The Optical Constants of Sputtered U and a‑Si at
30.4 and 58.4 nm.
M. B. Squires, David D. Allred and R. Steven Turley
Department of Physics and Astronomy,
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Figure 1. Example of a multilayer with a
uranium oxide cap. |
Introduction
Optical constants are used to compute the response of a
material to light. Previously published
optical constants for uranium and a‑Si over portions of the extreme
ultraviolet (EUV) are questionable. The
optical constants of a‑Si from peer-reviewed literature1,2 are not consistent with optical constants
calculated from the atomic scattering factors of crystalline Si3. The optical constants for uranium and silicon
predicted reflectivities higher than we measured. Therefore, we have fit the optical constants
of sputtered uranium and amorphous silicon using reflectance measurements.
Optical constants are important in the design of optical
devices that may be used in multilayer optics, plasma diagnostics, lithography,
and space optics. Specifically, we were
involved in the design and fabrication of space flight mirrors for the IMAGE4
explorer satellite. The proper design of
these devices depends on reliably knowing the optical properties of many
materials. It is also possible to learn
about the basic electronic properties of a material by measuring its optical
properties.
We used the optical constants of many materials to design
multilayer mirror coatings for three cameras which were part of the IMAGE
mission satellite. An iterative process
was used to select the materials and design the multilayer coating because the
optical constants were not well known.
The multilayer samples that were made were used to obtain the optical
constants of a‑Si and U at 30.4 and 58.4
nm. We were not certain if the
individual optical properties of a‑Si and uranium could be distinguished
in a multilayer, but we were partially successful in the determination of the
optical constants of a‑Si and uranium in the EUV. Many different multilayers were prepared to
understand the reflective properties of a‑Si and uranium; we will only
report on multilayers that have an a‑Si/U G of 0.7±0.03 and have a
uranium oxide overcoat. Here G is the ratio of the thickness of the top layer to the D-spacing.
Interaction of Light and
Matter
When light interacts with matter it is primarily the
electrons and their energies that determine the optical properties of the
material. Classically, the interaction
of light and matter is described by the dielectric constant, e, of the material.
It describes how an electric field is modified in the presence a
material. The dielectric constant
depends on the material's electronic structure and the frequency of the incident
light. In most materials, e depends on the cumulative effect of several
electrons. In the lower energy portion
of the spectrum (visible, IR, microwave, etc.) e is principally determined by the energies of the
valence electrons that form chemical bonds.
In the higher energy portion of the spectrum (x ray, etc.) e depends on the energies of the core electrons. When high-energy radiation interacts with a
compound e depends on the densities
and stoichiometric ratios of the core electrons in the material, and depends
very little on the bonding properties.
The wavelengths of light used in this paper fall between
these two extremes. The bonding of the
valence electrons and the properties of the core electrons are both factors in
determining the optical properties of a material. It is not completely understood how low and
high energy effects combine in the medium energy region (vacuum ultraviolet,
EUV). This paper will report the optical
properties of two materials, with specifics on how the materials were deposited
and characterized.
The refractive index, n, and the attenuation factor, k,
will be reported instead of e, because n, k are used in existing optical software,
have readily apparent physical interpretation, and are proportional to atomic
scattering factors. The relationship
between e and n, k is e1=n2‑k2, e2=2nk. A full development of the relationship
between n, k and e is found in reference 7.
Commonly, n determines the wavelength of light in a material. At higher energies (δ=1‑n) is reported instead
of n, because n differs little from unity at higher energies. The attenuation factor, k, is used to
calculate the percentage of light that is absorbed per unit length. These optical constants are used in the Fresnel equations5 to calculate the reflectance
from an interface of two materials.
Deposition and Characterization
with x rays
The optical properties of uranium and a‑Si were
calculated from single angle (14.5o from normal) reflectance
measurements of multilayer mirrors deposited via sputtering. Sputtering is used to deposit thin coatings
of materials onto substrates. Sputtering
is usually done in a medium vacuum, 1x10‑1 to 1x10‑3
torr (750 torr =1 Bar). At these
pressures the mean free path between molecules in the chamber is comparable to
the distance between the sputtering target and the substrate. This allows for better sputter rates,
coverage, density, and adhesion of the sputtered material. Before sputtering begins, the deposition
chamber is evacuated to about 10‑6 torr to remove nitrogen,
oxygen, and water vapor. This diminishes
the incorporation of impurities in the deposited film that will change the
optical properties of the materials being deposited. The partial pressures of water and nitrogen
in the system are typically less than 10‑6 torr before
deposition. The partial pressures of all
the gases in the deposition chamber are measured using a quadrupole residual
gas analyzer (RGA). (Ferran Scientific)
Deposition can begin after the base pressure in the
chamber is 3 x 10‑6 torr or lower. After the base pressure has been reached the
entrance to the vacuum pump is mostly blocked or throttled. The pressure in the deposition chamber rises to 3‑7 x 10‑6 torr after the
entrance is throttled. Ultrahigh purity
argon (99.999% pure) is then flowed into the system until the steady state
pressure of about 10‑3 torr is
reached. The argon (Ar) pressure is
maintained by mass flow controllers and is measured by the RGA. Nobel gases are commonly used for sputtering
because they do not form compounds with other materials. Ar is used to create a
plasma for sputtering because it is least expensive of the noble gases,
has a large enough mass to efficiently eject material from the surface of the
target, and readily forms a plasma.
