1 Experimental and Theoretical Investigation of Absorption and Emission Cross-Sections
in Rare Earth Doped GaN Epilayers
A thesis presented to
the faculty of
the Russ College of Engineering and Technology of Ohio University
In partial fulfillment
of the requirements for the degree
Master of Science
Ajay Sandeep Vemuru August 2008 2 This thesis titled
Experimental and Theoretical Investigation of Absorption and Emission Cross-Sections
in Rare Earth Doped GaN Epilayers
by
AJAY SANDEEP VEMURU
has been approved for
the Department of Electrical Engineering and Computer Science
and the Russ College of Engineering and Technology by
Wojciech M. Jadwisienczak
Assistant Professor of Electrical Engineering and Computer Science
Dennis Irwin
Dean, Russ College of Engineering and Technology
3 ABSTRACT
VEMURU, AJAY SANDEEP, M.S., August 2008, Electrical Engineering
Experimental and Theoretical Investigation of Absorption and Emission Cross-Sections
in Rare Earth Doped GaN Epilayers (96 pp.)
Director of Thesis: Wojciech M. Jadwisienczak
Currently literature demonstrates that solid-state materials, including semiconductors
doped with lanthanide ions, have revolutionized modern science and technology.
Optoelectronics is developing rapidly, partially because of the interesting properties of
the semiconductors doped with lanthanide ions and has come to the forefront of material
science, biochemistry, molecular biology and the medical sciences. This thesis
concentrates on optical investigations of GaN semiconductor thin films implanted with
lanthanides (rare earth impurities) for the development of a new class of efficient lightemitting device. Specifically, the study discussed in this project is intended to investigate
absorption and emission phenomena in epitaxially grown thin films with a focus on
waveguide slabs of nanometer size. Though well understood, the techniques used here for
measurements were never applied to those materials having high technological relevance.
The study utilizes the absorption and emission cross-sections data that are not available in
the literature for Er3+ and Yb3+ ions implanted GaN. These parameters are of high
importance for accurately modeling of any light emitting devices such as light emitting
diodes and lasers. Furthermore, this project compared and analyzed cross sections of
investigated rare earth ions with different concentrations in GaN.
4 Approved: __________________________________________________________________________________ Wojciech M. Jadwisienczak
Assistant Professor of Electrical Engineering and Computer Science
5 To my parents
Murthy & Annapurna
6 ACKNOWLEDGEMENTS
First and the foremost, I would like to thank my advisor, Dr. Wojciech Jadwisienczak, for
providing me an opportunity of working with such excellent laboratory facilities to obtain
practical hands-on experience in optics as well as electronics. I also thank him for
providing me with the necessary motivation and interest all throughout the course of the
project. I would also like to thank him for giving me a chance to attend and present the
results of my work at various conferences. This thesis would have been incomplete
without his invaluable input and timely reviews.
I would like to express deep appreciation to the committee of Student Enhancement
Award 2007 for providing me with the financial support for the project. I thank Dr. Savas
Kaya, Dr. Ralph Whaley and Dr. Lewei Chen for their valuable suggestions for
improving the quality of the document.
I would like to express sincere gratitude to Issam Khoury, Bryan Jordan and Michelle
Bobo for providing me with an opportunity to work without making me feel the pressure
of coursework and research.
I appreciate the patience of Rambabu Nalluri and other friends for supporting, advising
and helping me throughout the two years of my graduate study.
7 TABLE OF CONTENTS ABSTRACT.........................................................................................................................3
ACKNOWLEDGEMENTS.................................................................................................6
LIST OF TABLES..............................................................................................................8
LIST OF FIGURES............................................................................................................9
1
INTRODUCTION ...................................................................................................... 11
2
THEORETICAL BACKGROUND ........................................................................... 17
2.1 A Brief Summary of III-Nitrides Doped with Rare Earth Ions ............................ 17
3
ABSORPTION AND EMISSION CROSS SECTIONS ............................................ 24
3.1 The Definition and Application of Absorption and Emission Cross Sections...... 24
3.2 Theoretical Methods for the Calculation of Absorption and Emission CrossSections ......................................................................................................................... 25
3.2.1 Fuchtbauer-Landenburg Theory ................................................................... 26
3.2.2 Reciprocity Method........................................................................................ 31
4
TESTING THE THEORY ......................................................................................... 38
5
EXPERIMENTAL TECHNIQUES .......................................................................... 42
5.1 Samples Information ............................................................................................ 42
5.1.1 The Ion Implantation Procedure ................................................................... 42
5.1.2 The Preparation Procedure ........................................................................... 46
5.1.3 The Post Implantation Process ...................................................................... 47
5.2 The Experiment Description of Spectroscopic Studies ........................................ 47
5.2.1 Overview ........................................................................................................ 47
5.2.2 The Direct Coupling of Light Technique ....................................................... 49
5.2.3 The Prism Coupling of Light Technique........................................................ 52
5.2.4 Photoluminescence and Cathodoluminescence Studies ................................ 61
5.3 Results .................................................................................................................. 63
5.3.1 GaN Doped with Er Ions ............................................................................... 63
5.3.2 GaN doped with Yb ions ................................................................................ 68
5.4 Discussion ............................................................................................................ 75
6
CONCLUSIONS ........................................................................................................ 85
7
FUTURE WORK ....................................................................................................... 88
8
REFERENCES .......................................................................................................... 91
8 LIST OF TABLES
Table 4.1: Parameters used in FL equations and their values ........................................... 39
Table 4.2: Parameters used in McCumber theory ............................................................. 39
Table 5.1: Parameters of the research samples used in experimental determination of
absorption and emission CS. ..................................................................................... 44
9 LIST OF FIGURES Figure 1.1: A simplified Periodic Table with lanthanide elements [2]. ............................ 12
Figure 1.2: Diagram of splitting of rare earth energy levels in solid state host. ............... 12
Figure 1.3: Flowchart showing the calculation procedure of absorption cross-section from
emission spectrum. .................................................................................................... 16
Figure 3.1: Transitions between two manifolds of a rare earth doped solid-state host. ... 32
Figure 4.1: Fluorescence spectrum reproduced from the Ref. [59]. ................................. 40
Figure 4.2: Absorption and Emission CS calculated using McCumber theory. ............... 41
Figure 5.1: Simulated implantation depth profiles for Er3+ ions doped GaN thin film
samples. ..................................................................................................................... 43
Figure 5.2: Simulated implantation depth profiles for GaN thin film samples implanted
with Yb3+ ions where a, b, c, d, e and f correspond to ionization energies of 14 keV,
21 KeV , 40 KeV, 60 KeV, 120 KeV and 180 KeV. ................................................ 45
Figure 5.3: Peak concentrations of Yb3+ ions in GaN thin film samples implanted with
different Yb3+ ion doses. ........................................................................................... 46
Figure 5.4: Experimental setup for transmitive mode absorption spectrum measurement.
................................................................................................................................... 48
Figure 5.5: Experimental setup of direct coupling of light technique. ............................. 50
Figure 5.6: Details showing the light propagation in the wave-guiding sample for direct
coupling techniques. ................................................................................................. 51
Figure 5.7: Experimental setup for the prism coupling technique. ................................... 59
Figure 5.8: Experimental details of the prism coupling. ................................................... 60
Figure 5.9: Setup for photoluminescence and cathodoluminescence in visible spectral
range. ......................................................................................................................... 61
Figure 5.10: Setup for photoluminescence and cathodoluminescence in IR spectral range.
................................................................................................................................... 62
10 Figure 5.11: Photoluminescence spectrum of GaN:Er annealed at 1100 ºC for 0.5 hrs in
N2 measured at 13 K under He-Cd laser excitation. ................................................. 64
Figure 5.12: Cathodoluminescence spectrum of GaN:Er annealed at 1100 ºC for 0.5 hrs in
N2 measured at 13 K. ................................................................................................ 65
Figure 5.13: Cathodoluminescence spectra of GaN:Er sample at different ambient
temperatures. ............................................................................................................. 66
Figure 5.14: Absorption and Emission CS of GaN:Er sample calculated using McCumber
theory. ....................................................................................................................... 67
Figure 5.15: Photoluminescence spectra of GaN:Yb (sample #3) at 12 K and 300 K. .... 68
Figure 5.16: Photoluminescence spectra of GaN:Yb (sample #4) at 12 K and 300 K. .... 69
Figure 5.17: Photoluminescnece spectra of GaN:Yb (sample #5) at 12 K and 300 K. .... 69
Figure 5.18: Photoluminescence spectra of GaN:Yb (sample #3, #4 and #5) at 12 K and
300 K. ........................................................................................................................ 73
Figure 5.19: The emission CS spectra of GaN:Yb (samples #3, #4 and #5) at 300 K. .... 74
Figure 5.20: The emission cross section spectra of GaN:Yb (samples #3, #4 and #5) at
300 K calculated using the FL equation. .................................................................. 74
Figure 5.21: Schematic diagram showing the energy transfer processes between GaN host
and RE ions creating RESI trap. Energy can be transferred to the 4f electrons
through: (a) collapsing of a bound exciton on RESI hole traps, (b) recombination of
a bound hole with an electron on distant donor, (c) recombination of a bound hole
with an electron in conduction band, (d) inelastic scattering process between FX and
4f shell electrons. ...................................................................................................... 77
Figure 5.22: Energy level band diagram of ground, first and second excited states of Er3+
ion in GaN with the transitions observed in our experiment at 12 K. ...................... 78
Figure 5.23: Energy band diagram of Yb3+ ions in GaN with the transitions at low
temperature. .............................................................................................................. 81
Figure 5.24: The statistical probability of RE ions clusters formation in semiconductors
as a function of RE ions doping concentration. ........................................................ 83
11 1
INTRODUCTION
Rare earth elements (RE) or lanthanides are the elements that are found in the Periodic
Table from the atomic number 57 to 71, as shown in Fig. 1.1. The main feature which
distinguishes RE elements from other species is an incompletely filled 4f subshell that is
screened by the completely filled outer 5s and 5p subshells.
Due to this, when incorporated into solid state hosts including semiconductors, the RE
elements give rise to sharp absorption and emission peaks that are almost independent of
the host material [1]. The RE ions in semiconductor hosts have their 4f energy levels split
due to the Coulomb interaction among electrons that gives rise to terms
2S +1
L with a
separation of order of 104 cm-1. These levels are further separated to J states of order 103
cm-1 by spin-orbit coupling and finally, the Stark field splits, partially or fully eliminating
the J degeneracy into 103 cm-1 energy separation, as shown in Figure 1.2 [1].
12 Figure 1.1: A simplified Periodic Table with lanthanide elements [2].
Figure 1.2: Diagram of splitting of rare earth energy levels in solid state host.
These splittings lift the parity rules so that RE ions can have transitions between levels
which are otherwise not allowed [3]. The observed emission and absorption spectra of RE
13 ions when embedded into a host are hence due to the transitions within the 4f states that
are split due to the local electric field. The splitting of the energy levels varies from hostto-host. This is a characteristic of the RE site symmetry, while the intensity of the
transition is a characteristic of the interaction of RE ions with the local environment.
For many years, researchers have been looking for a semiconductor host doped with REs
to be used in optoelectronic applications [4],[5],[6]. As the electronics industry is now
facing problems with increasing data rates and the decreasing size of the isolation
between components on a chip, the RE doped semiconductors may be suitable for optical
interconnects and for isolation at nanometer thickness. This may lead to the integration of
optics and electronics and an increase in the flexibility and performance of optoelectronic
devices [7]. As a leader of semiconductor industry Silicon was investigated extensively
as a host for Erbium (Er3+) ions. However, its indirect band gap energy inhibited efficient
light emission. Different morphological forms of Silicon, like porous Silicon [8], Silicon
rich oxide [9] and RE doped Silicon [10] that could be used for light emission have been
studied. The RE doping of Silicon was attractive compared to others, due to the
characteristic of Er3+ ion that has its emission from the first excited state between the
weakly split spin orbit levels 4I13/2→4I15/2 in the infrared (IR) spectra region at 1.5 μm
[11]. This wavelength is the low loss window for fiber optics, used by the
telecommunications industry [12]. The first demonstration of luminescence from the Erdoped Silicon was shown at low temperatures [13]. It was later observed that emission at
room temperature was very weak, due to the thermal quenching. Some studies have
considered co-doping with impurities like Oxygen and Carbon as alternatives for
14 improving the luminescence efficiency. These co-dopants helped in forming bonds with
RE ions that were more ionic in nature and similar to dielectric materials [14]. However,
non-radiative processes like the Auger process and back transfer processes competed
with radiative processes in transferring energy between 4f energy levels to reduce the
radiative efficiency at room temperatures [15]. Due to above facts, other semiconductors
were later explored to increase the efficiency of the luminescence from Er3+ ions in the
visible-IR spectral range. For example, the emission was reported from RE doped III-V
materials like GaAs [16], InP [17] and GaP [18]. It was found that the intensity of the RE
emission in these materials was less temperature sensitive and had relatively lower
thermal quenching compared to Silicon. The thermal quenching, a principle obstacle for
reducing emission at room temperature, was later found to decrease even further with the
increase of band gap of the semiconductors [19],[20]. The implementation of this concept
along with the III-Nitride (III-N) semiconductor thin film technology, which matured
enough at the time, opened up avenues to explore new hosts that are recognized currently
as potential materials for RE doping.
The III-N materials doped with RE ions have been considered attractive for electrically
pumped light-emitting devices such as light emitting devices (LEDs), electroluminescent
displays (ELD) and semiconductor lasers (SL). As a result of several years of extensive
research, researchers observed visible luminescence under optical and electrical
excitation from most of the RE ions doped GaN at room temperature [11],[21].
Recently, stimulated emission at 620 nm was demonstrated from Europium (Eu) doped
GaN thin films on Sapphire and Silicon [22],[23]. It is obvious that this stimulated
15 emission from Eu-doped GaN can be further improved by modeling certain parameters
such as absorption and emission cross-sections (CSs). These parameters can optimize the
emission at specific wavelengths by precisely controlling the amount of pumping energy.
For example, the material used for lasers needs be designed in such a way that it has
maximum absorption CS at the pump wavelength and a high emission CS at the lasing
wavelength. It is, therefore, imperative to mention here that there is need to investigate
the absorption and emission CSs in detail for RE-doped III-Ns before successful LEDs,
ELD’s and laser diodes (LDs) will be developed and commercialized.
