Terahertz Spectroscopy of vanadium dioxide films a-

Terahertz Spectroscopy of vanadium dioxide films grown on a-plane sapphire substrate

by

Tapas Mandal, BSc.

A Thesis

In

Electrical Engineering

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

Master of Science

in

Electrical Engineering

Approved

Dr. Ayrton Bernussi Chair of Committee

Dr. Zhaoyang Fan

Dominick Casadonte Interim Dean of the Graduate School

May, 2013

Copyright 2013, Tapas Mandal

Texas Tech University, Tapas Mandal, May 2013

ii

ACKNOWLEDGMENTS

I would like to thank Dr. Bernussi for his valuable supervision, advice and

guidance in experiments and data analysis for this work. Also I would like to thank Dr.

Zhaoyang Fan for being my committee member and his group for making the sample

and providing help during conductivity measurements using the van der Pauw method

.


iii

TABLE OF CONTENTS

ACKNOWLEDGMENTS ............................................................................ ........ii

ABSTRACT ........................................................................................................ ...v

LIST OF FIGURES................................................................................................vii

I. INTRODUCTION AND BACKGROUND........... ................. .........................1

1.1. Introduction to THz............................................................................................1

1.2.Vanadium dioxide (VO2): an introduction...........................................................2

1.3.THz time domain spectroscopy (TDS) experimental setup.................................5

II. SAMPLE FABRICATION AND THZ TRANSMISSION THROUGH VO2

FILMS GROWN ON a-PLANE SAPPHIRE SUBSTRATES AT DIFFERENT

TEMPERATURES..................................................................................................7

2.1. Sample fabrication and electrical resistivity measurements...............................7

2.2. THz transmission through VO2 films grown on a-plane sapphire substrates.....8

2.3. Determination of THz complex optical conductivity and refractive index........12

2.4. VO2 as anti-reflection coating films at THz frequencies....................................17

IΙΙ. INVESTIGATION OF BIREFRINGENCE EFFECTS IN VO2/a-PLANE

SAPPHIRE SUBSTRATES...................................................................................21

3.1. THz Transmission through VO2/a-plane sapphire for different rotation angles

at low temperatures....................................................................................................22


at temperatures within the phase transition...............................................................24


at temperatures corresponding to the metallic state of the VO2 film.........................25

3.4 Summary of birefringence and amplitude variation using THz transmission

through VO2/a-plane sapphire at different temperatures and at different rotation


iv

angles............................................................................................................................26

IV. CONCLUSION.....................................................................................................28

BIBLIOGRAPHY.......................................................................................................29


v

ABSTRACT

Vanadium dioxide (VO2) has been attracting considerable attention due its

unique reversible phase transformation property which changes from an insulator

(semiconductor) with monoclinic crystal symmetry to a metallic phase with a tetragonal

rutile structure. The phase transition is accompanied by 3-5 orders of magnitude change in

electrical conductivity. The phase transition can be driven by an external perturbation such

as temperature, electric field or laser excitation. The metal-insulator phase transition is of

particular interest to realize reconfigurable optical devices such as switches, filters,

polarizers and spatial light modulators.

High quality VO2 films have been obtained using different substrates and

deposition techniques. Among the various substrates used, sapphire is one of the most

common ones due to important attributes such as crystalline quality, mechanical

stability, and optical transparency in a wide range of frequencies. The substrate

orientation plays a fundamental role on the properties of the VO2 films which include:

transition temperature, resistivity-change during the metal-insulator phase transition,

thermal hysteresis loop width, and crystalline quality. Detailed investigations on the

influence of the substrate type and orientation are critical to obtain high-quality VO2

films for future device applications. VO2 has been recently used for switching and

modulation applications and for realization of reconfigurable metamaterial filters and

polarizers at terahertz (THz) frequencies. In the insulator phase VO2 grown on

sapphire substrate is almost transparent to THz radiation. In contrast, above the phase

transition, VO2 behaves as a metal and therefore is almost opaque to THz radiation.

This makes VO2 an ideal material for applications where high amplitude modulation is

a critical requirement.

In this work we performed detailed investigations on the THz transmission

through VO2 films grown on a-plane sapphire substrates. The temperature-driven

method was used to trigger the phase transition of the VO2 films. Measurements were

carried out at different temperatures using the THz time-domain spectroscopy

technique. Complex refractive index and optical conductivity and birefringence were


vi

determined for the VO2 films at temperatures below, during and above the phase

transition. Our results indicate that VO2 films grown on a-plane sapphire substrates

can be used as an anti-reflecting coating material at THz frequencies.


vii

LIST OF FIGURES 1.1 Chart illustrating different frequency regions.....................................................1

1.2 Crystalline structure of VO2 at two different phases:(a)monoclinic structure (insulator) and (b)tetragonal structure(metallic)..................................2

1.3 Schematic illustration of different sapphire plane orientations...........................3

1.4 (a)Photograph of the THz-TDS setup used in this work and (b) the corresponding schematic illustration of the setup...............................................5

1.5 THz-TDS system response in air: (a) time waveform (b) corresponding frequency spectrum.............................................................................................6

2.1 Temperature dependence of conductivity of a VO2/a-sapphire..........................7

2.2 THz (a) time waveform and (b) corresponding frequency spectra of VO2/a-plane sapphire at T=24 0C and at T=85 0C..............................................8

