CHARACTERIZATION OF POLY(3-HEXYLTHIOPHENE) BASED SCHOTTKY DIODES

by

ALEXANDROS IOANNIS DIMOPOULOS

B.Eng., University of Victoria, 2005

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF APPLIED SCIENCE

in

THE FACULTY OF GRADUATE STUDIES

(Electrical and Computer Engineering)

THE UNIVERSITY OF BRITISH COLUMBIA

(Vancouver)

April 2012

© Alexandros Ioannis Dimopoulos, 2012

ii

Abstract This thesis describes the fabrication and electrical characterization of Schottky

diodes based on the polymer semiconductor poly(3-hexylthiophene). Printed electronics

may not be able to benefit from high vacuum processing, either for economic or

technical reasons. The aim was to observe the effects on performance when Schottky

diodes were built at atmospheric pressure. 200 nm thick films of poly(3-hexylthiophene)

were formed on glass substrates by spinning a 1 wt% polymer solution in chloroform.

Vacuum deposited aluminum and gold where used for the Schottky and ohmic contacts

respectively. Two types of diodes were manufactured. One type (Au bottom) had its

Schottky junction formed by evaporating aluminum onto the polymer under high vacuum.

The other (Al bottom) had its Schottky junction formed by depositing the polymer onto

aluminum at atmospheric pressure. The final yield of usable devices was 35% for Au

bottom and 22% for Al bottom. The hole density and bulk mobility were derived from

both DC and AC measurements. The bulk mobility was found to range from 2×

10!!  cm2V-­‐1s-­‐1 to 6×10!!  cm2V-­‐1s-­‐1. The hole density was determined to be between

5×10!"  cm-­‐3and 3×10!"  cm-­‐3. DC measurements showed that Au bottom devices had a

current rectification ratio of 2×10! at ±2  V, 100 times greater than Al bottom devices.

The space charge limited current (SCLC) had to be considered to successfully model

the DC behaviour. The small signal behaviour was modeled with a 2nd order

series/parallel circuit, which was determined through impedance spectroscopy. Small

signal performance of both device types was predicted to be poor. The corner

frequency was determined to be less than 100 Hz for Al bottom devices, and less than 1

kHz for Au bottom devices. Large signal frequency performance of the diodes was

tested with a half-wave peak rectifier. The maximum operating frequency was

measured to be 40 kHz for Au bottom devices and 10 kHz for Al bottom devices.

iii

Table of Contents

ABSTRACT .......................................................................................................... ii  

TABLE OF CONTENTS ...................................................................................... iii  

LIST OF TABLES ................................................................................................. v  

LIST OF FIGURES .............................................................................................. vi  

LIST OF ABBREVIATIONS ............................................................................... vii  

ACKNOWLEDGEMENTS ................................................................................. viii  

DEDICATION ...................................................................................................... ix  

1   INTRODUCTION ............................................................................................. 1  1.1   THESIS ORGANIZATION .......................................................................................... 2  1.2   CONJUGATED POLYMERS ....................................................................................... 3  1.3   POLYTHIOPHENE .................................................................................................... 5  1.4   THE SCHOTTKY JUNCTION ..................................................................................... 7  1.5   CONCLUSIONS ....................................................................................................... 8  

2   EXPERIMENTAL METHODS ....................................................................... 10  2.1   DESIGN ............................................................................................................... 10  2.2   FABRICATION ....................................................................................................... 12  2.3   MEASUREMENT .................................................................................................... 16  2.4   CONCLUSIONS ..................................................................................................... 17  

3   DC MEASUREMENTS ................................................................................. 18  3.1   MEASUREMENT DESCRIPTION .............................................................................. 18  3.2   MODEL DESCRIPTION ........................................................................................... 19  3.3   MODEL FITTING ................................................................................................... 23  3.4   FIT RESULTS ....................................................................................................... 24  3.5   CONCLUSIONS ..................................................................................................... 29  

4   SMALL SIGNAL AC MEASUREMENTS ..................................................... 30  4.1   DESCRIPTION OF THE C-V TECHNIQUE ................................................................. 30  4.2   GENERAL CONSIDERATIONS OF THE CV TECHNIQUE ............................................. 31  4.3   SPECIFIC CONSIDERATIONS WITH P3HT ............................................................... 32  4.4   MEASUREMENT DESCRIPTION .............................................................................. 33  4.5   DATA PREPROCESSING ........................................................................................ 33  

iv

4.6   DATA PROCESSING .............................................................................................. 34  4.7   FIT RESULTS ....................................................................................................... 37  4.8   CONCLUSIONS ..................................................................................................... 41  

5   PRACTICAL DIODE USES .......................................................................... 42  5.1   PEAK RECTIFIER .................................................................................................. 42  5.2   SMALL SIGNAL USE .............................................................................................. 45  5.3   CONCLUSIONS ..................................................................................................... 46  

6   CONCLUSION .............................................................................................. 47  6.1   GENERAL CONCLUSIONS ...................................................................................... 47  6.2   FUTURE WORK .................................................................................................... 48  

BIBLIOGRAPHY ................................................................................................ 50  

v

List of Tables TABLE 3.1: CURRENT RECTIFICATION RATIO AT ±2 V. FROM DATA. ................................................. 26  TABLE 3.2: DIODE IDEALITY FACTOR (N). FROM FITS. ...................................................................... 26  TABLE 3.3: RSH (ΩCM2). FROM FITS. .............................................................................................. 27  TABLE 3.4: JS (ACM-2). FROM FITS. ................................................................................................ 27  TABLE 3.5: HOLE MOBILITY (CM2V-1S-1). FROM FITS. ....................................................................... 28  TABLE 3.6: HOLE DENSITY (CM-3). INDIRECTLY FROM FITS. ............................................................. 28  TABLE 4.1: HOLE DENSITY FROM AC MEASUREMENTS (CM-3). ........................................................ 40  TABLE 4.2: BUILT IN VOLTAGE FROM AC MEASUREMENTS (V). ....................................................... 40  TABLE 5.1: FORWARD BIAS CUTOFF FREQUENCY (HZ). ................................................................... 45  

vi

List of Figures FIGURE 1.1: THE TWO EQUIVALENT FORMS OF TRANS-POLYACETYLENE. .......................................... 3  FIGURE 1.2: POLYTHIOPHENE. ........................................................................................................ 5  FIGURE 1.3: REGIOREGULAR POLY(3-HEXYLTHIOPHENE). ................................................................ 6  FIGURE 1.4: P3HT STACKING. ........................................................................................................ 6  FIGURE 1.5: THE IDEALIZED SCHOTTKY JUNCTION. .......................................................................... 7  FIGURE 2.1: SAMPLE LAYOUT. VERTICAL DIMENSIONS ARE NOT TO SCALE. ..................................... 11  FIGURE 2.2: METAL LIFT-OFF WITHOUT (LEFT) AND WITH (RIGHT) FIRST UNDERCUTTING THE

PHOTORESIST. ...................................................................................................................... 13  FIGURE 2.3:SAMPLE HOLDER USED TO MAKE ELECTRICAL MEASUREMENTS OUTSIDE OF THE

GLOVEBOX. .......................................................................................................................... 17  FIGURE 3.1: TYPICAL J-V SCANS OF EXAMINED DEVICES. ............................................................... 19  FIGURE 3.2: SCHEMATIC OF THE MODIFIED SHOCKLEY EQUATION. ................................................. 20  FIGURE 3.3: DC MODEL USED. ...................................................................................................... 21  FIGURE 3.4: LOG-LOG J-V PLOT OF AN AL-BOTTOM DIODE (DEVICE B92L1Y) SHOWING DIFFERENT

TRANSPORT REGIMES. THE CURRENT IS OHMIC AT LOW BIASES AND SPACE CHARGE LIMITED AT

HIGH BIASES. ........................................................................................................................ 22  FIGURE 3.5:REPRESENTATIVE FIT RESULTS FOR AU BOTTOM (LEFT COLUMN), AU BOTTOM (F-SERIES)

(CENTER COLUMN), AND AL BOTTOM (RIGHT COLUMN) DEVICES. FIT QUALITIES ARE BEST (TOP

ROW), MEDIAN (MIDDLE ROW), AND WORST (BOTTOM ROW). ................................................... 25  FIGURE 4.1: A SMALL SIGNAL MODEL OF AN ORGANIC SCHOTTKY DIODE. ........................................ 32  FIGURE 4.2: EXAMPLE OF AC PRE-PROCESSING. ........................................................................... 34  FIGURE 4.3: IMPEDANCE SPECTRA OF A P3HT/AL SCHOTTKY DIODE (D93R1Z) BIASED AT 0.6 V

(LEFT) AND -2 V (RIGHT). DATA PRESENTED HAS BEEN PREPROCESSED. ................................. 35  FIGURE 4.4: FIT RESULT FOR DIODE F93R2Y BIASES AT -0.8 V. TOP: OBJECTIVE FUNCTION, BOTTOM:

BODE PLOTS. ........................................................................................................................ 37  FIGURE 4.5: IMPEDANCE FIT RESULTS FOR DIODE F93R2Y. JUNCTION (�) AND BULK (+) VALUES ARE

