The Epitaxial Nature of Copper Thin Films

Physics Capstone ThesisLaura Carpenter

Submitted in partial fulfillment of the requirements for the degree of Bachelor of Science in Physics from Marietta College.

Marietta, OH

April 25, 2014

The Epitaxial Nature of Copper Thin Films

Physics Capstone ThesisLaura Carpenter

This Capstone Thesis has been approved for the Marietta CollegeDepartment of Physics by:

______________________________________ __________ Dr. Dennis Kuhl Date

______________________________________ __________ Dr. Craig Howald Date

ii

The Epitaxial Nature of Copper Thin Films

Laura Carpenter

Research has shown that it is possible to grow epitaxial thin films in low vacuum.

Krastev and Tobin of Michigan State University along with Longiaru demonstrated the

epitaxial growth of Cu (100) at 10-5 Torr. Using a similar procedure, copper thin films

were grown on Si (100) substrates by thermal evaporation in Marietta College’s surface

science lab at 10-5 Torr. In this study the HF etching time of the Si (100) was varied per

growth to study its effect on copper’s epitaxy. In situ resistance measurements were

recorded, and θ−2θBragg diffraction was used to examine the epitaxy normal to the

surface after growth. The films ranged from 65 nm to 212 nm with HF etching times

between 2 minutes and 10 minutes. The x-ray diffraction results failed to show epitaxy

for these copper films.

iii

Acknowledgements

I would like to thank my advisor Dr. Dennis Kuhl for his guidance in this

project as well as the other physics faculty for their feedback throughout the year. I

appreciate Geoffrey Zang’s earlier work in the lab. Also, I am thankful for friends

and family who have supported me throughout my experiences at Marietta College

and more specifically in completing this capstone project. Lastly, I would like to

thank the Rickey family for their generous Rickey Scholarship.

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Table of Contents

The Epitaxial Nature of Copper Thin Films.....................................................................................iii

Acknowledgements........................................................................................................................iv

List of Tables..................................................................................................................................vi

List of Figures................................................................................................................................vii

Chapter 1: Introduction..................................................................................................................1

A. Surface Science...................................................................................................................1

B. Materials Structures and Crystallography...........................................................................2

C. X-rays..................................................................................................................................5

Chapter 2: Thin Film Growth..........................................................................................................7

A. Background.........................................................................................................................7

B. Effective Conductivity.........................................................................................................7

C. Substrate Preparation.........................................................................................................8

D. Growth in Thermal Evaporator...........................................................................................8

E. Four-wire DC Measurement Method..................................................................................9

F. Thickness Measurement Method.....................................................................................10

Chapter 3: X-ray Diffraction of Films.............................................................................................12

A. The Bragg Law...................................................................................................................12

B. Selection Rules..................................................................................................................13

C. XRD Procedure..................................................................................................................14

Chapter 4: Results and Discussion................................................................................................17

A. Thin Film Conductivity......................................................................................................17

B. Standard Bulk Copper, Si (100), and Au (111) X-Ray Scans...............................................21

C. Epitaxy of the Thin Films...................................................................................................26

Chapter 5: Conclusions.................................................................................................................29

Appendix A...................................................................................................................................30

References....................................................................................................................................32

v

List of Tables

Table 1 - Copper thin films HF etch times and thicknesses...........................................................17Table 2 - Film 3 Fuchs-Sondheimer fit parameters.......................................................................19

vi

List of Figures

Figure 1 - Structure of Materials.....................................................................................................3Figure 2 - Copper and Silicon Lattices7............................................................................................3Figure 3 - Crystal Planes and Miller Indices....................................................................................4Figure 4 -X-ray Tube........................................................................................................................5Figure 5 - X-ray Intensity versus Photon energy. This plot combines the effects of the Bremsstrahlung process and the transition of electrons from one orbital to another in the x-ray producing process..........................................................................................................................6Figure 6 - Electrical Measurement Setups....................................................................................10Figure 7 - Quartz Crystal Thickness Monitor.................................................................................11Figure 8 - Gold Electrodes Positioned on Quartz Crystal..............................................................11Figure 9 - Bragg Diffraction...........................................................................................................12Figure 10 - Bragg Diffraction for SC and FCC Crystals....................................................................14Figure 11 - Tel-X-Ometer X-ray Apparatus....................................................................................16Figure 12 - Effective conductivity vs. thickness of copper film 1...................................................18Figure 13 - Effective conductivity vs. thickness of copper film 2...................................................18Figure 14 - Effective conductivity vs. thickness of copper film 3...................................................19Figure 15 - Bulk Polycrystalline Copper XRD Scan.........................................................................22Figure 16 - OFC Copper XRD Scan.................................................................................................23Figure 17 - Si (100) XRD Scan........................................................................................................24Figure 18 - Au (111) XRD Scan......................................................................................................25Figure 19 - Gold Nanoparticles XRD Scan19...................................................................................25Figure 20 - Film 1 XRD Scan..........................................................................................................26Figure 21 - Film 2 XRD Scan..........................................................................................................27Figure 22 - Film 3 XRD Scan..........................................................................................................27Figure 23 - Film 4 XRD Scan..........................................................................................................28