2.3 THz transmission at different temperatures: (a) time waveform and (b) truncated frequency spectra...............................................................................10

2.4 Normalized THz amplitude transmission (to T=30 0C and at f=1 THz) at different temperatures. Symbols correspond to measurements and straight lines to simulations using equation (2.1) and DC electrical conductivity.........11

2.5 (a) Real (r) and imaginary (i) parts of the optical conductivity and (b)real (n) and imaginary(k) parts of the refractive index of a VO2/a-plane sapphire measured at T=80 0C.The solid lines in (a) corresponds to fittings using the Drude model......................................................................................13

2.6 Real (r) and imaginary (i) parts of the optical conductivity of a VO2/a-plane sapphire sample at (a)T=62 0C, (b)T=64 0C, (c)T=70 0C, and (d)T=80 0C........................................................................................................15

2.7 Temperature dependent refractive index and the extinction coefficient of a VO2/a-plane sapphire sample at (a) f=0.6 THz and (b) f=0.9 THz..................15

2.8 Simulated and measured THz transmittance through VO2/a-sapphire from at (a) f=0.6 THz and (b) f=1.2THz....................................................................17

2.9 THz spectra (non-truncated) of a VO2/a-plane sapphire sample obtained at three different temperatures during (a) heating and (b) cooling process..........19

3.1 Illustration of the experimental setup used to determine the birefringence in VO2/a-plane sapphire substrates ......................................................................21


viii

3.2 THz (a) time waveform and (b) frequency spectra for different rotation angles at T=250C...............................................................................................22

3.3 THz (a) time waveform and (b) frequency spectra for different rotation angles at T=65.5 0C...........................................................................................25

3.4 THz (a) time waveforms and (b) frequency spectra for different rotation angles at T=85.5 0C...........................................................................................26

3.5 Birefringence of VO2/a-plane sapphire sample at different angles for three different temperatures......................................................................................27


1

CHAPTER I

INTRODUCTION AND BACKGROUND

Terahertz (THz) is one of the least explored frequency regions of the

electromagnetic spectrum. This was mainly attributed in the past to the lack of

sources and detectors at THz frequencies. This has changed in the last decade

primarily due to advances in the development of photoconductive antennas for

THz generation. Commercial systems are now available and THz research

experienced an unprecedented growth in recent years.

1.1. Introduction to THz

THz falls in the frequency range between microwave and far infrared.

Figure 1.1:- Chart illustrating different frequency regions[1].

THz spectral region spans from 100 GHz (30 m wavelength) to 10

THz (see Fig. 1.1). In contrast to x-rays, THz radiation is low in energy and

non-ionizing, making it biologically safe. While transparent to clothing, paper,

and plastic, THz is reflected by metals so that it is of interest for imaging


2

concealed weapons without potential risk to the subject. Chemicals have

unique spectroscopic signatures, so that THz may be used for detection and

identification of explosives and other chemicals. Lastly, the attenuation of

THz differs for various organs, making it of interest for early cancer

diagnostic, tissue analysis, and other biomedical applications [2].

Despite compelling applications in areas of security, medicine, imaging,

and more recently, in communications, THz technology is still lagging in

advanced optical components for this frequency range. Advances in this area

require detailed investigations of the properties of new materials. Substrate,

coatings, and materials which optical properties can be modified dynamically

in the infrared or visible range are well-established, but at THz range have not

yet been well developed, and active optical elements remain to be explored [3].

1.2. Vanadium dioxide (VO2): an introduction

A promising material for THz optical device application is vanadium

dioxide (VO2).

Figure 1.2: Crystalline structure of VO2 at two different phases: (a)

monoclinic structure (insulator) and (b) tetragonal structure (metallic) [4].

The properties of VO2 can be controlled and varied from

semiconductor to conductor phase using variable temperature, optical

illumination, or applied electric field. This is an important attribute, since


3

semiconductors are transparent to below band gap light while conductors are

reflective. Therefore, the THz transmission can be dynamically modified from

transparent to reflecting modes by controlling the phase transition of the VO2

film and with large amplitude modulation. This can be further used to realize

switches and spatial light modulators for THz applications.

VO2 experiences a first order reversible phase transition from a room-

temperature insulator with monoclinic crystal symmetry to a metallic phase

with a tetragonal rutile structure at ~67 oC temperature (see Fig. 1.2) [5]. The

detailed origin of the phase transition in VO2 remains unclear. However,

electron Mott-Hubbart transition combined with structural modification and

Peierls-type transition are the most common explanations for the observed

phase transition in VO2 [6].

Figure 1.3: Schematic illustration of different sapphire plane orientations [7].

VO2 films have been grown on different substrates such as sapphire,

silicon, and quartz using different deposition techniques. Sapphire have been

widely used as the substrate for VO2 films and the most common

crystallographic orientation is the c-plane which consists of hexagonal lattice


4

symmetry as illustrated in Fig. 1.3. Other orientations, a-, m- and r- planes (see

Fig. 1.3) have been also used as the substrate for depositing VO2 films [8-12].