SHOWN. ................................................................................................................................ 38  FIGURE 4.6: DEPLETION CAPACITANCE FROM THE SUSCEPTANCE FOR DIODE F92R3Y. .................. 39  FIGURE 5.1: THE HALF-WAVE PEAK RECTIFIER. .............................................................................. 42  FIGURE 5.2: FREQUENCY RESPONSE OF RECTIFIER WITH AU BOTTOM (F-SERIES) DEVICES. ............ 43  FIGURE 5.3:FREQUENCY RESPONSE OF RECTIFIER WITH AL BOTTOM DEVICES. ............................... 44  

vii

List of Abbreviations AC Alternating current

DC Direct current

DI Deionized

HMDS Hexamethyldisilazane

HOMO Highest occupied molecular orbital

LUMO Lowest occupied molecular orbital

ME Mobility edge

P3HT Poly(3-hexythiophene)

PTFE polytetrafluoroethylene

RMS Root-mean-square

SCLC Space charge limited current

TFSCLC Trap free space charge limited current

TFT Thin film transistor

viii

Acknowledgements As I sail away, there are a number of people whom I would very much like to

thank for my adventure. My supervisor Dr. John Madden brought me to the strange new

shores of conducting polymers with an enthusiasm that is difficult to match. On many

occasions I felt as if I was following a path carved into an otherwise impenetrable

wilderness by Dr. Arash Takshi. My colleagues and friends in AMPEL 341 kept me

company around the campfire through many dark nights. I also happily acknowledge my

patrons, my family, who funded my expedition with a bottomless reserve of love and

patience, and even a little gold.

ix

Dedication

To adventurers everywhere

1

1 Introduction Inorganic semiconductors are a ubiquitous class of materials. Their widespread

use is primarily due to integrated circuit (IC) technology, which was first conceived in

the late 1950s when Jack Kilby demonstrated that all the elements of an oscillator

circuit could be constructed on a single silicon crystal. Robert Noyce also independently

formulated the concept [1]. Since then, ICs of every increasing complexity have become

ubiquitous. This has been due to the ability to form ever-larger perfect crystals as well

as an exponential decrease in circuit feature size. The result has been a doubling in

circuit density every 18 to 24 months in what is commonly known as Moore’s Law.

As popular as these materials have become, there are some applications for

which they are not ideally suited. High performance electronics demands that these

semiconductors be used in crystalline form. This limits their usefulness in flexible

structures. The size of the IC is also limited by the size of the crystal. In applications

where performance is less demanding, the semiconductors can be used in amorphous

or polycrystalline forms. This allows much larger circuits to be built, but the high

temperatures needed to process them still generally exclude the use of flexible

substrates. Some other drawbacks of silicon devices is that the bandgap is not

controllable, a fact which presents difficulties for sensors, light emission, and

photovoltaics. Antennas cannot be directly integrated into ICs, they must instead be

externally affixed. This represents a fixed cost in manufacturing which does not scale

with Moore’s law [2].

Various avenues are being examined to extend semiconductors past these

limitations. Some are process based, such as slicing devices from crystalline wafers

and transplanting them onto a flexible substrate [3], or finding ways to lower the

temperature needed to form poly-Si [4]. Others involve using new materials such as

graphene, engineered nanoparticles, or organic semiconductors.

Organic chemistry is a well-established discipline, which can effectively design,

synthesize, and purify new materials. This presents two interesting opportunities. First,

properties such as the bandgap can be tuned. Second, the material can be produced

inexpensively. Organic semiconductors can be divided into two groups: small molecules

2

and conjugated polymers. Many conjugated polymers have the advantage of being

soluble in liquid solvents at room temperature. Thus films of these polymers can be

formed at room temperature, which means that flexible substrates can be used.

Polymer solutions could be used as inks and integrated into industrial printing

processes, allowing arbitrarily large circuits to be produced inexpensively. Printing

would also allow direct integration with elements which cannot be built in the

semiconductor, such as antennas. For all of these interesting reasons, a conjugated

polymer was used in this work. Specifically, the well-known polymer poly(3-

hexylthiophene) was used.

The diode is a basic and versatile electronic device, with applications that include

rectification, demodulation, mixing, and filtering. The vast majority of conjugated

polymers are p-type semiconductors, which means that the Schottky diode is only diode

that can be practically built with them. Though a number of examples of P3HT based

Schottky diodes have been reported [5] [6] [7] [8] [9] [10], they are always formed under

high vacuum. This is a perfectly reasonable approach when exploring material

properties or as device demonstrations. This is however not ideal for considering

practical manufacturing issues since a high vacuum may not be economical or

compatible with processes such as roll-to-roll printing. A better analogue for a device

built using “cheap and dirty” manufacturing would be one formed at atmospheric

conditions. This thesis describes the construction and characterization of two types of

Schottky diodes. The first type had its Schottky junction formed under high vacuum, and

the second had its Schottky junction formed at atmospheric pressure.

1.1 Thesis Organization The rest of this introductory chapter presents an overview of background

information on conjugated polymers in general, poly(3-hexylthiphene) in particular, and

Schottky junction theory. The rest of this thesis is divided into four chapters. Chapter 2

covers the design and fabrication of the Schottky diodes as well as experimental

methods. Chapter 3 discusses the DC measurements, modeling, and characterization.

Chapter 4 does the same, but for small signal AC measurements. Chapter 5 briefly

3

considers the use diodes in electronic circuits. The final chapter concludes the work and

presents recommendations for future work.

1.2 Conjugated Polymers Polymers are generally thought of as being electrically insulating, and are

commonly used in this regard. For a solid to be electronically conductive, its electrons

need to be delocalized. This is not the case for many organic molecules since their

electrons are highly localized in σ orbitals [11]. A polymer that has alternating single and

double bonds along its backbone is known as a conjugated polymer. The double bonds

are due to π orbitals, which are delocalized.

Polyacetylene is a good illustrative example. It was also the first polymer to be

observed with a high conductivity, a discovery that lead to a Nobel Prize in Chemistry

[12]. The trans form of this polymer has two energetically equivalent forms, which are

shown in Figure 1.1. It is tempting to assign a resonance structure to trans-

polyacetylene and assume that conduction arises from a π orbital perfectly distributed

over the entire molecule, as in benzene. In reality, the resonance form, which would

result in metallic conduction, is unstable and polyacetylene takes a conjugated form.

The double carbon bonds are stronger than the single bonds and are thus shorter. This

causes a periodic distortion in the backbone, known as the Pieirls distortion, which

results in a splitting of the energy band. This mechanism is present in all conjugated

polymers and explains their semiconducting nature [11].

Figure 1.1: The two equivalent forms of trans-polyacetylene.

Conjugated polymers have wide bandgaps, polyacetylene for example has a

bandgap of 1.7 eV [12]. Accordingly, they have low intrinsic conductivities. Analogously

to inorganic semiconductors, they can be doped. The dopant species can either react

with the polymer in the form of a redox reaction, or affect it through electron-electron

repulsion [5]. In terms of energy structure, the result is a localized state in the bandgap.

At high enough doping levels, the bandgap can be filled and the polymer will exhibit

metallic conduction [11]. Molecular oxygen and water are known dopants for many

4

conjugated polymers [5]. This presents a problem since these polymers cannot be used

in an ambient atmosphere without introducing uncontrolled doping.

Thus far, only conduction along a single polymer chain has been considered.

This is a one-dimensional description and is inadequate for a thin film. The carrier

mobility in a thin film depends on the morphology since charges must travel between

polymer chains as well as along them. The π orbitals of adjacent polymer chains can

overlap if the chains are stacked together. This situation, known as π- π stacking,

extends charge delocalization into a second dimension. This can lead to a semi-

crystalline film composed of π- π stacked domains separated by amorphous regions.

While the mobility inside the domains may be large, the overall mobility is limited by

inter-domain transport. The degree of π- π stacking, and thus the mobility, is influenced

by the specifics of the deposition method and the surface energy of the substrate [13].

There is a low degree of π- π stacking in an amorphous film and charges must

hop between polymer chains. There is evidence of correlation between chain length and

hopping rate. A longer chain is more likely to have a region with a lowered barrier

somewhere along its length [5].

Because the charge delocalization is limited, it is not strictly correct to refer to

energy bands, as they may be very narrow or even nonexistent. Instead of a valence

and conduction band, the analogous concepts of highest occupied molecular orbital

(HOMO) and lowest unoccupied molecular orbital (LUMO) are respectively used. The

bandgap is thus the HOMO-LUMO energy difference [5].

Several mechanisms have been proposed to explain transport in conjugated

polymers. For semi-crystalline films, a mobility edge (ME) model has been proposed

and is considered promising [13] [14]. In this model, the ME is a defined energy that

separates mobile states from localized states. The mobile states are considered to form

a band and their density varies slowly at energies close to the ME. The localized states,

which are associated with grain boundaries and disordered regions, extend away from

the ME into the bandgap. Their density changes exponentially with energy [15]. The

regions of localized states are known as the band tails and their widths are a measure

of disorder in the semiconductor [14]. The model assigns a constant mobility to band

states and a mobility of zero to tail states. Transport occurs when charges are thermally

promoted from the tail to the band. Accumulating charge in the semiconductor shifts the

5

Fermi level towards the ME and increases the mobility [15]. This is done in a thin film

transistor (TFT) by charging the gate; the result is the increased field-effect mobility. It

can also be accomplished by doping the polymer [5]. Many conjugated polymers

behave as single carrier materials. This is can be explained as an asymmetry in the

band tails [5]. If for example, the tail extending from the LUMO is wider than the tail

extending from the HOMO, electrons will be more localized and thus less mobile. The

result is an intrinsically p-type material.

1.3 Polythiophene Polythiophene, shown in Figure 1.2, was first prepared in 1981 through electro-

polymerization of thiophene. Like polyacetylene, it is a planar molecule, it is a

semiconductor, and it can be doped.

