Variable Temperature Transport Measurements and Conduction

Mechanisms of Crystalline and Amorphous Titanium Dioxide Thin

Films

Acacia Patterson

An undergraduate thesis advised by Dr. Janet Tate

Submitted to the Department of Physics, Oregon State University

In partial fulfillment of the requirements for the degree BSc in Physics

Submitted on May 22, 2020

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Abstract

The electrical properties of amorphous and crystalline titanium dioxide polymorphs are reported.

Titanium dioxide is a widely used transparent semiconductor and it is a useful oxide model.

Using variable temperature transport measurements of thin films, it was possible to establish the

activation energy barrier for conduction. This was accomplished using an Arrhenius model.

Typical activation energies were 14 - 353 meV and higher activation energies correlated with

higher resistivity. To investigate the conduction mechanisms, Mott’s hopping conduction model

also was applied, and I investigated these models for different temperature regimes. For films

which could be described by Mott’s theory, the density of states was found. and most films had a

density of states value of about 1017 eV-1cm-3. Both conduction mechanisms were seen in

amorphous and crystalline films, but amorphous films predominantly exhibited hopping

conduction. Resistivity was higher for films which were amorphous and for films which were

crystalline, which warrants further investigation. The electrical properties did not distinguish

TiO2 polymorphs from one another, and anatase does not appear to be the least conductive phase

as I previously supposed.

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Table of Contents

Chapter 1: Introduction……………………………………………………………………………4

1.1 Purpose………………………………………………………………………………...4

1.2 Background……………………………………………………………………………5

1.2.1 Polymorphs………………………………………………………………..5

1.3 Annealing…………………………………………………………………………….6

1.3.1 Oxygen Deficiency………………………………………………………….7

1.4 The Hall Effect…………………………………………….…………………………..8

1.5 Conduction Mechanisms…………………………………….………………………...9

1.5.1 Semiconductors……………………………………………………….…………9

1.5.2 Electron Hopping and Lattice Vibrations……………………………………….9

1.6 Arrhenius Model……………………………………………………………………..11

1.6.1 Activation Energy……………………………………………………………...11

1.6.2 Mott’s Theory………………………………………………………………….11

Chapter 2: Methods………………………………………………………………………………13

2.1 Sample Preparation…………………………………………………………………..14

2.1.1 Sample Geometry………………………………………………………………14

2.1.2 Low Temperature Experimental Setup………………………………………...15

Chapter 3: Results and Discussion………………………………………………………………19

3.1 Semiconducting Behavior……………………………………………………………19

3.2 Crystallinity…………………………………………………………………………..19

3.2.1 1/kBT Fitting…………………………………………………………………...20

3.2.2 Resistivity and Activation Energy…………………………………………….23

3.3 Polymorphs…………………………………………………………………………..24

3.4 Mott’s Theory Density of States……………………………………………………..25

Chapter 5: Conclusion……………………………………………………………………………27

References………………………………………………………………………………………..29

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List of Figures

Figure Page

1 The structures of titanium dioxide: rutile, brookite, and anatase…………………………..….5

2 Phase formation relation to partial oxygen presure and film thickness…………………….…6

3 T/(1-R) vs. wavelength of brookite, rutile, and anatase.……………………..…………..……8

4 n-type (free electrons) and p-type (free holes) semiconductor types…………………..……...9

5 Ballistic transport in semiconductors…………………………………………………………10

6 A density of states graphs showing the energy values for particular energy levels

where the different states are denoted using capital letters……………………………….…….12

7 Pre- and post-annealed samples on a sample board showing the four corner contacts……....14

8 The van der Pauw configuration which shows the

orientation of the magnetic field, the input current, and the measured voltage………….……..15

9 Voltage vs. current to determine resistance for one pair of contacts…………………………...15

10 A model 7704A Lake Shore Hall measurement system………………………………………16

11/12 Resistivity vs. temperature of pre- and post-annealed thin films…..…….………………20