Many different ways exist for determining the CSs in semiconductor hosts. The
theoretical studies of absorption and emission CSs can be conducted with strong
knowledge of certain crystal parameters, while measurement is the more common way of
determining it. However, the ease of using such theoretical analysis depends on the
availability of critical data, such as crystal field splitting, which is frequently experiment
dependent. Because the CSs parameters are not available for RE ions in III-N’s this study
showed the measurement of the absorption spectra as the main focus of the work.
The samples used for measuring these parameters here at Ohio University were
commercial GaN wafers from CREE Inc. that were implanted with Er and Yb ions at the
National Laboratory, Berkeley, California. Our research attempted to measure the
absorption spectra of Er and Yb doped GaN using different experimental techniques. The
techniques used here for the measurement were derived from the concept of waveguide
coupling, where a thin film was considered analogous to an optical waveguide, and the
missing characteristics of the incident light were measured. In general, the study focused
16 on these missing features related to the absorption processes of the RE ion doped III-N
materials. However, the lack of RE ions absorption lines in the absorption spectrum
measured using these coupling techniques made us approach the problem of calculating
the CSs in a different way. Firstly, we measured the emission spectrum (step #1 in Figure
1.3) using the photoluminescence (PL) and the cathodoluminescence (CL) techniques
followed by calculation of emission CS (step #2 in Figure 1.3) using FuchtbauerLadenburg (FL) equations and subsequent calculation of absorption CS (step #3 in Figure
1.3) using McCumber theory, as shown in the flow chart in Figure 1.3. Figure 1.3: Flowchart showing the calculation procedure of absorption cross-section from
emission spectrum.
In the following sections, this thesis gives detailed information about the theoretical and
experimental approaches we used, the problems we faced, the data we collected,
theoretical analysis we used and our proposed improvements for each technique in the
future.
17 2 THEORETICAL BACKGROUND
2.1 A Brief Summary of III-Nitrides Doped with Rare Earth Ions
It has recently been shown that the incorporation of rare earth (RE) elements as dopant
atoms into III-N semiconductors such as GaN or AlN leads to a temperature-stable
luminescence material with wavelength that is nearly independent of the specific
semiconductor host. Luminescence from these materials and their alloys grown on
Sapphire or Silicon, doped by implantation or during the growth with Nd [24], Eu [25],
Er [26], Dy [26], Tm [27] Yb [28], Ce [29], Pr [30], Sm [31], Ho [31], Gd [32] and Tb
[33] has been reported so far. RE ion concentrations in these materials have varied in a
wide range without observed luminescence quenching or precipitation [26]. In particular,
RE doped GaN electroluminescent devices (ELDs) have been shown to have a versatile
approach for the fabrication of a variety of electrically driven optical light sources with
narrow line-width emissions from the ultraviolet to the infrared. Thus, optoelectronic
devices utilizing 4 f n transitions appearing in the nitrides’ forbidden bandgap “window”
are practically viable with these semiconductors [28].
18 These devices can be effectively designed with appropriate knowledge of the optical
properties of the RE doped semiconductor materials. The complexity of these
semiconductor materials, however, is extremely challenging for studying the optical
properties. The mixing of non-symmetrical crystal fields that give rise to sharp 4f
transitions has been a difficult topic to analyze; however, this process helps us in
understanding the energy migration process between the host and the impurity ions. Due
to the different growth and doping techniques employed, the possibility of RE ions being
incorporated in different lattice locations in the same host material is high. These
different lattice locations affect the local symmetry of the environment (site) that has
considerable influence on the optical properties of the incorporated RE ions. A good
knowledge of the different sites helps in engineering the occupational statistics
(substitutional occupation) to enhance the emission intensity [23]. Hence, in our study the
optical properties of the RE doped GaN for each doping technique was investigated to
obtain a good idea of the available sites [24],[26], [28], [31].
The investigation of the optical properties is frequently done using spectroscopy
techniques,
mainly
transmission
spectroscopy,
photoluminescence
(PL),
cathodoluminescence (CL) and photoluminescence excitation spectroscopy (PLE).
However, transmission spectroscopy is seldom used in case of RE-doped semiconductor
epilayers due to the small volume of RE ions in the doped layers that are optically active.
In PL and CL, the spectral signatures of RE ions are obtained in the process of photon
absorption, of desired energy (PL) and the collision of electron beam (CL), respectively.
A PLE spectrum is obtained by looking at a certain feature when the excitation source is
19 swept in a specific spectral range [11],[23]. From the review of literature it is evident that
Er3+ ion was the most extensively studied in III-Ns. The recent results of these
spectroscopic studies of Er ion doped GaN conducted by various research groups are
summarized in the next paragraphs.
The PL spectroscopy was used to study the emission properties of Er doped GaN grown
using different techniques. A variety of chemical and physical vapor phase deposition
techniques along with a suitable method of doping, either in-situ or ion implantation for
incorporating the RE ions were studied [34]. The first observation of luminescence from
GaN implanted with Er ion was made by Wilson et. al [36], which was followed by the
search for suitable growth techniques. The substrates used in this study were Sapphire,
Silicon or GaAs, and the samples were later co-implanted with O+ ions. The strong
emission from Er doped GaN was from the substitutional occupation of the RE ions for
Ga [36]. The first successful observation of luminescence from in-situ doped Er in GaN
was seen by Kim et. al. [24] using the Metal Organic Molecular Beam Epitaxy
(MOMBE) technique on Si or Sapphire as the growth technique.
The luminescence of Er ions in GaN grown by Metal Organic Chemical Vapor
Deposition (MOCVD) technique on Sapphire substrate was observed in the IR spetcrum
due to different centers with the main peak emission at 1.54 μm [37]. Similar results were
obtained later from the PL of GaN on Silicon grown by MOMBE techniques [38]. In both
cases, the PL was observed with a below bandgap energy excitation. When the samples
were excited with photons of energy exceeding the bandgap energy, the luminescence at
1.54 μm was not as strong as it was for the resonant excitation at 980 nm in the case of
20 GaN implanted with Er ions samples. However, a strong band edge in the visible
spectrum was observed for both implanted and MOMBE-grown materials. The above
bang gap excitation of GaN sample implanted with Er ions prepared by Solid Source
Molecular Beam Epitaxy (SSMBE) showed intense green lines at 537 nm and 558 nm
along with reduced band edge emission. From this, it was understood that the band edge
serves as a radiative recombination center that is reducing the efficiency of IR and visible
emission from incorporated RE ions [11].
Another kind of spectroscopy for studying various absorption bands of different radiative
centers is PLE spectroscopy. Several research groups measured the PLE spectra of Er
doped GaN grown using different techniques. The PLE spectra of MOMBE-grown Er
doped GaN samples were measured by Hommerich et. al.; these showed a broad
background signal, which can be attributed to the carrier mediated energy transfer to the
4f system involving defects in the host [39]. However, the PLE of Er implanted GaN
samples showed additional sharp features superimposing with the broad background
corresponding to intra 4f transition [44]. It is, therefore, clear that PLE spectroscopy helps
in studying the transition lineshapes and energy excitation processes of the emitting Er
centers in GaN.
In general, the spectroscopic study of RE-doped GaN learned through the techniques
mentioned above provided general information about luminescence of RE ions in III-Ns
at different wavelengths. The luminescence observed using the above spectroscopic
techniques involves optical excitation of the RE-doped semiconductors, which needs
another light source to optically excite the electrons in the ground state of the 4f subshell
21 to excited states. This knowledge will be very useful in developing different
optoelectronic devices including LEDs, LDs and displays. This requirement for having
additional light source can be eliminated by developing electroluminescent devices
(ELD) that use the mechanism of electroluminescence (EL). In EL, the emission
observed is due to the energy transferred to the 4f system, either by impact excitation or
by a electron hole recombination method which depends on the voltage bias applied to
the device.
The first such ELD was demonstrated at 1.54 μm with a device structure consisting of a
metal/i-GaN/n-GaN structure grown by the CVD process under reverse bias condition
[21]. The active layer, i-GaN, was doped with Er and O ions and the EL spectrum was
almost similar to PL, except that the emission from EL was three times more intense.
However, in this case under forward bias, no luminescence was observed. Following this
process, the EL was observed at 1.54 μm from Er doped GaN grown by different
techniques [11]. It is important to note that the intensity at the wavelength of the EL at
400 K was almost as strong as at 250 K [21]. The first visible EL spectrum was
demonstrated from ITO/GaN doped Er system grown by SSMBE technique [41].
It is obvious that color displays require emission at different wavelengths. This can be
achieved by doping GaN with a variety of RE ions, for example, Er, Eu, and Tm. GaN:Er
has emissions at 537 nm and 558 nm (green), GaN:Eu has emissions at 623 nm (red) and
GaN:Tm has emission at 478 nm (blue) [11].
22 It was also shown that co doping the ELD with Er and Tm induces peaks at both 537-558
nm and 478 nm, with results showing turquoise, a combination of green and blue [11].
Thus, GaN doped with RE ions systems could further be used as multiple color indictors
that change the color depending on RE ion composition ratio and/or the applied voltage.
Two such type of indicators exists (1) a voltage controlled (VC) ELD and (2) a
switchable color (SC) ELD. It was recently shown that VC ELDs emit a range of color
from red to green as the bias voltage is increased [42], while the SC ELDs emit red or
green depending on the polarity of the bias [43].
Recently successful demonstrations of laser action from Eu doped GaN first on Sapphire
and later on Silicon substrate have been made. The active layer was Eu doped GaN, while
the cladding and substrates were AlGaN and Silicon. The pumping of the system was
done at 337.1 nm, while the lasing occurred at 620 nm. This is believed to be the first
stimulated emission from semiconductors on Silicon [21],[23]. The above interesting results made the rare earth doped III-Ns and their alloys are
attractive for many applications related to communications, optoelectronics, full color
displays and flat panel displays (FPD). The absorption and emission CSs, paramount
parameters in optoelectronic device optimization process are the topic of the thesis. The
knowledge about them is needed for future device development. Therefore, designing
RE-doped GaN material for optimal emission helps them in faster commercialization.
The following paragraphs briefly discuss the present status and the future of a few new
applications.
23 Communications over long distances using fiber cables need repeaters at regular intervals
for boosting the optical signal. The process of amplification was done by converting the
signal from a optical domain to an electrical domain, amplifying the signal, then
converting back to an optical domain. This method requires lot of processing at each
repeater. Recently, the erbium emission at 1.5μm due to intra 4f transitions, in the low
loss window of fiber communications, is being called Erbium doped fiber amplifiers
(EDFA) [44]. Although these amplifiers have the advantages of high data rates and a
reduced need for signal regeneration they need intensive optical pumping for the
emission at the required wavelength. This can be overcome via III-Ns doped with Er for
inducing the 4f transition through electrical excitation. Hence, the III-Ns doped Er have a
potential to be used in long distance communications, although research is being done for
improving the bandwidth of the erbium amplifiers [11]. The primary requirement for FPD is the multiple color emission. The FPDs are made
either by additive generation from pure colors or subtractive generation from broad color
spectrum; the advantage of RE lies in the fact that it can be used in either ways. Well
saturated RGB colors are most important for full color display used in indicators,
watches, etc [45]. While II-VI semiconductors doped with RE ions are presently being
commercialized for these kinds of applications, the study of III-N doped with RE ions for
such displays has reached the higher goals of obtaining improved brightness and
durability for commercial applications [46].
24 3
ABSORPTION AND EMISSION CROSS SECTIONS
3.1 The Definition and Application of Absorption and Emission Cross Sections
The defined area within which an atom interacts with electromagnetic radiation is called
the cross section [47]. The CS is a parameter used in the modeling of lasers, optical
amplifiers, etc. The most relevant CSs for a medium are the absorption and emission CSs
in addition to the excitation CS. Knowing the absorption and emission CSs, one can
engineer the host material for active optoelectronic devices. For example, an ideal laser
medium should have a non-zero absorption CS at pump wavelengths and a zero
absorption CS elsewhere, so that the host absorbs most of the pump energy. Similarly, the
emission CS should be zero at all wavelengths other than the lasing wavelength to have
maximum emission at the lasing wavelength. The former is an ideal case; all the host
materials for optoelectronic devices need to be optimized to the ideal situation as close as
possible [48]. Another important parameter that can be calculated using the absorption
and emission CSs is the gain of an optical medium. The Eq. 3.1 provides the calculations
for gain [47].
25 ⎡N2
γ ( λ) = N 2σ em ( λ) − N1σ abs ( λ ) = N1⎢
⎣ N1
⎤
σ em ( λ) − σ abs ( λ)⎥
(3.1)
⎦
Where γ ( λ) is the gain of the medium at a particular wavelength (cm-1), σ em ( λ ) is the
emission CS at a particular wavelength, σ abs ( λ) is the absorption CS at a particular
wavelength and N1 and N2 are the population of the states 1 and 2 respectively.
Eq. 3.1 shows that the amount of light amplification can be calculated by means of the
absorption and emission CSs. The gain can actually be measured in different ways, which
give the most accurate results [49],[50], but the measurement of gain is not possible most
of the time due to many issues such as optical losses. Therefore, the calculation of gain
through absorption and emission CSs is more convenient compared to the measurement
of gain. The calculation of absorption CS is difficult without the knowledge about
concentration of the dopant, especially when low power light sources are used [51]. In
such circumstances, the absorption CS is calculated using the emission CS obtained from
the emission spectrum measured via experiments. Several theories are available to
calculate or model the CS values and we discuss them in the following sections.
3.2 Theoretical Methods for the Calculation of Absorption and Emission CrossSections
The modeling of absorption and emission CSs can be done using different methods, and
the complexity of the model depends on the complexity of the system. The following
section describes a few of the methods that can be used to calculate these parameters.
These methods are:
26 • Fuchtbauer-Landenburg theory [52],[53]
•
Reciprocity theory [54],[55],[56]
•
Judd-Ofelt theory [57],[58]
Only the first two methods, Fuchtbauer-Ladenburg theory and the Reciprocity theory are
used in this thesis and are explained in detail.