Figure 1.2: Polythiophene.

Also like polyacetylene, it is unfortunately insoluble. Conjugated polymers can be

made soluble by substituting side groups longer than butyl (4 carbon atoms) [11]. A

well-known example is the polymer used in this work, poly(3-hexylthiophene) (P3HT),

shown in Figure 1.3. It is an intrinsically p-type semiconductor. Field-effect mobilities

above 0.1  cm2V-­‐1s-­‐1have been observed in TFTs [13], though the bulk mobility is

commonly three to five orders of magnitude smaller [7] [16] [17] [8] [9]. P3HT has a

bandgap of 1.7 eV and an electron affinity of 3.15 eV [18].

6

Figure 1.3: Regioregular poly(3-hexylthiophene).

Because the monomers are asymmetric, they can couple in several different

orientations when forming the polymer. One of the couplings is particularly undesirable

because neighbouring side chains interact with each other, causing the backbone to

twist. This disrupts the π orbital and widens the bandgap. A high degree of regular

monomer coupling, known as regioregularity, is thus desirable [11]. Solution deposited

P3HT which is highly regioregular tends to self assemble in edge-on stacks [13], as

shown in Figure 1.4. The mobility is anisotropic since the π- π stacking delocalizes

charges in planes parallel to the substrate, which are separated from each other by the

insulating hexyl groups.

Figure 1.4: P3HT stacking.

7

1.4 The Schottky Junction Depending on their relative Fermi levels, either a Schottky or ohmic junction may

form when a metal and a semiconductor are brought into intimate contact. Charges will

flow between the two until the semiconductor’s Fermi level is brought in line with the

metal’s. The system will be in thermal equilibrium at this point [19].

Figure 1.5 shows the energy diagram of a Schottky junction to an idealized

crystalline p-type semiconductor. There are no traps in the bandgap, nor are there any

interfacial states in this case. The work function of the metal is smaller so holes flow

from the semiconductor to the metal. The migration of holes out of the semiconductor

results in a zone that is depleted of mobile charge known as the depletion region. This

negative space charge causes the bands to bend down. To compensate this negative

space charge, a sheet of positive charge has built up on the metal’s surface. As can be

seen in Figure 1.5, holes passing from the metal to the semiconductor must overcome a

potential barrier:

!! = ! +!!! −Φ! (1.1)

where ! is the semiconductor’s electron affinity, !!is the semiconductor bandgap,

Φ! is the metal’s work function, and q is the electron charge.

Figure 1.5: The idealized Schottky junction.

! !

!"

!#

!$!%

!

!&

!%'(! '

! "

)*)+,-./)/)-&0

1.2(,(./

8

This barrier depends only on material properties and is not affected by an applied

bias. Holes moving in the other direction must overcome the band bending, which at

zero applied bias is characterized by the built-in voltage !!". Since applying an external

bias can both reduce and increase the band bending, the Schottky junction is rectifying

[19].

If instead, the metal’s work function is larger than the semiconductor’s, an ohmic

junction occurs. The semiconductor bands bend up and there is an accumulation of

holes at the junction. No barrier is encountered if a bias is applied so that holes flow

from the semiconductor to the metal. Unlike in the Schottky junction, current is not

impeded when a reverse bias is applied. The accumulated charge acts like an anode

and is able to provide a large number of holes. The current is thus limited by the

semiconductor bulk [20].

The idealized assumptions made when describing the Schottky junction have to

be modified when considering a conjugated polymer. Interface states will be present

unless the semiconductor surface is entirely free of oxides and defect free. These states

reduce the Schottky barrier’s size from the ideal and cause it to become bias-dependent

[20]. In the idealized case, the band edges are sharp and holes come from a shallow

acceptor level. In the polymer, the holes come from localized states in the band tail.

Numerical simulations have shown that a wider tail reduces the built-in voltage [14]. The

charge density in the depletion region is likely to be smaller than the dopant density

since many holes are trapped in the tail [14]. The idealized case assumes that the

space charge density and the dopant density are equal. The overall result is a shorter

depletion width than predicted by the idealized case [14].

1.5 Conclusions Poly(3-hexylthiophene) has a lower mobility than crystalline semiconductors, but

has the advantage of being solution processable at room temperature. It may not be

possible to construct inexpensive printed diodes in a high vacuum. It would therefore be

interesting to see how their performance is affected by building them at ambient

pressures.

9

Schottky diodes are formed by selecting metals and semiconductors with

appropriate differences in their work functions. The ideal Schottky junction theory can

be used to approximately explain the diodes built in this work. However, certain

limitations must be kept in mind. Interface states introduced into the junction by

contaminants cause the Schottky barrier to be bias-dependent. The disordered nature

of P3HT will likely cause the band bending to be overestimated.

The discussion begins with experimental methods. The design and fabrication of

the P3HT Schottky diodes is discussed, as well as measurement issues.

10

2 Experimental Methods This chapter begins by discussing the design of the Schottky diodes. Material

selection is discussed as well as justifications for physical dimensions. Next, fabrication

details are covered, including difficulties encountered. Methods to avoid unintentional

doping of the semiconductor both during manufacturing and testing are also explained.

The test fixture used in measurements is described at the end of this chapter, though

specifics of each measurement are covered in appropriate chapters later in the thesis.

2.1 Design In its most basic configuration, a Schottky diode consists of a semiconductor

sandwiched between two electrodes with differing work functions chosen to form a

Schottky contact on one side, and an Ohmic contact on the other. The semiconductor,

poly(3-hexylthiphene), is a well known soluble conjugated polymer. While the

semiconductor was a solution processed organic material, the contacts were vacuum

deposited metals.

P3HT has a band gap of 1.7 eV and an electron affinity of 3.15 eV [18]. Thus

under idealized conditions, the Schottky contact should have a work function of less

than 4.85 eV, and the Ohmic contact, a work function larger than 4.85 eV. Aluminum

(Al) and gold (Au) with work functions of 4.05 eV and 5.2 eV respectively [6], meet this

criteria. This has in fact been extensively observed [6] [5] [7] [8] [9] [10].

Other metals, such as calcium and magnesium, have smaller work functions than

aluminum. However, these materials are more reactive and hence more difficult to work

with and diffuse more rapidly into the polymer than aluminum [5].

The Schottky diodes were built in a vertical configuration by laying thin films of

the materials one on top of the other. The two types of devices were made by switching

the stack order. Au bottom devices were built in the order of Au/P3HT/Al, and Al bottom

devices in the order of Al/P3HT/Au.

The substrate needed to be smooth and rigid since the P3HT was to be spin-

coated. Si wafers with a SiO2 coating were readily available and have the required

physical properties. However, they have a parasitic capacitance large enough to

prevent proper AC measurements [5]. Glass on the other hand does not have this

problem. The devices were built on 1” square chips made by dicing large format

11

microscope slides measuring 3” by 2”. This chip size was small enough to get multiple

electrode sets from a single glass slide, and large enough to comfortably manipulate in

a glovebox. Each 1” chip was divided into a 3×3 grid using 3 top and 3 perpendicular

bottom electrodes, to form 9 individually addressable diodes, as shown in Figure 2.1. A

chip with a set of diodes will be referred to as a sample.

Figure 2.1: Sample layout. Vertical dimensions are not to scale.

Since the current direction in the P3HT film is normal to the substrate, a thinner

film will reduce the series resistance caused by the semiconductor bulk. However, very

thin films are more susceptible to pinhole defects, which short-circuit a diode. No

special effort was made to minimize the semiconductor film thickness for fear of these

defects. It is difficult to model the film thickness from process parameters. The thickness

was assumed to be in the range of 100 nm to 250 nm based on published examples

that employ the same process parameters [5] [4] [9].

Current through the electrodes is primarily parallel to the substrate, and thus

thicker electrodes reduce the series resistance. A semiconductor film thicker than the

underlying electrode may be problematic. The film could be discontinuous at the

electrode edge, which would cause a short circuit. The electrode thickness was easily

controlled as it was continuously measured during vacuum deposition. The electrode

thickness was set to about 100 nm, which was thinner than the semiconductor. The

12

series resistance contribution from the electrodes should be no more than a few Ohms,

and is thus negligible.

The width of the electrode lines specifies the cross sectional area of the diodes.

A large area increases the device current, making measurements easier. A smaller area

reduces the chance of encountering a pinhole in the P3HT film. Electrical

measurements of diodes of similar construction, and with a cross sectional area of

2×10!!  m! have been reported [5]. This set an effective lower limit on the area of the

diodes since the same test equipment was used in this work. Such an area implies an

electrode width of about 50  µμm, half the width of a human hair. A shadow mask could

not be machined to that size in the available facilities. Features of this size would also

make alignment by eye inside the glovebox difficult. The width of both the top and

bottom electrodes was set at 1 mm.

2.2 Fabrication All bottom electrodes were patterned by photolithography instead of shadow

masking in order to save time through a higher throughput. Photolithography was

performed in the UBC nanofabrication facility which has a general cleanroom

classification of 10 000, except for the lithography room which has a classification of

1000, and this room’s wet-benches which are classified at 100 [21].

