Rights / License: Research Collection In Copyright - Non ...7094/eth-7094-02.pdfLinear and Non-Linear Spectroscopy of Semiconductors using Synchrotron Infrared A dissertation submitted

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Doctoral Thesis

Linear and non-linear spectroscopy of semiconductors usingsynchrotron infrared

Author(s): Friedli, Peter

Publication Date: 2013

Permanent Link: https://doi.org/10.3929/ethz-a-009904545

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DISS. ETH NO. 21090

Linear and Non-Linear Spectroscopy ofSemiconductors using Synchrotron Infrared

A dissertation submitted to

ETH Zürich

for the degree of

Doctor of Sciences

presented by

PETER FRIEDLI

Dipl. El.-Ing. ETH

born on February 3, 1982

citizen of Lützelflüh BE, Switzerland

accepted on the recommendation of

Prof. Dr. Jérôme Faist

Prof. Dr. Gottfried Strasser

Dr. Hans Sigg

2013

Abstract

This thesis deals with linear and non-linear optical gain of quantum cascade lasers (QCLs)

and the development of unique spectroscopic tools at the infrared (IR) beamline X01DC of the

Swiss Light Source (SLS) synchrotron. These tools consist of (i) an ultra-broadband pump-

probe system, and (ii) a diffraction-limited micro-spectroscopy transmission setup. These

tools enable the investigation of the IR response of condensed matter systems and devices

under conditions of strong electrical and/or optical excitation. It is shown that infrared

synchrotron sources complement conventional infrared sources by offering a high-brilliance,

broadband infrared spectrum and pulsed time-structure.

The first part of this thesis focusses on all-optical pump-probe experiments. A pulse of

synchrotron infrared with a length of 100ps overlaps on the samples with a broadly tuneable

pump pulse generated by non-linear generation from an Nd:YAG laser. This setup enables

the investigation of dynamic processes down to the 100 ps limit. As a showcase, the optical

gain and losses in Germanium-on-Silicon layers are investigated. A discussion is given on

the possibility to realise a laser on Si using strained and doped Ge layers. Also, a brief

introduction is given on the time-resolved investigation of photocatalytic processes using the

here introduced pump-probe tool.

The second part of the thesis deals with the characterisation of QCLs both in the linear

and the non-linear regime. QCLs are based on quantum wells and emit light in the mid-

and far-Infrared. Their structure allows to design the spectral properties of the emission

with a high degree of flexibility and tuneability. Light generation results from optical

intersubband transitions between electron states in the conduction band of the semiconductor

heterostructure. Because such laser devices contain single-mode waveguides (typically

i

ii

smaller than 10 x 3µm in cross-section), the brilliance advantage of a synchrotron source

enables new or more sophisticated measurements than those using alternative broadband

sources, such as a Globar. Here, the transmission measurement directly resolves gain and

losses in the broadband region of 0.1 - 0.7 eV. The spectrally resolved features are used

to benchmark the accuracy of the performance prediction of two established modelling

techniques against experimental data obtained from a high-performance QCL. For the first

time, it is quantifiably shown that the non-equilibrium Green’s function theory outperforms

density-matrix calculations in the high-energy tail of the gain because of the inclusion of

the carrier momentum distribution in k-space. The thus improved description of the total

intersubband gain and absorption over a broad energy range promotes the development of

broadband devices. Moreover, the setup is used for experimental investigations of advanced

QCL structures that operate under pulsed and cryogenic conditions, such as quantum cascade

structures based on quantum dashes and heterogenous quantum well stacks designed for

ultra broadband emission.

Furthermore, non-linearities in quantum cascade lasers were investigated. The large optical

matrix elements between the electron quantum states gives rise to strong third-order optical

non-linearities. As a direct consequence, phase-locking of longitudinal modes by four-wave

mixing is obtained which may eventually build the base for a frequency comb. Here, four-

wave mixing over more than 3 THz in the mid-IR is shown by simultaneously injecting two

lasers running at 67 and 70 THz, respectively, in an anti-reflection coated quantum cascade

laser. In non-coated devices, spatial hole burning, which is due to the intrinsic fast gain in

QCLs, is found to enhance this coupling even further.

Zusammenfassung

Die vorliegende Dissertation befasst sich mit linearem und nichtlinearem optischen Gewinn

in Quantankaskadenlasern (QCLs) und der Entwicklung von einzigartigen spektroskopischen

Messaufbauten an der Infrarot (IR) Strahlenlinie X01DC der Synchrotron-Lichtquelle Swiss

Light Source (SLS). Diese Instrumente umfassen (i) ein ultra-breitbandiges Pump-Probe Mess-

system und (ii) einen diffraktionslimitierten Mikro-Spektroskopie Transmissions-Messaufbau.

Dies ermöglicht die Untersuchung des optischen Verhaltens bei Infrarot Wellenlängen von

Systemen und Bauteilen aus kondensierter Materie unter starker elektrischer und/oder opti-

scher Anregung. Hier wird gezeigt, dass IR Synchrotronquellen konventionelle IR Quellen

durch ihre hohe Brillanz, ihr breitbandiges Spektrum, und ihre gepulste Zeitstruktur ergän-

zen und damit neue Anwendungsbereiche möglich machen.

Der erste Teil der Dissertation konzentriert sich auf optische Pump-Probe-Experimente.

Dazu wird mittels eines Synchrotron Lichtpulses von 100 ps Pulslänge die Charakteristik

einer Probe untersucht, die gleichzeitig mit einem breit durchstimmbaren, mittels nicht-

linearen Prozessen aus einer Nd:YAG Laserquelle generierten, Pump-Pulses angeregt wird.

Dieser Aufbau erlaubt es, dynamische Prozesse mit einer Zeitauflösung von besser als

100 ps zu untersuchen. Zur Demonstration werden die optischen Gewinne und Verluste

in Germanium Schichten untersucht. Die Möglichkeit, mittels verspanntem und dotiertem

Germanium eine Laserquelle in Silizium zu realisieren, wird diskutiert. Zusätzlich wird

eine Einführung zu den zeitaufgelösten Untersuchungen von photokatalytischen Prozessen

gegeben.

Der zweite Teil der Dissertation befasst sich mit der Charakterisierung von QCLs, sowohl

in ihrem linearen als auch nicht-linearen Regime. QCLs basieren auf Quanten-Töpfen und

iii

iv

emittieren Licht im Mittel- und Fern-Infrarot. Ihr Schichtaufbau erlaubt es, die spektralen

Eigenschaften der Emission direkt zu gestalten. Die Lichtgeneration erfolgt über optische

Intersubband-Übergange zwischen den Elektronenzuständen im Leitungsband. Da solche

Bauteile Wellenleiter mit sehr kleinen Dimensionen (Querschnitt < 3 x 10µm) aufweisen,

werden durch die hohe Brillanz des Synchrotron-Infrarotes neue oder fortgeschrittene Mess-

techniken ermöglicht, verglichen zu anderen breitbandigen Quellen, wie eines Globar. So

können mittels Transmissionsmessungen die optischen Verluste und Gewinne in einem breit-

bandigen Bereich zwischen 0.1 - 0.7 eV direkt bestimmt werden. Die spektral aufgelösten

Messdaten werden verwendet, um die Ergebnisse zweier etablierter Modellierungstech-

niken zu vergleichen. Es wird gezeigt, dass die Non-Equilibrium Green’s Function Theorie

sogenannte Density Matrix Modelle bei der Beschreibung der optischen Charakteristiken

im höher energetischen Bereich übertrifft. So wird die Beschreibung der Absorption bei

höheren Energien zwischen angeregten Zuständen nahe bei den aktiven Quantentöpfen

durch die Einbeziehung der Ladungsträger-Verteilung im Impulsraum optimiert. Als Resultat

ergibt sich eine verbesserte Beschreibung der optischen Gewinne, förderlich für die Ent-

wicklung von sehr breitbandigen Bauteilen. Ausserdem wurde der Messaufbau erweitert,

um neuartige QCL Strukturen, die unter gepulster Anregung und/oder bei sehr tiefen Tem-

peraturen betrieben werden müssen, charakterisieren zu können. So konnten qualitative

Rückmeldungen über den spektralen Gewinn in Kaskadenstrukturen gegeben werden, die

aus Quanten-Punken anstelle von -Töpfen bestehen, oder eine heterogene Quanten-Topf

Struktur aufweisen.

Darüber hinaus wurden nichtlineare Effekte in QCLs untersucht. Das grosse optische Über-

gangselement zwischen den Elektronenzuständen führt zu einer starken Nicht-Linearität drit-

ter Ordnung. Als eine direkte Konsequenz werden durch sogenanntes Vier-Wellen-Mischen

gleichmässig im Frequenzraum verteilte optische Moden angeregt, was die Basis für einen

Frequenzkamm im Infraroten bildet. Dieses Vier-Wellen-Mischen wurde im Mittel-IR über

mehr als 3 THz durch gleichzeitiges Einkoppeln von zwei Laser-Pulsen (67 und 70 THz) in

einen Anti-Reflexions-beschichteten Quantenkaskadenlaser gezeigt. In unbeschichteten Bau-

teilen wird dieser Effekt durch räumliches Lochbrennen, das wegen der schnellen Erholung

des optischen Gewinns möglich ist, zusätzlich verstärkt.

Table of Contents

Abstract i

Zusammenfassung iii

1 Introduction 1

1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Synchrotron Infrared Spectroscopy 5

2.1 Synchrotron Infrared Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 The IR Beamline at the Swiss Light Source . . . . . . . . . . . . . . . . . . . . . . 8

2.2.1 Fourier Transform Infrared Spectrometer . . . . . . . . . . . . . . . . . . 8

2.3 Transmission Micro-Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.2 Timing Scheme of the Measurement Setup . . . . . . . . . . . . . . . . . 11

2.4 Infrared Pump-Probe Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4.2 Optical Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4.3 Pump Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.4.4 Synchronisation of Pump and Probe . . . . . . . . . . . . . . . . . . . . . 21

2.4.5 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

v

vi Table of Contents

3 Direct-Bandgap Gain and Optical Absorption in InGaAs and Germanium 31

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.2 Experimental Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.2.1 Investigated Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.3 The Case of a III-V Laser Material (InGaAs) . . . . . . . . . . . . . . . . . . . . . 38

3.3.1 Direct-Gap Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.3.2 Transmission Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.3.3 Determination of Carrier Density from Reflection Measurement . . . . 41

3.4 Optically Pumped Germanium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.4.1 Indirect-Gap Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.4.2 Normal-Incidence Measurements . . . . . . . . . . . . . . . . . . . . . . . 45

3.4.3 Brewster-Angle Measurements . . . . . . . . . . . . . . . . . . . . . . . . 46

3.5 Absorption and Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.5.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.5.2 Measurement Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4 Gain and Loss of mid-IR Quantum Cascade Structures 55

4.1 Quantum Cascade Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.2 Overview on Measurement Techniques . . . . . . . . . . . . . . . . . . . . . . . . 63

4.3 High-Performance Quantum Cascade Laser . . . . . . . . . . . . . . . . . . . . . 66

4.3.1 Device Design and Processing . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.3.2 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.3.3 Correlation to Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.4 Topical Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.4.1 Empty Cavity Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.4.2 Broadband Quantum Cascade Lasers . . . . . . . . . . . . . . . . . . . . . 80

4.4.3 Quantum Cascade Structures based on Quantum Dashes . . . . . . . . 81

5 Four-Wave Mixing 85

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

Table of Contents vii

5.2 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.2.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.2.2 Coupled Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.3 Modelling of χ (3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.4 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

6 Conclusion 101

List of Abbreviations 103

Bibliography 105

Acknowledgements 125

Curriculum Vitae 127

List of Publications 129

Chapter 1

Introduction

Contents1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1 Overview

This thesis is devoted to the development of broadband and time-resolved infrared (IR)

measurement techniques at a synchrotron light source, and the investigation of gain, loss

and non-linearities in quantum cascade lasers using those techniques. Synchrotron IR

(SRIR) consists of broadband, pulsed radiation, which covers the full range from the near-

down to the far-IR, and allows for time-resolved investigations with a time resolution of

100 ps. Furthermore, its high-brilliance makes it especially well-suited for the investigation

of small micron-sized semiconductor samples. Quantum cascade lasers are semiconductor

heterostructures emitting in the mid- and far-IR. Their layered structure is engineered to

create a lasing material, where population inversion between the electrons of different quan-

tum states builds up. Extensive modelling is used nowadays to predict these characteristics

a priori to minimise prototyping costs. These models, even though already highly evolved,

1

2 Chapter 1. Introduction

need experimental feedback in order to increase their accuracy. This is where SRIR comes

into play: it allows for investigation of ready-to-sale devices with optical waveguides sized

in the micron-range, and also to benchmark modelled broadband gain and loss features.

