Eindhoven University of Technology

MASTER

Kelvin probe microscopy on organic ferroelectrics and organic transistors

Roelofs, W.S.C.

Award date:2010

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Master thesis

Research group Molecular Materials and Nanosystems

Department of Applied Physics

Eindhoven University of Technology

Kelvin probe microscopy on organic

ferroelectrics and organic transistors

Christian Roelofs

July 2010

Supervisors: Graduation commission:

dr. ir. M. Kemerink dr. ir. M. Kemerink prof. dr. ir. R.A.J. Janssen prof. dr. ir. R.A.J. Janssen dr. ir. C.F.C. Fitié dr. E.P.A.M. Bakkers ir. S.G.M. Mathijssen dr. P.A. Bobbert

prof. dr. R.P. Sijbesma

200nm

3

Preface For my graduation I have worked on two different projects and therefore this report consists of two

parts. In the first part the ferroelectric properties of molecules with a benzene-1,3,5-tricarboxamide

(BTA) core, which form columnar stacks and contain a molecular dipole moment, are studied. In the

second part the temperature dependent charge transport in self-assembled monolayer field-effect

transistors (SAMFETs) is studied.

In both projects Kelvin probe microscopy on organic materials is performed, but apart from this,

these two projects have little in common. However, the two materials can be combined in one

device. Naber et al. have used an organic ferroelectric material as gate dielectric in organic transistors

to create a rewritable, non-volatile memory device: the ferroelectric field-effect transistor FeFET.[1]

The FeFET uses a gate voltage to align the ferroelectric polarization, which induces either more or less

charge carriers in the conduction channel of the FET. By this the transistor can be switched in the on-

and off-state at zero gate bias, as is shown in figure 1, and a memory device is created. The working

mechanism of FETs and ferroelectric polarization switching are extensively desicribed in this report.

Figure 1: Measurement of the current to the drain of a FeFET as function of the applied gate bias. Drain voltage is set at -10V. In this device source, drain and gate electrodes of gold are used, a ferroelectric organic material P(VDF-TrFE) as gate dielectric and the organic material MEH-PPV as semiconductor. At a gate bias of about -40V the ferroelectric is switched which turns the transistor on and a gate bias of +40V to switch the ferroelectric back and turn the transistor off again.

5

Table of Contents

Part 1: Ferroelectric properties of molecules with a BTA-core

Summary ...................................................................................................................................... 7

1.1 Introduction ...................................................................................................................... 9

1.1.1 Ferroelectricity and its applications ...................................................................................... 9

1.1.2 Switching theories ................................................................................................................. 9

1.1.3 The BTA molecule and structure ......................................................................................... 11

1.2 Poling and switching ....................................................................................................... 13

1.2.1 Experimental Setup ............................................................................................................. 13

1.2.2 Alignment of columns ......................................................................................................... 13

1.2.3 Hysteresis of polarization .................................................................................................... 14

1.2.4 Characterization of the switching process .......................................................................... 16

1.2.5 Stability of polarization ....................................................................................................... 20

1.3 AFM imaging ................................................................................................................... 23

1.3.1 The setup ............................................................................................................................. 23

1.3.2 Sample preparation ............................................................................................................. 23

1.3.3 The measured topography .................................................................................................. 24

1.3.4 Surface potential ................................................................................................................. 25

1.3.5 Poling with tip ...................................................................................................................... 27

1.4 Conclusions ..................................................................................................................... 30

1.4.1 Recommendations............................................................................................................... 30

Part 2: The charge transport in SAMFETs

Summary .................................................................................................................................... 33

2.1 Introduction .................................................................................................................... 35

2.1.1 Goal of the project .............................................................................................................. 35

2.2 Theory ............................................................................................................................. 36

2.2.1 FET ....................................................................................................................................... 36

2.2.2 Mobility models ................................................................................................................... 37

2.2.3 Density of States .................................................................................................................. 38

6

2.3 Experimental setup ......................................................................................................... 43

2.3.1 Non-contact AFM ................................................................................................................ 44

2.3.2 Preparation of the SAMFET ................................................................................................. 48

2.4 Results ............................................................................................................................. 50

2.4.1 Measuring the Density of states ......................................................................................... 50

2.4.2 Model fits ............................................................................................................................ 51

2.4.3 Mobility ............................................................................................................................... 53

2.4.4 Potential profiles ................................................................................................................. 54

2.5 Conclusion ....................................................................................................................... 55

2.5.1 Recommendations .............................................................................................................. 55

Bibliography ............................................................................................................................... 57

Appendix A: Simulations of measured DOS ............................................................................... 59

Appendix B: Simulation of ME-model with T0=420K ................................................................. 62

7

1 Part 1:

Ferroelectric properties of molecules with a

BTA-core

Summary

In this part of the report, the ferroelectric properties of an organic material consisting of molecules

with a benzene-1,3,5-tricarboxamide (BTA) core are studied. BTA molecules form columnar stacks by

hydrogen bonds and contain a molecular dipole moment. These dipoles are aligned forming a macro-

dipole and the material is polarized using an electric field. In a ferroelectric this polarization is

remained when the field is removed.

By doing triangular pulse experiments hysteresis in the polarization is shown, indicating that the

material has ferroelectric properties. However, the material is shown to depolarize in time. This

depolarization is temperature activated with an activation energy of ~1 eV and the extrapolated

depolarization time at room temperature is 6-20 hours.

Measurements with a block pulse show that the material switches its polarization direction

extrinsically, which means that domains are nucleated and grow. The switching speed is temperature

activated; it increases exponentially with the reciprocal temperature.

Atomic force microscopy (AFM) shows a alignment of the BTA columns perpendicular to the

electrodes in polarized thin films. Using scanning Kelvin probe microscopy (SKPM) surface potentials

of 10-20V are measured at room temperature, showing that the films are polarized. Measurements

at elevated temperatures show depolarization and that the surface potential may be screened by

charges, which are tentatively associated with impurities.

9

1.1 Introduction

1.1.1 Ferroelectricity and its applications

Ferroelectrics are materials in which a stable, spontaneously generated electric polarization can be

reversed by inverting the external electric field.[2] When the field is higher than the so-called

coercive field EC, the ferroelectric switches its polarization direction. In this way ferroelectrics have a

memory effect because they contain information of the direction of the last applied electric field.

The memory functionality can be used for many applications in electronic devices such as ferroelectric capacitors, field-effect transistors and diodes. Organic nonvolatile memory devices based on ferroelectricity are a promising approach toward the development of a low-cost memory technology.[3-5] The great potential of such materials is demonstrated by recent work of Asadi et al. who showed that

a phase-separated interpenetrating blend of a ferroelectric and semiconducting polymer can be used

to fabricate a non-volatile memory device.[6] Asadi also showed the possibility to tune the on/off

ratio by varying the injection barrier in organic resistive switches. [7]

Another potential application of ferroelectric materials is to enhance the output voltages of photo-

voltaic devices.[8]

Discotic molecules with a benzene 1,3,5-tricarboxamide (BTA) core are studied in this report. These

molecules are attractive components because they are easy to access synthetically and they are

known to form columnar hexagonal liquid crystalline (LC) phases over a wide temperature range

when side chains of sufficient length are attached.[9-10]

Apart from the purely academic interest, columnar LCs with axial polarity have attracted attention

because of their potential application in ultrahigh density memory devices. Ultimately a single

column is used to function as a memory element.[11]

1.1.2 Switching theories

There are two general mechanisms via which the polarization switching process in a ferroelectric can

occur: intrinsic and extrinsic switching. In intrinsic switching it is assumed that all dipoles will switch

direction collectively, whereas in extrinsic switching the dipoles switch in growing domains after a

nucleation step.

Intrinsic switching

In an ideal ferroelectric, the dipoles in the system are perfectly correlated and they switch either

coherently or not at all. This process does not involve a nucleation step and is therefore called

intrinsic switching. The intrinsic switching mechanism is well described by Tan et al. and by Ricinschi

et al. [12-13]. In summary, the switching rate depends on the change of the free energy G that is

gained by changing the polarization P. G is given by the Landau-Devonshire expansion:

2 4 602 3

0 0 0

( )

2 4 6

a T T B CG P P P EP

(1.1)

10 Chapter 1.1: Introduction

where a, B and C are positive constants, T is the temperature, T0 is the super cooling temperature and

E is the external electric field. This function in fact represents the trade-off between gain of energy

between dipoles and the loss in entropy when dipoles align in the same direction. In figure 1.1

instructive graphs of equation (1.1) are shown of the normalized free energy g as function of the

normalized polarization p in four temperature ranges.

Below T0, stable polarized states exist, that are formed spontaneously (figure 1.1a). Above T0, up to

the Curie temperature 20 16 / 3cT T aC B , the polarized states are still stable, but also a metastable

unpolarized state exists, which means that the material does not polarize spontaneously (figure

1.1b). Slightly above TC the polarized states are metastable and the unpolarized state is stable, the

material can be polarized in this case, with a chance to depolarize in time (figure 1.1c). At even higher

temperatures, above the so called super heated temperature Tsh, the polarized states are not stable

at all and the material cannot be polarized (figure 1.1d).

Figure 1.1: Free energy g versus polarization p calculated for various electric fields, lowest field corresponds to the highest curve for p > 0 (lowest curve for p < 0) and the highest field corresponds to the lowest curve for p > 0 (highest for p < 0). The following temperature regimes are shown: a) below super cooled temperature T<T0, there are two stable ferroelectric states, b) between the super cooled and curie temperature T0<T<TC, there is a metastable unpolarized state, c) between the curie temperature and the super heated temperature TC<T<Tsh there are two metastable polarized states and a stable unpolarized state. d) above the super heated temperature T>Tsh, there is no polarized state when no field is applied.[12]

The switching rate is now determined by the slope of G and the viscosity coefficient γ as is given by

the Landau-Khalatnikov equation:

dP G

d P

. (1.2)

This gives rise to two typical features for intrinsic switching: the polarization does not switch at all

below the coercive field and, second, the switching speed increases with decreasing temperature.

The latter is the result of a lower G for the polarized state relative to the unpolarized state for lower

temperatures.

Intrinsic switching is to our knowledge not yet experimentally proven. There are some indications

that this process is seen in thin ferroelectric films where nucleation is suppressed by the film

thickness, but this is still under discussion.[14-17]

a) b) c) d)

1.1.3 The BTA molecule and structure 11

Extrinsic switching

In almost all real ferroelectric materials extrinsic switching (also called nucleated switching) is

observed.[15, 18-20] This process is started by localized nucleation of domains with an opposite

polarity followed by their growth by domain wall motion. This process is more probable than intrinsic

switching because of defects and impurities in the material and electrode interfaces. Relatively little

energy is needed to switch polarization in a small nucleation volume around a defect compared to

the energy needed to switch the material collectively.

Merz et al. investigated and described the switching time ts of extrinsic ferroelectric switching. They

concluded that the switching time dependency on the electric field E can be divided into two regimes.

At low fields nucleation of the domains is slow and this process is the dominant effect that

determines the total switching time, ts is then exponentially dependant on the electric field:

1 expst tE

(1.3)

where α and t1 are constants. At higher fields, nucleation becomes faster and domain growth starts

to become the dominant effect. In this case the switching speed (or reciprocal switching time), is

linearly dependant on the electric field:

1 / st kE (1.4)

with k a constant.

1.1.3 The BTA molecule and structure

The material studied in this chapter consists of discotic molecules with a benzene 1,3,5-

tricarboxamide (BTA) core, see figure 1.2. Three different side groups are used which are named after

their number of carbon atoms. This material is known to form columnar hexagonal liquid crystals

(LCs) [21].

Figure 1.2: The chemical structure of a BTA molecule studied in this chapter, three different side groups are used which are named after their number of carbon atoms. BTA molecules form columns by hydrogen bonding (right) and create a large macrodipole. On the right, a column of BTAs with three methyl substituents is shown in stick rendering. [21]

Columns: Macrodipole

hydrogen-bonded

stacking

Benzene 1,3,5-tricarboxamide

discotics (BTAs)

12 Chapter 1.1: Introduction

The oxygen atom of the amide group is slightly negative charged and the nitrogen atom slightly

positive. The three amide groups in the molecule all point in the same direction which creates a

strong dipole in the molecule. When these molecules form columns all these dipoles point in the

same direction along the column axis to create a macrodipole.