13 A plot of the logarithm of resistivity vs. 1/kBT for a sample that was

amorphous or crystalline……………………………………………………….………….....21

14/15 The Log(ρ) vs. 1/kBT or 1/kBT1/4 for pre- and post-annealed samples

of brookite, rutile, and anatase ………………………………………………...…………22

16 Log(ρ) vs. 1/kBT1/4 or 1/kBT for an amorphous film in the “mid-low” temperature

range of 193 – 273 K…………………...….…………………………………...……………..23

17 Log(ρ) vs. hopping energy which shows a general pattern of increasing

resistivity for an increasing energy ……………….……………………………..……...…….24

18/19 The relationship between resistivity and phase in which resistivity increases

from left to right, and the concentration of phases are demonstrated with color............…25

20 The DoS values for amorphous films. Eleven films demonstrated similar DoS

values, but 7 had unreasonably large values……………………………………..…………26

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Chapter 1: Introductions

1.1 Purpose

Titanium dioxide (TiO2) has important implications in renewable energy and in

technology. TiO2 is a well-known and important material, and its polymorphs anatase and rutile

have been well-studied and utilized. However, because of the difficulty in producing the pure

polymorph brookite, there is less data on its properties. For instance, as a photocatalyst, TiO2

thin films can be used in the photodegradation of organic pollution [1]. The photocatalytic

behavior of brookite is unclear [2]. TiO2 is used as a pigment in many types of products, it is

used in hydrophobic/self-cleaning surfaces, and it is used in photochromic materials [3]. Finally,

TiO2 films are used as gas sensors and as protective, anti-reflective, or antibacterial coatings [4].

This project aims to uncover the electrical properties and the conduction mechanisms of TiO2

thin films by examining brookite, rutile, and anatase films and by investigating the effect of

annealing1 on these materials. I measured temperature dependent electrical transport properties to

obtain the activation energy, resistivity, and residual resistivity of TiO2 thin films. Residual

resistivity is a parameter of the material when temperature is infinite. In our investigation of these

films, we hypothesized that anatase, which has fewer oxygen vacancies, had a lower resistivity in

amorphous2 films compared to ordered films. In addition, since amorphous films have defect

states (states where charge carriers can exist in the material’s band gap) which trap carriers in

1 The heat treatment of a material to transform an amorphous material into a crystalline material (as an example, annealing can be used to make metal weapons stronger).

2 Unlike crystalline materials, amorphous materials do not have long-range, ordered structures, though they do have short-range order.

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potential wells and then repel free carriers, it is expected that polycrystalline films will have a

lower conductivity than crystalline films [5].

1.2 Background

1.2.1 Polymorphs

Titanium dioxide has 3 polymorphs, or phases, which are different crystalline

structures that have the same stoichiometry3. These polymorphs, brookite, rutile, and

anatase are demonstrated in Figure 1.

Figure 1: The structures of titanium dioxide: rutile, brookite, and anatase [6].

The ability of TiO2 to form different crystal structures is known as polymorphism in

which rutile is stable and anatase and brookite are metastable4 [6]. I am investigating

TiO2 thin films, which are a coating of TiO2 on fused silicon dioxide substrates. The films

are produced in-house, and a member of the Tate lab, Okan Agirseven, is investigating

3 The ratio of atoms in a compound. TiO2 has perfect 1:2 stoichiometry whereas TiO2-x has imperfect 1:2 stoichiometry. 4 When a system is capable of forming multiple states, metastability occurs when a system settles in a state with higher energy compared to a state with the lowest possible energy.

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the conditions (partial oxygen pressure and temperature) which produce pure brookite

films.

Previously, the Tate group had used pulsed laser deposition (PLD) to produce TiO2

films, and we have begun to utilize the method of RF sputtering to create brookite,

anatase, and rutile films [6]. In his work, Agirseven found a relationship between the

partial oxygen pressure and the likelihood that particular phases would form. Figure 2

demonstrates this correlation.

Figure 2: Phase formation relation to partial oxygen presure and film thickness [7]. The graph demonstrates that anatase forms at higher oxygen pressure, brookite forms at intermediate pressure, and rutile forms at low pressure.