3.2.1
Fuchtbauer-Landenburg Theory
The Fuchtbauer‐Landenburg (FL) theory analyses the fluorescence spectrum and
relates it with the emission CS. This analysis ground itself in the fundamental Einstein
coefficients [53]. According to the FL theory, the emission CS at a particular wavelength
is proportional to the fifth power of the wavelength times the fluorescence intensity. This
is one of the forms of FL equations. Its derivation from the basic Einstein equations is
shown below. However, alternative forms of the FL formula that can be used in the
calculation of integrated emission CS values depending on the requirements of the system
[52],[53].
The basic Fuchtbauer-Ladenburg equation relates the Einstein Bij coefficients to the
integrated absorption coefficient for a two-level degenerate system i and j with
degenaracies di and dj respectively. The formula is given by Eq. 3.2.
⎛dj
∫ α (v )dv = ⎜⎝ d
i
⎞ B hv
N i − N j ⎟ ij
⎠ c /n
(3.2)
where α (v ) is the absorption coefficient in cm-1, Bij is the Einstein coefficient, Ni ,and Nj
are the population of i and j levels respectively and h, v, c and n are the Plancks constant,
27 frequency of radiation, speed of light and refractive index of the medium, respectively.
The absorption coefficient can be used to calculate the absorption CS using the Eq.3.3.
σ abs (v) =
α (v)
N
(3.3)
The Eq. 3.2 is derived from Einstein’s equation that relates the stimulated emission and
absorption under an assumption that the levels of the degenerate system are equally
populated or have the same rate of induced transition, which is given by Eq. 3.4.
d j B ji = di Bij
(3.4)
This equation cannot be applied to RE-doped semiconductor hosts, as it is not a valid
condition due to the different populations of the levels.
A different form of the FL equation was used that originated from Einstein relations,
connecting the stimulated and spontaneous emission which is given by Eq.3.5 and Eq. 3.6
[59].
σ ij (v) =
d j λ2
Aij gij (v)
di 8πn 2
(3.5)
λ2
A ji g ji (v)
8πn 2
(3.6)
σ ji (v) =
where λ is the peak wavelength, β is the branching ratio of the transition, n is the
refractive index, τ is the radiative lifetime of the transition and g ji (v ) gives the lineshape
of the transition.
28 The next form of the FL equation used here is to calculate the emission CS from the
fluorescence spectrum of the system. This equation was derived by Aull et. al [52] and is
considered here again as it is worth deriving for a clear idea of the assumptions used in
this research.
The intensity of the fluorescence spectrum for transition j→i is measured under steady
state low level excitation and is given by the Eq. 3.7.
I ji (v ) dv = GA ji g ji (v ) hvdvN j
(3.7)
where g ji (v ) is the normalized lineshape, Aji is the probability of spontaneous emission
per unit time, Nj is population density in j level and is given by N j = f j N tot . The
parameter f j is the ratio of pumped population of the level j to the total population of the
excited states (Ntot). Parameter G is the calibration function of the experimental setup
used to detect the emission spectrum.
Solving Eq 3.6 for A ji g ji (v ) and using it in Eq 3.7, we get the equation in terms of
emission CS. The resultant equation after simplification appears in Eq. 3.8.
I ji (v)dv = G
8πn 2 3
hv dvσ ji (v)N j
c2
(3.8)
where c is the speed of light, h is the Plancks constant.
This is the intensity of the transition between one set of levels in the excited and the
ground manifolds. However, the total intensity of radiation is a sum of all the frequencies
of the transition and integration of all such transitions of the excited ions in the system
29 due to steady state pumping. The equation for the overall intensity over all frequencies
and all different transitions is obtained from Eq. 3.7 and using Eq. 3.9. 1
= ∑ f j ∑ A ji =
τR
j
i
η
τf
(3.9)
we get Eq. 3.10.
∫∑
ij
Iij (v)
GN totη
dv =
τf
hv
(3.10)
where η is the radiative quantum efficiency, τf and τR are fluorescent and radiative
lifetimes.
The CS can be calculated using Eq. 3.10, which relates the CS to the sum of intensities of
all individual transitions. Substituting the Eq. 3.10 in Eq. 3.7 and solving for CS, we get
Eq. 3.11.
σ ji =
where,
∑I
ji
ηc 2
τ f fi ∫
I(v)
dv8πn 2 hv 3
hv
I ji (v)
(3.11)
(v) = I(v) , and the total fluorescent emission spectrum, includes the
ij
emission from all ions present in the system. This calculation of CS using Eq. 3.11 is prone to errors due to the integration of the
individual transitions in Eq. 3.10, where all the line-shape parameters and sidebands of
the transitions overlap. Accounting to the overlapping caused by other transitions can
30 solve this problem of error prone calculation. The effective CS calculation, depending on
the population of the level from which the transition is made, eliminates the effect of
overlapping. The effective CS is given by Eq. 3.12. σ eff = σ ji (v) + ∑
k,1
fk
σ k1 (v)
fj
(3.12)
Substituting Eq. 3.10 into Eq. 3.11 will yield Eq. 3.13.
ηλ5
σ em (λ) =
τ f f i 8πn 2c
I( λ )
(∫ λI(λ)dλ)
(3.13)
In the above Eq. 3.13, η is, in general, considered unity assuming the absence of nonradiative processes. This equation is used to calculate the emission CS from a given
fluorescent spectrum and knowledge of the radiative lifetime of the excited state.
The third form of the FL equation for calculating either the emission or absorption CS
with the other known is given by Eq. 3.14.
di ∫ v 2σ ij (v)dv =d j
∫v σ
2
ji
(v)dv
(3.14)
The fourth form of FL equation that is used when the polarization of the light is taken
into account is given by Eq. 3.15 [53].
π ,σ
σ em
(λ) =
8πcτ
∫
3λ5 Iα ( λ)
dλλ[n π2 Iπ ( λ) + 2nσ2 Iσ ( λ)]
(3.15)
linewidth
where Iα ( λ) is the polarization dependant intensity.
31 The above Eq. 3.15 gives the polarized emission CS in arbitrary units. Special care needs
to be taken while measuring the Iπ ( λ ) and Iσ ( λ ) parameters as these parameters are
measured relative to each other and should be on the same scale of units. Among all the
available forms of FL equations, we use the Eq. 3.13 in this work due to the randomly
polarized nature of the light source used in our experiment.
3.2.2
Reciprocity Method
Derivation of the formula
The theory of reciprocity, in terms of the absorption and emission CSs, dates back to
Einstein in 1917, where he described the relations connecting the rates of spontaneous
emission, stimulated emission and the absorption of radiation in a free space two level
non-degenerate system. According to the above theory, when a two sharp level system is
considered, the relation between the emission and absorption CSs between the upper and
lower levels is be given by Eq. 3.16 [47].
σ abs = σ em
(3.16)
where σ abs is the absorption CS and σ em is the emission CS.
Einstein predicted that a two-level system might have degeneracy in its upper-level and
lower-level, which is a situation normally with free ions [47]. When the above situation
takes place, the ratio of the absorption and emission CSs is not unity anymore, but is the
ratio of degeneracy of the upper-level to that of lower-level as shown below.
32 d1σ abs = d2σ em
(3.17)
where d1 and d2 are the degeneracies of the lower and upper levels.
The above theory, called reciprocity theory, is valid only when an impurity is in free
space. When we consider a diluted distribution of impurity ions in a medium the situation
is more complicated. It is the generalization of the above situation proposed by
McCumber [54] called the McCumber theory that can be applied for a laser medium with
a dilute distribution of impurities. The crystal field splitting removes the degeneracy of
the impurity ion forming manifolds with a spread of energy levels as shown in Figure 3.1.
Figure 3.1: Transitions between two manifolds of a rare earth doped solid-state host.
These levels have energy comparable to that of the thermal energy and hence, the
population distribution of the levels occur according to Boltzmann distribution. Due to
this scenario, the emission from the higher level of the upper manifold is weaker than that
33 of the lower level of the same manifold and a similar case with absorption. The
absorption and emission CSs are given by the Eq. 3.18 and 3.19 [60].
⎡exp(−E i /kT) ⎤
⎥σ ij (v)d j
Zl
⎣
⎦
(3.18)
⎡exp(−E j /kT) ⎤
⎥σ ji (v)di
Zu
⎣
⎦
(3.19)
σ abs (v) = ∑ di ⎢
ij
and
σ em (v) = ∑ d j ⎢
ij
where Zl and Zu are the partition functions of the lower and upper levels and given by [53]
Z = ∑ dk exp(−E k /kT )
k
(3.20)
where Ei and Ej are the energies of the lower and upper levels, k is the Boltzmann
constant, T is the temperature in Kelvin, d1 and d2 are the degeneracy of the lower and
upper levels and σ ij and σ ji are the individual CSs. The term in the square brackets in
Eq. 3.18 and Eq. 3.19 gives the Boltzmann distribution of the population in the different
levels of d degeneracy.
The transition between any two levels of the upper-manifold and lower-manifold can be
considered for the derivation and the energy of any transition as shown in Eq. 3.21 [60].
E j − E i = hv − E ZL
(3.21)
34 where EZL is the zero line energy (energy between the lowest Stark levels of the two
manifolds under consideration), h is the Planks constant and v is the frequency of the
wave emitted or absorbed.
Diving Eq. 3.18 by Eq. 3.19 and using Eq. 3.20, we produce Eq. 3.23 [60]
σ em (v) = σ abs (v)
⎡ (E − hv)⎤
Zl
exp⎢ ZL
⎥⎦
⎣
kT
Zu
(3.22)
Using Eq. 3.20, Eq. 3.21 and Eq. 3.22 along with Eq. 3.23 [54]
ω = 2πv =
(E j − E i )
h
(3.23)
where ω is the angular frequency of the radiation, and h is reduced Plancks constant.
From the above discussion, we can derive the McCumber equation (Eq. 3.24) [54]
⎡ h(μ − ω ) ⎤
⎣ kT ⎥⎦
σ em (v) = σ abs (v)exp⎢
(3.24)
where hμ is the net free energy to excite one impurity from a lower Stark level to a
higher Stark level, and where
⎛ hμ ⎞ ⎛ N ⎞
exp⎜ ⎟ = ⎜ j ⎟
⎝ kT ⎠ ⎝ N i ⎠ eq
(3.25)
Eq. 3.23 can also be written out as an equivalent to Eq. 3.26
35 ⎡ε − hv ⎤
σ em (v) = σ abs (v)exp⎢
⎥
⎣ kT ⎦
(3.26)
which is the exact McCumber relation for absorption and emission CSs at any particular
frequency v. ε which is temperature dependant excitation energy is calculated using the
Eq. 3.26 and Eq. 3.27 shown below. ⎛Nj ⎞
ε
⎜ ⎟ = exp(− )
kT
⎝ N i ⎠ eq
(3.27)
and d2
⎛N j ⎞
⎛ ΔE 21 ⎞
⎟
⎜ ⎟ = exp⎜
⎝ kT ⎠
⎝ N i ⎠ eq
1+ ∑ exp(−δE 2 j /kT)
j= 2
d1
1+ ∑ exp(−δE1 j /kT)
(3.28)
j= 2
where ΔE 21 is the energy difference between the lowest level of each manifold, and δE ij
is the difference of energy between the ith level and the lowest level of the jth manifold as
shown in Figure 3.1.
To use the above equation, one needs a detailed knowledge of the complete electronic
structure of the incorporated RE in a host. An alternate approximate method for
calculating the ratio of the population of sublevels at thermal equilibrium was developed
in [61] and is given by Eq. 3.29
⎛ −ΔE 21 ⎞ 1− exp(−δE1 /kT) 1− exp(−d jδE 2 /kT)
N2
= exp⎜
⎟
⎝ kT ⎠ 1− exp(−δE 2 /kT) 1− exp(−diδE1 /kT)
N1
(3.29)
36 All the parameters of the above equation were explained before. In this approach, we
made two approximations were made
•
the sublevels are equally spaced in energy such that E ij = ( j −1)E i and
•
δE1 , δE 2 are the low energy and high energy half widths of the emission
spectrum or the absorption spectrum measured at room temperature, respectively.
These approximations reduce the number of necessary parameters needed in calculating
the McCumber theory. Hence, the choice of either exact or approximate McCumber
theory depends on the trade off between accuracy and the knowledge of energy-level
splitting in the host. The McCumber theory derived here is valid only under certain
assumptions, which if violated would result in huge distortions of the calculated CS
values. The next section of this thesis gives a detailed description of the assumptions
made and the conditions required for obtaining reasonable CS values.
Assumptions and Analysis of McCumber Theory
The following assumptions are critical in calculating the CS values using McCumber
theory to obtain reasonable accuracy [61]:
•
The lifetime of the manifold is longer than that of the time taken to achieve
thermal equilibrium in each manifold.
•
The spectral width of every level is small when compared to thermal distribution,
kT.
37 The first assumption is satisfied most of the time, but the second assumption needs to be
carefully verified. The second assumption breaks at temperatures other than room
temperature, due to the effect of broadening phenomena on the transitions.
Two types of broadening contribute to the lineshape of a transition between any two
levels that are (1) homogeneous broadening and (2) inhomogeneous broadening. If
different impurities in the medium affect the lineshape in a similar way, it is called
homogeneous broadening. The homogeneous broadening is represented by a Lorentzian
function that has slower decaying wings. An example of homogeneous broadening is the
reduced lifetime of sublevels in the Stark manifold, where the line width is broadened
equally by ions occupying the same centers in the host [47].
When different impurity ions in the medium affect the lineshape in different ways, it is
called inhomogeneous broadening and is represented by a Gaussian function. An example
for such broadening can be seen when two similar impurity ions are in two different
lattice centers, in the same medium, interacting with different electric fields [47].
The lineshape of the emission CS in Eq. 3.11 is distorted when the wings of these
Guassian or Lorentzian functions are multiplied by an exponential function [61]. At high
temperatures, the second assumption breaks due to the dominance of homogeneous
broadening that is dependant on temperature. At low temperatures, inhomogeneous
broadening dominates and is independent of temperature, but in this case, kT decreases
with temperatures violating the second assumption [60]. Hence, the usage of McCumber
theory gives accurate results subject to the agreement of the above assumptions.
