studying the optical properties of - Physics and Astronomy

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STUDYING THE OPTICAL PROPERTIES OF
THE NPD MIRRORS
by
Yenny N. Martinez
Submitted to the Department of Physics and Astronomy in partial fulfillment
of graduation requirements for the degree of
Bachelor of Science
Brigham Young University
April 2002
Advisor: David D. Allred
Advisor: R. Steven Turley
Signature: _________________________
Signature: _________________________
Thesis Coordinator: Justin Peatross
Department Chair: R. Steven Turley
Signature: _________________________
Signature: _________________________
Abstract
In photographs taken from recent space missions, evidence has been found that
water was once present on Mars’ surface. To explain the absence of the water today,
several hypotheses have been developed. One of these hypotheses speculates that
because Mars lacks a magnetic field, its atmosphere has been depleted by interaction with
the solar wind. In 2003, the European Space Agency plans to send a spacecraft to Mars
in order to test this hypothesis. One of the several instruments on the ESA spacecraft, the
Energetic Neutral Particle Analyzer, contains a time-of-flight neutral particle detector
(NPD). This NPD will measure the momentum of neutral particles formed by the
interaction of the solar wind and Mars’ atmospheric particles. The XUV research group
at BYU designed and fabricated the start surfaces, which were delivered in the summer of
2001. This thesis will be based on the study of effects caused by changes to the
magnesium fluoride layer of the actual NPD mirrors. This research will be done through
modeling using the program IMD and actual reflectance data taken.
Acknowledgments
I would like to deeply thank Spencer Olson, David Allred, and R. Steven Turley for the
help and insight they have given me throughout this research. I would like to express
thanks to Matt Squires, Mike Newey, Shannon Lunt and all other students that have
assisted me with this research and the review of this thesis. All my friends that are there
for me through thick and thin have my love and appreciation. Finally, I want to deeply
thank my wonderful family who always supports me in all my goals and choices.
CONTENTS
List of Figures
v
List of Tables
v
1
Introduction
1
2
Mars Exploration
3
3
4
5
6
2.1
Reasons for Mars Exploration and the Mars Express Mission ................. 3
2.2
Analyzer of Space Plasma and Energetic Atoms (ASPERA) ................... 5
2.3
Neutral Particle Detector Start Surface ..................................................... 6
Theory
8
3.1
Particle Reflectivity and Electron Emittivity ............................................ 8
3.2
Electromagnetic Waves ............................................................................ 9
3.3
Fresnel Coefficients and Reflectance ........................................................ 11
3.4
Thin Films ................................................................................................. 14
3.5
Microchannel Plates .................................................................................. 17
Computational Modeling
18
4.1
Manufacturability ...................................................................................... 18
4.2
Global Optimization and the Generic Algorithm ...................................... 19
4.3
Local Optimization and the Simplex Algorithm ....................................... 21
4.4
IMD ........................................................................................................... 21
4.5
Models for a Start Surface ........................................................................ 22
Experimental Instruments
26
5.1
Evaporation System .................................................................................. 26
5.2
DC-Sputtering System .............................................................................. 26*
5.3
Reflectometry ............................................................................................ 18
5.4
Ellipsometry .............................................................................................. 19
Experimental Setup
19
6.1
Substrate .................................................................................................... 33
6.2
Transmissive Layer ................................................................................... 33
6.3
Reflective Layers ...................................................................................... 33
6.4
Final Design .............................................................................................. 33
7
Experimental Results and Analysis
21
8
Future Work
24
LIST OF FIGURES
1
Mars ............................................................................................................. 3
2
Schematic drawing of the NPD sensor ........................................................ 6
3
The incident, reflected and transmitted wave fields at a boundary .............. 12
4
Light scattering through a multilayer ........................................................... 14
5
The interior of an electron multiplier tube – part of an MCP ...................... 17
6
Schematic diagram of the Generic Algorithm ............................................. 19
7
LIST OF TABLES
Chapter 1: INTRODUCTION
By observing Mars’ surface from space, spacecrafts have documented the
existence of visible riverbeds and river canyons on the surface of this planet, suggesting
that water once ran through these channels[1]. It is now evident that if this water actually
did exist on Mars’ surface, it is not present anymore. To explain the disappearance of the
water, several hypotheses have been developed. A leading explanation and the one
important for the context of this thesis is the following: Mars’ lack of a magnetic field
allowed charged, energetic particles from the solar wind to interact directly with Mars’
atmosphere, causing its erosion. Because of the lack of an atmosphere, water could not
be sustained on Mars’ surface. Magnetic fields deflect solar-wind ions before they
penetrate the planet’s atmosphere. Unlike our Earth, Mars is exposed to the full force of
the incoming solar wind because it lacks a planet-wide magnetic field.
In 2003, the European Space Agency plans to send a spacecraft to Mars in order
to test this hypothesis as well as aid in determining other facts about water’s existence on
Mars. The main instrument on board to test this hypothesis is the Energetic Neutral
Particle Analyzer. This instrument contains a time-of-flight neutral particle detector
(NPD). This NPD will measure the momentum of neutral particles formed by the
interaction between the solar wind and Mars’ atmosphere.
When a neutral particle enters the NPD it reflects off of a surface called the start
surface. The impact of the neutral particle on the start surface can cause the emission of
an electron that is attracted by an electric field to a detector called the start MPC. When
the emitted electron hits the start MCP a timer is started. This timer is stopped when
the stop detector is hit by the emitted electron of a stop surface when this surface is
impacted by the still-traveling neutral particle. Energetic light entering the NPD may
also reflect off the start surface and create noise in the signal of the stop detector. In
space, there is an abundant supply of vacuum ultraviolet light, particularly the Lyman
alpha line at 10.2 eV, which is energetic enough to cause this effect. This presents a
problem to the performance of the NPD.
There are two necessary properties that the start surfaces needs in order to
improve the data taken by the NPD: 1) the surfaces must have ample electrons to emit
when hit by the neutral particles, and 2) the surfaces must poorly reflect ultraviolet light
at the grazing incidence angle of 15 ± 5°. The XUV research group at BYU was asked
to create the start and stop surfaces, meeting these two conditions. By using two
types of algorithms, we developed a theoretical multilayer model that optimized the
desired characteristics for the NPD mirrors. We tested potential mirrors for their
reflectance at 15° in the ultraviolet to determine the optimal design for the start surface.
Finally a design was chosen and the start surfaces were fabricated and delivered in the
summer of 2001. Because of the time constraints put on the NPD project, the optical
properties of these surfaces were not entirely understood.
The topic of this thesis is to implicitly analyze the optical properties of these NPD
mirrors by focusing on the middle layer used to fabricate them, the magnesium fluoride
layer. Of course, the actual NPD mirrors are not available to me anymore. However, I
will model the effects that can occur because of changes in this middle layer.
Chapter 2: MARS EXPLORATION
2.1 Reasons for Mars Exploration and the Mars Express Mission
Mars’ position in the solar system gives
its exploration a unique importance: its form
and features were a result of being in the
middle of two types of accretion zones. On one
side there was the “outer volatile-rich more
oxidized region” from which the asteroid belt
was formed, and on the other side there was the
“inner, more refractory and less oxidized
FIGURE 1: Mars
region” from which our Earth and the other inner planets formed. Understanding Mars
and its characteristics is important for the further understanding of our Earth’s
formation[2].
One of the more interesting questions asked about Mars is whether liquid water
existed or even currently exists on its surface. When this question is answered, the
hypothesis of possible life on Mars will have strong evidence either against or for it. This