As noted above, the substrates were glass microscope slides measuring 2” by 3”

with a thickness of about 1 mm. The substrates were first cleaned in order to ensure

proper adhesion of the photoresist. The cleaning sequence was: a boiling acetone bath,

a boiling isopropyl alcohol bath, a deionized (DI) water rinse, drying with compressed

nitrogen, and a two minute dehydration bake on a hotplate. Once the substrates were

properly dried, they were primed with hexamethyldisilazane (HMDS) by spin coating in

order to improve photoresist adhesion. The positive photoresist S1813 was then applied

by spin coating at 5000 rpm for 50 s. The photomask was printed onto a Mylar sheet

using an ordinary office laser printer with a resolution of 600 dpi. Metallization was done

in a large electron beam evaporator capable of holding half a dozen substrates at a time.

The unwanted portions of the newly deposited metal films were washed away with

acetone, which dissolves the underlying photoresist. Once lift-off was complete, the

13

substrates were diced with a diamond saw and cleaned before being transferred into

the glovebox. Cleaning was done with acetone, isopropyl alcohol, DI water, and finally

an oxygen plasma treatment.

Figure 2.2 depicts how undercutting the photoresist before metallization can

improve lift-off results. Patterned photoresist always has sloping edges. This greatly

increases the chances that metal deposited onto the bare substrate will be connected to

the metal on top of the photoresist. When lift-off is performed, the edges of electrodes

will be shorn off.

Figure 2.2: Metal lift-off without (left) and with (right) first undercutting the photoresist.

This would not noticeably affect the final size of the electrodes due to their very

small aspect ratio. Sharp vertical protrusions do present a problem as they might reach

through the P3HT layer and cause a short circuit. This was the suspected failure

mechanism in early test devices. Undercutting the photoresist creates an overhanging

structure that will cause a break in the subsequently deposited metal film, thus avoiding

sheared edges.

Photoresist undercutting was attempted via two approaches: dipping the

exposed photoresist in toluene [22], and using an optical diffuser during exposure [23].

Neither technique proved effective. Profilometery of several completed electrodes

revealed sheared edge spikes ranging from 50 nm to 200 nm beyond the electrode

surface. The spikes were reduced to a few tens of nanometers after manual polishing of

the electrodes. All samples were polished before use regardless of whether or not

!"#$%##

14

undercutting was performed. Unfortunately, these complications cancelled the expected

time savings.

The resolution and contrast of the photomask were likely too low to define

adequately sharp edges. A mask produced with a better printer may have yielded better

results. There are also bilayer photoresists specifically for lift-off, but these were not

readily available.

The cleaned electrodes were immediately transferred to an argon-filled glovebox

where the remaining manufacturing took place. The glovebox was outfitted with a built

in thermal evaporator, and was also equipped with a hot plate, a spin coater, and an

analytical balance. The argon used had a purity of 99.999%. The system included a

solvent filter as well as a water and oxygen trap. However, neither oxygen nor moisture

sensors were present so some impurities may have been present.

Solution processing of conjugated polymers has long been considered the key to

developing low-cost organic electronics. High-speed printing techniques are of

particular interest, but are difficult to implement and beyond the scope of this work.

Common processing methods used in device research are dip casting and spin

coating.

Dip casting involves dipping a substrate into the polymer solution and then slowly

drawing it out. As the substrate is pulled away from the solution, the solvent on it

evaporates, and a solid film is left behind. The process is capable of forming thin, well

ordered films, but the drawing speed must be very slow. A typical drawing rate is 1

mm/min [24]. Also, enough solution must be prepared so that a sample may be totally

submerged.

In spin coating, a small volume of solution is deposited on a substrate, which is

then spun at high speed to evenly spread the solution. The solvent quickly evaporates,

leaving a solid film behind. The length of time needed depends largely on the

evaporation time of the solvent used. It is much faster than dip coating since the entire

substrate dries at once, typically less than one minute. Since the film dries more quickly

than in dip casting, the polymer chains have less time to orient themselves, resulting is

a less ordered film. This can be somewhat affected by selecting a solvent with a higher

boiling point [25].

15

The P3HT films were deposited by spin coating since a spin coater was available.

It is also a better analogue for high speed manufacturing processes due to the shorter

processing time.

P3HT was obtained from Sigma-Aldrich and used as received. The polymer was

in the form of crystalline granules; it had a number average molecular weight of 64 kDa,

and a regioregularity of over 98.5%. Chloroform was used as the solvent as it is known

to dissolve P3HT well [5] [7] [9]. Concentrations of about 1% by weight yield films of

around 120 nm in thickness [5] [9]. A concentration of 15 mg/mL was used,

corresponding to almost exactly 1% by weight. The solvent and polymer were placed in

a sealed vial and stirred for at least two hours at 40 °C. The solution was then passed

through a 0.45 μm polytetrafluoroethylene (PTFE) syringe filter into a clean receptacle

and immediately used in order to remove any remaining particles. Using a pipette, each

sample was entirely coated with the solution and then spun at 1000 rpm for 40 s. This

process was immediately repeated to form a double-layer P3HT film. Adding this

second layer reduced the number of short-circuited devices from about 50% to 30%.

This second layer likely plugged pinholes in the underlying film. The samples were then

placed on a hotplate set to 120 °C for 10 minutes to drive out any remaining solvent.

The film thickness was later determined by profilometry to be about 230 nm.

The final manufacturing step was to deposit the top electrodes. The samples

were fitted with a shadow mask and placed in the glovebox’s built-in thermal evaporator.

The deposition rate was kept to about 1  Ås-­‐1. It has been suggested that a low

deposition rate may limit metal diffusion into the polymer and thus reduce the

occurrence of short circuits [5]. The electrodes were deposited to a thickness of 100

nm at a pressure of 2×10!!  Torr. One set of samples (the F-series) had their top

electrodes deposited at a pressure of 1.5×10!!  Torr, due to a fault in the evaporator.

The resulting devices still functioned as diodes, but their reduced performance was not

recognized until the data was analyzed.

16

A total of 11 Au bottom, and 12 Al bottom samples, each with 9 devices, were

manufactured. 30% of both Au bottom and 40% of Al bottom devices were short-

circuited. Eliminating devices which had an extremely poor DC reverse characteristic or

which short-circuited during measurement further reduced the yield. The final yield for

Au bottom devices was 35% (35 devices) and 22% (24 devices) for Al bottom devices.

2.3 Measurement Measurement leads were limited to 30 cm by performing electrical

measurements outside of the glove box. A special sample holder was prepared so that

finished samples could be taken out of the glovebox without exposure to oxygen or

water. A small polypropylene box with a gasket was fitted with wires and a set of gold

plated spring clips to hold one sample at a time. The assembly is shown in Figure 2.3.

The sample holder was placed inside of a custom-made grounded aluminum shield box

in order to reduce interference during measurements. Relevant measurement details

are covered in the next chapters. The thicknesses of the P3HT films were measured by

profilometry once electrical measurements were completed.

17

Figure 2.3:Sample holder used to make electrical measurements outside of the glovebox.

2.4 Conclusions P3HT based Schottky diodes were successfully manufactured using two different

sequences. Devices with Au as the bottom layer had a final yield of 35 %. Devices with

Al on the bottom had a yield of 22%. The higher throughput of the lift-off process did not

translate into saved time due to difficulties encountered. Patterning by shadow mask

would also have been effective.

18

3 DC Measurements A current density-voltage (J-V) scan is the most basic way to examine a diode. In

this chapter, a DC model of the P3HT/Al diodes is described and fitted to

measurements. The model parameters reveal information about the quality of the

diodes as well as the bulk hole mobility in the P3HT film. The hole density is also

derived.

3.1 Measurement Description Measurements were made with the Model 6430 source measurement unit (SMU)

from Keithley Instruments Inc. [26]. The I-V scans were performed outside of the

glovebox, as described in chapter 2.

The bias was applied as a linear staircase sweep with a step size of 10 mV.

There was a delay time of 100 ms between the rising edge and the start of a

measurement. Each measurement was averaged over one power line cycle, or 17 ms.

The temperature was not controlled and was assumed to be 296 K. Each device was

measured multiple times over periods of time stretching from several hours to about 10

days.

Typical results are shown in Figure 3.1. The F-series devices are clearly inferior

to the rest of the Au bottom devices. They are included as they were also used for small

signal tests presented in chapter 4.

19

Figure 3.1: Typical J-V scans of examined devices.

3.2 Model Description The current density of a Schottky diode is ideally modeled by the Shockley

equation

! = !! exp!"!"# − 1 = !! exp !" − 1 (3.1)

where ! is the ideality factor and !! is the reverse saturation current density. The

exact expression of !!  depends on the transport mechanism over the barrier, which is

not exactly understood and is beyond the scope of this work. A diffusion mechanism is

expected due to the low mobility of carriers in P3HT, causing !! to depend on both

temperature and bias [5] [27]. As can be seen in Figure 3.1, the forward current of the

measured devices is not purely exponential. The recorded data cannot be modeled by

2 1 0 1 2 3 410 10

10 9

10 8

10 7

10 6

10 5

10 4

10 3

10 2

10 1

Applied bias (V)

Cur

rent

den

sity

(Acm

2 )

Au bottomAu bottom (F series)Al bottom

20

an ideal diode alone, and a more elaborate model is instead needed. Figure 3.2 depicts

the equivalent circuit of the modified Shockley equation, which is commonly used in

photovoltaics. The series resistor !! accounts for the voltage drop across the

semiconductor bulk, and the shunt resistance !!"models the bias dependence of !!.

This model was not used as it has been shown to be inadequate for modeling a polymer

based Schottky diode [28].

Figure 3.2: Schematic of the modified Shockley equation.