The substrate orientation influences fundamental properties of the VO2 films

such as transition temperature, resistivity-change during the metal-insulator

phase transition, thermal hysteresis loop width, and crystalline quality as

characterized by stoichiometry, grain size, density of boundaries, and defects

[3]. Different optical, electrical and structural characterization techniques have

been used to determine the properties of the VO2 deposited on different

substrates [13]. Among those techniques, THz spectroscopy is of particular

importance. As mentioned above, at low temperatures (below the phase

transition temperature) the VO2 /sapphire is in the insulator state and it is

essentially transparent for the THz radiation while at high temperatures (above

the phase transition temperature) the VO2 /sapphire is in the metallic state and

the film considerably reflects the THz radiation. This makes the VO2 an ideal

material for THz amplitude modulation applications. More recently THz

optical transmission through VO2 films grown on c-, m- and r-plane sapphire

oriented substrates have been reported [3]. However, the THz transmission

properties of VO2 films grown on a-plane sapphire substrate remains

considerably less explored.

In this thesis we investigated the optical THz transmission properties of

VO2 films grown on a-plane sapphire substrate at different temperatures and

sample rotation angles. Modulation amplitude, characteristic temperature and

thermal hysteresis loop width were obtained and compared with reported

results on VO2 films grown on sapphire substrates with other crystallographic

orientations. Frequency dependent optical conductivity, refractive index, and

birefringence were determined at temperatures within and above the VO2

phase transition.


5

1.3. THz time domain spectroscopy (TDS) experimental setup

Conventional THz TDS was used to investigate the optical properties

of VO2 films. The THz setup consists of two photoconductive antennas used

for THz generation and detection. A ~70 mW mode-locked femtosecond laser

with center emission at 1560 nm wavelength, 90 fs pulse duration, and 100

MHz repetition rate was split into two equal intensity beams and then focused

into each photoconductive antenna. A photograph and the corresponding

schematic illustration of the setup used in this work are shown in Fig. 1.4. All

THz measurements shown in this work were obtained in the transmission mode

at normal incidence.[14] Time waveforms were obtained by changing the

position of the delay line (translation stage) and measuring the amplitude at the

THz detector antenna using a lock-in amplifier. THz transmission experiments

at different temperatures were realized by placing the VO2 /sapphire on the top

of an electronically controlled thermo-electric heater/cooler with a ~5 mm

circular diameter aperture at the center. The focalized THz beam size on the

surface of the sample was ~5 mm in diameter.

Figure 1.4:- (a) Photograph of the THz-TDS setup used in this work

and (b) the corresponding schematic illustration of the setup [14].

Figure 1.5 shows the system response (in the air without any sample) of

the THz-TDS system used in this work. Time waveforms can be measured


6

over a ~200 ps time delay range. The time waveform corresponding to the

THz pulse is shown in Fig. 1.5(a) and it consists of the typical asymmetric

Gaussian-like derivative pulse with pulse width of ~1 ps. The corresponding

spectrum, which is obtained by performing a Fast Fourier Transform (FFT) of

the time waveform, is shown in Fig. 1.5(b). The practical frequency spectrum

for our setup ranges from 0.1 to ~1.5 THz.

Figure 1.5:- THz-TDS system response in air: (a) time waveform (b)

corresponding frequency spectrum.


7

CHAPTER II

SAMPLE FABRICATION AND THz TRANSMISSION

THROUGH VO2 FILMS GROWN ON a-PLANE SAPPHIRE

SUBSTRATES AT DIFFERENT TEMPERATURES

2.1. Sample fabrication and electrical resistivity measurements

VO2 films investigated in this work consisted of ~150 nm thick layer

deposited over ~460 μm thick a-plane sapphire substrates. The deposition was

carried out at 5750C growth temperature using the reactive sputtering

technique. Details of the deposition conditions can be found in[15].

Figure 2.1 shows measured conductivity of VO2/a-plane sapphire at

different temperatures. This measurement was carried out using the van-der-

Pauw method based on a Hall system. As can be seen in Fig.2.1 when the

temperature is increased from 17 to 100 0C the film conductivity increases by

almost four orders of magnitude, a characteristic of the insulator-to-metal

phase transition of VO2 films. The typical thermal hysteresis loop can be also

observed in Fig. 2.1. We determined characteristic temperatures (TC) during

heating and cooling processes of 68.8 and 64.4 oC, respectively which

corresponds to a thermal hysteresis loop width ΔTC=4.4 0C .

Fig 2.1:-Temperature dependence of conductivity of a VO2/a-plane

sapphire.


8

2.2 THz transmission through VO2 films grown on a-plane

sapphire substrates

We have performed THz transmission measurements through VO2 /a-

plane sapphire in the temperature range 25-95 0C. Figure 2.2 shows examples

of THz transmission measurements at two different temperatures: T=240C and

T=850C. The two temperatures were selected below and above the metal-

insulator phase transition temperature of the VO2 film. Figure 2.2(a) consists of

the main transmitted pulse along with two pulse replicas located at ~9.0 ps and

~17.9 ps from the main pulse, as a result of reflections at VO2-a-sapphire-air

interface. We can observe in Fig. 2.2 that the amplitude signal decreases

significantly when the temperature varies from T=24 0C to T=85 0C. This

results from the characteristic metallic behavior of the VO2 at high

temperatures. Another distinct signature of the metallic state of the VO2 film is

the π-phase shift of the reflected pulse at high temperatures, when compared to

the reflected pulse at temperatures below the onset of the phase transition as

shown in Fig. 2.2(a).