is because life is dependent on the accessibility of water. The current European Space
Agency (ESA) project, the Mars Express, will be launched in 2003 to explore the
possibilities. Its exploration will be “the most thorough search of the red planet yet for
liquid water[2].”
Evidence was found about 100 years ago that frozen water exists at the Martian
poles, and water vapor has also been found in its thin atmosphere. Because of the visible
riverbeds and river channels now on Mars’ surface, this evidence is believed to be
strongly sound. However, it is well known that liquid water is not found on Mars’
surface. So what happened to this flowing liquid? “Something happened within 100
million years (which is a short time in geological terms). The atmospheric pressure and
temperature decreased very quickly. Why? No one knows,” stated Agustin Chicarro, an
ESA project scientist working on the Mars Express mission. Evidently, because of the
drastic change in climate on Mars, it became a cold, dry planet.
There are two explanations for what happened to this liquid water: it could have
evaporated into space like most of the atmosphere; or it could currently be trapped in
rocks underground. “Water can either sink or escape. If there is any liquid in the
subsurface, then it’s no more than a few kilometers down. We need to know the total
surface and subsurface distribution of water. To know whether it escapes outside the
planet, we need to look at the escape processes from the atmosphere,” says Marcello
Coradini, the solar system missions’ coordinator for the ESA[2]. The Mars Express will
probe the first possibility.
Currently, Mar’s atmospheric pressure is about 0.6% of Earth’s atmosphere. This
is in contrast to the similar, Earth-like atmosphere Mars probably had billions of years
ago. In order to study how this liquid water could have evaporated out of Mars’ surface,
the depletion of the atmosphere needs to be understood. One of the Mars Express’
instruments, the Analyzer of Space Plasma and Energetic Atoms (ASPERA-3), will
explore the procedure of this erosion.
In the case of the Earth, it is known that the magnetic field it produces deflects the
solar wind away from the atmosphere. Since Mars lacks a magnetic field, this field
shielding is not present for the atmosphere, leaving the outermost atmospheric layers
open for bombardment of charged particles from the solar wind. The gases found in
these outer layers become ionized because of this interaction and leave the atmosphere
along with the solar wind. This mechanism is postulated to be the reason for the loss of
most of Mars’ atmosphere. It is also postulated that as Mars’ water evaporated from its
surface, the vapor reached the upper atmosphere where sunlight can break up the
molecules into hydrogen and oxygen. These individual atoms could easily ionize and
eventually be swept away from the atmosphere by the solar wind[3].
The Mars Express will be equipped with eight instruments designed to observe
different aspects of Mars in search for answers to what happened to the liquid water. The
mission is expected to last for nearly two Earth (one Martian) years[2].
2.2 Analyzer of Space Plasma and Energetic Atoms (ASPERA-3)
As stated before Mars’ atmosphere is believed to have been ionized by its
interaction with charged particles from the solar wind. As these ions leave the
atmosphere, they can become neutral atoms again by stripping electrons off neutral
background gas atoms. Now, these newly formed neutral atoms move through space
with kinetic energy, relying on the fact that the original ions were energetic. Since they
are neutral in charge, these atoms are undeflected by electromagnetic fields and travel in
a straight line from their formation[3].
One of the four sensors on the ASPERA-3 instrument is responsible for detecting
these energetic neutral atoms (ENAs). Through the detection of ENAs, the erosion of the
Martian atmosphere is hoped to be understood, eventually leading to answers about the
disappearance of liquid water. ASPERA-3 is designed to build a global image of the
region in the upper atmosphere that interacts with the solar wind through the detection of
ENAs and their direction of travel. “From a position close to apocenter (the point on
Mars Express’s orbit most distant from Mars), the neutral particle imager will generate
instantaneous images of the whole planet that reflect the density of the plasma. We will
be able to see the plasma escaping the planet,” says Lundin[3]. Similar tracking of the
Earth’s atmosphere by ENA detection has previously been implemented, and its success
has shown the importance for this type of investigation.
2.3 Neutral Particle Detector Start Surface
The ASPERA-3 instrument is the holder of the time-of-flight Neutral Particle
Detector (NPD), the sensor in charge of detecting the ENAs. A schematic diagram of the
NPD layout is shown in Figure 2 below.
The NPD sensor is a one-dimensional pinhole camera with a 90° field of view.
Charged particles are deflected from entering the sensor by an electrostatic deflection
system also used as a collimator. Only ENAs are theoretically allowed to continue their
START SURFACE
TO STOP DETECTOR (MCP)
-e
CHARGE PARTICLE
DEFLECTION
-e
STOP SURFACE
TO START DETECTOR (MCP)
FIGURE 2: Schematic drawing of the NPD sensor
path into the detector. As the neutral particles enter the detector, they will impact a start
surface, causing secondary electrons to be released. These secondary electrons will be
detected by a start microchannel plate (MCP). After reflection off the start surface, the
ENAs continue their travel and hit a stop surface, again releasing secondary electrons.
These electrons are detected by a stop MCP, allowing a time-of-flight measurement of
the ENA particle[4]. Background information about MCPs is found in chapter 3[5].
In reality, the NPD detector is subject to background noise from 121.6 nm
radiation due to H2 gas present in the Martian atmosphere[6]. This radiation comes about
through the excitation of this gas by solar radiation. Therefore, for optimal performance
the NPD detector requires a start and stop surface having two main characteristics. First,
both surfaces need a high secondary electron yield upon neutral particle impact. Second,
the surfaces need to be poor reflectors of ultraviolet light at an incident angle of 15º.
Another secondary requirement imposed on the NPD mirrors is that the start surfaces
should be very smooth, therefore optimizing specular particle reflection. This
requirement is not necessarily imposed on the stop surface. These imposed properties on
the NPD mirrors should be stable with time[4]. Background information on particle
reflectivity and electron emissivity is given in Chapter 3.
Chapter 3: THEORY
3.1 Particle Reflectivity and Electron Emissivity
Electrically scattered particles and waves reflect off a surface according to the law
of specular reflection: the incident angle of the incoming particle or light (measured
according to the normal of the surface) equals the angle the reflected object makes with
the normal to the surface. The direction the reflected particle or light takes depends on
the smoothness of the surface reflecting. For example: take particles aimed at a surface,
all traveling in a parallel path relative to each other. If the reflecting surface is smooth on
the order of the size or wavelength of the object being reflected, then the reflected
particles will continue to follow a parallel path according to the law of reflection. They
will follow a parallel path after reflection because their reflected angle will be relatively
the same.
If, however, the reflecting surface is rough or irregular, diffuse reflection occurs.
As our hypothetical stream of particles impacts the surface in question, each individual
particle obeys the law of reflection. Yet, the individual particles reflecting off the rough
surface do not have the same angle of reflection[7]. This type of reflection causes the
paths of the particles to deviate from a relative parallel path. The principle of reflection
is important for the correct reflection of ENAs. After reflecting off the start surface, the
ENAs need to travel toward the stop surface, causing secondary electrons to be ejected
and the stop detector to be triggered. The correct reflection of the ENAs off the start
surface will ensure that there is no loss of counts at the detector. ENAs are on the atomic
scale, with sizes on the order of angstroms1. Therefore, our surfaces are required to be
smoothed as measured on the order of angstroms[8].
Another important quality of the NPD mirrors was the high emission of electrons
upon impact of the surface by ENAs. As was previously stated, this was one of the two
important characteristics these multilayers needed. In order to have high electron
emission, the surfaces used for the multilayers need an ample supply of electrons. Work
done by ESA affiliates showed that chromium, tungsten, titanium, and their various
oxides were suitable for emitting an electron upon impact. Therefore, we developed
models for suitable NPD mirrors based on these different materials. In reality, the
existence of an oxidized layer buildup on most metals is inevitable. Because of this fact,
our theoretical multilayer surfaces included an oxidized metal on the top of the surfaces
in our calculations[8].
3.2 Electromagnetic Waves
Electromagnetic radiation propagates differently in materials than in free space
because of the presence of charge. The electric field of an electromagnetic wave in an
absorbing medium is represented by the following sinusoidal function:
  
