Universität Regensburg
Naturwissenschaftliche Fakultät II - Physik
Institut II - Experimentelle und Angewandte Physik

Blinking Phenomena in InGaN Quantum
Wells

Diplomarbeit von Christian Feldmeier aus Wörth a.d. Donau
unter Anleitung von PD Dr. Ulrich T. Schwarz von der Universität Regensburg
und Prof. Dr. Ruggero Micheletto von der Yokohama City University
durchgeführt an der Yokohama City University, Japan
Regensburg, November 2009

Contents
Introduction

1

I

3

Background

1 InGaN/GaN quantum wells
1.1 Material system . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Crystal structure . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Internal electric fields . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Spatial inhomogeneous indium distribution . . . . . . . . . . . . .
1.5 GaN based LEDs . . . . . . . . . . . . . . . . . . . . . . . . . . .

5
5
6
7
7
8

2 Random telegraph signal
2.1 Quantum jump theory . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Power law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Deep traps and the random telegraph signal . . . . . . . . . . . .

11
11
13
14

3 Plasmons and coupling of quantum wells to plasmons
17
3.1 Bulk plasmons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Surface plasmons . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2.1 Surface plasmon polaritons . . . . . . . . . . . . . . . . . . 18
3.2.2 Localized surface plasmons . . . . . . . . . . . . . . . . . . 19
3.3 Coupling of InGaN quantum wells to surface plasmons . . . . . . 21
3.4 Coupling of surface plasmons to light . . . . . . . . . . . . . . . . 23
3.5 Quantum confined stark effect screening vs. surface plasmon coupling 24
3.6 Plasmons in nanoclusters of metallic indium . . . . . . . . . . . . 25

II Experiments

27

4 Samples29

5 Time intensity profiles
5.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Different types of blinking points . . . . . . . . . . . . . . . . . .

31
31
33

iii

Contents
5.2.1
5.2.2
5.2.3

Two level blinking points . . . . . . . . . . . . . . . . . . .
Multi level blinking points . . . . . . . . . . . . . . . . . .
Interpretation . . . . . . . . . . . . . . . . . . . . . . . . .

34
35
38

6 Simulations

41

7 Temperature dependence of the blinking
7.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Photoluminescence changes . . . . . . . . . . . . . . . . . . . . .
7.3 Two level blinking points . . . . . . . . . . . . . . . . . . . . . . .
7.4 Multi level blinking points . . . . . . . . . . . . . . . . . . . . . .

45
45
46
46
46

8 Surface plasmons and the blinking phenomena
8.1 Photoluminescence enhancement . . . . . . . . . . . . . . . . . . .
8.2 Changing emission pattern . . . . . . . . . . . . . . . . . . . . . .
8.3 SEM images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.4 Cleaning the sample . . . . . . . . . . . . . . . . . . . . . . . . .
8.5 Photoluminescence changes . . . . . . . . . . . . . . . . . . . . .
8.6 Statistics on the changes . . . . . . . . . . . . . . . . . . . . . . .
8.7 Comparisons between photoluminescence movies and SEM images
8.8 Changes in vacuum . . . . . . . . . . . . . . . . . . . . . . . . . .

55
55
56
57
60
60
64
65
67

9 Memory effect
9.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2 Photoluminescence changes . . . . . . . . . . . . . . . . . . . . .
9.3 Systematic illumination interval sequence . . . . . . . . . . . . . .

73
73
74
76

Summary

79

Bibliography

81

iv

Introduction
In the last decades the group III nitrides aluminum nitride (AlN), indium nitride(InN), gallium nitride (GaN) and their ternary alloys have gained much attention
as a promising material system for a variety of semiconductor devices such as
blue-emitting lasers, high-power transistors or bright light-emitting diodes (LED).
GaN based LEDs are an interesting issue due to their role in full color display
and lighting applications. Despite this importance the precise nature of the lightemitting process hasn’t been understood completely yet, due to the complex
material physics and engineering involved [1, 2].
An astonishing phenomenon that hasn’t been understood yet is a blinking occurringin indium gallium nitride/gallium nitride (InGaN/GaN) quantum wells. At highindium content the photoluminescence of these quantum wells shows intense lightemitting centers. Surprisingly some of these centers are optically not stable, theirphotoluminescence changes, they blink (fig. 0.1) [3].
An effect like this has been observed in a wide variety of scientific fields ranging
from fluorescent proteins over polymers to semiconductor nanostructures. The
link between these different areas is the unstable luminescence occurring always
in nanoscale light emitters. As the blinking occurs in many different fields andsystems, one might think there should be an universal answer to explain thisnanoscale blinking, but even over ten years after the first observations a satisfactory
explanation is without reach [4].
This thesis deals with the blinking phenomena in InGaN/GaN single quantum
wells and should contribute to the understanding of the underlying mechanism.
For this purpose a set of different experimental methods was applied to investigate
on the blinking phenomenon. The thesis is structured as follows:
The first part introduces to the fundamental concepts that are of importance forstudying the blinking phenomena in InGaN quantum wells. In chapter 1, properties of group III nitrides and InGaN quantum wells, special optical properties
related to the experiments and the function of GaN based LEDs are explained. In
chapter 2, different theoretical models describing a blinking behavior and associated causes are discussed. Chapter 3 concentrates on plasmons and the couplingof quantum wells to surface plasmons in metal surfaces, enabling them to enhancethe emission of the quantum well. The coupling between InGaN quantum wells
and surface plasmons in gold nanoparticles and gold films is especially addressed.
In the second part of the thesis the materials, methods and experimental resultsof this work are discussed. The samples used for the experiments and their photo-1

Introduction

Figure 0.1: The images show the photoluminescence of a InGaN/GaN single quantum wellat different times. Bright points of high intensity can be observed. The circled point changes
intensity, it blinks. The size of the images is about 5 x 5 µm.

luminescent characteristics are described in chapter 4. In chapter 5, time intensity
profiles of different blinking points are analyzed. The blinking is categorized
into 3 different types of blinking by the number of intensity levels and different
statistics involved. In this regard numerical simulations based on a theoreticalmodel were done in chapter 6. After studying the dependence of the blinking
behavior and statistics on the temperature in chapter 7, in chapter 8 surface
plasmons coupling to InGaN quantum wells are addressed. New blinking points
could be generated by means of enhanced light emission through surface plasmon
coupling. In chapter 9, a optical memory effect of InGaN quantum wells wasfound by using a systematic illumination interval sequence. In the end the final
part gives a brief summary of the obtained results.

2

Part I
Background3

1 InGaN/GaN quantum wells
GaN based quantum heterostructures are the essential part of many importantelectrooptical devices such as light-emitting diodes (LEDs) or laser diodes. As all
experiments of this thesis deal with optical effects in InGaN/GaN single quantum
wells, this chapter will give a brief introduction to the properties of this remarkable
materials and to effects related to the experiments.

1.1 Material system
The binary group III/group V direct bandgap semiconductor gallium nitride(GaN) and its ternary alloy with indium nitride (InN), indium gallium nitride(InGaN) provide the basis for InGaN quantum wells. For these structures a thin
InGaN layer forming the active layer of the heterostructure is sandwiched between
two thicker GaN layers. The smaller bandgap of InGaN results in a quantum
well which is called single quantum well for one single layer of InGaN and multiquantum well for several layers of InGaN between layers of GaN.
The bandgap of InN Eg,InN is about 0.7 eV lying in the infrared range and theone of GaN Eg,GaN is about 3.4 eV lying in the ultraviolet range. Therefore inprinciple the bandgap of InGaN can range from ultraviolet to infrared, dependingon the ratio of GaN to InN. The resulting band gap of InGaN Eg,InGaN can becalculated by [5]:Eg,InGaN (x) = xEg,InN + (1 − x)Eg,GaN − bx(1 − x)(1.1)

In this formula b is the bowing parameter which is 1.21 for the system InGaN, x
describes the amount of InN, (1 − x) accordingly the amount of GaN.
However, shifting the emission towards longer wavelengths demands higher concentrations of indium which results in lower efficiency. Additionally, technicalproblems in the growing of GaN with high indium contents limit the applicationof GaN based quantum wells to the range form near UV to green.

