Eindhoven University of Technology

MASTER

Device physics of blue organic LEDsexperiments and modeling

Billen, J.G.J.E.

Award date:2005

Link to publication

DisclaimerThis document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Studenttheses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the documentas presented in the repository. The required complexity or quality of research of student theses may vary by program, and the requiredminimum study period may vary in duration.

General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.

• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain

Device physics of blue organic LEDs: Experiments and modeling

Master of Science Thesis of Joris Billen

Supervisors Prof. dr. R. Coehoorn Philips Research Laboratories Eindhoven dr. ir. S.I.E. Vulto Philips Research Laboratories Eindhoven dr. P.A. Bobbert Eindhoven University of Technology

July 15t\ 2005

Abstract

An uninvestigated area in the present-day research of polymer light-emitting diodes (pLEDs) is the electron current in blue polymers. It is important to understand the electron contri­bution to the current since it might play a key role in understanding the mechanisms that cause the limited lifetime of blue double carrier devices. Modeling of the electron current can be used in a double carrier device model to provide information about the position of the recombination zone. In the first part of this thesis, measured J(V)-curves for electron-only pLED devices of blue polyfluorene-based polymers are presented and modeled for different LEP layer thick­nesses and temperature. Characterization experiments are carried out using photovoltaic measurements and electrical impedance spectroscopy. The effect of the cathode on electron injection and mobility is studied. Two devices are under investigation: one with a Ba/ Al cathode and one with a LiF /Ca/ Al cathode, showing improved injection. J (V)-curves of devices with a Ba/ Al cathode (the archetype cathode within Philips Re­search) can not be described using the trap filled limited mobility model, that was successful for OC1 C10-PPV electron-only devices. Instead a concentration dependent mobility model where charge transport is described by hopping through a Gaussian density of states is used. The device is found to be injection-limited. When a Schottky barrier of <P B = 0.52 eV and a disordered electron energy landscape of width O' = 0.22 e V is assumed, this model is ca­pable of describing the J(V)-curves for a thickness variation of the light-emitting polymer layer (L = 78 - 158 nm) and a wide range temperature variation (T = 293 - 193 K). The found temperature dependence of the mobility is smaller than expected. For the device with a LiF /Ca/ Al cathode, there is a difference in bulk mobility although the same polymer is used. The reason for this is not understood. LiF /Ca/ Al devices are described by the trap filled limited mobility model, with an exponential distribution of traps defined by Tt = 1465 K, a mobility of µn = 5.66 x 10-9m2 /Vs, a Schottky barrier <P B = 0.20 eV, and a trap concentration of 0.13 %. In the second part of this thesis, models for the electron current are applied in double carrier devices for the two different cathodes. For the hole current a field and tempera­ture dependent mobility, that showed in previous investigation to describe the LEP layer thickness and temperature variation for hole-only devices using the same blue polymer, is implemented. Then we are able to describe the current in double carrier devices very well. It is found that for the double carrier device with the Ba/ Al cathode more excitons are found next to the anode at all V. For a double carrier device with LiF /Ca/ Al cathode, the recombination zone is close to the cathode at low V, and shifts towards the anode for higher V. The implications from the model for the recombination efficiency are examined and found in agreement with previous measurements.

Contents

1 lntroduction: polymer light-emitting diodes (pLEDs) 1 1.1 Historica! perspective . . . . . . . . . . . . . . . 1 1.2 Technology assessment . . . . . . . . . . . . . . . 2 1.3 Scope and background of this graduation project 3 1.4 Outline of this report . . . . . . . . . . . . . . . . 4

2 Polymer light-emitting diodes 6 2.1 Solid state physics of 7r-conjugated polymers. 6 2.2 Structure of a polymer LED . . . . . . 9 2.3 Electro-luminescence in polymer LEDs . . . . 9

3 Electron-only devices: properties and device characterization 12 3.1 Devices under investigation . . . . . 12 3.2 Fabrication of electron-only devices . 16 3.3 J(V)-characteristics . . . . . . . . . 16 3.4 Temperature and thickness variation 18 3.5 Selection of samples . . . . . . . . . 18 3.6 Device characterization and determination of Vi( theory and setup . 21

3.6.l Photovoltaic measurements . . . . 22 3.6.2 Electrical impedance spectroscopy ... . 3.6.3 Electro-absorption measurements .... .

3.7 Device characterization and determination of Vii: results . 3.7.l Photovoltaic measurements .. . 3.7.2 Impedance spectroscopy .... . 3.7.3 Electro-absorption measurements 3.7.4 Conclusions ........... .

4 N umerical modeling 4.1 Transport equations describing polyLED device physics

23 26 27 27 30 35 35

37 37

4.2 Models on the electron mobility . . . . . . . . . . . 4.2.l Field and temperature dependent mobility . 4.2.2 Trap filled limited mobility (TFL) 4.2.3 Concentration dependent mobility

4.3 Electron injection in polymer LEDs . . . . 4.3.l Ohmic injection .......... . 4.3.2 Injection-limited modified Schottky harrier 4.3.3 Injection in a Gaussian DOS . . . . . . . .

5 Modeling of the electron current in blue electron-only diodes with a:

39 39 39 41 42 42 44 45

Ba/ Al cathode 48 5.1 Experimental J (V)-curves . . . . . . . . . . . . . . . . . . . . . . . . 48 5.2 Modeling using the field and temperature dependent mobility model 49 5.3 Modeling using a trap filled limited (TFL) mobility . . 51 5.4 Concentration dependent mobility in a Gaussian DOS 54

5.4. l Gaussian DOS without an injection harrier 54 5.4.2 Gaussian DOS with an injection harrier 55

5.5 Conclusions and discussion . . . . . . . . . . . . . 63

6 Modeling of the electron current in blue electron-only diodes with a LiF /Ca/ Al cathode 65 6.1 Experimental J(V)-curves . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 6.2 Modeling assuming concentration dependent mobility in a Gaussian DOS 66

6.2. l Gaussian DOS with an injection harrier . . 66 6.2.2 Gaussian DOS without an injection harrier 68

6.3 Modeling using a trap filled limited mobility . 70 6.3.l Trap filled limited mobility . . . . 70

6.4 Conclusions . . . . . . . . . . . . . . . . . . . 72 6.4. l Devices with a LiF /Ca/ Al cathode . . 72 6.4.2 Comparison with devices with Ba/ Al cathode . 74

7 Double carrier devices 77 7 .1 Double carrier device characterization and determination of Vii'. results 77

7 .1.1 Electrical impedance spectroscopy . 77 7.1.2 Electro-absorption measurements . . 78

7.2 Double carrier devices with Ba/ Al cathode 79 7.2.l Experimental J(V)-curves . . . . . . 79 7.2.2 Modeling of J(V)-curves . . . . . . . 80 7.2.3 Modeling of charge and exciton distribution 82 7.2.4 Discussion . . . . . . . . . . . . . . . . . . . 87

11

7.3 Double carrier devices with LiF /Ca/ Al cathode 7.3.l Experimental J(V)-curves ....... . 7.3.2 Modeling of J(V)-curves ........ . 7.3.3 Modeling of charge and exciton distribution

8 Conclusions and Outlook 8.1 Conclusions ...... .

8.1.1 Electron-only devices . 8.1.2 Double carrier devices

8.2 Outlook . . . . . . . . .

A Modified Schottky model

91 91 91 94

97 97 97 98 99

107

B Modeling of electron-only device with Ba/ Al cathode using trap filled limited mobility 108 B.1 TFL mobility with field-dependent mobility . . 108 B.2 TFL mobility with injection harrier. . . . . . . 109

B.2.1 Infl.uence of Schottky harrier height cl> B 111 B.2.2 Infl.uence of trap depth ksTt, 'Y and conclusions . 111

C Conversion from efficiency to efficacy 113

D Simulations using the model successful for double carrier current in a device with a Ba/ Al cathode 114

lll

Chapter 1

Introduction: polymer light-emitting diodes (pLEDs)

1.1 Historica! perspective

Plastics or polymers ( organic materials) are indispensable in the luxury living standard that today's western society has got used to. They combine benefits in processibility and mechanica! properties. They can be produced at low temperatures, are easy to modify, and at the same time show a high strength and a light weight. This has made them successful in many applications as substitutes for traditional natura! resources as wood and metals. In the early days of polymers, applications were concentrated in packaging and domestic applications, making them primarily a subject of interest for the chemica! industry. The beginning of the physically interesting plastic electronics era was the discovery in 1977 in Philadelphia of a conducting high mobility polymer 1: chemically doped polyacetylene [1]. These doped conducting polymers were initially unstable in air, brittle, and difficult to process. In the following years these problems were overcome, creating stable and easily processable materials. The most revolutionary finding in polymer LED history was achieved in 1990 at Cambridge University. By accident, light-emission was noticed from polyphenylene vinylene (PPV) by Burroughes et al. [2]. Organic semiconducting polymers with a band gap in the visible spectrum were discovered. PPV was found to emit yellow-green light when sandwiched be­tween a pair of electrodes. The initia! device efficiencies were very low, but the researchers quickly realized the commercial potential of this discovery, especially for the manufacture of displays that emit their own light. Companies like Philips, DuPont Displays, Cambridge Display Technologies, and Seiko Epson turned their head to the new technology.

1This discovery led toa shared Nobel prize in chemistry in 2000 for MacDiarmid, Heeger and Shirikawa "for the discovery and development of conductive polymers".

1

Philips Research played a leading role in the development of pLED. The company started with the project in 1992 and launched a high profile commercial pLED product ten years later in 2002. An innovative shaver made use of a small pLED display to indicate personal shaving minutes and appeared in a blockbuster Hollywood production [3] . In 2004, the potential of pLED for mobile telephone applications was proved when a polymer display was incorporated in the 'Magie Mirror' mobile telephone.

1.2 Technology assessment

The polymer LEDs give rise to a new concept for thin displays. They have significant advantages over the main display technologies that are used nowadays being liquid crys­tal display (LCD) and the classica! cathode-ray tube display (CRT). A pLED display (figure 1.1) is the first candidate in line for an ultimate display, having strong advantages on its contenders:

Figure 1.1: The Philips 13" pLED TV prototype.

• There is almost (circa 1 µs delay) instantaneous light emission when a current is applied. This is essential for video applications. The cathode in a CRT needs to warm up and and LCD is slower due to the alignment of molecules upon application and removal of an electric field

• The colour of the emitted light is determined by the material properties (the band gap of the semiconducting polymer) . By tuning of the band gap, all colours can be generated.

2

• There is no back light needed for pLED displays as for displays based on LCDs. The dark contrast in a <lark environment is higher than for an LCD. Also there is a better viewing angle.

• Emission of light already takes place at low voltages, suited for battery operated mobile applications. As noted, the first commercial products were a shaver and a mobile phone.

• The structure of a polyLED consists only of three layers on a glass substrate: a light­emitting polymer sandwiched between two metal electrodes. This makes it easy to construct. It does not need vacuum (like TL, incandescent lamps or CRT) or separate light sources (back lights, ambient light).

However, for a wide range of consumer electronic products, the useful lifetime (time taken for the device luminance to drop to half of its initial value) must exceed 10 000 hours (this number can vary with product conditions). Full colour displays typically use groups of three adjacent pixels emitting red, green and blue light. Although the green and red polymers currently available easily meet the stability specifications required for a range of consumer electronic products, a long-time stable blue pLED has until now presented a greater challenge.

1.3 Scope and background of this graduation project

The cause of degradation of the blue devices and limited lifetime, is not yet fully under­stood. One approach by Philips Research is to develop a model that describes the physical processes in the polymer LED device. First this model will treat the initial unstressed device. In the light-emitting polymer holes and electrons are injected. They can recombine and photons are emitted. It is likely that the degradation is related to the electrical stress that the device experiences: the current that flows. To distinguish between the effects of the hole current and the effects of the electron current, devices are produced in which only holes flow (hole-only devices) or only a current of electrons flow ( electron-only devices). The hole current was investigated in a previous graduation internship [4]. The focus of this graduation project is on the charge transport in electron-only devices. Previous findings from the hole results on currents will be joined with results for electron currents to combine them in a complete device model for a double carrier device (chapter 7 in this report). When the unstressed device is fully understood, the aim is to extend the model to see what the changes are in the physical properties when a voltage is applied to the device and light is emitted. This is beyond the scope of this internship. There is little liter at ure on electron-only devices. They are difficult to process ( chapter

3

3), so few groups are capable of producing them. Blom et al. has explained the thick­ness variation in OC1 C10-PPV electron-only devices using a model consisting of traps [23, 25, 36] (subsection 4.2.2). For small molecule electron-only LEDs (Al/ Alq/Ca devices) the thickness and temperature dependence has been described using traps by Brütting et al. [37], on the condition that a field and temperature dependent mobility was included (subsection 4.2.1). In the early years on LEDS the focus was on the red and yellow PPV-devices. At typical driving voltages, the electron current in these devices is many orders of magnitude lower than the hole current. Only at voltages much higher than typical driving voltage, the elec­tron current will dominate. This is in contrast with devices with blue fiuorene polymers where the electron current becomes dominant already at lower voltages. lts properties are still an unknown area and therefore might be a key in the understanding of the degradation process. Therefore indirectly this work contributes to one of the major questions in plastic electronics, being one the most booming research areas from the last decade. The project focuses on challenging-physics and has a direct and important technological application.

1.4 Outline of this report

In chapter 2 the semiconducting nature of some organic materials is explained, starting from solid state physics. The light-emitting diode is introduced, and it is shown how a simple architecture leads to processes of electro-luminescence. Chapter 3 focuses on electron-only devices, which play the leading role in this report. Starting from fabrication details, the exact structure of the electron-only devices under investigation, and their energy alignment, it is explained why these devices show only an electron current. J(V)-curves for electron-only devices are introduced and it is discussed how we will test our model by examining these curves after variation of temperature and light-emitting polymer layer thickness. Characterization measurements are carried out for determining the built-in voltage of the devices using techniques as photovoltaic measure­ments, impedance spectroscopy, and electro-absorption. Chapter 4 describes the theoretica! background behind the modeling. The transport equa­tions that have to be solved to resolve the currents that run through a device are discussed. The models for the electron mobility that will be used, are introduced. We will compare two existing models and one recent candidate. The classica! space charge limited current with a field and temperature dependent mobility is a first candidate. The standard model so far in the (few) articles on electron-onlies, consisting of traps, will be used because of its good results for electron-onlies with PPV as polymer. Finally the recent concept of a concentration dependent mobility while carrier transport is treated as a hopping pro­cess between localized states in a disordered energy landscape, represented by a Gaussian

4

density of states, is stated. Different methods to treat injection of charge carriers are discussed. This injection process determines the boundary conditions for the transport equations. Here ohmic injection, a modified Schottky barrier, and injection into a Gaus­sian DOS are discussed. The central issue in the report is the application of the proposed models to experimental data. An extensive overview will be shown and discussed in chapter 5 for a device with a Ba/ Al cathode and in chapter 6 for a device with a LiF /Ca/ Al cathode. The issue in this electron current investigation is to create a model describing the total current in a device with both hole and electron current. Therefore in chapter 7 the findings are tested for the double carrier devices with Ba/ Al and LiF /Ca/ Al cathodes. The hole current properties are taken from previous research. We will show that we succeeded in describing the double carrier current as well. It is investigated where in the device recom­bination takes place. Finally, the conclusions from this complete 10-months work are combined in chapter 8. This comprises the findings of this first extensive investigation of electron current in blue LEDs.

5

Chapter 2

Polymer light-emitting diodes

2.1 Solid state physics of 7r-conjugated polymers

Conjugated polymers are intrinsic semiconductors. They lack intrinsic mobile charge, but are able to transport charge injected by electrodes. The main constituent of conjugated polymers is the carbon atom. It is the nature of the bonds between the carbon atoms that gives rise to the interesting physical properties. To understand this, it is necessary to look at the molecular orbitals (MOs). These consist of atomie orbitals (AOs) and their shapes are derived from quantum mechanics. They represent the region in space in which the probability of finding an electron is highest. Carbon in the ground state has four electrons in the outer electronic levels (2s+2p). The

Figure 2.1: Ethylene molecule showing O"- and 7r-bonds.

orbitals of these electrons may mix, under creation of four chemical bonds, to form four equivalent degenerate orbitals referred to as sp3 hybrid orbitals in a tetrahedral orienta­tion around the carbon atom. If only three chemical bonds are formed, they have three coplanar sp2 hybridized orbitals that are at an angle of 120° with each other. Hybridiza­tion between such orbitals or neighboring C-atoms leads to so-called a-bonds. These are associated with a highly localized electron density in the plane of the molecule. This is

6

shown for ethylene (C2H4) in figure 2.1. The one remaining free electron resides in the Pz orbital, perpendicular to the plane of the sp2 hybridization. The Pz orbitals on neighboring atoms overlap to form so-called w-bonds. Carbon-carbon double bounds, containing one a- and one w-bond do not have rotational freedom of the CH2 units with respect to each other; it is a rigid molecule due to the overlapping of 2pz-orbitals. By filling the MOs upwards with the number of electrons available in a bond, the electronic configuration of the ground state can be determined. The filled orbitals are called bonding MOs. Unfilled orbitals are labeled anti-bonding MOs and are indicated by an asterisk (*). A combination of two atomie orbitals on the respective atoms in a carbon-carbon w-bond always leads to generation of one houding and one anti-houding MO. Deeper lying molecular orbits are less important in this story since they do not contribute in the optical and electrical properties of a polyLED. It is said that the electronic configuration of ethylene in the ground state is w2, meaning that the highest occupied molecular or bit (HOMO) is 7r and contains two electrons. The first excited state of the ethylene molecule is found by placing one electron in the lowest unoccupied molecular orbital (LUMO). This MO is labeled w*. It is anti-bonding and the strength of the double bound has a lower energy in this excited state than in the ground state. The electronic configuration of this excited state is labeled (w, w*). In polymer LEDs the active materials are polymers which consist of repeated units contain­ing alternately of single and double honds. Such molecules are said to show w-conjugation, or w-delocalization. This implies that houding (and anti-houding) electrons in the HOMO (LUMO) are smeared out over many bonds. This is due to the fact that the AOs on many carbon atoms take part in the formation of the HOMO and LUMO. In a molecule containing alternating single and double bonds each carbon atom takes part in one double bond. Thus each atom contributes one Pz orbital and one electron to the w-MO. The general effect of adding together more interacting orbitals, is to slightly spread the range of energies covered by the orbitals, to fill in the energy range with energies lead­ing to energy bands, and to lower the energy separation between the HOMO and LUMO. Filling the MOs with electrons results in a completely filled HOMO band, and a completely empty LUMO band. The energy difference between them is the band gap: energy levels between the HOMO and LUMO levels do not exist. The band gap is determined by the number of conjugated monomer units. The concept of a band gap is shown in figure 2.2 (left picture). In a molecular crystal, all conjugated bonds are aligned perfectly, and true energy bands

with metallic-like behavior are found. In contrast, the polymers used in LEDs contain many structural defects and are amorphous. In the polymerization reaction, polymer segments with different conjugation length are formed. This random morphology it the reason for both structural and energetic disorder. The energetic disorder leads to a density of states

7

monomer polymer

7r:*-r-'J <. __ , HOM - 1 LUMO ap band gap Eg

i ___ /I.,.. 1f:-,

', ·,,

~c;,.LUMO

band gap

Figure 2.2: Repeating units with different LUMO and HOMO levels give rise to aforbidden energy area : the band gap E 9 (left picture). The disorder also induces a Gaussian DOS (right picture) around the HOMO and the LUMO level.

(DOS), that is experimentally shown to be Gaussian distributed 1 in the tail of the DOS (figure 2.2, right picture) [45]:

g(E) = ..!:i_exp (-~) .../'ina 2a2 (2.1)

with Nt the total site density (states/m3 ) and the width of the Gauss curve characterized by a. The charge transport can then be regarded as a hopping process between localized sites. Generally hopping from a site i to a site j is considered as a thermally assisted process with Miller-Abrahams transition rates of the form [7]:

= voexp [-2aRïj - k;T(Ej - Ei)]

voexp [-2aRiJl h < Ei) (2.2)

with va an attempt frequency, Rij the distance between sited i and j, a the inverse local­ization length of the localized wave functions under consideration and Ei the on-site energy of site i.

As noted before, the HOMO density of states of a LEP is completely filled with elec­trons. By the removal of an electron (creation of a hole) out of the HOMO the system will become electrical conducting. Electric transport in the HOMO is always described in terms of holes, while transport in the LUMO is always described in terms of electrons. Electrons can only go down the LUMO upon the application of an electric field, while holes go up the HOMO.

1 We note that for FET applications when higher energy states are more important the DOS can be better approximated by an exponential DOS [40].

8

2.2 Structure of a polymer LED

The device structure of a polymer LED is shown in figure 2.3. It consists of a glass substrate with an anode layer of indium tin oxide (ITO) on top. A typical value for the ITO thickness is 150 nm. On top of the ITO layer, a 100 nm hole-conducting layer is coated of poly­(3,4-ethylenedioxytiophene)/(polystyrene sulphonic acid) (PEDOT:PSS) with a ratio of PEDOT to PSS of 1 to 6. For these materials the two main requirements are matched. The anode is transparent (the light is coupled out through the anode side) and there is a match with the work function of the LUMO level (PEDOT work function is 5.1 eV close to HOMO fora common polymer as OC1 C10-PPV, 5.3 eV [8]). The light-emitting polymer is spin coated on top of the PEDOT:PSS. On top of this a low work function metal cathode is evaporated. There is not a standard cathode choice for the injection of electrons. For a red polymer as OC 1 C10-PPV often Ca is used [23]. Materials matching the work function of the LEP LUMO are scarce for the blue materials that have the widest band gap and thus the lowest LUMO level (typically 2.2 eV compared to 2.9 eV for MEH-PPV [8]). Cathode choices are limited to alkali, earth alkaline metals such as Ba and Ca, and rare earth metals.

Light-output

- Glass

----

ITO

PEDOT:PSS

LEP

Figure 2.3: A pLED consists of a glass substrate, an ITO/PEDOT:PSS anode, a light­emitting polymer (LEP) and a low work function metal.

2.3 Electro-luminescence in polymer LEDs

The polyLED shows direct conversion of electrical energy into light. This process is called electro-luminescence and is schematically shown in figure 2.4. When the polymer is sandwiched between the two electrodes, an equilibrium is established and the Fermi energy levels of the electrodes will align. This results in an internal negative

9

(a) V = 0 (b) v = Vbi Evo.c Evac Evac

·····························

c/>a LUMO

·1 LUMO

•,! EF ....L EF

Cathode Anode Cathode Anode Cathode

Figure 2.4: Energy diagram representing the basic principles of a light-emitting diode. When brought in contact, the Fermi energy levels of anode and cathode align (a). In (b) a voltage is applied equal to the built-in voltage of the device. When the voltage is further increased, holes and electrons get injected and light is emitted (c).

electric field at 0 V (figure 2.4a). When a voltage is applied (figure 2.4b) across the device, the internal field will decrease until at V = Vbi, the built-in voltage, there will be a fiat band condition where there is no net field across the device. When the voltage is now increased (figure 2.4c), the internal field becomes positive and holes can be injected from the anode side and drift to the cathode. Meanwhile electrons enter the device from the cathode side and drift towards the anode. At some point holes and electrons come close and recombine forming an exciton that can decay in emitting a photon. The same processes can be found back in the characteristic J(V)-curve of the device. An

example of such a curve for a device with a blue polymer, a standard ITO /PEDOT:PSS anode and a Ba/ Al cathode is shown in figure 2.5. At V = 0 (a) the diffusion current and the drift current due to a negative electric field cancel each other and there is zero current. For higher voltages the negative internal field decreases and there is some current due to diffusion. V = Vbi (b) is the fiat-band condition: there is no net field inside the device. When the voltage is now further increased, the internal field becomes positive. The current now rapidly rises with increasing voltage. The drift current dominates and the holes ( electrons) that are injected drift under the infi uence of the electric field towards the cathode (anode). The injected holes and electrons can recombine and form excitons, and light-emission occurs.

In reality not all the holes and electrons injected in the device will recombine forming

10

1000

100

10

.r

~ 0.1 -..

0.01

1E-3

1E-4 (b)V=V.

0 2 4 6 8 10

v.,"M

Figure 2.5: A typical J(V)-curve for a device with ITO/PEDOT:PSS, a blue-emitting polymer and a Ba/ Al cathode. The same notations as in figure 2.4 are used: at V = 0 there is an internal negative field (a). When a voltage is applied, a current starts to flow. Above vbi (c) the internal field becomes positive, holes and electrons get injected and the device starts to emit light.

photons that reach the eye of the customer. There are several loss mechanisms that lead to an overall external efficiency:

'fJext = 7Jint'f]out = 'f]P L 7JST7Jrec7Jout · (2.3)

7Jext is typical around 3.1 % for the polymers under investigation [ 6]. The factors that de­termine the internal efficiency 7Jint are the photoluminescence quantum efficiency in a film on quartz 7JP L, the fraction of singlet excitons ( 'f]ST), and the fraction of charge carriers yielding excitons 7Jrec· Finally the escape probability (fraction of light coupled out) is called 7Jout· In chapter 7 of this report we will provide an estimation for 'f]rec·

11

Chapter 3

Electron-only devices: properties and device characterization

Electron-only devices are introduced. These are polymer diodes, in which the cathode is a low work function material. This creates an energy harrier for hole injection. Therefore in these devices there is only an electron current and no light-emission occurs. The used polymers and cathodes are introduced and their energy alignment is discussed. Photovoltaic measurements, electrical impedance spectroscopy, and electro-absorption mea­surements are introduced and carried out for characterization of the devices.

3.1 Devices under investigation

The light-emitting polymers of the devices under investigation are polyfiuorene-based. The structure of polyfiuorene is shown in figure 3.1. Several kinds of polyfiuorenes can be pro­duced by tuning the side group (R). The light-emitting polymer under investigation is a copolymer of such fiuorene-based monomers and a hole-transporting (HT) unit. Such a HT unit enhances hole injection but does not contribute to the electron transport and it is assumed that they are of no importance for our electron-only devices. This used blue­emitting polymer will be denoted as BP in the rest of this report. It is delivered by the DOW Chemical Company.