The high-brilliance and the pulsed structure also allows for the investigation of next genera-

tion heterostructures, such as broadband quantum cascade lasers, or structures based on

quantum dots.

In addition to the investigation of quantum cascade lasers over the last four years, several

other experiments and systems were explored using the well-defined time-structure of the

SRIR. These include investigations of the optical properties of the semiconductor material

germanium, and the reaction chemistry spectroscopy of chemical compounds such as TiO2,

promising for solar applications. The 100 ps time-resolution of SRIR is well-suited to

investigate electron and hole carrier dynamics upon excitation with strong visible, near- or

mid-IR laser pulses. Such dynamic studies provide an understanding of the principle of gain

build-up in semiconductors and the onset of reaction changes occurring at the surfaces of a

catalyst.

The IR wavelength range has always been of high importance in technology. A vast amount

of molecules have their fundamental vibration modes in the mid-IR, such as CO2, CO or

Methane, and can be distinguished with their absorption features in chemical sensing appli-

cations such as photoacoustic [1,2] and absorption spectroscopy [3–6]. The investigation

of the spread of these trace gases is important for environmental monitoring. In medicine,

the analysis of biomarkers in human breath allows for the ex-vivo detection of diseases [7].

At high-security places, such as airports, IR measurements provide the detection of liquids

and/or dangerous compounds, such as TNT or Sarin gas [8], and the discrimination of met-

als and plastics [9]. The two transparency windows in the mid-IR (at 3-5µm and 8-12µm,

where atmospheric absorption is low) allow for telecommunications applications, such as

short-distance communications [10, 11]. In IR countermeasures (e.g. the distraction of

heat-seeking missiles), intense IR sources are needed, such as high-power continuous-wave

quantum cascade lasers.

In summary, synchrotron based spectroscopy in the IR provides the following key advan-

1.2. Outline of this thesis 3

tages:

• Broadband, spectroscopically-resolved information;

• High-brilliance to investigate small-sized samples;

• Short light-pulses to look at time-dependent features.

1.2 Outline of this thesis

In every chapter, an overview on state-or-the-art of science and technique is given as an

introduction. In chapter 2, the measurement setups installed at the IR beamline X01DC are

introduced. They consist of the IR pump-probe system with 100 ps time resolution, and

the transmission setup on which most of the quantum cascade work has been performed.

Chapter 3 gives details on optical losses and gain in optically pumped InGaAs and germa-

nium. In Chapter 4, the transmission measurement of a high-performance quantum cascade

laser is compared to simulations using two different models for intersubband gain (the

non-equilibrium Green’s function theory and the density-matrix approach). Furthermore, ad-

vanced quantum cascade structures based on quantum dots and with broadband capabilities

are presented. In Chapter 5, non-linearities in quantum cascade lasers are investigated. It is

shown, that the fast gain in QC structures allows for four-wave mixing over a large spectral

bandwidth, which potentially forms the base for a frequency comb operation in the mid-IR,

as recently demonstrated by Hugi et al. [12].

Chapter 2

Synchrotron Infrared Spectroscopy

Contents2.1 Synchrotron Infrared Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 The IR Beamline at the Swiss Light Source . . . . . . . . . . . . . . . . . . 8

2.2.1 Fourier Transform Infrared Spectrometer . . . . . . . . . . . . . . . . . 8

2.3 Transmission Micro-Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.2 Timing Scheme of the Measurement Setup . . . . . . . . . . . . . . . . 11

2.4 Infrared Pump-Probe Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 15

2.4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4.2 Optical Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4.3 Pump Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.4.4 Synchronisation of Pump and Probe . . . . . . . . . . . . . . . . . . . . 21

2.4.5 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.5 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

In this chapter, a brief overview of the general properties of synchrotron infrared (IR)

radiation and the IR beamline X01DC are presented. The two different IR experimental

methods - transmission micro-spectroscopy and optical pump-probe spectroscopy - are

described. The pump-probe spectroscopy applied to the investigation of chemical reactions

illustrates the potential of the latter method.

5

6 Chapter 2. Synchrotron Infrared Spectroscopy

2.1 Synchrotron Infrared Sources

IR radiation covers all the wavelengths of the electromagnetic radiation between the visible

(VIS) light (740 nm ≈ 1.7 eV) and the microwaves (1 mm ≈ 1.24 meV). The specific range ac-

cessed in this thesis covers the near-IR (0.74 - 3µm) and mid-IR (3 - 14µm).

In electron storage rings, electrons are forced on a closed orbit by magnetic deflection and

continuous acceleration. Each time the direction of the electrons is changed, synchrotron

light is emitted. This light is extremely broadband (from the X-Rays to the IR region) and of

high-brilliance1.

After the first electron storage ring, which was built in the 1960s [13], a series of technologi-

cal achievements have led to today’s third generation synchrotron sources. The idea of using

the specific properties of synchrotron radiation in the IR spectral range originated in the

1970s [14] and the first beamlines designed to extract IR radiation for useful spectroscopy

were built in the late 1980s [15–17].

Synchrotron radiation IR (SRIR) sources extend some of the performances provided by

traditional thermal broadband IR sources. A thermal sources behave like a blackbody

described by the Planck equation, which gives the spectral emissivity as a function of

the source temperature T . Because of their thermal inertia, thermal sources offer stable

operation, at the cost of a limited brilliance and no intrinsic time structure. A widely used

mid-IR thermal source is a heated (1300 K) silicon carbide rod, commercially known as a

Globar [18]. For the near-IR, regular halogen lamps can be used, which consist of a tungsten

filament enclosed in a glass bulb filled with halogen gas. This setup is possible, because glass

is transparent in the near-IR, contrary to the strong absorption in the mid-IR. Halogen lamps

are operated at higher temperatures than a Globar. Hence, the overall emission spectrum is

blue-shifted.

Synchrotron radiation differs from thermal radiation in two main points. First, it offers

enhanced brilliance, see Fig. 2.1. This feature allows for fast and diffraction-limited investi-

1Brilliance is defined as photon flux per spectral bandwidth per source size per source divergence.

2.1. Synchrotron Infrared Sources 7

gations and is useful in various fields of science, ranging from life-science to high-pressure

condensed matter physics. The technique is widely exploited [19] and is termed micro-

spectroscopy or spectro-microscopy . This topic is addressed in detail in Sec. 2.3. Second,

because of its pulsed nature, synchrotron radiation allows time-resolved experiments on

a time-scale below 100 ps for synchrotron. The fourth generation sources, known as free-

electron lasers (FELs), even exceed those performances in terms of time-resolution (below

100 fs) and power. It is fair to mention, however, that these kind of IR sources are expensive,

limited in availability, without straightforward access, and most importantly, exceedingly

sensitive to perturbations of various origin.

1

2

4

6

810

2

4

6

8100

2

S/N

im

pro

vem

ent

@ 2

70

0 1

/cm

4 5 6 7 8 9

102 3 4 5 6 7

aperture size (µm)

1

2

4

6

810

2

4

6

8100

2

IR sig

nal im

pro

vem

ent

Signal improvement factor ==>

<== S/N improvement factor

Figure 2.1: Synchrotron IR (SRIR) exceeds the standard thermal broadband source (Globar) by up to

two orders of magnitude for small apertures.

Few experiments have exploited the characteristic time-structure offered by a synchrotron

source. To the best of our knowledge, only one IR pump-probe setup achieved a 100 ps-time

resolution together with a maximum pump-probe delay of several hundreds of ns [20,21].

This is due to the fact that most other setups use a 1:1 pumping scheme, in which the (laser)

pump source runs at the same frequency as the synchrotron probe, which is usually in the

range of ∼100 MHz. Hence, these systems mainly allow for probing of processes in materials

that have fully recovered after ∼10 ns.

The system developed during this work allows for ultra-broadband pump-probe spectroscopy

with a tuneable near- to mid-IR laser pump, a synchrotron source as probe and is tailored to


provide pump-probe delays of up to 1 ms [22].

2.2 The IR Beamline at the Swiss Light Source

The Swiss Light Source (SLS) is a third generation synchrotron light source running at

2.4 GeV. It operates in a so-called top-up mode that keeps the total beam-current nearly-

constant between 400 - 402 mA by periodically (≈140 s) injecting electrons into the orbiting

electron bunches. At the IR beamline X01DC, pulses of synchrotron radiation are emitted

with a repetition rate of 500 MHz every time an electron bunch is deflected by its bending

magnet. The radiation is filtered by a slit-mirror, which reflects only low energy radiation,

see the left part of Fig. 2.2. An arrangement of mirrors transports the light (1:1 imaging) to

the input focii of different experimental stations. From there, elliptical Au-coated mirrors

focus the light to the entrance pupil of the Fourier transform IR (FTIR) spectrometers that

equips every station. All beamline mirrors are qualified for imaging in the visible part of the

spectrum, in order to ease the optical alignment. Further details on the beamline layout are

available online [23] and in [24].

The SLS operates with an asymmetric filling pattern of its 480 electron buckets (each bucket

is separated by 2 ns) [25]. First, a train of 390 buckets are each filled with a standard charge.

Then, there is a train of empty buckets for ∼150 ns, followed by a single strong bucket

containing four times the standard charge, and a further train of empty buckets for∼30 ns, as

shown in the right top part of Fig. 2.2. The single bucket, termed camshaft pulse, completes

a revolution of the SLS with a repetition rate of 1 MHz.

2.2.1 Fourier Transform Infrared Spectrometer

An FTIR spectrometer consists of a Michelson interferometer, where an optical wavefront

is amplitude-divided with a beamsplitter along two paths. Subsequently, the interference

pattern of light recombining from the two branches is measured. Fig. 2.3 illustrates the

optical arrangement.

2.2. The IR Beamline at the Swiss Light Source 9

Sig

nal [

a.u.

]

1.20.80.40.0Energy [eV]

Beamsplitter: CaF2 KBr

30 ns! Pulse separation: 2 ns!

Pulse length!100 ps!

Dipole magnet!

Slit-mirror!

Camshaft!!

Swiss Light!Source!

100 ps pulses!80 meV – 1.5 eV!

UV!X-Ray!

Figure 2.2: Schematic of the SLS asymmetric filling pattern and SRIR pulse distribution. The inset

shows the bandwidth of the broadband SRIR with tow different FTIR beamsplitters [22].

The optical path length along one arm is constant, the other one can be changed with a

moveable mirror. This introduces known phase-shifts. The intensity modulation recorded at

the detector carries the phase modulation and is known as the interferogram. The Fourier

transform of the interferogram (unit cm−1) is related to the source spectrum (unit cm). One

advantage of an FTIR spectrometer over a grating spectrometer (introduced in Chap. 5) is

the ability to measure the entire spectrum simultaneously, which is known as the Fellgett’s

advantage. Furthermore, the optical throughput increases with the square of the measured

frequency, which is the Jacquinot’s advantage. Hence, FTIR spectrometers theoretically are

expected to be 2000 times more sensitive than grating spectrometers. However, because of

the large detector bandwidth requirement imposed by FTIR spectroscopy, Fellgett’s advantage

is effective only [27].

IR spectroscopy using the Fourier transform technique is sensitive to intensity instabilities

carried by the light that enters the spectrometer; they manifest themselves as spectral

artefacts in the data. A detailed study of this noise in SRIR from two comparable IR ports

(Soleil and SLS) is reported in [28]. Luckily, by changing e.g. the velocity of the moving

mirror, the spectral position of these artefacts, if known, can be shifted to regions without

any importance.