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Chapter 1: Introduction

A. Surface Science

Studying the epitaxial nature of copper thin films grown at Marietta College was

necessary to evaluate the effectiveness of the growth procedure used over the years in

view of future surface science studies with adsorbates. In order to perform surface

science with thin films, it is important to know the arrangement of the atoms on the

surface being studied. If the film is of an epitaxial nature then the atoms are ordered

based on the ordering of an underlying substrate, rather than randomly dispersed.

These clean ordered surfaces are standard in surface science research.

Surface scientists study the physical and chemical nanoscale interactions by

adhering specific adsorbates to the surface. Adsorbates can affect the resistivity and

reflectivity of thin films; this is not well understood for a vast range of materials at this

time.1 Gold is one of the materials that will be studied in the surface science lab at

Marietta College in the future. Not much sticks to gold which makes it a candidate for

clean surfaces. One adsorbate that does stick is a sulfur organic molecule, which will be

used in the lab. Cu (100) is also a good material for surface science studies. For this

reason, the epitaxy of the copper films was investigated in view of future surface science

studies. Beyond academia, epitaxial growth is ideal in many industrial settings; in fact, it

is the fundamental process behind the manufacturing of semiconductor devices like

LEDs, power electronics, and microchips.2

A thin film is a layer of material with the thickness of a nanometer to several

micrometers. These films have application in everyday household items like mirrors.

Mirrors typically have a thin metal coating on the backside of glass to provide

reflectance. Also, ferromagnetic and ferroelectric thin films are being studied for

application in computer memory.3 In general, thin films have application in optics,

chemistry, mechanics, magnetics, and electricity. This includes antireflective coatings on

1

solar cells, CDs and DVDs, chemical sensors, friction reduction, and piezoelectric

devices.4

In 1996 Krastev and Tobin from Tufts University concluded that copper thin film

deposition at a pressure of 10-5 Torr resulted in ordered films when grown on etched Si

(100) substrates, and disordered films when grown on unetched Si (100) substrates.5

They also discovered that their ordered films were epitaxial, which means that the

copper assumed the crystal structure of the substrate.5 They were the first to report

epitaxy above 10-6 Torr.

Copper thin films have been grown at Marietta for around 8 years, using a

process similar to that of Krastev and Tobin. A Si (100) wafer is cleaned with chemicals

then placed in a thermal evaporator where 99.9999% copper is deposited onto the

silicon substrate. The addition of the Tel-X-Ometer x-ray apparatus to the lab has made

it possible to determine the structure of these films normal to the surface. This tool

gives information about the film’s epitaxy. In addition to epitaxy, the effective

conductivity is also monitored for each film. By adjusting a variable in the preparation

of the films, epitaxy and conductivity can be investigated for correlations. In this

research the HF etching time of the Si (100) wafer was varied per copper growth. It was

proposed that a larger etch time would yield more ordered films and perhaps less

surface scattering.

B. Materials Structures and Crystallography

The atoms inside a material, whether copper or silicon, organize in three

particular ways creating either a single crystalline, polycrystalline, or amorphous

material. Single crystalline solids display infinite periodicity, while polycrystalline solids

exhibit local periodicity, and lastly amorphous solids have no periodicity.6 The structure

of a material determines its electronic, magnetic, optical, and mechanical behavior

which is of interest in materials science research. Figure 1 provides a visual of the

atomic makeup of these three different types of materials. Notice that the

polycrystalline material has grain boundaries where the disoriented crystal grains meet.

2

Figure 1 - Structure of Materials

The Bravais lattice for both copper and silicon is face centered cubic (FCC).

Silicon’s atomic structure adds complexity to the simple FCC crystal lattice, resulting in a

diamond lattice where two identical atoms are placed symmetrically about the FCC

lattice point.7 Figure 2 displays the geometry of monocrystalline copper and silicon.

Figure 2 - Copper and Silicon Lattices7

Commercial Si (100) wafers were used as substrates because their atoms are

organized by the same FCC lattice as monocrystalline copper. The copper atoms align

3

with the silicon atoms to create an ordered film. It should be noted that Voice, Krastev,

and Tobin observed a 45° shift of the copper lattice relative to the silicon. With this

orientation the Cu (010) planes were parallel to the Si (011) planes.8 This shift

counteracts the misalignment due to the differences in the lattice constants of silicon

and copper. The lattice constant quantifies the size of the unit cell for a particular

crystal lattice. The lattice constant for silicon is 543.09 pm, and the lattice constant for

copper is 361.49 pm.9 The rotation lowers the mismatch from 40% to 6%.8

The numeric notation that was just used to describe the silicon and copper

crystal planes is called Miller indices. Figure 3 shows the relationship between the

numbering system and the physical crystal planes for a cubic lattice in an x, y, z

coordinate system with atoms on the vertices and origin in the back left corner. The

(100), (200), and (111) orientations are especially prevalent in this project. The indexes

represent the inverses of x, y, z space. Given (100), the zeroes in the y and z

components mean that the plane is parallel to both y and z, and the 1 is the value of x.