The energy alignment of the used polymer is shown in figure 3.2. The LUMO level is measured by the supplier using cyclic voltammetry measurements (CV) to be at 2.2 eV. The energy levels of the used cathode is not without discussion. For single crystalline Ba the work function is at 2.5 eV [10]. In the energy picture it is assumed that the Al capping does not infiuence the work function. LiF /Ca/ Al is probably at a lower work function (expected from higher J(V)-currents as will be shown in figure 3.5). Also its value re­mains uncertain and the injection process is intrinsically different as will be pointed out

12

Figure 3.1: Structure of a polyfiuorene unit that is the main building black of the blue polymers used in this report.

in chapter 6. An important point in the discussion in this report will be the appearance of a possible injection problem for the Ba/ Al cathode. In chapter 6 the subject of the energy level diagram will be revisited (figure 6.11) and we will present our view based on experimental data and modeling. Another important property of the used polymer is the number of electron-transporting sites, Nc· This is also called the site density and from the composition of the polymer, this value is estimated at Nc = 0.75 - 1.5 x 1027 m-3 . Assuming a perfect crystal (Nc = 1/a3

with a the average distance between two sites), this results in a = 1.10 - 0.87 nm 1. This means that the electrons are closer together than the holes that have a = 1. 77 nm (hole transporting unit density Nv= 1.8 x 1026 m-3 [4]). A comparison between the currents in electron-only, hole-only, and double carrier devices

Energy

Al

_1=YM_Q_fil _ L~ ~~ _ LUMO PF 2.2 eV

4.2eV

HOMO Hr 5.1 eV HOMOPF 5.8eV

LiF/Ca/ Al <2.5 e V

Ba/Al 2.5 eV

Figure 3.2: Energy levels of the used electrode materials and the blue polymer, before con­tact has been established. HT stands for the hole transporting unit, PF for the fiuorene. All the energy levels for PF and HT were measured directly by cyclic voltammetry-measurements (indicated by straight lines) except for the LUMO level of the HT that was derived from the measurement of the HOMO level. It is assumed that Ba/ Al has the same work function as Ba. For the LiF /Ga/ Al work function, it is assumed that the work function is some­what smaller then the Ba/ Al value (based on higher J (V)-curves; figure 3. 5 later on in this chapter).

1There wil! be some chains that are located in such a way that at some places within the polymer this value can be lower or higher, but it will be a good estimation when averaged out over the whole polymer.

13

of similar thickness is shown in figure 3.3. The electron current for devices with BP be­comes dominant at higher voltage. The current through the electron-only device is much smaller at low V but increases fast and at high V it becomes dominant. This is in contrast with PPV-devices were electron current is many orders lower than the hole current (up to 80 V fora 300 nm device) [25]. The double carrier current is found to be about three times higher than the hole-only current.

1000 ·'

100

10

N~

E 0.1 ~ ...,

O.Q1

... :~.~::~ ::::: ... :y ..... / hole-only """

" • ·!...-- electron-only

1E-3

1E-4

1E-5

V-V"M

Figure 3.3: Comparison of the hole currents (Au cathode), electron current (Ba/ Al cathode) and the current in a double carrier device (Ba/Al cathode)of the same LEP layer thickness L = 80 nm (4). The dotted lines represent the expected continuation from the curves. At higher voltages ( around 7 V) the electron current becomes dominant. The measurements were corrected for the built-in voltages {2.4 V for double carrier, 0.68 V for electron-only device, and 2.1 V for hole-only device).

The main focus will go out to the BP with a Ba/ Al cathode. For this device the double carrier (with an ITO/PEDOT:PSS anode instead of Al) and hole-only devices (with an Au cathode) have been extensively studied in the past within Philips Research. In combination with these previous studies, in chapter 7 we will have a look at the modeling of double carrier devices. Since it has been shown by several groups [27, 28] that the use of a LiF /Ca/ Al cathode dramatically enhances the current density for blue polymers at a given voltage, also BP electron-only devices with a LiF /Ca/ Al cathode are investigated. This report will show that blue LEDs with a Ba/ Al cathode are injection-limited (i.e. that the concentration through the device is constant, as will be shown in figure 5.13a) in contrast to LEDs with a LiF /Ca/ Al cathode, so an extensive motivation for the used cathodes is given on the next page.

14

Cathode materials for electron injection

Carrier injection from the cathode into the emitting layer is a crucial process. The electron injection probability is strongly dependent on the match between the Fermi levels of the cathode and the LUMO level. Our devices have Ba/ Al or LiF /Ca/ Al cathodes. In the first reports on modeling of electron-only devices, such as the paper of the Blom group [25] on PPV, a Ca cathode is used. There the injection was not considered to be the limiting factor (for single crystalline Ca the work function is at 2.8 eV [10]). The LUMO level of this red PPV is much lower than for the blue polymers used in this study (LUMO level for MEH-PPV is at 2.9 eV [8] against 2.2 eV for blue fluorene polymers, figure 3.2 ). For metal-organic interfaces it is assumed that the injection barrier can be controlled by a careful choice of cathode. This is a result of the Schottky-Mott theory that states that the vacuum level aligns at the interfaces and can be considered continuous throughout the device [ 11]. Then a variation in barrier height can be seen in a changing built-in volt­age (~<I> B ~ e~ Vbi) and directly mirrors the change in the work function of the cathodes (~<I>B ~ ~cjJ(cathodes)). Hence fora low work function material, efficient injection is ex­pected and therefore there is no need of doping for these organic semiconductors. This is in contrast with inorganic semiconductors as Si or Ge, for which interfacial dipoles play an important role and there is pinning of the Fermi level. In practice materials possessing all the desired properties have not yet been devised. Low work function metals, such as Mg, Li, Cs, Sr, Sm, Ba, Ca, and Yb are highly reactive and have been shown to interact with the organic layer onto which they have been evapo­rated. Diffusion of the cathode into the organic quenches luminescence in a double carrier device [9], especially when recombination occurs close to the electrode. Furthermore these materials interact with the environment (atmospheric oxidation), resulting in quick degra­dation. A stable metal that works as a capping layer is used. This is often Al, due to its decent air-stability. In this report we will use Ba as the low work function metal.

It was found that devices with LiF /Al bilayer cathodes, have substantial electron injec­tion capability, high efficiency and low turn-on voltages compared to a traditional injector as Mgo,9Ago.1 [26]. This is a bit surprising since LiF is a very insulating material. How­ever experimentally it seems that an ultra thin layer of LiF backed by an Al layer is an effective electron injector. This made especially LiF /Al (and also CsF /Al) promising can­didates for a new generation of cathodes. But compared to Ca, a LiF /Al cathode did not provide better injection. This however changes when a thin layer of Ca is introduced forming LiF /Ca/ Al as shown by Brown et al. [27]. They measured built-in voltages in double carrier devices for different cathodes using electro-absorption. A higher built-in voltage reflects a lower harrier for electron injection. The built-in voltages are largest for

15

LiF /Ca/ Al (2. 71 V) and CsF /Ca/ Al (2.55 V) cathodes, both higher than for Ca (2.43 V) or LiF /Al (2.31 V). This is proof of a further decrease of the harrier height to electron injection due to the presence of Ca. They also measured that the luminance at fixed V of LiF /Ca/ Al is somewhat higher than for CsF /Al while the current is much higher for CsF /Al. Also a LiF /Ca/ Al cathode shows the highest efficacy (light output divided by the required current density) at high voltages. Therefore we choose to look at a LiF /Ca/ Al cathode. The mechanism behind this enhancement is not yet understood and different theories are developed [27, 28, 51, 52, 53, 54, 55, 56]. The thickness of the LiF layer is 3 nm 2 . From the variation of the thickness of the LiF layer in LiF /Al devices, it was shown that there is no further lowering of work function for thicknesses above 3 nm [27]. The thickness of the Ca layer is 5 nm (10 nm in the Brown reports). How to treat the injection in the physical model for a LED is treated in section 4.3.

3.2 Fabrication of electron-only devices

The device structure of an electron-only device is shown in figure 3.4. As a substrate, 0.7 µm glass is used. This goes through a multi-step cleaning procedure. An Al layer is evaporated directly on the glass under vacuum conditions. Al is used instead of Ca as in the report of the Blom group [23], because it is less reactive. The thickness is 30 nm. This small thickness is chosen since Al is known to be little transparent and a thicker layer would result in a completely nontransparent anode, which is not desirable when some of the characterization measurements will be carried out. Note that the devices do not contain any ITO or PEDOT:PSS layer to prevent hole injection. The polyftuorene­based light-emitting polymer of typical thickness between 60 and 160 nm is applied by spin-coating in a glove box in nitrogen environment. The low work function cathode is then evaporated on the LEP. This is either Ba/ Al (5 nm/100 nm) or LiF /Ca/ Al (3 nm/5 nm/100 nm). The Al layer works as a capping and is chosen because of its decent air­stability. Finally the entire device is protected from water and oxygen using a metal lid with a getter. The total production process is carried out under cleanroom conditions.

3.3 J(V)-characteristics

The characteristic J(V)-curves of electron-only devices with blue polymers are shown in fig­ure 3.5. Two electron-only devices with a comparable LEP layer of around L = 100 nm are shown. The curves have been corrected for their leakage currents ( currents under reverse bias) and the built-in voltages. For Vbi the values measured by photovoltaic measure­ments, later on in this chapter, were used. The most interesting property of J(V)-curves of

2 0ptimized by Cambridge Display Technology.

16

Glass

No light-output

30 run Al

LEP (60-160 nm) 5nmBa/100nmAI

or 3 run LiF / 5 run Ca / 100 run Al

Figure 3.4: Architecture of an electron-only polyLED device. A light-emitting polymer is sandwiched between the Al anode and the cathode. This is either Ba/ Al or LiF /Ga/ Al.

electron-only devices, is their steep slope (> 5) on log-log scales. The highest J(V)-curves are found for the device with BP and a LiF /Ca/ Al cathode. This suggests a better injec­tion for this cathode.

1000...-~~~~~ ....... ~~~~~~~

100 10

0.1 ~ 0.01 5_ 1E-3 ....,

1E-4

1E-5

1E-6 1E-7+-~~~~~ ....... ~~~~~~,....,..

0.1 10

Figure 3.5: J(V)-curves of electron-only devices for BP with Ba/ Al cathode and LiF /Ga/ Al cathode. All have an Al anode. The devices have comparable LEP layer thicknesses {100 nm for BP with LiF/Ga/Al cathode, 92 nm for BP with Ba/Al cathode). The curves were corrected f or the leakage current and the built-in voltage /rom photovoltaic measurements (subsection 3. 7.1).

17

The J(V)-curves were taken using a Keithley 2400 Source Meter in combination with a Lab View program to apply a voltage and measure the current that is generated through the device. The maximum voltage was chosen in such a way that the current never exceeded a current of 5 mA, to prevent the device from damaging. For all the measurements pixels of size 3 x 3 mm2 were used.

3.4 Temperature and thickness variation

To see whether we can develop a model to describe the polymer LED, we will investigate various models that predict the current through the device. In this report the scope is on the electron current as discussed before. The properties of current induced by the applied voltage are mainly determined by the mobility, that will change with temperature and field (and hence V). The common method to check if the used model is correct, is to see if it can describe the variations when the thickness of the light-emitting polymer layer (LEP layer L) and the temperature T is changed. Different samples with various thicknesses of L have been constructed, ranging from L = 55 nm to polymer layers as thick as L = 161 nm. L is determined by the spinning speed during production. L is checked first using a DekTak profilometer. Afterwards the thickness is double-checked using an impedance measurement to determine the capacity of the device, which is related to the thickness as will be described in equation 3.7. Combining these measurements, an agreement of L with an error margin of only 4 nm is achieved. Furthermore the J (V)-curves will be measured at different temperatures. The samples are cooled down using liquid nitrogen, and the temperature is monitored using a J-type thermocouple. In this way we can vary the temperature between 293 K and 173 K. A combination of the thickness and temperature variations will be used to judge if the applied models are correct. Results for the temperature and thickness variation will be discussed in chapter 5 for Ba/ Al and chapter 6 for LiF /Ca/ Al.

3.5 Selection of samples

To obtain typical J(V)-curves as shown in section 3.3, there was need for making a selec­tion of the devices. A part of the samples produced, <lid not satisfy the requirements of a hysteresis-free and reproducible J(V)-response. This is in contrast with hole-only devices and double carrier devices, where no such selection procedure was required. In this section the unwanted properties of samples that were rejected for investigation are described. An ideal diode characteristic would show zero current under reverse bias and an increasing current under forward bias conditions. In practice however, there will be a nonzero current in the reversed condition related to defects. We will denote this as the leakage current

18

l1eak. This leakage current is assumed to be symmetrical around zero. Therefore for high l1eak, the "real" current at lower positive voltages, will be hidden in the leakage current. An example of such a leak device is shown in figure 3.6a. The leakage current was found to vary from sample to sample (order 10-3-102 A/m2 at -6 V), and only devices with neg­ligible ]zeak < 10-2 A/m2 were selected for modeling. We note that leakage current is not typical only for electron-only devices, hut is also noticed in hole-only and double carrier devices. For some samples the first few J(V)-curves were not found to be completely reversible for electron-only devices, in contrast to BP-based hole-only devices. This effect was most important for the Ba/ Al-BP samples. Therefore, each sample was cycled a few times (typ­ically 4-6 times) between positive and negative bias voltage. This was monitored real-time on the computer, until the J(V)-curves coincided. Only then a J(V)-curve was taken for being modeled. This is shown in figure 3.6b. Note that for other samples this effect did not occur and coinciding J(V)-curves were found already from the first cycles. An oddity of the electron-only devices is that some samples showed a transition between

1000 1000 (b) (a)

100 100

10 10

1 •.......... ············ 1

î 0.1 NE 0.1

0.01 ~ 0.01 -,

1E-3 Jleak -,

1E-3

1E-4 1E-4

1E-5 1E-5

1E-6 1E-6 -6 -4 -2 0 2 4 6 -10 -5 0 5 10 15 20

v,"M v,"M

Figure 3.6: (a) J(V)-curve for a device with high leakage current. The leakage current is symmetrical. The dotted line is the mirror image of the current density under reverse condition. At low voltage the actual current is hidden in Jzeak under forward bias. Only above the dashed line the leakage current is not dominant anymore. (b) An example of a sample that had to be conditioned to show reversible J (V)-curves. The first 5 cycles were not reproducible, afterwards all the curves coincided.

different possible states. Electrical stability, in which a device exhibits two states of dif­ferent conductivities at the same applied voltage, has been reported and patented for an organic electrical bistable device, comprising of thin Al layer embedded within the organic material by the UCLA-group [12]. Similar behavior has been reported by IBM [13]. Little

19

is known about the reason of the multistable behavior and it imposes itself as a promising technique for memory applications. Possibly the discovery of this effect will lead to an increase in interest in electron-only-like devices. This, in our case unwanted, memory behavior was noticed for several samples, except the

1000~~~~~~~~~~~~~~

100

10

I 0.1 ...., 0.01

1E-3

1E-4

(a)

1E-5+-~-..--..---.---t'--r-~-.-~-..-~--t -6 -2 0 2 4 6

v.,"M

NÊ ~ ....,

1000

100

10

0.1

0.01

1E-3

1E-4

1E-5

1E-6 -8 -6 -4 -2 0 2 4 6 8

v.,"M

Figure 3. 7: Two J(V)-curves of samples with Ba/ Al cathode that show multistable behav­ior. The voltage is changed 0.5 V every 0.1 s. (a) shows the J(V)-curve for a sample of L = 73 nm with BP as the polymer and a Ba/ Al cathode were the numbers from 1 to 8 denote the chronology of the measurement. In a high conductivity state (e.g. 4 and 5) the device does not act like a diode anymore. Often similar behavior was found with less transitions between the different states as in (b) for a sample with L = 112 nm. The numbers represent the chronology in time.

ones with the LiF /Ca/ Al cathode. In figure 3. 7a results are shown for a BP electron-only device with a Ba/ Al cathode that shows multistable behavior. This is clearly another situation compared to the leak samples. The high currents under reverse bias are not permanent as for a sample with high leakage and the behavior <lid not disappear after a while (this might seem the case from the example figure, but in all cases it was seen that the sample kept making transit ion to other states). This is not a case of damaging of the sample, since there is a transition back to the first state of low conductivity and current. An multistable device with less chaotic transitions is shown in figure 3. 7b. We stress that this behavior did not occur for all the samples. For every thickness, a batch of 9 devices, fabricated under completely the same high quality conditions as explained in section 3.2, was constructed and only a minority of the samples showed this effect. As already mentioned, the BP with the LiF /Ca/ Al cathode (that has the highest J (V)-curves) didn't show the memory behavior. To quantify the denoted effects, we divide all our sam­ples into 3 categories: the samples that showed fine reproducible J(V)-curves with low

20

leakage current after a few cycles between positive and negative bias voltage, the samples that showed reproducible J(V)-curves but with high leakage current, and the samples that showed a multistable behavior. The results are shown in table 3.5. For completeness, we note that for the LiF /Ca/ Al devices, the cathode layer was deposited in another evapora­tion chamber. It is not clear if and how this aff ects the results concerning multistability. This is behind the scope of this report. The table shows that we have disposal of a large

Table 3.1: Overview of the occurrence of unwanted pmperties for the pmduced samples. They can be split up into 3 parts: the one that show high leakage currents as in figure 3.6, the ones that make transition between different states as in figure 3. 7 and the remaining samples that don't suffer these unwanted pmperties. As shown here almost half of the prnduced samples show high diode behavior. These will be selected for further investigation.

polymer cathode fine samples leak samples multistable samples BP Ba/ Al 15 out of 39 17 out of 39 7 out of 39 BP LiF /Ca/ Al 24 out of 27 3 out of 27 0 out of 27

number of stable samples with very low leakage currents. These were selected for further investigations and modeling of the J(V)-curves.

3.6 Device characterization and determination of Vbi: theory and setup

The built-in potential Vii originates from the equilibration of the Fermi level throughout the heterostructure and is due to unequal dipole layers at the cathode/polymer and an­ode/polymer interface. Therefore when a bias voltage Vbias is applied, the actual field that is experienced by a carrier in the device equals Vbias - Vii· The measurements have to be corrected for this built-in field. The rule of thumb is that Vbi is determined by the difference in vacuum work functions of the electrodes (Schottky-Mott, section 3.1):

vbi = c/Janode - c/Jcathode· (3.1)

From the energy diagram 3.2 this would result in Vbi ;:::;j 1.6 V. A correction of that magni­tude on the voltage-axis will dramatically change the shape of our J(V)-curves. Therefore in the following subsections, a few techniques are described that were used to measure Vbi·

At the same time, some of the proposed techniques can be used for further characterization of the devices, as discussed in detail in this section.

21

3.6.1 Photovoltaic measurements

Theory

Photovoltaic measurements provide a simple method for determination of the built-in volt­age, by looking at the difference in current through an illuminated sample and a sample in the clark. This technique has been used to detect the built-in voltage for MEH-PPV samples with different cathodes and the found values were independent of light intensity, sample thickness and incoming wavelength [29]. In the following discussion we distinguish between the clark current (hark), caused by the application of a voltage, and the pho­tocurrent due to the illumination of the sample (Jphoto)· This is shown in figure 3.8. The measured Jlight is the sum of Jphoto and Jdark·

At zero bias voltage the clark current will be zero since a negative drift current and a positive diffusive current compensate each other, resulting in a net zero current. Under illumination however, the current Jphoto at V = 0 will not be 0 since the polyLED acts as a photovoltaic cell. Photogenerated charges drift under the influence of Vii to pro­duce a small photocurrent (short circuit current lsc)· This current is negative, since the electric field in the device is negative. When now a positive bias voltage is applied, the field decreases so the diffusion current will become dominant. Therefore the total clark current Jdark will be positive. At some point this positive clark current will compensate for the negative photocurrent resulting in Jlight = 0. The voltage at which Jlight = 0 is called the open circuit voltage, Vac· Suppose now V is further increased. The current is then a result of competition between forward diffusion and reverse drift, the farmer being the dominant component in the clark. Under illumination then photoinduced charge injection can take place in four ways. Just below Vbi, additional contributions to the current are due to forward diffusion and reverse drift of holes ( electrons) photogenerated at the anode ( cathode) and d ue to forward drift and reverse diffusion of holes ( electrons) photogenerated at the cathode (anode). At the compensation voltage V = Vo this net photocurrent is zero. Vo is determined from the competition between the diffusion and the drift of the photogenerated carriers. In genera!, Vo is somewhat lower (a few tenths of Volts) than Vbi because of diffusive transport of charges and it is believed to follow [29]:

Va = Vbi - kT ln µn 92 + µP93 e µn91 + µp94

(3.2)

with µn and µP the electron and hole mobility, 91 and 92 photogeneration rate of electrons near the anode and the cathode, and 93 and 94 photogeneration rate at the anode and cathode. In theory this compensation voltage can be measured by taking a J(V)-curve of a sample

in the clark and subsequently one of an illuminated sample and look at the point of inter-

22

llight=ldark + Jphoto

Jphoto(Vo"' Vb;) = 0 I 1 I 1 Jphoto

I I I I

I I I I

---0 J - - ' ~ - - - -Voc - - - Vo ~ Vbi

vbias

Figure 3.8: Principles of a photovoltaic measurement. The compensation voltage V0 , at which the photocurrent vanishes, is close to vbi.

section. To obtain a result with higher accuracy however, a light modulation technique is used (see next section).

Experimental set-up

The set-up shown in figure 3.9 is used. As a light source an Oriel Xe lamp driven by an Oriel Universal Power supply 40-200 Wis used. Two diaphragms and two lenses are used to reduce stray light and to focus the beam onto the sample. An optical chopper operated at driving frequency 1 Hz is used to block and let through the light. Using a computer, at every Vbias the difference between the illuminated and the dark current is calculated. The sample is placed somewhat closer than the focal point, in a way that the spot is just large enough to illuminate the whole 3x3 mm2 sample (circle with radius 1.5 mm). Ina first approach the power of the light source was set at 55 mW. This value will be varied to see the effect of the lamp power. The power on the sample is measured using a Coherent Radiation Ine Model 210 power meter.

3.6.2 Electrical impedance spectroscopy

Electrical impedance spectroscopy (EIS) is a known characterization method for several properties such as mobility, conductivity, dielectric constant, interfacial processes between the organic layer and the electrode, etc. [17]. Ina typical EIS measurement, a sinusoidally voltage is applied superposed on a constant de background voltage Viias:

V(t) = Viias + Vacsin(wt). (3.3)

23

45 cm 2lcm ?cm

L Dl D2 Ll

D P.C.

Figure 3.9: The setup of a photovoltaic measurement. A Xe lamp (L) is used as light source. Two diaphragms (Dl and D2) reduce stray light. The incident light is focused onto the pixel of the LED using two lenses (Ll and L2). In between there is an optical chopper (C) that periodically blocks and lets through the light at a frequency of 1 Hz. The difference between the illuminated and the dark current is processed using a computer to see where the photocurrent vanishes.

As a result a current will flow. This will be phase-shifted by an angle b..</> with respect to the applied voltage. The differential impedance Z is defined as the ratio between the applied voltage V ( t) and the resulting current I ( t):

Z = V(t) - Viias . J(t) - J(Viias)

(3.4)

Usually this is a complex quantity and the real component is called the resistance R (Z') while the imaginary part is reactance X (Z") resulting in Z = R+iX with JZI = )R2 + X2 and b..</> = arctan ~. The reciprocal of the impedance is called the admittance Y ( w) of which the real part is called the conductance G(w) and the imaginary part the susceptance:

I(w) . Y(w) = V(w) = G(w) + iB(w). (3.5)

When dealing with circuit elements that are connected in series, the concept of impedance is used because it is mathematically more straightforward. For parallel connected circuit elements it is easier to work with capacitance. It is known that a pLED often can be represented by an equivalent circuit of a contact resistance (unwanted, due to cables used) in series with a RC-element (figure 3.10). The contact resistance does not depend on the de voltage.

From a simple measurement under reverse bias, the capacitance C and therefrom the LEP layer thickness L can be found. During a frequency sweep, the voltage is kept constant

24

c

R

Figure 3.10: A polymer light-emitting diode can be represented as an equivalent circuit circuit of a contact resistance Re in series with a parallel RC-circuit.

while the frequency f = w /2n is changed. For a pure capacitor the current lags behind on voltage resulting in a phase angle b.</> = -n /2 and the reactance is given by:

(3.6)

This occurs below the built-in voltage and the device behaves as a pure capacitor without a current fiowing. Then the capacitance is given by:

C = ErEoA

L (3.7)

with C the capacity, Er the dielectric constant, Eo the electric permittivity in vacuum, A the surface, and L the LEP layer thickness. From C the LEP layer thickness L or Er can be derived. In our measurements for thickness determination, Viias = -1 V and the frequency is varied from f = 10 - 106 Hz. In a voltage sweep the de voltage Vbias is varied while the frequency is kept constant. It is noted by van Dijken et al. [18] that in double carrier devices at the built-in voltage a peak in the capacitance arises for hole-only (Au cathode) and double carrier devices of PPV. This is an empirical method to determine Vii, since there is no accepted theory behind this finding. An intuitive theory is that at the built-in, under fiat band conditions in the absence of an internal field, the charge carriers can jump in and out of the LEP layer more easily because of the ac voltage. It is suggested by Shrotriya et al. [19] that the increase in capacitance for double carrier devices is related to the start of majority carriers that get injected. Then the capacitance decreases when also minority carriers get injected and the charge in the device is decreased due to recombination. This results in a peak. This however is not consistent with the finding that also in hole-only devices, the peak is observed and therefore this theory is not satisfactory.

25

3.6.3 Electro-absorption measurements

Theory

A widely accepted technique to measure the internal field of a device is to perform electro­absorption measurements [22, 27]. This is based on the fact that a field induces a change of the absorption coefficient. A LED device can be thought of a LEP layer on a mirror (the cathode top layer of reflecting Al) for which under illumination the reflection R is changed because apart of the incoming light is absorbed in the LEP. This is dependent on the length L of the LEP layer and the absorption coefficient a, and for a fixed de voltage this is given by:

R = 1- 2La. (3.8)

When now a modulated ac voltage is superposed, there will be a change in reflection:

L::.R = Ro - R = 1- 2L(ao + L::.a) - (1- 2Lao) = -2LL::.a (3.9)

with Ro and ao the change in reflectivity and absorption coefficient due to the modulation. Furthermore it is known that the change in absorption coefficient is related to the squared field [22]:

Vdc - Vbi Vac ( )

2

L::.a ex F 2 ex L + Lcos(wt) (3.10)

This shows Vbi can be revealed by looking at the change in reflectivity. From equation 3.9-3.10 then follows:

-1:::.R ex a + bcos(wt) + ccos(2wt) (3.11)

with b ex Vac(V de - Vbi) and c ex Vd1c· The change in reflectivity of a film will be measured after a sinusoidal voltage is applied across it. By comparing this with a reference signal, one can examine where bcos(wt) vanishes and this leads to Vbi.