51 InGaN/GaN quantum wells

band gap Eg [eV]lattice constant a [Å]
lattice constant c [Å]

InN
0.7
3,545
5,703

GaN
3.4
3,189
5,185

Table 1.1: The lattice constants a and c and the band gaps Eg of indium nitride (InN) andgallium nitride (GaN)

Figure 1.1: The hexagonal wurtzite structure of GaN or InN grown in [0001] direction. Nitrogenatoms are black, gallium or indium ones are grey. (from [6])1.2 Crystal structureGroup III nitrides can crystallize both in zinc blende and hexagonal wurtzite
structure. As the wurtzite structure is thermodynamically much more stable itis usually used for electrooptical devices. Fig. 1.1 shows the wurtzite structure.
It is a hexagonal crystal system with its unit cell characterized by the lattice
parameters a, c and u. c is the distance between two identical hexagonal latticeplanes, a the distance between the atoms in one lattice plane, u describes thebond length in c direction and thus the distortion of the unit cell. All group III
nitrides GaN, InN and AlN and their ternary and quaternary compounds can havethis crystal structure but with different lattice parameters a and c and different
band gaps Eg . Table 1.1 shows a comparison of the lattice parameters and bandgaps of InN and GaN.
Wurtzite structure lacks inversion symmetry i.e. the centres of positive and61.3 Internal electric fields
negative charges are not identical. This and the fact that the III-N bond hasstrong ionic character leads to spontaneous polarization aligned along the [0001]
direction. The lack of inversion symmetry gives also rise to special properties thatare due to polarization such as piezoelectricity.

1.3 Internal electric fields
Internal electric fields play a very important role and have a strong impact on theproperties of GaN based quantum wells. Apart from the spontaneous polarizationstrong piezoelectric fields occur. Caused by the different lattice constants of
GaN and InN the thin InGaN film is strained in the quantum well i.e. its lattice
parameters are not the same as the ones in equilibrium. This causes a strong
piezoelectric field which can get as strong as 3 MV/cm for a Indium concentrationof 22%. Compared to this the spontaneous polarization is very small (about 100
kV/cm) and neglectable [7].
The internal fields cause a deformation of the quantum well bands as shown in fig.
1.2. This results in a red shift of the emission towards longer wavelengths. As thisis similar to the Stark effect in atom physics this effect is called quantum-confined
Stark effect (QCSE). Along with this the internal fields cause a confinement of theelectron and hole wavefunction on opposite sides of the quantum well separating
the holes and electrons. The overlap between the electron (Ψe ) and the hole
wavefunction (Ψh ) gets smaller compared to the situation without electrical field.
This leads to a smaller oscillator strength which is the overlap integral of both
functions. With decreasing oscillator strength the transition probability and thus
the radiative combination efficiency decreases. In a wide quantum well (thick
InGaN layer) this effects gets even more important because the separation of the
wavefunctions is bigger.
Another electrical field inside the quantum well that has a strong influence on
the optical properties is the electrical field arising from the separation of opposite
charged carriers. The field between electrons and holes has the opposite directionof the piezoelectric field and therefore screens the piezoelectric field. The emission
therefore shifts back to higher energies [8].
In LED structures there is an additional internal electrical field of the p-n junction
which is directed from the p-doped to the n-doped area.

1.4 Spatial inhomogeneous indium distribution
The indium concentration is not homogeneously distributed in the InGaN layer.
During the growing process InGaN tends to precipitate cluster like structureswith especially high indium content. These clusters can clearly be observed in7

1 InGaN/GaN quantum wells

Figure 1.2: Scheme of the quantum confined stark effect (QCSE) (after [9]). The internal
fields cause a deformation of the quantum well bands. This results in a red shift of the emission
towards longer wavelengths. The electrons and the holes get confined on opposite sides of thequantum well leading to a separation of holes and electrons. The overlap between the electron(Ψe ) and the hole wavefunction (Ψh ) gets smaller. The transition probability and thus theradiative combination efficiency decreases, the quantum well emission gets weaker.

TEM images of the quantum well as reported in [10] and [11]. Spatially resolved
photoluminescence showed that the spatial distributions of the optical properties
of InGaN depend on the indium composition. Areas of high photoluminescenceintensity coincide with areas of high indium content [12]. The band gap of areasof high indium content is smaller than the one of the surroundings with lower
indium concentration. Carriers can be trapped and localized in these potential
minima hindering the pathways to nonradiative recombination centres and thusincreasing the probability for radiant recombination [13]. The sizes of the island
like areas with high indium content can range from 20 nm to 70 nm [13], or justmeasure a few nanometers [14]. Other groups report on sizes as large as 0,2 to 1
µm [12].

1.5 GaN based LEDs
Quantum wells can be excited in several ways. The light emission is then referred
to as photoluminescence, for excitation by means of electromagnetic radiation, as
cathodoluminescence, when excited by a beam of electrons, as radioluminescence
for ionizing radiation and as electroluminescence in the case of an exciting electricfield.
Conventional light sources like light bulbs or fluorescent lamps work on the basisof either incandescence or discharge in gases. By contrast the light generation
through LEDs is based on a fundamentally different process providing lots ofadvantages over conventional light sources. LEDs are characterized by their small

8

1.5 GaN based LEDs

Figure 1.3: The schematic diagram shows a p-n homojunction (left) and a p-n heterojunction(right) both under forward bias. In homojunctions, carriers diffuse over the diffusion lengths Ln
and Lp before they recombine. In heterojunctions, carriers are confined by the quantum well.
(adapted from [16])size and weight, better efficiency permitting energy savings, long lifetime anddurability and control over emission properties.
LEDs consist of a p- and a n-doped semiconductor layer. Donor impurities
create states near the conduction band while acceptors create states near thevalence band. This shifts the Fermi level closer to the conduction bands for
n-doped semiconductors and closer to the valence band in the case of p-doped
semiconductors. Joining these different doped semiconductors together in very
close contact results in a p-n junction. Electrons diffuse into the p-doped area
whereas holes diffuse into the n-doped area causing a space charge in the so called
depletion layer. The electric field of the space charge opposes the diffusion process
in equilibrium state. Applying forward bias removes this equilibrium state andinjects electrons from the n-side into the p-n junction where they recombinate
with holes (fig. 1.3).
During the recombination radiative recombination processes compete with nonradiative processes. To obtain high efficiencies as many electron-hole couples as
possible have to recombine radianting photons. This means the non-radiative
carrier lifetime τnr should be large compared to the radiative carrier lifetime τr .
With this the quantum efficiency η can be defined as [17]:η=τnrτnr + τr

(1.2)

expressing the ratio of exited carriers that relax via radiative recombination to
the total recombination.
Often a thin semiconducting layer with smaller bandgap than the surrounding
areas is located between the p- and the n-doped area. The resulting quantum
well confines both the electrons and the holes resulting in higher recombination
probability and increasing efficiency (fig. 1.3). The emission wavelength hence
depends on the quantum well band gap and the width of the quantum wellinfluencing on the strength of the quantum confined Stark effect. Due to theirbandstructure InGaN/GaN quantum wells are used for LEDs emitting in the91 InGaN/GaN quantum wells
range from UV to green [16, 17].