After the Ar gas is ionized in the chamber, the
positively charged Ar ions are accelerated toward the negatively charged
target. When an Ar ion strikes the
surface of the target material there is a significant probability it will eject
one or more atoms of the target material from the target surface. The surface of the 4" diameter target
does not sputter uniformly because magnets below the target confine the plasma
in a broad ring that is about 2/3 the diameter of the target. Because of this confinement the center and
rim of the target tend to sputter at a lower rate than where the plasma is
confined. The substrates are rotated
over the target to increase the uniformity of the deposited material on the
sample. Parts of the target are blocked
off or "masked" to increase the uniformity of the material on the
sample. The shape and size of the masks
are determined by an iterative process of measuring the spatial uniformity and
then changing the masks. The thickness
of the deposited material is controlled by the time the substrate is over the target. Because the materials are deposited a few
atoms at a time the thickness can be controlled to atomic dimensions.
The thickness of the multilayer mirrors is determined by
x‑ray diffraction. X‑ray
diffraction involves reflecting x rays off a sample into a detector at varying
angles. As the angle
is scanned, the path length of the x rays inside the multilayer changes. The detector sees a series of narrow, bright
lines in a dim background that come from constructive and deconstructive
interference of the light reflecting from the layers of the multilayer. After the data has been saved it is compared
to a model. By varying the thickness of
the layers in the model the bright and dim lines can be used to fit the reflectance
data to the actual thicknesses of the layers in the multilayer. The spatial uniformity is also determined by
measuring the thickness of a multilayer coating at various places on a
sample. The ratio of the top layer
thickness to the thickness of the d‑spacing is Γ. For the multilayers used in this paper a‑Si
is the top layer. The presence of the
uranium oxide overcoat does not change the Γ of the a‑Si/U
multilayer.
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Figure 2. Chamber 1 |
The top layer of our multilayer mirrors is uranium, which
readily oxidizes, 1.5 nm oxidizes in a few minutes when exposed to air.11 We
found that having uranium oxide on the top of the multilayer increases the
reflectance at 30.4 nm and decreases the reflectance at 58.4 nm. The apparent thicknesses of the uranium oxide
layers are not the same for all of the multilayers. Many multilayers were made to determine the
optimal thickness of the uranium capping layer, 1.7 nm. The approximate thickness of the uranium
oxide layer was calculated by knowing the thickness of the pure uranium layer
deposited in vacuum and then calculating the change of volume of the uranium
when it oxidized in air, based on the density.
Uranium expands by a ratio of 1.97:1 and 3.2:1 in volume when oxidized
to UO2 and UO3. (Ref. 11 p 65).
Auger studies suggest the oxygen/uranium ratio in the surface oxide is 4:1.
This is not out of the question since UO2(OH)2
is known and has this ratio of oxygen to uranium.
Reflectivity Measurements
and Analysis
We use a McPherson, model 225, 1‑meter scanning VUV
monochromator to isolate one wavelength of light created in a plasma lamp. The light from the monochromator can be
reflected off a mirror and into a detector, or the light can be directly
measured to monitor the intensity of the plasma lamp. The system is evacuated by a vacuum pump
mounted directly behind the diffraction grating, because vacuum ultraviolet
(VUV) and EUV light is strongly absorbed in air. The channeltron detector operates at a high
electrical potential and would be destroyed by electrical arcing if operated
above 1x10‑4 torr. The detection chamber is pumped by a Varian
550 turbo molecular pump mounted directly behind the diffraction grating. The detector chambers are evacuated through
the exit slits and by a separate Varian 300 turbo molecular pump to assure the
detectors could be operated safely.
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Figure 3. Chamber 2 |
A McPherson, model 629, hollow cathode plasma lamp is
used to produce EUV light. The plasma is
made by flowing a gas in a region of high potential
difference. The pressure in the plasma
lamp is on the order of 0.1 torr, about ten thousand times less then
atmospheric pressure. EUV light is
created by collisions of gas atoms with electrons or other ionized gas atoms. These collisions cause electrons to be
excited to a higher energy level in the atom.