Experimental set-up

The setup shown in figure 3.11 is used. A Nichia violet laser diode (>. = 409 nm) with light output power P = 45 mW is split up through a beam splitter. A first signa! is focused using a mirror and a lens (L) onto a signal detector. The second signal is focused on the 3 x 3 mm2 pixel. A frequency generator generates an ac signa! (f = 1131 Hz and a peak to peak voltage Vacpp = 0.50 V). Together with this, a de signa! is applied that is raised in steps of 0.2 V. The reflected signal of the illuminated sample is lead through a mirror and a lens (L) to the second input frame of the signal detector. This is connected to a EG&G Princeton Applied Research loek-in amplifier that detects the difference in reflectivity L::.R

26

L

- - 0-Ro - - - - - - - - -o-

D

_ _ _ _ ----- L

_ - - ..R- - - - LED

~~ ~ ~~~ ~:_~:=:=~=~==_ =_ =_ =_=_ =_ =_ ~ =_ =-~---~ ~, L B

f= 1131 Hz Vacpp

Vdc

Loek-in

C.R= ...

c.q, = ...

F

Figure 3.11: A blue diode laser (L) is focused onto a beam splitter (B). The light beam is split in two. The first beam is guided through two mirrors (thick lines) and a lens (L) into a detector (D) as a reference signal (R). The other beam is focused on the sample. A constant ac voltage and a varying de voltage are applied using a frequency generator (F). A part of the beam is absorbed and a refiected signal (Ro) is focused on a mirror and then through a lens (L) on the detector. This is connected to the loek-in amplifier, that detects the difference in refiectivity b..R and the difference in phase angle b..cf>.

and the difference in the phase angle b.cp. For different de signals, this data is read out and the built-in voltage is detected where b.R vanishes and the phase changes in sign. It will turn out that the electro-absorption measurement will not be successful for the electron-only devices (next section), hut the above described technique will be used in the chapter on double carrier devices (fi.gure 7.2) to measure the built-in voltage.

3. 7 Device characterization and determination of Vbi: results

3.7.1 Photovoltaic measurements

The compensation voltage Vo that is a measure for the built-in voltage is measured, as described in subsection 3.6.1. We noticed that the value of Vo was somewhat affected by the illumination time. Such a measurement is shown for a sample with a Ba/ Al cathode in fi.gure 3.12. An initia! measurement shows Vo = 0.68 V. After 30 minutes of illumination Vo is shifted 0.14 V. The fi.gure shows that after 30 minutes of recovery Vo is still 0.08 V higher than the initia! value. This effect was found to be reversible for a relaxation time of more than one day. A sample that was measured twice shortly after each other (illumination typically 30 sec­onds for each measurement), showed a shift in Vo of a 0.03 V. Therefore every measurement in this report was performed by unblocking the light exactly when the measurement was started. No samples were illuminated longer than about 30 seconds. For a device with

27

2.5

~:~ :'.'.'.'.~>:::::::··. 1.0 •.. .."... V0=0.82V

:i 0.5 •• • •••• ••• •• l ~ 0.0 ---------------------•---------·----·---------

:E 5 t • • t • • • -f-D. v =o.sa v • •• v

0=0. 7G°\1 • ••

i -1.0 ° • • • • 2 ..., -1.5 3

-2.0 initia! measurement (1) •

-2.5 after 10 minutes of lllumination (2) • • after 30 minutes recovery (3) • 1

-3.0 +-.--.~-.-~....-.--.~-.--~....-.--.~-i 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90

v.,"M

Figure 3.12: Photovoltaic measurement after illumination for a L = 161 nm sample of BP with a Ba/ Al cathode. The compensation voltage V0 shifts to the right. This effect was found to be reversible after more than 24 hours of recovery.

a LiF /Ca/ Al cathode the infl.uence of the power of the lamp, the wavelength dependence and the temperature dependence was studied. Figure 3.13a shows that the compensa­tion voltage indeed is affected by the lamp intensity. For a value of light output power Pzamp = 20 mW the compensation voltage is 0.1 V lower compared to the value at 55 mW. An even lower lamp intensity didn't cause the illuminated signal to give a detectable dif­ference compared to the dark signal and could therefore not be used to determine Vo. For an electron-only device with a LiF /Ca/ Al cathode, the temperature dependence of the photocurrent is shown in tl.gure 3.13b. For a lower temperature of 263 K, Vo increases about 0.1 V. At 233 K the difference between illuminated and dark starts to diminish. Vo is very comparable to the result of 263 K though. For the measurements at low T a plastic casing is place around the set-up which starts condensing at low T. At even lower temperatures an accurate measurement was not possible anymore due to reduced signal. We did not find a linear increase of Vo with T as expected from equation 3.2. For ITO /MEH-PPV /Al diodes it was already found by Malliaras [29] that Vo is lower at room temperature than the actual value of Vii· This is also found for our devices. The previous work however did not report on an effect of the power of the lamp source Pzamp· The dependence on the wavelength was examined using a blue wide band filter Schott BG 12 of thickness 3 mm (cuts off everything above 525 nm and under 325 nm and a has transmission peak of 653 at À = 402 nm), and resulted in Vo = 0.49 V (not shown here).

28

This is probably the result of the reduced transmission due to the filter (65 %) so that this situation is comparable to the measurement with the full spectrum of the Xe lamp with P1amp = 30 mW from tl.gure 3.13a with Va = 0.50 V. The noticed changement is thus a power effect. When using a Schott OG575 cut-off filter that cuts off everything un­der 550 nm, the photovoltaic measurement was unsuccessful. The light with such a large wavelength falls outside the range of the absorption spectrum ( absorption goes to zero at 460 nm) and using such a filter is similar to doing a dark measurement. We conclude that there is no contribution of the light that falls outside the absorption edge of the polymer. The photovoltaic measurement is only indirectly dependent of the wavelength of the used light due to a possible reduced effective lamp power.

:; ai

0.10...-----,--~-..-----.--~--.

P".., = 0.55 mW 0.05 ·." " .. ~°i0.54 v

~i 0.00 ...., I~

...., -0.05

P"..,=0.20 mW V

0=0.45V

P,.,,. = 0.30 mW V

0=0.50V

-0.10-+-----,--~-..-----.--~--1 0.40 0.45 0.50

v..,,M 0.55 0.60

:; ai

0.05

(b) () 0

0 T=263K 0

o0

V0

=0.64V DDO 00

o 0 T=233K

ii. 11 • 0

00 /V0 =0.67V o•.._ o

D Ä .& 0 ---------------Q ___________ <!-•••• üO--~-----------

/ 0 0 " 0 • ...

~i 0.00 ...., 't ....,

-0.05 T = 293 K v, = 0.55 v

0 0

0 0

0 0

()

0

0 0

0 0 0

-0.10-+-~-.-~--.-~-.--~-r-~-r-.......,_--1 0.45 0.50 0.55 0.60 0.65 0.70 0.75

v,..,M

Figure 3.13: Compensation voltage dependence for a 150 nm sample of BP with a LiF/Ca/Al cathode on (a) power of the used light source at room temperature. The in­tensity of the signals should not be compared since during the measurement the difference in signal between dark and light current is amplified and the gain factor is different f or the different P1amp. (b) The dependence of Vo on temperature at P1amp = 55 mW is shown.

An overall conclusion is that the light intensity and the diffusion process in the device influence the measurement. With increasing light intensity, Vo shifts upwards. Meanwhile Vo is higher than Vbi (equation 3.2). We choose to look at the values at room temperature and with a low Ptamp, but still high enough to ensure a clear measurement of where the difference between illuminated and dark currents diminishes. The measured values of Vo for the devices under investigation are shown in tl.gure 3.14. Because of the denoted inftuences, an error bar of 0.15 V is assumed. For a device with a Ba/ Al cathode Va = 0.55 + 0.15 V is found while for a device with a LiF /Ca/ Al cathode Va = 0.68 + 0.15 V. This shows that

29

from photovoltaic measurements the Vo and hence the built-in voltages Vii for blue LEDs are within the same range: around 0.6 V.

0.3

0.2

0.1

0.0+-~~~~~~~~~~~~~-'

40 60 80 100 120 140 160

L[nm]

Figure 3.14: The compensation voltage V0 for the Al-polymer-cathode devices under in­vestigation for various thicknesses. The solid squares represent devices with Ba/ Al cathode and BP as the polymer and have V0 = 0.68 ± 0.15 V. The open circles have BP as poly­mer and a LiF/Ca/Al cathode, and have V0 = 0.55 ± 0.15 V. In both cases the anode is Al. All measurements occurred with the full spectrum of the lamp at room temperature and P1amp = 55 mW. Therefore an error of 0.15 V is incorporated.

3.7.2 lmpedance spectroscopy

Equivalent circuits and frequency sweeps

The equivalent circuit for an electron-only device is examined. A frequency sweep was taken at 3 V over a range from f = 10 Hz to f = 1 MHz. It was found then that all the devices containing blue polymer can be represented by an equivalent circuit of a resistor in series with a parallel circuit of a resistor and a capacitor, as was the case for the double carrier device. This is shown in figure 3.15a, 3.15b and 3.15c for a sample with a Ba/ Al cathode. The fitting values for Re, R, and C are shown in figure 3.15a. The dots represent measurements, the lines the fits. The phase angle dependence of the frequency figure 3.15a is very well described. In figure 3.15b the impedance dependence of the frequency is fitted with high accuracy. Figure 3.15c shows the Cole-Cole (imaginary part of impedance in function of real part) plot for the same resistor and capacitance values. Also this is very well fitted. The frequencies are given at a few points. The minimum is found at the value

30

-0.3

:;:; -0.6 f! ~ -0.9

-1.2

-1.5

10

0

-200

-400

a -600

N -800

-1000

-1200

0

R,-RC R, = 150.2 n R= 2241 n C = 3.057 x 10~ nF

100

V..,=3V

Ba/Al and BP

1000 10000 100000 1000000

f[Hz]

f= 10 kHz

f = 1/(2xRC) - 25 kH

1 " V..,=3V

Ba/Al and BP

(c)

500 1000 1500 2000 2500

Z'[O]

1000

g: 100

~

10

(b)

V-=3V Ba/Al and BP

1+-~~~~~~~~~~~~~

10 100 1000 10000 100000 1000000

f[Hz]

Figure 3.15: An impedance measurement at Vbias = 3 V for a LED with Al - BP - Ba/ Al for (a) the phase angle, {b) IZI, and {c) Cole-Cole plot. This can be accumtely described by an Rc-RC network with the values shown in {a).

expected from equation 3.6. For different V, the values of R an C and change. Even accurate fits could can then be found. Also for the LiF /Ca/ Al cathode similar results are found.

Measurement of the LEP layer thickness

Using a frequency sweep, the thickness of the LEP layer L is checked. This is shown in figure 3.16. When at Viias = -lV, a frequency sweep is carried out, the attention goes out to the frequency range at which the phase angle is -7r /2 ~ 1.57 rad. In figure 3.16a it is

31

o.o....-~~,..-.~ ......... ~~......-~~-~ .......... -0.2

-0.4

-0.6

î -0.8 .!::. ê -1.0 <l

-1.2

-1.4

-1.6

• • • •• ••

• • •

._ ...... " ..•..... _"_""." ." 10 100 1000 10000 100000 1000000

f[Hz]

4.0 ................ "." ....... ... "" . .. "".

3.5 • • •

3.0

G:' .s 2.5 (.)

2.0

1.5

1.0

• • • • .•

10 100 1000 10000 100000 1000000

f [Hz]

Figure 3.16: A frequency sweep (a) can be used to see when t:::..rjJ = -n /2 rad and the LED behaves as a pure capacitor. At Viias = -1 V, when no current fiows, the value at low frequencies of the capacitance in (b) can be used to determine the thickness of the device through equation 3. 7.

shown that for all the low frequencies under 10 000 Hz, the LED behaves as a capacitor. For higher frequencies the contact resistance Re starts to become dominant and the phase angle increases. For the low frequencies the capacitance is related to the thickness of the device by equation 3.7. Thus from the capacitance (figure 3.16b), it is seen that C = 4 nF at low frequencies and therefrom it is derived that for this device L = 64 nm, assuming Er= 3.2 [4]. This is done for all our samples. By comparing the thickness measured by a surface profilometer and compare this with the values from impedance measurements found for different Er, the dielectric constant was found to be Er = 3.2 for blue polymers. This is somewhat higher than the typical values in literature for PPV giving Er = 3.0, but in agreement with previous findings [4].

32

Voltage sweep

A voltage sweep is applied to look for a peak in the capacitance. The results for f = 190 Hz are shown in figure 3.17 and the change in Cis shown for the two samples. It seems like no peaks appear. But when we zoom in around the area indicated by the arrows, a peak was found for the LiF /Ca/ Al-BP, i.e. the LED with the highest J(V)-curves. For Ba/ Al no peak appears. This might be a consequence of a possible injection harrier for the electrons, so that no charge is present in the device around Vbi· For LiF /Ca/ Al the normalized

5.o~~~~~~~~~~~~~~

4.8

4.6

4.4

4.2

f = 190Hz .·· ".".·

.·

!i:' E. 4.0 () 3.8

3.6 BalAI • BP / " __ "._.,_""" ••• "_."." ••••••• ""-•• !.:., ...... " •• _ ••• _ ••••• - ........ "·.·

3.4 1 / 3.2 =~:.'.=~~~.~:.: ................ "···

0.0 0.5 1.0 1.5 2.0 2.5 3.0

v_M

Figure 3.17: The capacitance C from an impedance measurement for different bias voltages at f = 190 Hz for the devices under investigation. The arrow indicates the area that did show a peak in capacitance for BP with LiF/Ca/Al when enlarged (figure 3.18}.

capacity (the capacity at each V divided by the capacity at V = 0) is shown in figure 3.18a for different frequencies between f = 90 Hz and f = 10 kHz. A very weak peak appears at Viias = 0.83 V. This is above the estimated built-in value from photovoltaic measurements (0.55 V). For the low frequency (f = 90 Hz) the peak is hidden in an other steep increase in capacitance. This increase is found for all frequencies, but starts at higher Vbias for increasing f. The real part of the impedance (resistance) is shown in figure 3.18b. It is clear that the rise in normalized capacitance is related to the peak in Z'. For increasing frequency the peak in Z' shifts to the right and also the steep increase in C shifts to the right.

33

1.04 ...---~-..--~--.-~--r-..--~----. (a)