Since the indexes are reciprocals of physical space, the (200) orientation would have a

plane parallel to the y and z with an x value of ½.

Figure 3 - Crystal Planes and Miller Indices10

4

C. X-rays

X-rays were discovered by Wilhelm Roentgen. They are a form of electromagnetic

radiation with wavelength of about 1.0 Angstrom.11 At Marietta x-rays are produced in

the Tel-X-Ometer’s x-ray tube which consists of a copper anode target and a cathode.

The cathode is heated by an applied current (0 to 80 μA) and consequently begins to

emit electrons by thermionic emission. The electrons are accelerated across the high

voltage potential difference between the copper anode and the cathode. This potential

difference is adjustable. The two settings are 20kV and 30kV, the latter being the ideal

operating voltage, since the larger potential difference yields increased currents and

ultimately higher intensities. The accelerated electrons collide with the copper target

and emit x-rays. This is depicted in Figure 4.

Figure 4 -X-ray Tube

The interaction of the electrons with the atoms produces x-rays through the

Bremsstrahlung process.12 The electrons decelerate, and hence lose energy, as they

approach the copper atoms. This deceleration is due to the electric force between the

incident electrons and the electron clouds of the copper atoms. The electrons’ lost

energy is emitted in a continuous spectrum of x-rays.

5

If the incident electrons knock copper electrons out of their low energy orbitals

then electrons in higher energy orbitals fall into these holes which are more

energetically favorable. In this process they emit x-rays. The energies of these x-rays

are simply the difference in the energy levels of the shells, from initial shell to final

shell.11 Two characteristic x-rays are produced in this process: the Kα x-ray from the n=2

to n=1 energy transition and the Kβ x-ray from the n=3 to n=1 energy transition.11 The

Tel-X-Ometer’s x-ray tube emits both of these characteristic x-rays. Kα has a

wavelength of 154 pm while Kβ has a wavelength of 138 pm.

Figure 5 gives a visual of the Bremsstrahlung continuous spectrum along with the

characteristic x-rays.

Figure 5 - X-ray Intensity versus Photon energy. This plot combines the effects of the

Bremsstrahlung process and the transition of electrons from one orbital to another in

the x-ray producing process.13

6

Chapter 2: Thin Film Growth

A. Background

Following the process reported by Krastev and Tobin, I have grown four copper

thin films on silicon substrates in Marietta College’s thermal evaporator at 10 -5 Torr with

thicknesses varying from 65 nm to 212 nm. In situ electrical resistance measurements

were collected in each run to monitor the resistivity. As the copper atoms deposit onto

the silicon substrate, initially they form islands.14 Eventually a continuous film is reached

with a resistivity mostly due to the interaction of conduction electrons with the

surface.14 Once the thickness is greater than the mean free path then the resistivity

nears the bulk value. Conductivity has an inverse relationship to this resistivity.

B. Effective Conductivity

The effective conductivity of the copper thin films was of interest in determining

a correlation between epitaxy and the surface scattering of electrons. It differs from

conductivity because the film’s geometrical factors are dropped. This is useful, because

a specific film size is not of concern. The effective conductivity depends on the change

in conductance throughout the growth. It can be described mathematically with the

following equation.

σ eff (t )= LWdG (t)dt

[1]9

L represents the length of the film, W represents the width, and the derivative, dG (t)dt

,

is the change in conductance over thickness. The effective conductivity was plotted

versus the thickness of the film.

7

Some mathematical modeling was done on the data using the Fuchs-Sondheimer

model, which takes into account the effects of surface scattering. This is a classical size

effect model. In this model effective conductivity is described in the following way.

σ eff (t )=σ0(1− l2

(t−t 0+ l)2 ) [2]9

σ 0 is the bulk conductivity, l is the mean free path, t is the thickness, and t 0 is the

thickness when the film is continuous. There are a few assumptions made in this model.

It is assumed that the film is uniform throughout. Also, surface scattering does not

change with thickness. Lastly, plane parallel interfaces are assumed.

C. Substrate Preparation

An ordered, single crystal Si (100) wafer 250 – 300 microns thick was used as the

substrate. Before etching the substrate, the silicon was cleaned with acetone in an

ultrasonic bath for 15 minutes and then with methanol for 15 minutes. The ultrasonic

bath uses high frequency sound waves to agitate the solvent, removing contaminants

from the substrate’s surface. Next, the substrate was etched with hydrofluoric acid.

