, converging to a constant value for low Q
Sbulk(0) # kBT p XT, (2)
where p denotes the density of scatterers and XT the isothermal compressibility [2]. It is an
experimentally established fact, that S(Q) stays practically constant (within a few To) in the range 0° < Q < Qmax/4, if Qmax is the position of the first amorphous maximum [2]. In contrast to this smooth behaviour of Sbuik(Q), S;nterface(Q) increases rapidly at low Qjj, as
the diffuse scattering of rough interfaces is essentially centered in an angular ring around the
specularly reflected beam. To discuss experimental data along these lines and to determine the Q-regions dominated by interface and bulk diffuse scattering respectively, it is necessary to
measure in a wide range of Qjj The standard experimental method to vary Qjj is the so called
rocking scan, where the sample is rocked around the specular position [3, 4]. However, at the
same time, this implies a variation in Qi = Qz, which will strongly infuence the recorded curve
by way of transmission effects such as the Yoneda wings. Finally, the incident and exit angles
can only be varied in a limited range without dumping the beam onto the sample surface. A schematic picture of the accessible Q-range in the plane of reflection is shown in figure I.
These disadvantages can be overcome, if the detector is moved out of the plane of reflection,
while keeping incident and exit angles constant. In our case, we used a position sensitive detector (PSD) aligned along the surface normal (see Fig. 2). This is basically the scattering geometry of grazing incidence diffraction (GID) [5]. We now want to show, that this geometry is useful in the study of diffuse scattering as well.
2. Experimental details.
We used an amorphous tungsten/carbon (W/C) multilayer, grown by a magnetron sputtering
process, with 60 periods of repeating layer thickness d = 48.7 h. The individual W and C layer
thickness was dw
= 23.7 hand dc
= 25 h, respectively. These values had been determined by previous specular and nonspecular measurements [6]. The experiment was performed at
the D4-beamline at Hasylab, Hamburg, using a W/Si mulilayer as a monocl~romator with a bandwidth of1.5% centered around
= 1.58 1. For this wavelength, the critical angle of the top W layer is ac
= 0.56°. All data reported here have been recorded with entrance slits of 0.I
mm and 1.5 mm for the vertical and horizontal direction respectively. Behind the sample the beam was collimated horizontally by two slits to a divergence of 0.6°. To reduce scattering by air, a flight tube between sample and detector had been installed. With a sensitive length of 40.2 mm at a distance of 309 mm, the PSD covered a range of 0° < of < 7.4° in exit angle.
The PSD signal was recorded in 500 channels by a multi channel data aquisition system.
Holding the angle of incidence fixed at a;
= 1.48°
= 2.64ac, the angle 2b is now subsequently increased from 0° to 10°. In figure 3 the integrated intensity over all 500 PSD channels is shown
as a function of 2b, including a correction for polarization and scattering volume effects. In the measured range, the intensity decreases by more than two orders of magnitude, which is in sharp contradiction to the functional behaviour of amorphous scattering, and can only be
explained by diffuse scattering at rough interfaces. Amorphous scattering can therefore be only of little importance in this range.
Of course, our geometry allows a further increase in 2b (Qjj) to investigate the wide angle
range. Figure 4 shows the corrected, integrated intensity for 10° < 2b < 60°, where the diffuse intensity attains its minimum at 2bm;n ci 22°, and then increases again to the first amorphous peak at 2bmax = 39.5°. The measured intensity contains contributions of both the W and C layers. However, the atomic number of Z = 74 makes W such a strong scatterer, that the C layer can almost be regarded as a mere spacer. Indeed, 2bmax coincides with the first
amorphous maximum measured of a single W layer. The minimum 2bm;n, indicated by the
arrow in figure 4, gives a rough estimate for the the value of Qji, where interface and bulk
scattering are of the same quantity. For smaller Qjj values, the amorphous scattering becomes
1576 JOURNAL DE PHYSIQUE III N°9
a ~ob
~
~ Q
'
a
'~ 10~
10~
10~
'
~~~
0 3 ~ ~ 9°
Fig. 3. The diffuse intensity, integrated over the exit angle cvf, in the range o° < 20 < 10° at cv; = 1.48°
= 2.64cvc. The rapid decay of intensity indicates that rough interfaces are the dominating
source of scattering.