3.ox10'~-~-..-~--....---~-~~

1.03 90 Hz

0.83V

> 1.02 . ." " ,.,. : : .·

."· .· .· . i 1.01

~~~g~f ;~f~~:~~-~'-'~_'._ 1.00

0.0 0.5 1.0

v~"M

1.5 2.0

(b)

2.5x106

2.0x101 f=90Hz.

I 1.s.10' Q. f..j 1.0x10'

5.0x10'

0.5

A

"".

1.0

v ••• M

1.5

Figure 3.18: An impedance measurement shows a peak in normalized capacitance at about 0.83 V Jor LiF/Ca/Al and BP (a). The real part of the impedance (Z') is shown in (b). A, B, and C represent the voltages where the increase in capacitance starts for three increasing frequencies. These three voltages are also shown in (b). They are related to the peak in Z'.

34

2.0

3.7.3 Electro-absorption measurements

During the electro-absorption measurements for electron-only devices it was noticed that the loek-in amplifier was not able to detect a signal of .6.R. Vbi for electron-only devices could not be measured using electro-absorption technique. To quantify this experimental finding, a simulation was carried out for the electron-only device using the software package "The essential Macleod" (Thin Film Center Ine.). This allows the user to simulate the reflectivity of the electron-only stack. The used reflection coefficient n = 2.0956 and the extinction ( absorption) coefficient k = 0.3041 at À = 410 nm were obtained from ellipsometry measurements within Philips Research. For À = 410 nm (close to the used value of 409 nm) it was simulated that the reflectivity is 86.843 for the electron-only stack. Suppose now that the applied modulation causes a change in absorption coefficient of 503. It is then found that the reflectivity changes 0.0263. This small signal that we are interested in, is detected together with the total reflected signal of 86.843 by the detector. This means that the modulated signal that we are looking for is about 3340 times smaller than the unmodulated background signal. The small signal due to modulation has a certain angular frequency w. Due to the large reflected signal however, the loek-in amplifier is not able to detect this desired signal. Electro-absorption will be used in chapter 7 on double carrier devices. For the transparent ITO /PEDOT:PSS the above mentioned problems do not arise since these materials have much smaller absorption coefficients ( at À= 410 nm kPEDOT:PSS = 0.025, krro = 0.0507 while kAl = 4.54) [20].

3. 7.4 Conclusions

• The values of Vbi are all small compared to the 1.6 eV expected from the difference in work function (figure 3.2) between single crystalline Al and Ba. We find values around 0.6-0. 7 V. An explanation for that could be that the Al might be oxidized during the fabrication forming a monolayer of Ah03. This is known [42] to have a lower work function than the 4.2 eV from pure Al. From our findings this shift is expected to be about 0.9-1.0 eV meaning that our device actually has an anode with an effective work function at 3.3 eV.

• It was not possible to find a difference between Ba/ Al and LiF /Ca/ Al samples within the experimental uncertainty of about 0.15 V. This suggests that there is nota large difference in barrier between the two cathode materials. We ascribe the uncertainty to the denoted issues of signal drift and lamp power. For the exact determination of the built-in voltages, the photovoltaic measurement is a fair method but has some limitations.

35

• The electro-absorption measurements for electron-only devices failed because of the high refiectivity of the Al anode.

• For deriving Vbi from the impedance spectroscopy measurements, the empirical method of looking at a peak in a voltage sweep during an was used. A very small peak oc­curred only for the LiF /Ca/ Al, but not for Ba/ Al. The values found here were close (within 0.3 V) to the ones from photovoltaic measurements. There was no large shift in Vbi, unlike the situation noticed for hole-only BP devices, where Vbi shifts about 1.7 V downwards when light is used [4J (2.4 V from impedance spectroscopy against 0.7 V from photovoltaic measurements and electro-absorption). This shift was ascribed to the use of a Au cathode.

• An overview of the found Vbi for electron-only devices for the different measurements carried out is shown in table 3.2.

• We choose to correct the J(V)-curves using the built-in values from the photovoltaic measurements, being 0.55 V for LiF /Ca/ Al and 0.67 V for Ba/ Al. This is certainly a good estimation and a change of a few tenths of a volt will not affect the results that are found in comparing the applicability of the different models.

Table 3.2: The values /or built-in voltage /rom several observations are summarized /or the electron-only device with the Ba/ Al cathode and the device with a LiF /Ga/ Al cathode. For the device with the Ba/ Al cathode, impedance measurement did not show an accurate result. The electro-absorption measurement failed /or devices with bath cathodes. Modeling denotes the values that will be used in the following sections /or correcting the measurements.

Vbi [VJ Ba/ Al photovoltaic measurement 0.68 + 0.15

impedance electro-absorption

modeling 0.68

36

Vbi [VJ LiF /Ca/ Al 0.55 + 0.15

0.83

0.55

Chapter 4

N umerical modeling

4.1 Transport equations describing polyLED device physics

Studies of J(V)-curves yield information about what process dominates the operation of a pLED. When the injection of carriers is not restricted by injection barriers, the carrier transport is called bulk-limited. For single carrier devices with ideal injection it was shown by Mott [30] that this leads to a space charge limited current (SCLC) that is equal to:

9 y2 IscL = SErEoµ L3 ( 4.1)

with µ the mobility, Er the dielectric constant, Eo the electric permittivity in vacuum, L the LEP layer thickness and V the voltage. This is also known as the Mott-Gurney law and is observed to provide a good description of experimental J(V)-curves in case of PPV hole-only devices at low fields. Here a constant µ is assumed.

In general however, the mobility depends on temperature, field, and concentration. To describe the problem to resolve J, three differential equations have to be solved, called the transport equations. These are introduced below. The total current is the sum of the electron current In and the hole current lp:

(4.2)

with nn the electron concentration, np the hole concentration, e the charge of an electron and E the electric field. It is assumed that the current is constant through the device: J(x) = J while nn(x), np(x), and E(x) are dependent on the position. The recombination rate (number of electron-hole pairs formed per second and per m 3) is

37

called R1 0c(x). Equation 4.2 leads to:

dJn dx

dJp dx

(4.3)

( 4.4)

In case of Langevin recombination, when recombination is based on a diffusive motion of positive and negative carriers in the attractive mutual Coulomb field, Rzac is given by:

(4.5)

with brec = 1 a recombination prefactor. The recombination rate is based on field­independent mobilities. Recombination leads to a decrease of the carrier concentration. From equations 4.3-4.4 it follows that the current density gradients are then given by:

dnp dx

eR1 0 c(x) [ 1 dµn (E(x)) 1 dE(x)] µn (E(x)) eE(x) - nn(x) µn (E(x)) dx + E(x) ~

eR10 c(x) [ 1 dµp (E(x)) 1 dE(x)] = - µP (E(x)) eE(x) - np(x) µp (E(x)) dx + E(x) ~

(4.6)

(4.7)

with E the electric field. These equations are known as the continuity equations (particle conservation). The field itself should satisfy Poisson's law

(4.8)

with f the dielectric constant and p the charge density. These three coupled differential equations 4.6-4.7-4.8 determine F(x), nn(x) and np(x) together with two boundary conditions which are necessary to predict J(V). N ote that in all the modeling of electron-onlies np ( x) = 0 so the pro blem sim plifies to solving (from equation 4.2 and 4.8)

(4.9)

(4.10)

38

with a boundary condition for the carrier concentration at the cathode/polymer interface. The boundary conditions are dependent of the injection. In section 4.3 they will be dis­cussed. In some situations the problem can be solved analytically [16, 22]. In this report, a numerical solution is generated using a computer program developed within Philips Re­search.

4.2 Models on the electron mobility

4.2.1 Field and temperature dependent mobility

A first approach is to start from the space charge limited current and ~dd a dependency of the mobility on the temperature:

(4.11)

or to take the mobility also field dependent. In the latter case, a novel self consistent solution of equations 4.2-4.8 must be found and equation 4.11 is no longer valid. The mobility is parametrized using a field dependency factor "fn, a mobility at zero field µn,o, and an effective energy harrier An that determines the temperature dependence of µn,o [21]:

µn (T, E) = µn,oexp [- ~~;] exp [ 'Ye (T) JE J (4.12)

where the field dependency factor 'Yn(T) is itself temperature dependent through a char­acteristic Tn,o:

'Yn(T) = Bn ( k;T - kB~n,o) . (4.13)

These equations are empirically found and originate from the fair results mainly for hole­only devices ([24]).

4.2.2 Trap filled limited mobility (TFL)

J(V)-curves of e--only devices often yield steep slopes. This is also seen fora semiconductor with traps that are exponentially distributed [35]:

( Nt) (E- Ec) nt (E) = kTt exp kBTt (4.14)

with nt(E) the trap density of states at energy E, Ec the energy of the conduction band, Nt the total density of traps and kBTt an energy characterizing the trap distribution. The

39

traps will be gradually filled with increasing local carrier density, i. e. with increasing field and the current will increase very fast until all traps are filled. The problem can then be solved analytically for the exponential trap distribution given above. This can be applied to J(V)-curves of electron-only devices. This theory implies

(4.15)

with r = Tt/T, Nc the effective density of states in the conduction band, and C(r) = rr (2r + 1r+1 (r + l)-r-2

. Carriers that occupy trap states have an indirect effect on the conductance since they still contribute to the charge density. This theory has been applied for the explanation of the steep slopes of J (V)-curves of e - -only devices with Ca/PPV /Ca [36] of thicknesses larger (220 - 370 nm) than the ones that are handled in this report. These results shown in figure 4.1 are considered as the main­stream theory behind electron-only devices. Also for small molecule LEDs (Al/ Alq/Ca

10'

100 Hole Only 310nm

300 ~."!) ... ············· 10·1

10·2

N

E ~ 10·3

''Û'· -,

10"

10·5 . L=220 nm

10-6 1 10 100

Vbias (V)

Figure 4.1: Thickness dependence of J(V)-curves (dots) for PPV electron-only devices is described by a trapped filled limited current (solid lines) /36}.

devices) the thickness dependence has been described using traps for L = 97 - 294 nm by Brütting et al. [37], on the condition that a field and temperature dependent mobility was included of the form of equation 4.12. We note that the model including traps has never been successfully applied to blue polymers, nor for different classes of polymers than PPV like the fluorenes used in this report.

40

4.2.3 Concentration dependent mobility

Previously the mobility was only described in terms of its field and temperature de­pendence. It was found from comparing the field-effect mobility of OC1 C10-PPV in a field-effect transistor (FET) application with the typical hole mobility in a LED with the same polymer, that the mobility differs over more than 3 orders of magnitude (from µFE ~ 10-4cm2 /Vs to µP ~ 10-7 cm2 /Vs) [39]. This was explained by the fact that one important parameter was overlooked: the carrier concentration dependence. In a FET, the applied gate voltage gives rise to accumulation of charge in the region of the semiconducting layer close to the insulator. As these accumulated charge carriers fill the lower-lying states of the organic semiconductor, the additional charges in the accumulation layer will occupy states at relatively high energies. Hence these additional charges will move easier to neighboring sites, resulting in an increased mobility. This theory was intro­duced by Vissenberg and Matters [40] and applied to explain the temperature dependence of the field-effect mobility in a thin-film transistor. In a disordered semiconducting polymer the tail of the density of states (DOS) is shown to be Gaussian [45] (equation 2.1). In the following subsection it will be shown how this infiuences the mobility.

Gaussian DOS

Recently Pasveer et. al [41] studied the carrier concentration dependence of the mobility in a Gaussian DOS, characterized by a width of the Gaussian er (equation 2.1), through an exact numerical solution of the Master Equation, that represents hopping of charge carriers on a lattice of sites. The equation describes a relationship between the occupation proba­bilities of all sites on a lattice. The solution is thus in terms of the carrier concentration p and can be converted to current. Then they showed that the found p- and E-dependence from the numerical solutions were successful in describing the experimental p- and E-dependence of the hole current in NRS­PPV LEDs for er= 0.14 eV. In their approach, the dependence on the field and the dependence on the concentration are separated and the mobility is then parametrized and can be expressed in terms of a density-independent prefactor f (T, E) in combination with a density dependent mobility µ(T,p):

µ (T,p, E) ~ µ (T,p) f (T, E). (4.16)

In this case the p-dependence ofµ for different temperatures can be well described by

( 4.17)

41

with a the width of the Gaussian, p the concentration, Nc the site density of electron transporting sites, and the power ó given by:

(4.18)

The temperature dependence of the mobility prefactor for the special case of NRS-PPV LEDs discussed in their paper is described by:

( 4.19)

with P1 = 0.42 and P2 = 1.8 x 10-9 m2 /Vs. Finally, the field-dependence could be parameterized by

f (T, E) ~ exp [ 0.44((a /ksT) 312 - 2.2) ( !+ 0.8 ( E:a) 2

- 1)] (4.20)

with a the average intersite distance. The quality of the parameterization is shown in figure 4.2. The dots are the results from the solution from the Master equation. The results of the parameterization equations (solid lines) 4.16, 4.17, and 4.19 to describe the dependency of the mobility on the concentration are shown in the left picture for typical value of the inverse localization wavelength (a = 10/a) for values of a/kBT up to 6. The typical concentration value for LEDs is p = 10-5a-3 while for FETs the concentration is around p = 5 x 10-2a-3 . This picture explains the higher observed field-effect mobility in FETs compared to the hole mobility in LEDs. The right picture shows the results for the parameterization of the field dependence of the mobility for the typical LED and FET values. This shows that the parametrization is optimized for the low-density region, that is important in LED applications and hence this report.

4.3 Electron injection in polymer LEDs

To solve the differential equations 4.6-4.7-4.8 a boundary condition is needed. For electron­only devices we need to know the carrier concentration at the cathode/polymer interface.

4.3.1 Ohmic injection

By definition, in an ohmic contact the carrier concentration at the contact L is independent of the field at the contact. If the carrier concentration at the cathode-polymer interface (L) would be infinite ( nn ( L) = oo) at high field, enough carries are available to be injected. However physically nn(L) can not exceed the LUMO site density Nc· Upon modeling

42

:4' 10-"' :::1.

10·"li.......--::::..

10·"' ~~~~~~~~~~~~~~~ 10"; 10·• 10"' 10" 10~ 10·1 10-15 ~-~~-~-~-~-~-~-~

P [a-3] 0 2

E [o/ea) 3

Figure 4.2: The parameterization {lines) of the Pasveer et. al [41} equations introduced in this section describe very well the dependence of mobility on concentration p {left). Also the dependence on the field E for a typical concentration in a LED is very well described {right picture). The inset shows that the parameterization is not so accurate for a typical FET concentration at high fields.

J (V)-curves under the assumption of an ohmic contact, the carrier concentration is taken equal to half of the site density of the electron transporting unit Nc:

(4.21)

This situation occurs when the Fermi level of the injecting metal coincides with the LUMO level of the semiconducting polymer and is shown in figure 4.3.

Figure 4.3: Ohmic injection. There is a match between the Fermi level of the cathode and the LUMO level of the polymer, resulting in ideal injection.

43

4

4.3.2 Injection-limited modified Schottky harrier

Injection-limitation occurs due to a finite concentration of charges at the contact. Then it is possible that at high fields there are not enough charges available to be injected and the current is limited. Good results to describe this occurrence are found for the Scott­Malliaras modified Schottky model [31, 32]. This takes into account surface recombination, charges recombining with their own images, and results in:

(4.22)

with il> B the injection harrier, q the electronic charge, E the electric field, E the organic permittivity, kB Boltzmann's constant, T the temperature, and

(4.23)

with f = e3 E/47rEk~T2 the reduced field. In equation 4.22 a term is subtracted from il> B as a correction for the image charge effect. When an electron is injected, a hole is created in the cathode. The actual harrier height then reduces by the attractive interaction between the injected electron with its image charge in the metallic electrode. This is shown in figure 4.4. The reduction of the harrier height, .6.if>(E) is dependent on the field:

.6.if>(E) = /eE. v~ (4.24)

The effective electron concentration at the cathode/polymer interface (at distance L from

LUMO 4>B

~1 1

4>B

EF

Figure 4.4: Schottky hamer model for injection. The harrier cl> B is lowered to «I>'a by the Coulomb field, binding the injected carrier with its image charge within the electrode. The dotted line represents the situation when this image charge would have no infiuence.

44

the anode) that will be used as the boundary condition in the simulation program is assumed to be given by a Boltzmann factor

(L) _ N (-e(<I>s - .6.<I>(E(L)))) nn - cexp ksT . ( 4.25)

By making a comparison with equation 4.22 it is seen that 4'1j; 2 ~ 1. In appendix A it is shown fora L = 100 nm sample that this will lead to an error of a factor two above 2 V, which would lead to an error in the fitted value of <I> B of 0.05 eV or less. For our purposes, this simplification is therefore allowed. We note that the equation above is a good approximation to the Fermi-Dirac distribution function if <I> B - .6.<I> » ksT.

4.3.3 lnjection in a Gaussian DOS

It has been assumed that the DOS is Gaussian distributed within the polymer. Therefore it is expected that also injection at the interface has to be treated as injection into a Gaussian DOS. Leading work in this area has been carried out by Wolf, Arkhipov, and Bässler. They studied the current injection from a metal to a disordered hopping system, through Monte Carlo simulation [33] and compared this to an analytic theory [34]. They claim that the primary injection event is essential and determines the temperature- and field dependence of the injection process. First a carrier jumps into the semiconductor and then it has a certain probability to escape or fall back to the electrode. The idea of injection into a Gaussian DOS is shown in figure 4.5. Lower states become available and injection is improved. The Gaussian width at the interface is called a int in order to include the option of a different Gaussian distribution at the interface than the one in the bulk abulk· This different disorder at the interface is assumed e.g. by Baldo [38] who claims that for Alq3 aint = 0.40 eV is much higher than the bulk value of abulk = 0.13 eV. Typical PPV-values for the bulk value for holes are abulk = 0.112 eV [47] for OC1C10-PPV or abulk = 0.14 eV for NRS-PPV [41]. The used approach in this report for the electron concentration at the anode, is an extension of the classica! thermionic emission model similar to the Arkhipov approach. Because of

45

the Gaussian width there is an enhancement g.

Nc 1+00

(-E2 ) 1 dE exp -.- !2.:::§.E J27iCJint -oo 2CJmt 1 + exp kBT

Nc 1+00 (-E2 ) 1 dE exp -- E .P'

J27iCJint -oo 2CJint 1 + exp~ kBT

(4.26)

Note that this effect is only of importance if there is an injection barrier. If there is no injection barrier, the outcome of the integral is Nc/2, and this is high enough to insure ohmic-like injection.

"'a "'' B

O'int

LUM

Figure 4.5: Schematic representation for injection into a Gaussian DOS. The LUMO level at the interface is not taken as a delta-shaped function but has a spread in energy that is Gaussian. This enhances injection.

Summarizing, an overview of the models that will be investigated is given in table 4.1.

46

Table 4.1: Overview of the applied models and the used free parameters. "Conventional" stands for the field and temperature dependent mobility, "traps" for the trap filled limited mobility, "Pasveer et. al" for the concentration dependent mobility with a Gaussian DOS, and Gaussian injection for the Pasveer et. al model with injection into a Gaussian DOS. "auto" indicates that the model already describes the dependency of the quantity in that row. The asterisks (*) indicate that these values are taken fixed in our modeling studies.

conventional traps Pasveeer et. al Gaussian injection E-dependence Bn & Tn,o Bn & Tn,O auto auto T-dependence ~n ~n Pi & P2 Pi & P2

p-dependence auto auto injection harrier <I>B <I>B <I>B <I>B trap sites Nt trap distribution Tt disorder bulk (1 Cl bulk

disorder interface Cl int site density* 1.5 x 1027 /m3 1.5 x 1027 /m3 1.5 x 1021 /m3 1.5 x 1027 /m3

relative permittivity* 3.2 3.2 3.2 3.2

47

Chapter 5

Modeling of the electron current in blue electron-only diodes with a Ba/ Al cathode

The applicability of the three different models explained in section 4.2, being the field and temperature dependent mobility model, the trap filled limited mobility, and the con­centration dependent mobility in a Gaussian DOS, will be investigated in detail for the electron-only devices. Since the main goal is the full characterization of the Al-BP-Ba/ Al diodes, we start with the modeling of this device. In the next chapter LEDs consisting of Al-BP-LiF /Ca/ Al are examined.

5.1 Experimental J(V)-curves

J(V)-curves for devices of a stack of Al-BP-Ba/ Al with six different thicknesses of the LEP layer between 55 nm and 161 nm are shown in figure 5.1. All the curves are corrected for V bi = 0.68 V from photovoltaic measurements and for a symmetrical leakage current as described in chapter 3. The current density decreases with increasing thickness. From figure 5.la, it is clear that the data does not obey a power law behavior J ex vx over the entire range of the applied voltage. This is a first difference compared to the electron-only J(V)-curves for OC1 C10-PPV described by the Blom group [23]. A second important finding is the high slope of the curves. As indicated for the 55 nm sample the slope for (V - Vbi) = 1 to 2.5 V (J < 10 A/m2) is about 5, while for higher V - Vii (J > 10 A/m2) the slope has increased up to 8. Figure 5.lb shows the J(V)-data for a temperature variation between 293 K and 193 K, in steps of 20 K. The current density decreases with decreasing temperature. For lower

48

temperatures, the slopes at the highest V increase even further up to 15 for J > 10 A/m 2

at T = 193 K.

1000..----~-~-~~~~~-~

100

10

î 0.1

..., 0.01

1E-3

1E-4

L = 161 nm

1E-5+---~-~-~~~~~---' 1 10

1000 {b)

100

10

NÊ 0.1 ~ ..., 0.01

1E-3

1E-4

1E-5 1 10

Figure 5.1: (a) Thickness dependence of J(V)-curves for BP with Ba/Al cathode on a double logarithmic scale for samples of L = 55 - 78 - 92 - 122 - 158 - 161 nm. {b) J(V)­curves at different temperatures between 293 K and 193 Kin steps of 20 K for L = 122 nm. All the data were corrected for Vbi = 0.68 V and a symmetrie leakage current.

5.2 Modeling using the field and temperature dependent mobility model

In this section we investigate the appropriateness of the field and temperature dependent mobility model, discussed in section 4.2.1. As noted before, this was the basis of the first successes in modeling of J(V)-curves of hole-only and double carrier devices. The model yields a quadratic behavior for the voltage dependence for low voltages at which the field dependence of the mobility is only weak. High slopes of the J(V)-curves are obtained at high voltages, due to the exp( 1../E) field dependence of the mobility ( equation 4.12) 1.

The results for a thickness variation at 293 K are shown in figure 5.2a for the situation without an injection barrier. The mobility µn and the 'Yn are optimized for the 122 nm

1 Note that the field dependence for the field and temperature dependent mobility model (and also for traps in the next section) will be described in terms of 'Yn· This will be optimized at different T. This is equivalent to describing the field dependency in terms of En and Tn,o through equation 4.13. The temperature dependence for the field and temperature dependent mobility model was included in the report by changing manually the mobility µn (T) at each T. From all these values .6.n can be derived as in equation 4.12. The values for En, Tn,o, and .6.n will only be derived ifthe field and temperature dependent mobility model is found to hold for our devices.

49

sample so that the simulation was perfect at room temperature for V = 0.92 V and for V = 10.32 V. Then the intermediate voltage regime (2-7 V) can not be described better than shown. More important, the thickness variation is not well described. When introducing an injection harrier of intermediate value 0.40 eV (other intermediate values of harriers yielded similar results) in figure 5.2b, the current density will be somewhat lower at higher V, and therefore a somewhat higher mobility µn is required. Then still the best possible simulation does not accurately describe the J(V)-curve of the 122 nm sample nor the thickness variation. The approach will be now to look now at different T, optimizing again µn and "fn, and see if the simulations describe the experiments. An important issue will then be if the mobility follows exponential behavior ( equation 4.12) with the field and if the temperature dependence of 'Y is described through equation 4.13. We analyze the data for the 122 nm sample and look at the measurements at different T.

1000 1000 (a) (b)

100 100

10 10

î 0.1 NÊ ~ 0.1 ..., ...,

0.01 0.01

1E-3

1E-4 1E-4 <1>

6 = 0.40 eV

10 10

V-V.;M V-V.,M

Figure 5.2: Simulations of the J(V)-curves for a thickness variation using the field and temperature dependent mobility. ( a) shows the results without an injection barrier for 'Yn = 1.24 x 10-3 (m/V)11 2 and µn = 3.7 x 10-15 m2 v- 1 s- 1 optimized for L = 122 nm. (b) shows the results, for an injection barrier <I> B = 0.40 e V for ( again optimized for L = 122 nm) 'Yn = 9.98 x 10-4 (m/V)11 2 and µn = 3. x 10- 14 m2 v- 1s- 1 .

For each T, the fitting was carried out by adjusting two parameters: µn,oexp [-eb.n/kBT] (the term before the second exponential in equation 4.12 which we will denote as µfit) and 'Yn· These were adjusted so that the simulation was perfect at room temperature for a point at low V = 0.92 V (somewhat higher for low T) and one at highest V. The fits (solid lines) are shown together with the experimental data (dots) in figure 5.3a without an injection harrier and in 5.3b with <P B = 0.40 eV. It is impossible to fit the data for all temperatures at the same time accurately for intermediate V, except at the two lowest

50

temperatures. It seems that there is no large difference in the shape between the ohmic injection fit and the injection-limited one. µfit should show an exponential behavior on temperature, because of equation 4.12. This is not the case, as indicated by the deviation from the dashed line in 5.3c. Also 'Yn does not vary linear with 1/T (dashed line in figure 5.3d) as expected from equation 4.13. This means that the actual fits described by the field and temperature dependent mobility (values on the dotted line) will be worse for lower temperatures (not shown here). Furthermore, for each thickness, another set ofµ fit and 'Yn was required (not shown). If this model would be physical correct, it would provide one set of fitting parameters that can be applied for all thicknesses, giving better fits than the ones shown here, and of which the temperature dependence could be explained using the denoted equations 4.12-4.13. However this is not the case.

5.3 Modeling using a trap filled limited (TFL) mobility

