narrow rocking curve multilayer x-ray mirrors - ICDD

Copyright(c)JCPDS-International Centre for Diffraction Data 2000,Advances in X-ray Analysis,Vol.43 223
NARROW ROCKING CURVE MULTILAYER X-RAY MIRRORS
S. M. Owens ∗
Laboratory for High Energy Astrophysics, Goddard Space Flight Center, NASA,
Greenbelt, MD
R. D. Deslattes
Atomic Physics Division, National Institute of Standards and Technology,
Gaithersburg, MD
J. Pedulla
J. Pedulla Associates, Silver Spring, MD
Abstract
Over the past few years multilayer x-ray optics, or mirrors, have become a commercially
viable product for the manipulation of hard x-rays (~8 keV). Multilayer design has
typically been along the following formula: choose a pair of stable materials with high
electron density contrast; investigate their chemical compatibility for thin film deposition;
investigate the interface characteristics of the bilayer system; optimize deposition
parameters to provide a stable and repeatable yield. A few material combinations have
been found to produce high quality mirrors, including but not limited to W/Si, Mo/Si, and
Ni/C. The use of such high contrast pairs necessarily yields wide rocking curves
compared to perfect crystal analyzers. If one manufactures multilayer mirrors from two
low-density materials, or ultimately, alternating densities of the same element or
material, the rocking curve of the Bragg peak can be directly engineered to tailor the
angular divergence of the beam to the specific application.
Introduction
By artificially growing a large number of thin layers of alternating density with periodic
thickness one can simulate the reflecting effects of a one-dimensional crystal, but with a
less stringent reflection range than perfect crystal optics. Such structures, called
multilayer x-ray mirrors, have become a standard component in the toolbox for the design
of x-ray analysis equipment. The reflectivity as a function of angle of a Pt/C multilayer
mirror is shown in Figure 1. Like crystal optics, though, multilayers have their own
limitations, some of which arise due to the choice of materials with high electron density
contrast.
One of the major differences in operation between multilayers and perfect crystals is the
rocking curve of reflection, or the angular range over which x-rays are efficiently
reflected through the optic. Multilayers have rocking curves on the order of 100 to 225
arcseconds (0.03 to 0.06 degrees), while the widest perfect crystal reflection commonly
used is the Ge(111) reflection, which has a rocking curve of 16 arcseconds. Thus, there is
currently a wide gap between the widest perfect crystal reflectors and the narrowest
multilayer mirrors that deserves to be addressed.
∗ This work performed as a National Research Council Postdoctoral Research Associate at the National
Institute of Standards and Technology, Gaithersburg, MD

Copyright(c)JCPDS-International Centre for Diffraction Data 2000,Advances in X-ray Analysis,Vol.43 224
1
Simulation of a 30(Pt/C) Multilayer
0.1
Reflectivity
0.01
0.001
0.0001
10 -5
0 0.5 1 1.5 2 2.5
Grazing Angle (deg)
Figure 1. Simulated reflectivity of a 30 bilayer Pt/C multilayer mirror for 8 keV (Cu Kα 1 ) x-rays. The
FWHM of the peak at 1.16 degrees is 0.063 degrees or 225 arcseconds.
Multilayer Basics
A multilayer mirror is typically comprised of a number (25 – 100) of bilayers of materials
like W/Si, Mo/Si, or Ni/C. Historically, the high-density material is termed the
“reflector”, and the low-density material the “spacer”, even though scattering occurs at
the interface between materials, and not in the materials themselves. This misnomer may
lead one to assume that high-density reflector and low-density spacer materials are
necessary to achieve high performance. While this is not entirely true, the choice of high
electron density contrast means that a large amount of radiation is scattered at each
interface, and the maximum possible reflectivity is achieved with relatively few bilayers.
If only a small number of interfaces contribute to the reflection the rocking curve is
relatively wide, according to standard diffraction theory.
By designing a multilayer mirror using a pair of materials with lower contrast, less
radiation is scattered at each interface, more interfaces can contribute to the reflection
process and a narrower rocking curve is the result. Taken to the limit, controlling the
density of alternating layers of a single element or material allows one to directly
engineer the reflectivity at each interface, and thus the total number of interfaces involved
in a reflection, yielding a high degree of control over the rocking curve width.