The space charge limited current (SCLC) needs to be considered due to P3HT’s

low mobility. This model describes transport in low conductivity materials and is typically

applied to insulators, including depleted semiconductors. A density of injected charge

exceeding the material’s intrinsic carrier density causes the formation of a space charge

region. As a result, the current is no longer ohmic. SCLC becomes dominant in P3HT at

electric fields exceeding 10!  V∙cm-­‐1 [7]. This should occur at an applied bias of about 2

V for the majority of devices examined in this work. This effect can be accounted for by

adding a non-ohmic impedance element in parallel with !!, as depicted in Figure 3.3.

Here, the semiconductor bulk is represented by the parallel combination of the resistor

!! and the SCLC impedance element. The actual junction is modeled with the ideal

diode ! and the resistor !!".

21

Figure 3.3: DC model used.

The applicability of this model to the current work is suggested by its successful

application in similar published work [7]. Examining the I-V data on a log-log plot, as in

Figure 3.4, lends further support. Linear regions in the plot indicate regions where the

current density is a power function of bias, with the exponent equal to the slope of the

line. The unity slope at low biases indicates ohmic conduction. The slope at high biases

is 2, which indicates a trap free space charge limited current (TFSCLC) [16]. This

means that all the traps in the bulk have been filled [16] and that the current density can

be expressed as

! =98 ∙!!!!!! !!! = !!! (3.2)

where ! is the thickness of the semiconductor film, !!!! is the permittivity of the

semiconductor, and ! is the bulk mobility [7]. Given this dependence, the bulk mobility

can be easily extracted from the J-V data, provided that data is recorded up to biases in

the SCLC regime.

22

Figure 3.4: Log-log J-V plot of an Al-bottom diode (device B92L1Y) showing different transport

regimes. The current is ohmic at low biases and space charge limited at high biases.

Three equations govern the DC model. The voltage across the entire device is

given by

!! = !! + !! (3.3)

where !! is the voltage dropped across the semiconductor bulk, and !! is the voltage

across the junction. The current density through the semiconductor bulk is described as

! =!!!!+ !!!! (3.4)

where ! is proportional to the bulk mobility, as described in (3.2). The current density

across the junction is equal to the current density through the bulk and is given by

! =!!!!"

+ !! exp !!! − 1 (3.5)

10 2 10 1 10010 7

10 6

10 5

10 4

10 3

Applied Bias (V)

Cur

rent

Den

sity

(Acm

2 )

dataslope = 1.03slope = 2.16

E field ~ 105 V cm 1

23

where ! includes the ideality factor !, which is a measure of the quality of the rectifying

junction, as described in (3.1). A perfect junction has an ideality of 1; an increase in !

corresponds to a decrease in quality.

3.3 Model Fitting Determining the model parameters is not a straightforward process. They cannot

be directly extracted from measured data since the model depends on the hidden

variables !! and !!. The strategy employed was to iteratively solve the set of equations

(3.3)-(3.5) using the nonlinear least-squares facilities in MATLAB. The algorithm is

outlined here:

1. Solve (3.4) and (3.5) over the forward bias for the parameters. • Assume that !! and !! are correctly known. • Update the parameter values.

2. Solve the system of equations at each bias point for variables !! and !!. • Assume that the parameters are correctly known. • Update the voltage values.

3. Check the parameters for convergence. • Repeat if needed.

Convergence was defined as a relative change of less than 10!!  between

iterations. The maximum number of iterations was set at 100.

There is no guarantee that the solver would converge to the desired solution, or

even to any solution, when starting from an arbitrary initial guess. It is therefore

important to start with an initial guess as close as possible to the final solution. This was

done by dividing the data into three bias ranges and assuming different model elements

dominated in each one. The resistors were assumed to dominate over reverse biases,

the SCLC element at high biases, and the diode and resistors over the intermediate

range. As discussed earlier, the bias at which the SCLC begins to dominate can be

found on a log-log plot.

The SCLC parameter, !, was estimated from a linear fit to the high bias data on

a log-log scale. For the other parameters, a first coarse estimate was refined by least

24

squares fitting. !! was coarsely estimated from the physical dimensions of the P3HT

film and an assumed resistivity of 1.47×10!  Ωcm based on literature values [29].

 !!"was coarsely estimated by performing a linear fit over the reverse bias range and

subtracting the coarse value of !!.The contributions of !! and !!"over the intermediate

bias region were cancelled, and then !! and ! were estimated from a linear fit in a semi-

log scale.

A least squares fit over the intermediate bias range was then performed in order

to refine the initial values of all parameters but !.

Initial estimates of the internal voltages were then found by solving (3.4) and

(3.3) for !! and !! respectively.

3.4 Fit Results Each device had been measured multiple times. The DC model was fitted to

each resulting data set, with varying results. Only the model parameters from the best

fits were considered. This required a “quality of fit” metric

!"# =1!

!! − !!!!

!!

!!!

(3.6)

where !! is the measured current density and !! is the fitted current density. Good

fits will have small QoF values. For each device, only the fit with the best QoF was

retained. Figure 3.5 shows some representative results. Fitting was most successful

with Al bottom devices, least successful for Au bottom devices excluding the F-series,

and F-series fits falling in between. The fitter may have had more difficulty with very low

current data, as was present in most Au bottom devices. A finer tuning of the parameter

bounds imposed on the fitter may correct this. The results presented below are from a

further reduced set of fits. For each device type, only fits with an above median QoF

were retained. The minimum, median, and maximum values listed are from this reduced

set of fits.

25

Figure 3.5:Representative fit results for Au bottom (left column), Au bottom (F-series) (center column), and Al bottom (right column)

devices. Fit qualities are best (top row), median (middle row), and worst (bottom row).

0 1 2 3 410 10

10 1

10 7

10 4

bias (V)

J (A

cm2 )

0 1 2 3 410 8

10 6

10 3

10 1

bias (V)

J (A

cm2 )

0 0.5 1 1.5 210 8

10 6

10 4

10 2

bias (V)

J (A

cm2 )

0 1 2 3 410 10

10 8

10 5

10 3

bias (V)

J (A

cm2 )

0 1 2 3 410 8

10 6

10 3

10 1

bias (V)J

(Acm

2 )0 0.5 1 1.5 2

10 8

10 6

10 4

10 2

bias (V)

J (A

cm2 )

0 1 2 3 4

10 10

10 8

10 6

10 4

bias (V)

J (A

cm2 )

0 1 2 3 410 7

10 5

10 3

10 1

bias (V)

J (A

cm2 )

0 0.5 1 1.5 210 7

10 4

10 2

bias (V)

J (A

cm2 )

QoF = 8.4E 3QoF = 3.0E 2QoF = 1.3E 1

QoF = 3.1E 1

QoF =1.7

QoF = 8.1E 2

QoF = 1.4E 1

QoF = 1.8E 2

QoF = 1.4E 1

26

The first results, presented in Table 3.1, are directly from the data instead

of the fit results. These are the current rectification ratios at ±2 V. At 2 V, the bias

is large enough for the device to be well out of the ohmic region, but the current

should not yet be dominated by the SCLC mechanism. The Au bottom devices,

excluding the F-series, demonstrated a rectification of 1.8×10!, which is in line

with reported values [16] [4]. The Au bottom devices outperformed the Al bottom

devices by two orders of magnitude. Unexpectedly, the F-series Au bottom

devices had the smallest rectification ratio of all.

Device type Min Median Max

Au bottom 3.3×10! 1.8×10! 5.6×10!

Au bottom (F-series) 1.1×10! 2.0×10! 1.8×10!

Al bottom 7.3×10! 2.2×10! 7.5×10! Table 3.1: Current rectification ratio at ±2 V. From data.

The ideality factors of the diodes were extracted from the fits by assuming

a temperature of 296 K (a thermal voltage of 26 mV) and are presented in Table

3.2. The results from the Au bottom devices are comparable to published results

[10] [28] [7] [5]. The Al bottom devices could not be compared to reported

examples since ideality factors for such a device geometry have not previously

been reported.

Device type Min Median Max

Au bottom 1.8 3.4 4.4

Au bottom (F-series) 3.5 9.9 12

Al bottom 3.1 4.4 6.5 Table 3.2: diode ideality factor (n). From fits.

!!" and !! are also directly related to the quality of the junction and are

presented in Table 3.3 and Table 3.4.

27

Device type Min Median Max

Au bottom 5.3×10! 3.7×10! 2.6×10!

Au bottom (F-series) 2.5×10! 3.8×10! 8.2×10!

Al bottom 7.9×10! 1.9×10! 5.5×10! Table 3.3: RSH (Ωcm2). From fits.

Device type Min Median Max

Au bottom 2.1×10!!" 7.9×10!!" 6.1×10!!!

Au bottom (F-series) 7.0×10!! 3.1×10!! 1.3×10!!

Al bottom 6.2×10!! 1.3×10!! 2.5×10!! Table 3.4: Js (Acm-2). From fits.

The model parameters which relate to the junction are generally

consistent with the observed diode rectification. That is, the Au bottom devices,

excluding the F-series, have the superior junctions, and the F-series devices

have the worst junctions. The !!" values are however inconsistent, indicating

that the Al bottom devices have the worst junctions by a factor of two.

Small signal junction resistances derived from AC measurements,

presented in chapter 4 also indicate that the F-series devices have the least ideal

junctions.

It was expected that the Al bottom devices would be the worst performing.

The Al electrodes of these devices were exposed to oxygen before deposition of

the P3HT layer, which undoubtedly led to the formation of an interfacial oxide

layer. In fact, the worst performing devices were the Au bottom F-series devices.