As a next attempt to model the J(V)-curves, the model using traps (section 4.2.2) is used to analyze the data. It is recalled that this model provides a successful description of electron mobility OC1 C10-PPV [23]. The J(V)-curve in this model is determined by three parameters: the carrier mobility µn, the trap density Nt, and the trap distribution param­eter Tt. The latter follows directly from the slope of the logJ-logV characteristic in the TFL regime. We start using the successful approach followed in the article of the Blom group [36] for PPV electron-only devices and look at the TFL mobility model for a field-independent mobility. The trap distribution parameter Tt follows from the slope of the measured curve. The 122 nm sample showed a slope of around 6.5 for higher V. According to equation 4.15, this yields Tt = 1611.5 K resulting in a width of the exponential trap distribution of kBTt = 137.5 me V. Note that this value is comparable to the value of Tt = 1500 K found by the Blom group for PPV. In this first attempt to simulate the data, a typical 2 LED electron mobility of µn = 1 x 10-10m2v-1s- 1, as in the article of the the Blom group, is assumed. Then the number of trap sites Nt is optimized for fitting. Figure 5.4 shows the best possible result. This was found for Nt = 1.3 x 1024 m-3 (0.0683 traps). Above 5 V, the fit starts bending off as a result of the fact that trap sites are getting filled. A gradual transition to ordinary space charge limited current occurs, associated with a quadratic J ex: V2 dependence. If the trap concentration would be increased, the bending would start at higher voltages but then the J-values would be too low.

2 This value is found for red OC1 C10-PPV but is of the same order as a typical value for green fiuorene­based polymer [43]10-9 m2V- 1s-1

. It is noted that the actual value of the mobility can still differ from these values but these values seem a good starting point. Even a change in mobility of two orders will only change the found parameter for optima! trap concentration, while the result for the applicability of the model will not change.

51

1000

100

10

1

NË 0.1

~ 0.01 ..,

1E-3

1E-4

1E-5

1E-6

V-v., [V]

(c) o-----c 1 E-14

0 ------•---~ <1>

8 = 0.40 eV

1 E-15 ····-o.. ;;-----1E-16 1E-17

~ 1E-18 NS 1E-19 '-;f 1E-20

1E-21 1E-22 1E-23

-. .,_ /"

no harrier """"

0

10

--- 0

0

1 E-24-i-.~~~~~~ .......... ~~~~~.-.--1 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4

1000fî [K"1)

1000

100 (b) 11>

8 = 0.40 eV

10

1

N~ 0.1 E ~ 0.01

....., 1E-3

1E-4

1E-5

1E-6 10

V-V.,M

0.0032~~~~~.....--.~~~~~~~~

0.0030 (d) 0.0028 0.0026 0.0024

i"' 0.0022 ~ 0.0020 - 0.0018 ~ 0.0016

0.0014 0.0012 0.0010

0

""" 0

3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4

1000fî [K"'J

Figure 5.3: Simulations (solid lines) of J(V)-curves for field and tempemture dependent mobility model and comparison to experimental data {dots) of a 122 nm sample of BP with a Ba/ Al cathode. The T-dependence is fitted from room tempemture to 193 K in steps of 20 K, without an injection barrier (a) and with an injection barrier of if>B = 0.40 eV {b). The fits were chosen in a way that one point at low V and one point at high V matched. The field dependent mobility µfit at different T for optimal fits is shown together with the

expected exponential behavior ( dashed lines) from equation 4 .12 ( c). The optimal field de­pendent factor 1'n is shown at different T with the expected linear behavior ( dashed lines) from equation 4.13 {d).

By increasing the mobility the curves shift upwards hut the bending remains. If now also the trap concentration is increased, what will prevent the traps of getting filled in the used voltage range, the increased trap density leads to a lower J(V)-curve, so the mobility has

52

to be further increased. An example for increased mobility is shown for 0.333 traps and µn = 1.42 x 10-1 m2v- 1s-1 in figure 5.4b 3 . The predicted curves are straight lines while the slope of the experimental data increases with increasing V. Furthermore the thickness variation is not at all well described. If the trap concentration is increased to a higher value, up to several percents, the fits do not improve (see footnote) while the mobility becomes a few orders larger, bringing it toa value much higher (above 10-5m2v-1s-1) than earlier observed electron LED mobilities (10-9m2v-1s- 1 for green fluorene-based polymer [43] or 10-10m2v- 1s-1 for PPV [23]).

1000 (a)

1000 slope = 6.5 (b)

100 ,/-·· 100

10

1 10 experimental data

122nm

NE 0.1 NE ~ ~ 0.1 ...., 0.01 simulation

..., 1E-3 0.01

1E-4 1E-3

1E-5 1E-4 1 10 1 10

V-V01

M V-V0,M

Figure 5.4: Simulations of J(V)-curves for the trap filled limited mobility model, using a trap depth of 137. 5 me V. ( a) shows the result for a typical value of mobility in a LED of µn = 1x10-10m2 V- 1s-1, for 0.0863 traps. There is a transition to quadratic behaviour becaus of filling of traps. In {b) the mobility is increased to µn = 1.42 x 10-7 m2 V- 1 s- 1 and the trap concentration is increased to 0.33% to prevent the filling of all the trap states.

Next it was investigated whether the inclusion of field dependent mobility, an injection barrier, varying the trap concentration, variation of the trap depth or a combination of these parameters was able to describe the experimental J(V)-curves. Therefore an exten­sive study of possible combinations of a wide range of parameters was carried out. This is discussed in appendix B. The main conclusion is that no combination of parameters for the

3It is noted that two of the parameters in this model, being the mobility and the trap concentration are equivalent as long as the regime where the traps are getting filled is not reached. This means that for traps that are not significant getting filled, changing the mobility and hence the trap concentration at the same time will cause exactly the same fits for one J(V)-curve and vice versa (changing the trap concentrations). In other words, if here the concentration of traps was taken much higher, then we would end up with a mobi!ity that was also higher but the fit for the 122 nm sample would look exactly the same and vice versa.

53

trap model is able to describe accurately the J(V)-curves of a device with a Ba/ Al cathode for one thickness at all V. One of the main arguments for rejecting the TFL mobility is that we measure increasing slopes while this model expects decreasing slopes, due to traps that get filled) or because of the inclusion of a harrier. Further a variation of thickness and temperature is not predicted correctly at all either. It is noted that as indicated in section 3.1 the và.lue for the site density Nc is assumed to follow from the average intersite distance a. For the blue polymer under investigation, the estimated values are between Nc = 0.75 x 1027 m-3 (a = 1.10 nm) and Nc = 1.5 x 1027 m-3 (a = 0.87 nm). The shown discussion is for the upper limit of Nc = 1.5 x 1027 m-3 . The main contribution of Nc will be to the percentage concentration of traps (Nt/Nc)· For the lower limit of Nc, result­ing in slightly different fitting parameters, the parameterization method described below was also examined but the results for the applicability of the model with traps were similar.

In the next section, a model within which the mobility increases with the voltage because of an increasing concentration will be considered.

5.4 Concentration dependent mobility in a Gaussian DOS

Our next approach is to study the effect of a concentration dependent mobility in com­bination with a Gaussian DOS, as described in subsection 4.2.3. The important physical parameter is now the width of the Gaussian ( o').

5.4.1 Gaussian DOS without an injection harrier

We first assume ohmic injection of the electrons, i. e. energy level matching of the cathode metal Fermi level Ep and the LUMO level of the polymer. In this model O' is the dominant parameter. The field dependence is already included through equation 4.20. We first notice that increasing O' results in an increased slope. This is shown in figure 5.5a. Here the mobility prefactor µo(293 K), that shifts the whole curve upwards or downwards, is changed for every O' 4 . The simulations are almost straight lines on a log-log scale. When now the experimental data of the L = 122 nm device is simulated, a Gaussian width of O' = 0.36 eV leads to a good fit for a low data point at V - Vi; = 0.92 V and a high V - Vbi = 10.32 V point (figure 5.5b). However the curvature

4 The value of the prefactor should not be compared to the actual mobility µn from the last section. The mobility in this model is given by equation 4.16. If cr is high, the prefactor will be very low, Jike the 10-3s m2 /Vs we find for cr = 0.38 eV in figure 5.5, while the actual mobility (product ofthis prefactor with the concentration and field dependent term), is of the order io- 12 m2 /Vs. It is noted that the mobility is now different everywhere in the device (because the concentration is different) and at all V (due to the field dependence) and at every T (cr/ksT changes).

54

of the best possible simulation does not match the experimental data and the results for the other thicknesses are not described accurately at all.

1000 (a)

100

10

N" E ~ 0.1

~~nment . · "• _...a- 0.2 eV

0 · •• •• .··

a= .3 ev ............. ···· •• •• ... ·· o=0.1 eV ...,

0.01

1E-4 1 10

V-V.,M

Figure 5.5: Simulations of J(V)-curves Jor the concentration dependent mobility with a Gaussian DOS. (a) Simulation for different a for L = 122 nm. For each a another mobility pre factor µ0 (293 K) is used to yield values of J in the desired range (10- 4 _

1 d3 A/m2 ). (b) The optimized simulation for fitting the experiment is a = 0.36 e V and µo(293 K) = 1.30 x 10-3s m2 /Vs is shown. The arrows indicate the data files that accom­pany the simulations.

5.4.2 Gaussian DOS with an injection harrier

Schottky injection harrier

Again, in order to take the possible mismatch between energy levels of the LUMO and the Ba/ Al (figure 3.2) into account, an injection harrier is introduced. It was found that fora= 0.22 eV, a harrier of <I> B = 0.52 eV, and µo(293 K) = 2.02 x 10-13 m2 /Vs the data for the 122 nm sample could be fitted very well. Then the thickness was varied, as shown in figure 5.6. There is very good agreement between experiment and simulation for the whole range of thicknesses. Although there is some small deviation for the thick-est sample at higher field, this is the first model that is able to describe the J(V)-curves accurately for a large range of thicknesses for a fixed set of fitting parameters. The found a = 0.22 eV is higher then the 0.10-0.14 eV values found for holes for various types of PPV-based polymers. This means that we face a a/kBT that is of order 8, which is much higher than the values for which the used analytica! compact expressions for concentration and field dependence of the mobility are optimized (figure 4.2). We now investigate how sensitive the model is for the injection harrier for a fixed value

55

1000

100

10

NE ~ 0.1 ....,

0.01

1E-3 "= 0.22 eV <1>

8 = 0.52 eV

1E-4 10

V-V.,M

Figure 5.6: Simulation of the J(V)-curve for the concentration dependent model with a Gaussian DOS with width a = 0.22 e V in combination with an injection barrier <l>B = 0.52 eV for µ 0 (293 K) = 2.02 x 10- 13 m2/Vs. This is the first model that is able to describe a thickness variation for L = 78 - 158 nm.

of a = 0.22. The simulation for three different harriers is shown in figure 5. 7. For each harrier height, the mohility prefactor µo(293 K) is changed in order to fit the data at V = 0.92 V. We note that for a harrier of <I> B = 0.35 eV, there was only minor difference compared to the ohmic injection. When the harrier is increased and the mohility prefactor lowered, the slope increases. For <I> B = 0.52 eV there is a match with the measured data. Further increasing of the harrier (and decreasing µo (293 K)) again decreases the slope. For a a < 0.22 eV it was not possihle to fit the measurement. Further it was found that the error in the value from fitting for the harrier is rather small. Already from a small variation of <I> B, larger then a few hundredths of a volt, the simulations were not accurate anymore. However, it was pointed out in appendix A that a modified Schottky model is used that causes a small deviation at higher V from the actual Schottky-Mott model. Therefore we include a somewhat larger uncertainty of <I> B = 0.52 + 0.10 eV. Also the error in a from fitting is rather small: a = 0.22 + 0.02. Suhsequently, it is checked if this model is capahle of descrihing the temperature depen­dence. We focus on the 122 nm sample. All the parameters remain the same, hut there is need for determination of µo (T). In a first approach this parameter was implemented manually for 293 K. It was noticed that all thicknesses were very well descrihed using this same µo(293 K), which is an important requirement. Then the optima! µo(T) fitting values from 293 K to 193 K were determined. In figure 5.8a the µo(T) (open circles) are very accu­rately descrihed in terms of equation 4.19 for P1 = 0.17747 and P2 ~ 1.4864 x 10-7 m2 /Vs

56

1000y-,---~--~~~~--~--.

100

10

1 ~ 0.1 ....,

0.01

1E-3

11>8 = 0.52 eV

8 = 0.70 eV

10

Figure 5. 7: Simulations of J(V)-curves for L = 122 nm for three injection barriers in combination with a Gaussian DOS Jor a = 0.22 e V. The mobility pre factor µo (T) was changed for every barrier in order to let the simulation coincide with the V = 0.92 V data point. For small 'l>B = 0.35 eV (µ 0 (293 K) = 3.4 x 10-13 m2/Vs), the slope of the sim­ulation is too low. For higher '1> B = 0.52 e V (µ 0 (293 K) = 2 x 10-13 m2 /Vs), the slope of the injection-limited fit increases. Further increasing of the barrier to '1> B = 0. 70 e V (µ 0 (293 K) = 4.3 x 10-9 m2 /Vs) leads to decreasing slope.

(straight line). The value for P1 deserves some discussion however. It is a measure for the temperature dependence of the mobility. It is shown by Coehoorn [48] that for organic semiconductors where generally is assumed Nc/ci = 10-3 , 0.44 < P1 < 0.50 for various semi-analytical models. The value found in this work reveals a much lower temperature dependence. A possibility is that we are not dealing with a situation of N c/ a 3 = 10-3 .

Then the expected value of P1 can be lower than 0.44. The temperature dependence can now be very accurately described, as shown in tl.gure 5.8b. There is some deviation for lower V, especially for T = 253 K and 233 K. This could be explained by the fact that our model does not takes diffusion into account. For very low T, 213 K and 193 K, there is also deviation for high V. Maybe the model has to be adjusted for such a high er /k3T > ll. These values are much higher than the ones investigated in literature until now. Currently the field-dependence is described by the Pasveer et. al parameterization, equation 4.20. In the Pasveer et. al paper, it was shown that the used parameterization for the field dependence is very accurate below a field of E = 3 er/ ea. For our 122 nm sample at high V = 10.32 V, starting from er= 0.22 eV, we encounter a field of about 0.33 er/ ea. This is much lower then the value where the parameterization of the field

57

(a) 1E-1~ "'--,

1E-14 "''' 1E-1& ''><,

'iii" ',..._ <'. 1E-16 '"-\

NE "" :::::1- 1E-17 '"' ' optimal µ0(T) "-~ 1 e-1s 'l "-.Z - µ0(aii..,T)=P2exp[-P1(a/k8T) ""

1e-1e. P,=0.17747 ""'·"" 1E-20 P,=1.4864e-7 m

2Ns "'

1E-21+----.--~--.-----,..---.----,-----i 8 10 11

crfk,,T 12 13 14

1000

100

10

.r' 0.1 E ~ 0.01

..., 1E-3

1E-4

1E-5

1E-6

(b)

er= 0.22eV cll

8 = 0.52 eV

10

Figure 5.8: Simulation of J(V)-curves of an electron-only device with a Ba/Al cathode for a concentration dependent mobility in combination with a Gaussian DOS (a = 0.22 e V) and an injection barrier of <Ï>B = 0.52 eV (b). For the mobility prefactor µo., the temperature dependence shown in (a) is assumed with P1 = 0.17747 and P2 = 1.4864 x 10-7 m2 /Vs.

is not accurate anymore. It is shown in figure 5.9 that the effect of the field is small at this a /ksT. The solid line shows the fits fora concentration dependent mobility in a Gaussian DOS for a = 0.22 eV with the injection harrier of <I> B = 0.52 and the mobility from figure 5.8 and the inclusion of the field dependence from the Pasveer et. al parameterization. The dotted line shows the fit for the same situation, but without any field dependence. There is hardly any difference at T = 293 K. If now the same is clone for T = 193 K, there is some more deviation. Now a voltage of 14.3 V is applied resulting in 0.46 a / ea . This is still well below 3 a /ea where the parameterization fails. This shows that the parameterization for the field, optimized for a/ksT < 6, is still usable in our situation.

58

Figure 5.9: Simulations with and without the electric field dependence of the Pasveer et. al model are shown to denote the importance of the field dependence. The dotted line is the measurement, the dashed line a simulation without field dependence and the solid line a fit with the field dependence from the Pasveer et. al parameterization [41}. There is only small contribution at T = 293 K. At lower T = 193 K, there is a larger effect.

59

Injection treated into a Gaussian DOS

The J(V)-curves for Ba/ Al using an injection barrier are very well described by the Schot­tky injection model. However the question is whether one should in fact model injection as described in section 4.3.3 (injection into a Gaussian DOS). In this approach also states at lower energy become available, as was depicted in figure 4.5. It will then become easier to inject an electron and the J(V)-curves will be shifted upwards. It is possible that the disorder at the interface differs from the bulk value. Hence we dis­tinguish in the next discussion between aint at the interface and abulk for the bulk value. Furthermore it is also interesting to see how the shape of the J(V)-curve is affected. There­fore bath infiuences are shown separately. It seems wise to start from the value that showed the best fits using the Schottky model, being abulk = 0.22 eV, <I>B = 0.52 eV andµ given by equation 4.16 with the parameters for µo(T) found in the previous section (P1 ~ 0.18). Figure 5.lüa shows the J(V)-curves for different values of aint· Also the result from the previous section using the Schottky model is shown. As expected, the injection into a Gaussian density of states is much easier, resulting in higher J. For higher aint the effect saturates: there is no difference between aint = 0.22 eV and aint = 0.30 eV. In figure 5.lüb the mobility µo(293 K) is changed so that all the fits coincide with the experimental data point at V = 0. 92 V in order to "normalize" them. Clearly the fits are fiattening for aint > 0.05 eV. For the same disorder at the interface as in the bulk (aint = 0.22 eV) the model does not predict the typical steep increase that was measured.

The barrier height and the mobility used in figure 5.lOa were found from empirical fits using the Schottky barrier and can be reexamined when this new injection model is introduced. The effect of varying <I> B is examined for abulk = 0.22 eV. Again the mobility is chosen as a variable. This means that µo(T) is varied for different <I> B· As stated in subsection 4.2.3, the mobility and hence the current density is linearly dependent on this prefactor so this will shift the whole curve upwards or downwards but the shape will remain unchanged. The results are shown in figure 5.11. There is no significant difference between <l>B = 0.30 eV and <l>B = 0.65 eV. Also increasing the barrier up to <l>B = 0.90 eV and 1.20 eV while increasing the mobility prefactor µo(293 K) about 1 order does not show the steep plots from the experiment. Note that the value of <I> B = 1.20 eV is already much higher than what we would expect based on the energy levels (figure 3.2). This could suggest that there is need for a higher abulk·

To be able to fit a point at low V = 0.9 V and one at high V = 10.3 V, as in the approach followed when fitting using the Schottky model, we find that high values of abulk = 0.38 eV carne about. Depending on the disorder at the interface an optimal barrier <I>B and µo(293 K) is determined. This is shown for the specific case of aint = 0.12 eV in figure 5.12a. For low harriers (0.40 eV and 0.50 eV) there is hardly any difference between the curves, that bath show straight lines on a log-log scale. For higher barrier <I> B = 0.60

60

10• (a) 8:~and 0.30 10000

10• 0.08 (b) a" [eV]

1000 0.05 10• r 0.05 chottky

103 100 .08

NE 102

Ni 10 0.10

~ 10' 0.22 and 0.30 ...,

10• ...,

10"' 0.1

10-2 . measurement 0.01 l'o ( 293 K ) changed so that ·

- simulation for various a1~ J ( V= 0.92 V) same lor all fits 10"' 1E-3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

V-Vb,M V-V"M

Figure 5.10: (a) Simulations of J(V)-curves for L = 122 nm for concentration dependent mobility and a Gaussian DOS (O' = 0.22 e V) and an injection barrier (<f> B = 0.52 e V) with injection into a Gaussian DOS for different values of O'int = 0.02 - 0.05 - 0.08 - 0.10 -0.22 - 0.30 e V. (b) The same fits are shown with a varied mobility pref actor µo(293 K) so that all the fits coincide for V = 0.92 V.

1000

100

10

NÊ ~ 0.1 ...,

0.01

1E-3

1E-4

C1J8 = o.es ~v ·

<1>8

= 1.20 eV

• measurement -simulation

10

Figure 5.11: Simulations for L=122 nm J(V)-curve fora concentration dependent mobility and injection into a Gaussian DOS with the same disorder at the interface as in the bulk (O'int = O'bulk = 0.22 e VJ. The mobility pref actor µo(T) was optimized for each harrier to fit the data at V = 10.92 V.

61

e V, the fit starts to show a bit of curvature and within a small range of increasing barrier (to 0.65 eV) the fit bends off strongly. This same tendency was found back for all values of aint'. under a certain critical value of the barrier all the fits show straight lines, above this value a small increase of the harrier leads to a curved fit on a log-log scale. Higher values of the interfacial disorder leads to higher values of that critical harrier. This is shown in figure 5.12b for O"int = 0.20 eV where </>B = 1.00 eV seems best. This failed however in predicting the thickness and temperature dependence (not shown here). A further increase of the Gaussian width at the interface would lead to even higher harriers which is incompatible with the energy picture from figure 3.2. We can conclude that injection into a Gaussian DOS is not able to accurately describe the measurements. All fits suggest O"int = 0 eV as the best choice.

1000

100

10

N~

E ~ 0.1 -..

0.01

1E-3

1E-4

(a)

<1>8

= 0.60 eV

• measurement - simulatlon for "1n1 = 0.12 eV

10

1000

100

10

"' E ~ 0.1 -..

0.01

1E-3

1E-4

(b)

<1>8

= 0.90 eV

• measurement - simulation for: "•~ = 0.20 eV

10

Figure 5.12: Simulation for the J(V)-curve of a 122 nm device using the concentmtion dependent model using the injection into a Gaussian DOS for describing the measured sleep slope. The optimal simulation being O'bulk = 0.38 e Vis used in all simulations. The disorder at the interface is shown for O'int = 0.12 eV in (a). A higher disorder at the interface (b) O'int = 0.20 e V predicts a high harrier of iP B = 1.00 e V. µ 0 (T) was optimized for each barrier

. to fit the data at V = 10.92 V.

62

5.5 Conclusions and discussion

The only model that explains high slopes that increase with higher V is the concentration dependent mobility in combination with a Schottky harrier. The field and temperature dependent mobility model and the model with traps both failed. One of the main conclusions, is that the electron current is injection-limited and can be very well described by a Schottky injection harrier. This is in agreement with the CV­measurement that suggested the energy levels in figure 3.2, from which a harrier around 0.3 eV is expected. The obtained barrier height of 0.52 + 0.10 eV is somewhat higher. When the uncertainty in energy levels (Ba/ Al same work function as Ba) in the energy picture is considered, the obtained value is within the range of expectations. Further, the general assumption of the injection into a Gaussian DOS, doesn't give accurate results. From the simulations, we have seen that at typical applied voltages (V = 1 - 10 V), the injection harrier limits the current density. The carrier concentration through the device is examined for the successful simulation for the concentration dependent mobility in a Gaussian DOS for a- = 0.22 eV and <P B = 0.52 eV. In figure 5.13a it is shown that at each V the carrier concentration through the device is constant. For comparison, the same situation but with ohmic injection is shown in figure 5.13b. Now the carrier concentration at the cathode/polymer interface is so high that there are always enough carriers available to provide a bulk-limited current that is not limited by injection. An overview of the successful parameters obtained can be found in table 5.1. There are four parameters optimized for fitting (parameters between the horizontal lines), being P1 and P2 to describe the temperature dependence of the mobility prefactor, a- to denote the width of the Gaussian DOS and the harrier <P B· Er and Nc are assumed to be known. The value of a- deserves some discussion. We find a- = 0.22 eV. The found value here is al­most double of the values for PPV-devices with only hole-currents, that yield a- = 0.10 - 0.14 eV. The electron energy landscape of the blue polymer is thus much more disordered than the hole energy landscape (for which a- = 0.14 eV [4]). In this disordered landscape it is likely that some charges can hop further in distance than their neighbors and it is ex­pected that variable range hopping becomes important. This is known [48] to happen

when a- / ksT » ( ~ N: )113 ~ 8.11 for cx3 / Nc = 100 with Be ~ 2.8 the critical percolation

number [40] 5 . When this criterion is not fulfilled (a-/ksT « 8.11), nearest neighbor hop­ping is dominant.

5 The exact value of a 3 / Nc is not known but it is estimated around 102-103

.

63

1E21

~ ~ 1E20 E ~ c. 1E19

Y:v,,-: .1?~0? Y.(~: ~~. ~~'.l. . . . . .... Y:V".=.6;6,6Y. i,: ~ .5;2/"!f!l:) •••••••••••

Y:V".=~-~~ y ,(J,: ç.~~~.m,'l, ....

~:v!'.=.o;s.s.v. (: ~.o:D?~~ ~r;i:l ... V-V~ = 0.11V(J=0.00001 A/m2

)

1E18-r-.~~~~......-~~~~~~......-~-.1

1E-22 1E-18 1E-14 1E-10 1E-6 0.01 100

distance trom calhode [nm]

1E26

~ 1E25

~ ·~ 1E24

~ c. 1E23

1E22

V= 0.52V V= 2.21 V V= 5.76V V=9.70V

1E-22 1E-18 1E-14 1E-10 1E-6 0.01 100

distance trom cathode [nm]

Figure 5.13: The concentration through the device at different V /or a situation with an in­jection barrier ( a) as in the successful simulation of the Ba/ Al device using the concentration dependent mobility in a Gaussian DOS /or a = 0.22 e V and <I> B = 0.52 e V. The constant carrier concentration at all V shows that the device is injection-limited Also at the anode, the f ar right in this figure, the carrier concentration is f ound to be constant. A logarithmic scale starting /rom the cathode is used, to show that at the interface the concentration is equal to the concentration /ar /rom the cathode. In (b) it is shown how a situation /or ohmic injection would look like.

Table 5.1: The overview of the parameters needed to describe the thickness and temperature variation of an electron-only LED with a Ba/ Al cathode using a concentration dependent mobility in a Gaussian DOS with a Schottky barrier. The values between the horizontal lines (Pi, P2, a, <I>B) were optimized through fitting. Er and Nc are known.

E-dependence of µ p-dependence of µ T-dependence ofµ

a barrier cl> B

auto auto

P1 = 0.17747 & P2 = 1.4864 x 10- m /Vs 0.22 eV 0.52 eV

64

Chapter 6

Modeling of the electron current in blue electron-only diodes with a LiF / Ca/ Al cathode

We look at a device consisting of the same polymer BP as in the previous chapter, hut with a different cathode namely LiF /Ca/ Al. As noted before, experimentally higher J(V)­curves are noticed compared to Ba/ Al (figure 3.5), suggesting there is better injection using this cathode. In this chapter we first try to model the J(V)-curves using the concentration dependent mobility in a Gaussian DOS. This is inspired by the finding for a Ba/ Al cathode in the previous chapter, where a = 0.22 eV and a harrier of 0.52 eV yielded good results. It is expected that the bulk properties should be the same for Ba/ Al and LiF /Ca/ Al cathodes and that the differences take place in the treatment of injection merely. However we find that this is not the case. Next, the model of a trap filled limited mobility will be revisited for this cathode, since the J (V)-curves suggest that this model might be more successful than it was for the devices with a Ba/ Al cathode.

6.1 Experimental J(V)-curves

The J(V)-curves at room temperature are shown in figure 6.la for various thicknesses. The current density at fixed voltage decreases with thickness. The curves show much straighter, parallel lines than the ones for Ba/ Al. The curving shapes from BP with a Ba/ Al cathode are not found (figure 5.1). These curves are more like the results for PPV in literature measured by the Blom group [36].

65

..., 0.1

0.01

2 3 4 5 6 7 8 910

V-V.,M

1000...-~~-~ .......... ---~~........---.

100

10

~ 0.1

~ 0.01

..., 1E-3

1E-4

1E-5

(b)

1E~-1--~,....._,,.....,.........,.:c~-·~··~~~~~--1 0.1 10

Figure 6.1: Experimental J(V)-curves for devices with LiF /Ga/ Al cathode for a variation of thickness (L = 100 - 129 - 149 nm) (a) and a temperature variation from T = 293 K -T = 1 73 K in steps of 20 K f or L = 129 nm (b). All the curves are corrected f or symmetrical leakage currents and a Vb; = 0.55 V, as determined by photovoltaic measurements.

The temperature dependence for the L = 129 nm sample is shown for T = 293 K to T = 173 Kin figure 6.lb. Again, for the higher voltages (V - Vbi > 3 V) the curves are straight lines on a log-log scale. Also the increase of the slopes of the curves for lower temperatures is less than for devices with Ba/ Al cathodes: at T = 193 K, the slope is about 9 for LiF/Ca/Al while for Ba/Al (figure 5.la) it was 15 for high V.

6.2 Modeling assuming concentration dependent mobility in a Gaussian DOS

6.2.1 Gaussian DOS with an injection harrier