38 4 TESTING THE THEORY
To test our approach of calculation of both absorption and emission CS from the
experimental emission spectra, we reproduced CS data from Ref. [59] that used a similar
method. The idea was to calculate the emission CS from the measured fluorescence
spectrum using FL equation (Eq. 3.12) derived in the previous section and subsequently
calculate the absorption CS from emission CS using McCumber equation (Eq. 3.23).
The Ref. [59] deals with the determination of the absorption and emission CSs of Er
doped Ti:LiNbO3 waveguide. The fluorescent spectrum of the waveguide was measured
in the IR spectral range, 1400 nm–1700 nm, which concentrates on 4I13/2→4I15/2 transition
of Er3+ ion. This experimental spectrum is further used in the calculation of absorption
and emission CSs using FL and McCumber equations, respectively. This calculated
absorption CS is then verified with the experimentally measured absorption CS value.
The experimental fluorescence spectrum presented in Ref. [59] was reproduced in this
work using a MATLAB programming package for simulations developed for calculating
absorption and emission CSs.
39 In addition the MATLAB code is developed to calculate the absorption and emission
CSs. A list of all values from [59] used for simulating the emission and absorption CSs
spectra are given in the Tables 4.1 and 4.2, respectively [59].
Table 4.1: Parameters used in FL equations and their values.
Parameters Used
Value
Refractive Index (n)
1.45
Speed of Light (c)
2.998×108 m/s
Radiative Lifetime (τ)
2.34 ms
Fraction of pumped population (fi)
1.7237
Quantum Efficiency (η)
1
Table 4.2: Parameters used in McCumber theory.
Value
Parameters Used
kT
200 cm-1
di, dj
8,7
δE1 , δE 2
60 cm-1, 44.5 cm-1
ε
0.8074 cm-1
ΔE 21
6535.9 cm-1
The reproduced experimental fluorescence spectrum shown in Figure 4.1 is used to
calculate the emission CS in absolute units (m2). The emission CS generated in this way
is used in the calculation of absorption CS using McCumber theory. The Eqs. 3.25
40 through 3.27 are implemented. The spectrum of absorption and emission CSs obtained
from the calculation is shown in Figure 4.2. In the above table, the parameter fi is the fraction of pumped population and is calculated
using the Boltzmann distribution relation. The lifetime τ, speed of light c, and refractive
index n are constants.
Fluorescence Intensity [a.u]
1.0
Ti:LiNbO3 waveguide
0.8
0.6
0.4
0.2
0.0
1450
1500
1550
1600
1650
Wavelength [nm]
Figure 4.1: Fluorescence spectrum reproduced from the Ref. [59].
41 2.5
2.0
-24
2
Cross Sections [ x10 m ]
Emission cross section
Absorption cross section
1.5
1.0
0.5
0.0
1450
1500
1550
1600
1650
Wavelength [nm]
Figure 4.2: Absorption and Emission CS calculated using McCumber theory.
The results obtained from this procedure are in good qualitative agreement with the data
presented in the paper [59]. The absorption and emission CSs found in the Ref. [59] are
2.3×10-24 m-2 and 2×10-24 m-2 while the values simulated here are 2.25×10-24 m-2 and
1.94×10-24 m-2, respectively. The analysis presented in this chapter after successful
verification was further used as a tool for analysis of selected RE ions doped GaN
absorption and emission CSs.
42 5
EXPERIMENTAL TECHNIQUES
5.1 Samples Information
5.1.1
The Ion Implantation Procedure
The GaN epilayers used in this work were grown along the c-axis by a MOCVD process
on a 2 in. diameter Sapphire substrate at CREE Inc. The thickness of the films is 1.4 μm.
Samples were implanted with the Er3+ and Yb3+ ions at the Lawrence Berkeley National
Laboratory, Berkeley, California. Implantation was done using Metal Vapor Vacuum arc
ion technique (MEVVA). This technique makes use of the ion beam created from the
plasma and generated at the cathode. The plasma generated from the material of cathode
plumes away from the cathode that hits a set of extractor grids. This streaming of metal
plasma generates an ion beam [62]. The ion beam that contains the RE ions is made to hit
the target at high speeds. The ion beam is inclined at an angle of 7° to the normal in order
to avoid channeling of the ions. The maximum beam current and extraction voltages that
could be generated were 500 mA and 60 kV, respectively. The maximum depth of ion
43 implantation estimated with the ion implantation simulation software was found to be
around ~60 nm. The details of Er and Yb doped GaN thin films are given in Table 5.1.
The simulated implantation profiles of Er and Yb doped GaN are shown in Figure 5.2,
5.3 and 5.4.
The profiles shown in Figure 5.1 were calculated using Pearson distribution function.
Implantation was done at room temperature with energies given in Table 5.1.
3+
Sample #2 GaN: Er
Integrated Depth Profile
Peak Concentration
19
-1
4.33x10 cm
Projected Range
220 nm
19
2
Concentration [cm ]
10
18
10
17
10
16
10
d
f e
0
100
200
300
c
400
b
500
600
700
a
800
900
1000
Penetration Depth [Angstroms]
Figure 5.1: Simulated implantation depth profiles for Er3+ doped GaN thin film samples.
44 Table 5.1: Parameters of the research samples used in experimental determination of absorption and emission CS.
Sample
Epilayer/
Substrate
Growth
Method
Thickness
Carrier
Concentration
[µm]
[cm-3]
Rare Earth
Ion
Implantation
Energy *
Calculated RE
Ion Peak
Concentration
[keV]
[cm-3]
---
---
#1
GaN/Sapphire
MOCVD
1.4
5×1016
undoped
#2
GaN/Sapphire
MOCVD
1.4
5×1016
Er
#3
GaN/Sapphire
MOCVD
3.1
5×1016
Yb
60/120/180
8.15×1020
#4
GaN/Sapphire
MOCVD
3.1
5×1016
Yb
60/120/180
2.0×1021
#5
GaN/Sapphire
MOCVD
3.1
5×1016
Yb
60/120/180
3.4×1021
14/21/40/
60/120/180
4.4×1019
* Rare earth ions were implanted with multiple energies to generate semi-homogenous distribution of impurities in
GaN epilayer.
45 3+
2
Concentration [cm ]
Sample #3 GaN: Yb
Integrated Depth Profile
Peak Concentration
20
-1
8.14x10 cm
Projected Range
220 nm
20
10
19
10
c
18
b
a
10
0
100
200
300
400
500
600
700
800
Penetration Depth [Angstroms]
Figure 5.2: Simulated implantation depth profiles for GaN thin film samples implanted
with Yb3+ ions where a, b, c, d, e and f correspond to ionization energies of 14 keV,
21 KeV , 40 KeV, 60 KeV, 120 KeV and 180 KeV.
Figure 5.4 shows variations of the peak concentrations (in at. %.) of all Yb doped GaN
samples as a function of the implanted ions penetration depths. The implantation profiles
of one of the samples of Yb doped GaN is shown in Figure 5.3.
46 Concentration [at. %.]
4.0
Sample #3
3.5
3.0
2.5
Sample #2
2.0
1.5
1.0
Sample #1
0.5
100
120
140
160
180
200
220
Penetration Depth [Angstroms]
Figure 5.3: Peak concentrations of Yb3+ ions in GaN thin film samples implanted with
different Yb3+ ion doses.
5.1.2
The Preparation Procedure
The samples selected for absorption and emission CSs analysis in the experiment are Er
and Yb doped GaN. This project also studied undoped GaN as a reference. The
preparation of the specimen included mechanical cutting of the big wafers into smaller
pieces, which was done here at Ohio University. A native oxide is developed after
mechanically cutting the samples. This is removed by etching the small samples in HClH2O environment for 1 min and subsequently, by washing them with deionized water and
organic solvents. The samples are then blown dry with nitrogen gas.
47 5.1.3
The Post Implantation Process
After the samples were implanted, diced and cleaned post implantation thermal annealing
was performed in a conventional furnace, ATS 301B 4/92 Model 3110 of Applied Test
Systems Inc. that is operated in Nitrogen (99.99%), ambience to temperatures 1200 °C.
All the samples in this work were annealed at1000 °C for 20 mins under the flow of N2
and NH3 at a flow rate of 200 sccm.
5.2 The Experiment Description of Spectroscopic Studies
5.2.1
Overview
The primary goal of the thesis was to study CSs of samples listed in the samples section.
In general, the absorption spectrum, needed for calculating the absorption CS of samples,
can be measured using various techniques. The techniques used in this work for the
measurement of absorption spectra are: (1) the direct coupling of light and (2) the prism
coupling of light.
These techniques are different from the transmittal measurement approach more
commonly used for measuring the absorption spectrum in bulk materials. The transmittal
method of absorption spectrum measurement was not applicable here because of the very
thin RE ion implanted epilayers resulting in small volume containing RE ions interacting
with probe light. The Figure 5.1 shows the experimental setup of the transmittal method.
48 All samples used in this work were thin films with epilayers measuring a thickness of
around 1.4 μm and the implanted layer thickness around ~60 nm. The thickness of the
layer is very small compared to that of bulk samples due to which significant amount of
RE ions do not interact with the incoming radiation. The idea of the new approach is to
increase the probability of interaction of optically active RE ions with the radiation by
extending the path of probing light traveled in the epilayers by flipping the sample by 90°.
Figure 5.4: Experimental setup for transmitive mode absorption spectrum measurement.
Let us illustrate this process with one of the samples studied here. Taking into account the
thickness of the sample #2 from Section 5.1, this study calculated the approximate
number of RE ions in the studied samples that might interact with the probing light
assuming the beam diameter of 250 μm and transmittal geometry. The concentration of
RE ions in the active area in the transmittal geometry was found to be 1.70×105
49 atoms/cm3 while that in this approach it is 4.35×1012 atoms/cm3. This result clearly
indicates that the present geometry maintains a seven orders of magnitude increase in the
number of the atoms interacting with the probing beam, providing the main reason behind
the implementation of this technique to attempt to measure the absorption specta
spectrum.
The following section of this thesis explains in detail the principles of the direct and
prism coupling of light techniques. Both experimental processes capitalize on increasing
the concentration of interacting RE ions with probing light beam for absorption
measurement.
5.2.2
The Direct Coupling of Light Technique
The phenomenon of direct coupling (edge coupling or end fire coupling) is used to make
light enter the wave-guiding sample from the front edge of the wave-guiding slab. The
coupled light excites all the modes the wave-guiding sample can support due to the
scattering of light. Figure 5.5 shows the experimental setup used for the direct coupling
of light approach. The setup consists of the following parts: (1) a light source (2) a
sample (3) a set of collimating lenses (4) fiber cables (5) a spectrograph and (6) a detector
Apogee CCD camera.
The light source used here in the experiment is a halogen lamp that emits light in the
visible spectrum. The lamp has a reflector that reflects the light emitted from the back of
the lamp to the front and is enclosed in a chamber with a small opening on the front for
50 the fiber optic cable. The fiber that is a meter long with a core diameter of 600 μm and
SMA 905 connectors on both ends are used to guide the light from the source to the lens
so as to reduce the light loss due to scattering. The light guided by the fiber is focused on
the wave-guiding sample by a collimating lens, C240TM-B from Thor labs. Inc. This
process is used rather than focusing to reduce the amount of scattering of light inside the
wave-guiding sample.
Figure 5.5: Experimental setup of direct coupling of light technique.
51 Figure 5.6: Details showing the light propagation in the wave-guiding sample for direct
coupling techniques.
As shown in Figure 5.6 the collimated light entering the wave-guiding sample travels
along its length before getting collected by another lens that focuses the beam into a fiber.
The fiber was mounted on the goniometer to provide the freedom of angular positioning
for efficient light collection. The other end of the optical fiber was equipped with a
F240SMA-B lens. The focal length of the lens was chosen such that the focal point was
on the entrance slit of the Digikrom 240 spectrograph equipped with a grating of 300
groves/mm and blaze at 500 nm. A shield on top and bottom of the wave-guiding sample
prevents the probe light sliding on the surface of the wave-guiding sample from reaching
the detector, an Apogee charge coupled device (CCD) camera. KestrelSpec software was
used for data acquisition.
52 The Direct Coupling of Light Experimental Procedure
To verify the concept of the procedure, we used wave-guiding samples of bigger
dimensions and monochromatic light (637.8 nm) to experimentally prove the idea of
direct coupling. Samples used for this purpose were micro slides of dimensions 3’’x1’’
and thickness 1mm. The light source used was a He-Ne laser of output power 8 mW
having randomly polarized beam. The detector used here was a compact easy-to-use
OceanOptics USB2000 spectrofluorometer, which has a dispersive element and a CCD
element embedded into one single unit. The data acquisition software used was
OOIBase32.
After we tested the procedure using monochromatic light, we attempted to couple white
light into the same samples using the same technique. The streak of light was not
observed in this approach due to the scattering of light along the width of the sample.
However, the detector captured the light coming out of the sample. We have repeated the
same experiments substituting the glass slide (micro sample) with RE-doped GaN waveguiding samples. Despite the coupling of white light into the RE-doped GaN samples we
was not able to detect any spectral signature indicating the light absorption by RE ion
impurities in GaN.
5.2.3
The Prism Coupling of Light Technique
Coupling light into wave-guiding sample-using prism is another technique exercised in
this research. In this technique, the light is made to enter the waveguide through the
53 surface with the help of a prism that has a higher refractive index than that of the
waveguide. Light energy is coupled into the film by a phenomenon called optical
tunneling, similar to the tunneling of electrons through a barrier, and the efficiency of the
coupling depends on many factors like the incident angle, the wavelength of incident
light and the material used [63]. The design of these factors is considered critical and is
dealt described in the next thesis section.
Design of Prism Coupling of Light Approach
As has already been stated above, the light coupling takes place most efficiently when the
parallel component of the propagation vector of the incident light, kn p sin φ p ( k = ω /c , ω
being the angular frequency of the incident light, c the speed of light and np the refractive
index of the prism) is equal to the propagation constant of the desired mode in the
waveguide represented by the Eq. 5.1 [64].
β = kn p sin φ p
(5.1)
Here, the energy is transferred from the incident light to the desired mode in the
waveguide with the help of evanescent waves, generated in the gap between the prism
and the waveguide. The energy from this mode gets scattered into other modes, which
also travel along the length of the waveguide due to the difference in refractive index.