E  E0ei ( K r t  )

where K 
2n~
0
3.2.1
~  n  i is called the
is called the (complex) wave number and n

(complex) index of refraction. K determines the direction of propagation and in an

isotropic medium, it is perpendicular to E0 . The parameters n and  depend on the
1
1 angstrom = 1 x 10-10 meter. The units for angstroms are symbolized by Å.
material the wave is traveling through – these are the optical constants of the material.
These parameters determine the change in wave velocity and intensity of the radiation.
Inserting these parameters into Equation 3.2.1 and assuming that its propagation direction
is along the positive z axis, we obtain:


 ~ i  20n z t  2 z


E  E0 e
e 0 .
3.2.2
The phase of the wave has been absorbed into the amplitude of the wave, making the
amplitude complex.
There are two parts to this wave: the usual oscillatory behavior of the wave,
represented by the first exponential, and a decaying part, contained in the second
exponential. The complex parameter  of n~ causes the decay in the traveling wave.
The decay of the amplitude for this wave is physically explained as the absorption of the
wave in the material, in which the energy of the traveling wave is decreased. Looking at
the second exponential, one notices that amplitude decay can be accelerated by traveling
further in the material or by increasing the complex parameter  of a material.
The indices of refraction for typical materials at wavelengths in the extreme
ultraviolet are complex. The real part is very close to 1, and the imaginary part is not
zero. This presents two problems: 1) the contrast in the real part of the index of
refraction is small between vacuum or other materials, so little reflection occurs, and 2)
the electromagnetic wave is completely absorbed before traveling very far in the material.
Because of these two factors, it is necessary to fabricate multilayer thin films to
manipulate ultraviolet light. Section 3.4 goes into more detail on what thin films are and
what types of structures are needed when working with wavelengths in this regime.
Multiplying Equation 3.2.2 by its complex conjugate gives us the expression for
the intensity of the radiation:
I  I 0 e z
where the absorption constant  
4
0
3.2.3
and I0 is the intensity of the incident radiation.
Of the total radiation energy incident on an object, a fraction is reflected from the surface,
a fraction is transmitted, and the remaining fraction is lost through electronic absorption
processes and by scattering at surface and volume imperfections[9].
The idea of electromagnetic destructive interference becomes important in our
theory for the NPD mirrors. The specific optical design target for the NPD mirrors is that
at an incident grazing angle of 15 ± 5°, the amount of background ultraviolet light
reflected is minimized in order to avoid incorrect triggering of the stop detector. This
background ultraviolet light is seen to be mostly the Lyman alpha line, with a wavelength
of 1215.7 Å and energy of 10.24 eV. Because of the wave property of light, we can
produce multilayer surfaces that achieve minimum reflection at the desired incident
angle. All waves interfere either constructively or destructively, depending on the phase
of the different components of the wave as they meet. Therefore, the NPD mirrors were
designed to cause this ultraviolet light to destructively interfere, reducing the amount of
noise reaching the stop detector[8]. ***BOTH PHASE AND AMPLITUDE OF THE WAVES
NEED TO MATCH.
3.3 Fresnel Coefficients and Reflectance
For the sake of simplicity, we will ignore the imaginary portion of the index of
refraction in this section. The following notation can be rewritten in complex terms, but
since only the real part of the field corresponds to the physical field, it is easier to display
it in real terms. Because only the real part of the index will be regarded, the complex


wave number K becomes k , the real wave number. As stated before, the amplitude of
an electromagnetic wave traveling in an isotropic medium is confined to a plane

perpendicular to k . We are also assuming that there exists a distinct interface between
two materials, therefore supposing that there is no roughness of the surfaces.
As light reaches a boundary between two media with different indices of
refraction, a certain amount reflects off the boundary and a certain amount transmits
through. (In section 3.2, however, we noticed that ultraviolet light is violently absorbed
by most materials because of the large value of  for these wavelengths.) Therefore, we
can express the electric field of light reaching a boundary between two media as two

orthogonal components in the plane perpendicular to k , as shown in Figure 3. Three k

vectors are seen in this figure: k i represents the incident electromagnetic wave, making

an angle  i with the normal to the surface. k r specifies the reflected plane wave and it

makes an angle  r with the normal to the surface. Finally, k t represents the transmitted
FIGURE 3: The incident, reflected and transmitted wave fields at a boundary
electromagnetic wave, which makes an angle  t with the normal to the surface. This
plane, containing all three k-vectors, is called the plane of incidence. We define the
component of the electric field perpendicular to the plane of incidence as the s
polarization. Likewise, the p polarization corresponds to the component of the electric
field that is parallel to the plane of incidence.
From the relationships between the three different k-vectors and electric field
components, we derive two well-known laws of wave phenomena (the law of reflection
was introduced in Section 3.1):
r  i
Law of Reflection
3.3.1
ni sin  i  nt sin  t
Snell’s Law
3.3.2
The amount of light reflected off the boundary depends on the index of refraction
of both media and the angle of incidence of the light with the boundary with respect to
the normal to the boundary. Augustin Fresnel derived certain equations that relate the
reflected and transmitted electric field amplitudes to the incident electric field amplitude.
This relationship is different for the different polarization. These equations are (only the
reflection Fresnel coefficients are shown):
rs 
rp 
E s cos   n 2  sin 2 

Ei cos   n 2  sin 2 
Ep
Ei

 n 2 cos  n 2  sin 2 
n 2 cos  n 2  sin 2 
where    i is the incident angle and n 
3.3.3
,
3.3.4
n2
. As seen before, for materials in the
n1
extreme ultraviolet the index of refraction for materials is complex. Since the index is
complex, the incident angle is also complex, making  unequal to the physical reflected
angle.
The fraction of reflected light of each polarization is known as the reflectance. It
is also different for each type of polarization:
Rs  rs
R p  rp
2
3.3.5
2
3.3.6
Two incident angle extremes are of interest: as the incidence angle approaches   90 ,
the reflection Fresnel coefficients approach
rs  1
and
rp  1
3.3.7
and the reflectance for both polarizations approaches 1. As the incidence angle
approaches   0 , the reflection Fresnel coefficients both approach
rs  rp 
1 n
1 n
3.3.8
and the reflectance is found through Equations 3.3.5 and 3.3.6.
3.4 Thin Films
Most of our common elements are opaque to ultraviolet light, causing absorption
of this energetic light. This absorption is due to interband electron transitions in the
material[9]. Yet, as introduced in Section 3.3, reflections occur at the boundary between
materials of different index of refraction, even for ultraviolet light. Therefore, in order to
manipulate ultraviolet light, thin film structures known as multilayer mirrors are
fabricated.
A thin film is a very thin layer of some material; in our case, these materials are
FIGURE 4: Light scattering through a multilayer
chromium, magnesium fluoride, and tungsten. These thin films are often laid on top of
each other in any desired order by thermal evaporation or dc magnetron sputtering on top
of a thicker material called a substrate. These thin layers have thicknesses of hundreds of
angstroms whereas the substrate has thicknesses of millimeters. The order of the layer
deposition depends on the desired performance of the multilayer. Figure 4 shows a
simplified model of how a multilayer works.
Ultraviolet light can be guided in a desired direction by reflecting off the surfaces
of the different layers in a multilayer. This guidance is improved by the surface’s
smoothness, thickness, and other subtle factors. Because of the difference between the
indices of refraction of the materials, the different surfaces reflect a specific amount of
light, depending on the surface’s characteristics. For the NPD mirrors, we desired that
the reflection of UV light to be as suppressed as possible, so we rely on the destructive
interference of light as it reflected off the different surfaces. In order to achieve
destructive interference, the correct thicknesses and optical constants for the thin films
need to be used.
Antireflection from a multilayer structure requires a transmissive material layer
sandwiched between two reflective material layers. This amounts to a multilayer
structure composed of a combination of alternating high and low index of refraction
materials. Because the indices will alternate, reflection will occur at more than one
boundary. Therefore, the superposition of all of the reflected waves needs to be taken
into account. As stated before, the following notation is valid for complex refractive
indices, even though we use real index notation. We will assume the multilayer structure
in question is a repeated high-low refractive index thin film structure[10].
When radiation traveling in free space enters a medium of a specific index of
refraction n , its speed changes from v  c to v 
equal to v 
c
. Radiation feels a change of speed
n
c
, depending on the index of refraction of the thin film it is traversing,
n
independent of whether it is coming from free space or another film of a different index
of refraction. This change in velocity corresponds to a change of the initial wavelength
from   0 to  
0
n
, therefore changing the wave number of the initial
electromagnetic wave to k 
2