This was the key component of the substrate preparation. Two percent aqueous HF was

used for the cleaning in an effort to eradicate the SiO2 layer leaving an inert, flat, H-

terminated surface.6 Once cleaned and etched the film was attached to a microscope

slide with Dow Corning high vacuum grease then placed directly in the thermal

evaporator at room pressure. The vacuum chamber was slowly pumped to 10-5 Torr.

D. Growth in Thermal Evaporator

The thin film growth took place in a thermal evaporator system which is a

vacuum area with evaporation capabilities. Pumping down the thermal evaporator was

8

necessary to reduce particulates. The pumping process took about 3 hours. It required

work from both a mechanical pump and diffusion pump. Roughing the chamber with

the mechanical pump lowered the pressure to around 10-2 Torr. This initiated the

evacuating process. The diffusion pump brought the chamber to an even lower

pressure, 10-5 Torr. The diffusion pump used hot oil to reduce the pressure. A coil of

pipe spiraled around this pump with water flow to prevent overheating and to condense

the oil vapor. A cold trap was filled with water near the top to minimize oil vapor

contamination. The pressure was monitored with an ionization gauge which is effective

for pressures between 10-3 and 10-10 Torr.

99.9999% copper wire (0.25 mm diameter) was the source of copper used in the

deposition process inside the thermal evaporator. The wire was wrapped around a

tungsten filament directly across from the substrate. The filament was warmed with an

applied current until the copper began to melt and then some copper atoms obtained

enough energy to escape the solid state. As a gas, they travelled to the cold silicon

substrate and then condensed. This continued until a desired thickness was obtained.

E. Four-wire DC Measurement Method

To determine the conductivity throughout growth, voltage and current were

measured across the thin film. Conductivity describes a material’s ability to conduct

electric current. This is an important material property studied frequently in material

science and nanotechnology because it is crucial to advancing electronics.

Initially four-wire DC measurements were made using the setup on the left in

Figure 6. A slightly different method (setup on the right) was used later involving a lock-

in amplifier to get a more precise measurement. This device can extract a signal in very

noisy environments. The lock-in amplifier outputs an oscillating signal with an

amplitude of 1.00 V and a frequency of 1.00 kHz. The current was determined by

measuring the voltage across a 1 ohm resistor shielded inside of a metal box. The

amplifier was also used to measure the voltage across the film. With this current and

9

voltage data, the resistance and ultimately conductivity could be determined

experimentally.

Figure 6 - Electrical Measurement Setups

F. Thickness Measurement Method

A vibrating quartz crystal thickness monitor similar to the one in Figure 7 was

used to monitor the thickness throughout film growth. It is composed of a quartz crystal

and gold electrodes as shown in Figure 8. This device uses piezoelectric resonance to

vibrate and measure the mass of deposited copper.14 It was positioned inside the

vacuum chamber near the silicon substrate so that copper particles gathered on both

the silicon substrate and the quartz crystal. An oscillating voltage was applied to the

crystal causing resonance when the driving frequency matched the natural frequency of

the quartz. As copper accumulated on the quartz crystal, its shape was altered which

gave rise to a new resonant frequency. The thickness monitor converted the change in

frequency to a change in mass, using the following mathematical expression where ∆ m

represents the change in mass, A represents the area between the electrodes, ρq

10

represents the density of the quartz, vqrepresents the shear wave velocity in quartz, f 0

is the resonant frequency, and ∆ f is the change in frequency.

∆ m=A ρq vq2 f 0

2 ∆ f [3]14

Figure 7 - Quartz Crystal Thickness Monitor15

11

Figure 8 - Gold Electrodes Positioned on Quartz Crystal16

12

Chapter 3: X-ray Diffraction of Films

A. The Bragg Law

The theory behind the crystal diffraction of x-rays lies in the Bragg Law which

results from the periodicity and geometry of the crystal.17

2d sinθ=nλ [4]

Figure 9 - Bragg Diffraction

The constructive interference that occurs at Bragg angles is depicted in Figure 9. If

lattice planes are spaced by d where θ is the angle between the beam and the lattice

plane, then the pathlength difference for the reflected rays is 2dsinθ. When the rays

constructively interfere the pathlength difference is equivalent to an integer number of

wavelengths, represented by nλ. This discussion concerns only elastic scattering;

inelastic scattering creates more complications. In this research, the wavelengths of

concern are the two characteristic x-rays of wavelength 154 pm and 138 pm. Each set

of planes has a Bragg angle for each characteristic x-ray.