Figure 2.2:-THz (a) time waveform and (b) corresponding frequency

spectra of VO2/a-plane sapphire at T=24 0C and at T=85 0C.


9

The corresponding frequency spectra of the waveforms shown in Fig.

2.2(a) are depicted in Fig. 2.2(b). The spectra exhibited periodic fringes

associated with Fabry Perot resonances arising from multiple reflections at the

VO2-a-sapphire-air interface. We can also observe from Fig. 2.2(b) a π-phase

shift between maxima (or minima) at high and low temperatures in the

frequency spectra. The frequency separation between consecutive fringes is

related to the thickness of the substrate and not to the VO2 film and this was

observed for all temperatures, except to that one corresponding to the anti-

reflection condition which will be discussed later. The amplitude ratio between

the two spectra remains essentially constant in the frequency range 0.1-1.5

THz.

An important parameter which qualifies VO2 films for THz switching

and spatial light modulation applications is the amplitude modulation depth

(Am) which is defined as Am=(Alow-Ahigh)/Alow , where Ahigh and Alow are the

THz field amplitudes above and below the phase transition temperature,

respectively. From Fig. 2.2(a) we determined Am~78.6% for the VO2 film

grown on a-plane sapphire substrate, which is comparable to the amplitude

modulations of ~74%, ~82% and ~84% obtained for VO2 films grown on c-,

m- and r- plane, respectively [3]. This result suggests that VO2 grown on a-

plane sapphire substrate is also an excellent choice to realize THz switches and

modulators.

Fundamental optical parameters such as optical conductivity ()

(complex and imaginary) and refractive index (n) (complex and imaginary) of

VO2 films can be determined using a simplified model which does not include

multiple reflections. This requires elimination of the Fabry-Perot fringes from

the frequency spectra (see Figure 2.2(b)). This can be simply accomplished by

“truncating” the THz waveforms for time delays below the first pulse replica

(t<41 ps).


10

Figure 2.3: THz transmission at different temperatures: (a) time

waveform and (b) truncated frequency spectra.

Figure 2.3 shows time waveforms and the corresponding frequency

spectra obtained using this procedure for a VO2/a-plane sample for selected

temperatures. Similar to the results shown Fig. 2.2, the increase in temperature

reduces the transmitted signal as a result of changes of the VO2 electrical

conductivity from insulator to metallic state. As can be clearly seen in Fig.

2.3(b) the fringes were essentially eliminated from the spectra and, as

expected, the amplitude in the frequency domain systematically decreases as

the temperature is increased. We can also observe from Fig. 2.3(b) that the

decrease in the amplitude with the temperature follows closely the overall

shape of the spectrum at room temperature, or during the insulator state of the

VO2 film. Therefore we did not observe any further significant frequency

dispersion modification during or above the phase transition of the VO2 film in

the measured THz frequency range.

The decrease in the THz field amplitude by the VO2 films with the

temperature is related to changes in the frequency () dependent complex

conductivity ( ( ) ) and the film thickness through the expression[16-20] :


11

0

( ) 1( ) 1 ( ).

sf s

ss f

E n

E n z t

(1.1)

Here, ( )f sE is the complex field amplitude transmitted through the VO2 film

plus the substrate, ( )sE is the complex field amplitude transmitted through

the reference substrate (without the film), zo is the free space impedance

(~376.7), ns is the refractive index of the sapphire substrate (ns~3.0), and tf is

the VO2 film thickness (tf ~150 nm). It is evident from equation 1.1 that the

normalized THz amplitude decreases with the increase in the film conductivity

for a fixed film thickness and substrate refractive index. This is in good

correspondence with the experimental results shown in Figs. 2.2 and 2.3 where

when the conductivity increases (as temperature increases) the THz

transmission amplitude decreases.

Equation 1.1 can be used to determine the characteristic temperature TC

which specifies the insulator-metal-insulator transition of VO2, provided the

temperature dependence of the conductivity is known. TC is usually determined

from measurements of electrical resistivity (or conductivity) versus

temperature. As shown in Figs. 2.2 and 2.3 the change in the THz amplitude

with the temperature can be also used to determine TC. Figure 2.4 shows

Figure 2.4: Normalized THz amplitude transmission (to T=30 0C and at

f=1 THz) at different temperatures. Symbols correspond to measurements and


12

straight lines to simulations using equation (2.1) and DC electrical

conductivity.

transmitted field amplitude (at f=1.0 THz) at different temperatures normalized

to the field amplitude at T=30 0C. The typical thermal hysteresis loop is also

observed, in agreement with previous reports and with the conductivity

measurements shown in Fig. 2.1.We also show in Fig. 2.1 the simulated

amplitude THz transmission ratio ( ) / ( )f s sE E for the same sample at

different temperatures, also normalized to T=30 oC. In the simulations we have

used the temperature dependent film conductivity obtained from the DC

electrical measurements (see Fig. 2.1). Good agreement between simulation

and experiment is evident from Fig. 2.4. The characteristic temperatures Tc

during heating and cooling temperature processes were determined from the

first derivative of ( ) / ( )f s sE E or using a least square fitting of

( ) / ( )f s sE E with a Boltzmann lineshape as a function of temperature. We

determined TC=65.4 0C and TC=61 0C during the heating and cooling

processes, respectively. This corresponds to a thermal hysteresis loop

temperature ΔTC=4.4 0C which is in good agreement with conductivity

measurements shown in Fig. 2.1 and similar to those reported in [3] where ΔTC

=4.9 0C, 3.8 0C and 3.2 0C were determined for the VO2 films grown on c-,m-

and r- sapphire planes, respectively.