10

2 Random telegraph signal
The blinking points observed for this thesis show different blinking behaviors(section 5.2). We think that all these different kinds of blinking are based on
one fundamental blinking behavior which randomly switches between just two
intensity levels. A signal that switches between an on- and a off-state is called
random telegraph signal (fig. 2.1). Such a signal has been observed in manydifferent systems like macroscopic InGaN clusters [18] quantum dots [19, 20] or,like in our case, in InGaN/GaN single quantum wells [3].

Figure 2.1: A time intensity profile of a blinking point that had been taken for this thesis.
The blinking point shows random telegraph behavior. The intensity switches randomly between
two levels, an on- and an off-state.

This section will give a brief introduction to different mechanisms that can cause
a random telegraph signal and the different statistics and causes associated withthem.

2.1 Quantum jump theory
The simplest model for the random telegraph signal was developed by Cook andKimble [21]. It describes a fast fluorescent cycling of a electron between two states|1i and |2i, interrupted by infrequent jumps to a third state |3i, a metastableunfluorescent shelf state. From this third state the electron can relax into the112 Random telegraph signal
ground state |1i and fluorescent cycling between the |1i and |2i starts again. The
system is in the on state when the electron is cycling between |1i and |2i and in
the off state when the electron is ’trapped’ in state |3i.
A quantum jump random telegraph signal like this has been observed in single
ions or molecules [22, 23]. But also random telegraph signal of quantum dotsthat can be described by the quantum jump model could be found [19, 24]. Aoki
et al [18] reported on random telegraph noise in the luminescence of individual
macroscopic InGaN clusters. These clusters had been formed in InGaN multiple
quantum wells and showed a blinking behavior with exponentially distributed
probabilities of on and off times.
In the theory of Cook and Kimble [21] the intensity of the on state is considered
to be Ion = I0 , the intensity of the off state is zero Iof f = 0. The probability
density for the off times Tof f in the fluorescent signal is derived as:
Wof f (T ) = R− e−R− T(2.1)

And analogically the probability density for the on times:
Won (T ) = R+ e−R+ T(2.2)

R+ is the transition rate from on- to off-state and R− the transition rate form offto on-state. Both distributions are exponential just varying in the different time
constants R+ and R− .
Using the correlation function the frequency spectrum of the intensity fluctuations
can be calculated to:S(ω) = πm2I δ(ω) +σI2 (R+ + R− )
ω 2 + (R+ + R− )2

(2.3)

I0 R−
R+ + R−(2.4)

with the mean intensity
mI = hIi =and the variance of the intensity:
I02 R+ R−
σ = hI i − hIi =(R+ + R− )2
2

2

2

(2.5)

Except for the first part, which is the zero-frequency component, the frequency
spectrum is a Lorentzian.
This model is based on a single electron in the three level system. In the InGaN
single quantum wells used for this thesis a large number of carriers are involvedin the radiation process, which makes the situation somewhat different from thistheory. Additionally the intensity in the off state of the blinking points in the
InGaN single quantum wells is not zero as it would be in the quantum jump
theory. Nevertheless this model can be applied to our system when the switchingis attributed to a charging and decharging of a single localized state by a single
carrier. This will be discussed in more detail in section 2.3.

12

2.2 Power law

2.2 Power law
Other groups reported on a random telegraphic blinking that didn’t show exponential distribution of on and off times as predicted by the quantum jump theory.
For example the blinking of single fluorescing nanocrystals of cadmium selenite
showed power law statistics of on and off times [25, 26] which indicate a much
more complex underlying system than the quantum jump one.
The power law describes the relationship between two quantities, the size of anevent and its probability. The sizes of power outages, the intensities of earthquakes
or the population of cities are typical examples for power law distributions. Such
distributions are signs for highly complex underlying processes. Mathematically aquantity x obeys the power law if the probabilities are distributed likeP (x) ∝ x−α(2.6)

The exponent α is called the scaling parameter and typically lies between 2 < α < 3with some exceptions [27].
The most important property of a power law distribution is its scale invariance,
i.e. a constant scaling factor c only causes a proportional scaling of the whole
distribution:
P (cx) ∝ P (x)(2.7)
The integral
Z ∞P (x)dx = ∞

(2.8)

0

diverges and therefore makes it impossible to identify a inherent scale of a problem
that is described by a power law [4].
Blinking statistics following the power law have been attributed to a number ofdifferent causes. One model derives a potential law distribution for the off times
starting from deep traps surrounding the quantum dots. The depth of the traps is
exponentially distributed. And a carrier can only escape the trap when its energy
is bigger than the depth of the trap. In this model the transition rate from off toon state is therefore described by a thermal activation function. The probability
density of the off times is given by:
P (τof f ) =αkB T Γ(1 + αkB T ) −mτof f
AαkB T(2.9)

with τof f being the duration of the off state and m the exponent of the potential
law, that has to be determined experimentally [26].
Other approaches assume that the carriers leave the traps by a tunnelling mechanism [26] or start form fluctuations in the proximity of the quantum dots [28].

13

2 Random telegraph signal

2.3 Deep traps and the random telegraph signal
The described blinking behaviors and associated statistics can be causes bydifferent effects. One possible reason can be carriers trapped in localized centres,
deep traps. This was reported in a work of Sugisaki et al [24]. As our systemseems to base on the same mechanism this section will explain the observations of
Sugisaki et al and its interpretation.
In his work the optical properties of self assembling single InP quantum dots
(QDs) were investigated. The InP QDs were sandwitched between two layers of
GaInP. When excited with 488 nm light about one per 107 QDs showed blinking
behavior. Most of these points were found near small flaws. After scratching
the sample intentionally the number of blinking points was increased. After Si-δ
doping between the QDs and the GaInP cap layer, however, no increase of thenumber of blinking points could be observed. This suggested that the unstable
fluorescence was related to deep traps caused by defects.
At higher temperatures the not blinking points showed lower intensities because ofstronger interaction between excitons and phonons at higher temperatures. This
increases the nonradiative decay resulting in lower luminescence intensity. Thisobservation could be described by a simple thermal activation model:
I(T ) =

I(0)1 + ae−E/kB T(2.10)

a is a temperature independent constant, E the thermal activation energy and kB
the Boltzmann constant. The thermal activation energy varied from dot to dot.
The blinking InP QDs showed a blinking behavior switching between an on and a
off state. The distribution of on and off intervals could be described by a single
exponential decay function which is consistent with the quantum jump model
explained in section 2.1.
Non/of f (t) = N (0)e−t/τon/of f(2.11)

τon/of f are the average on or off times. The difference in intensity between on andoff state ∆I was found to vary from dot to dot. Furthermore some points thatswitch between more than just two levels were be found.
Excitation power dependence measurements showed that the switching times ofall blinking dots could be fitted with a single exponential function.
τP = P −η

(2.12)

P is the excitation power, the exponent η was found to be different for each QD.
All these observations proposed a model for the blinking that is based on localized
deep traps caused by defects. Carriers can be trapped in the deep localized states.
If one of these traps is located near a QD the local electric field generated by the14

2.3 Deep traps and the random telegraph signal
trapped carrier impacts on the quantum well and deforms it, the overlap of theelectron wavefunction Ψe and the hole wavefunction Ψh decreases and so does
the transition probability and the emission intensity (cf. quantum confined starkeffect, section 1.3). After a while the trapped carrier relaxes by recombination
with another carrier, mediated by phonons or by photon-reabsorbation. The local
field is removed and the QD switches back to the on state again. With different
distances between traps and QDs the strength of the electrical field in the QD
and thus the difference between on and off state intensity ∆I = Ion − Iof f varies.
If there is more than just one trap near the QD the electric fields superpose andthe intensity can switch between more than two intensity levels (fig. 2.2). The
trapping processes in different traps are independent of each other, therefore any
switching between all different intensity levels is possible.
With decreasing temperature the switching got slower and the off times τT could
be described by a thermical activation function:τT =τof f (0)1 + ae−E/kB T(2.13)

a is again a temperature independent constant and E is the thermal activationenergy.