The material was studied with dielectric relaxation spectroscopy (DRS) by Fitié.[21] In DRS the

interaction of electromagnetic waves with matter is probed. In this study a relaxation process is

observed in the high-temperature region (~120-200°C) of the LC-phase. This process is ascribed to a

cooperative 180° switch of the polar amide groups within the columnar structure. This process is a

strong indication that this material could show ferroelectric behavior.

In the next chapter further experiments are done to investigate the ferroelectric properties of the

BTA. In chapter 1.3 the alignment of the BTA is visualized by atomic force microscopy (AFM) and the

polarization by scanning Kelvin probe microscopy (SKPM).

13

1.2 Poling and switching

1.2.1 Experimental Setup

The BTA is placed in a glass cell with transparent Indium tin oxide (ITO) top and bottom electrodes

(electrode area 0.81 cm2, cell spacing 5 m). This allows observing the material optically, while

applying an electric field over the sample. The electrodes are connected using a highly conductive

two-component silver loaded epoxy adhesive (figure 1.3b).

Because the BTA is an insulating dielectric, this cell is considered as a capacitor and is placed in a

circuit as shown in figure 1.3a. The current flowing to the capacitor is determined by measuring the

voltage over a 10 kΩ resistance with a Tektronix TDS5052B digital oscilloscope. The input voltage is

generated by an Agilent 33250A waveform generator and amplified with a Krohn-Hite Corporation

model 7600 wideband amplifier. The cells were clamped in a Linkam THMS 600 heating stage to heat

the samples.

Figure 1.3: a) Scheme of the setup that consists out of a capacitor (the LC cell with the BTA material in it), a resistor, an oscilloscope and a voltage power supply. b) Photo of a LC cell, with one electrode connected.

1.2.2 Alignment of columns

The BTA columns are aligned perpendicular to the electrodes by applying an electric field of 30 V/µm

over the cell at a temperature of 150°C. The alignment of the columns of the BTA is checked using

polarization optical microscopy (POM) with a Jeneval microscope equipped with crossed polarizers.

When the material aligns perpendicular to the elctrode, birefringence disappears and no light comes

through, which is visible in the dark area of figure 1.4.

Both C10 and C18 aligned within 5 minutes at these conditions. The smallest BTA, C6, still shows

some birefringence under these conditions. This BTA aligns totally at higher fields and a higher

temperature (170°C, 35V/µm). Unfortunately, the cells are not stable at these more extreme

conditions and start to show breakdowns which make them unusable.

The aligned state is stable in the absence of an electric field for all three BTAs. The texture of C10

remains virtually black under POM for days indicating that the alignment of the columns is preserved

at room temperature. As is expected based on the differential scanning calorimetric (DSC) results

from Fitié, a birefringent texture is formed for C6 and C18 at lower temperatures as a result of

crystallization.[21] Interestingly, we found that the black texture reappears for C18 when the sample

is heated above the melting point of the crystalline phase without a field across the cell indicating

that the basic columnar structure and its alignment are unaffected by the crystallization process for

this BTA.

a) b)

14 Chapter 1.2: Poling and switching

Figure 1.4: POM-photo of the BTA material in the LC cell, where the columns are aligned under the electrode area, resulting in a black texture. A birefrigent structure is visible away from the electrode area where the columns are not aligned.[21]

1.2.3 Hysteresis of polarization

In a next step the ferroelectric behaviour of the aligned samples is studied by applying a triangular

wave to the cell. The resulting current is shown in figure 1.5a for C10 and figure 1.5c for C18, plotted

together with the applied voltage.

At a certain moment a clear peak in the current is observed due to the switching that disappears

again when the switching is finished. The onset of the peaks clearly occurs after the applied field

passed 0V, consistent with a real ferroelectric. Also some conduction that increases linearly with the

field is visible due to background conduction and dielectric charging. This effect is much stronger for

C10 than for C18.

Another interesting parameter to look at is the polarization P of the material, which is obtained by

integrating the current I,

1

P IdtA

(1.5)

where A is the area of the electrode. The result of this integration is shown in figure 1.5b for C10 and

in figure 1.5d for C18. The charge resulting from background conduction and dielectric charging is not

a result of the flipping of the amide groups. Therefore, this current needs to be subtracted from the

total current, which is indicated with a dotted line in figure 1.5b and d. Both the integration of the

total current and the subtracted current are shown in these figures. A clear hysteresis in the

polarization is visible; the material stays polarized in the same direction, even when no field is applied

and switches direction with an opposite electric field, which is typical for a ferroelectric material. [2]

Out of these experiments the remanent polarization Pr (the polarization at zero field) and the

coercive field Ec (the field where the polarization goes through zero) are determined. These values

are shown in table 1. Some spread is found in the values for Pr which is probably mainly caused by

small air bubbles in the samples which were optically observed.

1.2.3 Hysteresis of polarization 15

Figure 1.5: Results of the ferroelectric switching experiments under a triangular wave input voltage for C10 (top, a & b) and C18 (bottom, c & d) at 100 °C. a, c) The input voltage (grey, right axis) and the current through the resistor (black, left axis) as function of time. Conditions are given on the top right. The baseline used for integration of the current peak is indicated by the dotted lines. b, d) Polarization against field (P-E hysteresis loops) calculated from the data in a) and c) respectively, with equation (1.5). The polarization evaluated based on the total area under measured voltage curves is plotted in dark gray and the polarization based solely on the area of the peak is plotted in black.[21]

Table 1: Results of ferroelectric hysteresis measurements with a triangular wave input. [21]

T, °C Pr, C/cm2 [a]

Ec, V/m [a]

Fmax, Hz [b]

C10 C18 C10 C18 C10 C18

70 NA [c]

1.6 ± 0.2 NA 25.8 ± 0.3 NA 0.1

100 1.8 ± 0.3 1.7 ± 0.1 29.2 ± 1.9 25.2 ± 0.9 0.2 0.5

120 1.5 ± 0.3 1.6 ± 0.1 28.1 ± 1.7 23.1 ± 1.5 0.6 1.0

150 1.6 ± 0.3 1.4 ± 0.1 26.6 ± 2.3 21.0 ± 1.1 3.0 5.0

[a] Values are averaged over at least three measurements from at least two unique cells. The

reported error margin is the standard deviation of the measured values.

[b] Maximum driving frequency that allowed the polarization to saturate at the given

temperature. All measurements were conducted at or slightly below this frequency.

[c] The polarization did not saturate completely at this temperature, even at the lowest

frequency (0.1 Hz).

16 Chapter 1.2: Poling and switching

1.2.4 Characterization of the switching process

In the following experiments a symmetric block signal was applied to the LC-cell as shown in figure

1.6. The ferroelectric is poled for a time tp, then switched with a reversed field for a time ts and the

system is relaxed for a time tr at zero field. These times are varied for the different experiments.

Figure 1.6: Schematic view of the electric field that was applied to the cell. The polarization time tp, switching time ts and relaxation time tr are varied for different experiments.

Direct switch

The switching mechanism of the ferroelectric is investigated by abruptly switching the poled

ferroelectric (tr=0 and tp=ts). A period of tp=1s proved to be enough to switch the ferroelectric totally,

but also periods of 10s are used to measure the behaviour at larger timescales.

A typical switching curve for C18 is shown in figure 1.7 on a log-log scale. In this figure three things

are observed. First, an RC-peak in which we are not interested, because the cell, with a certain

capacitance, is charged over the resistance that gives rise to this peak. Then a peak appears due to

the switching of the amide groups and finally the background conduction is visible.

10-5

10-4

10-3

10-2

10-1

100

10-3

10-2

10-1

100

101

te

Curr

en

t (m

A)

Time (s)

tm

RC-peak

Figure 1.7: Result of a typicall switching curve (in red) for C18 in which three things are observed. First, an RC-peak in which we are not interested. Then a peak appears due to the polarization switching, the polarization charge is indicated with the shaded area. Finally, the background conduction is visible. The time tm at which the maximum switching current is reached is used as a measure for the switching time. The discontinuities in the noise level of the curves are due to combination of several measurements to cover the full time range with sufficient accuracy.

1.2.4 Characterization of the switching process 17

10-2

10-1

100

101

10-3

10-2

The peak due to the polarization switching is typical for an extrinsic switching mechanism [12, 19],

but may also be observed in intrinsic switching. [13] First, domains with opposite polarization are

nucleated and start to grow, which increases the current. This current drops again when the

switching is finished.

In the switching curves of C10 another current peak is showing up, better visible in the inset of figure

1.8b, which was not expected to be observed. Probably, this is due to a charge trapping effect that is

more pronounced for C10 then for C18. The extra current was also found in the hysteresis

measurements, see figure 1.5.

10-5

10-4

10-3

10-2

10-1

100

101

10-3

10-2

10-1

100 40 V/m

34 V/m

28 V/m

22 V/m

16 V/m

Curr

ent

(mA

)

Time (s)

C18, 100OC

10-5

10-4

10-3

10-2

10-1

100

101

10-3

10-2

10-1

100

40 V/m

34 V/m

28 V/m

22 V/m

16 V/m

Cu

rre

nt

(mA

)

Time (s)

C10, 100OC

Figure 1.8: Currents measured after a total switch at 100°C with various fields for a) C18 and b) C10. In the inset of figure b an amplification is drawn, showing an extra peak that is observed for C10, indicated with the arrow. The discontinuities in (the noise level of) the curves are due to combination of several measurements to cover the full time range with sufficient accuracy.

The total polarization

The polarization charge is determined by integrating the switching peak up to the end of the peak te.

First, the RC-peak and the background conduction were subtracted from the signal, because these

currents are not due to the switching of the amide groups. The RC-time that was needed to

reproduce the RC-peak were 5-10 µs.

The value of te is determined by determining the crossing points of drawn straight lines at the right

edge of the peak and over the background conduction, see figure 1.7. This could not be determined

for the C10 BTA because of the second peak appearing here and it is not possible to subtract this

peak from the signal in a well-defined way. Therefore was chosen to determine te at 36 V/µm,

because the second peak is not visible at this field, and this ending time is used in the integration for

all other fields. The results are shown in figure 1.9.

a) b)

18 Chapter 1.2: Poling and switching

15 20 25 30 35 40 45

1.0

1.5

2.0

2.5

3.0

3.5

P (C

/cm

-2)

Electric field (V/m)

80°C EC = 27.2 V/m

100°C EC = 25.0 V/m

120°C EC = 22.7 V/m

Total polarization of C18

2Pr

15 20 25 30 35 40

0

1

2

3

4

5

6

7

Po

lari

za

tio

n P

(C

/cm

2)

Electric field E (V/m)

80°C

100°C

120°C

140°C

Total polarization of C10

Figure 1.9: The change in polarization for a total switch as function of the applied electric field at different temperatures for a) C18 and b) C10. The material gets more polarized when a larger electric field is applied. This value saturates at the coercive field Ec which is estimated and shown in the figure for C18. By determining the polarization for C10, the second peak is included what causes another behavior and a higher polarization. (Lines are guide to the eye)

For C18 the total polarization saturates at the coercive field. This field drops with increasing

temperature. These fields are comparable to the values found in the triangular wave experiments.

Above the coercive field the material should be totally poled. This is also the case for C18 where the

polarization nicely saturates at 2Pr as is expected for a full switch.

The spontaneous polarization for C10 does not seem to saturate at the coercive field. In addition, the

saturation value of the polarization is roughly twice as high as for C18. This is a result of the

integration of the second peak, which cannot be subtracted from the measurements. When

integrating the second current peak separately in the field region where both peaks could be

observed, is found that the charge related with this secondary process is comparable to the charge

related with the polarization effect of the macrodipoles in the BTA, which explains the saturation

value found to be two times too high. In the triangular wave experiments (figure 1.5b) this doubled

value for the polarization is also observed when no background is subtracted.