1.3 Annealing In the RF sputtering process, we produce amorphous films at room temperature.

We then use the process of annealing to form crystalline films from the amorphous films

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which are either brookite, rutile, or anatase. See figure 2 for the parameters which cause

the polymorphs to form. Amorphous and crystalline films demonstrate different electrical

properties, and the annealing process consistently produces the different polymorphs of

TiO2.

1.3.1 Oxygen Deficiency

Semiconductors are intrinsic (pure) or extrinsic (doped). The addition of

impurities by doping increases the conductivity of a material, and we dope TiO2 with

oxygen vacancies to form TiO2-x. Oxygen vacancies result in an excess of electron charge

carriers because the titanium atoms have electrons which would have formed Ti-O bonds.

These delocalized electrons fill defect states below the conduction band, and they can

move into the conduction band or to other defect states with the addition of energy. A

greater number of vacancies corresponds to increased carrier concentration, but the

mobility of carriers is reduced by the presence of defects. In addition, the interaction of

carriers with each other reduces their mobility, so when more energy is added to the

system to move carriers to the conduction band, there will be more carriers and less

carrier mobility. Because the deposition of anatase requires more oxygen, we expected

that this polymorph would have fewer oxygen vacancies and would therefore be more

resistive. A graph that shows the oxygen absorption of the polymorphs is given in figure

3 where rutile is red, brookite is blue, and anatase is green. Values farthest from 1

indicate the most absorption. The graph demonstrates that rutile and brookite have a

higher absorption than anatase, which means anatase demonstrates greater transmission.

Therefore, anatase has the fewest oxygen vacancies since a high absorption corresponds

to greater oxygen vacancies.

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Figure 3: T/(1-R) vs. wavelength of brookite, rutile, and anatase [8]. Transmission is symbolized with a T and reflection is given as R.

1.4 The Hall Effect

The Hall effect gives the film carrier concentration and carrier mobility [9]. When current

and a magnetic field which are perpendicular to the film are applied, the trajectory of charge

carriers is determined by the Lorentz force. The separation of carriers causes a potential which

can be measured, and this gives the carrier concentration and mobility. In addition, the sign of

the Hall coefficient demonstrates the sign of the charge carriers in which electrons are negative

and electron holes are positive. This can be used to determine whether a material is a p-type or

an n-type semiconductor. A diagram of n- and p-type semiconductors is given in figure 4.

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Figure 4: n-type (free electrons) and p-type (free holes) semiconductor types [10].

1.5 Conduction Mechanisms

1.5.1 Semiconductors

TiO2 is a wide-gap semiconductor, which prevents electrons from being excited to

higher energy levels except at very high temperatures (which would damage the

material). However, TiO2 conducts charge when electrons in defect states in the band gap

of the doped material are promoted to the conduction band.

1.5.2 Electron Hopping and Lattice Vibrations

Crystalline materials generally experience ballistic conduction, which is limited

by an interruption in periodicity that occurs from the introduction of isotopes

(impurities), thermally activated lattice vibrations (phonons), and grain boundaries when

a material has multiple crystalline structures. Ballistic conduction in semiconductors is

demonstrated in figure 5 where the energy to transition to higher states is Eg.

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Figure 5: Ballistic transport in semiconductors. Electrons are promoted from the valence band to the conduction band. The required energy for these excitations is band gap or activation energy respectively [11].

Some semiconductors also experience hopping conduction, which we expect to be the

primary conduction mechanism in amorphous materials. Unlike ballistic conduction in

which band states are extended and delocalized, the band states in hopping conduction

are localized and allow carriers to be excited from defect states in the band to other defect

states or to the conduction band when the final state has an energy that is practically the

same as the initial state. In figure 5, this energy is labelled as ED.

To discuss the conductivity mathematically, we can use the relationship:

𝜎 = 𝑛𝑒µ. 1)

Where σ is conductivity, 𝑛 is carrier density, e is the charge of an electron, and µ is

mobility. The number of transport carriers increases exponentially in a semiconductor

when the temperature increases (discussed later), and an increase in temperature results in

more phonons which disrupt periodicity. The carrier mobility decreases by a power law

(much less than an exponential law) because of the increase in phonons. Since e is

constant, there is a trade-off between carrier density and mobility and σ increases.