15

2 Random telegraph signal

Figure 2.2: Model for the blinking caused by carriers caught in deep traps. (a) shows thequantum well with the electron and hole wavefunctions Ψe and Ψh and two deep traps. The
overlap of the wavefunctions is big and thus the luminescence intensity strong. In (b) a carrier
is trapped, the quantum well deformed and the overlap of the wavefunctions reduced. The
luminescence intensity gets weaker. (c) shows the effect of a carrier trapped in a trap closer tothe QD. The resulting local electric field in the quantum wells is stronger, leading to a bigger
deformation and separation of the wavefunctions. In (d) both deep traps are charged, the fields
of both charges superpose and the luminescence intensity reaches a minimum. As the trappingand detrapping processes of both traps are independent of each other, the photoluminescence
can switch between any of the levels. For a single trap the point switches between only two
intensity levels. (after [24])16

3 Plasmons and coupling ofquantum wells to plasmons
The easiest model for a bulk metal in equilibrium condition describes it as a latticeof ions with a plasma of electrons moving in the Coulomb field of other electrons
and ions. When the equilibrium is disturbed by an external electromagnetic
field the external field enforces a collective oscillation of the conduction band
electrons as the inertia of electrons are much smaller than the ones of the ions.
The quantum of such an oscillation is called a plasmon. Although it is a general
phenomenon in matter, metals provide by far the best evidence for plasmons,since the conduction electrons in metals can move quasi-free. From the quantum
mechanics point of view plasmons are treated like quasi particles.
Oscillating charges are inherently associated with an electromagnetic field. Therefore boundary conditions play an important role in the theoretical description ofplasmons and result in the distinction between bulk plasmons (in bulk materials)
and surface plasmons (on metal-dielectric interfaces). Surface plasmons are once
more subdivided in surface plasmon polaritons and localized surface plasmons.
This chapter will introduce to the main characteristics and properties of plasmons
with a special focus on the coupling of InGaN quantum wells to surface plasmons
in gold films and gold nanoparticles and the enhanced light emission associatedwith this coupling.

3.1 Bulk plasmons
If the electrons oscillate within a bulk material the plasmons are called bulk
plasmons or volume plasmons and describe longitudinal oscillations. The eigen
oscillation frequency of the plasma ωp in bulk metals is called plasma frequency:
ωp =

N e2
m∗ 0

(3.1)

It depends on the density of electrons N, the effective mass of the electrons m∗ ,the electron charge e and the permitivity of free space 0 . This relation can bederived by assuming that the response of the electrons can be described as asimple harmonic oscillator. The phase and amplitude of the plasmon oscillation17

3 Plasmons and coupling of quantum wells to plasmonsin the bulk material relative to the external field depends on the relation of theplasma frequency to the frequency of the driving field [29, 30].

3.2 Surface plasmons
Collective excitation modes of the oscillations of quasi free electrons that propagate on the interface of a metal and a dielectric medium are called surface
plasmons. Recent literature distinguishes between surface plasmon polaritonsand localized surface plasmons [31]. Surface plasmon polaritons propagate on
extended interfaces with scales that are much larger than the optical wavelength,
whereas localized surface plasmons are confined in geometries much smaller thanthe optical wavelength. Such geometries can be small metal objects, metallic
protrusions, structures, voids covered with metal or metal nanoparticles. For thisreason they are often referred to as particle plasmons [31–33].

3.2.1 Surface plasmon polaritons
Surface plasmon polaritons are plasmons that propagate in the interface of a metal
and a dielectric medium. This interface is extended and much larger than the
optical wavelength. Surface plasmon polaritons are analogous to bulk plasmons
with the restriction that they are bound to surface electrons.
The oscillations of the carriers in the interface are accompanied by a longitudinal
and transverse electromagnetic field. The field is maximal at the interface anddecays exponentially with increasing distance from the interface and is therefore
said to be evanescent or called near-field in nature. This behavior is observed inboth directions, i.e. the wave is both evanescent in the metal and the dielectricmaterial with different decay rates δm and δd respectively. Fig 3.1 shows theoscillating charges on the metal dielectric interface and the accompanying fields.
The dispersion relation of surface plasmons, i.e. the dependence of the surface
plasmon frequency ω on the wavevector k, shows the change of surface plasmon
properties at different frequencies. Fig. 3.2 shows a typical dispersion relation of
surface plasmon polaritons. The solid line is the dispersion relation for surface
plasmon polaritons in the interface between air and metal, the dashed line between
the same metal and a material with higher refractive index than air. The graphs
hit asymptotic limits ωair and ωn with increasing energy. This asymptotic limit
depends on the metal and the surrounding material. If the metal is chosen in a
way that the resulting asymptotic limit of the surface plasmon polaritons lies inor close to the emission band of the semiconductor the excitons and the surface
plasmon polaritons can couple [31].

18

3.2 Surface plasmons

Figure 3.1: (a) Schematic picture of the distribution of oscillating charges on a metal dielectricinterface and the fields accompanying them. The magnetic field Hy is transverse. The componentof electric field E that is perpendicular to the interface is |Ez |. It is evanescent, has a maximum
at the interface but decays exponentially both in the dielectric and the metallic medium (b).
The decay rate is δd for the dielectric medium and δm for the metal. (Adapted from [34]).

3.2.2 Localized surface plasmons
Colloidal solutions of nanoparticles of the metals gold, silver and copper show
bright intense colors. However these colors can’t be observed for the same materials
in bulk or individual appearance. The colors are due to particle plasmons excitedin the nanoparticles when resonant to the incident light [35]. The fascinating
intensive colors of noble metal nanoparticles have historically been of interest incraft work, for example for staining the glass of church windows. Nowadays its
optical properties attract much attention due to a variety of exciting scientificapplications like biological imaging or sensing, medical photothermal therapyof cancer [36], transport of electromagnetic energy at scales below diffraction
limit [33] or the strong enhancement of photoluminescence in quantum wells [37]and more effective LEDs [38], to name a just a few.
In the case of nanoparticles the plasmons are called localized surface plasmons as
the plasmons are confined in geometries that are much smaller than the optical
wavelength. Localized surface plasmons can also be observed in similar sized
metallic structures, objects or voids covered with metal [33]. The confinement inthese small areas changes the boundary conditions and with that the resonanceconditions.
For the wavelength of the light being much smaller than the diameter of thenanoparticles and for spherical nanoparticles the surface plasmon oscillation mainly
dominated by its dipolar mode.

19

3 Plasmons and coupling of quantum wells to plasmons

Figure 3.2: Scheme explaining the coupling of the quantum well to surface plasmon polaritons(SPP) and the subsequent coupling of SPP to light (from [31]). The picture shows a typicaldispersion relation of SPPs illustrating the relation between the energy (frequency ω) and themomentum (wavevector k). The solid line shows the dispersion relation for an interface between
air and metal, the dashed line between the same metal and a material with higher refractive
index than air. The graphs hit asymptotic limits ωair and ωn with increasing energy. Thisasymptotic limit depends on the metal and the surrounding material. If the metal is chosen in a
way that the resulting asymptotic limit lies in or close to the emission band of the semiconductor
the excitons and the SPP can couple. If the emission of the quantum well should be enhanced
the SPP subsequently have to couple to light which is not possible because the momentum k2 is
to high. A rough surface or periodic structure can scatter SPP of high momentum k2 to SPP of
smaller momentum k1 (blue arrow). When k1 lies inside the light-line it can couple to light andemission enhancement gets possible.