The time of maximum current

The time tm at which the maximum switching current is reached, is used as a measure for the

switching time. Therefore, the signal was differentiated and the position where dI/dt=0 was

determined. This time is shown in figure 1.10 as function of the applied electric field E and as function

of the temperature T.

The switching time dependency as function of the electric field is well fitted with a exponential

dependence, which is used by Merz to describe extrinsic switching when domain nucleation is the

time limiting step: [20]

1 expmt tE

(1.6)

where α and t1 are constants.

a) b)

1.2.4 Characterization of the switching process 19

C18, 80°C

C18, 100°C

C18, 120°C

C10, 80°C

C10, 100°C

C10, 120°C

0.02 0.03 0.04 0.05 0.06 0.07

10-4

10-3

10-2

t m (

s)

1/E (m/V) 2.4 2.5 2.6 2.7 2.8 2.9

10-4

10-3

C18, 40V/m

C10, 40V/m

C18, 30V/m

C10, 30V/m

C18, 20V/m

C10, 20V/m

t m (

s)

1000/T (1/K) Figure 1.10: a) The time of the largest switching current as function of the reciprocal electric field for C10 and C18 BTAs at three different temperatures. The lines represent a fit to equation(1.6). In the inset the data is shown on a linear scale for the high field range E=40-25 V/µm, where the switching time increases linearly with the reciprocal field, equation (1.4) b) The time of the largest switching current as function of the reciprocal temperature for C10 and C18 BTAs at three different fields. The solid lines are exponential fits through the data points to equation (1.7). The errors are estimated by taking 10% of tm,.

However, the data seems to deviate from the fit in the high electric field range, which may be caused

by domain growth that starts to become the time limiting step. The switching time should then be

linearly dependant with the reciprocal electric field, equation (1.4). [19] Therefore, tm is plotted

linearly in the inset of figure 1.10a for E=40-25 V/µm, which indeed shows a linear dependency.

Merz describes that the maximum switching current Imax follows this same dependence.[22] It seems

that this is also the case in our results.

An interesting check would be to vary E by varying the thickness of the cell. This will then also tell

something about the role of the interaction between the molecules and the electrodes in the

switching process. For very thin cells interaction with the electrodes is expected to become the

dominant effect.[15] If, for example, the domains are nucleated at the electrode, an increase of the

switching speed is expected to be observed for thinner cells, because of a decreasing bulk to

electrode surface ratio.

In extrinsic switching the system has to overcome an activation energy to form a nucleus/domain.

Therefore, the temperature dependence is fitted by an Arrhenius type of function

0 exp Am

B

Et t

k T

(1.7)

with t0 a time constant, EA the activation energy and kB the constant of Boltzmann. The activation

energy that follows out of the fit is shown in table 2 at the end of this chapter. This energy is about

half the value of the corresponding relaxation process of the amide groups described in paragraph

1.1.3, where the process in the bulk of the material is probed with DRS. This lower value can be

explained by inhomogenity of the material. There may be molecules that are less surrounded by

other molecules and therefore need less energy to switch polarization than molecules that are

perfectly surrounded. Nucleation will start at these spots, so a lower activation energy is needed for

the nucleation process. In addition, the activation barrier may be lowered by the externally applied

a) b)

0.03 0.040.0

4.0x10-4

8.0x10-4

t m (

s)

1/E (m/V)

20 Chapter 1.2: Poling and switching

electric field, see also the discussion of intrinsic switching (paragraph 1.1.2). However, there is an

increase of activation energy with increasing field, which is not understood.

Ohmic conduction

In figure 1.8 it is visible that after the switching peak still some current flows through the LC-cell. The

current at 10 s after the voltage pulse is plotted in figure 1.11. The conduction increases linearly with

the electric field indicating that this current is caused by some Ohmic leakage and is not a

contribution to the switching process.

0 5 10 15 20 25 30 35 40 45

0

2

4

6

8

10

12

14

16

18

20

22

24

Cu

rre

nt a

fte

r 1

0s (A

)

Electric field (V/m)

C18

C10

Figure 1.11: The current flowing through the cell after 10 s at 140°C. The straight lines are linear fits to the data points.

1.2.5 Stability of polarization

The depolarization of the material is measured to determine the stability of the polarized state.

Therefore the ferroelectric is uniformly poled for a period of tp=1s with 40V/µm and relaxed with zero

field for a variable period tr. Since the polarization should not be subsequently switched –we want to

see the spontaneous relaxation– the switching time is set to zero, i.e. ts=0s (see figure 1.6 for the

definitions of these times). The polarization that was lost during tr is determined by integrating the

signal that was received after a repolarisation pulse. Integrating was done the same way as before.

Figure 1.12 also shows a result of a comparable experiment, where the material is first switched in

the opposite direction (i.e. ts=1s). This should lead to the same value in the end, if the material totally

depolarizes.

1.2.5 Stability of polarization 21

0 20 40 60 80 1000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Pr C10

P (C

/cm

2)

tr (s)

C10, ts=1s

C10, ts=0s

C18, ts=1s

C18, ts=0s

Pr C18

Figure 1.12: The polarization that was received with a repolarization pulse after the field was taken away for a period of tr for C10 and C18 (140°C). Both the results are shown where the material was first switched in the opposite (ts=1s) and same (ts=0s) direction before the field was taken away. The polarization that is received saturates to the value of the spontaneous polarization, indicating that the polarization is totally lost when waited long enough. The lower value of Pr for C10 with respect to C18 is not observed in all samples. The lines connecting the data points serve to guide the eye.

The results show clearly that the polarization is not stable. The polarization loss increases with

increasing relaxation time and saturates at Pr. This indicates that all of the initial polarization Pr is lost

when the field is removed for long enough times at these temperatures. As expected the same

saturation value is found after first switching the polarization into the other direction and 2Ps is found

for C18 when switched directly.

It is interesting to note that the extra peak, as is observed for C10 in figure 1.8b, is in this experiment

only observed when switching to the opposite direction. This also results in a value larger than 2Ps for

C10 when switched directly. When poled to the same direction or when the system is relaxed long

enough, this peak disappears. A reason for this current could be a release of trapped charges.

Charges that are trapped during poling are released rapidly when the electric field is switched, but

they are not released when repoling in the same direction or when they have already been released

during the relaxation time. The lower value of Pr found for C10 is not observed in all samples.

The depolarization curves did not give a good fit with a single exponential decay. This is probably a

result of a variation in decay times due to inhomogenity of the material. The results, shown in figure

1.13a, were therefore fitted with a stretched exponential

( )

1 expr r

r

P t t

P

(1.8)

where τ is the characteristic depolarization time of the material and β<1 is a constant. β tells

something about the width of the distribution in decay times, the distribution is narrow when the β

values are close to 1. Fits were made with β-values between 0.4 and 0.6.

22 Chapter 1.2: Poling and switching

C10 C18

80°C

100°C

120°C

140°C

0 20 40 60 80 100

0.0

0.2

0.4

0.6

0.8

1.0

P/P

r

tr (s)

2.4 2.5 2.6 2.7 2.8 2.9

1

10

100

De

po

lariza

tio

n t

ime

(

s)

1000/T (1/K)

C18

C10

Figure 1.13: a) Normalized polarization received after a repolarization pulse as a function of the relaxation

time tr. The lines represent stretched exponential fits (equation (1.8)) to the data sets ( = 0.4-0.6). b) The depolarization time τ that followed out of the fits of figure a as function of the reciprocal temperature. The error bars correspond to the standard deviations from the fits in figure a. The solid lines are Arrhenius fits (equation (1.7)) through the data points.

In figure 1.13b the depolarization times (resulting from the fits) are shown as a function of the

reciprocal temperature. As reported earlier for the maximum switching time, also these

depolarization times fit well to an Arrhenius type of function, equation(1.7). The activation energies

are shown in table 2. Despite the limited number of data points available for the depolarization

process and the fit with the stretched exponential, a striking agreement between the activation

energies associated with depolarization and the R-relaxation in the DRS study is found.

The fact that the material depolarizes tells us that the unpolarized state is the stable state, and the

polarized state is may be a metastable, which suggests that the material is in the state of figure 1.1c.

The material is therefore not properly ferroelectric at temperatures above 80°C. By extrapolating the

fits the depolarization time is estimated to be around 6-20h at 25°C. The depolarization for C18 could

be slowed down even more because of a phase transition to a crystalline state around 70°C. This

might lead to a ferroelectric phase at lower temperatures.

Table 2: Activation energies of the flipping of amide groups for different processes. The energies and time constants follow from fits to Arrhenius’ law, equation (1.7). The activation energies found in the DRS study represent an average value of the bulk relaxation process. When the material is forced to switch, first the sites with the lowest energies will switch (nucleation) by which the rest will follow, resulting in a lower activation energy. When the material depolarizes, also the sites with the lowest energies will switch first, what lowers the activation energy. Unexpected is the increase of activation energy with increasing field.

Material C10 C18

Process Switching Depola- DRS Switching Depola- DRS

20 V/µm 30 V/µm 40 V/µm rization

20 V/µm 30 V/µm 40 V/µm rization

Ea

(eV) 0.54 0.66 0.66 1.11 1.52 0.73 0.75 0.78 0.93 1.32

(kJ/mol) 52 64 64 108 147 71 73 75 90 127

t0 (s) 7.6E-11 6.5E-13 3.7E-13 1.0E-14 7.9E-23 1.6E-13 4.2E-13 1.1E-14 5.2E-12 7.9E-20

a) b)

23

1.3 AFM imaging

1.3.1 Experimental setup

Atomic force microscopy (AFM) and scanning Kelvin probe microscopy (SKPM) measurements are

done with a Veeco Dimension 3100 AFM connected to a Nanoscope IIIa controller equipped with an

extender module, operating in the dark in ambient air. Heating experiments were performed with a

Veeco MultiMode AFM with a heating head. Ti/Pt-coated Si tips (NSC36/Ti-Pt, MikroMasch) with

force constant of ~1 N/m, resonance frequency of ~100 kHz and apex radius of ~40 nm were used.

Topographic images are taken in tapping mode (a.k.a. intermittent contact mode), potentials were

measured by SKPM in lift mode with a typical lift height of 25 nm, using the amplitude modulation

technique with an AC voltage modulation of 3 V superimposed on the DC tip potential. Care was

taken that the scanning tip did not affect the polarization of the probed layers.

1.3.2 Sample preparation

Thin films were prepared by spincoating the BTA material dissolved in chloroform (40 mg/ml) with

750 RPM on a ITO coated glass substrate. This resulted in 300-400 nm thick films for C18 and in 400-

500 nm thick flims for C10. This thickness proved to be enough to be sure that no shorts will be

created upon poling.

Figure 1.14: Sketch of how a thin BTA film is poled. The BTA columns are aligned at the location where the electrodes overlap.

The samples were poled and the columns were aligned perpendicular to the electrodes at 140°C by

applying a voltage of 10V over the film for 15 minutes, using a drop of mercury (Hg) as counter

electrode as shown in figure 1.14. The voltage and the drop of Hg were removed after the sample

cooled down to 30°C.

24 Chapter 1.3: AFM imaging

The homeotropic alignment was confirmed by POM where no light comes through the sample in

regions where the columns are aligned because no birefringence occurs there (figure 1.15).

Figure 1.15: POM-photo of the C10 BTA material film, where the columns were aligned under the Hg-electrode. A) with crossed polarizers b) with aligned polarizers. C) Micrograph of C18 film at the edge of a drop. AFM scans were made in the poled areas (lower left square) and unpoled areas (upper right square).

1.3.3 Topography

AFM scans taken at poled and unpoled regions are shown in figure 1.16 for C10 and figure 1.17 for

C18. The effect of poling is well visible in the structure of the surface, especially for C18. The

morpgology changes from columns that are ordered in-plane to columns that are ordered out-of-

plane, so the alignment is visible with AFM.