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1.6 Arrhenius Model

1.6.1 Activation Energy

The film activation energy EA, which is the energy necessary for carriers to be

excited from defect states, can be found using the Arrhenius relationships [12]:

𝜌 = 𝜌(𝑒𝑥𝑝 +,-./0

1. 2)

𝑛 = 𝑛(𝑒𝑥𝑝 +2,-./0

1. 3)

Where ρ is the resistivity, ρ∞ is the residual resistivity, n is the carrier density, kB is

Boltzmann’s constant, and n∞ is a parameter for carrier density when the temperature is

infinite. When plotting ρ vs. 1/kBT, the fit gives the values of EA, ρ∞, and n∞.

1.6.2 Mott’s Theory

Mott’s theory says that resistivity vs. 1/kBT1/4 should be a better fit for amorphous

samples compared to resistivity vs. 1/kBT. A good fit of r(T) to 1/kBT1/4 indicates that

electron hopping is the primary conduction mechanism [13]. In addition, the theory says

that if a fit of 1/kBT1/4 is more accurate, the density of states for a material can be

determined. The density of states for TiO2 is given in figure 6.

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Figure 6: A density of states graphs showing the energy values for particular energy levels where the different states are denoted using capital letters [14].

The density of states can be found with the relationship:

𝐵 = 26 + 7891 :;

<(,>). 4)

where B is the experimentally determined hopping energy and 1/α is the localization

length of the wave function, which is unknown. We can approximate this value using the

atomic spacing, which is approximately 100pm. N(EF) is the density of states at the Fermi

energy level (EF), which has dimensions of number/energy•volume [13].

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Chapter 2: Methods

To perform resistivity and Hall measurements, I soldered indium contacts onto samples

and used a model 7704A Lake Shore Hall measurement system. These contact points allow us to

apply a current on one contact and measure the resulting voltage on another pair of contacts, and

this is repeated for all contacts. The measurement system had a limit of 6 volts, and depending

on the resistance of the sample, I used an excitation current of 100 pA - 3 mA. I was able to

determine if an excitation current was acceptable because the Hall system displays an error when

the signal is too small to measure. We also used a dwell time (the time for a state to settle at a

particular value) of 2 seconds. Resistivity values were determined by measuring resistance

(given by Ohm’s law) and dividing by the film’s thickness. These thicknesses are found using a

scanning monochromator and with ellipsometry, which are performed by Tate lab’s Cameron

Stewart and Joseph Kreb respectively.

There are systematic errors in the measurement of Hall voltage including

voltmeter/current meter offset and thermoelectric voltages produced by the contacts or sensor

wiring which is caused by a change in temperature. Another source of error is the Nernst effect

voltage which is caused by a change in temperature and results in a diffusion of electrons

(current). The magnetic field acts on this current which creates a voltage that is affected by the

magnetic field but not by the applied current, and this source of error cannot be compensated for

by current or field reversal. If the sample geometry is “bar” and not the van der Pauw

configuration I used, the largest error is typically a misalignment voltage, which is produced

when the applied current runs through 2 contacts and the magnetic field is 0 [15]. To reduce error

in resistance measurements, the Hall effect uses positive and negative electrical and magnetic

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fields as well as multiple contact points on the sample. An image of these films on a sample

board is given in figure 7.

Figure 7: Pre- and post-annealed samples on a sample board showing the four corner contacts.

2.1 Sample Preparation

2.1.1 Sample Geometry

As demonstrated in figure 8, samples were prepared in a van der Pauw

configuration to measure with a Lakeshore Hall measurement system, which will be

discussed subsequently. The resistance of the contacts used to measure the system was

minimized by using 4 contact points (2 for the current source and 2 for voltage

measurements).

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Figure 8: The van der Pauw configuration which shows the orientation of the magnetic field, the input current, and the measured voltage.

Contacts were made sufficiently small and confined to the corners of the square

samples, and the resistance of the contacts was confirmed by measuring the film

resistance and determining an Ohmic relationship. We determined this with an IV-curve

that had a correlation greater than 0.999990. An example graph is given in figure 9.