Source'

Direc*on'of'Travel'

Detector'

Beamspli6er'

Movable'M

irror'

Fixed'Mirror'

Figure 2.3: Layout of a FTIR spectrometer based on the Michelson interferometer technique. A colli-

mated beam is split onto two branches with a beam splitter and subsequently combined

after reflection from the two end mirrors. Adapted from [26].

FTIR spectrometers are either run in continuous- or step-scan operation. Usually, in the

case of low signals and/or high time-resolution, the step-scan mode outperforms continuous

operation.

2.3 Transmission Micro-Spectroscopy

2.3.1 Overview

The investigation of laser devices, where active material is embedded in a waveguide, re-

quires the coupling of light into these usually small (i.e. near-diffraction limited) waveguides.

SRIR with its high-brilliance is the optimal choice. The coupling of SRIR is achieved in a

commercial IR microscope, connected to a Vertex 70v FTIR spectrometer. As a figure of

merit, approximately 10µW of power is transmitted through a 10µm diameter pinhole

placed in the focal plane of the 15x Schwarzschild objective shown in the right part of

Fig. 2.4. SRIR radiation is directly focussed onto the cleaved facet of the QCLs mounted

on a Peltier-cooled copper-finger. A free-standing wire-grid polariser selects the transverse-

magnetic (TM) or -electric (TE) modes. The transmitted light is collected by the second

2.3. Transmission Micro-Spectroscopy 11

microscope objective, that has been properly aligned to the top facet. After spatial filtering

by the aperture of the second objective, the light is refocused onto the built-in liquid nitrogen

cooled mercury cadmium telluride (MCT) detector. Optimal alignment is achieved in three

steps: a) optimising on the chopped SRIR signal from the detector, b) confirming true

waveguiding by observation of the optical absorption at the bandgap of the cladding material

(≈ 5000 cm−1) and c) a low pass filter to select only the low-energy part of the transmitted

light.

!!MCT!!!Detector!

FTIR!modulated!

QCL!

Polarizer!

SRIR!from!SLS!Data!Signals!

Control!Signals!

Electrical!Pulse!

Generator!

SLS!Reference!(500MHz)!and!EPICS!

SchwarzF!child!

lenses!

Sample!/!Hold!Card!

Digital!AcquisiKon!System!

FTIR!Spectrometer!

2.5

2.0

1.5

1.0

0.5

0.0

Detector,Signal,[V]

6050403020100Time,[ns]

Figure 2.4: Overview of the optical and electrical components of the transmission micro-spectroscopy

setup for pulsed QCL operation. The system is locked to the SLS reference frequency of

500 MHz. The pair of Schwarzschild lenses shown on the right provides dispersive-free

focusing of the SRIR

2.3.2 Timing Scheme of the Measurement Setup

In the case of continuous-wave (CW) pumped QCLs, the FTIR spectrometer is run in fast-

scan. The built-in MCT detector thus integrates the SRIR in time, i.e. the pulsed structure

of the SRIR is disregarded. This yields a high signal-to-noise ratio, because the full SRIR

intensity is used.


During pulsed QCL operation, however, only the camshaft pulse is used for the measurement.

For its detection, a fast MCT detector from Vigo Inc. with an analog bandwidth of 800 MHz

and a spectral sensitivity from 2.5 - 8µm is employed. A typical time record of the electron

bunches is plotted in the inset of Fig. 2.4. Since the camshaft has a time delay of more than

30 ns to the adjacent standard bunches, it can be resolved with a detector/amplifier system

with a bandwidth of 30 MHz, while still providing a true time resolution of 100 ps. In the

case of the continuous-wave Globar source, the same detector parameters would deliver a

time resolution of 10 ns only. The benefit of this approach is the camshaft peak-intensity

approximately 2000 times larger than that of a Globar source. Part of this advantage is

however lost by the combined effect of source instability and the need to restrict the scan

length to the 140 s of the top-up period. Thus, the high bandwidth of the detector combined

with the fast data acquisition system (DAQS) allows the 100 ps long pulses to be resolved.

Of course, pulsed experiments suffer from reduced signal intensity because (a) only 1% of

the available synchrotron light is carried by the camshaft pulse, and (b) the experiments are

often performed at reduced repetition rate. In spite of this drawback, averaging over many

pulses sufficiently increases the signal-to-noise (S/N) ratio even for measurements performed

with unbiased QCLs, when the absorption is high. The minimally measurable absorption was

found to be approximately 10 cm−1. Due to the gated measurement technique, pulse energies

of less then 1 fJ were detected at reasonable S/N ratio.

Here, the FTIR is run in step-scan mode. This means, that the internal mirror is held at a

constant position during sampling. The sampling of the peak amplitude of the camshaft pulse

is performed with a fast analog sample/hold card (AnaPico AP3501). This sampled value is

held for several 100 ns at the output port of the sample/hold card and read in by a 16bit

resolution, 3 MHz analog bandwidth, multi-channel module (PXI-6251DAQ) from National

instruments (NI) at a rate of 1 MHz. The averaging is performed on a NI PXIe-1062Q PXI

system running a real-time operating system (PXIe8108RT). Both the sample/hold card and

the data acquisition system operate locked to the SLS reference frequency of 500MHz. This

locking is a crucial element of the measurement setup, since it eliminates practically all

time-jitter effects. The setup is triggered by control signals from the experimental physics and

industrial control system (EPICS) based SLS control system.

2.3. Transmission Micro-Spectroscopy 13

After integration over typically 100 ms, which corresponds to roughly 100’000 camshaft

pulses, the pumped and unpumped transmission signals are fed as a three-level analogue

voltage-train to the 16bit analog-to-digital converter (ADC) of the Bruker spectrometer, see

Fig. 2.5. In the following, the sampling and averaging procedure is repeated for the next

mirror position. In this way, the full step-scan spectra is recorded simultaneously for pumped

and unpumped transmission.

IR#Detector#SU#

SP#SU#

FTIR#in##Step2Scan#Mode#

Digital#Acquisi<on#System#

Make#averages#Measure#

N#camshaCs#

Move#mirror#

PAV#U#AV#P2U)#AV#

###Read######(P2U)AV####UAV###PAV#

Trigger#for#DAQS#Output#

M(n21)# M(n)# M(n+1)#Mirror#step#

SP#

Current#Pulse#Generator#

Figure 2.5: Schematic of the SRIR pulse-train transmitted through a pumped sample and DAQS oper-

ation. The unpumped (SU) and pumped (SP) camshaft signals are sampled and averaged

and sent as a three-value voltage train (SU , SP , SU − SU) to the FTIR spectrometer.

The QC structures are pulsed with a HP 8114A high-power pulse generator at a repetition

rate of typically 130 kHz using a duty-cycle below 1% to avoid thermal heating. The pulse

generator is locked to the EPICS control system by a square wave at a frequency of 130 kHz.

In this scheme, one out of eight camshaft pulses is transmitted through the electrically

biased QC structure, while the other seven are recorded as the unpumped reference trans-

mission signal. In this way, the accuracy of the measurement is increased by this inherent

normalisation possibility. The temperature of the QC structures is either controlled with

a Peltier-cooler at 10 C < T < 40 C, or using a He-flow cryostat for experiments at low


temperatures (<100K). The thickness of the ZnSe windows of this cryostat is chosen to be

only 1 mm in order to minimise the effects due to dispersion.

The targeted wavelength range and resolution of the experiment determines the amount of

mirror-steps and measurement time needed for the full scan. The maximum measurement

time is limited by the SLS top-up period to usually ∼140 s, which defined the maximum

number of mirror steps to usually approximately 1000. As shown in Fig. 2.6, measuring

across a top-up event introduces a step-feature in the interferogram. After Fourier trans-

formation this shows up as a high frequency wobble artefact, together with an artificial

baseline offset [22]. In order to synchronise the measurement to the top-up period, a C#

application was developed. This routine monitors the top-up event record supplied by EPICS,

and starts a measurement directly after the top-up sequence is fully finished. In a second,

more elaborate, version, the routine is additionally able to run series of measurements,

where the voltage of the pulse generator and the time-delay with respect to the camshaft

pulse are remotely controlled.

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

Nor

mal

ized

Inte

rfero

gram

25002000150010005000

FTIR Mirror Step

120011001000

1.101.051.000.95

24802440

Figure 2.6: Interferogram, which includes two top-up events. The step-like features introduces

spectral artefacts upon the subsequent Fourier transformation [22].

2.4. Infrared Pump-Probe Spectroscopy 15

2.4 Infrared Pump-Probe Spectroscopy

2.4.1 Overview

The broadband FTIR pump-probe (IRPP) setup was recently presented [22]. It allows

the optical characterisation with SRIR as the optical probe (100 ps time resolution) and

a widely tuneable near- and mid-IR laser system as the optical pump. Compared to ex-

isting synchrotron IRPP systems, it provides both improved spectral and time bandwidth

at maximum temporal resolution. A schematic overview of the full system is given in

Fig. 2.7.

• !OPUS!• !C !

Spectrometer!PC!

Sample'

!!Transmission!!!Detector!

Digital!!Acquisi9on!!

System!

NI=!BNC!

ZTEC!Digi9zer!

X01DC!Control!Rack:!Event!

Receiver!Card!

1kHz!Trigger!

IRPP!Lab!Notebook!

LabView:!

• !IRPP!Main!• !Delay!&!Filter!• !Top=Up!Mon.!• !ShuTer!

Ch.!1!Ch.!2!

!!Reflec9on!!!Detector!

Pump!Laser!

Op9cal!Parametric!Genera9on!

Master!Oscilla=tor!

SRIR!From!SLS!

Vector!Modulator!

Photo!Diode! Piezo!

SLS!500!MHz!

RS232!

Local!IP!

IP!

IP!IP!

EPICS!

Mirror!Step!Trigger!

Experiment!Trigger!Processed!Detector!Signals!

Phase!Locked!Loop!

Filterbox!

ShuTer!USB!

!FTIR!

Spectro=meter!

ADC!

Trigger=box!

Control!Hutch!

IP!

Figure 2.7: The schematic of the IR pump-probe setup shows the optical path of the synchrotron IR,

all components of the measurement setup, and their interconnection.

The SRIR probe features a bandwidth from the visible light up to 12.5µm. The full-

bandwidth (visible to mid-IR) FTIR-modulated SRIR power delivered to the IRPP setup is


between 500µW to 1 mW. Transmission and reflection SRIR spectra are recorded simultane-

ously.

The optical pump is a tuneable IR laser system, consisting of a regeneratively-amplified

Nd:YAG pulsed pump laser launched into an optical parametric generation system, delivering

100 ps long pulses at a repetition rate of 1 kHz. It covers most of the NIR and MIR range

and is especially well-suited to investigate condensed matter processes with time constants

between the 100 ps resolution of the pulse, and 1ms (the time until the next pump pulse

arrives).

2.4.2 Optical Setup

Two different focusing units for the IRPP setup were developed:

(A) For large samples, a 100 mm parabolic mirror focusses the SRIR beam onto the sample.

When properly aligned, the overall throughput is 95% (λ >1µm) through a 200µm pinhole.

Using two detectors, both transmitted and reflected SRIR signals are recorded simultaneously,

as shown in Fig. 2.8(a). The pump laser is focused onto the sample using a lens with a

focal length of approximately 30 cm in order to make sure, that the pump spot is always

larger than the probe spot, and to have sufficient depth of field useful to ease alignment

work.

(B) For small samples, a micro-focusing unit using a pair of objectives in confocal config-

uration was developed, see Fig. 2.8(b). A 15x Schwarzschild lens focuses the SRIR probe

beam to a spot size below 25µm onto the sample. The transmission is collected by a

second Schwarzschild objective and then refocused onto the detector. The reflection can

be measured simultaneously by the use of a half-space entrance mirror before the first

Schwarzschild lens. The pump laser is focused onto the sample by a series of small mirrors

and a standard lens to achieve a spot size of around 35µm.

The several orders of magnitude power difference between the pump and probe beams

requires careful filtering of the detectors. It should be emphasised that because the pump


laser light is not modulated through the FTIR bench, it will not directly impact on the spectra.