Schottky harrier model

The only model capable of describing the Ba/ Al cathode was a concentration dependent mobility model with a Gaussian DOS (section 5.4). In combination with a Schottky in­jection barrier of <l>B = 0.52 eV, it was noticed that for er= 0.22 (figure 5.7) this was capable of describing the thickness and temperature variation. We use the same approach and try to fit a point for intermediate LEP layer thickness (L = 129 nm) at V = 0.92 V and see what barrier predicts the result for high voltage too. The value er = 0.22 eV is assumed to investigate whether, as may be expected, the bulk properties are the same for both cathodes. The barrier is optimized. The best possible fit yielding <I> B = 0.48 eV, is

66

shown in figure 6.2 1 . This is however not able to predict the L = 129 nm curve and the thickness variation is very badly described. Note that in this plot µo(293 K) was varied for each thickness to let the V = 0.92 V data point coincide with the fit. When µo(T) was taken as a free parameter, no set of parameters leaded toa good fit. For a = 0.22 eV the fits are thus not satisfactory, no matter what choice of <I> B and µo(T). Therefore the temperature dependence is not further investigated.

1000

100

10

N"' E ~ 0.1 ....,

0.01

1E-3

1E-4 10

V-V0,M

Figure 6.2: Simulations of J(V)-curves for an electron-only device with a LiF /Ga/ Al cath­ode using a concentration dependent mobility and a Gaussian DOS with a Schottky barrier. a = 0.22 e V (/rom Ba/ Al results), <I> B = 0.48 e V and µ0 (293 K) = 4.52 x 10- 13m 2 /V s were optimized.

It has been argued that LiF cathodes can dissociate and that Li + then dopes a part of the polymer [53]. This could result in an interface region that is so highly doped that the electron has no difficulty traveling through it. Then the actual thickness that is relevant and that should be put in the simulation is smaller than the physical thickness of the LEP layer. Therefore we try to model the data with a decreased effective thickness. The same mobility and a = 0.22 e V was used as in the previous chapter for Ba/ Al. The fits are optimized for 129 nm leading to a harrier of <I> B = 0.50 eV. This is the value from the optimal simulation. In this approach the harrier could be comparable to the harrier for Ba/ Al, since the improved injection is due to a reduced effective thickness. The decrease of the thickness through doping is also optimized. The best possible results are found for a decrease of 9 nm. The thickness variation is shown in 6.3a. The shape of the measured 129 and 149 nm samples are badly described. For the 100 nm sample, the J-values are too

1 For bath higher as lower harrier and again optimizing the µ 0 the simulation flattens further off compa­rable to figure 5.7.

67

low. The temperature variation for the 129 nm (Leff = 120 nm) is shown in figure 6.3b. This prediction fails at high V, w here much steeper increasing slop es are predicted then the ones measured that are straight. It is concluded that the theory of doping is not able to describe the measurements.

1000 1000 (a)

100 (b)

100 10

10

0.1 NÊ 0.1 NÊ 0.01 $

0.01 S 1E-3 ...., ...., 1E-4

1E-3 1E-5

1E-4 1E-6

1E-5 1E-7 0.1 10 0.1 10

V-V0,M V-V0,M

Figure 6.3: Simulations of J(V)-curves for thickness variation for concentration depen­dent mobility and Gaussian DOS (a = 0.22 e V) with a Schottky barrier (<I> B = 0.50 e V). P1 = 0.17747 and P2 = 1.48647 x 10-7 m2 /Vs to describe the mobility are taken from Ba/ Al results. An effective thickness Let! = 9 nm smaller then the actual physical LEP layer is assumed to simulate a doping effect. The chosen barrier of <I> B = 0.50 e V and the decrease of 9 nm in relevant thickness were optimized to fit the 293 K measurement for L = 129 nm at V = 10.32 V. The thickness variation is shown in (a). The temperature variation is shown in (b) for a sample with L = 129 nm and simulations for Let f = 120 nm.

6.2.2 Gaussian DOS without an injection harrier

In the previous section the concentration dependent model with a Gaussian DOS including an injection barrier was not capable of describing the experimental curves. From the higher current density values at the same voltage, it was expected that the barrier was somewhat smaller than 0.52 e V found for Ba/ Al. In this section it is supposed that LiF /Ca/ Al causes ohmic injection and no barrier is assumed. Results are shown in figure 6.4. It is found that a very high sigma is needed of CT= 0.38 eV is able to describe the thickness dependence fairly well. This is not compatible with the finding of CT = 0.22 e V for Ba/ Al. The disorder of the Gaussian is a bulk property and has to be the same when only the cathode is changed.

Sticking to this very disordered value CT = 0.38 eV, it is examined what happens for the

68

1000

100

10

NÊ ~ 0.1 ....,

0.01

1E-3

1E-4 10

Figure 6.4: Simulations of J(V)-curves for a thickness variation of BP with LiF /Ga/ Al cathode for concentration dependent mobility and a Gaussian DOS using CJ = 0.38 e V and ohmic injection.

temperature variation (figure 6.5a). The temperature dependence is already described in the Pasveer et. al model, through equation 4.17. In this equation the term µo(T) itself is dependent on a /ksT through equation 4.19 determined by P 1 and P2. In simulating, first µo(T) is determined manually at each T by optimizing in such a way that the simulation describes a data point around 10 A/m2. Then it is seen what values for P1 and P2 come about and if with these values the simulation is accurate also above and below 10 A/m 2 .

These optimized results are shown in figure 6.5a for the optimized µo from figure 6.5b. The temperature dependence is not described accurately. The data is not well described below 10 A/m2

.

Fitting using a concentration dependent mobility and a Gaussian DOS leads to a remark­ably high a and inaccurate predictions for temperature variation. The shape of the mea­sured curves ((figure 6.la and figure 6.lb)) are clearly different than for the Ba/Al cathode in the previous chapter (figure 5.1). This suggests that the trap filled limited mobility model might be applicable for a device with a LiF /Ca/ Al cathode. This will be discussed in the next section.

69

1000~~~-----~-~~--

100

10

0.1

~ 0.01 ~ 1E-3 ....,

1E-4 1E-5 1E-6 1E-7.....,_...,..:...,.~-----~-~~--1

10

1E-35 (b)

1E-45

1E-55

1E-65 ;;;

1E-75 N~ .§. 1E-85 ~ ... 1E-95

:e 1E-105

1E-115 • optimal µ0(T)

1E·125 - µ0(T) = P

2exp[-P

1(a/k

0T)2

)

1E-135.!.---------------' 14 16 18 20 22 24 26

alk.T

Figure 6.5: The simulations for J(V)-curves fora temperature variation of a L = 129 nm device for concentration dependent mobility and a Gaussian DOS for ohmic injection. a = 0.38 e V is used for the temperature variation ( a) between 293 and 193 K in steps of 20 K. The used parameterization for the mobility prefactor is shown in (b). P 1 = 0.47 and P2 :::::: 104 m2 /Vs are used, found from fitting the optimal values for µo(T) using equation 4.19.

6.3 Modeling using a trap filled limited mobility

6.3.1 Trap filled limited mobility

In this section, the TFL mobility model will be used. Starting from the straight curves for lower temperatures, this seems a good candidate to model the LiF /Ca/ Al samples. Since the measured J(V)-curves do not have increasing slopes at high fields (figure 6.lb), the field dependence of the mobility (inclusion of '"Yn as in equation 4.12) can be neglected in a first approximation. A slope of about 6 at room temperature results in a trap depth of 5 x kBTt = 125 me V. Then there are still two more parameters: the trap concentration and the mobility. The approach is to start for a fixed trap concentration Ntf Nc at T = 293 K and therefrom determine the mobility µn to obtain a good fit. When this combination of Nt and µn is able to explain the the thickness variation, the experiments at lower T are examined to see if the model holds. In this way we ended up with only one trap concentration and one accompanying mobility that gave accurate results. This was for 0.133 traps (Nt = 2 x 1024 m-3 density of trap sites for Nc = 1.5 x 1027 m-3 total density of sites) and µn = 5.66 x 10-9 m2 /Vs.

The thickness variation for these parameters is shown in figure 6.6a. This is described quite correctly. The temperature variation is shown in figure 6.6b. The agreement is very well for a temperature range until about 213 K. The lowest two temperatures are less ac-

70

1000 1000 (a) L=129nm (b)

100 100

10 10

NE NE 0.1

$ 0.1 $ 0.01 ....,

...., 1E-3 0.01

1E-4 1E-3 1E-5

1E-4 1E-6 1 10 0.1 10

v-v.,M V-V"'M

Figure 6.6: A simulation for a device with LiF /Ga/ Al cathode using the trap filled limited mobility for kBTt = 125meV, a barrier .PB = 0.20 eV, and a trap concentration of 0.13% and a mobility of µn = 5.66 x 10-9 m2 /Vs. The thickness variation is shown in (a) for L = 96, 129 and 149 nm. The temperature dependence of a device with L = 129 nm is shown in (b) for temperatures between 293 K and 173 K in steps of 20K.

curately described. In figure B.3 (appendix A) it was shown that a small injection harrier does not inftu­ence the fits significantly for bulk transport determined by trapping. Here a harrier of <I> B = 0.20 eV is assumed. At a somewhat higher harrier of <I> B = 0.39 eV the fits are of equal quality for the high temperatures. However for the lower T, where higher Vare used, the curves start to show some difference resulting in bending off downwards. This is shown in figure 6.7. Here at three values of T, the comparison is made between measurements and the simulations with small harrier (0.20 eV) and larger harrier (0.39 eV) 2 . For the high harrier, the simulations at all T bends downwards at higher V and this is not found in the measurement. From the energy levels in figure 3.2 and the built-in voltages (both around 0.6 V, chapter 3)

a large difference in harrier between Ba/ Al and LiF /Ca/ Al is not expected and from the 0.52 eV from the previous chapter for Ba/Al and the 0.20 eV harrier for LiF/Ca/Al in this chapter, we find a difference of about 0.3 eV.

2 This value is taken because impedance measurements for double carrier devices (figure 7.1) will suggest a harrier for a device with LiF /Ca/ Al cathode that is 0.13 e V Jower than for a device with Ba/ Al cathode, for which the harrier was found at 0.52 eV.

71

1000~--~~~-~~~~~~

100 • measurement

- ·· · simulation <1>8 = 0.20 eV

10 ·· ."". simulation <1>8 = 0.39 eV

1

0.1

~ 0.01

~ 1E-3 .., 1E-4

1E-5

1E-6 ,;/ 1E-7+-----~..,.............,r--~~~~""'T"-_,

0.1 10

V-V0,M

Figure 6. 7: Measured J(V)-curves at 293 K, 253 K, and 213 K. The simulations for 0.13% traps, kaTt = 125 me V, and 5.66 x 10-9 m2 /Vs are shown for <I> B = 0.20 e V (solid lines) and <Pa= 0.39 eV (dashed line).

6.4 Conclusions

6.4.1 Devices with a LiF /Ca/ Al cathode

The straightforward approach to start with the mohility model used for devices with a Ba/ Al cathode and assume a lower harrier <lid not work. The model including a Gaussian DOS to descrihe the room temperature J(V)-curves of a device with a LiF /Ca/ Al cathode, suggests a very high er = 0.38 e V. This is not successful for the temperature variation. The model using traps predicts hetter the LiF /Ca/ Al hehavior with straighter more linear J(V)-curves on log-log scales. It was noticed that the trap concentration is lower (0.133) than values found in literature for PPV electron-only devices. The mohility and trap depth (kBTt = 125 meV) were of the same order as for PPV, as reported in [23]. The injection harrier 'PB = 0.20 + 0.10 eV is found. The fit is not very sensitive to 'PB. However, from photovoltaic measurements (figure 3.14), it is not expected that the difference in harrier between the two cathodes is as high as the difference of 0.52 eV that would be found if the results for Ba/ Al in the previous chapter and ohmic injection were assumed for LiF /Ca/ Al. An overview of the used parameters is shown in table 6.1. The electron concentration through the device is shown in figure 6.8. Although there is an injection harrier of approx­imately 0.20 eV, the current is not injection-limited even at the highest current densities.

72

Table 6.1: The overview of the parameters needed to describe the thickness and temperature variation of an electron-only LED with a LiF /Ga/ Al cathode using the trap filled limited mobility with a Schottky barrier. The values between the horizontal lines, were optimized through fitting. Er and Nc are assumed to be known.

E-dependence of µn T-dependence p-dependence

auto

constant µn

Tt Nt/Nc

harrier <I> B

5.66 x 10- m /Vs 1465 K 0.13 3 0.20 eV

There are still enough carriers available at the contact to provide the device with bulk­limited current and the concentration through the device is not constant. This is in contrast with the situation found for Ba/Al (figure 5.13a) where the current is injection-limited.

1E25~~~~~~~,....-~..--~~~-..

1E24

1E23

.r 1 E22 J = 154 Alm' ( V-V" = 7.2 ':J. . . . • . . . • • " E 1E21 "" "" """" "• • •••••• ~ ' J = 5.2 A/m

2 ( V-V °' = 4 Y) ••••• • • • " " " •

'E 1E20 • • • • • • • • • • • • • "" ""

.J! 1E19 Q.

1E18 J = 0.0006 A/m

2 ( V-V" = 0.86 V) ••••• • •

1E17 ••••• , , ••••••••• • • • • • • •"

1E16-'-~~~~~~,....-~..--~~~___,,

20 40 60 80 100 120

distance from anode [nm]

Figure 6.8: The carrier concentration through the device at room temperature for an electron-only device with a LiF /Ga/ Al cathode of L = 122 nm using the trap model fora con­centration of 0.13% traps, kBTt = 125 me V, µn = 5.66 x 10-9 m2

/ Vs, and <I> B = 0.20 e V. At all current densities, the current is not injection-limited.

73

6.4.2 Comparison with devices with Ba/ Al cathode

It became clear that the shapes of the J (V)-curves of devices with Ba/ Al cathode and LiF /Ca/ Al cathodes are intrinsically different. This is indicated in figure 6.9. Here the results of measurements for T = 293 K, 233 K, and 193 K are shown for Ba/ Al and LiF /Ca/ Al of similar thickness. The J-values for Ba/ Al are multiplied by a constant number of 6 to put them more or less over the LiF /Ca/ Al measurements. This shows the different shape in curves. Ba/ Al devices show curving curves over the whole range of V that increase strongly at lower temperatures. LiF /Ca/ Al shows near-straight lines of which the slope only increases slowly. Although in the previous chapter modeling using traps was already examined, this seems a

..., J,,_ = 6 x J

J,,,""" = 6 x J -LlF/Ca/Al cathode; L = 129 nm

10

Figure 6.9: The measured J(V)-curves at T = 293 K, 233 K and 193 K fora L = 122 nm devices with LiF/Ca/Al cathode {straight lines) and a L = 129 nm with Ba/Al cathode (dots), for which the current density was multiplied by a constant factor of 6 to put the curves f or the two cathodes over each other.

good point to turn back to the Ba/ Al data. If traps are important in samples with a Ba/ Al cathode, the bulk parameters should be the same. An injection harrier is included because of the results from the previous chapter. This is optimized to fit the data at V = 10.32 V, leading to qi B = 0.45 e V. This is shown in figure 6.10. For comparison, also the ohmic injection case is shown ( qi B = 0 e V). The injection-limited curve shows no agreement with the experimental data. The inclusion of a harrier leads to a fit that flatteus off at higher V. The measured curves are getting steeper with increasing V. This fin ding strengthens the statement from the last chapter that traps are not able to describe the Ba/ Al data.

74

1000..----~~ ........... -~~~~.....,---.

100

10

1 0.1

~ 0.01

~ 1E-3 ..., 1E-4

1E-5

1E-6 1E-7+---~~,..,...,.,.-~~~~,......,---<

0.1 10

Figure 6.10: Simulation of J(V)-curve of Ba/ Al with L = 122 nm Jor the trap filled limited mobility /or at T = 293 K. The bulk parameters are obtained /rom the successful LiF /Ga/ Al fits: 0.13% traps, kBTt = 125 me V, and 5.66 x 10-9 m2 /Vs. 1> B = 0.45 was optimized. For comparison, also the ohmic injection {1> B = 0 e VJ is shown.

Finding a unified model for LiF /Ca/ Al and Ba/ Al is not straightforward. In literature LiF /Ca/ Al currents have never been modeled for double carrier devices nor for electron­only devices. The reason of enhanced injection for this cathode is not understood. Our findings suggest that separate models for the bulk transport in devices with the two cath­odes might be necessary, although we cannot provide an explanation for this.

From fitting and the experiments in chapter 3, now a conclusion can be made about the energy alignment. This is shown in figure 6.11. From the position of the LUMO of the polymer from CV measurements at 2.2 eV, and from the «I>B = 0.5 eV, it follows that the effective work function of Ba/Al is at 2.7 eV. This is somewhat higher than the value for single crystalline Ba [10]. This can be a consequence of the Al capping (single crystalline Al is at 4.2 eV). LiF/Ca/Al is at 2.5 eV, as it leads to a small injection harrier of about 0.2-0.3 eV. This however does not lead to injection­limitation. This explains why the current density at fixed V is higher for a device with LiF /Ca/ Al cathode than fora device with Ba/ Al cathode (figure 3.5). From determination of the built-in voltage of electron-only devices ( conclusions section chapter 3), it is shown that the effective work function of the bottom Al electrode is 3.3 eV. The found values for the cathode materials are also consistent with the built-in voltages that will be derived in the next chapter for double carrier devices with ITO /PEDOT:PSS as the anode. There Vbi = 2.4 V will be found for a device with a Ba/ Al cathode and 2.52 V for a device

75

with a LiF /Ca/ Al cathode (table 7.1). Finally the single particle gap of the fl.uorene-based polymer is found to be 3.6 eV. This is in agreement of the results of Liao et. al [46] who find a 7r-7r* -gap of 3.55 e V for poly (9,9 dioctyfl.uorene) (PFO) using XPS and UPS.

_l-!J..:M o _ m J x~ x _ Energy LUMO PF 2.2 eV LiF/Ca/Al 2.5 eV

Ba/Al 2.7 e single particle gap of Al 3.3 eV

host polymer is 3.6 eV

PEDOT 5.1 eVHOMO HT 5.1 eV ------HOMO PF 5.8 eV

Figure 6.11: The energy alignment in a device with BP. HT stands for hole transporting unit and PF for the polyfiuorene. For an electron-only device the Al has a work function of </; = 3.3 eV. The Ba/Al(</>= 2.7 eVJ has an injection barrier of 0.5 eV. LiF/Ca/Al has a work function </; = 2.5 e V. These values are in agreement with built-in voltages for double carrier devices with Ba/Al cathode (2.4 VJ and LiF/Ca/Al cathode (2.5-2.6 VJ, derived in the next chapter.

76

Chapter 7

Double carrier devices

In this chapter we use the results obtained for electron-only devices ( chapter 5-6) in a full device model for the double carrier device, introduced in figure 2.3. Again two devices are under investigation: one with the standard Ba/ Al cathode and one with a LiF /Ca/ Al cathode. The results for the built-in measurements are stated and the J(V)-curves are introduced. Then the found models for electron current are used in combination with the results for hole current from previous work [4]. It is shown that the J(V)-curves of the double carrier device are described very well for a thickness and temperature variation for both cathodes. Finally the distribution of the electrons, holes, and excitons through the device is calculated and this provides us valuable information about the recombination zone. These are the first results ever achieved for blue polymer LEDs, based on profound modeling.

7.1 Double carrier device characterization and determina­tion of Vbi: results

7.1.1 Electrical impedance spectroscopy

Using electrical impedance spectroscopy, the empirica! method for determination of Vbi

to look at a peak in the capacitance (subsection 3.6.2) is used. For the double carrier devices with Ba/Al cathode (figure 7.la), a peak occurs around V = 2.39 V for all frequen­cies. This is in the line with the onset of J(V)-curves (2.4 V), and previous findings by van Mensfoort [4] for photovoltaic measurements (2.2-2.4 V) and electro-absorption (2.3-2.4 V). For the device with the LiF /Ca/ Al cathode(figure 7.lb), the peak is shifted to the right and located at 2.52 V. This suggests that the harrier is about 0.13 + 0.05 V lower for the LiF /Ca/ Al cathode.

77

1.2 1.20 ..----.-----.-~--.--..--......... --...-~--. (a)

1.15

(b) LiF/Ca/AI cathode

1.10

1.05

~ 1.oo-L..iw..1v.-10t11N,,_..,...._.--

8 0.95

0.90

0.85 Ba/Al cathode

2.39V

0.80-1---.-----.-~--.--..-----...-~-1 0.0 0.5 1.0 1.5 2.0 2.5 3.0

v_M

2.52V

1.1 1

> ~ 1.0

&2 u

0.9

0.8 1.0 1.5 2.0 2.5 3.0 3.5

v.,"M

Figure 7.1: Electrical impedance spectroscopy experiments showing the normalized capaci­tance. For the double carrier device with the Ba/Al cathode (a), a peak arises at V = 2.39 V. For the device with the LiF/Ca/Al cathode (b), a similar peak arises at higher V = 2.52 V.

7 .1. 2 Electro-absorption measurements

4.0

The electro-absorption measurement performed previously by van Mensfoort [4] fora dou­ble carrier device with a Ba/ Al cathode, showed a built-in voltage between 2.3-2.4 V. The measurement for a double carrier device with LiF /Ca/ Al cathode is now carried out. The difference in refl.ectivity between the reference signal and the illuminated signal van­ishes between 2.4 V and 2.6 V (figure 7.2a). In that regime also the phase angle changes sign (figure 7.2b). This is expected to happen at the built-in voltage. Together with the findings for Ba/ Al, this strengthens our believe that for a double carrier device with a LiF /Ca/ Al cathode, the electron harrier is 0.2 + 0.1 V lower compared to a double carrier device with a Ba/ Al cathode. A similar result of a lower electron harrier was already found from modeling of the electron-only devices (this report) and a difference in onset voltage between devices with the two cathodes ( onset voltage at 2.4 V for Ba/ Al while 2.5-2.6 V for LiF /Ca/ Al [44]). In the following discussion all the LiF /Ca/ Al J(V)­curves will be corrected for Vbi = 2.52 V and the Ba/ Al J(V)-curves for Vii = 2.39 V. An overview of all the obtained information on built-in voltages for double carrier devices is given in table 7 .1.

78

0.9 (a) 160 ~ 0.8 120

0.7 80

0.6 v. =2.52 v

=i 0.5

"' ~ 0.4 v.=2.52V

<l 0.3

0.2 . j. 0.1 .. 0.0

-1 0 2 3

vbla,M

40

·~ 0 & -40 <l

-80

-120

-160

4 5 -1 0 2

v""M

3 4

Figure 7.2: Electro-absorption measurements on a double carrier device with L = 90 nm and a LiF /Ga/ Al cathode. ( a) The detected difference in refiectivity between the absorbed signal and the reference signal is shown. This vanishes at Vbi = 2.52 V. (b) The difference in phase angle for increasing voltage is shown. lts sign changes at Vi; = 2.52 V.

Table 7.1: The values for built-in voltage from seveml observations are summarized for the double carrier device with the Ba/ Al cathode and the device with a LiF /Ga/ Al cathode. For the device with LiF /Ga/ Al cathode, no photovoltaic measurements were carried out. M odeling denotes the values that will be used in the f ollowing sections f or correcting the measurements.

onset J(V)-curve impedance

electro-absorption photovoltaic measurement

modeling

Vbi [VJ for Ba/ Al 2.4 (figure 2.5)

2.39 (figure 7.la) 2.3-2.4 [4J 2.2-2.4 [4J

2.39

Vii [VJ for LiF /Ca/ Al 2.5-2.6 [44J

2.52 (figure 7.lb) 2.52 (figure 7.2)

2.52

7 .2 Double carrier devices with Ba/ Al cathode

7.2.1 Experimental J(V)-curves

5

The result for a thickness variation of the LEP layer for a clou ble carrier device with a Ba/ Al cathode is shown in figure 7.3a. The current density at fixed V decreases with thickness. The curves have slopes of around 2.5, increasing at higher V.

79

The temperature variation is shown in figure 7.3b. The current density at fixed V decreases with T. For the lowest temperature of 173 K, the slope for V - Vbi = 2 to 7 V has increased to about 4 while above 7 V, it increases up to 9.5. We note that the J (V)-curves for double carrier devices did not require a profound selection of the samples, as for the electron-onlies. No memory effects as in figure 3. 7 were found.

1000 1000 (a) (b)

100 100

10 10

N" N" E E $ 0.1 L=165nm $ 0.1 ..., ...,

0.01

/ 0.01

1E-3 1E-3 ~

T=173K 1E-4 1E-4

0.1 10 0.1 10

V-V.,M V-V.,M

Figure 7.3: (a) Thickness dependence of J(V)-curves for double carrier de­vice with BP and Ba/ Al cathode on a double logarithmic scale for samples of L = 65 - 77 - 102 - 139 - 165 nm. (b) J(V)-curves at different temperatures between 293 K and 173 Kin steps of 20 K are shown in for L = 139 nm. All the data was corrected for Vi; = 2.39 V and a symmetrie leakage current.

7.2.2 Modeling of J(V)-curves

The thickness variation for a double carrier device with Ba/ Al cathode will now be mod­eled by combining the models that described the electron-only devices ( chapter 5 of this report) and the hole-only devices [4]. For the electron current model, the concentration dependent mobility for a Gaussian DOS (a = 0.22 eV) with a Schottky injection barrier cl> B = 0.52 eV, and P1 and P2 to describe the mobility prefactor (equation 4.19) found in figure 5.8. are used. The hole current is described by the field and temperature dependent mobility model (sub­section 4.2.1). The field dependent factor at T = 293 Kis taken 'Yp = 5.4 x 10-4 (m/V) 112

and the mobility is µP = 9 x 10-12m2 /Vs. These values were obtained by optimiz­ing the simulation for the L = 139 nm sample. They are somewhat higher then pre­vious findings within Philips based on hole-only devices (µp = 5.9 x 10-12 m2 /Vs and 'Yp = 3.2 x 10-4 (m/V) 112 [44]).

80

Figure 7.4a shows that the model also describes the other thicknesses very well. There is only some significant deviation for the device with L = 77 nm (the second high est curve). This discrepancy might be a consequence of the possible error of 4 nm in the measured thickness through impedance measurements (using the method depicted in figure 3.16). The temperature variation is shown in figure 7.4b. Now "(p and µp are varied at each T. The used values are shown in table 7.2. The higher T are very well described. For the lowest T a deviation occurs for V < 1 V. The effective onset voltage seems to have shifted to somewhat higher voltages at lower T.

1000..--~~~~~,---~~~~ ......... 1000~-~~~~~..---~~~~~

100

10

NE 0.1 ~ ..., 0.01

1E-3

1E-4

100

10

î 0.1

..., 0.01

1E-3

1E-4 .. 1E-5+--~~~~~..----~~~-.-.-i 1E-5+--~~~~~..---~~~~..,..,,

0.1 10 0.1

V-V0,M

Figure 7.4: Simulations of J(V)-curves for a double carrier device using a concentration dependent mobility in a Gaussian DOS (u = 0.22 e V) with a Schottky injection barrier (<!> B = 0.52 e V) for electron current and the field and temperature dependent mobility model for hole current. A correction for Vi; = 2.39 V was made. In (a) the results are shown for the thickness variation for L = 65 - 77 - 102 - 139 - 165 nm with the field dependent parameter for holes /p = 5.4 x 10-4 (m/V)11 2 and a hole mobility of µP = 9 x 10-12 m2 /Vs. The temperature variation is shown in (b) for T = 293 - 273 - 253 - 233 - 213 K. Naw the hole parameters /p and µp are optimized at each T (table 7.1).

10

We now turn back to the single carrier and double carrier device and see what our found model predicts. For L = 80 nm the current density is simulated for the hole-only devices, the electron-only devices and the double carrier device. This is shown in figure 7.5. It is observed that the electron current density is a few orders lower than hole and double carrier current density at fixed V, for low V. It is found that the current in the double carrier device is dominated by the hole current and that only at V > 4 V there is a contribution of the electron current. The difference between the hole and the double carrier current is very small. The figure suggests that the electrons only become dominant

81

Table 7.2: Overview of physical parameters for holes that were most suited to simulate the total current for a temperature variation for a L = 139 nm double carrier device with a Ba/ Al cathode using for holes the field and temperature dependent mobility model, when the electron current is treated as concentration dependent with a Gaussian DOS a = 0.22 e V and a Schottky barrier of 0.52 e V.

T[K] µp[m 2/Vs] "lp [(m/V) 1 l 293 9 x 10- 5.4 x 10-273 3.1 x 10-12 5.1 x 10-4

253 9 x 10-13 7.0 x 10-4

233 3.28 x 10-13 7.6 x 10-4

213 9.5 x 10-14 8.3 x 10-4

at current densities above J > 1 x 103 A/m2 and hence the holes still dominate the total current in a double carrier device. This finding of negligible influence of electrons is not in agreement with the measurements from figure 3.3. For devices of similar thickness the double carrier current was about three times higher than the hole-only current. In figure 7.5 we see that the hole-current is not simulated well anymore. This suggests that maybe the electron current becomes more important in a double carrier device than that it is in a single carrier device. We will come back on this important issue but will first have a look at what our model predicts for the charge and the exciton distribution.

7.2.3 Modeling of charge and exciton distribution