2.3. Determination of THz complex optical conductivity and

refractive index

Equation 1.1 can be used to determine the frequency-dependent

complex conductivity ( ) . In this case both the THz field amplitude and

phase are considered and equation 1.1 was solved for each frequency using a

root finding algorithm with complex arguments. Figure 2.5(a) shows the

calculated frequency dependent real (r) and imaginary (i) parts of the


13

complex optical conductivity for a VO2/a-plane sapphire at T=80 0C. The real

part of the conductivity is essentially constant in the investigated THz

frequency range with average r ~2.3×103

-1cm-1, in good agreement with the

DC electrical conductivity shown in Fig. 2.1 for T=80 0C. The determined r is

similar to that reported for VO2 films grown on c-plane sapphire substrates [3].

The imaginary component i is considerably smaller than r but exhibits a

slight increase with the frequency.

Figure 2.5. (a) Real (r) and imaginary (i) parts of the optical

conductivity and (b) real (n) and imaginary(k) parts of the refractive index of a

VO2/a-plane sapphire measured at T=80 0C.The solid lines in (a) corresponds

to fittings using the Drude model.

Assuming that the complex conductivity of VO2 films in the metallic

state (T>TC) can be described by the Drude model, the complex conductivity is

related to the plasma frequency (p) and the momentum relaxation time ()

through the expression:

2

( )1/

o pi

(2.1)

where o is the vaccum permittivity. In the Drude approximation, the complex

refractive index is related to the conductivity through the expression


14

2 2

0

( )( ) [ ( )] [ ( ) ( )] 1n n i i

(2.2)

where, n(ω) and ( ) are refractive index and the extinction coefficient of the

film, respectively. Figure 2.5(b) shows the refractive index and the extinction

coefficient of VO2/a-plane sapphire at T=80 0C. The high refractive index and

the extinction coefficient (in the range 35-100) values determined for VO2

above the phase transition temperature is a characteristic signature of the

metallic state of the film. Using Eqs. (2.1) and (2.2) to fit the real and

imaginary parts of the conductivity, we can determine the parameters and p

for the VO2/a-plane sapphire in the metallic phase. The solid lines shown in

2.5(a) are the corresponding fits for the conductivity. It is evident from this

figure that the Drude model describes effectively the metallic behavior of the

VO2 films above the transition temperature. We determined from Fig. 2.5(a)

=3.0 fs and p=2864 rad·THz for the VO2/a-plane sapphire at T=80 oC. These

values are comparable to those reported for VO2 films grown on c-,m- and r-

planes [3].

In order to obtain additional information about the optical conductivity

of the VO2/a-plane sapphire sample investigated here, we determined r and i

for temperatures lying within the phase transition. Figure 2.6 shows the optical

conductivity at T=62, 64 and T=70 0C. The optical conductivity at T=80 0C

(see Fig. 2.5(a)) is also shown for comparison purposes. As shown in Fig. 2.6

the real part increases significantly with the temperature while the imaginary

part remains very small, close to zero. We determined from Fig. 2.6

r=~2×102, ~3×102, ~1.3×103 and ~2.3×103 Ω-1cm-1 at T=62, 64, 70 and 80 0C, respectively. These values are in close agreement with those obtained from

the DC conductivity measurements (see Fig. 2.1). Although the VO2/a-plane

sapphire clearly exhibited a metallic behavior at temperatures above the phase

transition, it should be pointed out here that its conductivity is still about an


15

order of magnitude smaller than that of a conductor such as gold (r_Au

~17000 Ω-1cm-1).

Figure 2.6. Real (r) and imaginary (i) parts of the optical

conductivity of a VO2/a-plane sapphire sample at (a) T=62 0C, (b) T=64 0C, (c)

T=70 0C, and (d) T=80 0C.

Figure 2.7 Temperature dependent refractive index and the extinction

coefficient of a VO2/a-plane sapphire sample at (a) f=0.6 THz and (b) f=0.9

THz.


16

As shown in Fig. 2.5 both the refractive index and the extinction

coefficient of a VO2/a-plane sapphire decrease with the frequency in

accordance with equations 2.1 and 2.2. In order to investigate the effect of the

temperature on both parameters we show in Fig. 2.7 the temperature

dependence of n and at two different frequencies: f=0.6 THz and f=0.9 THz.

As the temperature increases both n and increases due to the increase in

conductivity of the VO2 film. In the temperature range 58T90 oC the

refractive index varies from 14 to 75 and from 14 to 59, respectively, at 0.6

and 0.9 THz. A similar trend was observed for the extinction coefficient.

Differences in magnitude of n and for both frequencies are again associated

with the frequency dependence of these parameters as shown in Fig. 2.5.