The first demonstration of the prism coupling in thin films was shown in [63]. Varying
the angle of incidence in the Eq 5.1 one can excite different modes. However, if a broad
spectrum of light is coupled using the prism coupling technique, the incident angle of
every wavelength needs to be changed accordingly. This lets one to couple the light at the
54 same spot on the waveguide called as the wet spot. The angle is known as synchronous
angle as shown in Figure 5.8 [65]. This makes the coupling of achromatic light difficult
for incident light of broad spectrum to occur. In my study, many attempts were made to
couple a broad spectrum of light into waveguides by adding a dispersion element
between the prism and the sample that eliminates the dispersion mismatch between the
prism and the waveguide [65],[66]. The first to design a prism coupler to couple the
entire white light spectrum was Hammer [65]. However, Mendes et.al. [66] provided a
more accurate approach by using the effective refractive index, rather than the normal
refractive index. The design parameters for the prism were calculated using the equations
developed in Ref. [66] for any particular spectrum range and for the waveguide of
interest. However, little discrepancy was observed while trying to reproduce the results.
This project considers that the error generated is probably due to discrepancy in
considering the effective refractive indices and effective thickness values of the sample.
Let us consider here the basic idea behind the achromatic coupling for reducing the
variation of refractive index in a broadband spectrum of light by closely matching the
dispersion characteristic between the prism and the waveguide. The dispersion gives
information about the change of refractive index with wavelength. Hence, the change of
refractive index of prism with wavelength should be similar to that of the waveguide
given by the Eq. 5.2.
dN w dN p
=
dλ
dλ
(5.2)
where Nw and Np are the effective refractive indices of the waveguide and the prism.
55 The equations for the dispersion of waveguide can be calculated by using the Eq. 5.3
[66].
dNw
= a+
dλ
∑
bj
j= f ,s,c
dnj
dλ
(5.3)
where a and b are modal and material dispersions. The parameters f, s and c represent
film, substrate and cover (air) respectively and n is the refractive index of the
corresponding material. The parameters a and b are given by Eq. 5.4.
∂φ
a = ∂λ
∂φ
−
∂N w
(5.4)
∂φ
b = ∂λ
∂φ
∂N
(5.5)
and Eq. 5.5.
−
The partial derivatives in the above are given by Eq. 5.6, Eq. 5.7 and Eq. 5.8.
⎡2π
n
∂φ
= 2 f 2 1/ 2 ⎢ +
∂n f (n f − N w ) ⎢⎣ λ
(N w2 − n 2j )1/ 2 ⎤
∑ 2 2 ⎥
⎦
j= s,c (n f − n j ) ⎥
∂φ −2πt 2
= 2 (n f − N w2 )1/ 2
∂λ
λ
(5.6)
(5.7)
56 −
Nw
∂φ 2π
=
t
2
∂N w
λ (n f − N w2 )1/ 2 eff
(5.8)
and Eq. 5.9.
n (n 2 − N 2 )1/ 2
∂φ
= 2 s,c2 1/f 2 2w 2 1/ 2
∂n s,c (n f − n s,c ) (N w − n s,c )
(5.9)
where t is the thickness of the thin film, and teff is the effective thickness of the sample i.e.
thickness dependant on the polarization of the incoming light.
The prism desired for coupling is designed depending on the dispersion calculated by Eq.
5.3 for a particular sample and a fixed range of wavelength. We have calculated the
refractive indices at different wavelengths for various samples using the first order
Sellmeier equation given by Eq. 5.10.
n eff = A +
λ2
λ2 − B
(5.10)
where A and B are fitting parameters with values A=4.37 and B=0.088, respectively.
From the above approach, the dispersion value for the undoped GaN (sample #1)
waveguide of thickness 47.7 μm is calculated to be around -8×10-4/nm. A suitable prism
with nearly the same dispersion value was not found. So a Rutile prism was used that was
found to have a close match for the necessary dispersion characteristics calculated for the
wave-guiding RE-doped sample. Rutile is one of the materials that can give both a high
refractive index contrast and a closer dispersion value to that of the samples used for
wave guiding and efficient coupling of light. The following process is the calculation of
57 the dispersion of the Rutile prism that verifies it as a suitable material for achromatic
coupling using the prism technique for the undoped GaN sample.
The equations again have been taken from Ref. [66]. The effective refractive index of the
prism is given by Eq. 5.11.
N p = n i sin θ i cos φ + (n 2p − n i2 sin 2 θ i )1/ 2 sin φ
where θi is the incident angle of incoming light and
(5.11)
is the base angle of prism.
Differentiating the effective refractive index with respect to wavelength gets the
dispersion of the prism given by Eq. 5.12
dN p
dn
=c p
dλ
dλ
(5.12)
where
c=
n p sin φ
( n − n i2 sin 2 φ i )1/ 2
2
p
(5.13)
The refractive indices for the prism at various visible wavelengths have been taken from
the Rutile prism supplier website [67]. The base angle of the prism ϕ = 45 deg and
refractive index of air, ni is 1 (air). Using Eq. 5.12, the dispersion of the prism was
calculated to be -3.0013×10-4 /nm. The angle of incidence was assumed to be normal.
The dispersion has a non-positive value, which shows that the refractive indices decrease
as the wavelength increases. This kind of dispersion is said to be normal dispersion.
The Abbe number can be calculated from the dispersion by the Eq. 5.14 [66].
58 v=
n p −1
dn
( λc − λ f ) p
dλ
(5.14)
where λc and λf are wavelengths of 486.13 nm and 656.27 nm, respectively.
The Prism Coupling of Light Experimental Setup
The prism coupling of light setup is shown in Figure 5.3. The light source used was a
Tungsten white light source (element #1 in Figure 5.3) with an output optical power of
100 W. The lamp is enclosed in a chamber with a reflector attached, directing all the light
emitted towards the front. The other sources were semiconductor lasers, HL6335G/36G
and HL6535MG, both powered by Hitachi and operating at 635 nm and 658 nm,
respectively. The lens (element #2a in Figure 5.3) is used to focus the light emitted by the
lamp into the fiber. A fiber is used to guide the light and reduce the amount of scattering.
A polarizer (element #4 in Figure 5.3) is used to polarize the light from the lamp before
getting coupled into the sample. This along with the goniometer (element #8 in Figure
5.3) helped in exciting the desired mode by varying the incidence angle of the polarized
light. The goniometer in this setup had both sample and the collecting lens mounted on
top of it to collect maximum amount of light coming after traveling through the waveguiding sample. This helped in changing the angle of incident light depending on the
mode to be excited. A right-angled Rutile prism (element #5 in Figure 5.3) was used to
couple light into the sample (element #7 in Figure 5.3). The prism was firmly pressed on
the sample surface to reduce the air gap in between the bottom surface of the prism and
59 the top surface of the sample. A shield was used to prevent light sliding on the surface of
the sample (element #6 in Figure 5.3).
Figure 5.7: Experimental setup for the prism coupling technique.
The Prism Coupling of Light Experimental Procedure
The experiment was conducted using a He-Ne laser light source to prove the idea of
coupling monochromatic light into the wave-guiding sample using the prism coupling
technique. The first sample used was a micro slide of a 3’’×1’’ dimension and 1 mm
thickness. A monochromatic light was chosen to prove the coupling first because of its
60 easy handling. This process eliminates the dispersion due to different wavelengths, and
the intensity of the light from the laser is much higher than that of the white light source.
See Figure 5.8 for the experimental details of the prism coupling.
Figure 5.8: Experimental details of the prism coupling.
In the next step we coupled white light from a Tungsten white light source into RE-doped
wave-guiding samples and detect all the outcoming light. Although, the detector detected
the light from the wave-guiding sample, the spectra showed no traces of the RE ions
absorption. Because of that the implanted ions which made us to change the approach of
calculating the CS. Then we intended to measure the emission spectrum and calculate
the absorption and emission CSs from emission spectrum as the theories being used have
the flexibility to be used in either way. The emission was measured using
61 photoluminescence and cathodoluminescence techniques, described in the following
thesis.
5.2.4
Photoluminescence and Cathodoluminescence Studies
The photoluminescence (PL) and cathodoluminescence (CL) measurements were used to
investigate the luminescence properties of the RE-doped GaN samples. Figures 5.9 and
5.10 show the experimental setups for the PL and CL measurements in visible and IR
spectral ranges respectively. Figure 5.9: Setup for photoluminescence and cathodoluminescence in visible spectral
range.
In both PL and CL experimental set-ups the samples were placed on the cold finger using
a fixed mechanical mount. The cold finger was located inside of a closed cycle helium
cryostat that could operate at temperatures ranging from 8.5 K to 330 K. A two-stage
62 vacuum pump system evacuated the chamber prior to the experiment creating a pressure
of 5×10-4 to 1×10-7 Torr.
For PL measurements a He-Cd laser operating at a wavelength of 325 nm and 20 mW
output power was used while for CL, an electron gun attached to the same vacuum
cryostat operating up to 5 keV and maximum current emission ~75 μA was used. The
electron beam was incident on the sample at an angle of 45°.
Figure 5.10: Setup for photoluminescence and cathodoluminescence in IR spectral range.
The luminescence from the sample was then collected by the quartz lens and passed
through the long pass filter to the dispersive unit. The dispersive unit used here was a
HR320 monochromator-spectrograph in Czerny-Turner configurations, equipped with the
holographic gratings of 150 groves/mm with a blaze at 500 nm. A back-illuminated CCD
camera of Princeton instruments Inc. with a UV/AR coating (model# TEA-CCD-512TK)
was then used to detect the optical signal.
63 The detection system for the IR measurements consisted of a quartz lens, filters, a
chopper, a Germanium (Ge) detector, a lock-in amplifier and a SR830 100 kHz DSP
amplifier from Stanford Instruments. This detection system did not include a dispersion
unit to spectrally resolve the peaks due to the weak luminescence in the IR spectra range
from sample #2. Hence, the resolution of the system was fixed by the bandwidth of the
filter used in front of the detector (15 nm). A EO-817 liquid nitrogen cooled-Ge detector
from North Coast Optical Systems Inc was implemented to cut off excitation
wavelengths. The optimal spectral response for the Ge detector was in the range 0.8 μm
to 1.7 μm. A light beam chopper was used to provide reference to the lock-in, which
generated a train of pulses ranging in frequency from 10 to 4 kHz. Finally, a Labview
code to control the lock-in was developed.
5.3 Results
This thesis section we will present the results obtained from PL and CL experiments of
Er and Yb implanted GaN samples. Furthermore, calculation of the results of absorption
and emission CSs spectra using FL and McCumber equations from the PL and CL data
obtained at room temperature are presented. 5.3.1
GaN Doped with Er Ions
Figure 5.11 shows the PL spectrum of GaN implanted with Er (sample #2) under above
band gap excitation of He-Cd laser at 13 K.
64 1539.6 nm
1.0
4
4
PL Intensity [a.u.]
I13/2 I15/2
0.8
0.6
1550.8 nm
0.4
1589.8 nm
0.2
0.0
1480
1500
1520
1540
1560
1580
1600
1620
1640
Wavelength [nm]
Figure 5.11: Photoluminescence spectrum of GaN:Er annealed at 1100 ºC for 0.5 hrs in
N2 measured at 13 K under He-Cd laser excitation.
The transition lines belonging to the 4I13/2 and 4I15/2 manifolds are clearly represented by
the peaks at 1539.6 nm, 1550.8 nm and 1589.8 nm, respectively. Each peak represents a
transition between different Stark levels of the first excited manifold and the ground
manifold. A shoulder at 1550.8 nm can also be clearly seen, followed by a peak at 1589.8
nm. The full width at half maximum (FWHM) of the dominant peak at 1539.6 nm is 15.8
nm (78.4 eV).
Figure 5.12 shows the CL of the same sample GaN:Er3+ (sample #2) under electron
excitation, with an acceleration energy of 5 keV. The main peak at 1538.9 nm belongs to
65 the transitions between 4I15/2 and 4I13/2 manifolds. Two satellite peaks at 1569.6 nm and
1579.5 nm are also visible.
Energy [meV]
840
830
820
810
4
13 K
I13/2
1.0
800
790
770
760
750
4
I15/2
1.0
1538.9 nm
0
0.8
CL Intensity [a.u.]
CL Intensity [a.u.]
780
0.6
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
50
100
150
200
250
300
1.0
0.9
0.8
0.6
0.5
0.4
0.3
0.6
0.2
0.1
0.0
50 100 150 200 250 300
T [K]
1569.6 nm
0.4
0.8
0.7
0
0.4
1579.5 nm
0.2
0.2
1480
1500
1520
1540
1560
1580
1600
1620
1640
Wavelength [nm]
Figure 5.12: Cathodoluminescence spectrum of GaN:Er annealed at 1100 ºC for 0.5 hrs in
N2 measured at 13 K.
The dominant peak has a FWHM of 7.6 nm (163.1 eV) and is clearly shifted compared to
the PL spectrum appearing in Figure 5.11 by 0.7 nm.
The inset in the Figure 5.12 shows the thermal quenching of the CL intensity observed in
the temperature ranges from 11 K to 300 K. The solid squares show the experimental
results of the integrated CL intensity at corresponding temperatures, where the solid line
is shown as a guide for the eye. 66 1538.9 nm
4
CL Intensity [a.u.]
I13/2
4
I15/2
1569.6 nm
1579.5 nm
11 K
1515.7 nm
1558.6 nm
200 K
300 K
1500
1550
1600
1650
Wavelength [nm]
Figure 5.13: Cathodoluminescence spectra of GaN:Er sample at different ambient
temperatures.
Figure 5.13 gives the comparison of three selected CL spectra at different temperatures
under identical excitation and detection conditions. As the temperature is changing from
11 K to 300 K, it can be seen that the peaks at 1569.6 nm and 1579.5 nm disappear and
new peaks start to appear at 1515.7 nm and 1558.6 nm. The position of the main peak at
1538.9 nm remains constant, while its intensity is reduced at room temperature (shown in
the Figure 5.12 inset). This reduced CL intensity is due to the thermal quenching of Er3+
ion emission. It should be noticed that the thermal quenching of RE ions in III-N
materials was much lower than that of other semiconductor hosts. In addition to this
67 thermal quenching the change of CL intensity with temperature also indicates the
presence of different RE ions active centers discussed in the next thesis section.