However, laser light may generate additional noise, drive the detectors into their non-linear

regime, or even worse, damage them.

Transmission)

Reflec.on)

Pump)Laser)SRIR)

Sample)

DAQS)

(a) Standard Setup.

Pump%Laser%

SRIR%

Sample%Transmission%

CCD%

(b) Micro-Focus Setup.

Figure 2.8: Photos of the IRPP setups, which show the optical paths for pump, probe-transmission,

and probe-reflection, respectively.

A shutter and filter wheel (remotely controlled) are added in the optical path of the pump in

order to allow an automated measurement with different pump intensities.

2.4.3 Pump Performance

The customised laser pump system was manufactured by Eskpla Optics. The system is split

in two parts, namely a Nd:YAG pump laser and an optical parametric generation (OPG) box.

First, high-energy 100 ps long pulses delivered by a 1 kHz Nd:YAG regenerative amplifier

(RegA) at an average power of 2.8 W, and a quasi continous-wave (CW) 83.3 MHz pulse

train (Master-Oscillator MO) at an average power of 5.3 W are created. The system then

uses a series of three-wave mixing processes with this high-intensity pulses, namely optical

parametric oscillation (OPO), optical parametric amplification (OPA), difference frequency

generation (DFG) and second harmonic generation (SHG) in order to provide the near-

and mid-IR radiation [29]. These three-wave mixing processes are introduced theoretically

below. This system is rather complex but offers a level of average power in the watt-range


and can be tuned with a high degree of flexibility. The optical parametric generation (OPG)

covers 94% of the 1.1 - 16µm tuning range, see Fig. 2.9.

2

468

10

2

4

68

100

2

4

68

1000

Pul

se E

nerg

y [µJ]

5 6 7 8 9100

2 3 4 5 6 7 8 91000

Photon Energy [meV]

DFG

OPA Idler OPA Signal

Idler SHG

Figure 2.9: Pump pulse energy as a function of photon energy for the tuneable pump-source. The

DFG, OPA, and SHG tuning ranges are indicated by dashed rectangles [22].

In three-wave mixing, three photons at angular frequencies ω1, ω2 and ω3 interact with

each other, and need to fulfill both energy conservation (~ω3 = ~ω1+~ω2) and momentum

conservation (~k3 = ~k1+ ~k2, where ki is the wave vector). While the energy conservation

can usually be satisfied easily, the second condition needs further attention. In general, three

different scenarios are distinguished, see Fig. 2.10.

(A) In optical frequency conversion, either the sum (sum frequency generation: ω3 =ω1+

ω2) or the difference (difference-frequency generation: ω2 = ω3 −ω1) of the two input

frequencies is generated. If the input frequencies coincide, the process is called second

harmonic generation.

(B) In contrast to the above process, the aim of optical parametric amplification lies in the

amplification of one of the input waves, e.g. ω3, by transferring energy from the other input

wave, e.g. ω1. In this case, the created auxiliary photon at frequency ω2 is called the idler,

and the initial wave at ω3 is called signal.

(C) Finally, in optical parametric oscillation, the non-linear element is placed inside a feedback

cavity, and only one pump wave at frequency ω1 is supplied to the cavity. An additional


wavelength-selective element, usually a grating mirror, is introduced into the cavity to select

a distinct set of frequencies ω2 and ω3.

Sum$Frequency,Genera/on,

ω3#

ω1#

ω2# ω2#

ω1# ω3#

Crystal# Filter#

ω1#

ω3#

ω2# ω1#

ω3# ω2#

Crystal# Filter#

Difference$Frequency,Genera/on,

ω1#

ω3#

ω2# ω1#

ω3# ω2#

Crystal# Filter#

Parametric,Op/cal,Amplifica/on,

ω3#

ω1#

ω3#

ω2# ω1#

ω3#

ω2#

Crystal# Filter#

Parametric,Op/cal,Oscilla/on,

Cavity#Mirrors#

Figure 2.10: Optical Parametric Generation of IR light.

In order to fulfil the conservation of momentum, mainly two approaches are followed:

(A) In a quasi-phase matching, materials with different refractive indexes are stacked to-

gether to form a periodically-poled structure. In this way, the different propagation speeds

of the participating waves can be compensate for. Usually, several such structures with

different periodicity are combined, and matching to the requested wavelength is enhanced

by temperature-tuning. A very common example in the mid-IR is periodically-poled lithium

niobate (PPLN).

(B) In birefringent materials, the refractive index is anisotropic. The propagation velocity

of light therefore depends on the polarisation and the propagation direction with respect

to the crystal axes. The phase-matching condition is then fulfilled by angle-tuning of

the crystal, in order to achieve nearly-identical propagation speed and direction of the

participating fields. The conversion efficiency is limited due to beam walk-off, namely

the slight direction mismatch between the fields, until no interaction between the fields is

left.


Building up on this theoretical background, the system can now be described in more details.

In the OPG box, the quasi CW train drives a synchronously pumped OPO, which consists of

a PPLN crystal and a diffraction grating as selective wavelength element. The OPO delivers

two quasi-CW trains, namely OPO-signal and OPO-idler. The wavelength of the signal and

idler fulfil both energy conservation with respect to the Nd:YAG wavelength, and also the

diffraction condition of the grating. The OPO-signal is sent to the OPA as a seed, which is

synchronously pumped with the Nd:YAG RegA 1 kHz train. The OPA uses two pairs of angle-

tuned potassium titanyle arsenate (KTA) crystals, which need to be exchanged depending on

the requested wavelengths. Because OPA-signal and OPA-idler are orthogonally polarised,

they can conveniently be separated using a Rochon polariser. To reach higher wavelengths,

DFG between the OPA-signal and OPA-idler is performed in an angle-tuned GaSe crystal.

The tuning range of the system is extended towards the NIR by SHG of the OPA-idler using a

pair of angle-tuned KTA crystals.

BD#

BD#OPO#

DFG#OPA#

Quasi)#CW#Train#

1kHz#RegA#

Diffrac9on#Gra9ng#PPLN#

KTA#Crystals# GaSe#Crystal#

DFG#

OPA)Signal#or#OPA)Idler#

OPO)Signal#

OPO)Signal##

BS#

BS#

Rochon#Polarizer#

Flip)Mirror#

BD#

Figure 2.11: Layout of the optical parametric generation box. The KTA-Crystals are seeded by the

OPO-Signal and pumped by the 1 kHz regenerative amplifier (RegA). A flip-mirror is

used to either generate the DFG or pass the OPA. OPA-Signal or -Idler are selected with

a Rochon polariser.


2.4.4 Synchronisation of Pump and Probe

The length of the piezo-controlled master oscillator (MO) cavity of the quasi-CW Nd:YAG can

be adjusted with sub-nm precision, which allows for a tuning of the repetition rate around

83 MHz. A 100 Hz bandwidth phase-locked loop (PLL) is used to control the position of the

cavity mirror, and so synchronises the MO to the SLS. The sixth sub-harmonic of the SLS clock-

rate (83.3 MHz = 500 MHz/6) is used as a reference frequency. A digital pulse-picker selects

one pulse in every 83520 pulses (this number must be a multiple of the 480 electron buckets

of the SLS filling pattern for phase-lock) for regenerative amplification. When the PLL has

locked the MO to the SLS clock-rate, the 1 kHz RegA pulses are also implicitly locked to the

SLS, and in particular, they are locked to the camshaft pulses.

The initial locking of RegA and camshaft occurs at an arbitrary phase, see the upper panel

in Fig. 2.12. Thus, an offset of up to 500 ns between the pump and nearest camshaft pulse

is possible. A radio frequency (RF) vector-modulator (VM) is used to add a phase-shift on

the 500 MHz SLS clock-rate fed to the input of the PLL. Using this tuneable phase-shift, the

pump laser and camshaft pulse are brought into overlap, see the lower panel of Fig. 2.12. In

this way, the VM fully replaces a physical optical delay line and provides an easy-to-access

digital delay control.

toff$

P$U$

SRIR$

Pump$

SRIR$

Pump$

U$

Ini$al'Phase,lock'

Temporal'overlap'

Figure 2.12: Time-Sketch of the SRIR pulse-train. In the initial phase-lock, the pump-probe offset is

up to 500 ns. The vector modulator allows achieve temporal overlap [22].


2.4.5 Data Acquisition

The DAQS described above for transmission spectroscopy is used in a slightly different

configuration to capture and process two channels simultaneously. In this way, transmis-

sion and reflection studies can be correlated within a single measurement, both for the

unpumped and pumped case. The FTIR is run in step-scan mode. For each mirror step, the

DAQS integrates the camshaft signals over a predefined number of laser pulses (typically

85).

The signals from the fast detectors, are sampled by a 14-bit, 250 MHz bandwidth PXI digitiser

module (ZTEC ZT410–21). The SLS 500 MHz clock-rate bypasses the internal PXI clock

to allow for reproducible sampling of the camshaft pulses. Averaging is done in real-time

on the module itself. After data processing, the two detector signals are fed as a six-level

analogue voltage-train from the multi-channel module of the PXI to the ADC of the Bruker

spectrometer, see Fig. 2.13.

The setting of the pump-probe delay is performed by a third version of the C# routine. In

addition, also the filter wheel is controlled.

2.5. Applications 23

Reflec%on(RP(

RU( RP(

FTIR(in((Step2Scan(Mode(

Digital(Acquisi%on(System(

Make(averages(

Move(mirror(

T P,AV(

T U,AV(

T (P2U),A

V(

R P,AV(

R U,AV(

R (P2U),A

V(

Read(

M(n21)( M(n)( M(n+1)(Mirror(step(

2(

Op%cal(Pump(

Transmission(

TU(TP( TP(

Exp.((Trigger(

CamshaN(current(Top2up( Top2up(

C#(

Full(Measurement(

Start(Measurement(Write(EPICS(values(

RU(

TU(

Figure 2.13: Two detector channels are simultaneously recorded. Averaging of the peak amplitudes

and background subtraction is done in real-time. The data transmission to the FTIR is

controlled by additional synchronization signals.

2.5 Applications

As discussed above, synchrotron-based IRPP experiments offer a unique experimental niche.

They combine focus capability, extended spectral coverage and dynamic bandwidth. In this

section, several possible application fields and experiments are discussed.

Condensed Matter

Dynamics occurring in condensed matter, such as carrier diffusion, electron-hole or quasipar-

ticle recombination on small samples, can be well investigated with the spectral coverage


and 100 ps time resolution of the pump-probe system.. A synopsis of different processes and

their characteristic times is given in Fig. 2.14.

tim

e r

eso

lve

d F

TIR

10!"

10!#

10$

10%

10&

Time

(s)

fs s

pe

ctr

osco

py

syn

ch

rotr

on

ba

se

d

tim

e r

eso

lve

d F

TIR

Dynamic Events

pico

nano

micro

mili

femto

e-e scattering

Thermalisation of electrons

Decay optical phonons

Auger recombination

Quasi particles

Carrier diffusion

Phase change materials

E/H recombination

direct gap

Nanostructure transport

E/H recombination

indirect gap

Impurities, traps

Electron-Phonon equilibration

Rate

(s-1)

Figure 2.14: Synchrotron-based time-resolved FTIR bridges fs-laser based and conventional FTIR

spectroscopy. Various relevant dynamic processes in condensed matter, such as carrier

diffusion and recombination can thus be investigated.

As a showcase, a detailed description of the electron-hole recombination dynamics after opti-

cal excitation in germanium and InGaAs is discussed in Chap. 3.

Also, using IR pump-probe spectroscopy, the density and relaxation dynamics of interband

defects in phase change materials (PCM) were investigated. PCMs, such as Ge-Sb-Te

are promising candidates for future non-volatile memory applications [30]. The memory

writing operation here critically depends on the distinct electrical properties of PCM in its

amorphous phase, which is dominated by a large defect density within the bandgap [31].

The combination of the IRPP time resolution, spectral bandwidth and tuneability of the pump

laser allows for the characterisation of the extended absorption tails at specific excitation


energies.

Chemistry and Biology

Chemical and biological processes usually consist of a complex chain of reactions between

transient species with lifetimes varying from (sub-)fs to ms. Following these kind of processes

requires a time-resolved spectroscopic method that covers an ultra-large time-bandwidth.