Copyright(c)JCPDS-International Centre for Diffraction Data 2000,Advances in X-ray Analysis,Vol.43 225
Preliminary Results
Using our Dual Ion-Beam Assisted Deposition (DIBAD) facility, we have a wide range
of materials available for deposition, allowing for a number of interesting material
combinations. Our first attempt at reducing the electron density contrast of the bilayer
was a Ti/C combination. This bilayer is a reasonable start, as it is not significantly
different from the standard Ni/C bilayer typically produced in our lab. A 60 bilayer
mirror was grown on a 3” x 3” float glass substrate, with a total bilayer spacing of 38.8 Å
and Γ = 0.52 and yielded 39% peak reflectivity and a rocking curve width of 76
arcseconds at a Bragg angle of 1.16 degrees. The experimental and modeled reflectivity
curves are shown in Figure 2, and the model parameters are in Table 1. Using these layer
parameters and extrapolating to 100 bilayers, this system should yield 49% reflectivity
with a rocking curve width of 50 arcseconds. The peak reflectivity eventually saturates at
around 55% with 150 bilayers using the parameters determined for our prototype mirror.
1
Experimental and Modeled Reflectivity
for a 60(Ti/C) Multilayer
Reflectivity
0.1
0.01
0.001
0.0001
Experiment
Model
10 -5
10 -6
0 0.5 1 1.5 2 2.5 3 3.5 4
Grazing Angle (deg)
Figure 2. Experimental and modeled reflectivity for a 60 bilayer Ti/C multilayer mirror. The first Bragg
peak at 1.16° has a peak reflectivity of 39% and a FWHM of 76 arcseconds (0.021 degrees).
Layer Thickness (Å) Interface (Å) Density (g/cm 3 )
Ti 20.2 2.4 4.49
C 18.6 4.2 2.27
Glass --- 1.0 2.55
Table 1. Modeled parameters for the prototype 60 bilayer Ti/C multilayer mirror.

Copyright(c)JCPDS-International Centre for Diffraction Data 2000,Advances in X-ray Analysis,Vol.43 226
1
100x(Ti/C) and 150x(Ti/C)
0.6
0.1
100x(Ti/C)
150x(Ti/C)
0.5
Reflectivity
0.01
0.001
Reflectivity
0.4
0.3
100x(Ti/C)
150x(Ti/C)
0.2
0.0001
0.1
10 -5
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
0
1.1 1.15 1.2 1.25
Grazing Angle (deg)
Figure 3. Extrapolated performance of 100 and 150 bilayer Ti/C mirrors based on the model parameters
from the prototype 60 bilayer sample.
Experimental and Modeled Reflectivity
for 20x(Si/Si 3
N 4
) Multilayer
10 0 0 0.5 1 1.5 2 2.5 3
10 -1
10 -2
thick (Å) inter (Å) density
Si 70.6 3.5 2.68
20x(
Si 3
N 4
16.8 1.1 3.13
Si 61.9 1.0 2.66
Flt Gls 1.0 2.52
Reflectivity
10 -3
10 -4
Experiment
Model
10 -5
10 -6
10 -7
Grazing Angle (deg)
Figure 4. Experimental and modeled reflectivity for a 20 bilayer Si/Si 3 N 4 multiayer mirror. The total
bilayer thickness is 78.7 Å, and Γ = 0.21. Further simulations indicate that Γ = 0.5 yields the highest peak
reflectivity. The first Bragg peak has a reflectivity of 3% and a rocking curve of 77 arcseconds.