It is evaluated that the surface remains unchanged at areas where a drop of Hg has been, without a

potential applied.

Figure 1.16: AFM-image of a spincoated C10 film a) before poling and b) after poling. A clear change in the topography is visible.

2.0µm 1.5µm

a) b) c)

a) b)

1.3.4 Surface potential 25

Figure 1.17: AFM-image of a spincoated C18 film a) and c) before poling, b) and d) after poling. Bunches of columns seem to reorient from an in-plane structure to an out-of-plane structure.

The diameter of the measured columns is estimated in figure 1.17d to be of the order of 20 nm. The

diameter of a single BTA stack is ~2,5 nm [21]. This means that the columns seen by AFM consist of

bundles of 40-100 BTA stacks.

1.3.4 Surface potential

The topography only gives information the alignment of the films. SKPM has been performed to learn

something about the polarization of the aligned films. When the polarization remains after the

poling, the potential at the surface Vs is expected to have a sign opposite to the applied potential to

the Hg-electrode with a value in the order of:

0

rs

r

P dV

(1.9)

with d the thickness of the film and εr the static dielectric constant of the material. Vs is expected to

be around 26V using the values for C18 (Pr=1.6 µC/cm2, d=350 nm, ε0=8.85 F/m and εr=24)[23].

The measured surface potentials found for the poled C18 films have a value between 10 and 20V,

with a sign opposite to the voltage applied to the Hg electrode. This shows that the depolarization is

indeed slowed down by lowering the temperature, as was suggested in paragraph 1.2.5. Histograms

of the measured potentials at a 10 x 10 µm2 area for both a negative and a positive poled sample and

for an unpoled sample are shown in figure 1.18.

2.0µm 2.0µm

200nm 200nm

a) b)

c) d)

26 Chapter 1.3: AFM imaging

The measured surface potentials are slightly lower than the theoretically predicted 26V, this can have

two reasons. First, the samples may be slightly depolarized what lowers the potential. Another

reason can be some charges present at the surface that screen the ferroelectric potential.

SKPM at aligned C10 films shows a potential around 0V with mainly the same sign as was applied to

the Hg-electrode. Apparently, the films of this material are screened or not properly polarized. In

fact, in literature this behavior is always observed in SKPM at ferroelectric surfaces.[24-26] Only

totally screened ferroelectric surfaces have been observed with SKPM so far and potentials found

here for C18 are unique. [27]

-20 -15 -10 -5 0 5 10 15

0.2

0.4

0.6

0.8

1.0

No

rma

lize

d

nu

mb

er

of

co

un

ts

Surface potential (V)

Figure 1.18: Histograms of the measured potentials of an area of 10 x 10 µm2 C18 material. The values found

for a poled area with a positive (negative) potential applied to the Hg-electrode is shown in blue (red). The histogram for an unpoled area is shown in black.

As can be seen in the spread of the histograms in figure 1.18 and in its potential maps in figure 1.19, a

variation in the measured potential is found. Local depolarization and/or screening can explain the

variation in the surface potential. The potential can also vary by a variation in thickness of the film.

However, this is less probable because no direct correlation is found between the topography of the

film and the surface potential (c.f. figure 1.17 and figure 1.19).

Figure 1.19: a) Potential map of an unpoled C18 sample, topography is shown in figure 1.17a. b) Potential map of a positively poled C18 sample, topography is shown in figure 1.17b.

2.0µm 2.0µm

a) b)

1.3.5 Poling with tip 27

Heating

An interesting experiment to investigate the screening is to measure the surface potential while

heating the sample. The material depolarizes when the temperature becomes high enough and only

the screening potential is visible then.[24] For C10 it is indeed observed that the potential slightly

increases, showing that there was still some polarization that is lost during heating which reveals the

screening charges. The original polarization is not recovered upon cooling.

For C18 the potential decreases with increasing temperature, showing the depolarization, see figure

1.20. However, two types of behavior are observed for equally prepared samples. In the first case

(figure 1.20a), the potential drops and an opposite potential is visible which also disappears later on.

This is as expected in advance; the polarization is lost, causing a decrease in potential and revealing

the screening charges that also disappear later on.

In the other case (figure 1.20b), the potential drops linearly and the initial potential is gained back

while cooling, these results are not yet understood. The film may depolarize while heating and

polarizes again when cooled. Alternatively, the pyroelectric effect is playing a role.[28] The material

expands when the film is heated which causes the dipoles to become more spaced what results in a

larger potential drop over the film thickness. Probably a competition is going on here between the

ferroelectric charges and the screening charges, where the screening charges wins for higher

temperatures.

More measurements are needed to get a better understanding of the effect of heating on the

potential. It would be interesting to find the similar behavior as is observed in figure 1.20b and heat

this sample to 100°C and evaluated if the polarization still will be received back upon cooling. Also

samples with a higher starting surface potential can be measured then.

20 30 40 50 60 70 80 90 100

-2.0

-1.5

-1.0

-0.5

0.0

0.5

Su

rfa

ce

po

ten

tia

l (V

)

Temperature (°C)

-4

-3

-2

-1

0

1

2

30 40 50 60 70

Temperature (°C)

Su

rfa

ce

po

ten

tia

l (V

)

Heating

Cooling

Figure 1.20: a) The surface potential measured at a negatively poled (positive Hg-electrode) C18 film while heating the film with 10°C/min. The potential decreases with increasing temperature, indicating a depolarization of the sample. At a certain moment the potential becomes positive as a result of the screening charges. At 100°C two measurements are done, where the lowest point is taken 1 minute after the first, showing that the potential is slowly decreasing in time at this temperature. When cooled, the initial potential is not received back. b) The surface potential measured at another poled C18 film while heating and cooling the film with 1°C/min. The measured surface potential varies linearly with the temperature in this case. Interesting here is that the potential is received back after cooling.

1.3.5 Poling with tip

Some first attempts have been done to polarize the ferroelectric C18 film using the AFM tip. At room

temperature this was not successful. But at elevated temperatures (≈50°C) it did succeed for a

a) b)

28 Chapter 1.3: AFM imaging

incomplete aligned sample, see figure 1.21. The sample was poled with a potential of +10V at the tip

while scanning it over a small area (40 x 40 nm2) for 1 minute. Interestingly, the poling experiment

did not succeed at the spots where the columns seem to lie in plane. Further experiments have to be

done to check whether the same is possible at a totally aligned sample.

It is checked that the polarization potential is not affected by moving some material. Figure 1.21a and

c show that the topography of the scanned area is not changed after the polarization. This is

expected when molecules only change their dipole moment.

Figure 1.21: A first attempt to pole the film with the AFM tip at 50°C. The heights (a & c) and potentials (b & d) are shown before (a & b) and after (c & d) poling. Poling is done with a voltage of +10V at the tip for 1 minute at an area of 40 x 40 nm

2 at the location indicated in figure (d. This location is chosen because here

the columns seem to be aligned perpendicular to the sample.

To check whether this polarization is switchable, the sample has both been poled negatively as well

as positively at this location. It is indeed possible to switch, see figure 1.22, but the polarization

decreases in time. This may be stabilized by decreasing the temperature after poling. Also the surface

potential difference between the negatively and positively poled spots is not yet very high. Further

experiments are needed to improve this.

Important to note is that similar results can be obtained when screening charges are migrated

instead of a changed polarization of the material. The decrease of the potential in time is then

explained by a migration of charges back to the original position. Piezoresponse force microscopy

600nm 600nm

600nm 600nm

Poled spot

a) b)

c) d)

1.3.5 Poling with tip 29

(PFM) can be done to distinguish the change in potential as a result of polarization or migration of

charges.[5]

0 20 40 60 80 100 120 140

-400

-300

-200

-100

0

100

200

300

400

500

600

Poled with +10V at the tip

Poled with -10V at the tip

Surf

ace p

ote

ntial (m

V)

Time after poling (s)

Figure 1.22: The surface potential that was measured on a C18 film after polarization with the AFM tip for 1 minute at 45°C. The same spot is shown as was poled in figure 1.21.

30

1.4 Conclusions

The molecules with a benzene 1,3,5-tricarboxamide (BTA) core and with hydrocarbon tails of various

lengths (C6, C10 and C18) that are studied in this report show ferroelectric behaviour. We were

unable to study the C6 molecule because it did not align without breaking down. The remnant

polarization for both C18 and C10 was around 1.6 C/cm2, with a coercive field of about 28 V/µm for

C10 and 24 V/µm for C18. However, the polarization is shown to be unstable, hence the material is

not a proper ferroelectric in the temperature range investigated (80 –150°C). The stability can be

increased by decreasing the temperature; the depolarization time is estimated to be around 6-20h at

25°C. The depolarization for C18 could even be more slowed down because of a phase transition to a

crystalline state around 70°C which could make the material ferroelectric at lower temperatures.

From the switching dynamics, the switching process could be identified as extrinsic switching, where

the nucleation is temperature activated. The switching time is probably limited by the nucleation of

domains at low electric fields, the switching time starts to become domain growth limited in the

higher field region, E=25-40V/µm. The activation energy for the switching is comparable with the

values found in a dielectric relaxation study, where the cooperative flipping of amide groups is

studied.

For C10 a secondary process is observed causing a second peak in the switching experiments. This

process is probably related to charges that are trapped in the material during poling and are released

when the electric field is reversed.

AFM shows that spincoated thin films of the BTA C10 and C18 material can be aligned using a liquid

Hg-electrode. SKPM at C10 layers shows a surface potential around 0V, where the polarization is

screened by charges. When the sample is heated, the material depolarizes and the potential of the

screening charges is visible.

The surface potential of totally aligned C18 layers show a unprecedented high surface potential

around ±10-20V, with the sign depending on the polarity of polarization. [27] This shows that the

depolarization is indeed slowed down at lower temperatures. By heating these layers also

depolarization is observed, but these measurements are not yet totally understood.

Poling the sample using the tip seems to be possible at 50°C. However, more measurements are

needed to validate this.

1.4.1 Recommendations

Not everything of the ferroelectric switching mechanism of the BTAs is understood. There are no

experiments done to validate how the electrode interfaces play a role in the switching. To investigate

this, the structure and the material of the electrodes can be varied or the cell thickness could be

varied. If, for example, the domains are nucleated at the electrode, than an increase of the switching

speed is expected for thinner cells, because of a decreasing bulk to electrode surface ratio. By varying

the cell thickness also the field dependency can be checked.

AFM and SKPM images at thin films of the C18 BTA give promising results for further experiments.

More temperature dependent experiments have to be done to understand the variation in surface

1.4.1 Recommendations 31

potential upon varying the temperature. The sample can be poled with the tip, however this is not

yet shown for a fully aligned sample and so far only relatively small potentials have been reached.

Further, piezoresponse force microscopy (PFM) would be an interesting technique to get a better

understanding of the ferroelectric properties. This technique uses the ability of a ferroelectric

material to expand or shrink by application of an external applied bias.[5] This has the advantage that

it only probes the ferroelectric properties of the material and by that a distinction can be made

between the potential of polarization and the potential of screening charges, which could not be

made by SKPM alone. A problem can be the fact that contact-mode AFM is needed for this

technique, while the material is pretty soft which may prevent proper contact AFM imaging.

33

2 Part 2:

The charge transport in SAMFETs

Summary

In this report the temperature dependent charge transport in organic field effect transistors (OFETs)

is studied. The active organic material in the OFET is a self assembled monolayer (SAM) consisting of

molecules with a semiconducting quinquethiophene core, bounded to the gate dielectric.

The density of states (DOS) of the SAM is determined by measuring the surface potential using

scanning Kelvin probe microscopy (SKPM), while changing the charge density in the organic layer by

sweeping the gate of the OFET. At finite temperatures is shown that this technique only works when

an exponential DOS can be assumed. In the measured range the DOS is well described by an

exponent with a width of T0=420K.