None of the currently applied methods allows for full investigations over the entire time-

scale. More importantly, there is no explicit method for the investigation of such pro-

cesses in the interesting range between 1 to 100 ns. This particular time-scale is both

well-above the target time resolution of fs-laser based spectroscopy, and also much too

fast for investigation by conventional time-resolved step-scan FTIR (with an achievable

time resolution of ∼0.1µs). An overview of the relevant chemical processes is given in

Fig. 2.15.

10!"

10!#

10$

10%

10&

10'!"

10'!#

10'$

10'%

10'&

10'(

femto

pico

nano

micro

milli

Dynamic Events:Electron motion, transferand orbital jumps

Rot. and translational motion

Rot. and translational motion (large molecules, fluids)

“Ultrafast” chemical reactions”

“fast” chemical reactions

“slow” chemical reactions

Rot. and translational motion(large molecules, viscous systems)

Vibrational motionBond cleavages (weak)

Timescale(s)

Ratescale(s-1)

fs s

pect

rosc

opy

time

reso

lved

FTI

R

sync

hrot

ron

base

d tim

e re

solv

ed F

TIR

fast

sca

n F

TIR

(from “Modern molecular photochemistry” by Nicholas J. Turro)

Figure 2.15: Timescales in chemistry.


An interesting application is the study of transient mid-IR electron dynamics in the con-

duction band of Titanium dioxide (TiO2). TiO2 is a widely used semiconductor, and finds

application in different fields, such as (photo)-catalysis and solar cells. These applications are

initiated by surface and/or interface interactions. Even though the photocatalytic conversion

of solar light into chemical bonds through TiO2 was demonstrated in the 1970s by Honda

and Fujishima [32], followed by extensive research, there is little information about surface

intermediates and the time at which they appear. The IRPP system is well-suited to provide

this experimental foundation. It was used to investigate the efficiency of visible and near-IR

light absorption in TiO2 meant for solar cell applications [33]. To allow for such low-energy

absorption, the physics of TiO2 absorption however needs to be modified, because the large

band gap of TiO2 (3.2 eV) would require UV irradiation to induce charge separation. Without

modification, only 4% of the solar spectrum (UV) would therefore contribute to the solar

cell operation, and lead to a low efficiency. Despite different approaches made to improve

visible light absorption, the yield in the visible range is still insufficient. Today, the most

successful strategy to improve the efficiency implies the use of a visible light absorber that

does not affect the surface reactivity of TiO2. O’Regan and Grätzel [34, 35] developed a

dye-sensitised TiO2 solar cell, where the dye component extends the range of the solar

spectrum that can be usefully absorbed to produce electricity. In this approach, hot electrons

are promoted by the dye into the conduction band of TiO2, where they react with molecules

adsorbed on the unaltered TiO2 surface. This successful approach shifts the focus of light

harvesting to the sensitiser, which needs to be stable, feature broadband absorption, high

optical cross-section and also a good overlap with the energy levels of TiO2 in order to

achieve effective electronic interaction. This indirect injection of electrons is very efficient

with ruthenium-based dyes, because the excitation is possible with photons in the visible

range, as shown in Fig. 2.16.

The injection of electrons happens on a time-scale of 10 - 50 fs. However, the trapping of

conduction band electrons and the electron-hole recombination is typically much slower in

the 100s of ps up to a few ns. It is this difference of the injection and back-transfer times,

which gives rise to a high-energy conversion efficiency of dye-sensitised TiO2 solar cells.

Obviously, to study the electron dynamics in the ultrafast fs time domain, the 100 ps time


Au! λ = 532nm"

λ = 355nm"< 10 fs" < 5 ns"

< ns"

< 100 fs"

< 50 fs"

Ru dye"

μs - ms"

TiO2!

e-!

h+!

e-!

e-!

Figure 2.16: Electrons can either be injected directly (355 nm) or indirectly (532 nm) into the conduc-

tion band of TiO2. The relevant transitions are marked by arrows with the corresponding

characteristic timescales. The processes marked with red arrows are accessible by the

IRPP technique [33].

resolution of the IRPP technique is not suited. However, free carriers in the conduction band

or shallow traps give rise to a broad mid-IR (between 1.5 to 15µm) wavelength-dependent

absorption. Hence, this absorption can be used to probe the dynamics of electrons after their

triggering by a laser pump pulse.

The IRPP setup was equipped with a reaction cell in the sample plane, and a mass spectrom-

eter to follow the presence of various species created during chemical reactions, as shown in

Fig. 2.17. Additionally, second- (532 nm) and third-harmonic (355 nm) generation of the

pump Nd:YAG laser is used to allow for indirect excitation via the dye, and direct bandgap ex-

citation, respectively. The signal decay monitored as a function of time allows the free carrier

lifetime to be determined. Self-supported thin wafers of TiO2 (excited at 355 nm) and ruthe-

nium Ru-N719 coated on TiO2 (excited at 532 nm) were investigated under N2 flow to avoid

the presence of electron annihilators, such as O2 and CO2. The excitation of Ru-N719/TiO2

at 532 nm leads to a broadband absorption feature in the mid-IR, see Fig. 2.18. This is due

to the presence of free carriers in the conduction band.

For maximum pump-probe overlap, the highest absorption is detected. This supports the

current understanding that charge injection is very fast. Two models were used to reproduce

the broadband absorption: (i) the Drude model, widely used to fit free carriers in conduction


Synchrotron IR: Camshafts probe pulses

Cell

Unpumped and pumped Transmission

N2

Exhaust

Mass spectrometer

Dig

ital d

ata

acqu

isiti

on

and

proc

essi

ng

SLS reference signal (500MHz)

Vector modulator

Phase-locked loop

Pulsed laser (532nm pump)

Ekspla

Beam dump

Detector

Figure 2.17: The IRPP setup is extended by second-harmonic generation (532 nm) and a mass

spectrometer to follow the created species during chemical reaction [33].

bands, and (b) a Lorentz model with an adjustable offset energy for the description of

free carriers in shallow traps. The absorption α(~ω) given by the latter model is defined

as

α(~ω) =k0

(~ω− ~ω0)2+Γ2 , (2.1)

where k0 is a scaling factor, ~ω is the photon energy, ~ω0 is the offset energy (zero for

the Drude case) and Γ describes the scattering rate. Qualitatively, the best agreement was

reached with the Lorentz model with an offset energy of≈ 80 meV.

However, to make a strong determination of this offset, the measurement would need

to be extended to lower frequencies. Finally, the scaling factors k0(t) of the fits were

described by a two-exponential decay model. Here, the short time decay is associated to the

instantaneous effect of pump-probe overlap, while the other decay with τ= (5.9±1.2) ns

reflects shallow trap electron dynamics. The measured lifetime agrees with values reported

elsewhere [36]. It is ascribed to the relaxation of the electrons within the TiO2, and most

likely to charge trapping. For the case of direct-bandgap excitation, a shorter decay time of

τ= (2.5±0.4) ns was found. This is ascribed to non-radiative recombination of electrons

and holes. Noteworthy, this faster relaxation process is not available in the dye-coated TiO2

system, which renders the lifetime longer. This is one of the main reason why dye-sensitised

TiO2 solar cells provide a high energy conversion efficiency.

In summary, the feasibility of synchrotron-based time-resolved FTIR spectroscopy to study


-12

-10

-8

-6

-4

-2

0

Rela

tive

Tran

smiss

ion

Chan

ge [

%]

0.350.300.250.200.15Energy [eV]

Measurement and Model -100ps 0ps 300ps 1500ps

Figure 2.18: Time dependence of the mid-IR transmission of TiO2 coated with Ru-N719 dye irradiated

at 532 nm at a pulse energy of 6µJ at different pump-probe time delays [33]. The fits

(Lorentz model with ~ω0 = 80 meV) are shown with solid lines. The four distinct drops

are due to changes of the molecular vibrations in the dye.

electron dynamics in TiO2 was demonstrated. The decay processes of electrons generated

by bandgap photo-excitation and those of injected from photo-excited dye have been

examined.

Chapter 3

Direct-Bandgap Gain and Optical

Absorption in InGaAs and Germanium

Contents3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.2 Experimental Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.2.1 Investigated Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.3 The Case of a III-V Laser Material (InGaAs) . . . . . . . . . . . . . . . . . . 38

3.3.1 Direct-Gap Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.3.2 Transmission Measurement . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.3.3 Determination of Carrier Density from Reflection Measurement . . . 41

3.4 Optically Pumped Germanium . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.4.1 Indirect-Gap Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.4.2 Normal-Incidence Measurements . . . . . . . . . . . . . . . . . . . . . . 45

3.4.3 Brewster-Angle Measurements . . . . . . . . . . . . . . . . . . . . . . . 46

3.5 Absorption and Gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.5.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.5.2 Measurement Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

This chapter describes optical gain and loss studies of strained and doped germanium

(Ge) layers directly grown on silicon (Si) substrates. This investigation represents the first

31

32 Chapter 3. Direct-Bandgap Gain and Optical Absorption in InGaAs and Germanium

application of the broadband infrared pump-probe (IRPP) spectroscopy using the setup

described in the previous chapter. Here, the IRPP system was utilised to follow direct-

bandgap (DG) gain and optical absorption in InGaAs and Ge as a function of injected

carrier density, doping and strain. InGaAs serves as a reference system benchmarking

the new approach. The mid-IR reflection is used to identify the plasma frequency of the

(photo-excited and/or doping) carriers, and enables the determination of their density. The

mid- and near-IR transmission spectra are used to study the absorption and population

inversion processes. It is shown that although conditions for direct-gap inversion (and

so, optical gain) in Ge can be reached, the optical amplification needed for lasing does

not occur because of the competing effect of valence intraband (VIB) absorption. The

obtained results were published recently in [37] and are discussed and expanded upon in

this chapter.

3.1 Introduction

Nowadays, despite the impressive increase in component density in complementary metal-

oxide-semiconductor (CMOS) circuits, recent increases in computational power are delivered

with increasing difficulty. [38]. Apart from the advances in computational methods, such as

parallelism and smart caching, the main potential for increasing computer performance in

the future lies in the realisation of fast and low-latency on-chip communication methods.

Currently, this so-called inter-core communication is done using electrical signals carried

over sophisticated wire-grids connecting the cores. This type of transfer consumes large

parts of the total processor electrical and cooling power and is likely to increase as future

consumer level multicore architectures go beyond their current multi-core configurations.

These drawbacks can be largely avoided by the use of an all-optical inter-core data transfer

technology: it runs on low-power, provides easy multiplexing of signals at different frequen-

cies, is not susceptible to electronic noise, and removes the need for insulation between

wires as present in the electronic grid setup [39].

This is where the field of Si-photonics comes into play. Today, with the sophisticated tech-

3.1. Introduction 33

nology of Si, two out of the three basic elements for Si-photonics have reached maturity.

Ge-on-Si photodetectors provide high responsivity throughout the visible and near-IR spec-

tral range and offer high bandwidths [40]. Si photo-modulators based on Mach-Zehnder

interferometers1 or based on electro-absorption effects in Ge/SiGe multi quantum wells

provide high performance [41]. The main missing piece for a complete assemblage, however,

is an efficient, cost-effective light-emitter. Ideally, this emitter should be monolithically

integrable with Si to enable high component density, low-costs, and full scalability [42].

This difficulty of light emission arrises from a fundamental characteristics of Si - it is an

indirect-bandgap material, as illustrated in Fig. 3.1(b). In contrast to DG materials, see

Fig. 3.1(a), radiative recombination of carriers is a low probability process, because it

requires an interaction with a phonon to balance the momentum mismatch between the

holes populating the valence bands (Γ-valley) and the electrons populating the L-valley

conduction band. In Si, the main source of recombination is of the non-radiative type,

such as Auger recombination and free-carrier absorption, which is introduced later in this

chapter.