1514.8 nm
1537.8 nm
(a) Absorption CS
(b) Emission CS
300 K
-24
1557.5 nm
2
Cross Sections [m ]
2.0x10
4
4
I13/2 I15/2
-24
1.0x10
(a)
(b)
0.0
1500
1550
1600
1650
Wavelength [nm]
Figure 5.14: Absorption and Emission CS of GaN:Er sample calculated using McCumber
theory.
Figure 5.14 shows the calculated absorption and emission CSs spectra at room
temperature of GaN:Er3+ (sample #2). The trace (a) represents the absorption CS
spectrum obtained by using the emission CS which is, in turn, calculated from the
emission spectrum shown in Figure 5.13. The CS is calculated for the 4I15/2→4I13/2
transition of the Er3+ ion. The difference in the shape of the two spectra is in accordance
with the theory. The calculated peak absorption and emission CSs values are 2.27×10-20
cm2 and 2.24×10-20 cm2, respectively. No published data for the CSs in RE-doped GaN
68 hosts exist in the literature. However, CSs are extensively studied in a variety of Er doped
glasses and ceramic hosts and under resonant excitation conditions their absorption crosssection values are in the range of 0.4×10-20 cm2 to 1.3×10-20 cm2 [60]. The CSs calculated
here are less than those estimated for glasses, probably due to different excitation
mechanisms of RE ions involved in the semiconductor material.
5.3.2
GaN doped with Yb ions
Figures 5.15 through 5.17 show the PL spectra of GaN implanted with Yb ions with
different doses (sample #3, sample #4 and sample #5) in the spectral range 355 nm to
1160 nm. In these figures, curves (a) and (b) show the measured PL spectra at low and
room temperatures, respectively.
90000
671.5 nm
80000
3+
Sample #3 GaN:Yb
548.3nm
(a) PL at 12K
(b) PL at 300K
PL Intensity [a.u.]
70000
60000
50000
40000
2
F5/2
NBE
2
F7/2
30000
575.8 nm
20000
(a)
10000
(b)
0
400
600
800
1000
1200
Wavelength [nm]
Figure 5.15: Photoluminescence spectra of GaN:Yb (sample #3) at 12 K and 300 K.
69 676.1 nm
80000
3+
Sample #4 GaN:Yb
70000
(a) PL at 12K
(b) PL at 300K
PL Intensity [a.u.]
60000
547.5 nm
50000
2
F5/2
2
F7/2
40000
30000
NBE
20000
575.8 nm
(a)
10000
(b)
0
400
600
800
1000
1200
Wavelength [nm]
Figure 5.16: Photoluminescence spectra of GaN:Yb (sample #4) at 12 K and 300 K.
60000
545.9 nm
3+
Sample #5 GaN:Yb
(a) PL at 12K
(b) PL at 300K
PL Intensity [a.u.]
50000
40000
30000
691.2 nm
562 nm
2
F5/2
2
F7/2
20000
NBE
(a)
10000
(b)
0
400
600
800
1000
1200
Wavelength [nm]
Figure 5.17: Photoluminescnece spectra of GaN:Yb (sample #5) at 12 K and 300 K.
70 Each spectrum shown in Figures 5.15 through 5.17 contains at least three groups of
spectral features:
1. Near Band Edge emission (NBE): This consists of peaks at 356.5 nm, 368.6
nm and 377.2 nm, corresponding to free excitons (FX), bound excitons (BX)
to impurities and donor acceptor pair (DAP) features with phonon replicas.
These peaks are well resolved at low temperature in studied samples as shown
in Figures 5.15 through 5.17 by traces (a). However, FX peak exists at 381 nm
only at room temperature due to the high binding energy of 28 meV (the BX
are dissociated at elevated temperatures (trace (b)) [68]. Furthermore, the
DAP features typically observed in GaN epilayers overlap with BX peaks. The
spacing between the DAP peak replicas corresponds to the LO phonon
frequency equal to 751 cm-1. As the temperature was increased, the DAP
disappeared, but BX peaks are still present [73].
2. Broadband in the visible spectral range: Two distinct broadbands overlap each
other, with a low temperature maxima at 545.9 nm - 548.3 nm and 671.5 nm 691.2 nm (Figure 5.15-5.17 (traces (a))). As the ambient temperature
increased during the experiment the band peaking at shorter wavelengths
shifted, while the band peaking at longer wavelength disappeared (see traces
(b)). The fine structure decorating the broadband is due to the a micro-cavity
effect.
3. Group of lines in the near IR spectral range: This group of sharp lines
corresponds to the transitions between 2F5/2 and 2F7/2 manifolds of Yb3+ ions.
71 At low temperature, the group contains 29 lines representing transitions
between the lowest Stark level of the higher manifold to the Stark levels of the
lower manifold and their interaction with localized modes of lattice vibrations
[28]. Among so many peaks, the strongest ones are at 986.4 nm, 1008.2 nm
and 1016.6 nm, respectively. At room temperature, traces (b) show the peaks
with an integrated intensity half of that at low temperature.
Figure 5.17 shows the PL spectra of the GaN sample containing the highest concentration
of Yb3+ ions (sample #5). The spectral features observed for GaN implanted with lower
doses of Yb3+ ions remained in sample #5, while all peaks in the NBE were not clearly
distinguishable. Furthermore, the peak at 545 nm is red shifted with higher temperatures
as can be seen in Figure 5.17; here, the intensity of the peak at 696 nm is reduced while
the yellow peak intensity remains unchanged. The luminescence spectrum modulation
effect observed in this sample was more intense when compared to the spectra of samples
#3 and #4, probably due to their higher concentration of implanted Yb3+ ions. The most
probable cause of the observed modulation enhancement effect is due to the fact that the
epitaxial layers of thin films were modified, causing a micro-cavity effect. The higher
concentration of Yb3+ ions in the epilayer layer might have had effects on the modulation
through a change of refractive index introduced in the lattice strain (a significant
difference exists between Ga3+ and Yb3+ ions radii).
Figure 5.18 shows the comparison of the PL spectra at different temperatures for three
GaN:Yb samples, containing different Yb3+ ion concentrations. These PL spectra were
recorded with an increased spectral resolution, as compared with the spectra shown in
72 Figures 5.15 through 5.17. The spectra were artificially shifted for ease of comparison. In
general, the Yb3+ ion spectral features remained unchanged for Yb3+ doped GaN samples
of different Yb3+ ion concentrations. Our hypothesis is that larger than expected number
of Yb3+ ions transition lines indicated that Yb3+ ions can be involved in different centers.
A difference in intensity indicates a different crystal field surrounding the specific Yb3+
ion center, which governs the energy transfer process between the GaN host and Yb ions.
A detailed understanding of the process requires more analysis and theoretical
calculation. The strongest emission can be clearly seen from sample #4 at low
temperature, while the weakest comes from the sample #3; the same trend was observed
at room temperature.
73 10 K
300 K
2
PL Intensity [a.u.]
F5/2
2
F7/2
Sample #5
Sample #4
Sample #3
930
960
990
1020
Wavelength [nm]
1050 930
960
990
1020 1050
Wavelength [nm]
Figure 5.18: Photoluminescence spectra of GaN:Yb (sample #3, #4 and #5) at 12 K and
300 K.
The Figure 5.19 shows the calculated emission CS of all GaN:Yb samples at room
temperature. Using the collected PL spectra shown in Figure 5.18 this project calculated
the emission CSs for all studied Yb3+ doped GaN samples using Equation 3.13. The
calculated peak emission CS values of samples #3, #4 and #5 are 2.09×10-24 m2, 1.39×1024
m2 and 1.18×10-24 m2, respectively. After the calculation of emission CS we determined
the absorption CS for these samples.
74 Sample #3
Sample #4
Sample #5
-24
2
Emission CS [m ]
2.0x10
300 K
-24
1.5x10
-24
1.0x10
-25
5.0x10
960
980
1000
1020
1040
Wavelength [nm]
Figure 5.19: The emission CS spectra of GaN:Yb (samples #3, #4 and #5) at 300 K.
-25
6.0x10
Sample #3
Sample #4
Sample #5
-25
2
Absorption CS [m ]
5.0x10
300 K
-25
4.0x10
-25
3.0x10
-25
2.0x10
-25
1.0x10
0.0
960
980
1000
1020
1040
Wavelength [nm]
Figure 5.20: The emission cross section spectra of GaN:Yb (samples #3, #4 and #5) at
300 K calculated using the FL equation.
75 Figure 5.20 shows the calculated absorption CS spectra of all studied GaN:Yb samples.
These spectra were calculated from the Figure 5.19 using Eq. 3.15. The peak absorption
CS values for these samples are: 5.32×10-25 m2, 3.54×10-25 m2 and 3×10-25 m2,
respectively. These CS values, obtained via the above method, are low compared to the
value of 9.5×10-25 m2 of Yb3+ doped in borate glasses [60].
5.4 Discussion
As the previous section explains, the Er3+ and Yr3+ ions doped GaN samples were studied
using PL and CL experimental setups that used different excitation sources. Using these
PL and CL techniques, the energy transfer mechanisms responsible for the excitation of
RE ions are different, which are basically classified as (1) direct excitation and (2)
indirect excitation. The direct excitation mechanism involves the 4f electrons excited
directly with either absorption of resonant photons (PL) or colliding with hot electrons
(CL). The indirect excitation mechanism involves a transfer of energy to the 4f electrons
by electron-hole pairs generated by hot electrons or photons with energy exceeding the
band-gap. In CL excitation, the transfer of energy can also occur through an impact
excitation mechanism, which involves impurities outside the 4f shell to transfer energy. It
is well known that the transfer of energy from the semiconductor host to the 4f core
electrons takes place with a rare earth structured isoelectronic trap (RESI) [74].
An isoelectronic trap is formed when a dopant ion replaces a host ion with the same
number of valence electrons (isovalent). A RESI trap is formed when RE ions (Er3+, Yb3+
in our case) substitute for cation (Ga3+) in the host material (GaN). The traps are created
76 because the RE ions have higher ionic radii and smaller electronegativities that substitute
for Ga ions. It has to be noted here that Er3+ and Yb3+ ions in GaN most probably form
hole RESI traps, which are treated as structured impurities with unfilled 4f core shells.
After a RESI trap is formed it contributes to the energy transfer from the host to the 4f
core shells in different ways, as shown in the Fig. 5.21 and briefly described below [74]:
•
A bound exciton is formed due to the Columbic interaction between the positively
charged RESI trap and an electron from the conduction band, as shown in Fig. 5.
21(a). This exciton bound to the RESI trap transfers energy to the core 4f
electrons through an electrostatic perturbation.
•
A bound hole to the RESI trap recombines with an electron on a distant donor, as
shown in Fig. 5.21(b) transferring recombination energy to the core 4f electrons.
•
The energy transfer to the 4f core electrons involves a structured RESI trap
occupied by hole and an electron in the conduction band, as shown in Fig. 5.21(c).
•
The energy transfer to the 4f core electrons involves an inelastic scattering process
between a FX and the electrons of the 4f core shell (Figure. 5.21(d)). The transfer
of the energy takes place most effectively when the energy difference between the
final and initial states is resonant.
77 Figure 5.21: Schematic diagram showing the energy transfer processes between GaN host
and RE ions creating RESI trap. Energy an be transferred through: (a) collapsing of
bound exciton to RESI hole traps, (b) recombination of bound hole with an electron on
donor, (c) recombination of bound hole with an electron in conduction band, (d) inelastic
scattering process between FX and 4f shell electrons.
The following paragraphs of this section discuss the PL and CL spectra measured for Er3+
and Yb3+ doped GaN.
The PL and CL spectra of Er3+ doped GaN are presented in Figures 5.11-5.13 in the
previous section 5.3. The luminescence peaks observed in IR spectral shown in the
figures are characteristic of the intra- 4f-shell transitions of the Er3+ ion belonging to
4
I13/2→4I15/2 transitions. The peak positions observed in the PL and CL spectra of sample
#2 probably differ due to the emission from different sites occupied by Er3+ ions and
induced defects.
78 Figure 5.21 shows the energy band diagram for Er3+ ion in GaN host, generated using
theoretical energy level calculated in Ref. [60]. Frequently, an energy level band diagram
provides a good illustration of the transitions taking place between the 4f-4f energy levels
in the material. The band diagram shown contains the transitions of the Er3+ ions GaN
observed in the luminescence spectra measurements.
-1
-1
10180.0 cm
-1
10150.1 cm
-1
10117.5 cm
-1
4
10167.5 cm
I11/2
10137.4 cm
-1
10105.6 cm
Second Excited
Manifold
-1
4
I13/2
6643.1 cm
-1
6609.6 cm
6624.8 cm
-1
6590.7 cm
-1
-1
6539.2 cm
-1
6502.4 cm
-1
6501.8 cm
First Excited
Manifold
1540 nm
1545 nm
1569 nm
-1
-1
191.6 cm
-1
180.2 cm
190.7 cm
4
I15/2
153.4 cm
-1
-1
45.9 cm
-1
4 cm
GaN:Er
-1
112.9 cm
-1
15.1 cm
Ground Manifold
3+
Figure 5.22: Energy level band diagram of ground, first and second excited states of Er3+
ion in GaN with the transitions observed in our experiment at 12 K.
The FWHM of the peak in Figure 5.11 at 1539.6 nm is larger than reported in literature.
This may occur because of the co-existing centers, which emit photons at slightly
different energies. Furthermore, the peaks overlap (1550.8 nm) because of the low
resolution of the detection system used for measuring the luminescence (see Section
79 5.2.4). This result is supported by the FWHM of the peak in Figure 5.11 is 15.8 nm.
However, other possibilities for the recorded low-resolution Er ion spectra include
emission from the different centers that are away by a few nanometers and are not
resolved by the detector.
The fixed position of the 1538.9 nm Er3+ ion peak in Figure 5.13 at different temperatures
indicates that the emission comes from the same Er3+ ion center. The new peaks at 1515.7
nm and 1558.6 nm correspond to the thermal excitation of electrons to higher states in the
excited manifold. The reason for the disappeared peaks is presently unclear, although we
can speculate that emission from different Er3+ centers observed at low temperature is
thermally quenched due to the changes in local crystal field surrounding a specific Er3+
ion center.