Because there is a vacancy in a lower energy level the electron may
decay to the lower energy, and emit light that corresponds to the energy that
was lost by the electron.
Helium gas is used to produce light at 58.4 and 30.4
nm. Neutral helium has two electrons in
the 1s shell. When an electron is
excited to the 2p state and decays to the 1s state it will radiate light at
58.4 nm. This is a very intense spectral
line because it does not need much energy, compared to the 30.4 nm, to be excited,
the helium atom does not have to be ionized, and the 2p→1s is a probable
transition. The 30.4 nm line is created
by the 2p→1s transition in a singly‑ionized helium atom. This spectral line is not as bright as 58.4
nm because of the optical efficiency of the monochromator and detector are less
at 30.4 nm. It also depends on the percent ionization of the helium gas. The hollow cathode source was run in series
with a 2000S
ballast resistor to limit the current in the lamp.
The McPherson scanning monochromator is used to select a
specific spectral wavelength of light.
The McPherson monochromator can also scan smoothly through many
wavelengths making it possible to measure the reflectivity of a sample over a
range of frequencies of light. The
monochromator can isolate light from about 30.0 to 100.0 nm, and select with an
accuracy of about 0.05 nm. Our platinum‑coated
grating reflects about 12% of the light between 30.00 and 60.0 nm.
The principally unpolarized beam of light reaching the
sample is defined by adjustable entrance and exit slits. The vertical slits are
50‑300 microns depending on the intensity of the light. The horizontal slits are normally 0.5
centimeter in width, and were infrequently changed.
Measurement Chambers
Two chambers (Fig. 2 and 3) were used to measure the
reflectivities of multilayer coatings.
Chamber 1 was used to measure absolute reflectivity. It can only measure the reflectivity of one
mirror coating at a time. Chamber 2 can
be used to measure the reflectivity of three mirrors relative to a known
reference mirror. Using Chamber 2, we
could make reflectance measurements significantly faster than using Chamber
1. Both chambers were designed to
measure the reflectance of mirrors at 14.5o relative to normal to
satisfy the requirements for the IMAGE mission mirrors.
Absolute reflectivities can be measured using Chamber 1
because the intensity of the source and the intensity of the light coming off a
mirror can be measured by the same detector.
The distance from the exit slits to the back of chamber is the same as
the total distance from the exit slits to the mirror to the side of the
chamber. These two distances are
important because the light coming from the exit slit diverges. Measurements are made by attaching the
detector to the back of chamber 1and measuring the intensity of light. The detector is then moved to the side of
Chamber 1 and a mirror is put in the center of the beam. The intensity of the
light reflected from the mirror is measured.
The mirror is removed, and the detector is put on the back again to
check the stability of the source. This
process is repeated several times because the source changes with time.
Chamber 2 was designed to measure the reflectivity of the
curved mirrors for the IMAGE mission.
The reflectivity of flat samples could be measured with a special holder
that was designed to hold four flat mirrors at the same angle and position as a
curved mirror would be in Chamber 2.
Because of the design it is very easy to measure the reflectivities of
the other three mirrors relative to reference mirror of a known
reflectivity. Only one sample needs to
be aligned because the mirror holder was machined from one piece of aluminum
and the sample positions are fixed. The
relative alignment of the sample positions has been verified and is not a
significant source of error.
Detectors
During different phases of research either
one of two detectors was used to measure the intensity of the light coming from
the monochromator and reflecting off the mirrors. A CCD camera is used to image the spatial
variations in the plasma source and to check the alignment of the mirrors in
the chambers. A channeltron detector is
used in the majority of the measurements because it is more sensitive than the
CCD camera.
The CCD camera is a Princeton Instruments back‑thinned
CCD camera with 512x512 pixels in a 1.25 cm square active surface optimized for
detection in the EUV. The benefit of
using a CCD camera is its ability to produce an image. This is important because the plasma source
discharge is not spatially uniform and it is important to know the shape of the
plasma at different wavelengths. There
are, however, some disadvantages in using the CCD camera: the camera is not as sensitive as the
channeltron, the camera must be cooled to ‑50o C, and the chip
surface is very delicate.
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Figure 4.
Calculated vs. Measured Reflectance at 30.4 nm |
The channeltron detector is an AmpTek
model MD‑501. The channeltron
detector has a background count of less than a half count per second. This background is ignored in all measurements
because usual measurements average several thousand counts a second. The channeltron is used for the majority of
the measurements because the data collection is significantly faster than the
CCD camera, there is a small background, and the detector does not need to be
cooled. The main disadvantages of using
the channeltron detector are that it must be operated below 10‑4
torr and it does not image.