Different approaches may be employed to achieve coherent light emission directly in Si or in

Si compatible material platforms [39]: Raman-lasing in Si, defect implantation and the rare-

earth-doping of Si, zone folding in SiGe superlattices, the epitaxial growth of laser materials

onto Si, and Si-based quantum cascade emitters. The different approaches are discussed in

the following. The current state-of-the-art technique, however, is a hybrid Si laser consisting

of III-V laser materials wafer-bonded onto Si. This represents an effective workaround

solution. Drawbacks concern the high costs, complicated process flows and the lack of an

efficient thermal management at the wafer-interfaces [43].

Stimulated Raman scattering (RS)2, benefiting from the high RS cross-section in Si, can

provide optical gain and lasing in Si as demonstrated first in [44,45]. Following the first

demonstration in pulsed operation, the Si Raman laser was shown to run also in continuous-

1Mach-Zender interferometers split light into two channels and recombine the signals with a phase-shift to

either achieve constructive (1) or destructive (0) interference.2Raman scattering denotes the inelastic scattering of a photon, hence the subsequent emission of a photon

occurs at a slightly different energy


EΓ#EL#

Energy# Γ*valley#

L*valley#

Wave#vector#HH#

LH#

SO#

(a) The momentum of electrons and holes

match in direct-bandgap semiconductors,

such as InP and InGaAs. Efficient light

absorption and emission is possible.

EΓ# EL#

Energy#

L*valley#

Wave#vector#HH#

LH#

SO#

Γ*valley#

(b) In indirect-bandgap semiconductors,

such as Si or Ge, electrons and hole popu-

lations arise at different momentums. Non-

radiative recombination prevails emission

of photons.

Figure 3.1: Typical energy band diagrams for two types of semiconductors, showing the conduction

(blue) and valence (green) bands. The latter consists of light-hole (LH), heavy-hole (HH)

and Split-off (SO) bands.

wave (CW) [46]. This became possible because of the significant reduction of free-carrier

absorption by applying a strong electrical field [46]. However, this principle of light

generation requires an external pump, which may conflict with the need for miniaturisation

and simplicity.

Ng et al. [47] were able to show light-emission at room-temperature from a Si-based diode,

which had been implanted by boron to form a p-n junction. The implantation also gives

rise to dislocations, which modify the local band structure and spatially confine the charge

carriers. In this way, the carrier diffusion, and hence, the non-radiative recombination

path of carriers at point defects in Si is suppressed, and the fraction of radiative emission

increases. Implantation of Si with rare-earths, such as erbium, reveals luminescence at the

telecommunications-wavelength 1.55µm due to transitions within the erbium shown by

Ennen et al. under optical [48] and electrical [49] carrier injection. Emission from such

diodes was first achieved at room temperature by Zheng et al. [50]. Erbium-doped silicon

3.1. Introduction 35

microdisk lasers were demonstrated by Polman et al. [51] and Kippenberg [52] under optical

pumping. Most promising towards an electrically pumped diode laser seems the use of silicon

nanocrystals as sensitisers in a silicon-rich oxide [53,54].

The epitaxial growth on Si of chemically compatible group IV elements such as germanium

(Ge) and tin (Sn) also represents a promising alternative to fabricate a Si based laser

source. One of the approaches investigated in the 1980s was to create DG material from

superlattices obtained by alternating layers of Si and Ge deposited onto a Si substrate [55].

Such Si/Ge monolayer sequences were predicted to feature interband transitions with high

oscillator strengths, emerging from the bulk electron states at the conduction band-minima

at the L- or X-point of Ge and Si, folded back to the centre (Γ-valley) of the Brillouin zone.

The effect of folding has been demonstrated in photo reflection [56]. This concept was

recently revisited by Avezac et al. [57]. Their genetic algorithm predicts SL designs with

strongly enhanced (50x) DG matrix elements. However, no experimental verification is yet

available.

Reinforced by the steady advances in epitaxial growth of Si and Ge by molecular beam

epitaxy (MBE) [58], the quantum cascade laser (QCL) scheme [59] has become a viable

option for making a Si-based laser. The QCL approach indeed resolves the drawback of

the indirect bandgap as it relays on unipolar charge transport without any recombination

across the bandgap. However, it was found that for p-doped structures designed for emission

in the mid-IR (> 100 meV), the lifetime of the relevant states, the current transport, and

waveguide loss parameters are unfavourable compared to the traditional InAs or GaAs

based systems, due to the strong mixing between the diverse states in the valence band,

the low carrier mobility and strong free carrier absorption, respectively [60]. Si-based QCL

structures for the THz were shown to exhibit long lifetimes (> 20 ps) [61], but transport and

waveguide concerns may be severe as well. In fact, neither gain nor lasing structures have

been reported, in spite of intense research conducted in the past years by several groups

inclusive ours.

A plausible and natural approach, however, would be to make use of the DG transition at

an energy of 0.8 eV in Ge, which is close to the C-band telecommunications wavelength of


1.55µm. Due to the recent report of optical gain in Ge mesas by Liu et al. [62], scientific

interest has been raised again for the feasibility of a Ge-on-Si laser. They previously modelled

that by applying tensile strain and simultaneous n-type doping, population inversion in the

direct bandgap of Ge is achievable [63]. Tensile strain decreases the initial energy separation

of 136 meV between the L- and Γ-valleys. At the same time, due to the strong n-type doping

(> 6 · 1019 cm−3), the L-valley is pre-populated by electrons. With strong optical pumping,

efficient injection of electrons in the DG Γ-valley then becomes possible. In this way,

optically [64] and electrically [65] pumped lasing was reported in Ge. Those results seem

ambiguous, however, as will be explained in the results section of this chapter. Optical gain

in biaxially tensile-strained (0.4%) and n-type doped (2 · 1019 cm−3) germanium photonic

wires was reported independently [66]. The direct bandgap in Ge, however, is predicted to

be achieved with very large strain values only, which are 4.2% in the uniaxial [67] and ∼2%

in the biaxial [63] case, which is both technologically challenging. Micromachining-based

technologies to achieve such large values are currently being developed, and uniaxial strain of

0.98% and biaxial strain of 0.82% were recently reported [68].

Nevertheless, gain and optical absorption features in Ge have not been fully characterised

experimentally, despite a number of theoretical models and approximations being put

forward. The reported doping levels in the optically pumped Ge structures (1 · 1019 cm−3) as

well as the pumping-intensities were much lower than predicted by the model, demonstrating

the need for improved understanding of the mechanisms playing a role in the emission, and

experimental investigation of the relevant parameters, such as the balance between gain

and loss. This is addressed below.

3.2 Experimental Overview

The IRPP system is uniquely suited for studying the dynamics of gain and loss in optically

pumped samples. Its large spectral range gives access to and correlates the physics of the

carrier population inversion (at ∼1 eV), the free-carrier absorption of the injected carriers

(at ∼100 meV), and also the broadband absorption effects between 0.1 - 1 eV. In this way, as

3.2. Experimental Overview 37

shown in Fig. 2.14, physical phenomena such as Auger recombination, carrier diffusion, and

electron/hole recombination can be investigated simultaneously, under precisely the same

conditions of e.g. pumping, doping and strain.

3.2.1 Investigated Samples

Using low energy plasma-enhanced chemical vapour deposition, 1 to 2µm thick Ge layers

was grown on Si substrates [69]. This series of samples were n-type doped using phospho-

rous, and strain enhanced by rapid thermal annealing [70].

The In0.53Ga0.47As samples were grown on [001]-InP substrates by molecular beam epitaxy

(MBE), with elemental Si supplied by a effusion cell providing n-type doping [71]. Doping

densities from the not-intentionally-doped (NID) limit of 2.1 · 1015 cm−3 to 2.1 · 1019 cm−3

were prepared. Material composition and doping were determined by high-resolution x-

ray diffraction (XRD), Hall and secondary ion mass spectrometry (SIMS) measurements,

respectively [71].

A summary of the investigated samples is given in Table 3.1.

Table 3.1: Characteristics of the Ge and InGaAs samples. For not-intentionally-doped (NID) samples,

the maximum background doping is < 1 ·1015 cm−3 for Ge and < 1 ·1016 cm−3 for InGaAs.

For not-intentionally-strained (NIS) samples, the biaxial tensile strain is < 0.05%.

Sample Thickness (µm) Doping ( cm−3) Strain Growth Number

Ge#1 1.0 NID NIS 56426

Ge#2 1.0 2.5 · 1019 cm−3 NIS 56429

Ge#3 1.9 NID 0.25% 8300

InGaAs#1 4.1 NID NIS Ep939

InGaAs#2 1.0 2.1 · 1019 cm−3 NIS Ep962

InGaAs#2 1.0 5.3 · 1018 cm−3 NIS Ep963


3.3 The Case of a III-V Laser Material (InGaAs)

3.3.1 Direct-Gap Band Structure

When InGaAs is pumped optically, electrons are vertically excited across the DG, which

results in a non-equilibrium distribution of electrons in the Γ-valley of the conduction band

(CB), and a distribution of the holes in the valence bands (VB). The co-existence of electrons

and holes in the Γ-valley leads to a population inversion that changes the DG absorption

αDG into DG gain (i.e. αDG < 0), see Fig. 3.2.

HH"LH"

SO"

EFe"

EFh"

Γ"

αDG"<"0"αDG">"0"

αVIB"

EDG"

0"

Figure 3.2: Direct-bandgap gain or absorption is achieved in InGaAs, depending on the photon

transition energy. Intraband absorption in the valence band is present at the same time.

This is described by the Bernard-Duraffourg (BD) condition [72], which states that the quasi-

Fermi energy levels of the conduction and valence band have to be separated by more than

the direct-bandgap energy EDG in order to achieve optical gain, and reads

EFc − EF v > EDG, (3.1)

where EFc and EF v are the quasi-Fermi energy levels for the two bands. The BD condition

is discussed in detail in Sec. 3.5. Gain is achieved for all transition energies E in the range

EDG < E < EFc − EF v.

In addition to recombination with electrons (a bipolar process), the holes may undergo

unipolar vertical transitions between the light-hole (LH), heavy-hole (HH) and split-off

3.3. The Case of a III-V Laser Material (InGaAs) 39

(SO) bands of the VB driven by photo-excitation. The high absorption cross-section of

these unipolar, momentum-conserving transitions results in a strong broadband valence

intraband (VIB) absorption, that can be comparable in strength to DG absorption. The

measurement of the transmission through such an optically-excited sample reveals the

contributions from the DG absorption and/or gain, and the hole-induced broadband MIR

absorption. Finally, the charge carriers (induced by doping and/or photo-injection) give rise

to a plasma, whose frequency depends on the density and effective masses of the carriers.

The plasma response of the carriers is described by the complex dielectric permittivity of

the material, and manifests itself as a well-defined minimum in the reflection spectra, at the

characteristic plasma frequency ωp.

3.3.2 Transmission Measurement

Figure Fig. 3.3(a) shows the normalised broadband transmission spectra of the InGaAs#1

sample using the parabolic-mirror setup (c.f. Fig. 2.8(a)), when pump and probe pulses

are in full overlap. The unpumped spectrum shows a 725 meV DG absorption edge, the

expected Fresnel losses of ≈57%, and thin-film interference effects with an oscillation period

matching the InGaAs layer thickness. The pumped spectrum for a peak pump intensity of

150 MW cm−2 using a 200µm spot is considerably richer in terms of features, and exhibits

(i) a strong absorption band below 300 meV, (ii) a constant broadband absorption between

200 - 650 meV, and (iii) a recovery of the reflection-limited transmission above 650 meV,

with only a small net gain at 740 meV.

However, this gain is more clearly visible in Fig. 3.3(b), where the experiment is repeated

using a micro-focus setup (as shown in Fig. 2.8(b)). Here, the smaller illuminated sample

area (35µm pump) minimises carrier recombination by reducing the possibility of stimulated

emission. It was this effect that resulted in early gain-clamping in the material illuminated

by the bigger pump spot in the parabolic-mirror setup.

The reduced transmission below 300 meV originates from both the Drude-type free carrier

absorption (FCA) of the optically injected carriers and the increase in refractive index, as


100

80

60

40

20

0

Tran

smiss

ion

(%)

1.00.80.60.40.2Energy (eV)

pum

p-in

d. a

bsor

ptio

n

FCA Absbandgap

renormalization

InGaAs#1 Unpumped Pumped

(a) With the parabolic mirror setup (pump spot of

200µm), only a marginal gain is achieved upon

pumping with an intensity of 150 MW cm−2.