This measured DOS is used to describe the transfer curves of the OFET using the model of Vissenberg

and Matters (VM) and the mobility edge (ME) model. The VM-model describes the data well in the

temperature range T=200-300K. At lower temperatures lower values of T0 are needed to describe the

data. The ME-model is able to describe the data in the range T=100-300K, however here a value of

T0=510K is needed to give a proper fit the data.

35

2.1 Introduction

In organic field-effect transistors (OFETs) current can flow from source to drain through an organic

material and this current can be switched on and off with a gate electrode. These OFETs are very

useful to get a better understanding of the electric transport mechanism in the organic material. [29]

It is important to understand the charge transport through organic semiconducting materials when

these materials are used for electronic applications, such as organic light emitting diodes (OLEDs) and

organic solar cells[30-31]. The advantage of organic electronics is their flexibility and the potential to

be cheap to fabricate. Further, the emission color is relatively easy to tune by choosing the right

molecules which is useful for OLEDs. Also OFETS themselves are very useful to be applied in

integrated circuits.[32]

Various models are proposed to describe the charge transport in OFETs.[33-34] Two models which

are mostly used in literature are the variable range hopping model of Vissenberg and Matters

(VM)[35] and the mobility edge (ME) model [36]. The shape of the density of states (DOS) of the

active material is an important parameter in these models; in the models a certain DOS is assumed to

describe the measurements.[37]

Tal et al. described a method to measure the DOS in thin organic films directly using scanning Kelvin

probe microscopy (SKPM).[38] This technique is a good method to validate the assumed DOS in the

VM-model and ME-model.

In this report a self-assembled-monolayer (SAM) is used as active material, which fulfills the criterion

to be thin and therefore the DOS technique can be carried out on this material. The self-assembled-

monolayer field-effect transistor (SAMFET) is a promising technology to be used in electronic

applications.[32]

2.1.1 Goal of the project

In this report the DOS in SAMFETs is measured to predict the temperature dependent charge

transport in these FETs.

In chapter 2 the theory of OFETs and the method to measure the DOS will be discussed. In chapter 3

the used setup and the active material of the OFET are described. In chapter 4 the results of the

experiments are shown and discussed. The DOS measurements which are used to describe the

transfer curves using the VM-model and the ME-model are shown and discussed. Finally, in chapter 5

a conclusion of this work is drawn.

36

2.2 Theory

2.2.1 FET

In the experiments field effect transistors (FETs) are used to study charge transport in the organic

material (figure 2.1). The organic material in between the electrodes is a semiconductor, which

ideally contains no intrinsic charge carriers, it is not intentionally doped. Charges are introduced with

the gate electrode of the FET, which basically operates as a capacitor. By applying a voltage VG to the

gate, charges are accumulated into the organic material and form a conduction channel near to the

insulating gate dielectric. The charge carrier density n in the organic material is dependent on the

capacity per unit area C of the gate:

( )G t

Cn V V

q , (2.1)

with q the elementary charge and Vt the threshold voltage of the device, this is the voltage that has

to be applied to introduce the first mobile carriers in the channel, so where the transistor turns on.

Figure 2.1: Schematic view of an organic field effect transistor (OFET). The transistor is build up out of metallic source, drain and gate electrodes, a gate dielectric (SiO2) and the semiconducting organic material. A voltage VG is applied to the gate to accumulate charges in the organic material near to the dielectric material. With a sufficiently high gate voltage a conducting path is created between source and drain and a current is able to flow through the organic material when a bias Vsd is applied over the source and the drain.

With a FET an electric field can be created over the organic material in between the source and the

drain electrodes by applying a bias Vsd to the source with respect to the drain. This field activates

charges to move through the transistor, the current Isd flowing between the source and the drain is

then given by

sdsd

VI nq W

L (2.2)

with L the length and W the width of the channel. μ is the mobility of the charges in the conducting

channel. In principle, when the mobility is known also the current is known and, vice versa, by

knowing the current the mobility can be calculated:

2.2.2 Mobility models 37

( )

sd

sd G t

IL

CWV V V

(2.3)

In literature the mobility is generally calculated by differentiating the current, which has the

advantage to be threshold independent: [35, 39]

sd

sd G

IL

CWV V

(2.4)

Note that equations (2.1) to (2.4) only hold when Vsd<<VG, otherwise the charge density is not

constant throughout the channel, but it varies because the electrostatic potential V(x) varies in the

channel. To account for this VG has to be calculated with respect to this potential V(x), which is given

for a constant mobility by:

2 2 2 G G sd G G

xV x V V V V V

L . (2.5)

When the mobility is charge density dependent, this potential profile becomes different because of

varying gate effective voltage throughout the conduction channel.

2.2.2 Mobility models

The mobility is an important parameter for understanding the charge transport through the material,

it is a parameter that depends on the used material, on the temperature T and the charge density n.

Various models are proposed to describe it. In this report two models are used to describe the

mobility: the variable range hopping model from Vissenberg and Matters and the mobility edge

model.

Variable range hopping

In variable range hopping a disordered landscape for the charges is assumed. In this landscape the

mobility is determined by a trade-off between hops to states that are spatially nearby, but

energetically far apart and states that are further apart in space, but energetically close. Note that

states that are both spatially and energetically close are not considered, since these are not rate

limiting.

Because of the disorder in organic materials an exponential density of states (DOS) is assumed:

0

0 0

( ) expB B

N Eg E

k T k T

(2.6)

here kB is the Boltzmann constant, E is the energy, N0 is the total DOS and T0 is the width of the

exponential DOS. With this assumption Vissenberg and Matters derived the following expression for

the mobility:[35]

0 0/ / 1

4 20 0 0

30

( / ) sin( / ) ( ( ))

(2 ) 2

T T T T

G t

c B s

T T T T C V V

q B k T

(2.7)

with σ0 a conductivity prefactor, Bc≈2.8 the number of bonds in the percolation cluster and α-1 the

decay length of the localized wave function. This equation shows a close to exponentially increasing

mobility as function of the temperature; when the temperature increases the charges have more

energy to hop upward and therefore a larger chance to find a nearby state to which they can hop.

38 Chapter 2.2: Theory

The mobility increases with a power law dependency as function of the charge density; when the

charge density increases, the DOS is filling up, which causes the Fermi level to move upward in energy

where the DOS is larger and therefore more nearby states available to which charges can hop.

Mobility edge model

The mobility edge model (also called multiple trapping and thermal release model) assumes a valence

and a conduction band in which charges are mobile with a trap DOS in the energy gap in which

carriers are not mobile. Charge carriers need a certain energy to be thermally promoted above the

‘mobility edge’ to get out of the traps to become mobile. Below this energy the charges are trapped

and above this energy they have a constant mobility µ0. The effective mobility is given by ratio

between the number of mobile carriers Nmob and total carriers Ntot:

0mob

tot

N

N (2.8)

Usually an exponential trap DOS is used for the energies under the mobility edge, above this edge a

weakly energy dependant Eα or constant (α=0) DOS is used. [29] If we take the band edge at E=0, we

will obtain for the total DOS:

0 0

0

( ) exp for <0

( ) for >0

t

B B

t

B

N Eg E E

k T k T

Ng E E E

k T

(2.9)

with Nt the total number of traps. The number of mobile carriers follows from:

0 00

( , ) exp ft tmob f

B B

EN TNN f E E dE

k T T k T

(2.10)

where f(E,Ef) is the Fermi-Dirac distribution, the assumption made only holds for sufficiently low

mobile carrier densities: 0f BE k T . The position of the Fermi level Ef follows from the total number

of carriers in the device (equation (2.1)):

( , )G ttot f

acc

V V CN g E f E E dE

qd

. (2.11)

The ME-model has the same general characteristics for the mobility as the VM-model: exponentially

increasing mobility as function of the temperature and the mobility increases with a power law

dependency as function of the charge density.

2.2.3 Density of States

The density of states is defined as the number of states available in the material per unit energy and

per unit volume. As is made clear in the previous paragraph, it is important to know the DOS of a

material to get to a good description of the mobility in a material. Therefore, in this paragraph a

technique is described to determine the DOS directly with a single measurement, which will be used

in the experiments.

2.2.3 Density of States 39

Direct determination of DOS

Scanning Kelvin probe microscopy can be used to determine the density of states (DOS) of the

organic material in a FET directly. [38, 40] This technique uses the gate to vary the charge carrier

density in the organic material. The energy bands have to shift with respect to the Fermi level in

order to fill the free states in the material, as is illustrated for holes with a Gaussian density of states

in figure 2.2.

The amount by which these levels have to shift (qV∆) depends on the density of states at that specific

energy level. When the DOS is relatively small around Ef, the HOMO level has to shift a relatively large

amount to add a certain amount of holes to the device (going from a to b in figure 2.2), while when

the DOS is larger around Ef, the HOMO level has to shift a smaller amount to add the same amount of

holes in the device (going from b to c in figure 2.2).

Figure 2.2: The number of holes in the organic material (in this example α-NPD) increases by decreasing the gate voltage. In order to do this the HOMO band has to shift towards the Fermi level to fill its DOS with holes. Going from a) to b) the energy level has to shift a relatively large amount upon adding holes, because the DOS is relatively low around the Fermi level in this case. Going from b) to c) the same amount of holes is added but the HOMO level has to shift a smaller amount, because the DOS around the Fermi level is much larger here. [40]

With SKPM the potential of the surface of the organic material is measured, so the shift of the energy

levels (qV∆) of the top layer will be measured by this. Therefore negligible level bending perpendicular

to the gate is needed, which means that the introduced charge is homogeneously distributed over

the organic layer. According to Tal et al. this assumption only holds when the thickness of the organic

layer dorg and the gate voltage are small enough (dorg<10nm).[40] It would be interesting to validate

this criterion by simulations and to calculate the band banding when this criterion is not fulfilled.

If band bending cannot be ignored, like for thick layers and high VG, the charges are more

concentrated near the gate dielectric, whereas at the surface their concentration is lower. With SKPM

this surface is measured and therefore a smaller level shift will be measured in this case. The

measured DOS will then be higher than it is in reality.

The level shift V∆ is defined as the measured surface potential VSKPM with respect to the measured

surface potential at Vg=Vt:

( )SKPM SKPM G tV V V V V . (2.12)

40 Chapter 2.2: Theory

The hole concentration p in the channel increases proportionally with the gate voltage, as given in

equation (2.1). In this equation the level shift was neglected, by taking this shift into account and the

fact that the concentration is equally distributed over the organic layer we obtain:

( )G t

org

Cp V V V

d q (2.13)

The hole concentration is also obtained by integrating the occupied states:

( , )hfp g E f E E dE

(2.14)

where Efh is the Fermi level relative to the HOMO level and f(E, Ef

h) is the Fermi-Dirac distribution.

If now Eft is defined as the Fermi level at VG=Vt, then qV∆ is the shift of the Fermi level with respect to

Eft. Ef

h is then given by:

h t hf f fE E qV dE qdV (2.15)

Taking the derivative of equation (2.14) with respect to Efh the following equation is obtained:

( , )h

f

h hf f

df E Edpg E dE

dE dE

(2.16)

It is not possible to solve this equation for a general DOS. However, often an exponential DOS is used

which can be assumed to simplify equation (2.14), this is shown further on.

Zero temperature assumption

Another way to simplify equation (2.16) is by assuming T=0. Although this is not a very realistic

assumption, it is very instructive and it is still valid as long as the width of the DOS T0 is much wider

than the width of the Fermi-Dirac distribution T (T0>>T). In this case the derivative of the Fermi-Dirac

distribution becomes a δ-function at the Fermi level which simplifies equation (2.16) to:

( ) ( )h hf fh

f

dpg E E E dE g E

dE

(2.17)

Taking the derivative of equation (2.13) with respect to V∆ leads to:

2

1G

org

dVdp C

qdV dV d q

(2.18)

Combining equation (2.15), (2.17) and (2.18) finally leads to an expression for the DOS as a function

of the measured level shift V∆:

2

( ) 1G

org

dV Cg qV

dV d q

(2.19)

This equation shows that any DOS can be measured directly by changing the gate while measuring

the surface potential.