The absorption and emission CSs of the 4I15/2→4I13/2 transition of Er3+ ion shown in
Figure 5.14 were calculated using FL equations and the McCumber theory, respectively
(see Section 3.2). The deviation of the absorption CS from the emission CS is due to the
energy separation between Stark levels greater than kT. This makes the absorption CS
dominant in the spectrum at higher energy, while the emission CS dominates at low
energy and the two CSs overlap at a point where λ =
ch
ε
. To our knowledge, no
information was available to our knowledge regarding the values of absorption and
emission CSs of Er in GaN material. Most literature available deals with excitation CS of
Er ions in different hosts. Excitation CS is the fictitious area of the material which
interacts with the radiation and gets excited to the higher states depending on the
80 excitation wavelength. We compared the CSs with those of Er3+ ion doped glasses. Little
discrepancy was observed, as shown in Section 5.4.1. The difference is probably due to
the varying excitation mechanisms of rare earth ions involved.
Figures 5.15-5.17 show the PL spectra of Yb doped GaN samples measured at 12 K and
300 K. A detailed analysis of these PL spectra shape revealed that the emission band with
a maximum at ~548 nm did not change its position significantly (only 3 nm of blue shift
between sample #3 and sample #5). The FWHM of this band is ~60 nm for all Yb-doped
GaN samples, whereas the peak intensity of this emission band changed by ~20%
between analyzed samples. In contrast to this scenario, the emission band with the peak
maximum at a longer wavelength (~671 nm) changed its position with increasing Yb ion
concentration. The de-convolution process performed for PL spectra of Yb-doped GaN
measured at low temperatures showed in that the peak maximum of this emission band
red shifted by 19.6 nm between samples #3 and sample #5, respectively. Furthermore, the
FWHM of this band changes from 147 nm to 174 nm and the peak intensity of the 671
nm emission band drastically changed by 60% for the same set of samples. Also, this
emission band was not observed for any of Yb-doped GaN samples at 300 K, whereas the
band at shorter wavelength dominated the spectrum similarly to what was observed for
undoped GaN reference sample (not shown here, see [28]). It is known that implantation
processes introduce serious structural damages to the lattice structure generating surface
amorphization, point defects and defect complexes. Furthermore, increased Yb ions
concentration can stimulate creation of Yb ion complexes involving multiple Yb ions and
defects. Taking into account the above facts, we can speculate that the band at ~671 nm
81 involves implantation defects related to the possibility of clustering of Yb3+ ions
(discussed at the end of this section).
Figure 5.22 shows the energy band diagram corresponding to the 4f electron transitions
between the lowest Stark level of the 2F5/2 manifold and 2F7/2 manifold of the Yb3+ ions.
We attribute the high-resolution PL spectra manifold at low temperature shown in Figure
5.18 to at least two different centers occupied by Yb ions. The Yb ion has two spin orbit
manifolds, which are split into four and three Stark levels. Due to this, only four
transitions in emission and three transitions in absorption spectra are to be observed, but
the complex emission lines resulting from the transitions between the two manifolds
explain the existence of more than two emitting centers.
2
F5/2
10750 cm
-1
10647 cm
-1
10490 cm
First Excited
Manifold
-1
992.5 nm
939.2 nm
986 nm
952.2 nm
982 nm
414.3 cm
-1
358.1 cm
2
F7/2
310.7 cm
-1
-1
0 cm
Ground
Manifold
-1
3+
GaN:Yb
Figure 5.23: Energy band diagram of Yb3+ ions in GaN with the transitions at low
temperature.
82 At high temperatures, the energy transfer process from the GaN host to Yb3+ ion is less
effective due to the thermal quenching resulting in the reduced of intensity studied from
the spectra. The magnitude of thermal quenching of the 4f transition lines is almost the
equivalent in all samples with different Yb3+ ion concentrations.
The microcavity effect previously discussed in the Yb doped GaN spectra is due to the
refractive index gradient at the epilayer-substrate interface and epilayer-air interface. This
effect is enhanced in samples with a smoother surface. The modulation seen in the
spectra of low and medium concentration (samples #3 and #4) occurs only on the low
energy side of the broadband around 545.9 nm, while for the highest concentration
(sample #5) the effect is seen all along the spectra. This enhancement effect probably
occurs because the increased doping of the RE ion changes the refractive index of the
doped layer.
Figures 5.19 through 5.20 show the emission and absorption CSs of different Yb doped
GaN concentration samples. Despite extensive literature survey we could find no
previous studies recording the absorption and emission CSs results of the Yb3+ doped
semiconductors. The data presented here, hence, compared to that of Yb3+ ions doped
borate glasses (see section 5.4.2). The emission CS values obtained are a little lower than
that of the borate glasses probably due to different splitting of manifolds.
The absorption CS of the Er3+ doped GaN, sample #2, is one order of magnitude higher
than the absorption CS of the Yb3+ doped GaN (samples #3, #4 and #5), probably
because Er3+ ions can absorb radiation energy resonant to the energy difference of any
83 two of its excited manifolds which would finally result in transitions between the first
excited manifold and the ground manifold, due to non-radiative relaxation processes. But
this is not the case with Yb3+ ions which has just one excited manifold.
In summary, the CS of the highest concentration of Yb3+ ion has the higher absorption
and emission CS, which may indicate the presence of Yb3+ ion clusters; these can be
either formed between similar RE ions or between RE ions and different impurities
within the host. Increasing the concentration of the RE ions increases the statistical
probability of the forming of Yb3+ ion clusters due to dimers (two RE ions) and trimers
(three RE ions) in addition to isolated ions, as shown in Figure 5.24.
-1
10
-2
10
-3
Probability
10
n=1
-4
10
-5
10
n=2
-6
10
-7
10
n=3
-8
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
Concentration of RE Atoms [at.%]
Figure 5.24: The statistical probability of RE ions clusters formation in semiconductors
as a function of RE ions doping concentration.
84 Figure 5.24 shows the statistical probability of clusters forming as generated in Eq. 5.15.
Pn (c) =
12!
c n (1− c)12−(n−1)
(n −1)!(12 − (n −1))!
(5.15)
Where c is the concentration of the RE ions and n is the cluster size.
Hence, the higher the concentration of the ion in the sample, the higher is the absorption
and emission CSs due to clustering.
85 6 CONCLUSIONS
This project has calculated the absorption and emission CSs of GaN samples implanted
with Er3+ and Yb3+ ions. The emission spectra required for the calculations were obtained
from the PL and CL experiments conducted at room temperature. The CL spectrum of the
Er3+ doped GaN at room temperature was used for calculation of CSs while room
temperature PL spectra were used to calculate the CSs of Yb3+ implanted GaN samples.
The following are the main accomplishments from this work.
•
Research specimens were prepared in the following order: (a) GaN epilayers were
acquired and implanted with selected rare earth ions. The simulated implantation
depth profiles were Er3+ and Yb3+ ions in GaN. Projected ranges, and peak
concentrations were calculated using the Pearson distribution function; (b)
implanted GaN epilayers wafers were diced, cleaned and thermally annealed to
prepare specimens for spectroscopic analysis.
86 •
Experimental setups for GaN implanted with RE ions absorption spectra
measurement were designed. Two approaches were developed and tested: (a)
direct coupling of light and (b) prism coupling of light.
•
Luminescence spectra (PL and CL) of Er3+ and Yb3+ doped GaN were measured
in the UV-visible-IR spectra range at different temperatures.
•
An extensive literature survey was conducted on CSs of RE ions in different
solid-state hosts.
•
A MATLAB code was developed for the calculation of CSs, implementing the FL
and McCumber equations. It was tested by reproducing the results presented in
Ref. [59]. The simulation results generated using MATLAB were obtained via
this procedure and are in good qualitative agreement with the data presented in
the Ref. [59]. The absorption and emission CSs for Er3+ doped Ti:LiNbO3, found
in the reference, were 2.3×10-24 m-2 and 2×10-24 m-2, while the values simulated
here were 2.25×10-24 m-2 and 1.94×10-24 m-2, respectively. •
The calculated peak absorption and emission CSs values for Er3+ doped GaN were
2.27×10-20 cm2 and 2.24×10-20 cm2, respectively, while in a variety of Er3+ doped
glasses and ceramic hosts, the values were in the 0.4×10-20 cm2 to 1.3×10-20 cm2
range for both absorption CSs at resonant excitation.
•
The calculated peak emission CS values of Yb doped GaN (samples #3, #4 and
#5) were 2.09×10-24 m2, 1.39×10-24 m2 and 1.18×10-24 m2, respectively. The CS of
87 the highest concentration of Yb3+ had the maximum emission and absorption CSs.
It was proposed that an increase of absorption and emission CSs values of Yb3+
ion in GaN might be related to the presence of Yb3+ ion clusters
•
The absorption CS of an Er3+ doped GaN (sample #2) sample was observed to be
one order of magnitude higher than the absorption CS of Yb3+ doped GaN
(samples #3, #4 and #5), which is probably due to the different excitation of the 4f
electrons in the RE ions. This excitation difference comes from the fact that the
Er3+ can absorb radiation resonant to an energy difference between any two of the
excited manifolds, which might finally result in a transition between the first
excited manifold and the ground manifold. Where as the Yb3+ ion doped GaN
contains just one excited manifold, which is the only possibility that can either
absorb or emit.
88 7 FUTURE WORK
The calculation of absorption and emission CSs of thin films doped with RE ions is very
important when modeling light emitting devices. It is beneficial to know an experimental
absorption spectrum of the investigated material before calculating the theoretical CS
parameters. However, the project described here shows, the measurement of absorption
spectrum is limited to samples having a relatively large volume of optically active
impurities. These are the main issues limiting the absorption measurement in thin film
samples, especially of those implanted with impurities residing in the near surface. Our
experimental setup for the measuring of absorption spectrum was tested in two different
configurations, via direct light coupling and prism light coupling, respectively. Our
experimental work resolved many challenges successfully. However much scope still
remains for further improving of the experimental setup. Some of the following ideas
may positively contribute to the successful RE-doped GaN epilayer absorption
measurement in the future:
89 •
Reduce the edge roughness of the samples through which coupling of light is
done. In this way, the amount of light scattered due to the irregular surface is
reduced and more light is coupled.
•
Select specific crystallographic plains along which the sample is cleaved and
provide subsequent mechanical processing for producing the desired interface
angle. In this way, we believe, one may manipulate the incident angle of the
coupled light to sample through direct coupling approach.
•
The prism coupling approach can be improved by increasing the accuracy of the
parameters used in calculation of effective refractive index and effective thickness
of the sample. These parameters are dependent on the wavelength of the light
coupled. These parameters can be accurately measured using m-line technique
[63].
Furthermore, an extensive literature survey demonstrates another suitable and sensitive
technique, to measure the absorption spectrum of a very thin film sample called photothermal deflection spectroscopy (PDS) [71].
The PDS is more suitable for measuring the absorption of very thin film samples or thin
films with relatively small concentration of dopants. The principle of the technique
comes from the fact that a fraction of the energy of the radiation absorbed by a medium is
converted into thermal energy. This technique incorporates two light beams: a pump
beam and a probe beam. The pump beam is absorbed by the sample that causes the
temperature of the adjacent layer to change. This temperature change causes the
90 refractive index in the medium to vary accordingly. A probe beam is deflected depending
on the refractive index of the medium, which is related to the optical absorption of the
sample. This technique was used to measure the absorption in amorphous Er3+ doped
GaN [72].
The successful absorption measurement of RE-doped GaN epilayer may be easier if in
situ doped sample are available. In this way, the RE ions concentration can be controlled
during a sample growth process, resulting in a homogenous RE ion distribution in an
epitaxial layer. The optimal RE ions concentration in in-situ RE doped GaN thin films is
between 1-3 at. % , which is more than the RE ions concentration around 1 at. % in
samples studier here.
An alternative technique called Judd-Ofelt technique can be used for estimating both the
emission CS and transition strengths. This calculation is done using three parameters
based on a procedure of fitting theoretical and measured oscillator strengths. Hence, the
accuracy of the technique is dependent on the number of transitions observed [47], [57],
[58].
91 8 REFERENCES
[1] B. Henderson and G. F. Imbusch, “Optical Spectrocopy of Inorganic Solids”,
clarendon press, Oxford, 1989.
[2] L. A. Riseberg and M. J. Weber, “Relaxation phenomena in Rare-Earth
luminescence”, Progress in optics XIV, North Holland, 1976.
[3] G. B. Haxel, J. B. Hedrick, and G. J. Orris. (2002, November 20). Rare Earth
Elements—Critical Resources for High Technology [online]. Available:
http://pubs.usgs.gov/fs/2002/fs087-02/.
[4] A. P. Vajpeyi, S. Tripathy, L.S. Wang, B. C. Foo, S. J. Chua, E. A. Fitzgerald and
E. Alves, “Optical activation of Eu ions in nanoporous GaN films”, J. Appl. Phys.,
vol. 99, no. 10, pp. 104305, 2006.
[5] S. Nakamura and G. Fasol “The Blue Laser Diode, GaN Based Light Emitters and
Lasers”, Springer, 1997.
[6] S. Ossicini, L. Pavesi, F. Priolo “Light Emitting Silicon for Microphotonics”,
Springer, 2003.
[7] A. J. Steckl, J. H. Park and J. M. Zavada, “Prospects for rare earth doped GaN
lasers on si”, Mat. Today, vol. 10, pp. 7, 2007.
[8] L. T. Canham, “Silicon quantum wire array fabrication by electrochemical and
chemical dissolution of wafers”, Appl. Phys. Lett., vol. 57, no. 10, pp. 1046, 1990.
[9] L. Tsybeskov, K. L. Moore, D. G. Hall, and P. M. Fauchet, “Intrinsic band-edge
photoluminescence from silicon clusters at room temperature”, Phys. Rev. B, vol.
54, no. 12, pp. R8361 , 1996.
92 [10] G. S. Pomrenke, P. B. Klein and D. W. Langer, “ Rare Earth Doped
Semiconductors”, MRS Symp., Proc. No. 301, Pittsburgh, 1993.
[11] M. O. Manasreh and H. X. Jiang, “III-Niride Semiconductors Optical Properties I”
vol. 13, 2001.