In general, crystal structure can be studied through the diffraction of electrons or

neutrons as well. The Bragg Law only holds for waves of wavelength less than or equal

to 2d, which is why visible light cannot be used.17 Between 0.1% and 0.001% of the

13

incident radiation reflects off of each plane in the crystal.17 This means that in a perfect

crystal between 103 and 105 planes contribute to the diffraction intensities.

B. Selection Rules

Interestingly, Longiaru, Krastev, and Tobin obtained no Cu (100) peaks in their x-

ray diffraction data for polycrystalline or epitaxial copper films.6 The explanation behind

this lies in selection rules for x-ray diffraction. To determine the set of reflections for a

given crystal, the interference criteria and crystal structure must be taken into

account.18 The interference criterion is the Bragg Law, and copper’s crystal structure is

face-centered cubic.

Consider two Cu (100) planes in a given simple cubic lattice, one a depth d below

the other as shown in the top of Figure 10. According to the Bragg Law constructive

interference occurs when the pathlength difference between the two rays is an integer

number of wavelengths. It seems that x- rays reflecting off of all Cu (100) planes would

constructively interfere, causing a large intensity for that particular angle of diffraction.

However, since copper has a face centered cubic lattice there are atoms between the Cu

(100) planes as shown in the bottom of Figure 10, and this complicates the situation.

These atoms make up the (200) plane. The x-rays scatter off these atoms and

destructively interfere with the rays from the Cu (100) planes.18 This destructive

interference is due to the fact that the ray’s pathlength difference is half of the

pathlength difference between the two rays reflecting off of the Cu (100) planes. As a

result, XRD data does not have a peak for the Cu (100) diffraction angle because of this

destructive interference at the Bragg angle for the (100) planes. On the other hand,

there is no destructive interference at the Bragg angle for the Cu (200) planes, so the Cu

(200) peak shows up in x-ray diffraction.

14

Figure 10 - Bragg Diffraction for SC and FCC Crystals

C. XRD Procedure

X-ray diffraction is an important tool in characterizing materials in surface

science. The TEL-X-OMETER X-Ray Apparatus was used to x-ray the copper thin films

grown in lab. The particular method utilized was θ−2θ Bragg scanning. The data

yielded diffracted x-ray intensity versus 2θ, where θ is the Bragg angle. Two specific

factors contribute to the intensity of the diffraction peak. One factor is the atomic

density of the planes; more planes give a stronger signal. Also, the interval between a

set of planes effects the peak strength. For example, (200) planes are closer together

15

than (111) planes and would thus exhibit a higher intensity. Another factor is the

volume of the crystallites in the thin film being characterized.6

In their studies, Krastev and Tobin were able to unveil a noticeable difference

between the scans of a thin film polycrystalline sample, a sample grown on an unetched

substrate, and a sample grown on an etched substrate.6 The polycrystalline scan yielded

evidence of many orientations of the crystal’s unit cell; many peaks were seen in the

polycrystalline films because of disorder at the atomic level, similar to powdered

samples. The large Cu (200) peak of the etched substrate indicates that the copper

atoms aligned epitaxially with the Si (100) planes.

The interest of my research lies in the ratio of the Cu (111) peak and the Cu (200)

peak for the thin films grown at Marietta. A larger Cu (200) peak indicates that the film

is more ordered because the orientation of the crystal is primarily (100). A larger Cu

(111) peak indicates that the orientation is primarily (111), or perhaps polycrystalline. A

(111):(200) peak ratio of 2.17:1 is tabulated for powders.19 In this case, there is a lack of

(100) dominance and the crystal is likely polycrystalline, composed of all the possible

orientations. See Figure 3 for the geometry of the (111) plane.

The x-ray apparatus provides the necessary information about the orientations.

In this apparatus, the x-ray source shines on the sample, and the diffracted x-rays

disperse everywhere within the machine. A Geiger Muller tube is placed at an angle 2θ

from the incident beam. In this situation θ represents the grazing angle at which the x-

ray hits the crystal planes. The sample moves by the angle θ, while the GM tube moves

by the angle 2θ. The x-ray machine has several parameters that may be set to maximize

the quality of the results, including angle increment, time per increment, and scan angle

range. I typically used a very detailed scan: 0.05° increment, 10 seconds per increment,

and an angle range covering expected peaks. Figure 11 gives a visual of the apparatus.

16

Figure 11 - Tel-X-Ometer X-ray Apparatus

17

Chapter 4: Results and Discussion

A. Thin Film Conductivity

In general, the effective conductivities of the films increase during early growth,

then begin converging to a constant value. The conductivity should approach the bulk

conductivity of copper, 58 (μΩ-m)-1.20 The scattering of conduction electrons from the

surface lowers the effective conductivity.8 These conduction electrons collide with

surface defects and grain boundaries which prohibit a continuous uniform flow of

current consistent with that of bulk materials. The Fuchs-Sondheimer model gives a

mathematical expression for the theoretical behavior of this surface scattering. This

model yields information about three physical variables: the mean free path l, the bulk

conductivity σ 0, and the thickness when the film becomes continuous t 0.