203.3 Coupling of InGaN quantum wells to surface plasmons

α = 30 V

 − m + 2m(3.2)

α is the polarizability of the dipolar mode, V the particle volume, 0 the vacuum
permitivity, m the dielectric constant of the surrounding medium and (ω) =r (ω) + ii (ω) the dielectric function of the metal which depends on the frequency
and is complex. Strong resonance occurs at the frequency ω where r = −2m . Thiscondition is fullfilled for copper, silver and gold nanoparticles at visible wavelengths
which makes them suitable materials for a huge variety of applications. The big
optical polarization enhances the electrical field strongly at particles surface andcauses a strong enhancement of scattering and absorption of the electromagnetic
waves at resonance frequency [39].
The resonance frequency depends on the size and shape of the nanoparticle, themetal, the dielectric constant of the surrounding medium and interactions causedby the coupling between different nanoparticles. All this makes the resonancefrequency tuneable and therefore interesting for lots of biological and medical
applications [36].
The size dependence of gold nanoparticles in water was shown in a study of Link
et al [35] by the absorption spectra of particles of different sizes (fig. 3.3). Its
maximum blue-shifts with decreasing particles size. For gold nanoparticles withdiameters of 9, 22, 48 and 99 nm the absorbance maxima are located at λmax =517, 521, 533 and 575 nm. Compared to this the temperature dependence of theplasmon resonance for gold nanoparticles is very small [35]. For our experiments
where a InGaN/GaN single quantum well of 540 nm central emission coupled tosurface plasmons, we chose gold nanoparticles of 50 nm diameter. The resonancemaximum of the 48 nm gold nanoparticles (fig. 3.3) is located at 533 nm. So 50
nm gold nanoparticles were likely to show resonance to our sample (cf. section 4).

3.3 Coupling of InGaN quantum wells to surface
plasmons
If a metal is chosen in a way that its plasmon frequency matches the emission
spectrum of a quantum well, this metal can be placed on the quantum well andthe quantum well resonantly couples to surface plasmons. The electron hole pairs
transfer their energy to surface plasmons in the semiconductor metal interface via
the evanescent field instead of radiating it into free space [40, 41].
This coupling has been observed in a study of Okamoto et al [37]. They observed
large enhancements in the emission of InGaN/GaN quantum wells after putting
silver or aluminum layers 10 nm above the InGaN layer (fig. 3.4). This enhancement was attributed to the energy transfer from the quantum well to surface
plasmons in the GaN-metal interface and the subsequent increase of the density21

3 Plasmons and coupling of quantum wells to plasmons

Figure 3.3: The absorption spectra of goldparticles of 9, 22, 48 and 99 nm diameter in water,
normalized at their absorption maxima (left). The absorption spectra of gold nanoparticles
of 22 nm diameter in dependence of the temperature at 18◦ C and 72◦ C (right).(both images
from [35])of states and spontaneous emission rate.
In studies of Gontijo at al [42] the surface plasmon-quantum well coupling manifested itself in an suppression of the emission. A spectral sharp photoluminescencedip was observed after a 8 nm silver layer was placed 12 nm from a InGaN/GaN
quantum well. The spontaneous emission into surface plasmons was 55 times
faster than the normal spontaneous emission of a InGaN quantum well into freespace. Time-resolved photoluminescence measurements conducted in a study of
Neogi et al showed that the enhanced spontaneous emission into surface plasmons
was even 92 times faster [40].
As described in section 3.2.1 the surface plasmon electromagnetic field is evanescentand exponentially decays with increasing distance from the metal semiconductor
interface. Only electron hole pairs in the near-field of the surface can couple
to surface plasmons. For resonant coupling the active InGaN layer has to beplaced within the fringing field penetration depth of the electromagnetic field.
The penetration depth of the surface plasmon fringing field into the semiconductor
is given by:
1/2
λ ,GaN − ,metal
Z=
(3.3)
2π
,2
GaN
,GaN and ,metal are the real parts of the dielectric constant of GaN and the metal
respectively. For Ag this calculation leads to a penetration depth Z of 47 nm,
for Al 77 nm and for the case of Au 33 nm [37]. For this reason the thickness of
the GaN cap layer is crucial and can decide wheather a quantum well couples tosurface plasmons or not.
In the studies of Neogi et al the resonance strongly depends on the thickness of
the Ag layer [40]. In the case of nanoparticles coupling is stronger in areas with22

3.4 Coupling of surface plasmons to light

Figure 3.4: Okamoto et al showed that the photoluminescence of InGaN quantum wells cansignificantly be enhanced through a thin metal layer over the GaN cap layer (left). The blackline shows the photoluminescence spectrum of the quantum well without metal. A thin filmof aluminum (blue line) or gold (red line) caused a strong emission enhancement (right) (bothimages from [37])high density of nanoparticles than in an area with less particles because of thebigger number of coupled surface plasmon modes. [43].

3.4 Coupling of surface plasmons to light
The coupling between quantum wells and surface plasmons can either enhance or
suppress the light emission efficiency depending on if and how strong the surface
plasmons couple to light. In the studies of Gontijo at al the surface plasmon
quantum well coupling manifests itself in a suppression of the emission, whereas
the studies of Okamoto et al show an enhancement in the emission. However,in both cases the quantum well resonantly couples to surface plasmons [42, 44].
In one case the surface plasmons subsequently couple to light and the energy isradiated into free space, in the other case the energy of the surface plasmons isabsorbed in the metal.
Usually the probability of loosing energy through surface plasmons in LEDs ishigh. For most LEDs a metal contact has to be put near the the semiconductor
layer, causing high probability for the excitons to couple to surface plasmons.
The plasmons are unable to generate light directly due to their high momentum.
The energy lost to the surface plasmons is dissipated as heat and the efficiency of
the LED decreases [31]. In this case the plasmons decay in electron hole pairs.
This can happen intraband or interband then being converted in heat throughelectron-electron and electron photon relaxations [36].

23

3 Plasmons and coupling of quantum wells to plasmons
Surface plasmons have a smaller wavelength for the same frequency of a photon.
Therefore they cannot couple directly to free-space electromagnetic radiation of
the same energy, their associated wavevector being too large to satisfy conservationof energy and momentum. To couple surface plasmon polaritons to light the
momentum mismatch between light and surface plasmon polaritons must be
bridged i.e. both the frequency and wavevector of the surface plasmons and thelight must match. If the surface plasmons are scattered and thus loose momentum
the resulting momentum can match the momentum of the light (fig. 3.2) and thesurface plasmon polaritons can thus couple to light and enhance emission. The
surface plasmons can be scattered at suitable periodic structures [31, 34, 41, 45]
Okamoto et al use a similar method to achieve the scattering of the surface
plasmons. Instead of introducing a periodic structure they observed that only theinherent surface roughness and imperfections of the evaporated film can efficiently
scatter surface plasmon polaritons and increase the coupling to light [37].
For nanoparticles the inherent curvature itself causes relaxation of the k selection
rule for plasmons and the coupling of the particle plasmons to light is increased[46, 47].
Kwon et al reported on the first realization of a GaN based LED structurewith quantum well surface plasmon coupling. These structures were realized
by inserting a Ag nanoparticle layer between the n-GaN layer and the multiple
quantum well. By this it was possible to enhance the emission through thecoupling to surface plasmon and to maintain the p-n junction. [38]3.5 Quantum confined stark effect screening vs.
surface plasmon coupling
The main reason for the emission enhancement in InGaN/GaN quantum wells is
the coupling of the quantum wells to surface plasmons and the subsequent lightemission. But also screening of the QCSE through the electric fields of the surface
plasmons plays an important role in the enhancement process. This screening
both influences on direct emission and on the coupling strength between quantum
well and surface plasmons. First, the screening undoes the QCSE itself leading toincreased recombination probability of electrons and holes. Second, the screening
shifts the emission spectrum back to smaller wavelengths. This way the emission
spectrum can get closer or farer away from the surface plasmon resonance energy
resulting in higher or lower densities of surface plasmon states and thus in stronger
or weaker quantum well surface plasmon coupling [41].