The distribution of excitons through the device is now calculated (figure 7.6a) at different V. This provides information about at which position in the device recombination will occur, because some of these excitons will decay in emitting a photon ( others will decay non-radiatively, because of the contributions stated in equation 2.3). It is found that at all V, the exciton density is closest next to the anode. This is one of the most important findings suggested by the model in this report. A recombination close to the electrode can lead to non radiative energy transfer to the metallic electrode [58]. Thus the excess of excitons next to the anode can negatively affect the performance. Possibly exciton quenching is less destructive in our case close to the anode, because PEDOT is not a regular metal. The distribution of holes and electrons is calculated (figure 7.6b) at different V, assuming the model stated above that is capable of simulating the current through the device. It is found that the hole concentration is higher compared to the electron concentration at all

82

10000-r--~~-.-----~--~'7"""".,,..

1000

100

10

0.1

...., 0.01

1E-3

1E-4

1E-s-~~-----~---~..,...., 10

v-v., [VJ

Figure 7.5: The predicted J(V)-curves for the model for a double carrier device with Ba/Al cathode (d.c.), shown together with the measured {dots} and simulated (solid lines) hole-only curves, and electron-only curves for L = 80 nm at T = 293 K. For the holes µp = 9 x 10-12 m2 /Vs and /p = 5.4 x 10-4 {m/V)11 2 is used. For the electrons the model with a concentration dependent mobility and a Gaussian DOS fora= 0.22 e V and a barrier of iP B = 0.52 e Vis taken.

V. The electron concentration through the device is almost constant at fixed V due to the injection-limitation.

Now earlier measurements are introduced of the efficacy, which is the ratio of the lumi­nance (light intensity, expressed in cd/m2 ) and the current density. It will be investigated if our model is capable of predicting this kind of experimental data. Measured efficacies for double carrier devices with a Ba/ Al cathode and a LiF /Ca/ Al cathode are shown in figure 7.7. The efficacy increases, reaches a peak, and decreases again. For the device with a LiF /Ca/ Al cathode this peak is at lower V.

Now we are capable of simulating the exciton recombination efficiency 'r/rec, introduced in equation 2.3. This is the ratio of the amount of excitons per second and per m 2, divided by the total part iele current density ( J / e):

L

J nexciton ( X) dx 0 T/rec = ___ J_/_e __ _ (7.1)

It is the fraction of carriers that contributes to the current density that actually forms excitons. Assuming a non-shifting recombination density T/ext(x) with increasing V, the

83

1E31~(~a)~~~~~~~~~~~~.......,

j 1E30

~ 1E29 1

.! 1E28 \"""

!!! -----6 1 E27 ----+V.:__:-V-'l.....= ::5.=66:_:V:__j

"" i 1E26 \

~ 1 E25 ··········································· .. l/..:'!"l.= .. ~'.~.7..~ ........... . 6 1E24

············· ···················· .Y .. :Y":~:2.~".'. .....

"'" ~ 1E23 V-V. = 0.56V

1E22+-~~~~~~~~~~~~_,...

0 20 40 60 80 100 Distance from anode [nm)

1E26 (b)

; :~ ................. ::: .. : .. :.:: ...... :.::.:::::.: .... : .......... Y ...... ~ëf..:.:: ~CJ

1E19

0 20 40 60 80 100

Distance from anode [nm]

Figure 7.6: Distribution of excitons (a) and electrons and holes (b} through the L = 102 nm double carrier device with a Ba/ Al cathode at T = 293 K. The electron current is described through the concentration dependent mobility and a Gaussian DOS (a = 0.22 e VJ with a Schottky harrier of 0.52 e V. The hole current is described using the field and temperature dependent mobility model with µP = 9 x 10-12 m2 / Vs and /p = 5.4 x 10-4 (m/V)11 2 .

3

2 4 6 8 10

V-V bi

Figure 7. 7: Efficacy for double carrier device of 80 nm with LiF /Ga/ Al cathode and Ba/ Al cathode [5).

recombination efficiency can be converted linearly into efficacy ( explained in appendix C). Therefore the shape of the stated results for 'f/rec can be compared to the findings for the efficacy in figure 7.7. The result is shown in figure 7.8a in function of the applied voltage and in figure 7.8b in function of the current density. The increase in efficacy with voltage,

84

the found peak and the decrease at higher voltages are in agreement with the findings for the efficacy. It was noticed (not shown here) that at the peak value V - Vbi = 8.8 V, within the first 5 nm from the anode about 703 of the total amount of excitons through the device are formed. This was already expected from figure 7.6a. In appendix D the expectations for J(V)-curves and recombination efficiency using this model for a double carrier device with a Ba/ Al cathode are shown for various thick­nesses (L = 60 - 90 - 120 nm for T = 293 K) and temperatures (T = 293 - 253 - 213 for L = 90 nm). The measured peak in efficacy of 3.5 cd/ A arises at 7.6 V (figure 7. 7). We are now able

1.0

0.8

0.6

~ r::- 0.4

0.2

0.0 0

(a)

--····· 2

• • • •• 4

• • •

6

•••••••••• • •• • • • •• • ••

8 10 12

1.0 (b)

0.8

0.6 • • ~ • • r::- •

0.4 •

0.2

0.0 0.0 2.ox10• 4.0x105 6.0x105 8.0x105

J [Alm']

Figure 7.8: The recombination efficiency predicted by the developed model for L = 80 nm double carrier devices with Ba/ Al cathode for L = 80 nm is shown in function of voltage { a) and current density {b).

to verify if the above model is capable of predicting this result. At the modeled slightly higher peak position at V - Vbi = 8.8 V, the predicted T/rec = 0.67. If this is now con­verted to efficacy (shown in appendix C), we find that our model predicts the efficacy to be 3.28 cd/ A. This is close to the measured value of 3.5 cd/ A, certainly if we take into account the possible deviations in the assumed singlet/triplet ratio (taken at 25% but this can be higher) and outcoupling efficiency. The effect of an increasing T/rec can be attributed to harrier lowering. The harrier of 0.52 e V will be lowered due to the image charge effect (equation 4.24). Therefore we calculate the effective harrier ( <I> B - ~<I>) at the cathode, figure 7.9. With increasing field, the effective harrier becomes lower and the electron current increases. This leads to a better balance between holes and electrons and this enhances T/rec· The peak value corresponds with the field at which electron and hole current through the device are equal.

85

o.5o-~~~~~~~~~--.~~.----.

0.45

0.40

0.35

> 0.30 ~ 0.25 e 1 0.20 e"' 0.15

0.10

0.05

0.00+-~~~~~~~~~--.~~..---1

0 2 4 6 8 10 12

V-VoiM

Figure 7.9: The effective barrier for electrons, calculated through equation 4.24, at the cathode at different V. The dots are the calculations. The solid lines are a guide to the eye. The barrier is lowered at higher V, due to an image charge effect.

It is noted that there are two effects that our model does not take into account yet. It is found that the photoluminescence decreases with the field. Above the built-in voltage some of the excitons will be separated again because of the high field. It is measured for superyellow PPV 1 [49] that this effect is a Gaussian-like function symmetrie around the built-in voltage and can cause a decrease in 1/PL of 53 at 10 V, and 403 at 20 V. The measured efficacy curves will be sensitive to this contribution. Quenching of the photolu­minescence at high fields is not included yet in the simulation. Therefore the actual values of the recombination efficiency will be slightly lower, especially at high V. As mentioned already, another effect is a possible shift of the recombination zone at higher V that might effect the outcoupling efficiency. The outcoupling efficiency is not constant through the device [57]. If the recombination zone would shift with increasing V, the out­coupling efficiency will change and this effect might have a contribution that is included in the measured light and efficacy. This is not taken into account in the simulation yet. From our findings however, this contribution should be negligible since we find that the recombination will be close to the anode at all V.

1 There is no data available for BP.

86

7.2.4 Discussion

It was found that there was a discrepancy in simulating together the hole, electron and dou­ble carrier devices. Therefore we choose to look at the sensitivity of the model in function of small changes in hole mobility, barrier lowering, and the recombination prefactor.

Influence of variation of hole mobility µn

The approach used in this chapter so far was to start from the J(V)-curves for double carrier devices, describe the electron-current using the found model in chapter 5, and then optimize the hole mobility and the field dependency factor. The found values where then in fair, but not fully agreement with previous findings for hole-only devices. We now investigate what happens when the exact hole parameters found to describe a device of 80 nm, are combined with the findings for electron-only devices. Now at room temperature for the L = 80 nm device, 'Yp = 3.35 x 10-4 (m/V) 112 , µP = 7.5 x 10-12 m2 /Vs is used. These values are only somewhat lower than the "(p = 5.4 x 10-4 (m/V) 112 , µp = 9 x 10-12 m2 /Vs used in the previous section. It is shown in figure 7.lüa that now the simulation holds for hole-only devices, but the J(V)-curve for the double carrier device does not agree with experiment. The dotted lines show the simulations for the hole parameters required to simulate the double carrier current (same as previous subsection). In figure 7.lOb the recombination efficiency 'r/rec for the hole parameters needed to simulate the hole current ( filled squares) is shown together with the 'r/rec for hole parameters needed to simulate the double carrier current (open circles, same as previous subsection). For the hole parameters for fitting the hole-only device, the maximum in 'r/rec is at somewhat smaller V and is at a higher value of 0.8 compared to 0.7. We conclude that when we start from the findings from hole-only devices, the double carrier current is underestimated.

Influence of harrier lowering

If we start from the exact parameters found from hole only devices, the double carrier current is underestimated. For an electron-only device a barrier of <I> B = 0.52 eV was assumed. It is possible that in a double carrier device the barrier for electron injection is somewhat lower. It is known that a part of the emission spectrum of the BP is overlapping with its absorption spectrum [44]. This could cause a part of the emitted light to be absorbed again by the polymer itself, reducing the electron barrier. This possibility is partially inspired by the photovoltaic measurements that showed a compensation voltage that shifted to higher V under influence of light (figure 3.12). This could suggest a built-in voltage that is somewhat higher after longtime illumination, because of a smaller barrier. Therefore the J(V)-curves are shown for the initial electron barrier of 0.52 eV, and for somewhat lower barrier of 0.48 eV and 0.45 eV in figure 7.lla. For the hole mobility the

87

1000 1.0

(b) (a) simulation lor h·-only device

µ !rom d.c. J0J)-c~"·· 0.8 100 . . ......... " .......

slmulatlon lor d.c. device 0.6

NE µ,!rom d.c. J0J)-curve

10 ~ 5. o=' 0.4 ....,

0.2 slmulatlon tor h • -only device

0.1 µ, !rom h • -only J0J)-curve

0.0 10 0 2 4 6 8 10 12

v-v.,M

Figure 7.10: A comparison of the infiuence of the hole mobility is shown, by looking at the J (V)-curves ( a) and the recombination efficiency (b) for two hole mobilities: one that is capable in describing the J(V)-curves for hole-only devices ('Yp = 3.35 x 10-4 (m/V)11 2 ,

µp = 7.5 x 10-12 m2 /Vs) and one that is capable in describing the J(V)-curves for double carrier devices ('Yp = 5.4 x 10-4 (m/V)11 2 , µP = 9 x 10-12 m2 /Vs).

parameters found for simulating the double carrier device, are assumed. The infl.uence of a lower electron harrier on the recombination efficiency is shown in figure 7.llb. A lower harrier results in a higher peak at a lower V. There is already a large difference when the harrier is lowered only 0.04 eV. Here it is important to note that for the electron current, the µo(T) that were optimized for 0.52 eV (figure 5.8a) are still used. The high sensitivity for the small change in harrier is probably a consequence of the fact that we are still using µo(T) found from 0.52 eV. For a lower harrier, µo(T) should again be optimized and lower required µo(T) is required. If this optimization is carried out again for 0.45 eV and 0.48 eV, the effect of the lower harrier will certainly be smaller. In the shown picture the electron currents for the 0.45-0.48 eV harriers is overestimated. However we can conclude that if the harrier would be lowered due to the emitted light, the peak in 'r/rec will be higher and shifted to a lower voltage. We hereby note that the deviation in harrier needed to describe the effects shown here, will differ and will be higher than 0.04 and 0.07 eV.

Influence of variation of recombination prefactor brec

A similar discrepancy as the one we find here for the actual double carrier current density as compared to the current densities expected theoretically from the single carrier models, has been found previously for PPV devices [25]. We have treated recombination as Langevin

88

1000..--~~~~~.,---~~~~~ (a) /

100 <1>8 =0.52eV'----~'7'.1:'·

10 oi>

8 = 0.48 ev---~"'

î 0.1

..., 0.01

1E-3

1E-4

1E-5+--~~~~~.,---~~~~.....-i 0.1 10

0.8

0.6

~ "'"0.4

0.2

(b) i4 ••••••••• ~'o •

"t;;;::,· •

s" • •

• 0

• 0 ... 0 " • " • 0

" 0 ... 0 ...

0 ... oooo ......

... "" " ... 0 2 3 4 5 6 7 8 9

v-v., M

Figure 7.11: (a) J(V)-curves for double carrier device with L = 80 nm at T = 293 K for the electron barrier found for electron-only devices {0.52 e V) and for lower barriers of 0.45 e V-0.48 e V due to possible barrier lowering under infiuence of illumination. For the hole parameters /p = 5.4 x 10-4 {m/V)11 2 , µp = 9 x 10-12 m2 /Vs is assumed. The results f or the recombination efficiency are shown in (b).

10

recombination using equation 4.5 for the recombination constant R1oc· For double carrier devices with PPV it was found that the double carrier current could only described by optimizing R10 c, rather than taking it as predicted by the Langevin equation ( equation 4.5). R10 c was chosen four times larger as in the theory to be able to explain the difference in current between double carrier and single carrier devices. The infl.uence of the recombination prefactor brec (equation 4.5) is examined. Figure 7.12a shows the infl.uence on the J(V)-curves. It is found that these are not affected by brec for the voltages under investigation. Only at very high J > 105 A/m2 deviation occurs (not shown here). For increasing brec, the recombination efficiency (figure 7.12b) has a higher peak at a higher voltage.

From the investigation of the recombination efficiency, we conclude that the simulated 'T/rec is in good agreement with the measured efficacy. With increasing field, more carriers will form excitons increasing the efficiency because the effective harrier for electron injection is lowered. When there is balance in hole and electron current, there is a peak in efficiency and when Vis further increased, the efficiency decreases. However it is noted that the peak position and the peak value are very sensitive to possible uncertainties in hole mobility, harrier height, and recombination prefactor.

89

1000 1.0

(a) (b) ó

100 0.8 ·-.::~

" 10 • 'Cc ó ••

0.6 )0 ~ ~ • Oo "'7

...... .o 00

ó co E ~ .o ·~~ 00 ~ 0.1 i=' 0.4 0 "" !'l• "" ·$ .., 'j"" "" "" 0.01 o.o. ""

0.2 1E-3

1E-4 0.0 0.1 10 0 2 4 6 8 10 12 14

V-V.,M v-v., M

Figure 7.12: (a) The simulated J(V)-curves using the model to describe double car­rier current in a device with a Ba/ Al cathode are shown for three different values of brec = 0.5 - 1 - 2. (b) The infiuence on the recombination efficiency 7/rec is shown for the three values of brec·

90

7.3 Double carrier devices with LiF /Ca/ Al cathode

7.3.1 Experimental J(V)-curves

The J(V)-data for different temperatures going from 293 K - 173 K are shown in figure 7.13. There was no thickness variation since we had only a device with L = 90 nm at our disposal. At room temperatures the curves are straight lines on a log-log scale with a slope around 2.7. At lower T, the shape changes into curving J(V)-curves of which the slope increases with voltage, up to 7.8 for V - Vii > 5 V.

100

10

I T = 293 K

...,

0.1

0.01--~-~~~~-~-~ ............. 0.1 10

V-V.,M

Figure 7.13: Measurement of J(V)-curves for a L = 90 nm double carrier device with LiF /Ga/ Al cathode at T = 293 - 273 - 253 - 233 - 213 - 193 - 173 K. The data were corrected for vbi = 2.52 v.

7.3.2 Modeling of J(V)-curves

The same approach is followed as for modeling double carrier devices with Ba/ Al cath­ode, by combining the models that described best the electron-only devices ( chapter 6 of this report) and the hole-only devices [4]. For the electron current, traps of depth kBTt = 125 meV, a concentration of 0.133 and an electron mobility 5.66 x 10-9 m2 /Vs are used, found in the previous chapter. For the hole current, the field and temperature dependent mobility model including field and temperature dependence with a "lp and mo­bility µP optimized at each T is used. The results are shown in figure 7.14. The agreement is very good for the temperature variation.

The used values for "/p and µP are shown in table 7:3. The found values for the mobility

91

1000

100

10 ... E ~ ...,

0.1

0.01 0.1 10

v-v., [VJ

Figure 7.14: Simulations for J(V)-curves of a double carrier device with LiF /Ga/ Al cath­ode at T = 293 - 273 - 253 - 233 K. To describe the electron current, the trap filled lim­ited mobility for kBTt = 125 me V and trap concentration 0.13% is used for a mobility /J,n = 5.66 x 10-9 m2 / Vs which was capable to describe the electron-current in an electron­only device. For the hole current the field and temperature dependent mobility model that was shown to describe the current in hole-only devices (4} is used with the parameters shown in table 7.3.

are close to the values found for a double carrier device with a Ba/ Al cathode at high T. The results at room temperature, are very accurate considering the small uncertainties in e.g. built-in voltage that was corrected for, the temperature at which the LED really is (heating of the sample when there is a large current at high V; a few Kelvin will already influence the fitting parameter), and the site densities of electrons and holes. These issues all affect the used parameters. At lower T = 233 K however the results differ. The mobil­ities for Ba/ Al and LiF /Ca/ Al are shown together in figure 7.15. The agreement in mobility found at room temperature invalidates the theory that LiF /Ca/ Al, would act as a hole-blocker, as proposed earlier [44]. The used values for the 'Yp deviate somewhat from the values found for devices with Ba/ Al cathode.

In figure 7.16 the currents through single carrier devices (both hole- and electron-only devices) and double carrier devices of similar thickness are shown, as predicted using the found model for double carrier devices. Hence the electron currents are described using traps while the hole currents are described using the field- and temperature dependent model. The electron current in a single carrier device becomes higher than the hole current in a single carrier device from about 2 V (6 A/m2). This suggests that at higher V, for the double carrier device with a LiF /Ca/ Al cathode the electrons are the dominant charge

92

"'" :> .E.

1E-11

1E-12 ~Ba/Al

::i.~ 1E-13

/ LIF/Ca/Al

0.0036 0.0040 0.0044 0.0048

1fî [K"1]

Figure 7.15: The found values for the hole mobility µp that are required to simulate the J(V)-curves for double carrier devices with a Ba/Al cathode {table 7.2, filled squares) and a LiF/Ca/Al cathode (table 7.3, open circles).

Table 7.3: Overview of physical parameters that were most suited to simulate the hole cur­rent for a tempemture variation in a L = 90 nm double carn·er device with a LiF /Ga/ Al cathode using for holes the field and tempemture dependent mobility model when the elec­tron current is modeled through the trap filled limited mobility for kBTt = 125 me V, trap concentration 0.13%, and a mobility µn = 5.66 x 10-9 m2 /Vs.

T [KJ µp[m /Vs] 'Yp [(m/V)1 2] 293 1.2 x 10- 1.40 x 10-273 3.1 x 10-12 2.45 x 10-4

253 5 x 10-13 4.5 x 10-4

233 4.8 x 10-14 7.5 x 10-4

carriers. This is in agreement with experimental data. In figure 3.3 it was shown that fora hole-only L = 80 nm device the measured current density of 20 A/m 2 is reached at 3.1 V, while in figure 3.5 the same 20 A/m2 is reached at the same voltage for a L = 100 nm electron-only device with LiF /Ca/ Al cathode. Hence the crossover point will be in reality at somewhat lower V for a thinner LiF /Ca/ Al sample with L = 80 nm. This is in contrast with the findings for Ba/ Al (figure 7.5) where holes remain dominant up to 1000 A/m2.

93

1000

100

10

.r E ~ 0.1 ...,

0.01

1E-3

1E-4 0.1 10

Figure 7.16: The same parameters that are capable of simulating J(V)-curves for dou­ble carrier devices with a LiF /Ga/ Al cathode are used here to predict the J(V)-curve for a hole-only device and an electron-only device for L = 90 nm. The electron currents are de­scribed using 0.13% traps of depth kBTt = 125 me V fora mobility µn = 5.66 x 10-9 m2 /Vs. The hole currents are described using the field and temperature dependent mobility for µp = 1.2 x 10-11 m2 / Vs and 'Yp = 1.4 x 10-4 (m/V)112 .

7.3.3 Modeling of charge and exciton distribution

The distribution of charge carriers is now calculated. From figure 7.17a it is shown that more excitons are generated closely to the cathode at low V. At higher V the electron concentration through the device starts to increase while the hole concentration decreases near the cathode. In the exciton picture now there are more excitons close to the anode. The found situation is then comparable to the device with the Ba/ Al cathode, where at high V, the recombination will take place more often close to the anode. The distribution of holes and electrons is shown at different V in figure 7.l 7b. For low V = 0.08 V there are more electrons close to the cathode than to the anode. The device is not injection-limited yet, for this harrier of only 0.2 eV. Now the recombination efficiency can be calculated. This is shown in function of the applied voltage in figure 7.18a and in figure 7.18b for the current density. Both situations yield near-ideal efficiencies close to l. This means that the maximum possible amount of charges recombine forming excitons. If this is true then all the holes near the cathode and all the electrons near the electrons should be used up and their density should go to zero. The found straighter line for LiF /Ca/ Al is in contrast toa device with Ba/ Al cathode where a more outspoken peak in T/rec was found. The found efficiency should be compared to the

94

1E31..--~--.-----..,..----.---~--.---~

1 EJO (a) -v-v" = 3.52 v <r

1 29 \ V ... " ... V-V"= 1.59V

E E "----- ········V-V"=0.9V

-~ 1E28 \. - ------V-V"=O.OBV

~ ~~~~ ···.......................... . .. ~-:::,~,<::-··:>! _g 1E25 111

~ 1E24 ~ 1E23 § 1E22 ~ 1E21 ~ 1E201-~--.-----.---..,..---..,..---"-'

0 m ~ M 00

distance from anode [nm]

1E29-.--~--.------.-----..,..---..,..-~ (b) -v-v.=3.52V

1E27 "::,.0':> ............. v-v. = 1.59 v

1E25 . -<::-0 V ..... " .. v-v. = 0.90 V <r ·.· .. -V-V =008V ; :::: ., • ~CCC=czc.="·---·~~~~~~--~'.:" c: ~ 1E19 ························ ······· ti; -~ 1E17

1E15

1E131-~-.-----..,..----.-----..,..---"' 0 20 40 60 80

distance trom anode [nm]

Figure 7.17: Distr-ibution singlets (a) and electrons and holes (b) through the L = 90 nm double carrier device with a LiF /Ga/ Al cathode at T = 293 K. The electron cur­rent is described through the trap filled limited mobility for µn = 5.66 x 10-9 m2 / Vs, kBTt = 125 meV, a trap concentration of 0.13 %, and a Schottky barrier of 0.20 eV. The hole current is described using the field and temperature dependent mobility model with µP = 1.2 x 10-11 m2 / Vs and /p = 1.4 x 10-4 (m/V)112 .

efficacy 2 in figure 7. 7. From the efficacy curve it is seen that the LiF /Ca/ Al reaches a maximum in efficacy already at low V, in contrast to Ba/ Al for which the efficacy increases steadily with voltage. This is in agreement with our findings. Above 3 V the simulated efficiency gradually decreases with voltage. This decrease is also in agreement with the efficacy measurement. The simulation peaks at 3 V which is very close to the peak in the measurement V::::: 4 V. Further it seems that the measured decrease in efficacy is stronger. Therefore again we note that this can be consequence of photoluminescence quenching, where at a certain high field the formed exciton will be separated again (as explained in subsection 7.2.3). This effect is not taken into account yet. Then at high voltages the recombination efficiency will be lower. Only for low V < 2 V, we do not find the steep increase as in the measured efficacy. This might be related to an outcoupling effect, that is not included in the model yet. It has been shown for PPP [57] that the outcoupling is weaker near the cathode. We find that at low V, the exciton density (and therefore the emission zone) in a device with a LiF/Ca/Al cathode is higher near the cathode (figure 7.17a). A possible explanation is that in the measured efficacy, the maximum only becomes visible at somewhat higher V, when the emission zone has shifted towards the anode and outcoupling is better. From our findings we find a higher recombination efficacy LiF /Ca/ Al (1) compared to

2 The conversion from efficiency to efficacy is explained in appendix C.

95

1.0 .,...., ................................ ..,.=---,--~....--..----.,..-.---,,-, •• •••••••• (a)

0.9 ••••••••• 0.8

0.7

0.6

~ 0.5 I=' 0.4

0.3

0.2

0.1

0.0+-~..-----.--.----.~--...~--.-~-.-~~-1 0 2 4 6 8 10 12 14

1.0--i=""--.-----,-----.--~--,.--. ._......... (b)

••••••••• 0.8

0.6

~ I=' 0.4

0.2

0.0+-~--.-----,-----.--~--...--1 0 5000 10000 15000 20000

J [A/m2]

Figure 7.18: The recombination efficiency predicted by the developed model Jor double carrier devices with LiF /Ga/ Al cathode for L = 90 nm is shown in function of voltage ( a) and current density (b).

Ba/Al (0.7 at the peak, figure 7.8). From the efficacy measurements, the height of the measured peak in a double carrier device with a LiF /Ca/ Al cathode is comparable to the height of the peak for a device with a Ba/ Al cathode. In subsection 7.2.4 it was shown that a small change in the used hole mobility, electron barrier due to illumination, or recombination prefactor might result in a somewhat higher recombination efficiency. These issues provide a possible explanation for the finding of a somewhat larger difference in exciton recombination efficiency compared to the measurements for efficacy.

96

Chapter 8

Conclusions and Outlook

8.1 Conclusions

8.1.1 Electron-only devices

• J(V)-curves of electron-only devices are characterized by steep slopes on log-log scales, up to 8 for room temperature and as high as 15 for 193 K. This is much higher than for hole-only devices or double carrier devices (that have slopes 3-4 at room temperature).

• The built-in voltage for blue electron-only devices is not equal to the difference of the vacuum work function of the electrodes. Al might react forming aluminum oxide what can cause a shift to a lower energy level with an effective work function of 3.3 eV instead of 4.2 eV. The built-in of an electron-only device is at about 0.6 V.

• The model for the electron mobility assuming traps, successful for electron-only OC1 C10-PPV devices, is not applicable to a device with a blue polyfluorene and a Ba/ Al cathode. Instead, the concentration dependence of the mobility in combina­tion with a Gaussian density of states is necessary to describe the device that shows slopes that keep increasing with higher V. A value of the Gaussian width er= 0.22 eV is found, indicating a largely disordered energy landscape for electrons ( much higher than the value of 0.14 eV for holes in NRS-PPV). The found temperature depen­dence of the mobility, determined by P1 ::::::J 0.18 (figure 5.8) is much smaller than the expected 0.44 < P1 < 0.50 [48].

• The electron current in a device with a Ba/ Al cathode is injection-limited. The injection harrier for electrons is about 0.5 eV.

• The samples under investigation of electron-only devices with a Ba/ Al cathode needed to be selected before modeling. Some J(V)-curves show hysteresis-like multistable

97

behavior and have problems in reversibility. This situation is different from hole-only and double carrier devices, that sometimes have leakage currents but do not show multistable curves.

• The electron-only devices with a LiF /Ca/ Al cathode show J(V)-curves that cannot be explained using the same electron mobility model as used for devices with Ba/ Al cathode. The slop es do not increase as much for increasing V and decreasing T. These devices can be described using a model consisting of 0.133 traps with trap depth kBTt = 125 meV, a Schottky barrier «P B = 0.20 eV and a constant electron mobility µn = 5.66 x 10-9 m2 /Vs. The concentration dependent mobility model here is not capable of predicting the temperature dependence of the J(V)-curve.

• Devices with a Ba/ Al cathode and a LiF /Ca/ Al cathode should be regarded as intrinsically different: different models are required for the bulk mobility.