2.2.3 Density of States 41

Exponential DOS assumption

Expression (2.19) was first derived by Tal et al.[40] However, it can be generalized by assuming an

exponential DOS, which is also often assumed to describe the transport properties in organic

materials, equation (2.6):

0

0 0

( ) expB B

N Eg E

k T k T

(2.6)

When this is assumed, equation (2.14) can be approximated using the Euler gamma function Γ(x):

00

0 0 0 0 0

0

0 0 0

exp exp 1 1

1 exp

expsin /

hf

hB B Bf

B

hf

B

EN E dE T Tp N

k T k T k T T TE E

k T

E TN

k T T T T

(2.20)

This approximation holds when –Ef >>kBT0 (sufficiently low carrier densities) and when T<T0. Taking

the derivative of equation (2.20) with respect to Ef the following equation is obtained:

0

0 0 0 0 0 0

exp ( )sin( / ) sin( / )

hf h

f

f B B

ENdp T Tg E

dE k T k T T T T T T T

(2.21)

Combining equation (2.15), (2.18) and (2.21) leads to:

0 0

2

sin /( ) 1G

org

T T T dVCg qV

T d q dV

(2.22)

Note that this is the same expression as the one derived with the zero temperature assumption

(equation (2.19)), with the only difference of a temperature dependent prefactor. The big advantage

of this equation is that it is valid for any T<T0. The disadvantage is that this equation only holds for an

exponential DOS, but often a part of the DOS can be approximated by one or more exponents.

For an exponential DOS, the DOS can also be determined without differentiating by combining

equation (2.13) and (2.20):

0sin( / )( ) G T

org B

T TCg qV V V V

d q k T

(2.23)

This formula has the big advantage that no differentiating of the measured signal is needed which

reduces the uncertainty remarkably. The extra disadvantage of this method is that the calculated

result is a continuously increasing DOS and, as a consequence, possible features on top of the

exponential DOS are hidden.

Simulations of the measured DOS

Simulations of the measured DOS calculated with equations (2.19) and (2.23) are done to verify these

methods with an exponential, a stretched exponential and a Gaussian DOS. These are shown in

appendix A.

These simulations show that the stretched and Gaussian DOS cannot be distinguished from an

exponential DOS when only small ranges of the DOS are measured. Further is shown that when the

42 Chapter 2.2: Theory

Gaussian DOS becomes steeper than the Fermi-Dirac distribution, the slope of the Fermi-Dirac

distribution will be measured instead of the slope of the DOS.

Using equation (2.23), the decreasing part of the Gaussian DOS will be measured as if the DOS is still

increasing. This has the result that a small Gaussian DOS on top of another DOS will show up as a step

using this method.

In conclusion the best method to calculate the DOS is dependant from of the real DOS that is a priori

unknown. The best way to check the form of the DOS is done by using equation (2.19) or (2.22).

When a exponential DOS may be assumed then equation (2.23) gives the best results.

43

2.3 Experimental setup

2.3.1 The Omicron VT-SPM

Measurements are done with an Omicron variable temperature scanning probe microscope (VT-SPM)

(figure 2.3b). In the beginning of this project this setup did not work: the optical fiber was broken,

there was noise at the PSD signal, no connections for source and drain were available and the coarse

approach did not work. This setup has been made ready for the experiments as part of this project.

The system is located in ultra high vacuum (UHV), working pressure around 10-9 mbar, to allow

cooling without crystallizing materials at the sample. A flow cryostat with counter heating is used to

vary the temperature making use of liquid nitrogen or helium.

To contact the source and the drain of the transistor in the UHV a sample holder (figure 2.3a) is

made, which clamps metallic plates at the bondpads of the FET (a small piece of tin is placed in

between the metal contacts and the bondpads to ensure good electrical contact). This sample holder

makes contact with the direct heating wires of the setup that are lead outside the vacuum. The gate

is grounded together with the rest of the sample holder.

Figure 2.3: a) Photograph of the sample holder which can be placed in the UHV setup while being able to contact the drain and source, the gate is grounded. Two contacting metals press at the bondpads of the sample for electrical contact with the source and drain of the FET. b) Photograph of the UHV chamber of the Omicron setup.

The Omicron SPM is used as a non-contact atomic force microscope (nc-AFM). This method makes

use of an oscillating tip to measure the topography of the sample. The oscillation is recorded by a

photo sensitive diode (PSD), a laser beam is aimed at the cantilever of the tip, in such a way that its

reflection falls at the PSD (figure 2.4). The signal of the PSD is used as the feedback signal and it is

therefore important to reduce the noise in this signal as much as possible.

The coarse positioning of the AFM-tip is done with a slip-stick technique. The fine positioning and

scanning of the tip is done by piezo’s which have a range of 2 µm in the vertical direction and 10 µm

in both lateral directions.

a) b)

44 Chapter 2.3: Experimental setup

A Nanonis controller is used to control the system and to process all signals. In this controlling three

PI-feedback loops are used to determine the resonance frequency, control the tip height and control

the tip potential (figure 2.4). This is further explained in the next paragraph.

Figure 2.4: Schematic diagram of the three feedback loops used to control the tip height, tip potential and driving frequency. In red the laser beam directed via the cantilever at the PSD is depicted. The first feedback loop is inside the phase locked loop (PLL) to track the resonance frequency by keeping the phase difference between the tip driving signal and the tip oscillation constant. The second feedback loop is used to control the height by keeping the frequency shift at constant value ∆f0. A third feedback loop with a lock-in amplifier is used to control the potential of the tip. Care is taken that the feedback system of the height controller is slow enough, that it will not follow the AC-signal of the Kelvin controller.

2.3.2 Non-contact AFM and SKPM

Calculating the resonance frequency shift

In nc-AFM the change in resonance frequency fr is used to control the tip-sample distance and to

measure the surface potential. When the AFM tip approaches the sample electrical forces and van

der Waals forces are acting on the tip, which change its resonance frequency, as is derived as follows:

Figure 2.5: Schematic picture of an oscillating tip above the sample, with h the height of the tip apex above the sample, zo the height of the tip apex in the equilibrium state and z the displacement of the tip from its equilibrium state.

2.3.2 Non-contact AFM and SKPM 45

The displacement z of the tip is given by the following differential equation:

2

2

d zF m kz

dt

, (2.24)

where the acceleration of the tip is given by the sum of the forces F acting on the tip, m is the

effective mass of the tip and k the spring constant of the cantilever. The solution for this equation is

given by a harmonic oscillation: sin(2 )r

z A f t , with A the amplitude of the tip oscillation and

(1 / 2 ) /r

f k m the resonance frequency of the tip.

If now an extra force is acting on the tip, the motion of the tip will change. Taking for example an

electric force FE due to a potential difference V between the tip and the surface of the sample:

21

2

tip

E

dCF V

dh

, (2.25)

with h=z0-z the height of the tip apex above the sample. Ctip is the capacitance between the tip and

the sample, which is inversely proportional to the height of the tip: 1 /tip

C h . Using this relation for

Ctip equation (2.25) can be written as:

2

2E C

VF k

h

, (2.26)

where kc is a positive constant dependent on Ctip. Adding this force to equation (2.24), this results in

an nonlinear differential equation which is not solvable analytically. However, for small values of z,

the resulting equation can be simplified using a Taylor expansion:

2 2 2

2 2 30 0 0

2 ...( )

E C C C

V V VF k k k z

z z z z

.

(2.27)

The first term of this expansion gives rise to an offset of the equilibrium position of the tip. The

second term is proportional with z and therefore the prefactor should be added to the spring

constant of the cantilever, which will result in a lower resonance frequency of the tip:

2 3

021

2C

r

k k V zf

m

. (2.28)

The change in resonance frequency is very small compared to the original resonance frequency,

which allows equation (2.28) to be written as:

2

30

1 1

2C

r

k Vkf

m km z

.

(2.29)

Therefore the resonance frequency shift ∆fr as a result of a potential difference between tip and

sample is given by:

2

30

1 1

2C

r

k Vf

km z . (2.30)

46 Chapter 2.3: Experimental setup

Note the 30z dependency of the frequency shift, which means that very local potentials can be

measured.

When a Van der Waals force is used in this calculation instead of the electric force a similar result is

obtained.

Measuring resonance frequency

The resonance frequency of the tip is measured by the Nanonis OC-4 phase locked loop (PLL)

controller. The PLL measures the phase difference between the tip driving signal and the measured

tip oscillation. This phase difference is a good signal to be used as feedback signal, because its slope is

steep around the resonance frequency (figure 2.6), so a small change in the resonance frequency will

be measured directly by a phase shift. The controller keeps this phase difference constant (the phase

is locked) by adjusting the driving frequency using a feedback loop. In this way the known driving

frequency automatically follows the resonance frequency fr of the tip.

-5 -4 -3 -2 -1 0 1 2 3 4 5

0

50

100

150

200

250

300

350

400

Oscila

tio

n a

mp

litu

de

(m

V)

Frequency shift (Hz)

-100

-80

-60

-40

-20

0

20

40

60

80

100

Ph

ase

Figure 2.6: Typical result for a frequency sweep around the resonance frequency of the cantilever (fr=60.78 kHz). The amplitude of the cantilever oscillation is shown in black, which peaks at the resonance frequency. In red the difference in phase between the oscillation of the cantilever and the driving oscillation is shown in degrees. When the resonance frequency shifts, these graphs shift in the same direction. The phase difference is kept constant by changing the frequency of the driving oscillation in order to know the resonance frequency.

Height measurement

In nc-AFM the distance of the tip to the sample is kept constant, by keeping the resonance frequency

of the cantilever constant using a feedback loop for the height. When the tip approaches the sample,

the resonance frequency is lowered as is shown in equation (2.30). The feedback system has to lift

the tip then to keep the resonance frequency constant

2.3.2 Non-contact AFM and SKPM 47

0 5 10 15 20 25 30

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Fre

qu

en

cy s

hift

(Hz)

Tip Height (nm)

Figure 2.7: The resonance frequency of the cantilever when the tip approaches the sample. Following measurements are done at a frequency shift of -25 Hz.

The lower the resonance frequency that is chosen, the smaller are the needed variations in the height

for a certain change in the resonance frequency (figure 2.7), therefore height measurements become

more accurate when the tip is closer to the sample. However, the chance of crashing the tip also

increases when the tip is close to the sample. In the experiments a frequency shift of -25 Hz is used.

Measuring the surface potential

The surface potential VSKPM is measured using the Kelvin method, which uses the resonance

frequency shift because of the electrical force that is present between tip and sample when their

Fermi levels are unaligned, see equation (2.30). There is a quadratic dependency of the resonance

frequency shift to the voltage difference between tip and sample, see figure 2.8.

-1.0 -0.5 0.0 0.5-100

-75

-50

-25

0

Fre

qu

en

cy s

hift

(Hz)

Tip bias (V)

Figure 2.8: The shift in resonance frequency as function of the bias on the tip at a distance of about 10 nm from the sample. The force to the tip increases when the potential difference between tip and sample increases which results in a downshift of the resonance frequency, with a parabolic dependency as calculated in equation (2.30). The surface potential is in this case VSKPM=-260mV.

An AC-potential with known frequency is applied to the tip to be able to distinguish the electrical

frequency shift from the shift caused by a height difference. The resonance frequency shift caused by

48 Chapter 2.3: Experimental setup

the electrical force is extracted from the PSD signal using a lock-in amplifier. Thereafter, the signal

from the lock-in is nullified by adding a DC-voltage to the tip that is equal to the surface potential

using a third feedback loop.

This nullification is illustrated in figure 2.9 and works as follows. When the tip potential is negative

(positive) with respect to the sample, the resonance frequencyshift will be higher (lower) when the

AC-signal is positive than when the AC-signal is negative (positive), so the resonance frequency will

follow the AC signal exactly in phase (out of phase) which results in a positive (negative) signal of the

lock in-amplifier. If the tip potential is equal to the surface potential (Fermi levels are aligned) we are

at the top of the parabola of figure 2.8. When now the AC-signal is positive, the resonance frequency

will be lower, but also when the AC-signal is negative the resonance frequency will be lower. This

results in a resonance frequency shift with the double frequency of that of the AC-signal, which does

not result in a signal of the lock-in.