Table 1 gives each film’s etch time and thickness, and Figures 12-14 display the

effective conductivities of these films. During the fourth film growth, the lock-in

amplifier gave no reading. This is likely due to the lack of a continuous film. Thus, there

is no effective conductivity data for this film.

Film number HF etch time Thickness

1 2 min 65 nm

2 10 min 71 nm

3 2 min 75 nm

4 10 min 212 nm

Table 1 - Copper thin films HF etch times and thicknesses.

18

0 2 4 6 8 10 120

2

4

6

8

10

12

Fuchs-Sondheimer ModelEffective Conductivity

Thickness (nm)

σeff

(μΩ

-m)-1

Figure 12 - Effective conductivity vs. thickness of copper film 1

20 30 40 50 60 70 80-5

5

15

25

35

45

Fuchs-Sondheimer Model

Effective Conductivity

Thickness (nm)

σeff

(μΩ

-m)-1

Figure 13 - Effective conductivity vs. thickness of copper film 2

19

40 45 50 55 60 65 70 75

-20

-10

0

10

20

30

40

50

Effective ConductivityFuchs-Sondheimer Model

Thickness (nm)

σeff

(μΩ

-m)-1

Film

numberl σ 0 t 0

χ ν2

1 3.1±0.5nm 15±3 (μΩ−m)−1 37(+1/−8)nm 4.6

2 4.0 (+3.0/−0.5)nm 37±1(μΩ−m)−1 45 (+1/−5)nm 8.3

3 24.5±0.5nm 15±1(μΩ−m)−1 48 (+1/−2)nm 2.5

Figure 14 - Effective conductivity vs. thickness of copper film 3

Table 2 displays the mean free pathlength l, the bulk conductivity σ 0, the

thickness when the film becomes continuous t 0, and reduced chi-squared χ ν2, a measure

of the model’s accuracy. A reduced chi-squared value less than 1 means that the model

works, while a value above 1 indicates that the model is likely incorrect.

The mean free pathlengths of film 1 and 2 are reasonably close, while film 3’s is

larger. At the University of Wisconsin the electron mean free pathlength of copper films

was investigated. It was reported that a 69 nm film, grown by deposition, yielded a

20Table 2 - Film 3 Fuchs-Sondheimer fit parameters

pathlength of 29.4 nm.21 The data revealed that thinner films gave rise to lower mean

free pathlengths. We see a similar correlation between thickness and pathlength.

However, a linear relationship is not present as in the Wisconsin study. The low values

for film 1 and 2 could indicate impurities in the copper obstructing the electron’s path.

There is likely scattering from internal defects in addition to the surface scattering that

we expect for a thin film. A non-epitaxial film would have much disorder leaving many

obstructions to shorten the electron’s path. It is plausible that film 3 experienced a

cleaner growing environment and thus a larger mean free path, more comparable to

pure copper. Overall, the films grown in the lab exhibit relatively low mean free paths.

The conductivities for films 1 and 3 are quite low compared to the reported bulk

conductivity for copper, 58 (μΩ-m)-1. The low conductivity is concerning; although it

does make sense in regard to the low mean free path of film 1. Film 2 approaches the

bulk value closer than film 1 and 2. It reaches 37.3 (μΩ-m) -1 and then levels off.

Interestingly, film 3 which had a longer growth, experiences a similar leveling off as the

others, but this is followed by a rapid rise in the conductivity to 41.8 (μΩ-m) -1. This

seems to indicate that the film has two stages of scattering effects. Once the film

growth surpasses one stage of surface scattering effects and reaches 10 (μΩ-m) -1 it

experience another stage of increasing effective conductivity. The model does not fit

this second increase; this section of the data is interesting and unexplainable at this

point. We would not expect effective conductivity to level and then rise. In this film

growth software was implemented to record the measurements; however, this should

not have affected the data. Perhaps some defects in the crystal caused a delay in the

increasing effective conductivity.

The thickness at which the film becomes continuous varies from film to film,

depending on the point at which the islands merge. The Fuchs-Sondheimer model

doesn’t fit the experimental data well in the early stages of increasing conductivity.

After this, the model fits the data nicely for film 1 and 2. For each film the uncertainty in

the effective conductivity increases with increasing thickness. Thickness plays the

largest role in the uncertainty compared to the length, width, and change in

21

conductance. This is due to the difficulty of measuring such small masses on the

nanometer scale. The model fits well within the error bars for film 2 and 3; however not

completely for film 1. Visually, it looks as if the model fits the best as it levels off,

compared to the increasing slope. In regard to the model fit accuracy, the reduced chi-

squared calculation reveals that none of the models are likely the right fit. The model

for film 1 and 3 are the best though, since their reduced chi-squared values are closer to

one.