~
=I
4
~
~~
5 fi
10 20 30 40 50 60
29°
Fig. 4. The diffuse intensity, integrated over the exit angle of, in the range 10° < 20 < 60° at cv; = 0.78°
= 1.39cvc. The first amorphous maximum of the structure factor of W at 20
= 39.5° is
clearly identified.
more and more negligible, for higher Qjj values it dominates the scattered intensity with an increasing proportion. For simplicity, we call the two domains the interface-dominated and the
bulk-dominated range, respectively.
Let us now turn to the af-resolved data, I-e- let us investigate the intensity distribution along
the PSD channels for a given value of 2b. Within the small angle approximation sin a; ci a;, the PSD channel number is proportional to Qz, and to the exit angle af. We first move the detector to 2bmax to investigate the modulation of the coherent amorphous diffuse scattering along Qz, I.e. the possible interference effects of the multilayer periodicity, that are sometimes
called Bragg sheets or streaks. As can be seen in figure 5, there are no Bragg sheets and the
intensity profile is quite flat with the exception of a small cusp at channel no. 337. This
~ a~
~~4 fi~
I
U
~Q 10~
10~
~lf"
lo'
40 135 230 325 420
CHANNELNUMBER
Fig. 5. of resolved intensity distribution of W/C multilayer at o,
= o.78°, 20
= 39.5° (position
of first amorphous maximum). The PSD channel numbers are linear in of with 1 channel number
corresponding to Acvf
= -0.01°. The cusp at PSD channel no.337 is due to a dynamical effect at
Of " °Bragg~l.
dynamical effect occurs if the exit angle equals that of the first Bragg peak of
= aBragg,i, where standing waves are excited in the multilayer. A quantitative study of this effect has been given elsewhere [7].
Figure 6 shows the four PSD spectra in the interface-dominated range, at 2b = 0°, 0.8°, 1.5°, 10°. Here, a strong modulation is observed. The different peaks need some explanation:
in figure 6a the spectrum at 2b
= 0°(Q~ = 0) is shown. The primary beam is sketched at its
position in channel no. 429. It is the only peak observed, if the sample is moved out of the beam, of course. It has been blocked out by a narrow lead strip in order to protect the detector.
Knowing the geometrical distances, the specular beam is also quickly identified. Three more
peaks are present, spaced equidistantly in the positions of the 1., 2. and 3. Bragg peak. The
peaks of the intensity modulation occur at Qz
" n 27r/d, where n is a positive integer. We
want to point out, that these Bragg sheets can be calculated by a simpe kinematical theory,
and are not the result of any dynamical effect.
The intensity of the 2. Bragg sheet is small, which is the result of the multilayer structure factor due to dw t dc. Figure fib shows the same configuration at 2b
= 0.8°, where the tails of the specular beam are still visible, even though the element of resolution has left the plane of reflection completely. This diffuse tail of the specular beam is due to surface roughness.
The FWHM of the Bragg sheets begin to broaden and the peak-to-valley ratio has decreased,
so that the 2. Bragg peak has nearly vanished. When 2b is increased to 1.5°, even weaker modulations are observed, that finally vanish completely for angles of 2b > 3°, e.g. in figure
6d. The slight shift in the peak positions is due to the angle calibration and not to any physical
effect.
1578 JOURNAL DE PHYSIQUE III N°9
~ a
io~
a) 1.
~~
3. Bragg 5Weak
$
Q160' '
I j io~
~o> spec. beam
10°
~)
10~
IO'
10°
C) 11o'
10~
IO'
10°
d)
10~
lo'
10° ,
40 135 230 325 420
CRANNELNU~IBER
Fig. 6. cvf resolved intensity distribution in the interface-dominated range at cv, = 1.48°, same scale
as in figure 5. a) 20
= 0°. The position of the blocked-out primary beam is indicated, and the specular beam as well as the first three Bragg sheets can be identified. b) 20
= 0.8°. Increase in width of the
Bragg sheets. c) 20
= 1.5°. Decrease of modulation along Qz. d) 20
= 10°. No
more Bragg sheets.