243.6 Plasmons in nanoclusters of metallic indium

3.6 Plasmons in nanoclusters of metallic indium
During the growing process of InN it tends to spontaneously precipitate cluster-likemetallic indium particles. There are several evidences that these metallic indium
clusters are plasmonically active. For example the fluorescence of organic materials
located near indium clusters was significantly enhanced or the electroluminescenceof Si with In clusters increased strongly due to coupling to plasmons in the metallic
indium particles. Comparisons between cathodoluminescence and SEM imagesof a InN film with In clusters demonstrated strong emission enhancement at thelocations of the indium particles. The metallic indium clusters in the InN film
could both enhance the emission or absorb. Which effect appears depends on theform, orientation and quality of the clusters [33]. This effect is very similar to
the emission enhancement and suppression reported in the studies of Okamoto
et al [37] and Gontijo et al [42] where the interaction of a InGaN/GaN quantum
well with surface plasmons in metal films was investigated on.

25

26

Part II
Experiments27

4 Samples
The samples used for the experiments of this thesis were InGaN/GaN quantum
wells grown on an (0001) oriented sapphire substrate by metalorganic chemical
vapor deposition technique developed by Nichia Chemical Industries Ltd., Japan.
All the samples were single quantum well structures composed of an undoped GaN
layer (4 µm), an Inx Ga(1−x) N active layer (3 nm) and a undoped GaN cap layer(5 nm) (fig. 4.1). Four different samples with different indium concentrations x,
resulting in different photoluminescence spectra, were used. The main emission
peaks were located at 540 nm, 510 nm, 460 nm and 420 nm (fig. 4.1) at 365 nm
excitation wavelength and roomtemperature.

Figure 4.1: The structure of the four samples grown on a sapphire substrate with a 4 µm GaN
layer, a 3 nm InGaN active layer and a 5 nm cap layer (left). Different Indium concentrations x
result in different emission spectra with main emission peaks located at 420, 460, 510 and 540
nm (right).

The samples could be excited with the 365 nm or the 435 nm line of a mercury
vapor lamp. The band gap of GaN is about 3.4 eV (365 nm) and the one of
InGaN is under 2.95 eV (over 420 nm). The 365 nm line therefore excited boththe GaN barrier and the InGaN active layer [3].
At 365 nm excitation the photoluminescence showed points of very high intensity.
Fig. 4.2 shows the emission patterns of the 460 nm, the 510 nm and the 540
nm sample. On all samples intense luminescent centres could be observed, some29

4 Samples

Figure 4.2: The photoluminescence of the samples with 460 nm, 510 nm and 540 nm main
emission peak (from left to right) at 365 nm excitation. All samples show intense emitting
centres. The yellow circles mark blinking points. With increasing indium concentration more
blinking points can be observed.

of these bright points blinked. Most blinking points could be found on the 540
nm sample, less on the 510 nm sample and no blinking points could be observedon the blue emitting 460 nm sample. Excited with 435 nm none of the samples
showed intense emitting centres or blinking points.

30

5 Time intensity profiles
In contrast to normal intense luminescent centres blinking points change emission
intensity. In order to investigate on the blinking behavior time-intensity profiles
had to be plotted and analyzed. This chapter will explain the methods to provide
and analyze such time-intensity profiles and the results obtained from them.

5.1 Method
The experimental setup to get the time-intensity profiles of the blinking points
consisted of a photoluminescent microscope coupled with a CCD camera. Movie
files of the photoluminescence of the sample were taken and processed withdifferent scilab programs to analyze the blinking behavior.
The Olympus photoluminescent microscope BX51WI was used with different
Olympus objectives of the LMplanFLN series with 10x, 20x and 50x enlargements.
The videos for the time-intensity profiles were taken with 50x enlargement.
The samples were excited by the mercury vapor lamp Olympus U-LH 100HQ.
With filters the exciting wavelength could be switched between 365 nm and 435
nm.
To record the videos two different cameras were used, a Sony HDR-SR1 which
provided a framerate of 30 fps and a Casio EX-F1 that could be operated in highspeed mode with framerates of 300, 600 or 1200 fps. Operating the camera in 600
fps and 1200 fps mode turned out not to deliver good results. The light sensitivity
got too low so that even the brightest points could hardly be seen on the video.
As the cameras were conventional ones and not particularly designed for the
microscope, for the Sony camera the Olympus ocular UIS2 WHN 10x/22 wasused as a adapter. For the Casio camera a simple plano-convex lens with focal
length of f=100 mm replaced the adapter.
In most experiments the Sony camera was used. It only had a framerate of 30
fps and therefore was much slower than the second camera which in high speed
mode could achieve framerates of 300, 600 and 1200 fps. The slower camera waseasier to operate, as the correct alignment of the focus could be checked on amonitor. Whereas with the highspeed camera the focus could only be aligned
using the integrated display which in most cases resulted in videos of bad quality.
Furthermore the light sensitivity of the high speed camera got very low withincreasing framerate and the noise got very high. In the 300 fps mode it still31

5 Time intensity profiles

Figure 5.1: To locate the blinking points, for each pixel of the movie file the standard deviationof the intensity was calculated. The left picture shows the photoluminescence of the sample, theright picture shows the corresponding color-coded map of standard deviation calculated fromthe movie file. Red points show pixels with high standard deviation, blinking points, blue pixels
designate not blinking areas.

delivered good results only for the brightest blinking points (fig. 5.3), but weaker
blinking points could not be observed anymore. At 600 fps and 1200 fps the lightsensitivity got to weak to obtain meaningful results.
In order to analyze the temporal behavior of the blinking points different scilab
programs were used to process the avi-format movie files that had been taken of
the blinking points. The movie files delivered 3 different intensity values (blue, red,green). As the blinking points were green, the other channels didn’t provide any
further information. For this reason and to save computing time just the green
channel was used. The movies were cropped and the intensity values of each frameand pixel were used to calculate the standard deviation of each pixel. Mapping
the standard deviation (fig. 5.1) made it possible to localize the blinking points.
The red points in fig. 5.1 show pixels with high standard deviation (blinking
points), blue points show pixels with low standard deviation (not blinking). After
rechecking with the movie file a suitable blinking point was selected and the timeintensity profile of this point was extracted. As a blinking point consits of morethan one pixel the intensities of the pixels belonging to one blinking point weresummarized. With knowing the framerate the timescale could be calculated andthe time-intensity profile plotted. Fig. 5.2 shows two time-intensity profiles of ablinking point and of a not blinking area in its vicinity.
Errors caused by the camera could be minimized by setting off a not blinking area
against the blinking point. But the fluctuations of the not blinking area turned
out to be quite small compared to the blinking (fig. 5.2). Therefore in most cases
just the blinking points were taken into account regardless of a reference area.
At the University of Regensburg Anne Kuhnert took the time-intensity profiles ofblinking points using a photomultiplier reaching a sampling rate of 1-10 kHz [15].