The Schottky junctions of these devices were formed at a higher pressure than

the rest of the Au bottom devices. A higher level of contamination could therefore

be anticipated. The fact that these devices had an even poorer performance than

the Al bottom devices suggests a large amount of contamination, possibly oil

from the molecular diffusion pump.

Results for both hole mobility and hole density fall within the range of

reported values [16] [17] [4] [7] [9]. The mobility depends only on the model

28

parameter !. The hole density cannot be determined from a single model

parameter. It can only be extracted from !! together with the mobility.

Device type Min Median Max

Au bottom 4.4×10!! 2.5×10!! 5.2×10!!

Au bottom (F-series) 1.0×10!! 2.3×10!! 1.0×10!!

Al bottom 8.0×10!! 5.8×10!! 1.2×10!! Table 3.5: Hole mobility (cm2V-1s-1). From fits.

Device type Min Median Max

Au bottom 1.6×10!" 1.3×10!" 9.7×10!"

Au bottom (F-series) 1.8×10!" 1.0×10!" 6.1×10!"

Al bottom 2.9×10!" 8.0×10!" 2.0×10!" Table 3.6: Hole density (cm-3). Indirectly from fits.

Hole mobility values extracted from AC fits in chapter 4 agree with values

presented here and can be considered correct. On the other hand, hole densities

extracted from AC measurements are an order of magnitude larger than those

derived from DC fits. The values presented here should be considered

underestimated. The hole mobility derived from AC measurements depends on

the hole density from those same measurements. If the mobility is correct, then

the hole density should also be correct. This means that the DC fits

overestimated the size of !! by an order of magnitude.

29

3.5 Conclusions J-V scans of the diodes demonstrated that the Au bottom devices outperformed

the Al bottom devices in current rectification by two orders of magnitude. The F-series

Au bottom devices had a much poorer performance than expected. This emphasized

the extreme sensitivity of the Schottky junction to contamination when being formed. A

high quality vacuum is essential for forming a high performance Schottky junction.

A proper DC model of the P3HT/Al Schottky diode must take the space charge

limited current into account. The model used adequately explained the observed

behaviour. Better fits could be achieved by applying a finer control on the algorithms

used. A more sophisticated model, that for example incorporates a field-dependent

mobility, may also yield better fits.

The bulk hole mobility in P3HT was found to be in the range of 2×10!!  cm2V-­‐1s-­‐1

to 6×10!!  cm2V-­‐1s-­‐1. This is in agreement with reported values as well as results from

AC measurements presented in this work.

The hole density in P3HT was found to range from 10!"  cm-­‐3 to 10!"  cm-­‐3. While

this agrees with reported values, it is likely an order of magnitude too small. This may

be due to an overestimation of the bulk resistance.

The hole density and bulk mobility values measured in this chapter were

compared to values extracted from AC measurements. These AC measurements and

results are completely independent of the DC methods described in this chapter, and

are presented next in chapter 4.

30

4 Small Signal AC Measurements In this chapter, small signal measurements are used to determine the carrier

density, and thus the trap density, in the P3HT film. The bulk mobility is also determined

from these measurements. The conventional method for determining a semiconductor’s

carrier profile is not applicable to P3HT and a modified technique is used.

4.1 Description of the C-V Technique The capacitance-voltage (C-V) technique is a well-established method of

determining the carrier profile, which has been used with Schottky diodes, as well as pn

diodes, MOS capacitors, and MOSFETs [30]. The method is based on measuring the

variation of the junction’s depletion capacitance with bias. The differential capacitance

at a given bias is measured by applying a small amplitude AC signal over a DC bias.

The C-V technique is dependent on several assumptions: that the depletion

approximation applies, that the carrier density is invariant over a short segment of the

depletion width, and that the AC signal is small enough for the differential capacitance

to be approximately linear.

As long as these assumptions hold, it has been shown that the differential

capacitance at a given bias ! can be modeled as a parallel plate capacitor

! =!!!!! (4.1)

where ! is the differential capacitance, ! is the cross-sectional area of the device,

! is the relative dielectric constant of P3HT, and ! is the width of the depletion region

when the junction is biased at !  [31]�. This allows a direct measurement of the

depletion depth since the spread of the depletion region in a Schottky junction is limited

on one side by the metal.

It has also been shown that the carrier density at a given ! can be related to the

capacitance

! ! =−2

!"!!!!!!" !

!! (4.2)

31

where ! ! is the carrier density in the semiconductor at a depth of !from the

metallurgical junction, and ! is the elementary charge [30].

In the case of a spatially uniform carrier density, a plot of !!!against ! is linear,

and the depletion width can be described as

! =2!!!!" !!" − ! −

!"! (4.3)

where !!" is the built in potential of the junction (also called the diffusion potential)

[19].

In this case, the capacitance can be related to the bias by

1!! =

2 !!" − ! −!"!

!"!!! (4.4)

[19].

4.2 General Considerations of the CV Technique The spatial resolution of the carrier density extracted by the C-V technique is

characterized by the Debye length

!! =!!!!"!!!(!)

(4.5)

. One of the simplifying assumptions made under the depletion approximation is

a sharp boundary between the depletion and bulk regions of the semiconductor. In

reality, carriers diffuse over a distance characterized by !!. This means that carrier

density variations over distances less than !! are effectively meaningless. The

depletion approximation is satisfied if the step size in a C-V scan is no less than two to

three times !! [30]. The minimum probing depth occurs at zero applied bias. The

maximum depth is limited by the semiconductor’s breakdown electric field strength [30].

The differential capacitance must behave approximately linearly if the parallel

plate capacitor model is to be valid. In order to guarantee that this is the case, the AC

amplitude must be kept small relative to the DC bias [31]. Typical values range from 10

mV to 20 mV [30].

32

4.3 Specific Considerations with P3HT The usual procedure is to apply an AC signal of constant frequency while

sweeping the applied DC bias. The measured capacitance will be almost identical to the

depletion capacitance so long as the leakage current and the series resistance are quite

small. A typical measurement frequency is 1 MHz [30]. The high mobilities in materials

such as crystalline Si and GaAs means that free carriers provided by dopant atoms will

easily respond an excitation at such a frequency.

Using a single probing frequency with the devices in this work is problematic.

Several transport mechanisms have been proposed for polymeric semiconductors [15]

[32] [16]. They have in common a dependence on trap states that have an associated

time constant, which depends on their energetic position. This would imply a frequency

dependent differential capacitance, which has in fact been observed [33] [34]. If a lump

element circuit with frequency-independent components can adequately describe the

AC behaviour, then the C-V technique can still be used to extract the carrier profile.

Such a model exists [33] [34] [35] and is depicted in Figure 4.1

Figure 4.1: A small signal model of an organic Schottky diode.

The model elements correspond to physical features of the diode. !! and !!are

the junction resistance and capacitance, which account for the leakage current and the

depletion capacitance. !! and !!represent transport through the bulk and charge stored

in the bulk. Thus the depletion capacitance can be indirectly acquired by fitting this

model to the impedance spectrum of the diode. By fitting spectra at different biases, the

dependence of the depletion capacitance on DC bias, and consequently the carrier

profile, can be observed. !!should be linearly dependent on the depletion width, or

equivalently, inversely dependent on !!.

Rj

Cj

Rb

Cb

33

4.4 Measurement Description A Solartron 1260A impedance/gain-phase analyzer by Solartron Analytical [36]

was used to measure the impedance spectra. Measurements were carried out with a 10

mV amplitude signal. The frequency was swept from 1 Hz to 100 kHz with 50 steps per

decade. Spectra were measured at DC biases ranging from 2 V to -5 V in 200 mV

increments. Each measurement point was averaged over a period of up to 10 s before

being recorded by the impedance analyzer.

Measurements were completed outside of the glovebox, as described in chapter

2.

4.5 Data Preprocessing The impedance analyzer generated a separate data file for each DC bias setting.

All data pre-processing was done with MATLAB and applied independently to each

recorded spectrum. The parasitic effects of the measurement setup were measured and

subtracted from the data as a first pre-processing step. This had a minimal effect since

the parasitic elements were negligible over the frequency band of interest. Curiously, a

phase discontinuity was observed in all measurements. The discontinuity always

occurred at 66.07 kHz and ranged in size from approximately 1° to 20°, increasing as

the biased moved from away from 0 V. This was assumed to be due to an instrument

fault and was subtracted from the data. The final pre-processing step was to apply

some noise reduction filters. First, a median filter was used to eliminate outlying data

points; next a running average filter was used to smooth the noise. The real and

imaginary parts of the impedance were filtered separately.

34

Figure 4.2: Example of AC pre-processing.

4.6 Data Processing The applicability of the small signal model depicted in Figure 4.1 was confirmed

by examining the measured data. Figure 4.3 shows two representative impedance

spectra for a device biased at 0.6 V (left) and -2 V (right). A first order circuit could

account for the reverse bias response, but a second order circuit is needed to explain

the forward bias response.

Nonliear least-squares curve fitting utilities in the MATLAB Optimization Toolbox

were used to fit the small signal model. This was not entirely straightforward since the

tools only work with real valued functions. To get around this, various real-valued

functions derived from the impedance, such as the magnitude and phase, were fitted.

The best results were found when fitting the sum of the resistance and reactance. To

clarify, the impedance of the small signal model is

100 101 102 103 104 105102

104

106

108

frequency (Hz)

|Z| (

)

100 101 102 103 104 105100

50

0

50

frequency (Hz)

(!)

measuredpreprocessed

measuredpreprocessed

35

! = ! + !" =!!