. As radiation, entering a thin film with a transmission
angle of  t , traverses a thickness d of this thin film with index of refraction n , its
electric field phase is adjusted by:
  kd cos t 
2n
0
d cos t .
3.4.1
As radiation approaches the first boundary of our multilayer structure, a fraction
of it is reflected and a fraction of it is transmitted. The initial radiation travels from air
( n0  1 ) to a higher index of refraction ( n1 > 1). Therefore, at this boundary, the
reflected fraction of radiation acquires a phase shift of  . The transmitted fraction of the
radiation traverses the thin film and reaches the boundary between this thin film and
another thin film with a lower index of refraction ( n1 > n 2 ). Radiation reaching this
boundary will also feel part of it reflect and part of it transmit. However, at this
boundary, there is no phase shift adjustment to the electric field. The transmitted fraction
of the radiation approaches the next thin film boundary, which is similar to the boundary
between free space and the first boundary ( n 2 < n3 ). Therefore, the electromagnetic
wave experiences a phase shift of  . Here as well, the radiation will partially reflect and
partially transmit. The pattern continues through each boundary in the multilayer.
Notice that we have neglected absorption or scattering of the radiation, as stated in
Section 3.2.
In order for a multilayer structure to have low reflectance, we need the thickness
of each thin film to have a half-wave thickness. This amounts to the phase acquired by
the electric field (Equation 3.4.1) to equal  , giving the thickness of the layer as:
d
0
2n cos t
3.4.2
This amounts to the reflected wave in each layer meeting the wave in the previous layer
out of phase, therefore destructively interfering. In reality, because of the absorbing
characteristic of most materials in the extreme ultraviolet, the phase change after a
reflection is not exactly π but a phase change between 0 and π. Therefore, the layer
thicknesses necessary to create the same effect as theory will be different for the actual
fabricated mirrors.
3.5 Microchannel Plates
A microchannel plate (MCP) is a dense array of electron multiplier tubes fused
together to form a thin disc of a few centimeters in diameter. The MCP is the type of
signal collector found in the NPD sensor. All these electron multiplier tubes operate
independently. Therefore, the output of a MCP is a two-dimensional electron image
which preserves the spatial resolution of the original input radiation, except for a
determined linear gain of the initial signal[11]. Also, because of the small size of each
electron multiplier tube the timing of the particle impact can be determined very
accurately[12]. Figure 5 shows what occurs in the interior of one of the multilplier tubes.
FIGURE 5: The interior of an electron multiplier tube – part
of an MCP
Chapter 4: COMPUTATIONAL MODELING
Before fabricating the NPD mirrors, theoretical and physical models were
produced in hopes to optimize the NPD mirror’s performance. Several methods of
modeling were used in order to calculate good designs for these multilayer mirrors.
Because of the complexity of specifications for the NPD mirrors, both global and local
optimization algorithms have been employed. I begin this chapter by introducing the
important concept of manufacturability, the real limit to our success in fabricating these
multilayer structures. Following is a discussion on the differences between the two
different optimization schemes used in our calculations. An introduction to IMD, the
modeling program used in this project, will also be included. Finally, the procedure
taken to develop the merit function used for optimization will be discussed.
4.1 Manufacturability
Theoretical models work well for what they have been developed, and the reason
for creating one is to have a plan of how to create the actual fabrication and to have an
idea of how it will behave. Hopefully, the manufactured item will match the calculated
value. In reality however, manufacturing must be allowed to have discrepancies from the
theoretical model.
As seen in Section 3.4, multilayer designs depend both on the material used as
well as the thicknesses of the different material layers. Most of the error in the
manufacturing process will be present in the thickness of the layers. Therefore, the
model used for the NPD mirrors produced must be as insensitive to thickness deviations
as possible.
4.2 Global Optimization and the Genetic Algorithm
The point of optimization is to find the maximum or minimum value of some
function f which determines the performance of the theoretical model you are trying to
develop. This function may or may not depend on multiple independent variables. The
goal, however, is to find the value of the variables that will cause the theoretical model to
give the desired results. Global optimization attempts to determine these values by
sampling most of the solution space and finding the global extrema (truly the highest or
lowest function value) in that space[13].
The global optimization algorithm used for designing the NPD multilayer models
is the Genetic Algorithm (GA). A schematic diagram of how the GA works is shown in
Figure 6. The XUV research group at BYU previously has applied the GA to the
problem of optimizing the performance
of multilayer mirrors with certain
constraints[14]. These types of
algorithms perform better than
alternative methods in problems with
multiple parameters, discrete variables,
and discontinuities in the solution[15].
To apply the GA to a problem, a unique
merit function needs to be developed,
containing in it information on how
good or bad a solution is in fitting the
desired performance. Both
FIGURE 6: Schematic diagram of the Generic Algorithm
interdiffusion and roughness can be included in the constraints of the merit function, if
desired.
The GA mimics nature’s process for the optimization and refinement of a species
through the use of DNA and survival of the fittest. A set of trial solutions is created –
this is the population to be optimized. The specifications of the population are encoded
in a DNA-like array within chromosomes. Chromosomes consist of genes, which are
themselves made up of alleles. Each allele holds information about individual materials
or thicknesses in question. The genes are arrays holding the materials and thicknesses in
the multilayer structure[15]. This initial population is randomly chosen by the program
and the optimization begins.
Each member in the population is given a numerical ranking, based on the value
of their merit function in the environment they are exposed to. The parents with the
highest merit value are fit to propagate their genetic design to the next generation.
Children are created by crossover and mutation of the parent’s genes. After this, a new
generation is formed, composed of the children and parents with the highest merit value.
This process continues until the merit function ceases to change significantly[15]. This
means that the improvement from one generation to the next is minimal. This typically
occurs after 10-15 generations.
For a more complete explanation of the GA and its application to a similar
multilayer optimization problem, refer to reference [13], pages 15 to 25 and reference
[14], pages 2 to 6. In our application of the GA, our population consists of multilayers.
The rating function for our system computes a multilayer’s ability to cause extreme
ultraviolet light to destructively interfere.
4.3 Local Optimization and the Simplex Algorithm
Similar to global optimizing, local optimizing tries to solve a given problem by
finding a minimum value. Local optimizing algorithms take advantage of the decreasing
value of the function near a minimum to reach a solution, so only minima can be found.
Therefore, if the algorithm begins to solve near a minimum, it will converge to that value,
and there is no way of comparing this solution to a better solution.
A local optimizer operates in a continuous parameter space. Therefore, only
continuous variables, such as the thickness of a thin film in a multilayer, can be
minimized. Discrete variables, such as the type of material to use in a certain layer,
cannot be locally optimized, because, by changing a discrete variable we are entering a
completely different solution space. For a more complete description of different types
of local optimizers, refer to reference [10], pages 8 to 9.
The simplex algorithm is the local optimizing algorithm used, similar to the
genetic algorithm for global optimizing. This local optimizer is probably the slowest
local optimizer known but it is also the most robust and easiest to implement[15]. Unlike
the simplex algorithm, the genetic algorithm introduces randomness in its search. This is
done to help ensure the genetic algorithm probes all possibilities. Therefore, by using
both algorithms together, local extrema can be found and then randomly search for spaces
where the merit function has greater local extrema.
4.4 IMD
Using the solutions found with the genetic and simplex algorithms, we can
continue by modeling multilayer structures that will satisfy the limitations needed for the
NPD sensor to perform the best. The computer program used to model these theoretical
structures was IMD. For a fuller explanation of IMD and its functions, see reference
[16].
IMD is used for modeling the optical properties of multilayer structures:
reflectance, transmittance, electric field intensities, etc. In IMD, a thin film layer can be
composed of any material for which the optical constants are known or can be estimated.
Imperfections at an interface, such as roughness and/or diffuseness, can be included in
the models. These imperfections cause a reduction in the reflectance at the interface.
However, they become important to us, as stated in Section 3.1, because the length scale
of these imperfections are comparable in size to the short ultraviolet wavelengths we are
working with.
To use IMD, a “structure” is defined: the parameters that define the ambient
material, the mutilayer stack, and a substrate. A number of parameters can be assigned to
each structure element, i.e., the layer thickness, the interface roughness/diffuseness
parameters, etc. For all calculations, at least one wavelength and incidence angle must be