0 2 4 6 8 10

-1.5

-1.0

-0.5

0.0

0.5

Time (ms)

Vtip=

VA

C+

VD

C (

V)

Vsurface

-2.0

-1.5

-1.0

-0.5

0.0

Fre

quency s

hift (H

z)

0 1 2 3 4 5 6 7 8 9 10

-1.0

-0.5

0.0

0.5

1.0

V

tip=

VA

C+

VD

C (

V)

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

Time (ms)

Fre

qu

en

cy s

hift (H

z)

Figure 2.9: The tip potential Vtip (black dashed line) plotted together with the frequency shift (blue solid line) as function of time. The tip potential consists of a DC- and an AC-signal, in this example with an amplitude of 1V and a frequency of 200 Hz. The surface potential is at 0V. a) The DC bias is -0.5 V, so the tip potential is lower than the surface potential. This will result in an oscillation of the frequency shift which has the same frequency component as the applied AC-bias and in phase, so the lock in will measure a positive signal. When the tip potential is higher than the sample, the frequency shift will be out-of-phase and a negative lock-in signal shall be measured. b) The DC bias is 0V, so the tip potential is equal to the surface potential. This results in an oscillation of the frequency shift with double the frequency of the applied AC-bias and no single frequency component of the AC-bias is left, so the lock in will not measure a signal.

2.3.3 Preparation of the SAMFET

The organic material used in the FETs for charge transport is the p-type molecule chloro[11-(5’’’’-ethyl-

2,2’:5’,2’’:5’’,2’’’:5’’’,2’’’’-quinquethien-5-yl) undecyl]-dimethylsilane, see figure 2.10. This molecule is

designed to form a self assembled monolayer (SAM) at the SiO2 gate dielectric. A nice property of this

SAM is that it is very thin (~3nm), which is needed to determine the DOS of the material as discussed

in paragraph 2.2.3.

The molecule consists out of four main parts: 1) a ethyl end group to enhance stability and solubility,

2) an conjugated semiconducting quinquethiophene core, this is the active layer for the hole

transport, 3) an aliphatic –C11H22- spacer and 4) a monochlorosilane anchoring group, this group

reacts with the SiO2 of the gate dielectric to bind to the sample. [32]

a) b)

2.3.3 Preparation of the SAMFET 49

To induce self assembly of the molecules, the SiO2 gate dielectric was activated by an oxygen plasma

treatment followed by acid hydrolysis. The SAM was then formed by submerging the substrate in a

dry toluene solution of the semiconducting molecule. Full coverage of the SAM on the gate dielectric

was reached after an immersion time in the solution of 15 hours. It was shown that the SAM was also

grown under the gold contacts to get in full contact with the electrodes. [41]

Figure 2.10: At the left, a schematic overview of the self-assembly process is shown.1) A clean sample is put in the solution containing the molecules that are activated with a monochlorosilane anchoring group. 2) The molecules self-assemble on the SiO2. 3) The substrate is removed from the solution and is rinsed with toluene. At the right, the molecular structure of the organic material that is used in the FETs to create a conducting SAM is shown. The molecule consist out of four parts: an ethyl end group to enhance stability and solubility, a conjugated quinquethiophene core for the hole transport, an aliphatic spacer and an anchoring group to bind to the SiO2 of the gate dielectric. [32]

50

2.4 Results

2.4.1 Measuring the Density of states

In figure 2.11a a result of a gatesweep at 230K is shown from which the DOS is calculated. For

voltages above Vt the transistor is in the off-state and no current can flow into the channel to screen

the gate. Therefore, a linearly increasing surface potential is observed for VG-Vt>0. For voltages below

Vt the transistor is in the on-state and charges flow into the transistor to screen the gate, the surface

potential now only varies as a result of the shift of the HOMO level with respect to the Fermi level.

Remarkably, the sweep from positive to negative gate biases does not fall on top of the sweep from

negative to positive gate biases. This may have two reasons: stress or slow charges. If the device is

stressed while the transistor is in the on-state, positive charges are trapped that lower the threshold

voltage.[42] This effect causes the device to be turned off earlier and higher surface potentials are

measured in the off-state, as long as the traps in the device are filled.

However, this does not explain the overshoot to lower gate biases when the transistor is slowly

turned on. This effect can be explained by holes that are too slow to fill up the DOS when the gate

voltage is just below the threshold voltage. When the transistor is slowly turned on, at a certain

moment a few states for the holes are available to screen the gate, but because of this small DOS the

mobility is very low (see figure 2.12) and hardly any current can flow to fill up this DOS, which results

in lower surface potential than expected. When the gate voltage is decreased even more, at a certain

moment the mobility becomes high enough to fill the DOS and surface potential reaches its expected

value again. The same holds when the transistor is swept off. In this case the mobility gets low when

the transistor is almost in the off-state and holes get stuck by this, which leads to a higher surface

potential than expected.

Bürgi et al. derived an expression for the typical transit time τ for charges to form an accumulation

layer in a transistor with a square geometry[43]. In general the this transit time can be estimated by 2 / ( )GL V . Using the approximated value of the mobility µ=10-5 cm2/Vs at VG-Vt=1V, the transit

time is estimated to be τ ≈10-1s. This estimation differs just one order of magnitude from the

sweeping speed, which is in the order of seconds (167 mV/s). This also indicates that slow charges

may be a problem and it would be interesting to verify this estimated transit time experimentally.

A way to distinguish the effect of the threshold shift from the effect of the slow charges is by varying

the sweeping speed. The stress effect becomes more pronounced when swept slower, while the

holes get more time to move at slower speeds which makes this effect less important.

2.4.2 Model fits 51

-8 -7 -6 -5 -4 -3 -2 -1

-1.0

-0.5

0.0

0.5

1.0

Sweep + to -

Sweep - to +

VS

KP

M(V

)

VG(V)

-0.55 -0.50 -0.45

1019

2x1019

3x1019

Sweep + to -

Sweep - to +

Exponential fits

Calculated using

differentiation

DO

S (

eV

-1cm

-3)

VSKPM

(V)

T0=378K

T0=461K

5x1018

Figure 2.11: a) The surface potential in the middle of the channel (L= 10 µm) as a function of the applied gate bias at 230 K. The gate sweeps are done with a speed of 167 mV/s. b) The DOS calculated from the data of figure a) with equation (2.23). An exponential fit is made through the data points in the region where the on- and off sweep lie close together. The data in grey is calculated with equation (2.22) out of the sweep from negative to positive gate biases for comparison.

The DOS of the SAM is calculated by assuming an exponential DOS, equation (2.23):

0sin( / )( ) G T

org B

T TCg qV V V V

d q k T

.

(2.23)

The result is shown in figure 2.11b. The DOS is calculated with sweeps in both directions. An

exponential fit is made through the points in the region where these two measurements are close

together. This results in an average width of the DOS of T0=420K.

For comparison the DOS is also calculated with equation (2.22). Globally the found values are the

same, but it is clearly visible that there is a lot more noise using this calculation method as a result of

the differentiation.

It is good to note that the range of the measured DOS is just 0.04 eV. The fact that the measured DOS

fits an exponential DOS does therefore not mean that the real DOS is exponential. A stretched

exponent or Gaussian DOS can well be approximated by an exponential DOS for such a small range

(see appendix A). The only thing that can be said about this result is that the exponential DOS is a

good approximation for the real DOS in the measured range of 0.04 eV. By increasing the range of the

gate voltage or by increasing the region where the two sweeps fall on top of each other, this range

can be increased in future experiments.

2.4.2 Model fits

Transfer curves of a transistor with a channel length of 10 µm are compared with simulations of the

VM-model and the ME-model.

In figure 2.12a the transfer curves are compared with simulations of the transfer curve calculated

using the model of Vissenberg and Matters, equation (2.7). The width of the exponential DOS that

was found in the previous paragraph (T0=420K) is used in this simulation. Other parameters used are:

σ0=1.6x107 S/m, α-1=0.22 nm and Vt=1.6V. The simulation fits the data down in the temperature range

T=200-300K.

At lower temperatures the fits starts to deviate from the measurements, the VM-model predicts a

steeper gate dependency than what is measured. To check the deviation of T0 of the measured data,

the transfer curves are plotted on a log-log scale and are fitted with free parameters T0 ,σ0 and α-1 for

a) b)

52 Chapter 2.4: Results

each curve, see figure 2.13a. The values of T0 are determined out of these fits and are shown in figure

2.13b as a function of the temperature. Down to T=200K the values correspond well with the

measured value of T0=420K, but at lower temperatures the value of T0 starts to deviate to lower

values. Apparently the VM-model does not hold for this transistor for temperatures lower than about

200K.

Interestingly, T0 increases linearly with temperature in this regime, indicating that T0/T is a constant

and therefore the power of the charge carrier density is temperature independent (the slope in figure

2.13a is constant). This may be a 2D effect caused by the thin organic layer, this can be checked by

doing the same experiment with a thick layer of the same material.

VM-model

295K

260K

220K

180K

160K

140K

130K

110K

97K

77K

-30 -20 -10 010

-11

10-10

10-9

10-8

10-7

10-6

10-5

I sd(A

)

VG(V)

ME-model

295K

260K

220K

180K

160K

140K

130K

110K

97K

77K

-30 -20 -10 010

-11

10-10

10-9

10-8

10-7

10-6

10-5

I sd(A

)

VG(V)

Figure 2.12: The current Isd from source to drain as a function of the gate bias VG for various temperatures with Vsd=-2V . a) The measured data compared with simulations of the VM-model (T0=420K, σ0=1.6x10

7 S/m,

α-1

=0.22 nm and Vt=1.6V). The value of T0 followed out of the DOS measurements and give a good fit to the data for T=200-300K, at lower temperatures the fits start to deviate. b) The measured data compared with simulations of the ME-model (T0=510K, µ0=0.5

cm

2/Vs, Nt=1.4x10

26 m

-3 and Vt=1.6V). This model gives a good

fit for a much broader temperature range (T=100-300K). The measured value of T0=420K does not give a good fit with this model, see appendix B.

In figure 2.12b the transfer curves are compared with simulations of the transfer curves, calculated

using the mobility edge model, equation (2.8). Parameters used are T0=510K, µ0=0.5 cm2/Vs,

Nt=1.4x1026 m-3 and Vt=1.6V. This simulation gives a good fit in a broad temperature range (100-

300K). The measured value of T0=420K does not give a good fit, using this model (see appendix B).

However, the DOS of the ME-model looks differently than of the VM-model; the DOS is constant

above the transport level (equation (2.9)). Nevertheless, when this kind of DOS is assumed, one

would expect to measure an exponential DOS with even a higher value of T0 than the width of the

trap DOS. This is verified with the same type of simulations as described in appendix A.

It would be interesting to do DOS measurements at lower temperatures to examine what values are

found with this technique for these lower temperatures.

a) b)

2.4.3 Mobility 53

295K

260K

220K

180K

160K

140K

130K

110K

97K

77K

1 10

1E-11

1E-10

1E-9

1E-8

1E-7

1E-6

1E-5 Fit to VM-model

I sd (

A)

abs(VG-V

t) (V) 0 50 100 150 200 250 300

0

100

200

300

400

500

T0 (

K)

T (K)

Figure 2.13: a) The current Isd from source to drain as a function of the gate bias VG for various temperatures with Vsd=-2V on a log-log scale. Fits to the VM-model are made with T0 a free fitting parameter; the slope of the curves determines the value of T0. The threshold voltage is the same for all temperatures. b) The values of T0 found with the fitting in figure a) as function of the temperature. The same value found with the DOS measurements (T0=420K) is only found here for the temperatures above 200K.