1+ !"!!!!+

!!1+ !"!!!!

(4.6)

And the chosen objective function was

! = ! + ! (4.7)

Figure 4.3: Impedance spectra of a P3HT/Al Schottky diode (D93R1Z) biased at 0.6 V (left) and -2 V

(right). Data presented has been preprocessed.

Picking a good starting point for fitting routine increases the chances of

convergence on a proper solution. With this in mind, an iterative approach was taken to

selecting the initial guess values of the parameters. The impedance spectra can be

fairly well described by a first order parallel RC circuit. By assuming that the junction

100 105103

104

105

|Z| (

)

f (Hz)100 105

102

104

106

108

f (Hz)

|Z| (

)

100 10560

40

20

0

f (Hz)

(Z) (!)

100 105100

80

60

40

20

0

f (Hz)

(Z) (!)

36

rather than the bulk dominates the diode’s response, the impedance can be roughly

described as

!! =!!

1+ !"!!!! (4.8)

The reactance of equation (4.8) reaches a minimum of −!! 2 at the corner

frequency. This allowed easy extraction of initial guess values for !! and !!.

Obtaining the initial guess values of !! and !!was less obvious. The initial values

of !!were observed to satisfy equation (4.4). This allowed an initial approximation of the

carrier density and the depletion width to be determined. These results along with the

measured P3HT film thickness and a guessed bulk mobility of 10!! cm2V-1s-1 [5] led to

an initial guess of !!. There was unfortunately no clear way of extracting an initial guess

for !! from the impedance data. It was calculated in two steps. First, a rough guess was

calculated by assuming a !!!!corner frequency of 10!Hz, a value determined from data

inspection. Next a refined initial guess was found by a least squares fit to the full small

signal model using the initial guesses of all parameters and leaving only !!free.

Once initial values of the parameters were obtained, a least squares fit was

performed with all parameters left free. It was assumed that the initial guesses were not

too far from the solution point. The fit was repeated 100 times with different initial

conditions in order to increase the chances of finding the global minimum. The initial

point was perturbed by up to 50% and a sliding window was applied to the bounding

region.

37

4.7 Fit Results

Figure 4.4: Fit result for diode F93R2Y biases at -0.8 V. Top: objective function, bottom: Bode

plots.

Figure 4.4 shows a typical fit result. As can be seen, the fit to the chosen

objective function was successful. However, the Bode representation of the data might

bring into question the validity of the model since the fit resembles the response of a

first order circuit. The issue is clarified by examining the fit results of individual spectra

over the entire bias range, as shown in Figure 4.5. !!, !!, and !!exhibit a bias

dependence, whereas !!is scattered and far too large.

100 105102

104

106

108

frequency (Hz)

|Z| (

)

100 105100

80

60

40

20

0

frequency (Hz)

(!)

100 101 102 103 104 1055

0

5

10

15

20x 106

R+X

()

frequency (Hz)

datafit

38

Figure 4.5: Impedance fit results for diode F93R2Y. Junction (�) and bulk (+) values are shown.

The solver failed to converge to a reasonable solution for !!in most data sets;

especially those recorded when a reverse bias was applied. The conclusion drawn is

that !! is too small to affect the impedance over the recorded frequencies. The diode

impedance would have to be measured at frequencies above 100 kHz if !! were to be

properly determined. A lack of information about !! does not affect the characterization

of the diode since !! is required for determining the carrier profile and !!for determining

the mobility.

As can be seen in Figure 4.5, !! decreases with increasing reverse bias. This is

typical of a spatially uniform carrier density, which is also localized in energy. However,

!! starts to increase at biases below -3.4 V. This behaviour was observed in all the

measured devices when bias was lowered to this region. This does not appear to be an

artefact caused by the solver. The capacitance extracted directly from the impedance

spectra by assuming a first order circuit response is a reasonable approximation of !!,

especially in reverse bias. As can be seen in Figure 4.6, the increase in capacitance at -

3.4 V is also seen directly in the data. This is not likely due to the semiconductor being

fully depleted since the capacitance should be constant for biases beyond full depletion.

5 4 3 2 1 0 1 210 11

10 10

10 9

10 8

10 7

bias (V)

Cap

acita

nce

(F)

5 4 3 2 1 0 1 2102

103

104

105

106

107

bias (V)R

esis

tanc

e (

)

39

With amorphous semiconductors, !!! is not necessarily a linear function of reverse bias.

The capacitance may also increase with reverse bias if the density of states varies

rapidly near the mobility edge [20]. It is possible that the increase in capacitance is due

to localized states at the metal interface or inside the semiconductor. These states may

be aligned with the Fermi level when the applied bias is around -3.4 V, thus accounting

for the sudden increase in capacitance. If this interpretation is correct, the capacitance

should once again decrease past a certain reverse bias and continue along the

previous trend. A number of diodes were damaged during DC measurements when

large reverse biases were applied. The reverse bias was limited to -5 V during the AC

measurements for this reason.

Figure 4.6: Depletion capacitance from the susceptance for diode F92R3Y.

Impedance spectra with variations in temperature as well as bias would be

needed to map the energetic structure of the diode [35] [20].

The results in Figure 4.5 are typical and !!!!was observed to be linear with

reverse bias between 0 V and the bias at which !! reached a minimum. Without a better

5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 02

3

4

5

6

7

8x 10 10

bias (V)

B/ (F

)

10 kHz1 kHz100 Hz

40

understanding of the energetic structure, it can be assumed that most transport occurs

near the mobility edge and that the C-V technique yields a reasonable idea of the

carrier density.

Through linear regression and equation (4.4), the hole density and built in

voltage was extracted from !!. Three Al bottom devices from three different samples

were measured. Four F-series Au bottom diodes from two separate samples were also

measured. The results are summarized in Table 4.1 and Table 4.2.

Device Type Min Median Max

Au bottom (F-series) 6×10!" 3×10!" 6×10!"

Al bottom 2×10!" 5×10!" 1×10!" Table 4.1: Hole density from AC measurements (cm-3).

Device Type Min Median Max

Au bottom (F-series) 0.3 0.5 0.7

Al bottom 0.1 0.1 0.6 Table 4.2: Built in voltage from AC measurements (V).

The hole density values are within the range of reported values, though on the

high end [16] [35] [9] [17]. These values are likely overestimated since they depend on

the relative permittivity of P3HT. Many sources use a value of 3 [16] [9], which was also

adopted in this work. However, this value is derived from optical measurements [37]

and it has been shown that the relative permittivity actually increases with decreasing

frequency. The value at 100 kHz is about 4 and increases to 9 at 100 Hz [29]. The

larger hole density in the Au bottom electrode devices may be attributed to variations in

the spin coating process. These devices were all made in a single production run and

the Al bottom devices represent two production runs. The sample size was too small to

understand all variations that might result in manufacturing. A less ordered film with

more traps might lead to a larger hole density measure.

The built in voltage for the Al bottom electrode diodes was found to be smaller

than for the Au bottom electrode diodes. This may be attributed to an increased number

of interface states. For the first group of devices, the Al electrodes were exposed to air

41

before being transferred to the glovebox. For the second group, the Al electrodes were

evaporated onto the P3HT, forming a more intimate contact. The Al in the first group

may have formed a thin oxide layer while exposed to air, which resulted in an increased

number of interface states. The band bending and thus the built in voltage can be

decreased if these states have a net positive charge [20].

The bulk mobility was extracted from the fitted values of !! and the extracted

values for the hole density and built in voltage. Physically, !! is described by

!! =! −!!"#$ (4.9)

where t is the total P3HT thickness. By substituting equation (4.3), !! can be

related to the applied bias

!! =!

!"#$ −2!!!

!!!!!!!! !!" − ! (4.10)

thus making it possible to find the mobility. The extracted bulk mobility values

ranged from 4×10!!  cm2V-­‐1s-­‐1 to 6×10!!  cm2V-­‐1s-­‐1. There was no noticeable difference

between the two types of diodes, except for one of the samples with an Al bottom

electrode, which had a mobility five times larger. These values are within the range of

reported bulk mobility [16] [17] [4] [7].

4.8 Conclusions A small signal model of the Schottky diodes was fitted to impedance

spectroscopy data. Meaningful results for the bulk capacitance were difficult to obtain.

Extending measurements to at least 1 MHz may correct this. The hole density and

mobility in the P3HT films were extracted from the fitted model parameters. The results

agreed with reported values. The carrier profile suggests trap states are uniformly

distributed in space but not energy. Extending measurements to higher reverse biases,

as well as performing measurements at varied temperatures would clarify this.

The discussion is continued in the next chapter, where the results in Chapters 3

and 4 are used to examine the feasibility and challenges associated with practical use

of the P3HT diodes demonstrated in this work.

42

5 Practical Diode Uses The discussion up to this point has mainly been concerned with material

properties rather than engineering applications. This section briefly considers some

practical applications.

5.1 Peak Rectifier One of the envisioned applications of conjugated polymers is in the construction

of passive wireless devices such as RFIDs [2]. These devices have no on-board energy

storage and must scavenge their power from radio waves. The incoming AC power

needs to be rectified for digital components. One of the simplest rectifiers is the half-

wave peak rectifier circuit, depicted in Figure 5.1. The circuit is simply a first order low

pass filter in series with a diode [38]. As long as the filter’s corner frequency is below

the input frequency, the circuit will produce a fairly stable DC voltage. It also has

applications in signal processing as a peak detector, and in particular as an amplitude

demodulator [38].