Figure 9: Voltage vs. current to determine resistance for one pair of contacts. The resistivity is shown to be a reliable value because the correlation is 1.000000.

2.1.2 Low Temperature Experimental Setup

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The Lakeshore Hall measurement system includes a current supply, a magnet

power supply, a current source, a gaussmeter, a temperature controller, a nanovoltmeter,

a switch system, a picoammeter, and a platinum temperature probe. A diagram of the

system is given in figure 10.

Figure 10: A model 7704A Lake Shore Hall measurement system [15]. The computer software provides input to and outputs measurements from the temperature controller, the voltmeter, the current source, the current meter, the gaussmeter, and the magnet power supply (MPS). A temperature probe in the sample holder measures the temperature, and the hall probe (inserted between the electromagnets and the sample holder) measures the magnetic field. The MPS controls the magnets, and the switch system controls the current which is supplied to the contacts and the voltage which is measured. The system has an option to take the current meter out of the circuit when the excitation current is too high for the meter to measure without being damaged. Finally, the electromagnets are cooled in a closed refrigeration system.

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I submerged samples (encased in a sample holder) into a dewar of liquid nitrogen

so that they were above the liquid but subject to the vapor of evaporated nitrogen. The

samples cooled to about 77 K or as cold as the limitations of the measurement system

would allow, which varied because the resistivity of samples could be significantly

different. For example, one sample could not be measured below 99 K, and the resistivity

was about 25 kΩcm at this temperature. Another sample could not be measured below

246 K where the resistivity was 92 Ωcm. While the system warmed to room temperature,

I performed resistance and Hall measurements. The largest range for measurements was

77-295 K. Because resistance increased with decreasing temperature, a smaller excitation

current was necessary, but measurements were not made if the signal was too small. I

used a measurement settle time of 2 seconds to reduce the error in the measurements, and

a positive and negative current was applied to the 4 contact points and the voltage was

measured across the 4 points. For each value of temperature, a magnetic field in the range

of positive 7-10 kG was used depending on the resistance of the sample. Using a larger

field gives more accurate measurements, but it takes longer to ramp the system to large

values. I determined that 7 kG produced reliable values by performing room temperature

measurements with 7 or 10 kG and observing that both fields gave similar values. At 7

kG, the measurement time (in which the magnetic field must ramp to positive and to

negative values) was about 7 minutes. However, because the system warms while

measurements are performed, this may result in a significant error as electrons drift with

a change in temperature. At temperatures close to liquid nitrogen temperatures (77K), the

system warmed slowly because of the presence of liquid nitrogen vapor or liquid, and at

higher temperatures, the system warmed more quickly. For instance, the temperature for

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one sample changed from 154-167 K during the measurement time (7.13 minutes), and

when the measurement time was practically the same (7 minutes), its temperature

increased from 274-277 K.

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Chapter 3: Results and Discussion

This project began with an investigation into variable temperature Hall measurements,

which led me to apply several analyses to understand my findings. In this section, I discuss the

values I found and the shortcomings of my data. I also discuss the trends I found between films

which were amorphous or crystalline and the trends between the phases of TiO2. To understand

the variable results, I describe the analysis of these measurements including the applicability of

Mott’s theory (considering different temperature regimes) to determine conduction mechanism

and the density of states for these films.

3.1 Semiconducting Behavior

I measured 44 samples and found resistivity data for all, but I observed that the films

were typically too resistive to find reliable Hall data. This was apparent because the sign of the

Hall coefficient (which gives the n- and p-type semiconducting behavior of a material) alternated

between positive and negative. One sample, which had a low resistivity of 227 µΩcm at 213 K,

did have reliable Hall data, and the Hall coefficient demonstrated that the film was n-type. I

observed the expected semiconducting behavior in which resistivity decreased with increasing

temperature (with the rate of change being greater for low temperatures), but this behavior made

measurements at low temperatures less reliable. Though it may have been possible to get more

reliable values at room temperature, this was not the focus of my project. Ohm’s law gives the

relationship between current, voltage, and resistance. Because the system was limited to a

measurement of 6 volts, input current had to be small. The measurement system could input

currents as low as 100 pA or less (which was required for some samples), but this was too small

for the system to measure and use in calculations reliably.