100

80

60

40

20

0

Tran

smiss

ion

(%)

1.11.00.90.80.70.60.5Energy (eV)

tota

l gai

n

pum

p-in

d. a

bsor

ptio

nne

t ga

in

InGaAs#1 unpumped

-50ps 250ps 0ps 450ps 100ps 950ps

(b) With the micro-focus setup (pump spot of 35µm),

clear optical amplification exceeding the reflection-

limited transmission is achieved.

Figure 3.3: Normalised IR transmission spectra for sample InGaAs#1.

discussed below.

The constant broadband absorption spanning between 300 meV up to higher energies is

consistent with VIB absorption [73]. The broadness of VIB absorption originates from the

superposition of the three LH-HH, LH-SO, and HH-SO transitions, and is further enhanced

by impurity and carrier-carrier scattering [74]. As shown in [73] [74], this VIB absorption

extends up to the DG energy.

The increase in transmission at energies above 650 meV is due to the growing DG inver-

sion, which is superimposed on the VIB absorption. The onset of this increase indicates a

bandgap renormalisation of up to 75 meV with respect to the unpumped absorption edge,

as shown in Fig. 3.3(a). Renormalisation effects of this order have been measured in

doped InGaAs [75] and optically excited materials [76]. When the DG gain exceeds the

pump-induced VIB absorption, the InGaAs material provides optical amplification, as shown

in Fig. 3.3(b). Here, the transmission rises up to ≈90% when pump and probe overlap

maximally. If the optical amplification is high enough to match mirror loses, then the system

lases.


3.3.3 Determination of Carrier Density from Reflection Measurement

Free carriers of a given density and effective mass in a semiconductor have a well-defined

plasma frequency ωP , given by the following expression

EP = ~ωP = ~p

NT e2/mPε, (3.2)

as described in [77]. Here, NT is the total number of carriers, mP is the reduced mass (which

is taken as the weighted average of the masses of electron and different types of holes) and e

is the elementary charge. This follows from a simple Drude model of the motion of electrons

in the semiconductor material. The plasma response of the carriers enters into the (complex)

dielectric permittivity εr of the material

εr(~ω) = ε∞ ·

1−τS(ωP)2

τSω2+ iω

(3.3)

where ε∞ is the DC permittivity of the material and τS is the scattering time [78]. The

permittivity undergoes a phase change close to ωP . Hence, the optical properties of the

material differ above and below ωP . While above ωP , the semiconductor acts as a dielectric

material, below ωP its behaviour follows that of a metallic conductor. The transition from

one state to the other is accompanied by a minimum in the reflection spectrum, which is

used to measure and identify ωP .

The reflectivity R of a semiconductor surface exposed to air (vacuum) is given by

R=(n− 1)2+κ2

(n+ 1)2+κ2 , (3.4)

where n is the real index of refraction and κ is the extinction coefficient [77]. These parame-

ters are derived from the complex relative permittivity ε = ε1+ iε2 by

n=

r

1

2

p

ε21+ ε

22+ ε1

κ=

r

1

2

p

ε21+ ε

22− ε1

,

(3.5)

where ε1 = Re[ε] and ε1 = Im[ε] are the real and imaginary part of ε, respectively.

The ratio of pumped and unpumped reflection is then defined as differential reflection. A

characteristic blue-shift of the reflection minima with increasing carrier density is shown


in Fig. 3.4 for an InGaAs bulk material for different carrier densities. Here, ε∞ = 11.56,

mp = me = 0.041 ·m0, and tS= 20 fs were used.

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Pum

ped

/ Un

pum

ped

1.41.21.00.80.60.40.20.0Energy [eV]

Carrier densities [ cm-3 ] 1e19 2e19 3e19

4e19 5e19 1e20 2e20 4e20Energy Blueshift

Figure 3.4: The ratio of pumped and unpumped reflection (differential reflection) for bulk InGaAs

shows a characteristic blue-shift of the reflection minima with increasing carrier density.

In the case of thin-film layers grown on substrates, however, multiple-path reflections and co-

herent superposition have to be taken into account, c.f. Fig. 3.5.

Thin%film))))))))

Substrate)rSA)

tLS)

rLS)

rAL)

Coherent)Superposi7on) tLA)

tSL)tLA)×A)Probe)

Figure 3.5: Sketch of the multiple-path reflection. In the thin-film layer, coherent interaction takes

place, while the reflection on the back of the substrate is added incoherently.

The total reflectivity Rtotal is modelled by the FP model

Rtotal = A ·

tAL t LS rSA tSL t LA

2+

rAL +tAL rLS t LA · exp (2iδL l)1− rLA rLS · exp (2iδL l)

2

, (3.6)

where A accounts for the spread, i.e. divergence, of the beam on its path through the

substrate, t x y and rx y are the amplitude transmission and reflection coefficients at the

different interfaces (Air, Layer for the active material, and Substrate), respectively, and


δL takes into account the attenuation and phase shift during the path length l in the

active layer. In summary, the first part represents the non-coherent summation fully down

to the substrate-air interface and back, and the second part accounts for the multiple-

path coherent interaction in the active layer. The propagation constant δL is defined

as

δL =ωpεr

c. (3.7)

Fig. 3.6(a) shows an unpumped and pumped normalised broadband reflection spectra

from the n-doped InGaAs#2 thin-film layer grown in InP (n = 3.1). The energy of the

reflection minima clearly blue shifts upon increasing pumping. The ratio of pumped and

unpumped reflection spectra at different pumping intensities is shown in Fig. 3.6(b) (dots).

The double feature in the ratio RP/RU originates from the two ωP conditions, where the

first is the unpumped case and depends only on the dopant density ND , while the second

depends on the sum ND + NP . This series of reflection measurements for each sample

allows for the fit of the plasma-frequencies for the doped (ND) and photoexcited NP carrier

densities as the only two fitting parameters. The model yields excellent fit to the measured

ratio, and later on enables the correlation of carrier density with the determined gain and

losses.


1.0

0.8

0.6

0.4

0.2

0.0

Norm

aliz

ed R

eflec

tanc

e

0.400.350.300.250.200.150.10Energy [eV]

InGaAs#2 Unpumped Pumped

(a) An example of the absolute reflection spectra that

are used to generate the ratio spectra.

3.0

2.5

2.0

1.5

1.0

0.5

0.0

R p /

Ru

0.450.400.350.300.250.200.150.10Energy [eV]

InGaAs#2Pump Intensity ( MW/cm2 )

3 13 63 284 Drude Reflection Model

(b) The differential reflection spectra are fitted with

a Drude-model.

Figure 3.6: The IR reflection spectra, here for the InGaAs#2 sample, allow for the determination of

the optically-injected carrier densities.

3.4 Optically Pumped Germanium

3.4.1 Indirect-Gap Band Structure

Contrary to the DG III-V material as described in the previous section, Ge is of indirect-

bandgap (IG) type. This is illustrated in Fig. 3.7. The relevant section of the conduction-band

(CB, red) consists of two distinct minima valleys, which are the Γ- and the L-valley. The

structure of the valence band is analogous to that of InGaAs. N-type doping and tensile

strain act to bring the quasi-Fermi energy level of the CB closer to the minimum of the

Γ-valley.

The physics of direct-gap inversion and VIB absorption, however, is for Ge very similar

as for InGaAs. What differs, is that optical injection of carriers does not automatically

lead to inversion, because the L-valley in the CB has to be filled first. The high (2 ·

1020 cm−3) injected densities used to generate a population inversion at the direct-gap

simultaneously provide a proportionately high density of holes, creating a strong competing

VIB absorption.

3.4. Optically Pumped Germanium 45

HH"LH"SO"

EIG"

EFe"

EFh"

Γ"

αDG"<"0"αDG">"0"

αVIB"

L"

EDG"

0"

Figure 3.7: Upon pumping, the lower L-valley is filled first, which does not lead to population

inversion at the direct-bandgap. Only for very strong pumping, the Γ-valley is being

populated. However, also strong Intraband absorption in the valence band is then present.

3.4.2 Normal-Incidence Measurements

Normal-incidence (NI) broadband transmission and reflection spectra of sample Ge#1 at a

pump intensity of approximately 1 GW cm−2, as published in [22], are shown in Fig. 3.8(a)

and Fig. 3.8(b), respectively. To access the full bandwidth, two detectors are used and shown

in combination.

The pump-induced VIB absorption extends linearly from 350 meV up to the DG at 775 meV.

The strength of the VIB absorption is about 3500 cm−1. Above 830 meV, bleaching of the

DG absorption builds up, and thus the normalised transmission starts to exceed 100%.

Obviously, such a high VIB absorption suppresses any population inversion related gain

and therefore no optical amplification is observed. Due to the NI configuration, thin-film

interference effects create strong FP oscillations with a period of 150 meV. These oscillations

make the identification of a gain feature difficult and ambiguous, and motivate the move to

a Brewster-angle setup, described below.

The analysis of the reflection spectra follows Eq. 3.6. The injected carrier density is deter-

mined to be NP =2.5 ·1020 cm−3. The model gives a good fit of the measured data, as shown

in Fig. 3.8(b).


1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

Nor

mal

ized

Tra

nsm

issi

on

0.90.80.70.60.50.40.30.2

Energy [eV]

Vigo-MCT Teledyne-Judson InSb

(a) Normalised transmission spectrum.

2.0

1.5

1.0

0.5

0.0

Nor

mal

ized

Ref

lect

ion

0.90.80.70.60.50.40.30.20.1

Energy [eV]

Measurement Vigo-MCT Teledyne-Judson InSb

Model

(b) Normalised reflection spectrum.

Figure 3.8: Broadband transmission- and reflection-spectra of sample Ge#1. The spectra are com-

bined of data from the measurements with two detectors with different spectral coverage.

The transmission shows the strong VIB absorption, which extends from 350 meV up to

the DG [22].

3.4.3 Brewster-Angle Measurements

For an accurate determination of DG gain and absorption, samples Ge#1 to #3 are measured

in Brewster geometry. Here, the p-polarised light, i.e. the light whose polarisation lies in

the plane defined by the surface normal of the interface and the light propagation direction,

is not reflected. Hence, the angle between light propagation direction and the sample is

optimised to suppress reflection from the second interface, i.e. the boundary between the

thin-film and the substrate. Such a measurement for the case of sample Ge#1 is shown

in Fig. 3.9. The flat part of the unpumped spectrum below 740 meV is normalised to

100% transmission. As clearly evident, FP oscillations are efficiently removed from the

measurement.

The spectra differ significantly from the above shown InGaAs ones. First, the increase

of the transmission above the reflection-limited transmission during pumping is not even

achieved for maximum pump-probe overlap (∆ t = 0 ps). This means that no net gain,

i.e. optical amplification, is present in the structures. This can be directly attributed to

strong pump-induced VIB absorption. In fact, the cross-sections for the VIB absorption in

3.5. Absorption and Gain 47

100

90

80

70

60

50

40

Tran

smiss

ion

[%]

1.00.90.80.70.60.5Energy [eV]

Ge#1Measurement

P U

-150ps

-100ps

-50ps

0ps

Figure 3.9: Normalised IR transmission spectra for sample Ge#1 at an intensity of 285 MW cm−2

measured under Brewster geometry. The time-dependence reflects the overlap of optical

pump and probe, which results in measurements at different effective carrier densities.

[37]

Ge and InGaAs are practically identical, given the similar effective masses of the holes in

both systems. However, the absorption in the Ge samples is much stronger, because they are

examined under conditions of higher electron/hole densities needed to establish inversion of

the carriers at the Γ-point. In contrast, in photoexcited InGaAs, the gain from the inversion

rises faster than the induced VIB absorption, and optical amplification is achieved readily.

In Ge, the VIB absorption loss always exceeds the gain that can be generated from the

inversion.