2.4.3 Mobility

-25 -20 -15 -10 -5 0

0.0

5.0x10-3

1.0x10-2

1.5x10-2

2.0x10-2

2.5x10-2

295K

260K

220K

Lin

ea

r m

ob

ility

(cm

2/V

s)

VG (V)

4 6 8 10 1210

-7

10-6

10-5

10-4

10-3

10-2

Fit:=0exp(-E

A/k

BT)

EA=0.91 eV

=2.0 cm

2/Vs

Mobility at VG= -25V

ME-model

VM-model

Lin

ea

r M

ob

ility

(cm

2/V

s)

1000/T (1/K) Figure 2.14: The linear mobility calculated from the data of figure 2.12 with equation (2.4). a) The mobility as function of the gate voltage. b) The mobility at VG=-25V as function of the reciprocal temperature. The data is compared with the simulations of the VM-model and the ME-model, the same parameters are used in this simulation as in figure 2.12.

The mobility of the charge carriers in the OFET is determined by measuring the transfer curves of the

device (figure 2.12). The mobility µ of the material in the transistor in is then given by equation (2.4)

:[39]

sd G

L I

CWV V

(2.4)

The calculated motilities are shown in figure 2.14. Again is visible that the ME-model gives a better

description for the measured data.

a) b)

a) b)

54 Chapter 2.4: Results

2.4.4 Potential profiles

Another interesting experiment is measuring the potential profile in the channel of the transistor to

get more insight in the transport mechanism. This is done for two different temperatures and

compared with the two models, shown in figure 2.15a.

Both models do not fall exactly on top of the measured data, although they did give an appropriate fit

for the transfer curves in the temperature range 200-300K. A possible cause of this may be a varying

threshold voltage throughout the channel. There is an indication that this is the case, because when

the potential profile is measured when no voltage is applied, in the middle of the channel a 0.7V

higher voltage is measured than close to the electrodes (figure 2.15b). However, this can also be a

result of slow holes that need time to get out of the material or slow electrons compensating trapped

holes, which is easier near the electrodes and therefore the potential is measured lower there.

It would be interesting to measure the potential profiles at lower temperatures where the models

don’t fit the data anymore, to get more insight in the transport mechanism.

2 4 6 8 10 12

3

4

5

6

7

8

Po

ten

tia

l (V

)

Position (m)

295K

230K

ME-model

VM-model

0 2 4 6 8 10

-400

-200

0

200

400

Po

ten

tia

l (V

)

Position (m)

Electrode

Figure 2.15: a) The measured potential profiles at two different temperatures with VG=-8V and Vsd=-5V. The measured data is compared with simulations of the VM-model and the ME-model. The same parameters are used in this simulation as in figure 2.12, except for the threshold voltage that shifted because of long periods of measuring, Vt=-1V. b) The measured potential when no bias is applied to the transistor. The potential is about 0.7V higher in the middle of the channel than near the electrode.

a) b)

55

2.5 Conclusion

A technique using scanning Kelvin probe microscopy (SKPM) is further developed to determine the

density of states (DOS) of the semiconductor material in a field effect transistor (FET). With this

technique the gate of the FET is swept to shift the Fermi level in the material through the DOS. This

method to measure the DOS works at finite temperature when an exponential DOS is assumed, or at

T=0 for any DOS. Further, no band bending has to be assumed (thin layers <10nm).

The organic material studied in this report is a self assembled monolayer (SAM) consisting of

molecules with a semiconducting quinquethiophene core bounded to the gate dielectric. The

monolayer has a thickness of about 3nm, allowing the DOS technique to be used on this material. The

DOS is measured in a 0.04 eV wide region to be exponential with a width of T0=420K.

The measured DOS is used to predict transfer curves of the FETs in a temperature range of 77-300K

with the model of Vissenberg and Matters (VM) and with the mobility edge (ME) model. The VM-

model (with parameters: T0=420K, σ0=1.6x107 S/m, α-1=0.22 nm) gives a good description of the

measured data in the temperature range T=100-300K. At lower temperatures, lower values of T0 are

needed to give a proper fit to the data. The ME-model (with parameters: T0=510K, µ0=0.5 cm2/Vs,

Nt=1.4x1026 m-3) gives a good description of the data in a broader temperature range, T=100-300K.

However, with this model the data is not well described with the value found in the DOS-

measurements.

From the transfercurves the temperature dependant mobility of the holes in the FET is calculated.

This is also better fitted with the ME-model, than with the VM-model.

2.5.1 Recommendations

The way in which the DOS is measured and how the mobility can be predicted with it give promising

results for further experiments. In these experiments the differences that are observed by sweeping

the gate in both directions (figure 2.11) have to be investigated by varying the sweeping speed. Also

the range of the measured DOS can be increased, by increasing the range of the gate voltage that can

be applied or by increasing the region where the two sweeps fall on top of each other, which may be

done by sweeping slower. The assumption of an exponential DOS can be verified in these larger

ranges.

However, one has to be aware that band bending may occur at these higher gate voltages. It would

be interesting to do simulations to evaluate when band banding takes place and if it takes place to

find an expression for the band banding.

Further, it would be interesting to perform the DOS measurements at various temperatures, to

evaluate whether the same DOS is obtained for each temperature. Also potential profiles can be

measured at lower temperatures.

Both the VM-model and the ME-model did not give a full description of the measured transfer curves.

Potential profiles at various temperatures can be measured which may give a better insight in the

transport mechanism of the holes trough the organic material. The deviation of the models with the

measured data may be caused by a 2D effect as a result of the thin organic layer, this can be verified

by doing the same experiment with a thick layer of the same material.

57

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59

Appendix A: Simulations of measured DOS

In the methods to calculate the DOS, described in paragraph 2.2.3, assumptions have to be made:

T=0 or the assumption of an exponential DOS with T<T0. When these assumptions are not satisfied, a

deformed DOS will be measured. Simulation with other shapes of the DOS are done to investigate

how the DOS is deformed by the measuring method and to investigate when the measured DOS is

distinguishable from an exponential DOS.

In this appendix the measured DOS is simulated, using a Matlab script, and compared with the

original DOS. This script uses a given DOS g(E) to calculate the occupation of this DOS as a function of

the Fermi level. With the occupation the corresponding gate bias is calculated and in this way, the

change in the Fermi level and V∆ is known by a changing gate bias.

The colors of the result of the simulations shown in this appendix, correspond to the following:

Green line: The real DOS that is inserted in the simulation

Red line: Calculated DOS with equation (2.19), T=0 approach

Blue line: Calculated DOS with equation (2.23), exponential DOS assumption and no differentiation

First, the measured DOS is calculated if the real DOS would have the form of a stretched exponential:

0

0 0

( ) expB B

N Eg E

k T k T

,

(2.31)

with a ‘–‘-sign if E<0 and a ‘+’-sign if E>0. In the simulations values of No=1e26 m-3 and T0=400K are

used.

If β=1, the DOS has the form of a normal exponent. The calculated DOS with the exponential DOS

assumption is expected to fall exactly on top of the real DOS and the calculated DOS with the T=0

approach is expected to deviate with a constant(the difference between equation (2.19) and (2.22))

when T≠0. This is exactly what is found in figure A.1a. Also, when the temperature is lowered, the T=0

approach is found to come closer to the other results, as expected.

If β=0.7, the DOS starts to become curved, as is observed in figure A.1b. This curvature is also visible

in the calculated results, but slightly deformed. The resulting DOS from the T=0 approach becomes

more curved, while the result with the other approach is less curved.

If β=0.5, the DOS is even more curved (figure A.1c). In figure A.1d is zoomed in on a small region of

figure A.1c to see whether this curvature still can be observed in a small measurement range in the

experiment (paragraph 2.4.1). From this may be concluded that the exponential DOS cannot be

distinguished from a stretched exponent for such small regions.

Note that the T=0 approach matches the real DOS for small values of E. This is the result of the small

slope the stretched exponent has in this region, when this region would be described with a normal

exponent, T0 would be large here: T0>>T .

60 Appendix A: Simulations of measured DOS

-0.25 -0.20 -0.15 -0.10 -0.05 0.00

1018

1019

1020

1021

1022

No differentiation

T=0 approach

Real DOS

Gate voltage

E (eV)

DO

S(c

m2/V

s)

10-2

10-1

100

101

102

103

VG (V

)

-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.010

18

1019

1020

1021

1022

No differentiation

T=0 approach

Real DOS

E (eV)

DO

S(c

m2/V

s)

10-1

100

101

102

103

VG (V

)

-1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0

1019

1020

1021

1022

No differentiation

T=0 approach

Real DOS

E (eV)

DO

S(c

m2/V

s)

10-1

100

101

102

VG (V

)

-0.10 -0.08 -0.06 -0.04 -0.02

1021

2x1021

3x1021

4x1021

No differentiation

T=0 approach

Real DOS

E (eV)

DO

S(c

m2/V

s)

0

20

40

60

80

VG (V

)

Figure A.1: Result of a simulation of the measured DOS for a stretched exponent. In black (right axis) the gate voltage is shown that is needed to get the Fermi level to the energy level noted at the horizontal axis. a) Parameters used: T=300K, β=1. The blue and the green line fall exactly on top of each other. b) Parameters used: T=300K, β=0.7. c) Parameters used: T=300K, β=0.5. d) Zoom-in of figure c), this figure shows that the measured DOS can be approximated by a normal exponential DOS in the small range of 0.04eV.

Second, the measured DOS is calculated if the real DOS would have the form of a Gaussian:

2

0200

( ) exp22

N Eg E

(2.32)

Values of No=1e26 m-3 and σ0=0.086 eV (=1000K*kB) are used in all simulations.

In figure A.2a it is clearly visible what the temperature does with the Gaussian, it spreads the

Gaussian. On the log-scale this effect is visible by the fact that at a certain moment, when the

Gaussian becomes too steep, the steepness of the measured DOS is determined by the steepness T of

the Fermi-Dirac distribution. When the DOS is calculated using (2.23), where no differentiation is

used, the calculated function becomes continuously increasing function that does not decrease when

the real DOS is decreasing. In fact, a Gaussian will be measured as a step using this method.

a) b)

c) d)

Simulations of measured DOS 61

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4

0.0

2.0x1020

4.0x1020

6.0x1020

8.0x1020

1.0x1021

E (eV)

DO

S(c

m2/V

s)

10-1

100

101

102

VG (V

)

-0.3 -0.2 -0.1 0.010

16

1017

1018

1019

1020

No differentiation

T=0 approach

Real DOS

Exponent with T0=300K

Gate voltage

E (eV)

DO

S(c

m2/V

s)

10-1

100

101

102

VG (V

)

Figure A.2: Result of a simulation of the measured DOS for a Gaussian DOS. No=1e26 m-3

, σ0=0.086 eV and T=300K. In black (right axis) the gate voltage is shown that is needed to get the Fermi level to the energy level noted at the horizontal axis. a) The result on a linear scale. When the real DOS is decreasing, the measured DOS without differentiation is still increasing. b) The result on a log-scale. Here, also an exponent with T0=T=300K is shown for comparison in light blue, the slope of the two measured DOS approaches the slope of this exponent when the slope of the Gaussian DOS is larger than of the Fermi-Dirac distribution (T>T0)

a) b)

62

Appendix B: Simulation of ME-model with T0=420K

In this report the width of the exponential DOS is measured to be T0=420K. In paragraph 2.4.2 the

measured data is only compared with the ME-model with a width of T0=510K, because it fits better to

the data. Therefore in this appendix the ME-model is compared with the data using T0=420K. Other

parameters used are: µ0=0.2 cm2/Vs, Nt=2.2x1026 m-3 and Vt=1.6V.

ME-model

295K

260K

220K

180K

160K

140K

130K

110K

97K

77K

-30 -20 -10 010

-11

10-10

10-9

10-8

10-7

10-6

10-5

I sd(A

)

VG(V)

Figure B.1: The current Isd from source to drain as a function of the gate bias VG for various temperatures with Vsd=-2V. The measured data is compared with simulations of the ME-model (T0=420K, µ0=0.2

cm

2/Vs,

Nt=2.2x1026

m-3

and Vt=1.6V). When the measured value of T0=420K is used, each curve has a too small slope.