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 vList of Tables v1 Introduction 12 Mars Exploration 3

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

3 Theory 83.1 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

4 Computational Modeling 184.1 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

5 Experimental Instruments 265.1 Evaporation System .................................................................................. 26

5.2 DC-Sputtering System .............................................................................. 26*

5.3 Reflectometry ............................................................................................ 18

5.4 Ellipsometry .............................................................................................. 19

6 Experimental Setup 196.1 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 24LIST 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 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

FIGURE 1: Mars

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

-e

-e

CHARGE PARTICLEDEFLECTION

TO START DETECTOR (MCP)

TO STOP DETECTOR (MCP)

STOP SURFACE

START SURFACE

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

1 1 angstrom = 1 x 10-10 meter. The units for angstroms are symbolized by Å.

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:

3.2.1

where is called the (complex) wave number and is called the

(complex) index of refraction. determines the direction of propagation and in an

isotropic medium, it is perpendicular to . The parameters n and depend on the

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:

. 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 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:

3.2.3

where the absorption constant 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 becomes , 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 . 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 , as shown in Figure 3. Three k

vectors are seen in this figure: represents the incident electromagnetic wave, making

an angle with the normal to the surface. specifies the reflected plane wave and it

makes an angle with the normal to the surface. Finally, represents the transmitted

electromagnetic wave, which makes an angle with the normal to the surface. This

plane, containing all three k-vectors, is called the plane of incidence. We define the

FIGURE 3: The incident, reflected and transmitted wave fields at a boundary

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):

Law of Reflection 3.3.1

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):

3.3.3

, 3.3.4

where is the incident angle and . As seen before, for materials in the 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:

3.3.5

3.3.6

Two incident angle extremes are of interest: as the incidence angle approaches ,

the reflection Fresnel coefficients approach

and 3.3.7

and the reflectance for both polarizations approaches 1. As the incidence angle

approaches , the reflection Fresnel coefficients both approach

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

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

FIGURE 4: Light scattering through a multilayer

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 , its speed changes from to . Radiation feels a change of speed

equal to , depending on the index of refraction of the thin film it is traversing,

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 to , therefore changing the wave number of the initial electromagnetic

wave to . As radiation, entering a thin film with a transmission angle of ,

traverses a thickness d of this thin film with index of refraction , its electric field phase

is adjusted by:

. 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 (

) to a higher index of refraction ( > 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 ( > ). 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 ( < ). 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:

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.

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

FIGURE 5: The interior of an electron multiplier tube – part of an MCP

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

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 FIGURE 6: Schematic diagram of the Generic Algorithm

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.

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

FIGURE 7: Optimization using averaging and convolution merit functions

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 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

FIGURE 8: Distribution of incident particles

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 (

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]:

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

, 6.2.1

where eV, E is the photon energy, 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 12: AFM image taken of a MgF2 thin film deposited onto a Si wafer being held at ?

FIGURE 11: AFM image taken of a MgF2 thin film deposited onto a Si wafer being held at room temperature.

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 ~ 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

FIGURE 15: A relative diagram of the thicknesses of the different materials used for our real NPD mirror

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 ~ 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 ± 5 Å W

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

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

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?

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

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

W Thickness vs. MgF2 Thickness

0.2

0.22

0.24

0.26

0.28

0.3

0.32

0 4 8 12 16 20 24 28

W Thickness (A)

Refle

ctan

ce

65 A108 A119 A150 A180 A221 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.

FIGURE 18: Derivative of the reflectance functions for the trial NPD mirrors.

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.

The actual measurements made generally obey the theory except for the 150 and

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°.

FIGURE 21: Contour plot of reflectance as a function of MgF2 and W thickness. The grazing incidence angle for this plot is 15°.

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.

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

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[22] E. D. Palik, Handbook of Optical Constants of Solids, (Academic Press, Orlando, 1985), p.799.