[12] L. Pavesi, “Routes toward silicon-based lasers”, Mat. Today, vol. 8, no. 1, pp. 18,
2005.
[13] H. Ennen, J. Schneider, G. Pomrenke and A. Axmann, “1.54μm luminescence of
erbium-implanted III-V semiconductors and silicon”, Appl. Phys. Lett., vol. 43,
no.10, pp. 943, 1983.
[14] J. Michel, J. L. Benton, R. F. Ferrante, D. C. Jacobson, D. J. Eaglesham, E. A.
Fitzgerald, Y.-H. Xie, J. M. Poate, and L. C. Kimerling, “Impurity enhancement of
the 1.54-µm Er3+ luminescence in silicon”, J. Appl. Phys., vol. 72, no. 5, pp. 2672,
1991.
[15] S. Coffa, G. Franzo, F. Priolo, A. Polman and R. Serna, “Temperature dependence
and quenching processes of the intra-4f luminescence of Er in crystalline Si”, Phys.
Rev. B, vol. 49, no. 23, pp. 16313, 1994.
[16] K. Takahei, P. S. Whitney, H. Nakagome and K. Uwai, “Temperature dependance
of intra-4f-shell photo- and electroluminescence spectra for erbium-doped GasAs”,
J. Appl. Phys. Lett., vol. 65, no. 3, pp. 1257, 1989.
[17] H. Isshiki, H. Kobayashi, S. Yugo, T. Kimura and T. Ikoma, “Impact excitation of
the erbium-related 1.54μm luminescence peak erbium-doped InP”, Appl. Phys.
Lett., vol. 58, no. 5, pp. 484, 1991.
[18] G. M. Ford and B. W. Wessels, “Electroluminescence from forward-biased Erdoped GaP p-n junctions at room temperature”, Appl. Phys. Lett., vol. 68, no. 8, pp.
1126, 1996.
[19] P.N. Favennec, H. ’Haridon, D. Moutonnet, M. Salvi and M. Gauneau, Mater. Res.
Soc. Symp. Proc., vol. 301, pp. 181, 1993.
[20] W. Jantsch, S. Lanzerstorfer, L. Palmetshofer, M. Stepikhova and H. Preier,
“Different Er centres in Si and their use for electroluminescent devices” J. Lumin.,
vol. 80, no. 1, pp. 9, 1999.
[21] J. T. Torvik, R. J. Feuerstein, C. H. Qui, M. W. Leksono, F. Namawar and J. I.
Pankove, Mat. Res. Soc. Proc., vol. 422, pp. 199, 1996.
[22] J. H. Park and A. J. Steckl, “Demonstration of a visible laser on silicon using Eudoped GaN thin films”, J. Appl. Phys., vol. 98, no. 5, pp. 056108, 2005.
[23] J. H. Park and A. J. Steckl, “Laser action in Eu-doped GaN thin-film cavity at room
93 temperature”, Appl. Phys. Lett., vol. 85, no. 20, pp. 4588, 2004.
[24] S. Kim, S. Rhee, X. Li, J. Coleman and S. Bishop, “Photoluminescence and
Photoluminescence Excitation Spectroscopy of Multiple Nd3+ Sites in Ndimplanted GaN”, Phys. Rev. B, vol. 57, no. 23, pp. 14588, 1998.
[25] J. Heikenfeld, M. Garter, D. Lee, R. Birkhahn and A. Steckl, “Red Light Emission
by Photo- and Electroluminescence from Eu-doped GaN”, Appl. Phys. Lett., vol.
75, no. 9, pp. 1189, 1999.
[26] H. J. Lozykowski, W. M. Jadwisienczak and I. M. Brown, “Visible
Cathodoluminescence of GaN Doped with Dy, Er, and Tm”, Appl. Phys. Lett., vol.
74, no. 8, pp. 1129, 1999.
[27] J. B. Gruber, U. Vetter, H. Hofsass, B. Zandi and M. F. Reid, “Spectra and Energy
levels of Tm3+ (4f12) in AlN”, Phys. Rev. B, vol. 70, no. 24, pp. 245108, 2004.
[28] W. M. Jadwisienczak and H. J. Lozykowski, “ Optical properties of Yb ions in
GaN epilayer”, Opt. Mat., vol. 23., no. 1, pp. 175, 2003
[29] S. Aldabergenova, A. Osvet, G. Frank, H. Strunk, P. Taylor and A. Andreev, “Blue,
Green and Red Emission from Ce3+, Tb3+ and Eu3+ ions in Amorphous GaN and
AlN Thin Films”, J. Non-Cryst. Sol., vol. 299, pp. 709, 2002.
[30] H. Lozykowski, W. Jadwisienczak and I. Brown, “Photoluminescence and
Cathodoluminescence of GaN Doped with Pr”, J. Appl. Phys., vol. 88, no. 1, pp.
210, 2000.
[31] H. Lozykowski, W. Jadwisienczak and I. Brown, “Cathodoluminescence of GaN
Doped with Sm and Ho”, Sol. Stat. Comm., vol. 110, no. 5, pp. 253, 1999.
[32] J. Gruber, U. Vetter, H. Hofsass, B. Zandi and M. Reid, “Spectra and Energy
Levels of Gd3+ (4f7) in AlN”, Phys. Rev. B., vol. 69, no. 19, pp. 195202(7), 2004.
[33] W. Jadwisienczak, H. Lozykowski and I. Brown, “Cathodoluminescence Study of
GaN Doped with Tb”, Mat. Sci. & Eng. B, vol. 81, no. 1-3, pp.140, 2001.
[34] C. Munasinghe and A. J. Steckl, “GaN:Eu Electroluminescence Devices Grown by
Interrupted Growth Epitaxy”, Thin Sol. Films, vol. 496, no. 2, pp. 636, 2006.
[35] K. P. O’Donnel and B. Hourahine, “Rare earth doped III-nitrides for
94 optoelectronics”, Eur. Phys. J. Appl. Phys., vol. 36, pp. 91-103, 2006.
[36] R. G. Wilson, R. N. Schwatrz, C. R. Abernathy, S. J. Pearton, N. Newman, M.
Rubin, T. Fu and J. M. Zavada, Apply. Phys. Lett., vol. 65, no. 8, pp. 992-994,
1994.
[37] E. Silkowski, Y. K. Yeo, R. L. Hengehold, B. Goldenberg and G. S. Pomerenke,
Mater. Res. Soc. Symp. Proc., vol. 422, pp. 69-74, 1996.
[38] U. Hömmerich, J. T. Seo, J. D. MacKenzie, C. R. Abernathy, R. Birkhahn, A. J.
Steckl and J. M. Zavada, MRS Fall 1999 Meeting, paper W11.65.
[39] U. Hömmerich, J. T. Seo, M. Thaik, J. D. MacKenzie, C. R. Abernathy, S. J.
Pearton, R. G. Wilson and J. M. Zavada, Internet J. Nitride Semicond. Res., vol.
4S1, G11.6, 1999.
[40] H. J. Lozykowski, W. M. Jadwisienczak and I. M. Brown, “Cathodoluminescence
of GaN doped with Sm and Ho”, Solid. State. Comm., vol. 110, no. 253, 1999.
[41] A. J. Steckl, M. Garter, R. Birkhahn and J. Scofield, “ Green electroluminescence
rom Er doped GaN schottky barrier diodes”, Apply. Phys. Lett., vol. 73, no. 17, pp.
2450, 1999
[42] D. S. Lee, J. Heikenfield, R. Birkhan, M. Garter, B. K. Lee and A. J. Steckl, “
Voltage-controlled yellow or orange emission from GaN codoped with Er and Eu”,
Appl. Phys. Lett., vol. 76, no. 12, pp. 1525, 2000.
[43] J. Heikenfield and A. J. Steckl, “Alternating current thin-film electroluminescence
of GaN:Er”, Apply. Phys. Lett., vol. 77, no.22, pp. 3520, 2000.
[44] E. Desurvire, J. R. Simpson and P. C. Becker, “High-gain erbium-doped travelingwave fiber amplifier”, Opt. Lett., vol. 12, pp.888, 1987.
[45] A.J. Steckl , J. Heikenfeld, D.S. Lee and M. Garter, “Multiple color capability from
rare earth-doped gallium nitride”, Mat. Sci. Eng. B., vol. 81, no. 1, pp.97, 2001
[46] R. Allan. (2005, May 12). Advances Give LEDs/OLEDs That Extra Twinkle
[online].
Available:http://electronicdesign.com/Articles/ArticleID/10247/10247.html
[47] Rodica M. Martin, “Reciprocity between Emission and Absorption for Rare Earth
Ions in Glass”, Ph.D. dissertation, Dept. Phys., Worcester poly. Inst., Worcester,
MA, 1993.
95 [48] Dr. Rüdiger Paschotta. (2008, July 12). An Open Access Encyclopedia for
Photonics and Laser Technology [online]. Available: http://www.rphotonics.com/cross_sections.html.
[49] C. R. Giles and E. Desurvire, ”Modeling erbium-doped fiber amplififiers,” J.
Lightwave Technol., vol. 9, no. 271, 1991.
[50] R. E. Tench, and M. Shimizu, ”Fluorescence-Based Measurement of gain for
Erbium-Doped Fluoride Fiber Amplifiers,” J. Lightwave Technol., vol. 15, pp.
1559, 1997.
[51] M. P. Singh, D. W. Oblas, J. O. Reese, W. J. Miniscalco, and T. Wei,
“Measurement of the spectral dependence of absorption cross section for erbiumdoped single-mode fiber”, Symp. Opt. Fiber Measurements, Boulder, CO, NIST
Special Publication, vol. 792, no. 93, 1990.
[52] B. F. Aull and H. P. Jenssen, ”Vibronic Interaction in Nd:YAG Resulting in
Nonreciprocity of Absorption and Stimulated Emission Cross Sections”, IEEE J.
Quan. Elec., vol. QE-18, pp.925, 1982.
[53] S. A. Payne, L. L. Chase, H. W. Newkirk, L. K. Smith, and W. F. Krupke,
“LiCaAlF6:Cr3+: a promising new solid-state laser material,” IEEE J. Quan. Elec.,
vol. 24, no. 11, pp. 2243, 1988.
[54] D. E. McCumber, “ Einstein relations connecting emission and absorption spectra,”
Phy. Rev., vol. 136, no. 4A, pp. 954, 1964.
[55] D. E. McCumber, “Theory of phonon-terminated optical masers,” Phy. Rev., vol.
134, no. 2A, pp. 299, 1964.
[56] R. S. Quimby, ”Range and validity of McCumber theory in relating absorption and
emission cross sections”, J. Appl. Phys., vol. 92, no. 1, pp. 180, 2002.
[57] B. R. Judd, “Optical absorption intensities of rare earth ions,” Phys. Rev., vol. 127,
no. 3, pp. 750, 1962.
[58] G. S. Ofelt, “Intensities of crystal spectra o rare earth ions,” J. Chem. Phys., vol.
37, no. 3, pp. 511, 1962.
[59] P. L. Pernas and E. Cantelar, “Emission and absorption cross section calculation of
rare earth doped materials for applications to integrated optic devices”, Phys.
Scrip., vol. T118, pp. 93, 2005.
[60] S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway and W. F. Krupke,” Infrared
cross section measurements for crystals doped with Er3+, Tm3+ and Ho3+”, IEEE J.
Quant. Elec., vol. 28, no. 11, 1992.
96 [61] R. M. Martin and R. S. Quimby, ”Experimental evidence of the validity of the
McCumber theory relating emission and absorption for rare-earth glasses”, J. Opt.
Soc. Am. B., vol. 23, no. 9, pp. 1770, 2006.
[62] I. G. Brown, “The Physics and technology of Ion Sources”, John Wiley & Sons, pp.
331, New York, 1989.
[63] P. K. Tien, R. Ulrich and R. J. Martin, “Modes of propagating light waves in thin
deposited semiconductor films”, Appl. Phys. Lett., vol. 14, no. 9, pp. 291, 1969.
[64] P. K. Tien and R. Ulrich, “Theory of Prism-Film Coupler and Thin-Film Light
Guides”, J. Opt. Soc. Amer., vol. 60, no.10, pp. 1325-1337, 1970.
[65] J. M. Hammer, U.S. patent 4,152,045, 1979.
[66] S. G. Mendes, L. Li, J. Burke and S. S. Saavedra, “Achromatic prism-coupler for
planar waveguide”, Opt. Comm., vol. 136, pp. 320-326, 1997.
[67] Karl Lambrecht Corporation [online]. Available:
http://www.klccgo.com/couplingpr.html
[68] A. V. Rodina, M. Dietrich, A. Goldner, L. Eckey, Al. L. Efros, M. Rosen, A.
Hoffmann and B. K. Meyer, “Exciton energy structure in wurtzite GaN”, Phys.
Stat. Sol. B., vol. 216, no.1, pp. 21, 1999.
[69] R. Maalej, M. Dammak, S. Kammoun and M. Kammoun, “Theoretical
investigations of a single erbium center in hexagonal gallium nitride”, J. Lumin.,
vol. 126, no. 2. pp. 695, 2007.
[70] C. Jiang, F. Gan, J. Zhang, P. Deng, and G. Huang, “Yb: Borate Glass with High
Emission Cross Section”, J. Solid State Chem., vol. 144, no.2, pp. 449, 1999.
[71] W. B. Jackson, N. M. Amer, A. C. Boccara and D. Fournier,”Photothermal
deflection spectroscopy and detection”, Appl. Opt., vol. 20., no. 8, pp. 1333, 1981.
[72] S. B. Aldabergenova, M. Albrecht, A. A. Andreev, C. Inglefield, J. Viner, V. Yu.
Davydov, P. C. Taylor, H. P. Strunk, “Experimental mechanisms and structurerelated Er 3+ emission in amorphous and nanocrystalline GaN films”, J. Non-cryst.
solids, vol. 283, no. 1, pp. 173, 2001.
[73] H. Morkoc, “Potential applications of III-V nitride semiconductors”, Mat. Sci.
Eng., vol. B43, no. 1, pp. 137, 1997.
[74] H. J. Lozykowski and W. M. Jadwisienczak, “Photoluminescence and
cathodoluminescence of GaN doped with Pr”, J. Appl. Phys., vol. 88, no. 1, pp.
210, 2000.
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