3.2 Crystallinity

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Resistivity increased when temperature decreased for samples which were amorphous as

well as for samples which were crystalline. Resistivity decreased for 12 samples when they were

annealed, and resistivity increased for 9 samples when they were annealed. This behavior is

demonstrated in figures 11 and 12.

Figures 11 and 12: Resistivity vs. temperature of pre- and post-annealed thin films. Figure 11 demonstrates that “post-annealed” samples were more resistive, and figure 12 shows that “pre-annealed” films were more resistive. The range of temperatures was sample-dependent because I took data at temperatures as cold as possible, which depended on the sample’s resistivity.

For the amorphous films which demonstrated an increase in resistivity, lattice vibrations

may be the principal conduction mechanism, and we note a trade-off between carrier density and

mobility.

3.2.1/kBT Fitting

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Figure 13 shows an example of the data I observed for resistivity vs. 1/kBT.

Figure 13: A plot of the logarithm of resistivity vs. 1/kBT for a sample that was amorphous or crystalline. The graph shows different behavior of resistivity depending on the temperature range, and the best-fit line gives a sample’s EA, ρ∞, and n∞.

Though not as obvious with this temperature scale, and figures 11 and 12 may be more

useful to see this, the resistivity has different behaviors depending on the temperature

range. This results in different values of activation energy for different temperature

ranges since the energy barrier is the slope of ρ vs. 1/kBT. Figures 14 and 15 show the

different analyses to determine if 1/kBT¼ or 1/kBT were better fits to determine conduction

mechanism. The coefficient of determination was used to establish which fit was more

accurate.

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Figures 14 and 15 give the Log(ρ) vs. 1/kBT or 1/kBT1/4 for pre- and post-annealed samples of brookite, rutile, and anatase.

Because the resistivity behavior depended on the temperature, I evaluated these

fits for temperature ranges which were high temperatures, mid-high, mid-low, and low

temperatures. I also noted the number of data points in these sets since data with few

points may not be conclusive. An example of this for an amorphous film is given in

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figure 16, and this demonstrates that hopping is a better model.

Figure 16: Log(ρ) vs. 1/kBT1/4 or 1/kBT for an amorphous film in the “mid-low” temperature range of 193 – 273 K. The R2 is higher for the 1/kBT1/4 and there are a satisfactory number of data points (13), so I determined that hopping was a better conduction mechanism in this range.

3.2.2 Resistivity and Activation Energy

Using my resistivity data and the Arrhenius relationship given in equation 2, I

found energies of 14-353 meV. For context, I give the hopping energies which others

have found. Tang et al found energies of 76 or 60 meV for rutile [16], and for hydrogen

reduced TiO2, Ardakani found energies of 8meV-160 meV [17]. In addition, I found a

consistent correlation between increasing resistivity and increasing activation energy,

which is demonstrated in figure 17.

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Figure 17: Log(ρ) vs. hopping energy which shows a general pattern of increasing resistivity for an increasing energy.

3.3 Polymorphs

The relationships between phase or resistivity and activation energy were not especially

clear. Figures 18 and 19 gives graphs demonstrating an increase in resistivity for amorphous and

crystalline films with varying concentrations of rutile, anatase, and brookite.

1.0E-01

1.0E+00

1.0E+01

0 50 100 150 200 250

log(

Res

istiv

ity) (

Ωcm

)

Hopping energy (meV)

25

Figures 18 and 19: The relationship between resistivity and phase in which resistivity increases from left to right, and the concentration of phases are demonstrated with color. Though rutile may tend to have a lower resistivity compared to brookite and anatase, it is not possible to determine this relationship from this data.

Contrary to what was expected, we did not observe that anatase was the most resistive

polymorph, and, in general, the correlation between phase and energy was similarly unclear.

3.4 Mott’s Theory and Density of States

As expected, I found that 1/kBT1/4 (hopping conduction) was a typically a better fit for the

amorphous samples. 1/kBT (ballistic conduction) or 1/kBT1/4 was a better fit for crystalline

samples, but we expect this theory to apply to amorphous films. Since the amorphous films

demonstrated Mott’s theory, I found density of state values for the pre-annealed films. Eleven of

these films had a DoS of about 1017 eV-1cm-3 and one had a value of about 1021 eV-1cm-3.