From the temperature dependence of the refractive index we can

calculate the THz transmittance of the VO2/a-plane sapphire. A well-known

approach to evaluate the transmittance (or reflectance) is the transfer matrix

method which basically involves the solution of Maxwell’s equation for a

multilayer system. Considering the forward (E+) and backward (E-)

components of an incident electric field (E) into the multilayer system, the

amplitudes of the field on the left-side and right-side of an interface (with

index m) can be described by the following expression [21]:

1 1

1 1

1

1

1 m m

m m

i i

m mm

i im mm m

E Ee r e

t r eE Ee

(2.3)

where, δ is the phase shift as the wave traverses through the layer, mr and mt

are the reflection and the transmission Fresnel coefficients, respectively, The

transmittance T can then be obtained as [21]:

1

0

mET

E

(2.4)


17

Figure 2.8. Simulated and measured THz transmittance through VO2/a-

sapphire from at (a) f=0.6 THz and (b) f=1.2 THz

Detailed derivation of the equations used for a three-layer system

comprising an absorbing film over a dielectric substrate, placed in air, can be

found in [21]. The phase shift and the Fresnel coefficients depend on both n

and [21] which in turn vary with the temperature. Figure 2.8 shows simulated

and experimental transmittance of a of a VO2/a-plane sapphire at different

temperatures at frequencies f=0.6 THz and f=1.2 THz. Values of n and were

determined from THz transmission measurements and equations 2.1 and 2.2.

Measured transmittances were determined from the square of the ratio of

amplitudes ( ) / ( )f s sE E . Similar transmittance temperature dependences

were observed for the two frequencies. Although measured THz transmittances

shown in Fig. 2.8 exhibit an overall agreement with simulations the

quantitative agreement were not reproduced. We speculate that the observed

discrepancy is associated with the imprecision in the determination of both n

and .

2.4. VO2 as anti-reflection coating films at THz frequencies

It has been recently demonstrated that VO2 films can be used as thin

anti-reflection coatings at THz frequencies [3]. This can be accomplished by


18

tuning the temperature within the VO2 phase transition. This can be verified in

Fig. 2.3(a) where the pulse associated with the first reflection almost

disappeared at T=64 oC. Figure 2.9 shows THz amplitude field spectra of a

VO2/a-plane sapphire substrate obtained at three different temperatures during

the heating and cooling and cycles. In contrast to the results shown in Fig.

2.3(b) the complete time waveform was used in the Fourier-transform

calculation. For temperatures T<TC (Theating=30.0 0C and Tcooling=30.1 0C) and

for temperatures T>TC (Theating=88.0 0C and Tcooling=90.0 0C) the expected

Fabry-Perot resonances, with maxima and minima interference peaks shifted

by -radians, were observed in the frequency spectra during the heating (Fig.

2.9(a)) and cooling (Fig. 2.9(b)) cycles of the VO2/a-plane sapphire sample.

However, within the phase transition temperature we observed that the VO2

behaves as an anti-reflecting coating (ARC) film and the interference fringes

almost disappeared. The AR temperature condition (TARC) occurred at 66.0 and

60.2 0C during the heating and cooling cycles, respectively. This implies the

existence of film conductivity (ARC) where the reflections are suppressed.

ARC can be estimated using the wave propagation impedance approach. The

frequency dependent amplitude reflection coefficient (r()) is related to the

film conductivity through the expression [22]:

1 ( )

( )1 ( )

s o f

s o f

n z tr

n z t

(2.5)


19

Figure 2.9 THz spectra (non-truncated) of a VO2/a-plane sapphire sample

obtained at three different temperatures during (a) heating and (b) cooling process.

So, by setting ( )r =0 in (2.5) we can determine the ideal ARC

condition. Using ns=3.0 and tf=150 nm we determined the ideal conductivity

condition ARC~353.9 -1cm-1necessary to suppress all reflections in the THz

spectra. Using equation 2.1 and the spectra shown in Figs. 2.9(a) we

determined, at T=66.0 0C (heating cycle), ARC= 460 + i53 -1cm-1 at f=0.3

THz and ARC=497.0+i57 -1cm-1 f=1.2 THz. Similarly, at T=60.2 0C (cooling

cycle) we determined ARC=360.7 + i21.5 -1cm-1 at f=0.3 THz and

ARC=419.8+i66 -1cm-1 at f=1.2 THz. A reasonable agreement between the

ideal ARC and those determined from the THz spectra during the cooling and

heating cycles were obtained. The discrepancies between ideal and measured

ARC are attributed to inaccuracies to achieve the exact temperature

corresponding to the ARC condition which occurs during the phase transition

which temperature width is narrow. We anticipate that performing THz

transmission measurements with smaller temperature steps during the phase

transition will result in better agreement.

Using equation 2.5 and the ARC obtained during heating and cooling

cycles we determined residual amplitude reflections |r|=10.3%~12% (heating

cycle) and |r|=2%~8% (cooling cycle). Although the ideal AR condition was

not achieved for the VO2/a-plane sapphire substrate, it can be used to the


20

decrease significantly the reflections at the substrate/film-air interface and this

can be realized over a broad range of THz frequencies.


21

CHAPTER IΙΙ

INVESTIGATION OF BIREFRINGENCE EFFECTS IN

VO2/a-PLANE SAPPHIRE SUBSTRATES

Among several dielectric properties of materials, birefringence (n),

which refers to differences in refractive index at different wave propagation

directions within the sample, is of particular importance. THz device

performance can be strongly affected by birefringence. For instance, the

amplitude of THz waves transmitted (or reflected) by switches, polarizers,

filters and spatial light modulators can be modified by the presence of

birefringence in films and/or substrates[23].