325.2 Different types of blinking points

Figure 5.2: The left side shows a color-coded map of the standard deviation permitting the
localization of blinking points. The right side shows examples for time intensity profiles of ablinking point (point 2) and a not blinking area in the vicinity of the blinking point (point 1).

The time resolution of the here described method is much lower (30 fps forstandard mode camera, 300 fps for high speed camera) and a lot of postprocessing
had to be done. On the other hand, measurements that can not be done withthe photomultiplier are possible with the camera (e.g. temperature dependence
measurements). In spite of the lower timeresultion we could analyze the statisticof the blinking and verify that the blinking is subject to the quantum jump model
statistics. The blinking point we observed for this purpose blinks slower than theones of the samples used at the University of Regensburg. Furthermore the noise
was very small compared the distance of the two intensity levels and even without
digital filters meaningful results could be obtained.

5.2 Different types of blinking points
On the basis of the time intensity profiles different kinds of blinking points could
be characterized. The first type switching between two different intensity levels(’two level blinking point’). For such points clear on and off states could be defined
and the times spent in the on and accordingly in the off state could be counted
and the two level blinking points could be assigned to different blinking statistics.
The second type of blinking points showed more than two intensity levels or didn’t
show discrete intensity levels at all (’multi level blinking point’).

33

5 Time intensity profiles

Figure 5.3: Example for a time intensity profile calculated from a movie of a camera operatingin high speed mode. This way framerates of 300 fps could be achieved.

5.2.1 Two level blinking points
A very small amount of the blinking points showed two discrete intensity levels.
The intensity of these points switched between these two levels and clear on andoff states could be defined (fig. 5.4). A intensity histogram illustrates the on
and off states of the random telegraph signal and facilitates the selection of alimit between the on and the off state (fig. 5.5). The difference ∆I = Ion − Iof f
between the intensities of the on state Ion and the off state Iof f and the speed of
the blinking varied for different two level points.
Using a scilab program the timeintervals spent in the off or the on state could becounted. The probability distributions revealed two different kinds of statistics.

Figure 5.4: The time intensity profile of a two level blinking point. The intensity switches
between two states, a on and a off state.

Some two level blinking points show exponentially distributed probabilities of34

5.2 Different types of blinking points

Figure 5.5: The intensity histogram of a 30 min measurement reveals that the intensity only
switches between two levels. By means of these histograms limits between a on and a off state
could be determined and the on and off times could be counted.

on and off intervals (fig. 5.6). This indicates that the blinking is caused by aquantum jump like mechanism as described in section 2.1.
By contrast other two level blinking points were found that didn’t show exponentially distributed probabilities of on and off times (fig. 5.7). The probability
distributions of these points could be described by a power law (section 2.2) whichindicates a more complex underlying process than a quantum jump. Earlier works
conducted with the same samples at Kyoto University [3] reported on this kindof random telegraphic blinking but did not find blinking points with exponential
probability distributions.

5.2.2 Multi level blinking points
Besides the very rare two level blinking points most blinking points on the 540 nm
sample switched between more than two levels or did not show clear intensity levels
at all. Fig. 5.8 shows the time intensity profile of such a multi level blinking point.
As for such points clear intensity levels could not be observed in the histogram nostates could be defined and statistics on this kind of blinking were not possible(fig. 5.9). In section 6 a multi level blinking behavior could be simulated as asuperposition of several two level blinking behaviors.

35

5 Time intensity profiles

Figure 5.6: Counting the on and off times shows a exponential probability distribution of onand off times. Thus this distribution can be described by the quantum jump theory.

36

5.2 Different types of blinking points

Figure 5.7: Counting the on- and off-intervals of the blinking points shows a distribution thatcan be fitted with a straight line when plotted on double logarithmic axes (right) but not whenplotted single logarithmically (left). This indicates a power law distribution.

37

5 Time intensity profiles

Figure 5.8: The commonly encountered type of blinking point is a multi level blinking point.
In the time-intensity profile no discreate intensity levels can be identified.

5.2.3 Interpretation
We think the three different kinds of blinking described in this chapter all baseon the same underlying mechanism, which can in the easiest case be described by
the quantum jump mechanism. Deep localized states can act as traps for carriers.
Trapped carriers cause a local electric field deforming the quantum wells. If sucha trapped carrier is located in the vicinity of a strongly light emitting center it
can change the transition probability and thus the emission intensity of such abright dot either through strengthening or screening the quantum confined Stark
effect. When the carrier escapes the trap the local electric field impacting on theintensity of the bright dot is removed. This way the trapping and detrapping ofa carrier in a localized state can cause a random telegraph signal. This process
is illustrated in fig. 2.2. A blinking caused by this process shows exponentiallydistributed probabilities of on and off times (section 2.1).
Different distances of a trap to an intense light emitting center result in different strengths of the local electric field and thus in different changes in thephotoluminescence. The two level blinking points observed for this work showed
different distances ∆I = Ion − Iof f between the on state intensity Ion and theoff state intensity Iof f . The same observations were made for blinking points in
InGaN/InGa multi quantum wells in the work of Anne Kuhnert at the Universityof Regensburg [15].
The other two kinds of blinking points which are the two level points with powerlaw probability distributions and the multi level points are probably due to more
complex situations. The coupling of a strong light emitting center to more than
one trap leads to a superposition of several local electric fields and thus to a more
complex blinking behavior like the one of a multi level blinking point. Most of
the blinking points on the sample used for this work showed multi level blinking
behavior. Two level blinking points were extremely rare and hard to find. In
contrast the blinking points in Regensburg all switched between only two intensity38

5.2 Different types of blinking points

Figure 5.9: In the intensity histogram for a multi level blinking point no discrete intensity
levels can be observed.

levels [15].

39

40

6 Simulations
We think the three different kinds of blinking are all caused by a fundamental
blinking behavior being the two level blinking described by the quantum jump
theory. Both the multi level blinking and the two level power law blinking are
due to more complex situations i.e. the coupling of one blinking point to morethan just one deep trap. Anne Kuhnert characterized the behavior of blinking
points of a InGaN multi quantum well at the University of Regensburg. On
this sample only blinking points switching between two intensity levels could befound. Furthermore all these points showed quantum jump statistics [15]. To
check if a multi level blinking behavior can result from a superposition of different
quantum jump two level blinking points, a simulation similar to the one in [15]was performed.
First the blinking of a point that just couples to one single deep trap andfollows the quantum jump statistics was simulated. For this a array of uniformly
distributed random numbers x was generated. This numbers can be transformed
into exponentially distributed random numbers by:t = −ln(x)/b(6.1)

The new array of exponentially distributed numbers corresponds to the on/off
times in in the quantum jump model. Two arrays like this where generated,
one for the on-, one for the off times, each with different decay rate b. The two
intensities I1 and I2 were determined and incorporating the camera framerate andthe timeintervals intensity datapoints could be calculated.
A multi level blinking point that couples to more than just one deep trap was seen
as a superposition of two level quantum jump blinking behaviors. The resulting
multi level blinking point switches between maximal nlevel = n2trap levels, where
ntrap is the number of deep traps it couples to. The number of traps, the caused
intensity differences and the decay times could be chosen and data points could
be simulated for each single trap. A superposition led to the data points of amulti level blinking point.
This simulates the blinking behavior, but still without noise. The noise of themeasurements showed gauss shaped distributions. This was simulated with the
Box Muller transform [48, 49] which takes two arrays of uniformly distributed
random numbers x1 and x2 and calculates an array of normally distributed random
numbers x by:p
x = −2 ln x1 cos 2πx2
(6.2)

41

6 Simulations

Figure 6.1: Simulated data for blinking points calculated on the basis of the quantum jump
theory. Superposing different two level points leads to a blinking behavior where clear levels are
not longer observable. The graphs show the simulated data for a blinking point coupling to 1
trap (top left), 3 traps (top right), 5 traps (bottom left) and 10 traps (bottom right).