Copyright(c)JCPDS-International Centre for Diffraction Data 2000,Advances in X-ray Analysis,Vol.43 227
The next system investigated was a Si/Si 3 N 4 combination, where the resulting mass
density differs by only 0.5 g/cm 3 (modeled ρ Si = 2.66 g/cm 3 and ρ Si3N4 = 3.15 g/cm 3 ). Our
first attempt was a mirror with 20 bilayers which yields 3% reflectivity and a rocking
curve of 77 arcseconds at a Bragg angle of 0.6 degrees. A second mirror with 75 bilayers
yields 12% reflectivity at 0.82 degrees. Again, taking the modeled layer parameters and
extrapolating to 150 bilayers, this bilayer combination should yield 50% reflectivity and a
rocking curve of 33 arcseconds at a Bragg angle of 1.1 degrees. (The peak reflectivity
begins to saturate at ~60%, but not until >300 bilayers.)
Finally, the most scientifically interesting combination presented here comes when we
utilize the full power of our dual ion beam system and modify the density of component
layers in the bilayer. By appropriate application of the assist beam during deposition, we
can control the density of carbon layers from as low as 2.1 g/cm 3 to as high as 2.86
g/cm 3 . 1 By turning the assist beam on and off during carbon deposition, we have
produced multilayer x-ray mirrors using alternating high and low-density carbon layers
(HDC and LDC respectively). Our first prototype mirror with 24 layer pairs (Figure 5a)
has a peak reflectivity of 1% and a rocking curve of 72 arcseconds at a Bragg angle of 0.6
degrees. A second mirror with 50 layer pairs (Figure 5b) has a peak reflectivity of 4%
with a rocking curve of 45 arcseconds also at 0.6 degrees.
a) b)
Experimental and Modeled Reflectivity
of a 24 bilayer HDC/LDC Mirror
Experimental Reflectivity of a 50 bilayer
HDC/LDC Mirror
10 -1
10 -1
Reflectivity
10 -2
10 -3
10 0 0 0.5 1 1.5 2
Experiment
Model
Reflectivity
10 0 0 0.5 1 1.5 2
10 -2
10 -3
10 -4
10 -4
10 -5
10 -5
10 -6
10 -6
Grazing Angle (deg)
Grazing Angle (deg)
Figure 5. a)Experimental and modeled reflectivity of a 24 bilayer HDC/LDC mirror. The total bilayer
thickness is 60.9 Å and Γ = 0.63. b) Experimental reflecitivity of a 50 bilayer HDC/LDC multilayer. The
total bilayer thickness in this case is 79.5 Å and Γ = 0.50. With the particular incident beam optics used for
these measurements, the beam is not sufficiently narrow in angle to resolve the Kiessig fringes of the 50
bilayer mirror. The oscillations that appear are an aliasing effect between the incident beam and the actual
fringes.
Simulations based on these results indicate that a mirror made with 100 bilayers of high
and low-density carbon will yield a peak reflectivity of 33% and a rocking curve of 25
arcseconds, while 150 bilayers will yield a peak reflectivity of 50% and a rocking curve
of 19 arcseconds. One important difficulty in this system is that carbon layers tend to be
deposited under extremely high compression, causing either bowing of thin substrates
such as silicon wafers or shattering of the mirror stack after a large number of bilayers are

Copyright(c)JCPDS-International Centre for Diffraction Data 2000,Advances in X-ray Analysis,Vol.43 228
deposited. At least one deposition method has been proposed to alleviate this problem, 2
but it has not yet been implemented in our laboratory.
Extrapolated Reflectivity for 100x(HDC/LDC)
Extrapolated Reflectivity for 150x(HDC/LDC)
10 -1
10 -1
10 -2
10 -2
Reflectivity
10 0 0 0.5 1 1.5 2
10 -3
10 -4
Reflectivity
10 0 0 0.5 1 1.5 2
10 -3
10 -4
10 -5
10 -5
10 -6
10 -6
10 -7
10 -7
Grazing Angle (deg)
Grazing Angle (deg)
Figure 6. Extrapolated reflectivity curves for mirrors using 100 and 150 bilayers of high-density and lowdensity
carbon. The simulations are based on a bilayer thickness of 80 Å and Γ = 0.5. The peak reflectivity
at the first Bragg peak are 33% and 50% respectively.
Conclusions
The potential for producing narrow rocking curve multilayers has been demonstrated
using a few examples of prototypes from our deposition laboratory. The current lack of x-
ray optics that operate in the range between 16 and 100 arcseconds can be addressed with
by the appropriate choice of materials for the mirror system. All three of the material
systems described here should be able to produce mirrors with greater than 50%
reflectivity, and rocking curves of 50 arcseconds or less.
Such mirrors should have useful application in a variety of areas. In wavelength
dispersive x-ray fluorescence, mirrors with low atomic number layers can scan a wide
range of hard x-ray wavelengths without the hindrance of absorption edges. In diffraction
applications, one may be able to choose a mirror with the most appropriate rocking curve,
while maintaining the highest flux throughput possible. Also as can be seen by comparing
the Pt/C simulation to the other curves presented, the reflectivity away from the Bragg
peaks is much lower in these low contrast systems, significantly reducing the background
even before other measures are incorporated.
1 J. Pedulla, A. Bartos and R. D. Deslattes, “Hard High Density Carbon Thin Films for X-ray Multilayers
Optics”, MRS Symp. Proc., 342 (1994).
2 M. Gioti, S. Logothetidis, and C. Charitidis, “Stress relaxation and stability in thick amorphous carbon
films deposited in layer structure”, Appl. Phys. Lett., 73, 184 (1998).