specified. In addition, any of the parameters that describe the multilayer stack, such as
the layer thickness, or the incident beam, such as the polarization parameters, can be
designated as independent variables. Once the structure and independent variables are
defined, the total reflectance, transmittance or absorption can be computed, by selecting
them as dependent variables in IMD.
4.5 Models for a Start Surface
In order to create a theoretical model for a multilayer structure, one needs a
method of ranking the importance of the individual components needed to produce the
desired result. This is the task of the merit function – to compute the performance merit
of the component according to what is important for the model as a whole. Determining
the merit function for our NPD multilayer structure followed an evolution process. The
merit function initially developed aimed to minimize the reflectance of the surface at the
specific grazing angle of 15°. This function was then easily expanded to minimize the
reflectivity over a range of angles, thereby providing greater flexibility in the
manufacturing process. The minimum might not be as sensitive to deviations in the
thicknesses of the multilayer films. Below follows a discussion of the evolution of our
merit function[8].
The merit function was first designed to minimize the reflectance of the surface at
a grazing incidence angle of 15°. This type of merit function is simple and direct,
calculating the reflectance of the surface at one angle and returning the inverse of this
value. The optimization algorithms change the parameters of the merit function in an
attempt to maximize this inverse, thus minimizing the reflectance of the mirror at this
angle. The disadvantage of this merit function is that it only allows the minimization of
the reflectance at only one angle. This type of merit function greatly hampered our
manufacturing ability, since the models developed by it required the fabricated mirrors to
be accurate to achieve the desired results. As discussed in Section 4.1, we wish to create
models that are as insensitive to thickness deviations as possible.
The function developed to minimize the reflectance of a range of angles takes a
weighted average of the reflectance over the range of angles and returns the inverse of
this average. A weighted average is used to treat the range of angles as equally important
while at the same time decreasing the importance of the remaining angles. The
optimizing algorithms then set out to maximize the inverse of the average, therefore
minimizing the reflectance over this range of angles. Figure 7 shows the reflectance of a
multilayer design optimized by using this averaging method. This style of optimizing
allows slight discrepancies in the actual manufactured multilayer. Averaging causes the
optimization peak to be more like a plateau, so small deviations from the calculated
parameters will not change the performance of the multilayer very much.
FIGURE 7: Optimization using averaging and convolution merit functions
A few months after the NPD mirror project began at BYU, ESA affiliates
provided the XUV group with the plot shown in Figure 8, making our task clearer. This
plot shows the predicted distribution of neutral particles that will be incident on the start
surface as a function of grazing incident angle. We assumed that this plot also
represented the relative intensity of light incident on the surface, because the aperture
would limit the amount of entering light in the same format as it limits the amount of
entering particles. Therefore, it became
necessary to inhibit reflected light at the angles
where the intensity of particles was the highest.
To account for this time of optimization, our
merit function developed into the following.
To allow the desired angles to be
weighed heavier, the merit function developed
minimized the convolution of the reflectance
FIGURE 8: Distribution of incident particles
with the incident distribution curve (Figure 8) over a range of angles. In other words,
this merit function calculated the total intensity of light over a range of angles by
multiplying the reflectance of the different angles by the relative intensity of light that is
incident on the surface at that angle (Figure 8). The area of the resulting curve is then
added up to find the total influx of light for this angle. This mathematical operation is
called a convolution. Figure 7 plots the reflectance of a multilayer design optimized by
this type of convolution.
Next, a concern for the degree of fabrication of actual multilayers that this merit
function would allow caused it to be formatted into a more robust function. In order to
increase manufacturing abilities of the multilayers, there needs to be an allowance for
error in the calculations. The new merit function allowing this error minimized the
convolution of the reflectance with the incident distribution curve (Figure 8) over a range
of angles and adds a deviation factor to the calculated design. This merit function
therefore calculates the above procedure many times with slightly different layer
thickness parameters, and then returns the average of these calculations. Figure 7
compares the reflectance of multilayer structure designs optimized using the three types
of merit function. The solutions given by the last merit function resemble the solutions
from the averaging method very closely. The solutions from the last merit function are
compatible to the solutions derived from the other two merit function, and at the same
time, it increases our ability of multilayer structure fabrication by allowing discrepancies
in the layer thicknesses. Appendix A introduces the code for the final merit function
developed.
Chapter 5: EXPERIMENTAL INSTRUMENTS
Several systems were employed to develop and measure the NPD mirrors. Below
is an introduction to these systems and an explanation of their task in our project.
5.1 Evaporation System
There are a couple of ways to fabricate thin film structures. Two of the most
common methods used are evaporation and sputtering. The objective of these deposition
processes is to controllably transfer atoms from a source to a substrate where film growth
occurs atomistically[9]. Here, we describe the method of evaporation.
In order to grow two of the three films used in our NPD multilayer structures, we
used the method of evaporation. In this method, the material which is desired to be used
for film formation is thermally heated by conduction. This material is therefore allowed
to reach high enough temperatures, causing atoms to leave the source deposit themselves
onto a substrate held above the evaporating material. By evaporating material onto a
substrate, the layer thickness can be monitored and controlled to the scale of angstroms.
Therefore, the key variable influencing evaporation rates is the temperature. Table 1 lists
the evaporation characteristics of chromium and magnesium fluoride, the two different
films grown by evaporation.
5.2 DC-Sputtering System
In order to supply the top thin film of tungsten, we used a method called
sputtering. This method was necessary because of tungsten’s very high melting
temperature. Table 2 lists the sputtering yield of tungsten.
TABLE 1: Evaporation characteristic of chromium and magnesium fluoride
TABLE 2: Sputtering yield of tungsten
In sputtering, the target is a plate of the material to be deposited onto a substrate.
This target is connected to the negative terminal of a DC power supply, so it is also
known as the cathode. Several kilovolts exist between the target and the substrate that
faces it. After the chamber is evacuated, a gas (in our case, argon) is introduced and
becomes the medium in which a discharge is sustained. This discharge is essentially a
plasma composed of ions, electrons and neutral particles from the target and the argon
gas. The pressure inside the chamber can reach up to 100 mTorr. This glowing
discharge is maintained between the target and the substrate, and a film condenses on the
substrate[9].
5.3 Reflectometry
In order to measure the reflectance of the NPD mirrors at various angles, a
multiple angle reflectometer was used, depicted in Figure 9. The reflectometer consists
of a hollow cathode plasma light source, a vacuum monochromator, and a vacuum
FIGURE 9: Schematic diagram of reflectometry instrument used
variable-angle chamber. Light is produced in the hollow cathode by exciting gas flowing
in the hollow cathode until it is a glowing plasma. This light enters the vacuum
monochromator which selects a specific wavelength from the many being emitted by the
excited gas. Finally, this specific wavelength of light enters the variable-angle chamber,
in which the mirror is held. The mirror is mounted onto a motorized stage that allows us
to choose the incident angle of the light with respect to the mirror. Data is taken using a
photomultiplier tube and the reflectance is determined by an automated LabView
program. Because the background radiation found in space is the Lyman-alpha line
(   121.6 nm), given by the first transition of hydrogen, we used hydrogen as the gas to
produce the plasma[8].
5.4 Ellipsometry
Ellipsometry is a sensitive surface and film measurement done with polarized
light. A schematic diagram of an ellipsometer is found in Figure 9. This measurement is
used to extract information about the thickness and optical properties of a film. These
characteristics are determined by measuring and studying the change of polarization of
FIGURE 9: Schematic diagram of an ellipsometer [25]
initially polarized light as it reflects off the films surface at non-normal incidence[9].
Monochromatic, collimated light leaves the light source and enters a polarizer
which linearly polarizes this light. Then it passes through a compensator (a quarter-wave
plate) which changes the linearly polarized light into circularly polarized light. This light
then reflects off the surface of the studied film and travels toward a second polarizer that
is used as an analyzer. The light finally reaches the detector, a photomultipler tube that
exhibits polarization sensitivity. The orientations of the polarizer and the analyzer are
changed until light extinction occurs at the analyzer. When this happens, the phase
difference (Δ) and the amplitude ratio (tan(ψ)) for the p- and s- components of the electric
field can be obtained[17]:

Rp
Rs
 tan( ) e i
5.4.1
5.5 Atomic Force Microscopy
The roughness of a material thin film is a deciding factor in whether to consider
that material as a candidate for an NPD layer. As discussed in Section 3.1, the start
surface must be smooth on the order of the size of the particle being reflected in order for
correct specular reflection to occur. To test the smoothness of the surface, we use a
technique called atomic force microscopy (AFM).
In AFM, a probe consisting of a sharp tip located near the end of a cantilever
beam is dragged across the sample surface. Changes in the tip-sample interaction are
monitored by the bending of the cantilever in response to the force between the tip and
the sample. As the cantilever flexes, the light from a laser is reflected onto the split
photodiode, shown in Figure 10 as the A-B box. By measuring the difference signal (A –
B), changes in the bending of the cantilever can be measured[18]. Tip radii are in the
order of nanometers.
FIGURE 10: Schematic diagram of an atomic force microscope.
Chapter 6: EXPERIMENTAL SETUP
To achieve low reflectance from a multilayer structure, an appropriate thickness
of a transmissive thin film material is required on another reflecting material surface.
Based on the optimization thicknesses and materials calculated through our merit
function, certain materials were investigated and chosen as possible NPD mirror film
layers. Several possible NPD simulation mirrors were fabricated based on these
calculations and measurements were made. These simulation mirrors were a composition
of Cr, TiO2, MgF2 and W. The real NPD structures were fabricated based on our trial
NPD models. Following is a discussion of the substrate, the transmissive thin film
materials and the reflecting thin film material investigated as candidates and used for the
real NPD multilayers.
6.1 Substrate
The trial NPD mirrors were fabricated onto pieces cut from 4-6” diameter Si
wafers with an oxidized layer of 1.85 ± .25 nm. This thickness of oxide was determined
by ellipsometric measurements of a wafer before its use.
The substrates used for the actual NPD mirrors were supplied by the ESA. They
were made of Ti aircraft alloy (TiAl6V4) and were used because the coefficient of thermal
expansion of the alloys was seen to match the thermal expansion coefficients of MgF2
and Cr better than other materials. The reflectance of the bare Ti substrate was measured
to be 68 % at 15° grazing incidence[6].
6.2 Transmissive Layer
In antireflection, an appropriate thickness of the transmissive material allows
destructive interference to occur. Because of the wavelength the NPD mirrors will be
exposed to, there was a short supply of possible transmissive materials. This is because
of the relatively small band gap (BINDING ENERGY) between the conduction band
and the valence band of most materials. This small band gap allows electrons to absorb
radiation with energies equal to or less than the energy of the band gap, causing the
material to be significantly absorbing. A very large band gap energy has the chance of
making a material transparent. There exists two materials with a band gap equal to or
greater than 10.2 eV, the energy of the Lyman alpha line. These two materials are LiF
and MgF2. Because of this characteristic, they were suitable for the NPD transmissive
material layer[19].
By looking at the periodic table, it is evident why they would have a transparent
nature. Fluorine is very chemically active and the most electronegative of all the
elements[20]. Therefore, it readily accepts and holds electrons. Lithium and magnesium
readily give up their electrons and they behave like inert noble gases, helium and neon
respectively. Noble gases are extremely hard to excite, making them unsuitable for
radiation absorption.
Another material suggested for the transmissive layer was CaF2, because of its
current use in very ultraviolet optical systems. However, the band gap of CaF2 is barely
10.2 eV, making it rather inappropriate for this task. Another disadvantage to CaF2 is
that it is hydroscopic, i.e., it absorbs water out of the ambient. Water absorption by
optical films causes swelling of the thin film, changes in the refractive index, and overall
shifts in the spectral transmittance[9]. (Water absorption causes the material to become
more absorbing.) It turns out that LiF is hydroscopic, making it unsuitable as a
transmissive material. MgF2 became the choice for the transmissive material layer.
MgF2 is not particularly hydroscopic, but it has voids[19]. A void allows water
vapor to penetrate low-density films and gap between the columnar grains by capillary
action[9]. Additionally, if the MgF2 film contains crystallites in its structure, their grain
boundaries can cause an absorption tail for the refractive index below the material’s band
gap. This absorption tail is known as the Urbach edge, and it obeys the relationship
   0 exp[  ( E g  E )] ,
6.2.1
where E g  12.3 eV, E is the photon energy,  0 is a determined value for the absorption
coefficient, and σ is determined through fitting the designed data[21]. This relationship
states that the absorption coefficient rises exponentially as you approach the band gap.
If the substrate is heated the Urbach edge of the MgF2 film becomes steeper,
making the material transparent. At an energy of 10 eV, this would increase the
transparency by about a factor of 10 more than an unheated material. Based on this
information, we deposited MgF2 films on heated substrates over a range of temperatures
in search for changes in their performance. Unfortunately, heating these substrates led to
tiny facets on their surfaces, as seen in Figures 11 through 14. These figures show AFM
data taken for substrate temperatures of 90˚, 140˚, 235˚, and 400˚ C. The visible increase
in facets as a function of temperature discouraged the heating of our actual NPD mirror,
regardless of theoretical improvements about the material becoming more transparent
with annealing. We believe that these facets would result in additional specular
scattering of the ENAs, which is a negative effect.
FIGURE 11: AFM image taken of a MgF2 thin film deposited onto a Si wafer being held at room temperature.
FIGURE 12: AFM image taken of a MgF2 thin film deposited onto a Si wafer being held at ?
FIGURE 13: AFM image taken of a MgF2 thin film deposited onto a Si wafer being held at ?
FIGURE 14: AFM image taken of a MgF2 thin film deposited onto a Si wafer being held at ?
The trial NPD mirrors fabricated were made using MgF2 as the transparent layer.
Thermal evaporation was used to deposit these films onto the Si wafers using W boats as
discussed in Section 6.1. Several trial mirrors were made, using different layer
thicknesses for this material layer. Altering the thickness of the MgF2 allowed us to
probe the real minimum reflectance thickness possible, compared to the theoretical
calculations. A discussion of the results of this research is found in Chapter 7. MgF2 was
also used as the transmissive thin film for the actual NPD mirrors. The details on
deposition are found in Section 6.4.
6.3 Reflective Layers
Because of the optimization done through the merit function used, TiO2 or Cr had
been initially chosen as the reflective materials. The final design would consist of either
a TiO2 or Cr thin film as the bottom layer, a MgF2 thin film as the middle layer, and an
ultra thin WO2 film as the top layer. However, deposition considerations caused the TiO2
layer to be disregarded. TiO2 turns out to be a hard material to evaporate with the optical
properties stated by published literature[22]. The stoichiometry of the films depends on
the partial pressure of O2 in the evaporation chamber[6]. This makes the films
unpredictable for us.
Because of these complications, only the Cr thin film was kept as the reflective
layer. IMD simulations indicated that the multilayer reflectance did not change very
much after the thickness of the Cr film greater than about 28 nm. By the time the Cr film
is this thick, it is opaque to this wavelength. Therefore, the multilayer stack was made of
a low index of refraction material over a high index of refraction material. W was chosen
to be the top layer because of the high reflectance possible for particles. Also, the high
density of electrons found in W satisfies one of characteristics needed for the NPD top
surface. Theoretically, an ultra thin film of WO2 within the thicknesses of .1-4 nm does
not affect the overall reflectance of the multilayer substantially.
Several trial NPD mirrors were fabricated using different Cr thin film thicknesses.
These films were deposited via resistive evaporation after the deposition of the MgF2 thin
films. However, unlike the analysis done for the varying thickness of the MgF2 film, a
detailed study of the effects the Cr film had on the actual reflectance of the trial mirrors
has not been made. This type of probing would definitely improve the judgements made
in this thesis. A Cr film was also used as the reflective layer for the real NPD structures.
A detailed account of the Cr deposition is found in Section 6.4.
The effects of the top W layer was investigated in a similar fashion to the MgF2
films. Different W thin films were deposited onto the trial mirrors and a comment of the
effects will be presented in Chapter 7. The different W thicknesses were deposited via dc
magnetron sputtering. The actual NPD mirrors also contained a layer of W, and details
on this film’s deposition is found in Section 6.4.
6.4 Final Design
We fabricated the four final NPD multilayers in three steps. Cr was deposited
onto the NPD substrate in an oil-free closed-cycle cryopump vacuum system at a pressure
during the depositions of ~ 5  10 6 Torr. The deposition was done using resistive
evaporation. The temperature of the substrates during deposition was that of room
temperature. Our deposition rate for the Cr films was 1-3 nm per second and the final
film thicknesses were 29 ± 1 nm of Cr. The deposited thickness of the Cr films was
monitored using a quartz crystal film thickness monitor and was started and stopped by
the use of a pg. 40 ???? a mechanical shutter. The thickness of the film was also
determined through ellipsometric measurements on the witness Si samples placed inside
the chamber during the deposition.
The MgF2 films were deposited next in the same system and pressure ambient as
the Cr film deposition. This deposition was done using thermal evaporation, holding the
substrates at room temperature. Our deposition rate for the MgF2 films was .5-1 nm per
second and the target MgF2 film thicknesses were 10.5 ± 0.5 nm. These film thicknesses
were also monitored using the thickness monitor and determined by ellipsometry in the
same manner as for the Cr deposition.
The W ultra thin film was deposited last using dc magnetron sputtering. The
argon pressure supplied into the chamber was ~ 2  10 3 Torr. Our deposition rate for the
W films was .07 nm per second and the final film thicknesses were 0.8 ± 0.3 nm. Si
wafer pieces were placed next to the mirrors inside the chamber to act as deposition
witnesses and were used to determine the thickness of the film through ellipsometric
measurements. The substrates were at room temperature whilst the W was deposited.
The actual NPD mirrors were fabricated in the summer of 2001 under the
conditions stated above. A discussion on their final reflectance measurements is made in
Section 7.2. Our final design consisted of the following:

Substrate – Ti aircraft alloy

280 ± 5 Å Cr

105 ± 5 Å MgF2

8±5ÅW
FIGURE 15: A relative diagram of the thicknesses of
the different materials used for our real NPD mirror
Chapter 7: EXPERIMENTAL RESULTS AND ANALYSIS
As discussed in Chapter 6, a variety of trial NPD mirrors were fabricated by
altering the thicknesses of the two outer thin films eventually used for the actual mirrors.
After the test mirrors were deposited, reflectance measurements were made at the
wavelength of 121.6 nm using a McPherson model 225 1-meter scanning monochromator
and a variable angle sample chamber designed and built at BYU, as discussed in Section
5.3. An analysis of the effects the thickness of the MgF2 had on the reflectance of the
trial mirrors has been made. Furthermore, a similar study was made on the effects of the
W thickness on the reflectance for several MgF2 film thicknesses. Both of these topics
will be discussed in Section 7.1. In Section 7.2 we present the final results from
measurements made on the finished NPD mirrors.
7.1 Trial NPD Mirrors
We modeled a thin film structure that could demonstrate the effects of changing
the thicknesses of the MgF2 film or the Cr layer and the addition of a WO2 film has on
the multilayer. This is shown in Figure 16. This hypothetical multilayer structure is
composed of a Si substrate with a surface roughness of 0.1 nm, a Cr thin film of 27.5 nm
thickness, a MgF2 layer with a surface roughness of 0.4 nm, and a WO2 ultra thin film
overcoat. The reflectance of the multilayer structure is plotted versus the thickness of the
MgF2 film. The parameters changed in the multilayer structure to produce the four
curves shown are the grazing angle of incidence and the presence or absence of a 3.2 nm
WO2 layer. A WO2 was used instead of W in models because ultra thin W films quickly
oxidize in air to 2-3 nm. Two reflectance curves at the same angle (15° grazing incidence
FIGURE 16: Reflectance of trial NPD mirrors as a function of MgF2 film thickness, for 10°, 15°, and 20° grazing incidence
angle. From Fig. 18: Theoretical reflectance versus MgF2 film thickness of a “trial” NPD mirror.
angle) are compared and depict the effect of the WO2 film: the minimum reflectance
position of the curves has shifted to the right and increased from 15.9% to 18%. The
shift to the right implies an increase in the thickness of the MgF2 film. Therefore, an
increase in the thickness of the WO2 film implies an increase in the MgF2 film, with a
slight increase in the reflectance of the multilayer structure, as stated in Section 6.3.
The dependence of the reflectance as a function of grazing incidence angle and
thickness of the MgF2 film for actual test structures has been studied and the results are
shown in Figure 17. This graph shows the measured reflectance of the trial mirrors as a
function of the MgF2 film thickness for three different angles, namely 10°, 15° and 20°.
Third-degree polynomial mathematical fits are also shown in the graph along with the
least squares difference between the measured data and the mathematical fit. Figure 16
MgF2 Thickness vs. Angle
0.5
10 degree trendline
y = -1.1304E-08x3 + 8.1258E-06x2 - 1.3483E-03x + 4.5005E-01
R2 = .43
0.45
0.4
0.35
15 degree trendline
y = -3.9946E-08x3 + 2.4911E-05x2 - 3.9797E-03x + 4.2071E-01
R2 = .889
Reflectance
0.3
0.25
20 degree trendline
0.2
y = -3.9338E-08x3 + 2.4566E-05x2 - 3.6176E-03x + 2.9972E-01
R2 = .927
0.15
0.1
0.05
0
65
90
115
140
165
190
215
240
265
MgF2 Thickness (Angstroms)
10
15
20
Poly. (10)
Poly. (15)
Poly. (20)
FIGURE 17: Measured data on the trial NPD mirrors – reflectance as a function of MgF2 film thickness for 10°, 15°,
and 20° grazing incidence angle.
shows the theoretical reflectance for these same variables (the curves without the WO2
overcoat). There was no WO2 film contemplation for this particular set of calculations
since this overcoat was also missing in the actual multilayer structures.
As can be seen, the shape predicted by the theoretical reflectance is obeyed by the
actual measured data. The actual thickness of the MgF2 film required for minimum
reflectance at these three angles was calculated using Maple. The derivative of the
measured data can be seen in Figure 18. For 10° grazing incidence angle, the thickness
of the MgF2 film for minimum reflectance is 106.7 Å. Similarly, for 15° grazing
incidence angle, the corresponding thickness is 107.9 Å and at 20°, the thickness is 95.6
Å. The theoretical range for the thicknesses of MgF2 that will result in minimum
reflectance is ???? (CHECK THE IMD VALUES FOR THIS RANGE). IS THERE A
DISCREPANCY BETWEEN THEORY AND MEASUREMENTS?
FIGURE 18: Derivative of the reflectance functions for the trial NPD mirrors.
The effect of the presence of WO2 films of various thicknesses on test mirrors
was also studied. Several thicknesses of W were deposited onto different thicknesses of
MgF2. The reflectance of these trial mirrors was measured and Figure 19 shows the
results. The plot is made for a 15° grazing incidence angle. As can be seen, increasing
W Thickness vs. MgF2 Thickness
0.32
0.3
Reflectance
0.28
65 A
108 A
119 A
150 A
180 A
221 A
0.26
0.24
0.22
0.2
0
4
8
12
16
20
24
28
W Thickness (A)
FIGURE 19: Reflectance of trial mirrors as a function of W for different thicknesses of MgF2. The angle of
measurement is 15° grazing incidence angle.
the thickness of W can help decrease the reflectance of the multilayer structure depending
on the thickness of the MgF2 thin film. A simple graph is found in Figure 20. (Question
about Dr. Allred’s statements).
From the curves shown it is seen that as the thickness of the MgF2 film increases
from 6 to 12 nm, an increase of the W film thickness produces an increase in the
reflectance at an angle of 15° from grazing incidence. However, one can note that the
magnitude of the reflectance increase actually decreases as the thickness is increased over
this range of MgF2 thicknesses. At a MgF2 film thickness of 14 nm, increasing the
thickness of the W film actually decreases the reflectance of the multilayer stack. This
decrease in reflectance continues up to a MgF2 film thickness of 22 nm. Nevertheless,
the magnitude of reflectance decrease has decreased as the MgF2 thickness increased.
FIGURE 20: Theoretical reflectance as a function of W film thickness for different thicknesses of the MgF2 film.
The grazing incidence angle for this graph is 15°.
The actual measurements made generally obey the theory except for the 150 and
180 Å MgF2 films. Theoretically, these two thicknesses of MgF2 should decrease in
reflectance as the thickness of the W thickness is increased. Based on our measurements,
this doesn’t occur. WHAT COULD BE THE REASON?
Figure 21 shows a contour plot of the theoretical reflectance based on the