B. Standard Bulk Copper, Si (100), and Au (111) X-Ray Scans

One bulk copper sample, an OFHC copper sample, a Si (100) wafer, and a Au

(111) thin film were scanned as standards in this project to test the behavior of the Tel-

X-Ometer and provide insight about the thin films’ epitaxy. The bulk copper scan,

shown in Figure 15, yielded two peaks, one at 43° and one at 50°. These correspond to

the expected diffraction peaks of the (111) copper plane and the (200) copper plane,

respectively.6 It is important to note the ratio of these two peaks. This provides

information about the polycrystalline nature of the copper. The tabulated ratio for

powdered copper is 2.17:1 [Cu (111): Cu (200)].19 The bulk copper sample has a ratio of

1.7:1, which is similar to the powdered copper result. This indicates that the bulk copper

sample is fairly polycrystalline. All of the data was smoothed using EWMA (exponentially

weighted moving average). The IPython code for this smoothing technique is included

in Appendix A.

22

Figure 15 - Bulk Polycrystalline Copper XRD Scan

Similarly, the oxygen free bulk copper (OFC) yielded peaks at 43° and 50.5°,

shown in Figure 16, corresponding to the (111) and (200) planes. The ratio of the

(111) to (200) peaks for oxygen free copper is 1:1.2, which is not very consistent

with the ratio for powdered copper. This suggests that the OFC copper has a

somewhat more single crystalline nature with the (100) planes dominating.

23

Figure 16 - OFC Copper XRD Scan

In Figure 17, the scan of the Si (100) crystal displays constructive

interference at the 2θ angles 61.9° and 70°. These represent the Si (400) planes.6

We see one for each of the characteristic x-rays. Since the two characteristic x-rays

have different wavelengths, they also give rise to two different Bragg angles for the

same set of planes. All four copper films displayed strong silicon peaks. Thus, it is

clear that the skin depth of the radiation was greater than the thickness of each

film.

24

Figure 17 - Si (100) XRD Scan

A commercial polycrystalline Au (111) film was scanned for comparison and

insight into the Tel-X-Ometer’s ability to detect epitaxy. The scan revealed that the

Tel-X-Ometer does in fact have this capability. The Au (111) scan reveals peaks at

34.2°, 38.3°, 45.8° and 82.5° as shown in Figure 18. These represent the planes

(111), (200), and (222).22 Two different studies on gold nanoparticles reported

similar data, but with different peak intensities.22,23 Of the three datasets, the one

performed at Marietta is the most oriented toward (111) which would be expected

since it is a commercial epitaxial Au (111) film versus a distribution of gold

nanoparticles with numerous orientations. The ratio of the (111) peak to the (200)

peak is 11.7:1 compared to 1.3:1 in one of the studies of diffraction patterns and

optical properties of gold nanoparticles.23 The XRD result from this study is shown in

Figure 19.

25

Figure 18 - Au (111) XRD Scan

Figure 19 - Gold Nanoparticles XRD Scan19

26

C. Epitaxy of the Thin Films

A highly oriented epitaxial copper film grown on Si (100) can be identified by

the presence of a strong Cu (200) peak.6 Figures 20-23 display the XRD data for

films 1-4. The films grown at Marietta show no evidence of epitaxy normal to the

surface. The 212 nm, 10 min. etch film revealed a broad peak around 44° as can be

seen in Figure 23. This likely is an emerging Cu (111) peak which likely means the

film is highly disordered. This is the only scan that had any copper peaks. The

silicon peaks were present in every scan but no Cu (200) peaks.

Figure 20 - Film 1 XRD Scan

27

Figure 21 - Film 2 XRD Scan

Figure 22 - Film 3 XRD Scan

28

Figure 23 - Film 4 XRD Scan

29

Chapter 5: Conclusions

The copper thin films grown in Marietta College’s surface science lab do not

show signs of epitaxy. The x-ray diffraction results indicate that the films are closer to

the crystal structure of powders. Further, the conductivity data indicates that the non-

epitaxial films have a lower mean free path and bulk conductivity than the epitaxial films

reported in the literature.8 Lastly, the reduced chi-squared value indicates that the

Fuchs-Sondheimer model does not accurately produce the physical variables.

There is much research to continue in the surface science lab at Marietta. In

furthering this research, it would be interesting to see what effect 10% HF would have

on the films as an etchant. It is possible that using a stronger concentration of HF would

produce the desired H-terminated silicon substrate. A cleaner substrate with less

impurities should give rise to a more epitaxial film. Perhaps the Si (100) substrates

simply did not have a clean enough surface to grow an epitaxial film. Another issue that

could have led to the lack of epitaxy is the vacuum system. Refinements could be made

to the thermal evaporator to improve the vacuum conditions which could have resulted

in contaminations of the Si (100) surface hindering epitaxial growth. Issues with the seal

of the bell jar arose which likely were reducing the quality of the vacuum chamber.