Sapphire is known to be a birefringent material at THz frequencies. The

crystalline orientation of sapphire determines the magnitude of birefringence.

Due to symmetry considerations no birefringence is expected for c-plane

sapphire substrates (see Fig. 1.3) for THz incident waves parallel to the c-axis

and this was confirmed (not shown here) experimentally. In contrast,

birefringence was previously observed in a-, m- and r-plane oriented sapphire

substrates [24].However, no detailed experiments have been performed thus far

to study birefringence in VO2/ sapphire substrates. In this section we

investigate the effects of birefringence in VO2/a-plane sapphire substrates at

temperatures below, during and above the VO2 phase transition.

Figure 3.1. Illustration of the experimental setup used to determine the

birefringence in VO2/a-plane sapphire substrates.


22

We used the schematic setup shown in Fig. 3.1 to determine the

birefringence in VO2/a-plane sapphire substrate. The VO2/a-plane sample was

placed in a rotation stage (see Fig. 3.1) with a circular aperture at the center.

THz waves were transmitted through the sample at normal incidence. The

sample was rotated by 5o (or 10o) angle steps and the THz transmitted spectra

were obtained for each angle.

3.1. THz Transmission through VO2/a-plane sapphire for

different rotation angles at low temperatures

Figure 3.2 shows THz transmission time waveforms and frequency

spectra for selected rotation angles () at T=25 0C, which is well-below the

onset of the VO2 temperature phase transition (see Figs. 2.1 and 2.4).

Figure 3.2. THz (a) time waveform and (b) frequency spectra for

different rotation angles at T=25 0C

Since the refractive index of the VO2 at low temperatures is very

similar to that of the sapphire substrate and the film thickness (~150 nm) is

very small when compared to the substrate (~460 m), the THz main

transmission pulse delay positions shown in Fig. 3.2(a) are associated with the

sapphire substrate. It is clear from Fig. 3.2(a) that both the time delay peak

position and the amplitude of the main THz transmitted pulse (13.5<t<15.0 ps)

varies with the rotation angle. We determined a maximum time delay shift of


23

the main pulse of ~0.5 ps for 0o 180o. From the time delay shift we can

estimate the birefringence using the expression:

0

s

c tn

t

(3.1)

where, 0c is the speed of light in vacuum, t is the maximum time delay shift of

the main transmission pulse peak position for the different rotation angles, and

st is the thickness of the substrate. Using equation 3.1 we determined n = 0.33

for the VO2/a-plane sapphire sample at T=25 0C. The obtained birefringence is

in good agreement to that reported in [24] for a-plane sapphire substrates.

Another distinct signature of the birefringence in the THz transmission

through the VO2/a-plane sapphire sample is the presence of dual reflected

pulses at the time delay peak positions t=22.6 ps and t=24.2 ps (see Fig.

3.2(a)). The amplitude of these two reflected pulses changes significantly with

the rotation angle. As previously discussed these pulses are related to the first

reflection at the substrate/VO2 film-air interface. The birefringence can be also

determined from the time delay separation between these two replica pulses

and taking into account the multiple passes of the THz beam within the

sample. We determined n = 0.33 for the first reflected pulses which, as

expected, is the same as that one obtained when the main transmitted pulse was

considered.

The presence of birefringence in the VO2/a-plane sapphire sample also

affects the transmission THz frequency spectrum. As shown in Fig. 3.2(b) the

position and the amplitude of the interference fringes change with the rotation

angle. We determined a maximum shift of ~50 GHz between fringes when the

rotation angle was varied from 0o to 180o. Also the frequency dispersion varies

with the rotation angle, as can be clearly observed in Fig. 3.2(b) particularly

for the rotation angles =20o and =120o.


24

As shown in Fig. 3.2 the THz amplitude transmission through the

VO2/a-plane sapphire sample changes with the rotation angle and this may

impact the performance of THz devices based on VO2. In order to quantify the

effect of birefringence on the amplitude of THz transmitted pulses we use an

amplitude variation parameter (ΔAm) which can be defined as:

ΔAm=(Amax

- Amin

)/Amax (3.2)

where, Amax and Amin are, respectively, the maximum and the minimum THz

pulse peak-to-peak amplitude obtained over the measured rotation angle range.

From the THz amplitude transmission through the VO2/a-plane sapphire at

T=25 oC we determined ΔAm ~30.7 %.


different rotation angles at temperatures within the phase

transition

THz transmission measurements at different temperatures and at

different rotation angles were realized by placing the sample on the top of a

thermo-electric heater/cooler and then place the entire set over the rotation

stage, with the same THz input/output pulse configuration as shown in Fig.

3.1.In order to investigate possible effects of the VO2 film on the birefringence,

we performed THz transmission measurements at T=65.5 0C at different

rotation angles. The selected temperature lies within the VO2 phase transition

(see Figs. 2.1 and 2.4) and also corresponds to the anti-reflection temperature

condition (see Fig. 2.9).The obtained THz time waveforms and frequency

spectra for selected rotation angles for T=65.5 0C are shown in Fig. 3.3.