This way a noise value was generated and added to each data point.
The evaluation of the simulated data was done the same way than that of
the measured data. In the simulation the number of traps and the depth andprobabilities of on and off state of each trap can be varied. Changing thisparameters has a strong influence on the shape of the time-intensity-profile andthe histogram. Starting from a two level blinking system with only one trap,
adding more traps leads to a blinking behavior that doesn’t show clear intensity
levels anymore (fig.6.1). This way, data for a multi level blinking point that arevery similar to the measurements could be simulated (fig.6.2).

42

Figure 6.2: Time intensity profiles and histograms of a multi level blinking point. The left sideshows measured data, the right side simulated data. For the simulation 10 two level blinking
points were superposed, each of the points having other parameters and coupling strength.

43

44

7 Temperature dependence of theblinking
7.1 Method
For the temperature dependence measurements the microscopy cryogenic workstation RC102-CFM of Cryo Industries of America Inc. was used. The Model 32
B Cryogenic Temperature Controller permits the maintenance of stable temperatures.
For making statistics on two level blinking points like in section 5.2.1 long moviesof 30 minutes had to be taken. The observed area drifted about 10 pixels in thistime. This shift couldn’t be observed at room temperature and was therefore
probably due to vibrations of the cryostat pumps. To compensate this shift theposition of the relevant blinking point was localized by mapping the standard
deviation beginning with the first frame, then every 5 minutes and in the last
frame. This way the point could be traced and its ’route’ could be identified.
To get the time intensity profile of the blinking point the intensity values of all
pixels passed by the blinking point were summarized. The area just contained
one blinking point and the statistics depend only on the timeintervals spend in
the on and the off state and not on the intensity values of the on and off states.
This summarizing led to time intensity profiles of a two level point like the ones
observed in section 5.2.1.
On the basis of the associated intensity histogram a limit between on and off
state could be set and the probability distribution of times spend in the on andoff state could be determined. For this purpose it is important to normalize thedata in terms of the number of on and off events. All measurement periods took
30 minutes but at lower temperatures the blinking gets slower and the number ofswitching events smaller. This had to be considered when comparing statistics on
the on and off times at different temperatures.
The analysis of the temperature dependence of multi level blinking points wasquite easy as almost all blinking points showed this behavior. In contrast two levelblinking points were very rare and hence hard to find. Furthermore, after some
30 minutes measurements of the same point at different temperatures this point
often changed blinking behavior i.e. it switched off completely or turned into a
multi level blinking point. For this reason it was only possible to analyze the45

7 Temperature dependence of the blinking
temperature dependence of one blinking point obeying the power law distribution
at temperatures ranging from 315 K to 275 K.

7.2 Photoluminescence changes
Fig. 7.1 shows photoluminescence images of the same area on the 540 nm central
emission sample at different temperatures beginning from 310 K down to 80 K insteps of 10 K. The right half of the images appears very bright compared to theleft half. The right half is covered with a thin gold film that strongly enhances
the emission of our sample through resonant coupling of the quantum well tosurface plasmons in the gold film. This effect will be described in detail in section
8. This emission enhancement lets the strong light emitting points and thus
the blinking points disappear in a uniformly bright emitting area. Therefore no
blinking points can be observed on the right half. The left half however shows
blinking points. With lower temperatures these blinking points blink slower, getweaker and finally disappear. With decreasing temperatures the quantum well as
a whole gets brighter. As the probability for non radiating transition decreases
the efficiency of the quantum well increases.

7.3 Two level blinking points
30 minutes movie files of the same two level blinking point were taken at different
temperatures in the range form 315 K to 275 K. A comparison of the timeintensity profiles at different temperatures shows that the off intervals get longer
with decreasing temperatures (fig. 7.2). The carriers trapped in deep localizedstates in the vicinity of the blinking point leave the traps in non radiative processes.
The probability for such processes gets lower with decreasing temperature making
the carriers stay longer in the traps and thus causing longer off intervals. Counting
the intervals spent in the off and the on state shows that for lower temperatures
the probabilities for both longer on and off times increase (fig. 7.3).
Due to time constraints and the difficulties in finding suitable two level blinking
points it was not possible to analyze two level blinking points over a broader
temperature range or ones that can be described on the basis of the quantum
jump theory.

7.4 Multi level blinking points
Videos of a area with several multi level blinking points were taken at different
temperatures. With lower temperatures the blinking gets weaker until the blinking

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7.4 Multi level blinking points

Figure 7.1: The pictures show the photoluminescence of the sample at different temperatures.
The left side of the pictures is a area with a small amount of gold enhancing the emission. The
right part is covered with a film of gold enhancing the light emission. Many of the bright points
in the left half blink. With decreasing temperature the bright points and therewith the blinking
points disappear. The overall photoluminescence intensity increases with lower temperatures.

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7 Temperature dependence of the blinking

Figure 7.2: 100 s fragments of the photoluminescence intensity time trace of the same twolevel blinking point show longer off times for lower temperatures.

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7.4 Multi level blinking points

Figure 7.3: Counting the intervals spent in the on (top) and off state (bottom) shows that forlower temperatures the probabilities for both longer on and off times increase49

7 Temperature dependence of the blinking
points disappear in the background. This is illustrated by fig. 7.4 and fig. 7.5that show maps of the standard deviation of the photoluminescence intensity of aarea with several multi level blinking points at different temperatures.
The time intensity profiles of one single multi level blinking point at different
temperatures are shown in fig. 7.6. At high temperatures the point switches both
between distant and close levels. With lower temperatures the average intensity
decreases and the point just switches between near intensity levels and not between
distant ones anymore. At very low temperatures the blinking points disappears
in the background and its noise. A comparison of the intensity histograms of thispoint at different temperatures confirms these observations (fig. 7.7).
In the case of multi level blinking points the intense light emitting centres couple
to several deep traps and all the local electric fields of the traps impact on theblinking point. Traps of different depth i.e. different activation energies forthe trapped carriers have different probability distributions for off times. Withdecreasing temperature the probability for a long off time caused by a carrier
in a trap with high activation energy is much higher than for one with smaller
activation energy. This means that at low temperatures carriers can rather escapefrom shallow than from deeper traps. The carriers in deeper traps remain there
and thus reduce the average intensity and the blinking only occurs between close
intensity levels.

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7.4 Multi level blinking points

Figure 7.4: The standard deviation of the photoluminescent intensity calculated and mappedfor each pixel of a movie file at different temperatures of 310 K (top) and 300 K (bottom). The
standard deviation is plotted in z-direction, x and y specify the pixel coordinates. Red points
show areas of high standard deviation (blinking points) blue areas correspond to low standard
deviation.

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7 Temperature dependence of the blinking

Figure 7.5: The standard deviation of the photoluminescent intensity calculated and mappedfor each pixel of a movie file at different temperatures of 280 K (top) and 240 K (bottom). The
standard deviation is plotted in z-direction, x and y specify the pixel coordinates. Red points
show areas of high standard deviation (blinking points) blue areas correspond to low standard
deviation.

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7.4 Multi level blinking points

Figure 7.6: The time intensity profiles of the same multi level blinking point at different
temperatures. At higher temperatures the average intensity is higher and the point switches
between more distant intensity levels than at lower temperatures.

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7 Temperature dependence of the blinking

Figure 7.7: The intensity histograms of the same blinking point at different temperatures.
With rising temperature the distribution gets broughter and the average intensity higher.

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