However, 7 samples had values which were unreasonably large, which I determined by

comparing these samples to copper. Copper is a conductor which should be more conductive

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

3.93E-040.147

0.3157 1.27.91 9.8

1.00E+03

1650

5.10E+04

Phas

e Pe

rcen

tage

sIncreasing Resistivity (Ωcm)

Phase and Resistivity of TiO2"post" samples

brookite rutile anatase

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1.04E-03 47.18 12

17.622.9

27.2 35 56

Phas

e Pe

rcen

tage

s

Increasing Resistivity (Ωcm)

Phase and Resistivity of TiO2 "pre" samples

brookite rutile anatase

26

than titanium dioxide and therefore have more carrier states per energy level. Since copper has a

hopping energy of 7 eV [18], I found a DoS of about 1022 eV-1cm-3. Seven of my samples had a

DoS of 1024 – 1025 eV-1cm-3, which is higher than the DoS of copper. A table of my results is

given in figure 20.

Figure 20: The DoS values for amorphous films. Eleven films demonstrated similar DoS values, but 7 had unreasonably large values.

In addition, this analysis did not show clear trends between the polymorphs of TiO2.

DoS (eV-1cm-3)2 2.0E+175 3.1E+25

11 2.0E+1717 2.4E+2125 1.9E+1730 1.8E+1748 1.2E+1749 1.6E+1750 1.4E+1751 1.0E+1752 1.5E+1753 3.3E+1754 1.5E+1758 1.2E+1759 1.5E+2560 9.6E+2461 5.9E+2462 9.1E+2471 3.4E+2572 6.1E+2474 2.8E+25

27

Chapter 5: Conclusion

This project investigated the temperature dependent resistivity of semiconducting

titanium dioxide thin films, and, specifically, the difference between amorphous and crystalline

films and the difference between the polymorphs of titanium dioxide. To understand the

transport in these films, I examined conduction mechanisms, which could have been ballistic or

hopping.

With variable temperature measurements, I found the resistivity of these films. There

were not clear trends for the phase or crystallinity, so I used several analyses to better understand

the data. Using the Arrhenius model with resistivity values, I found activation energies of 14-353

meV. To determine if these films exhibited ballistic or hopping conduction, I compared the fits

of the behavior given by the Arrhenius model and the behavior from Mott’s theory. The

resistivity behavior depended on temperature, so I investigated different temperature regimes for

these fits. My results showed that amorphous films generally exhibited hopping conduction and

that crystalline films demonstrated ballistic or hopping conduction. Because the amorphous films

showed hopping conduction, I could use Mott’s theory to find the density of states. A typical

value was about 1017 eV-1cm-3, but many values were unreasonable. In addition, I found that

when resistivity increased, the energy barrier increased and vice versa. However, trends for the

polymorphs were not especially clear.

To further this project, additional pure phase films should be measured. I measured

mostly mixed phase films that may have grain boundaries which complexifies the electrical

transport. I was also unable to determine carrier concentration for these films, which might

provide further insight. Also, several of the films were photoactive, and it would be interesting to

28

explore the electrical properties and conduction mechanisms of these films. These investigations

would be valuable since titanium dioxide is widely used in technology including in solar cells,

gas sensors, and in self-cleaning surfaces, and its polymorph brookite has not been studied as

extensively as its other polymorphs.

29

References

[1] Yunxiao, B., and W. Xiaochang. “Features and Application of Titanium Dioxide Thin Films

in Water Treatment.” Procedia Engineering, 2011, doi:10.1016/j.proeng.2011.11.2714.

[2] Li, Z., S. Cong, and Y. Xu. “Brookite vs Anatase TiO2 in the Photocatalytic Activity for

Organic Degradation in Water.” ACS Catalysis, 2014.

[3] Mohallem, N., M. Viana, M. de Jesus, G. Gomes, L. Lima, and E. Alves. “Pure and

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