thicknesses of the MgF2 and WO2 film thicknesses. Minimum reflectance occurs at a
MgF2 film thickness ranging from 10 to 12.5 nm and a WO2 film thickness ranging from
0 to 0.4 nm.
FIGURE 21: Contour plot of reflectance as a function of MgF2 and W thickness. The grazing incidence angle for this
plot is 15°.
7.2 Real NPD Mirrors
I NEED TO SPEAK TO DR. ALLRED ABOUT THIS SECTION!!! I DON’T
KNOW WHAT FILES TO USE…
Chapter 8: FUTURE WORK
We have presented theoretical and measured data based on trial NPD multilayer
stacks made to mimic the performance of the actual NPD mirrors fabricated. A strong
implication of the studies on the effects of the W film layer is the correct deposition of
layer is vital. This is seen in Figures 19 through 21, where a slight increase in the W film
thickness either increases or decreases the reflectance of the overall multilayer.
Further studies on the effects of the Cr film thickness need to be made in order to
understand the full performance of the real mirrors. The trends of the reflectance
measurements are more important than the actual reflectance magnitudes because
of the difficulty in measurements at these low angles.
APPENDIX A: Merit Functions
merit-t min-avgrefl ( Stack & mirror, const Chromosome & chr, int meritindx )
{
//This merit function is for min-refl of the stack
float grazemin = chr[ meritindx ]. val;
float grazemax = chr[ meritindx + 1 ] .val;
float grazestep = chr[ meritindx + 2 ] .val;
float lambda = chr[ meritindx + 3 ].val;
//Compute average reflectivity for multiple angle
return
merit-t( 1.0 I avgrefla( lambda, mirror, grazemin, grazemax, grazestep ));
}//min-avgrefl
merit-t min-avgrefl-weighted ( Stack & mirror, const Chromosome & chr, int meritindx )
{
float lambda = chr[ meritindx + 3 ] .val;
/* Compute average reflectivity for multiple angle with weights
*according to gaussian quadrature.
*/
double a = 10, b =15;
//The range to integrate in.
double zi[2] = { 0.339981043584856, 0.861136311594053 };
double xi[4] = { .5 * (b + a – (b – a) * zi[1]), .5 * (b + a – (b – a) * zi[0]),
.5 * (b + a + (b – a) * zi[0]), .5 * (b + a + (b – a) * zi[0])};
double wi[2] = { 0.652145154862546, 0.347854845137454 };
//Now we need to enter the I function values (at xi).
double 1[4] = { 1.0, 0.875, 0.725, 0.63 };
return merit-t ( 1.0 / ( wi[l] * 1[0] * refla(lambda, mirror, xi[0]) +
wi[0] * I[1] * refla(lambda, mirror, xi[1]) +
wi[0] * I[2] * refla(lambda, mirror, xi[2]) +
wi[1] * I[3] * refla(lambda, mirror, xi[3]) ) );
}//min-avgrefl- weighted
merit-t min-avgrefl-weighted-var-extreme-size ( Stack & mirror, const Chromosome &
chr , int meritindx )
{
float lambda = chr [ meritindx + 3 ];
float deviation = chr [ meritindx + 4 ];
//The number of deviations to make.
int N = (int) chrl meritindx + 5 ];
static Stack* temp_stack = NULL;
if( temp_stack = = NULL) temp_stack = new Stack( mirror );
/* Compute average reflectivity for multiple angle with weights
* according to gaussian quadrature.
*/
static double a = 9, b = 20;
//The range to integrate in.
static double zi[2] = { 0.339981043584856, 0.861136311594053 };
static double wi[2] = { 0.652145154862546, 0.347854845137454 };
static double xi[4] = { .5 * (b + a – (b – a) * zi[1]), .5 * (b + a – (b – a) * zi[0]),
.5 * (b + a + (b – a) * zi[0]), .5 * (b + a + (b – a) * zi[1]) };
/* The above gives the following for xi:
* xi = { 9.7638, 12.6301, 16.3699, 19.2362 }
*/
// The distribution at xi: static double I[4] = { 0.149, 0.865, 0.528, 0.049 };
/* We'll make a temporary copy of mirror so that we can reset its data.*/
*temp_stack = mirror;
double meritval = 0;
/* Now let's loop through and do the deviation via gauss_deviate.*/
for ( int n = 0; n < N; n++ )
{
for ( int i = mirror.Numlayers() – 1; i >=0; i- )
{
mirror.Thick(i) = gauss_deviate(mirror .Thick(i), deviation);
}//for
meritval += 1.0 / ( wi[1] * I[0] * refla( lambda, mirror, xi[0] ) +
wi[0] * I[1] * refla( lambda, mirror, xi[1] ) +
wi[0] * I[2] * refla( lambda, mirror, xi[2] ) +
wi[1] * I[3] * refla( lambda, mirror, xi[3] );
mirror = *temp_stack;
//Reset the stack.
}//for
return merit-t( meritval / ( N * ( 0.5 * (b – a) ) ) );
}//min-avgrefl- weighted
REFERENCES
[1]
T. Phillips, The Solar Wind at Mars, WWW Document,
(http://science.nasa.gov/headlines/y2001/ast31jan_1.htm).
[2]
European Space Agency, Scientific Objective, WWW Document,
(http://sci.esa.int/content/doc/ed/15085_.htm).
[3]
European Space Agency, ASPERA: Energetic Neutral Atoms Analyzer, WWW
Document, (http://sci.esa.int/content/doc/29/21545_.htm).
[4]
M. Wieser, ASPERA-3: Start and Stop Surfaces for the NPD Sensor, WWW
Document, (http://www.phim.unibe.ch/~mwieser/diploma/node5.html).
[5]
M. V. Zombeck, Microchannel Plate Principles of Operation, WWW Document,
(http://hea-www.harvard.edu/HRC/mcp/mcp.html).
[6]
M. B. Squires, Low Reflective Surfaces at 121.6 nm for the Neutral Particle
Detector, Publication Paper Outline (Unpublished).
[7]
C. Salazar, The Optics Book: Reflection, WWW Document,
(http://library.thinkquest.org/C003776/ingles/book/reflection2.htm).
[8]
D. Garber, S. Olson, and C. Simmons, Start Surfaces for Neutral Particle Detector
of Mars Express Mission, English 316H Paper (Brigham Young University, Provo
UT, 2002).
[9]
M. Ohring, The Materials Science of Thin Films, (Academic Press, San Diego,
1992), pp. 79-113, 258-261, and 507-536.
[10] J. Peatross, Physics of Light and Optics, Brigham Young University Optical Physics
Book (Unpublished).
[11] Photonis, MCP Basics, WWW Document,
(http://www.photonis.com/special_products/microchannel/mpc_basics.htm).
[12] H. Schmidt-Böcking and R. Dörner, Microchannel Plate (MCP) Detectors, WWW
Document, (http://hsbpc1.ikf.physik.uni-frankfurt.de/det/det_mcp.html).\
[13] S. Lunt, The Use of Genetic Algorithms in Multilayer Mirror Optimization, Honors
Senior Thesis (Brigham Young University, Provo, UT, 1999).
[14] S. Lunt, R. S. Turley, and D. D. Allred, Design of bifunctional XUV multilayer
mirrors using a genetic algorithm, J. X-Ray Sci. Tech. 9, 1 (2000).
[15] S. Lunt and R. S. Turley, The Use of Genetic Algorithms in Multilayer Mirror
Optimization, pp. 3-11 (Unpublished).
[16] D. L. Windt, IMD – Software for modeling the optical properties of multilayer
films, Comp. in Phys. 12, 360 (1998).
[17] J. A. Woollam Co., Inc. A Short Course in Ellipsometry, pp. 15-17.
[18] A. Round, Atomic Force Microscopy, WWW Document,
(http://spm.phy.bris.ac.uk/techniques/AFM/).
[19] D. D. Allred (Private Communication).
[20] Tucows, Fluorine, WWW Document, (http://www.encyclopedia.com/html/f/fluorine.asp).
[21] O. R. Wood II, H. G. Craighead, J. E. Sweeney, and P. J. Maloney, Vacuum
ultraviolet loss in magnesium fluoride films, App. Optics. 23, 3644 (1984).
[22] E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press, Orlando,
1985), p.799.
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