Measurements and Data
Analysis
Most of the measurements were made using Chamber 2 by
aligning a molybdenum reference mirror (measured with Chamber 1) so the
greatest amount of light was reflected from the mirror at a given
wavelength. The intensity reflecting
from the reference mirror was recorded two or three times to monitor the
stability of the plasma lamp. The other
samples were then moved into the beam and the intensities of the three samples
were recorded two or three times. The
reference mirror was measured again to monitor the long‑term
stability. This process was repeated
several times to record the variations in the source, but did not give a
measure of the time variations of the source.
The raw data taken from the mirrors gave a range of
reflectivities for each mirror. There
were normal statistical variations because the detectors counted a certain
number of photons in a
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Figure 5.
Calculated vs. Measured Reflectance at 58.4 nm |
fixed time. There
were variations in the deposition of the multilayer mirror coatings and the
thickness of the uranium oxide, making each coating slightly different. Also, the reflectance is sensitive to surface
contaminants. There were variations in
the measurement of the reflectivities.
The plasma lamp may have been somewhat unstable and each mirror may have
been aligned slightly differently.
These variations can be classified as statistical and
experimental error6. The
majority of the error was experimental, because of the limitations inherent in
the measurement chambers. The
statistical error was a small factor in the error. The statistical error was reduced by
lengthening the exposure time until the statistical error was about 1%. The statistical methods used in the data
reduction are furthered explained in reference 4.
Data at 30.4 and 58.4 nm
All the mirror coatings consisted of seven periods of a-Si
on uranium with =0.7±0.03 over a range of d‑spacings from 15.0‑27.0
nm. These multilayers had a uranium
oxide overcoat on top of the seven periods of a-Si and uranium bilayers. All the mirrors were measured at 14.5o
from normal. All the mirrors were
measured multiple times, but some measurements were more reliable than others
and were so weighted. The error bars
(Figures 4,5) were calculated by the methods explained
in reference 7.
Calculated Reflectance is
Different than Measured Reflectance
At 30.4 nm (Figure 4) the measured reflectivity peak
position, relative to the calculated peak, is shifted 0.5 nm towards a higher
layer thickness. The calculated
refractive indices of uranium and a‑Si are both closer to unity (Table
1). The shift in the peak position and
the shift in the fitted optical constants are self-consistent. We are investigating the interdiffusion of
the uranium and a‑Si layers and the oxidation of uranium and a‑Si
to explain differences in the reflectivities of these multilayer mirrors.
At 58.4 nm (Figure 5), the shape of the reflectivity
versus period curve can be approximated by a straight line. This is not unexpected because the
multilayers were designed to have a broad minimum around 58.4 nm, however the reflectivity is significantly lower than the
calculated reflectivity. Both roughness
and surface oxidation can lower reflectance.
However, the reflectance is much lower than could be expected if
roughness were the only factor affecting the reflectivity. Longer wavelength light (i.e. 58.4 nm) is
scattered less by roughness than shorter wavelength light (i.e. 30.4 nm). It is well known that the effect of roughness
is to decrease the reflectance of a surface at shorter wavelengths more than at
longer wavelengths. Thus, even if the
roughness in the multilayers was more than seen in TEM8 in our
calculations it would have lowered the reflectivity at 30.4 nm much more than
at 58.4 nm. This is not seen. Multilayers capped with uranium oxide are between 1/2 to 1/3 less reflecting at 58.4 nm than would be
expected for stacks capped with silicon rather than uranium oxide. No decrease is seen in the reflectance at
30.4 nm, but an increase is seen in the reflectance as a result of the presence
uranium oxide layer on top of the last a‑Si layer. We conclude that the lowering of the
reflectance at 58.4 nm is caused by the presence of the uranium oxide layer,
rather than roughness or a deviation from the published optical constants of a‑Si
and uranium at 58.4 nm7.
The relative difference between measurement and modeled
reflectivities at 58.4 nm is more pronounced than at 30.4 nm. This shows the current understanding of
optical constants of a‑Si, uranium, and compounds like uranium oxide in
the lower to middle EUV may be deficient. This might be expected because 58.4
nm (21eV) is a lower energy then 30.4 nm (41eV), and would be more affected by
the atomic bonding of the materials in a multilayer. The typical energy of chemical bonds is a few
eV. The closer the energy of the light
is to the energy of the bonds in the material the stronger the effect on the
optical constants.
Calculated Optical
Constants