• An electron-only device with a LiF /Ca/ Al cathode shows a current density that is up to 6 times higher compared to the standard Ba/ Al cathode in blue electron­only devices. The injection harrier for LiF/Ca/Al is lower («PB = 0.20 eV), which is enough to provide ohmic-like behavior. This suggests a difference in injection harrier between devices with LiF /Ca/ Al and Ba/ Al cathodes of about 0.3 e V from modeling. This is in agreement with experiments as photovoltaic measurements, electrical impedance spectroscopy and electro-absorption (for double carrier devices) from which a difference in barrier of 0.2 + 0.1 eV is found. From the built-in voltages for electron-only devices however such a difference was not found.

• There is only a small field dependence of the mobility for electron-only devices. For devices with a Ba/ Al cathode, the field dependence is taken into account automati­cally by the Pasveer et. al model and at the typical driving voltages this has a small effect (figure 5.9). For the LiF /Ca/ Al cathode, no field dependence is needed in the successful simulations.

8.1.2 Double carrier devices

• The thickness and temperature variation for the J(V)-curves of devices with a Ba/ Al cathode is modeled successfully. For the hole current the field and temperature depen­dent mobility model is assumed. For describing the electron current a concentration dependent mobility in a Gaussian DOS of a = 0.22 eV is taken, and a Schottky injection barrier «P B = 0.52 e V is assumed.

• When the exact parameters found for hole-only devices are used, the double carrier current is underestimated.

98

• For the devices with Ba/ Al cathode there is a larger exciton density close to the anode than close to the cathode. This means that the recombination zone is closer to the anode.

• For a device with a Ba/ Al cathode, the simulated recombination efficiency increases for increasing voltage because of lowering of the electron barrier due to the image charge effect, and a peak is found. This is in good agreement with the observed peak in the measured efficacy.

• Holes are the dominant charge carriers in blue LEDs with Ba/ Al cathode for low voltages (V < 8 V for L = 80 nm device). At V = 8.8 V the hole and electron current become similar and the recombination efficiency peaks.

• The temperature variation in a device with LiF /Ca/ Al cathode is described very well. For the electrons a model consisting of 0.133 traps with trap depth kBTt = 125 meV, a Schottky barrier <I> B = 0.20 eV, and a constant mobility µn = 5.66 x 10-9 m2 /Vs is used. For the holes the field and temperature dependent model is used for parameters that deviate slightly (for the mobility 303 deviation at room temperature) from the ones found for Ba/ Al. These close mobilities imply that LiF /Ca/ Al does not act as a hole blocker.

• For a device with a LiF /Ca/ Al cathode there is a larger exciton concentration next to the cathode for low V, while at higher V - Vii ~ 1 V and above the exciton concentration is largest near the anode.

• In devices with LiF /Ca/ Al cathode, electrons become the dominant charge carriers already at low V ( around 5 V for a L = 90 nm device).

• For a device with a LiF /Ca/ Al cathode, the maximum possible recombination effi­ciency around 1 is found at all V < 7 V fora L = 90 nm device. This is in agreement with measurements of the efficacy for V > 2 V. However the measured steep increase in efficacy for V < 2 V for a L = 80 nm device is not found in the simulated re­combination efficiency. This measured effect can be attributed to an improvement of the outcoupling efficiency when the outcoupling shifts from the cathode towards the anode, which is not taken into account yet in the model.

8.2 Outlook

• The reason behind the difference in the electron mobility of the bulk when the cath­ode is changed, should be investigated. It is not clear why in a device with a Ba/ Al

99

cathode traps are not required to describe J(V)-characteristics and why in a de­vice with LiF /Ca/ Al cathode the concentration dependence of the mobility can be neglected.

• The reason for the large width (0.22 eV) of the electron density of states should be investigated.

• The hole current in this report is described using the field and temperature dependent model. This was best for hole-only devices. However the hole current can be treated fairly well also incorporating the concentration dependence and a Gaussian DOS for holes for er= 0.14 eV [4]. It should be investigated whether the double carrier device is described better then.

• It should be investigated why the current through a double carrier device is higher than what is expected from the models used for single carrier devices. The use of Langevin recombination might have to be reconsidered.

• Now the currents and the exciton distribution are known, the luminance L of the LEDs should be investigated. The model should be extended to look at the effect of efficiency-limiting factors as the formation of triplet excitons, non-radiative decay of singlet excitons, photoluminescence quenching and the losses because of outcoupling. This work is an essential step towards the full device characterization and complete understanding in the J(V)/ L(V) properties of blue pLEDs. The final stage will be then to examine what changes in a stressed device to understand the reason behind the limited lifetime of blue polymer LEDs.

100

Acknow ledgements

Finally I've carne to the part that I'm looking forward to for so long; immortalizing my gratitude to the fine people that helped me achieving this serious stack of research.

-HULDE-

In the first place I thank my direct supervisors Simone Vulto and Reinder Coehoorn for their guidance, efforts, time, patience, ideas, and giving me the opportunity to carry out my master's thesis at Philips Research. Reinder, I have experienced it as a true honor to perform my thesis under your supervision. You know to combine a seemingly inexhaustible knowledge with a very agreeable, friendly, clarifying approach towards your students and this is a very exceptional combination. Simone, your experience for years in pLED research has been an indispensable surplus. Even though you were officially transferred to another project somewhere in the half of my internship, you always made time for our discussions and your contribution from a somewhat different point of view than Reinder's, was vital for the succeeding of my thesis. I think the best way of expressing my gratitude to you both is to let you know that I realize that I can not carne up with better circumstances to perform a thesis.

Within Philips Research, I thank Siebe van Mensfoort for sharing his experience and fine results, Addy van Dijken for using the EIS, Edsger Smits for the help on EIS, Michael Büchel for using his electro-absorption set-up, Eduard Meijer for using his photovoltaic measurement set-up, Ralph Kurt for leading the INDIGO meetings on the blue LEDs, Michael Coelle for his interest in electron-only devices, and Frank van Abeelen for the introduction to the Macleod software. I thank Philips Research for the financial support. I thank all the students I shared rooms with and had lunch with for the joy during geosense, happy hours, and poker play. At the Eindhoven University of Technology I thank Peter Bobbert for being my university­linked supervisor and for bringing me into contact with Philips. I thank René Janssen for inviting me at his group to present my results.

101

I experience this graduation as saying farewell to an incredible positive chapter of my life and therefore would also like to thank a few people that did not directly contribute to the scientific contents of this work. I thank mister Wilfried Coenen for being the best thinkable partner in sharing thoughts on every single aspect of life and for the many hilarious situations that we ended up in, which I experienced as fuel to keep me going. Best wishes in Madrid, Wil! I also thank the rest of the original San Diego crew, Koen Weerts and Caroline Geuens, for spending with me the best three months of my life. Annemie Wijnants, I thank you for the positive contribution to my life that you offered me, and for sharing love and joy with me during five years. Too bad that you felt you had to break up with me 3 days prior to finalizing this thesis. I thank Bart Berghmans for smuggling me across the border twice a week against very interesting rates, even when oil prices kept on rising. I thank the homies down at the Bennekel 145, and especially Thijs Spuesens, for approxi­mately 80 kg macaroni, 3001 vla, 601 Heineken beer (ratio 2/week), and for introducing me into the somewhat different, but very positive, way of students living together in Holland. I thank Hans De Vrij, Tom Hanegreefs, Ronald Dehuysser, Steven Vanmechelen, and Ruben Clerx for being good friends from the LUC-years and high school. I will see almost all of you back in Leuven, in the near future.

Finally I thank my mother, Annie Leemans. After my father passed away in 1983, your strength, good advice, and tremendous efforts towards your children assured that we were raised in the best possible conditions, which is the basis of any later succeedings. Bedankt ma!

Joris Billen, July 4th, 2005, Eindhoven, The Netherlands

102

Bibliography

[1] C. K. Chiang, C. R. Fincher, Jr., Y. W. Park, A. J. Heeger, H. Shirakawa, E. J. Louis, S. C. Gau, and Alan G. MacDiarmid, Phys. Rev. Lett. 39, 1098 (1977).

[2] J. H. Burroughes, D. D. C. Bradley, A. R. Brown, R. N. Marks, K. Mackay, R. H. Friend, P. L. Burns, and A. B. Holmes, Nature 347, 539 (1990).

[3] James Bond in Die another day, Metro-Goldwyn-Mayer studios Ine. (2002).

[4] S. van Mensfoort, Charge transport in blue polymer Light-Emitting Diodes (Master's thesis, Eindhoven University of Technology, 2005).

[5] S. I. E. Vulto et al., Proceedings of the 12th International Workshop on Inorganic and Organic Electro-luminescence & 2004 International Conference of the Science and Technology of Emissive Displays and Lighting, p. 65, Toronto (2004).

[6] E. Meulenkamp, PolyLED training (Philips Research, Company Confidential, 2004).

[7] A. Miller and E. Abrahams, Phys. Rev. 120, 745 (1960).

[8] P. S. Davids, I. H. Campbell, and D. L. Smith, J. Appl. Phys. 82, 6319 (1997).

[9] M. Stoessel et al., J. Appl. Phys, 87, 4467 (2000).

[10] N. W. Ashcroft and N. D. Mermin, Solid State physics (New York, Holt, Rinehart and Winston, 1976).

[11] G. Hadziioannou and P. F. van Hutten, Semiconducting polymers (Weinheim, Wiley­VCH, 2000).

[12] L. P. Ma, J. Liu, and Y. Yang, Appl. Phys. Lett. 80, 2997 (2002).

[13] L. D. Bozano, B. W. Kean, V. R. Deline, J. R. Salem, and J. C. Scott, Appl. Phys. Lett. 84, 607 (2004).

103

[14] S. J. Martin, D. D. C. Bradley, P. A. Lane, H. L. Mellor, and P. L. Burn, Phys. Rev. B 59, 15133 (1999).

[15] I. H. Campbell, T. W. Hagler, D. L. Smith, and J. P. Ferraris, Phys. Rev. Lett. 76, 1900 (1996).

[16] R. H. Parmenter and W. Ruppel, J. Appl. Phys. 30, 1548 (1959).

[17] J. R. MacDonald, Impedance Spectroscopy: Emphasizing Solid Materials and Systems (New York, John Wiley & Sons, 1987).

[18] A. van Dijken, A. Perro, E. Meulenkamp, K. Brunner, Org. Electron. 4, 131-141 (2003).

[19] V. Shrotriya, Y. Yang, J. Appl. Phys. 97, 054504 (2005).

[20] Values obtained from "The essential Macleod" database for refractive and extinction coefficients at different >..

[21] W. D. Gill, J. Appl. Phys. 43, 5033 (1972).

[22] B. G. Martin, J. Appl. Phys. 75, 4539 (1994).

[23] P. W. M. Blom. M. J. M. de Jong, and C. T. H. F. Liedenbaum, Polym. Adv. Technol. 9, 390-401 (1998).

[24] P. W. M. Blom, H. C. F. Martens, and J. Huiberts, Synthetic Metals 121, 1621 (2001).

[25] P. W. M. Blom, M. C. J. M. Vissenberg, Materials Science and Engineering 27, 53-94 (2000).

[26] L. S. Hung, C. W. Tang, and M. G. Mason, Appl. Phys. Lett. 70, 152 (1997).

[27] T. M. Brown, R. H. Friend, I. S. Millard, D. J. Lacey, T. Buttler, J. H. Burroughes, and F. Cacialli, J. Appl. Phys. 93, 6159 (2003).

[28] T. M. Brown, R. H. Friend, I. S. Millard, D. J. Lacey, J. H. Burroughes, and F. Caccialli, Appl. Phys. Lett. 79, 174 (2001).

[29] G. G. Malliaras, J. R. Salem, P. J. Broek, and J. C. Scott, J. Appl. Phys. 84, 1583 (1998).

[30] N. F. Mott and R. W. Gurney, Electronic processes in ionic crystals (Oxford University press, London, 1940).

[31] J. C. Scott, G. G. Malliaras, Chem. Phys. Lett. 299, 115-119 (1999).

104

[32] J. C. Scott, J. Vac. Sci. Technol. A 21(3), 521 (2003).

[33] U. Wolf, V. I. Arkhipov, and H. Bässler, Phys. Rev. B 59, 7507 (1999).

[34] V. I. Arkhipov, U. Wolf, and H. Bässler, Phys. Rev. B 59, 7514 (1999).

[35] M. A. Lampert and P. Mark, Current injection in Solids (Academie, New York, 1970).

[36] P. W. M. Blom, M. J. M. de Jong, and J. J. M. Vleggaar, Appl. Phys. Lett. 68, 23 (1996).

[37] W. Brütting, S. Berleb, A. G. Mückl, Organic Electronics 2,1-36 (2000).

[38] M. A. Baldo and S. R. Forrest, Phys. Rev. B 64, 085201 (2001).

[39] C. Tanase, E. J. Meijer, P. W. M. Blom, and D. M. de Leeuw, Phys. Rev. Lett. 91, 21 (2003).

[40] M. C. J. M. Vissenberg and M. Matters, Phys. Rev. B 57, 12964 (1998).

[41] W. F. Pasveer, J. Cottaar, C. Tanase, R. Coehoorn, P. A. Bobbert, P. W. M. Blom, D. M. de Leeuw, and M. A. J. Michels, Phys. Rev. Lett. 94, 206601 (2005).

[42] J. Nowotny and C. C. Sorrell, Electrical properties of oxide materials (Trans Tech Publications, Zürich, 1997).

[43] D. Poplavskyy, W. Su, F. Pschenitzka, F. So, Proc. SPIE Int. Soc. Opt. Eng. 5519, 110 (2004).

[44] S. I. E. Vulto, M. Büchel, M. Kilitziraki, M. M. De Kok, E. A. Meulenkamp, Philips Research Technical Note, (2003).

[45] H. Bässler, Phys. Stat. Sol. B 175, 15 (1993).

[46] L. S. Liao, M. K. Fung, C. S. Lee, S. T. Lee, M. Inbasekaran, E. P. Woo, and W. W. Wu, Appl. Phys. Lett. 76, 3582 (2000).

[47] H. C. F Martens et al" Phys. Rev. B, 61, 7489 (2000).

[48] R. Coehoorn, W. F. Pasveer, P. A. Bobbert, and M. A. J. Michels, to be submitted to Phys. Rev. B.

[49] E. A. Meulenkamp et. al, Proc. SPIE Int. Soc. Opt. Eng. 5464, 90 (2004).

[50] Hung et al., Appl. Phys. Lett. 70, 152 (1997).

[51] Jabbour et al" Appl. Phys. Lett. 71, 2872 (1997).

105

[52] Mori et al., Appl. Phys. Lett. 73, 2763 (1998).

[53] Kido et al., Appl. Phys. Lett. 73, 2866 (1998).

[54] Shaheen et al., Journal Appl. Phys. 84, 2324 (1998).

[55] Wolf and Bässler, Appl. Phys. Lett. 73, 3848 (1998).

[56] E. Tutis, M. N. Bussac, and L. Zuppiroli, Appl. Phys. Lett. 75, 3880 (1999).

[57] J. Grüner, M. Remmers, and D. Neher, Adv. Mater. 9, No. 12, p. 964 (1997).

[58] P. W. M. Blom, M. C. J. M. Vissenberg, J. N. Huiberts, H.C. F. Martens, and H. F. M. Schoo, Appl. Phys. Lett. 77, 2057 (2000).

[59] http://www.cvrl.org/ (The Colour & Vision Research Laboratories, Institute of Oph­thalmology, London).

106

Appendix A

Modified Schottky model

In section 4.3 it was stated that in this report the modified Schottky model by Scott and Malliaras [31], would be used to treat injection-limited currents under the assumption that 4'l/;2 ~ 1 for all V. This appendix shows this function for increasing voltage (hence field). It is shown that the assumption that 4'l/;2 ~ 1 results in an error of 0.5 at higher fields.

1.2

1.0

0.8

~ 0.6 ... 0.4

0.2

0.0 0 2 4 6

VM

Figure A.1: The dependence of 41/;2 (with 1/; defined as in equation 4.23) on the voltage for a device with typical value of LEP layer L = 100 nm at room temperature.

107

Appendix B

Modeling of electron-only device with Ba/ Al cathode using trap filled limited mobility

In section 5.3, the trap filled limited mobility was used to simulate the J(V)-curves of an electron-only device with a Ba/ Al cathode. In this appendix the reader is convinced that even for the wide range of possible parameter choice in trap depth, field dependency, introduction of injection harrier, and mobility, traps do not describe the measured J(V)­curves.

B.1 TFL mobility with field-dependent mobility

We investigate if a field dependent mobility is possible to describe the increasing slope at higher voltages. Therefore a dependence on the field represented by 'Yn as in equation 4.12 is included. We start with the 122 nm sample, look for the optima! parameters and then see how the thickness variation is described. The lower slope for L = 122 nm is 4.2 and was simulated for Tt = 937.6 K (r=3.2 or ksTt = 80 meV), trap concentration 13 1. In figure B.la the best possible results for the 122 nm sample are shown for 'Y = 1.03 x 10-3 (m/V) 112 , which gives a good fit only above V - Vbi = 5.92 V. Above this voltage for 122 nm the agreement is good but for lower volt­ages, the experiment is not described accurately. The mobility µn was optimized. The other thicknesses are not described accurately at all. Figure B. lb shows a 'Y capable of simulat­ing the data for 122 nm altready at a lower V - Vbi = 2.92 V ('Y = 8.00 x 10-4 (m/V) 112).

1 It seems that when introducing 1 the best possible fit is already reached at higher trap concentration. Furthermore changing the trap concentration wil! not yield better results because of the denoted infiuence of mobility on trap concentration and vice versa as in the footnote on page 53.

108

Again the mobility is optimized. Now at intermediate voltages (2.92 V to 10.32 V) there is deviation. The thickness dependence is not described better in this case. Because of this negative results for the thickness variation, the temperature variation is not further exam­ined. We conclude that a TFL mobility model for bulk transport, assuming no injection barrier, cannot ex plain the data.

1000 1000 (a) (b)

100 100

10 10

N~ .r E E ~ 0.1 ~ 0.1 ..., ...,

0.01 0.01

1E-3 measurement 1E-3 measurement - simulation - simulation

1E-4 1E-4 1 10 1 10

v-v.,M V-V.,M

Figure B.1: Simulations for J(V)-curves using the trap filled limited mobility in combina­tion with a field dependent mobility term f or 1 % traps and kB Tt = 80 me V. The thickness dependence for (a) 'Y = 1.03 x 10-3 (m/V)11 2 and µn = 4.2 x 10-12 m2 v- 1 s-1 and (b) for 'Y = 8.00 x 10-4 (m/V)11 2 and µn = 2.45 x 10-11 m2 V- 1s-l (optimized for L = 122 nm) are shown.

B.2 TFL mobility with injection harrier

Because of the possibility of an injection problem based on the possible mismatch of the energy levels (figure 3.2), an injection harrier is introduced. The used injection model is a Schottky injection barrier from equation 4.22, because of its simplicity and successful use in the past for metal-semiconductor transitions. In this approach of a TFL mobility in combination with an injection barrier, we face variation of five independent parameters so an extensive study over all possible ranges is needed. The parameters of interest are the energy characterizing the trap distribution, ksTt, the height of the Schottky harrier <I> B, the total density of traps Nt, the mo bility µn, and the field dependence parameter 'Y· An endless range of possibilities will be excluded by starting with a well motivated choice of some parameters and afterwards looking more thoroughly at the influence of varying other parameters. In this way a good overview is obtained while

109

the physical influence of each separate parameter is examined. The fits are all constructed using the corrected data of a 122 nm sample of BP. For the trap depth we choose the value of kBTt = 137.5 meV, which would be able to explain a slope of 6.5 on a log-log scale in case we didn't have an injection problem. The harrier height is first chosen at 0.40 e V and will be varied in the next section. The density of traps Nt is varied in order to optimize the fit. For the factor that yields the field dependence, a value of 'Y = 1.0 x 10-4 (m/V) 112 is kept constant, because the assumption is here that the steep slope is explained by <leep traps rather then by a high field dependence. The effect of variation of 'Y will be discussed later. In figure B.2 the results are shown. The straight line represents the simulations with harrier (injection-limited current) and the dotted line the ohmic injection (no harrier). The aim of this figure is to compare the shape of the curves. Since the mobility is not known we could have chosen µn different for all situations. To keep the overview, the mobility is kept constant here since that the curves for those trap concentrations are would just shifted upwards and the shape would remain unchanged. There is only a significant effect of the injection harrier for the lowest trap concentrations. For 0.13 traps in the situation with the injection harrier, bending off is observed in contrast to the measured bending upwards. In the next paragraphs the attention goes out to the effect of the Schottky harrier height <:I> B.

10•~--~----~~-~~~ 105

104

103

102

101

N~ 10° ~ 10·1

:::; 10"' 10" 10" 10-6 10"

• measurement - <1>

6=0.40eV

·············· ohm Ic injection

10·1+--~~----~~-~~---' 1 10

Figure B.2: Simulations of the J(V)-curve for a 122 nm sample with Ba/ Al cathode for the introduction of an injection barrier of 0.40 e Vin combination with traps. Three different trap concentrations (solid lines) are shown for kBTt = 137.5 me V, µn = 1.6 x 10-s m2 v- 1

(optimized for 0.1% traps) and 1 = 1.0 x 10-4 (m/V)11 2 . Dotted lines represent ohmic injection to show the effect of the injection barrier that eaus es a lower slope at higher voltages.

110

B.2.1 Influence of Schottky harrier height <I>B

The influence of the Schottky harrier height is examined, by looking for the same trap depth kBTt = 137.5 meV in figure B.3 at a low (<I> B = 0.30 eV) and a high (<I> B = 0.70 eV) harrier. The mobility is optimized for 13 traps. For the other trap percentages, the same µn is taken. We are interested in the shape of the curves and this is not affected by µn. No difference was noticed between ohmic injection and the small harrier of <I> B = 0.30 eV (both straight lines that coincide). This means that for a small harrier, still enough carriers are availiable at the contact. The injection problem becomes visible at higher voltages. This is shown by comparing the dotted line ( <I> B = 0. 70 e V) with the straight line ( <I> B = 0.30 e V). Even though at high V, the device would like to drag more electrons from the cathode to the anode, these carriers are simply not available at the contact for <I> B = 0.70 eV. This effect seems more important for lower trap concentration. In all cases, the harrier causes a flatter slope, while the aim is to predict an increasing slope for increasing V. From these fits, the situation with <I> B = 0.30 eV seems best, but this fit is the same as one for ohmic injection. In figure B.1 it was already pointed out that even with the inclusion of a field dependence, the thickness variation could not be described then. In the next section, the variation of the trap depth and 'Y will be discussed and conclusions are drawn.

B.2.2 Influence of trap depth kBTt, / and conclusions

For 137.5 meV (explaining a slope of 6.5), it was seen that introduction of a harrier only has an effect above <I> B = 0.30 e V. The harrier is visible only at high V resulting in a lower slope of the J(V)-curve compared to the situation without a harrier. But for the low V the slope is still 6.5, while the experiments do show an inverse effect: low slope at low V and high slope at high V. Introducing a larger field dependency only increases currents at higher V. This suggests that we have to start from a lower trap depth, i.e. 80 meV for explaining the low slop es at low V. Then it was shown that for different field dependencies the thickness dependence was not explained (figure B.l). Also for intermediate (between 80-137 meV) trap depths (not shown here), it was noticed that no fits using traps were able to explain the experiments. It can be concluded that the Ba/ Al devices can not be modeled using a trap filled limited current. The mobility µn was taken as the last fitting parameter in all simulations. It only shifts the whole curve up or down and will not affect the shape of the curve, while the difficulty was to find simulations that predict increasing slopes. lts value affected directly the trap concentration that had to be chosen to obtain fits around the measured data. The trap concentration does have effect on the shape of the curves because for a low trap concen­tration traps are getting filled up and transition to quadratic behavior occurs.

111

100000

1000

10

." ~ \

01• IJ& • measurement 1E-3 - 4>

8 = 0.30 eV

1E-5 and ohmic injectio ·· ··········· 4>

8 = 0.70 eV

1E-7-+---~-~~~~~..,....,..-----1

1 10

Figure B.3: Simulation of J(V)-curve for 122 nm sample for different trap concentmtions in combination with a barrier height of 0.30 e V (solid line) and 0. 70 e V (dotted) for kBTt = 137.5 me V, µn = 5.29x10- 5 m2 v- 1 s- 1 and 1' = 1.0x10-4 (m/V)112 . The mobility does not affect the shape of the curve and to keep the overview is was optimized for 1 % traps and kept constant for the other trap concentrations. There is no difference between ohmic injection and the barner of 0.30 e V (solid lines that coincide and can therefore not be distinguished).

The main conclusion is that no combination of parameters for the trap model is able to describe accurately the J(V)-curves of a device with a Ba/ Al cathode for one thickness at all V. Further a variation of thickness and temperature is not predicted correctly at all.

112

Appendix C

Conversion from efficiency to efficacy

The luminous efficacy is the luminous intensity measured for normal emission per unit of current and takes into account the perception of light by the human eye [6]:

io K(>.) hv 'f/L = - = 'f/eff __ _

I 7r e (C.1)

with K(>.) = 683V(>.) lm/W, where V(>.) a dimensionless eye-sensitivity function [59] that is around 0.278 for blue polymer under investigation, hv = 2.5 eV the average light-emission energy for BP and 'f/eff defined as the efficiency in equation 2.3. This yields

T/L K(>.) hv

'f/P L · T/ST · T/rec · T/out · ---7r e

= 0.65 · 0.25 · T/rec · 0.20 · 683 · 0.278/7r · 2.5

= 3.28 cd/ A (for T/rec = 0.67)

with the photoluminescence efficiency T/PL = 0.65 measured within Philips for BP, the sin­glet:triplet ratio T/ST = 0.25 determined from quantum mechanics (but it is often assumed that the actual value can be somewhat higher, up until 0.50 [6]), and the outcoupling efficiency T/out = 0.2 estimated within Philips [6].

113

Appendix D

Simulations using the model successful for double carrier current in a device with a Ba/ Al cathode

The simulated J(V)-curves based on parameters for devices with Ba/ Al cathode are stated for double carrier devices, hole-only devices and electron-only devices for different thickness (60-90-120 nm) (figure D.la-b-c) and temperature (293-253-213 K) ((figure D.2a-b-c). The parameters found for simulating the J(V)-curves of a double carrier device are used in all simulations. This yields for electrons the concentration dependent mobility with a Gaussian DOS (a = 0.22 eV), a barrier of <I> B = 0.52 eV, and for hole mobility the parameters shown in table 7.2. The recombination efficiencies for the different thicknesses are shown in figure D. ld and for the different temperatures in D. ld.

114

100000 (a)

10000

1000

100

.r 10 E $ ..,

0.1

0.01

1E-3

1E-4 0.1

100000 (c)

10000

1000

100

N~ 10 E $ ..,

0.1

0.01

1E-3

1E-4 0.1

- d.c. device ········· h.o. device

··· ···· e.o. device

V-Vb!M

-d.c. device ········· h.o. device

e.o. device

V-Vb!M

L=60nm T = 293 K

10

L= 120 nm T = 293 K

10

100000

10000 (b)

1000

100

N~ 10 E $ ..,

0.1

0.01

1E-3

1E-4 0.1

1.0

0.9 (d)

0.8

0.7

0.6

"0.5 !

"'" 0.4

0.3

0.2

0.1

0.0 0 2

-d.c.device ········· h.o. device

e.o. device

L =90 nm T =293 K

10

V-V"[V]

L=120nm L = 90 nm .-•••••••

L = 60 nm cfl°"'""<i~ • ••••• 00 .·'

• •o. .• oo • D • • 0 0

• DO =- °o,, • 0 •

• 0 •• 0 •

0 • • DO ••

• CJ •• a DO."

:11~~··· 4 6

T = 293 K

8 10 12 14

Figure D.1: The predicted J(V)-curves based on parameters for devices with a Ba/Al cath­ode. For the electron mobility the concentration dependent mobility model with a Gaussian DOS for a = 0.22 e V, a Schottky barrier of 0.52 e V and for the hole mobility the field and temperature dependent mobility with parameters from table 7.2 is assumed. The then found J(V)-curves for a double carrier device with Ba/ Al cathode, electron-only device and hole-only devices are shown fora thickness variation at room temperature of L = 60 nm (a) - L = 90nm (b) - L = 120 nm (c). The recombination efficiency for three thicknesses is shown in (d).

115

100000

10000 (a)

1000

100

NÊ 10

s. 1 ..,

0.1

0.01

1E-3

1E-4 0.1

100000 (c)

10000

1000

100 .....

10 E s. .., 0.1

0.01

1E-3

1E-4 0.1

- d.c. device .. " ... " h.o. device

e.o. device

V-V~M

- d.c. device h.o. device

···········" e.o. device

L = 90 nm T =293 K

10

L = 90 nm T = 213 K

10

100000 (b)

10000

1000

100

N~ 10 E s. 1 ..,

0.1

0.01

1E-3

1E-4 0.1

1.0 (e)

0.9

0.8

0.7

0.6

~ 0.5 <=" 0.4

0.3

0.2

0.1

0.0 0 2

V-V~M

T = 293 K .... "

L=90nm T= 253 K

10

•• •• • • •• • •T=253K • •••

• cfYX"Joo •._ • 00 00

• o T = 213 K 0 o • 0 ......... 000

• 0 .& :.,.. Do

•• 0 AA ~ ... "" Do •• 00. :& ......

•• 00 ". ... ...~

4 6 8 10 12 14

Figure D.2: The predicted J(V)-curves based on parameters for devices with a Ba/Al cath­ode. For the electron mobility the concentration dependent mobility model with a Gaussian DOS for a = 0.22 e V, a Schottky barrier of 0.52 e V and for the hole mobility the field and temperature dependent mobility with parameters from table 7.2 is assumed. The then found J(V)-curves fora double carrier device with Ba/Al cathode, electron-only device and hole-only devices are shown for a temperature variation for L = 90 nm at temperature of T = 293 K (a) - T = 253 K (b) - T = 213 K (c). The recombination efficiency for three temperatures is shown in ( d).

116