3. Interpretation and conclusion.
We have introduced a method that allows for a straightforward distinction between different contributions of diffuse scattering from amorphous multilayers thanks to a large accessible range of Qjj and the use of a position sensitive detector along Qi
The experimental set-up is basically that used for grazing incidence diffraction, but it is useful in a wide range of diffuse scattering phenomena as well. In the case of our W/C multilayer, we
have shown that for 2b < 1.5° the contribution of amorphous scattering is less than 2% of the interface diffuse scattering. This means that we have quantified the contribution of amorphous scattering to nonspecular measurements to be only a minor part of the diffuse scattering. We
thus have to attenuate the statement made about amorphous scattering contributions made
in [6], although the computer simulation program used [7] gave excellent fits of the dynamical features, I.e. cusps or peaks, whenever the incident or exit angle equals a Bragg angle of the multilayer. However, we know now that intensity in this region is mainly due to interface and not bulk amorphous scattering. The explanation of this phenomenon is, that the dynamical
effects are due to the mode of wave propagation of scattered intensity throughout the mulilayer,
but are quite insensitive to the origin of the scattered intensity, at least in the limited range of Q covered by a rocking scan.
The conclusion that amorphous scattering can be neglected for small Q, cannot be drawn
a priori for any kind of sample. Our study is rather to be understood as an experimental
test of the amorphous contribution to diffuse scattering, so that the validity of the "only- interface-scattering" assumption can be justified. In general this will be the case, whenever
the measurements are not extended to higher Q, and if the sample does not exhibit strong
large scale inhomogenities, that result in a large XT of equation (I). To compare theoretically the quantity of the two contributions, it is of course necessary to know, how large a volume and how large a surface is probed by the incoming X-ray beam, as the cross sections for bulk and interface scattering are proportional to their scattering factors (Eq. (I) and Eq. (2)),
times the scattering volume and scattering surface, respectively. Quite similar to specular reflectivity, where for higher Qz the diffuse background has to be subtracted for better accuracy, the data of a diffuse scattering experiment might need to be corrected by subtraction of the
amorphous background before fitting. The quantity of the correction can be found by the method presented.
Let us now turn to the interpretation of the Qz-resolved measurements. Interestingly enough,
in the range of bulk-dominated diffuse scattering, apart from a small dynamical effect we do not observe any modulation along Qz. Thus, scattering from different layers adds up
incoherently and the multilayer structure does not manifest itself in the form of Bragg sheets.
This is in sharp contrast to the corresponding grazing incidence diffraction measurement of
crystalline superlattices, where the Qz spectrum taken at a the 2b-position of a Bragg peak
shows characteristic satellite peaks reflecting the superlattice structure, e.g. in [8]. From a
theoretical point of view, the difference is that in the case of a crystalline superlattice, the translation invariance is broken along Qz. while in the case of an amorphous multilayer only
short range correlations of atomic positions persist.
However, in the first part of the interface-dominated range, I-e- for 0° < 2b < 3° we do observe Bragg sheets, that stem from confonnal interface roughness and are not the result of any dynamical effect. Dynamical modulations occur only in multilayers with interfaces of
high perfection and at positions of specific values of incidence or exit angle and not at the values of Qz, where the Bragg sheets are observed [7]. We can monitor the decay of the
Bragg sheets towards higher Qjj corresponding to smaller wavelengths of interface fluctuations.
This behaviour can be well understood within the framework of kinetical roughening, where in
1580 JOURNAL DE PHYSIQUE III N°9
all growth models the height-height correlation function C(x,y, At) taken at different times, vanishes faster for the spatial Fourier components of long than of short wavelenths [9]. The
analogue in multilayers would suggest that long-wavelength fluctuations replicate better across subsequent layers than fluctuations of short wavelength. This interpolates the extreme cases
of no correlation and of perfect conformality, as has been predicted [10], and measured in the
rocking-scan-geometry ill, 12]. A quantitative analysis of our data along these lines will be presented elsewhere.
Acknowledgments.
This work was supported by the Bundesministerium f6r Forschung und Technologie under Contract No. OSSWMAXI. We thank H. Rhan and M. Binder for their help with the experiment and for fruitful discussions.
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