Similar to the results obtained at T=25 0C (Fig. 3.2) the time delay peak

position and the amplitude of the main transmitted pulse varies with the angle.

Also, the main transmitted pulses observed in Fig. 3.3(a) are once again

associated with the sapphire substrate and not to the VO2 film. Since the

temperature used corresponds to the ARC condition, the pulse replicas in the


25

THz time waveforms (Fig. 3.3(a)) and the interference fringes in the frequency

spectra (Fig. 3.3(b)) were not observed. Using equations 3.1 and 3.2 we

determined n =0.31 and ΔAm~33.8% at T=65.5 0C. These results suggest a

negligible influence of the VO2 layer on the birefringence of VO2/a-plane

sapphire sample.

Figure 3.3. THz (a) time waveform and (b) frequency spectra for

different rotation angles at T=65.5 0C.


different rotation angles at temperatures corresponding to

the metallic state of the VO2 film

We performed THz transmission though VO2/a-plane sapphire sample at

different rotation angles at T=85.5 0C. As shown in Figs. 2.1 and 2.4 at this

selected temperature the VO2 film reached the metallic state and the amplitude

of the transmitted pulses are considerably reduced due to the increased

reflectivity of the film (see Figs. 2.2 and 2.3).


26

Figure 3.4. THz (a) time waveforms and (b) frequency spectra

for different rotation angles at T=85.5 0C.

Figure 3.4 shows THz time waveforms and frequency spectra for

selected rotation angles at T=85.5 0C. Similar to the results obtained at T=25 oC (Fig. 3.2) and T=65.5 oC (Fig. 3.3) the time delay peak position and the

amplitude of the main transmitted pulse varies with the angle for T=85.5 0C.

The pulse replicas and the interference fringes are again observed in the THz

time waveforms and frequency spectra, respectively, and they also vary

significantly with the rotation angle. Using equations 3.1 and 3.2 we

determined n =0.32 and ΔAm~28.5 % at T=85.5 0C. These results suggest a

negligible influence of the VO2 layer on the birefringence of VO2/a-plane

sapphire sample. We confirmed the obtained birefringence value using the dual

reflected pulses shown in Fig. 3.4(a). Similar to the results shown in Fig.

3.2(b), the amplitude and position of the interference fringes in the frequency

spectra (Fig. 3.4(b)) at T=85.5 oC also changes with the rotation angle. The

results shown in Fig. 3.4 confirm a negligible influence of the VO2 film on the

birefringence of the VO2/a-plane sapphire sample.

3.4. Summary of birefringence and amplitude variation using

THz transmission through VO2/a-plane sapphire at

different temperatures and at different rotation angles


27

In order to summarize the birefringence results for the VO2/a-plane

sapphire sample, we show in Fig. 3.5 n for different angles at temperatures

T=25.0, 65.5, and 85.5 0C. As previously discussed, n was determined from

the time delay shift positions of the main THz transmitted pulse for different

angles utilizing equation 3.1.

Figure 3.5. Birefringence of VO2/a-plane sapphire sample at different

angles for three different temperatures.

As can be seen from Fig. 3.5 the changes in birefringence with the

rotation angle are very similar for the three investigated temperatures. This

confirms the negligible influence of the VO2 film to the birefringence results,

even when the VO2 is in the metallic state. Also, the dependence of the

birefringence magnitude with the rotation angle was found to be very similar

for the three investigated temperatures.


28

CHAPTER IV

CONCLUSIONS

We performed detailed investigations on the transmission properties of

VO2/ a-plane sapphire substrate at THz frequencies. THz amplitude

modulation depth as large as 78.6% was determined. This is comparable to

previous reported results for VO2 films grown on c-, m- and r-plane sapphire

substrates. Characteristic temperatures TC = 65.4 0C and TC = 61 0C during the

heating and cooling process, respectively, were obtained for the investigated

sample. This corresponds to a thermal hysteresis loop temperature ΔTC = 4.4 0C which is in good agreement with DC electrical conductivity measurements.

Using the Drude model approximation we determined frequency-dependent

complex refractive index to be in the range 40< (n or k) <100 for frequencies

varying from 0.2 to 1.4 THz when the VO2 is in the metallic state. Both n and k

were determined at temperatures from the onset of the phase transition (~58 oC) up to 90 oC (T>>TC) at f=0.6 and f=0.9 THz. A monotonic increase of n

(and k) ranging from ~8 to ~74, was determined when the temperature was

varied from 58 to 90 oC. The optical conductivity was also investigated in the

same temperature range. In the metallic state we determined average

r~2.3×103

-1cm-1, in good agreement with DC electrical conductivity

measurements. The anti-reflecting conditions for the investigated VO2 film

were determined as T=66.0 0C (heating cycle) and T=60.2 0C (cooling cycle).

The corresponding conductivities at these temperatures are in close agreement

with that predicted by the wave impedance theory. Birefringence analysis was

also performed in the VO2/a-sapphire substrate sample at different

temperatures. We determined n~0.32, at temperatures below, during and

above the transition temperature, suggesting negligible influence of the VO2

films on the birefringence. Our results revealed a change in THz amplitude

>28% due to substrate-related birefringence. This can have direct impact on

the performance of optical devices based on VO2/a-sapphire substrates.


29

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