variable temperature transport measurements and conduction
TRANSCRIPT
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.
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