The study of gold films is also another interest in the lab that will be explored in

the future. The motivation behind this research is surface science adsorbate studies as

well. The reflectivity and resistivity of gold films with a sulfur-based adsorbate can be

investigated with the equipment in the lab. Also, if the copper growth procedure were

improved, similar adsorbate studies could be done with the copper.

30

Appendix A

IPython Code for EWMA Smoothing and Output

31

32

References

1 Chang Liu, “Interactions of Adsorbates on Cu (100) Films Investigated by Surface Resistivity

Measurements,” Thesis (Tufts University), 2008, http://books.google.com/books?id=-

aNn_mgvIG4C&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=fal

se.2 Leslie A. Kolodziejski and Dr. Gale S. Petrich, “Epitaxial Growth and Processing of Compound

Semiconductors,” Epitaxial Growth of Semiconductors,

http://www.rle.mit.edu/media/pr141/rep141-i.1.2.pdf.3 "A survey of some new results in ferromagnetic thin films," Radu Ignat,

http://www.math.univ-toulouse.fr/~rignat/XEDP_IGNAT.pdf.4 “Applications of Thin Films,”

http://www.tf.uni-kiel.de/matwis/amat/semitech_en/kap_3/backbone/r3_1_2.html.

5 Minsu Longiaru, E. T. Krastev, and R. G. Tobin, “Epitaxy above 10-5 Torr: A student’s

introduction to thin film growth and characterization,” J. Vac. Sci. Technol. 14 (5), 2875,

(1996).6 “Structure of Materials,” http://fgamedia.org/faculty/rdcormia/NANO52/pdf/Structure%20of

%20Materials%20Handout.pdf.7 University of Colorado, “Bravais Lattices,” http://ecee.colorado.edu/~bart/book/bravais.htm.8 E. T. Krastev, L. D. Voice, and R. G. Tobin, “Surface morphology and electric conductivity of

epitaxial Cu (100) films grown on H-terminated Si (100),” J. Appl. Phys. 79 (9), 6865, (1996).9 “Lattice Constants of the elements,”

http://periodictable.com/Properties/A/LatticeConstants.html.

10 Science and Engineering Encyclopedia, “Miller Indices,”

http://www.diracdelta.co.uk/science/source/m/i/miller%20indices/source.html#.UuC8rbROnI

U.11 Robert Eisberg and Robert Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and

Particles, 2nd ed. (John Wiley & Sons, New York, 1985).12 P. E. J. Flewitt and R. K. Wild, Physical Methods for Materials Charaterisation, 2nd ed. (IOP

Publishing, Bristol and Philadelphia, 2003).

13 University of Basel, “Characteristic Spectrum,” http://miac.unibas.ch/PMI/01-BasicsOfXray-

media/figs/Characteristic_Spectrum.png.

14 Meredith E. Rogers, “Changes in conduction electron transport in thin metal films,” Physics

Capstone Thesis, May 2007.15 “Quartz Crystal Microbalance,” http://www.tectra.de/qmb.htm.

16 “High Precision Piezoelectric Blanks Quartz Crystal,” http://www.tradeindia.com/fp958920/High-Precision-Piezoelectric-Blanks-Quartz-Crystal.html.

17 Charles Kittel, Introduction to Solid State Physics, 7th ed. (John Wiley & Sons, New York, 1996).18 Sadoway, Donald. 3.091SC Introduction to Solid State Chemistry, Fall 2010. (MIT

OpenCourseWare: Massachusetts Institute of Technology),

http://ocw.mit.edu/courses/materials-science-and-engineering/3-091sc-introduction-to-solid-

state-chemistry-fall-2010 (Accessed 28 Apr, 2014). License: Creative Commons BY-NC-SA19 J. Yang, C. Wang, K. Tao, and Y. Fan, J. Vac. Sci. Technol. A 13, 481, (1995).20 NDT Resource Center, “Conductivity and Resistivity Values for Copper & Alloys,”

http://www.ndt-ed.org/GeneralResources/MaterialProperties/ET/Conductivity_Copper.pdf.21 Catherine N. Radomski, “The Mean Free Path of Electrons in Copper Films,” Thesis (University

of Wisconsin-Madison), 2003,

http://cmb.physics.wisc.edu/papers/theses/cathy_bailey_thesis.pdf.22 M.H. Majles Ara, Z. Dehghani, R. Sahraei et al. “Diffraction patterns and nonlinear optical

properties of gold nanoparticles,” J. Quant. Spectro. Radia. Transfer, 113, 366 (2012).23 Kien Cuong Nguyen, “Quantitative analysis of COOH-terminated alkanethiol SAMS on gold

nanoparticles surfaces,” Adv. Nat. Sci.: Nanosci. Nanotechnol., 3, 045008 (2012).