Figure 5.1: The half-wave peak rectifier.

A rectifier based on the P3HT diodes would need to operate at frequencies

greater than 135 kHz to be used in an RFID [2]. Voltage rectification is a large signal

operation so the AC measurements performed in chapter 4 cannot be applied here.

To measure the frequency performance, the rectifier was built by wiring a

conventional discreet resistor and capacitor to a P3HT diode. A 1  MΩ resistor and a

1  µμF capacitor were used for !! and !!, resulting in a filter corner frequency of 0.16 Hz,

well below the measurement range of 10 Hz to 500 kHz. The 10 Vpp sinusoidal input

was provided by an arbitrary waveform generator (Agilent 33220A) [39]. The output

voltage was measured with an oscilloscope (Tektronix TDS2000C) [40]. The rectifier

43

was kept in the same aluminum shield enclosure used during other measurements in

this work.

Results for four Au bottom devices (F-series) from two different samples are

shown in Figure 5.2. Results for three Al bottom devices from two different samples are

shown in Figure 5.3. The output voltages were normalized to their low frequency values

so that the 3 dB drop could be easily identified.

Figure 5.2: Frequency response of rectifier with Au bottom (F-series) devices.

101 102 103 104 10510

5

0

5

3

Frequency (Hz)

Nor

mal

ized

Out

put V

olta

ge (d

B)

F91 1XF91 1YF93 3YF93 3Z

44

Figure 5.3:Frequency response of rectifier with Al bottom devices.

The sample with the higher performing Al bottom devices (E92) received a heat

treatment prior to this test. It was placed on a hotplate set to 120 °C for ten minutes.

This treatment is reported to improve the mobility of P3HT films [24]. The order of

magnitude difference in performance is encouraging. It indicates that poorly performing

devices built at an ambient pressure can be easily improved. Even so, the Al bottom

devices had corner frequencies about four times lower than the Au bottom devices. The

best Au bottom device had a maximum frequency of 40 kHz, falling well short of passive

RFID requirements.

The output voltage was about half the input voltage amplitude. This is suggestive

of a diode resistance of around 1  MΩ. This requires a P3HT resistivity of around

5×10!  Ωcm, which corresponds to the range of hole density and mobility values

measured in chapters 3 and 4.

Reducing the diode resistance could boost the output voltage and corner

frequency of the rectifier. Most simply, the semiconductor could be made thinner. P3HT

films 20 nm thick can be produced through spin coating [25]. This represents a

reduction of film thickness, and thus resistance, of 90% from those made in this work.

Though, evaporating metal onto such a thin polymer film without significantly damaging

101 102 103 104 10510

5

0

5

3

Frequency (Hz)

Nor

mal

ized

Out

put V

olta

ge (d

B)

E91 3XE92 1XE92 3X

45

it may be difficult. The depletion width would also extend through the entire thickness of

such a thin film. Such a dramatic reduction in film size may not be needed. The corner

frequency of a similar rectifier has been reportedly increased by an order of magnitude

by halving the thickness of the semiconductor [8]. The semiconductor could be made

more crystalline by using a different solvent [25]. This has been reported to boost the

field effect mobility by an order of magnitude [25]. It should also have a positive effect

on the bulk mobility, but it has not been reported. The carrier density could also be

increased by controllably doping the semiconductor [41].

5.2 Small Signal Use The nonlinearity of a diode can also be exploited to build frequency multipliers.

Resistive diode multipliers use forward biased diodes as nonlinear resistors, and

reactive diode multipliers use reverse biased diodes as voltage controlled capacitors

(varactors) [42].

The small signal frequency performance of a Schottky diode can be

characterized by the forward bias cutoff frequency

!!! =1

2!!!!! (5.1)

where !! and !! are the diode’s resistance and capacitance at a bias of 0.1 V to the flat

band condition [19]. The utility of this metric lies in being able to compare devices with

different built in voltages. !!! was computed using the junction resistance and

capacitance, !! and !!, extracted from AC measurements in chapter 4. Results for Au

bottom (F-series) and Al bottom devices are listed in Table 5.1.

Bottom electrode Min Median Max

Al 28 63 120

Au (F-Series) 65 420 2800 Table 5.1: forward bias cutoff frequency (Hz).

The small signal performance of Au bottom (F-series) devices is better than that

of Al bottom devices, but still far too low for practical use. Increasing this performance is

not straight forward, especially for the Al bottom devices, since it would involve

increasing the quality of the Schottky junctions, by ensuring a clean interface.

46

5.3 Conclusions The applicability of P3HT based Schottky diodes to voltage rectification and

frequency mixing was considered in this chapter. Al bottom devices showed

consistently inferior performance. The best performing devices had poor enough

performance to make them impractical for the suggested applications. Heat treatment

appears promising for boosting performance. Better performance may also be achieved

by using thinner and better ordered P3HT layers. Improvements of almost two orders of

magnitude may be possible. A corner frequency of above 1 MHz has been reported for

a similar P3HT/Al diode based rectifier [8].

47

6 Conclusion In this thesis, two types of P3HT/Al Schottky junction diodes were fabricated,

characterized, and compared. Carrier density and mobility were derived from DC as

well as impedance measurements. Comparisons made included Schottky junction

quality, frequency performance in a rectifier, and small signal frequency performance.

6.1 General Conclusions Both varieties of diodes comprised stacks of the same materials: gold, poly(3-

hexylthiophene), and aluminum. Their difference was in the formation of the Schottky

junction. The first type, designated Au bottom, had its Schottky junction formed in a high

vacuum by evaporating aluminum onto a film of P3HT. The second type, designated Al

bottom, had its Schottky junction formed by depositing a film of P3HT onto aluminum at

a standard atmospheric pressure. Though all steps involving P3HT were carried out in

an argon-filled glovebox, the aluminum electrodes used in the Al bottom diodes had

been previously exposed to air. The final yield of usable devices was 35% for Au bottom,

and 22% for Al bottom. Due to an equipment fault, one set of Au bottom devices was

manufactured at an elevated pressure. Difficulties were also encountered during the

manufacturing of the bottom electrodes by lift-off. The cause was likely a

photolithographic mask of inadequate quality.

Current-voltage scans of the diodes showed that Au bottom devices had a

current rectification ratio of 2×10!, 100 times greater than for Al bottom devices. The

DC behaviour was properly explained by a model that took into account the space

charge limited current. Model fitting was done by least-squares and required an iterative

approach. The bulk mobility was extracted from fits and found to range from 2×

10!!  cm2V-­‐1s-­‐1 to 6×10!!  cm2V-­‐1s-­‐1 and is in line with reported values. The hole density

was also calculated from the fit parameters to be between from 10!"  cm-­‐3 and 10!"  cm-­‐3.

These values also agree with reported numbers.

Impedance spectroscopy was used to model the diodes’ small signal behaviour

with a 2nd order series/parallel RC circuit. The presence of a bulk capacitance could be

seen in the recorded spectra, but exact values proved difficult to determine. Fitted

values of the junction capacitance suggest a spatially uniform hole density of between

5×10!"  cm-­‐3and 3×10!"  cm-­‐3. While these values are in line with those reported in

48

literature, they are an order of magnitude larger than those derived from DC

measurements. These density values were used to extract mobility from the fitted bulk

resistance. The range of these mobilities was from 4×10!!  cm2V-­‐1s-­‐1 to

6×10!!  cm2V-­‐1s-­‐1. In this case the agreement between AC and DC derived mobilities

suggests that the values are correct. This implies that the AC hole densities are correct

and DC hole densities are underestimated by an order of magnitude and means that the

series resistance in the DC model was consistently overestimated. Fitted junction

capacitance and resistance values suggest poor small signal performance for both

device types. The maximum frequency is below 100 Hz for Al bottom devices, and an

order of magnitude larger for Au bottom devices.

The frequency performance of a half-wave peak rectifier built using the P3HT

diodes and conventional components was measured. The maximum operating

frequency with Au bottom diodes was 40 kHz, and 10 kHz with Al bottom diodes.

Heating the Al bottom diodes for 10 minutes at 120°C seemed to increase their

maximum frequency from 1 kHz to 10 kHz.

The Au bottom diodes consistently outperformed the Al bottom devices,

demonstrating the large sensitivity of the Schottky junction to contamination. This

suggests that practical diodes based on P3HT must be entirely manufactured in an inert

atmosphere, and that the rectifying junction may need to always be made in a high

vacuum. This is problematic if printing methods are to be employed since vacuum

deposited metals will have to be replaced with solution processable materials.

6.2 Future Work The small signal measurements should be extended in the following ways.

Measurement frequencies should be extended to at least 1 MHz to improve model

fitting. The reverse bias range should be doubled and temperature variation should be

introduced in order to probe the energetic structure of the Schottky junction.

The reverse breakdown voltage should be measured. This should be done after

all other electrical measurements are complete as it may irreversibly affect the diode.

49

Performance gains may be achieved by adjusting the fabrication. Bottom

electrodes should be entirely fabricated inside the glovebox and never exposed to air. A

solvent with a higher boiling point than chloroform should be used. Completed devices

should be heat-treated.

Major changes are needed if flexible and printable Schottky diodes are to be

explored further. First the glass substrate should be substituted with a flexible substrate.

Most significantly, the vacuum deposited metal electrodes need to be replaced with

materials which can be solution processed. Finally, devices should be entirely printed.

50

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