3.5 Absorption and Gain

3.5.1 Model

For a quantitative assessment of the absorption and the gain, the total absorption α(ω)

needs to be modelled:

α(~ω) = αDG(~ω)

fv(~ω)− fc(~ω)

, (3.8)


where ~ω is the energy of the photon, fv and fc are the Fermi-Dirac (FD) distributions for

valence band (VB) and conduction band (CB), respectively. The optical absorption in the

parabolic approximation of DG transitions reads

αDG(~ω) = Kabs

p

~ω− EDG, (3.9)

where Kabs is defined as

Kabs =q2 x2

vc

λ0ε0hnop

2mr

h

3/2

, (3.10)

where q is the electric charge, xvc is the optical matrix element, and nop is the refractive

index [79].

As a direct consequence, optical gain, which corresponds to negative optical absorption, is

achieved when

fc(~ω)− fv(~ω)> 0. (3.11)

The FD distributions are defined as

fc(~ω) =1

1+ exp

(EC(~ω)− EFc)/kB T

fv(~ω) =1

1+ exp

(EV (~ω)− EF v)/kB T

(3.12)

where EFc and EF v are the quasi-Fermi energy levels for the conduction and valence

band, respectively. They are calculated from the number of carriers in a fermi-sphere

as

EFc(N) =~2

2me(3π2Ne)

2/3

EF v(N) =~2

2mh(3π2Nh)

2/3,

(3.13)

where the factor 2 arises from spin degeneracy. The number of carriers is Ne = NP + ND for

electrons and Nh = NP for holes, where NP is pumping and ND doping density, and me and

mh are the effective masses of electrons and holes, respectively. The latter is a reduced mass

of the light- and heavy-hole masses, weighted under the parabolic band approximation [80],

which reads

mh =m3/2

HH +m3/2LH

m1/2HH +m1/2

LH

. (3.14)


The position of the energy levels EC(~ω) and EV (~ω) are defined as

Ec(~ω) = EDG +mr

mc(~ω− EDG)

Ev(~ω) =−mr

mv(~ω− EDG).

(3.15)

The reduced effective mass mr is calculated as

mr =

1

me+

1

mh

−1

, (3.16)

It follows, that Eq. 3.11 can also be expressed in terms of the position of the quasi-Fermi

energy levels, i.e.

EFc − EF v > EDG, (3.17)

where EFc and EF v are the quasi-Fermi energy levels for the two bands. This is the earlier

introduced Bernard-Duraffourg condition [72].

3.5.2 Measurement Fit

For the determination of the loss and gain created at the DG transition, the transmission

spectra shown in Fig. 3.3(b) and Fig. 3.9 are fitted to Eq. 3.8. The fitted parameters are

sample temperature T , direct-gap energy EDG, VIB absorption, and the variation of electron

mass m∗ with carrier density N .

Like in the case of the Drude-model for the reflection spectra, the individual reflection coeffi-

cients R at the interfaces are derived from the complex permittivity. Thin-film interference,

i.e. FP oscillations, are accounted for as well. The elevated temperature is deduced from

the absorption edge of the transmission spectra with an unpumped probe pulse during

the pump/probe measurement. It is found to be ∼ 400 K and is subsequently used in the

Fermi-Dirac distribution. The VIB absorption in Ge is found to depend linearly on ~ω. In

the case of InGaAs (with much lower carrier densities), it appears spectrally flat, consistent

with the behaviour observed in low intensity pumped Ge samples. It is the stronger Auger

recombination in InGaAs, which hampers the achievement of similarly high injected densities


as in the strongly pumped Ge. The VIB contribution to the spectra is fitted by looking at the

low-energy end of the spectrum.

The measured InGaAs#1 transmission (as introduced in Fig. 3.3(b)) and fit are shown in

the left panel of Fig. 3.10.

10000

8000

6000

4000

2000

0

-2000

Abso

rptio

n Co

effic

ient

[cm

-1]

1.00.80.60.4Energy [eV]

InGaAs#1, Δτ = 0ps Optical Amplification Direct-Gap Gain

Unpumped αDG (U)

Pumped αtotal (P) αVIB (P) αDG (P)

100

80

60

40

20

0

Tran

smiss

ion

[%]

0.5 0.6 0.7 0.8 0.9 1.0 1.1Energy [eV]

Meas. P U

Model P U

Figure 3.10: Left Panel: The JDOS model yields an excellent fit to the transmission spectra of sample

InGaAs#1. Right panel: The differential direct-gap (DG) gain is highlighted in yellow.

Due to the much lower pump-induced VIB absorption, optical amplification is achieved

(highlighted in orange) [37].

The unpumped and pumped transmission are well reproduced both below and above the

direct-gap energy. The FP oscillations are well matched with the sample thickness of 4µm.

In the right panel of Fig. 3.10, the contributions to the overall gain and absorption curve

are sketched individually. The VIB absorption is modelled as constant absorption with a

value of αV IB =1000 cm−1. The direct-gap gain −αDG reaches approximately 1750 cm−1 at

0.85 eV. The maximum net gain is the given by the sum of αV IB and −αDG to approximately

750 cm−1. The ranges of optical amplification and gain are highlighted as by orange and

yellow colors, respectively.

The transmission of sample Ge#1 (as introduced in Fig. 3.9) and fit are shown in the

left panel of Fig. 3.11. The conversion in the centre panel to absorption coefficient re-

veals a maximum value of up to 10000 cm−1, due to VIB absorption. Note that this value

exceeds even the DG absorption, showing that VIB is a significant process that must be


accounted for in any full treatment of optical gain and loss analysis. As evident, inver-

sion, and hence, also gain, is reached in the direct-gap transition, which is highlighted

in yellow. However, due to the strong pump-induced VIB absorption there is no optical

amplification.

10000

8000

6000

4000

2000

0

-2000

Abso

rptio

n Co

effic

ient

[cm

-1]

1.00.80.6Energy [eV]

Meas. Model αDG (U) αVIB (P) αDG (P)

Ge#1, Δτ = 0ps10000

8000

6000

4000

2000

0

-2000

Abso

rptio

n Co

effic

ient

[cm

-1]

1.00.90.80.70.60.5Energy [eV]

Meas. P U

Model P U

-150ps

-100ps

-50ps

0ps100

90

80

70

60

50

40

Tran

smiss

ion

[%]

1.00.90.80.70.60.5Energy [eV]

Ge#1Meas.

P U

Model P U

-150ps

-100ps

-50ps

0ps

Figure 3.11: Left Panel: The JDOS model yields an excellent fit to the transmission spectra of sample

Ge#1. Center Panel: The conversion yields absorption coefficients up to 10000 cm−1.

Right panel: The differential direct-gap (DG) gain is highlighted in yellow. However,

due to the strong pump-induced VIB absorption there is no optical amplification [37].

3.5.3 Discussion

The relation between pumping intensity and photoexcited carrier density is given in Fig. 3.12.

The vertical offset in carrier densities between the three InGaAs samples is due to the different

intrinsic doping levels. The measured non-linear behaviour between photoexcited carrier

density and pumping intensity is due to Auger recombination and is described further in

detail in [37]. The considerably higher carrier density in Ge compared to InGaAs for a

given pumping level, is due to the significantly different Auger recombination parameters,

which are rAug,Ge = 1 · 10−30 cm6 s−1 for Ge and rAug,InGaAs = 1 · 10−28 cm6 s−1 for InGaAs,

respectively [81].

The measured VIB absorption can be expressed as a function of determined carrier densities,

see Fig. 3.13. The observed VIB absorption is well described by a linear absorption cross-


1.5x1020

1.0

0.5

0.0Tota

l Car

rier D

ensit

y N T

[ c

m-3

]

150100500Pumping Intensity [MW/cm2]

InGaAs#1 InGaAs#2 InGaAs#3 Ge#1 Ge#2

Figure 3.12: The determined non-linear relation between photoexcited carrier density and pumping

intensity is due to Auger recombination. Partly shown in [37].

section model

αV IB(EDG) = σeNe +σhNh, (3.18)

where σe and σh are the cross-section of the electrons and holes, respectively. In the case

of the undoped samples, the electron and hole densities correspond to the photoexcited

carrier density, i.e. Ne = Nh = NP . For the n-type doped samples, the electron density

has to be taken as the total carrier density NT . From this figure, it is clear that σh σe,

because the absorption scales linearly with NP and not NT . Fitting to the experimental data

gives σh = 3.8 · 10−3 nm2 and σh/σe > 10, which is in good agreement to values reported

elsewhere [82]. The hole absorption cross-section is much higher, because it is related to

vertical transitions between the valence subbands, while this is not the case for the electrons.

As can be seen in Fig. 3.13, the absorption cross-section in the case of strained Ge is slightly

reduced. It should be noted that the higher absorption observed in the Ge samples is not

due to any inherently higher absorption cross-section in the Ge, but rather is due to the far

higher hole density that is reached in these samples, as they are optically pumped to the

high levels needed to reach the inversion condition. This is an unwanted consequence of the

present scheme to create a high density of electrons at the Γvalley-in the CB. As a far more

attractive alternative, high doping and/or strained structures would increase this density

without the parasitic high hole density.


0.60.0

5000

4000

3000

2000

1000

0Pum

p-in

duce

d VI

B Ab

sorp

tion

[ cm

-1 ]

1.61.20.80.40.0NT x 1020 [ cm-3 ]

ND

ND

Ge#1 Ge#2 Ge#3

InGaAs#1 InGaAs#2 InGaAs#3

Linear Fits

Figure 3.13: The measured pumped-induced valence intraband (VIB) absorption is linear with respect

to the injected carrier densities. Part of the data is shown in [37].

The measured peak gain is shown as a function of determined carrier densities, c.f. Fig. 3.14.

Both n-type doping and strain decrease the onset threshold of the peak gain, as visible

from the measurement, and also confirmed by the JDOS model. However, even though

a high gain of up to (850±50) cm−1 is achieved in for Ge, the simultaneously created

VIB absorption is always much stronger. For injected carrier densities of approximately

1 · 1020 cm−3, the VIB absorption is typically x10 higher than the gain. This demonstrates,

that optical amplification is not possible in any of the three investigated samples. In fact,

the VIB absorption is already more than > 500 cm−1 at the predicted gain onset densities of

around 0.3 · 1020 cm−3.

Hence, in Ge-on-Si, carriers excited by optical pumping lead to a strong direct-gap gain.

However, optical amplification is suppressed by the much stronger pump-induced VIB

absorption. This contradicts the straight-forward explanation of lasing in Ge-on-Si put

forward in [64]. In that article, the described pumping conditions correspond to an optically

injected carrier density of around 1 · 1019 cm−3, which is well below the reported density

needed for the onset of gain. It is therefore unclear, how optical transparency (as suggested

by the Fabry-Pérot oscillations) can be achieved, given that the pumped-induced absorption

is at least an order of magnitude stronger. Also, the slope of their reported emission versus

pump power only changes by a factor of ∼ 4 above threshold. In a standard laser system,


1000

800

600

400

200

0

Peak

Gai

n [

cm-1

]

2.01.51.00.50.0

NP x 1020 [ cm-3 ]

Measurement Ge#1 Ge#2 Ge#3

Model Ge#1 Ge#2 Ge#3

Figure 3.14: The measured pumped-induced VIB absorption is linear with respect to the injected

carrier densities. Part of the data is shown in [37].

this ratio is normally well-above 104. It is only with a much larger strain than the 0.24%

reported, that peak gain could possibly overcome the pumped-induced absorption. This

could be due to the applied processing, which uses a selective regrowth of micron-sized Ge

waveguides onto Si. As pointed out in [83], a high point defect density in epitaxially grown

Ge close to the Si substrate interface gives rise to increased non-radiative recombination

between electrons from the L-valley and holes, which is due to the energetically closely

placed trap states below the L-valley. This favourably increases the ratio of electrons in the Γ-

with respect to the L−valley, and was observed to lead to an increased photoluminescence

(PL). Due to high surface-to-volume ratio in the Ge micro-cavities reported in [64], this

effect is expected to play a major role as well, which could be a further explanation for the

observed lasing.

In summary, the current understanding of the direct-bandgap physics in Ge is improved by

the experimental data and their interpretation introduced above, and will help the quest for

a light-emitting structure directly implemented on Si.

Chapter 4

Gain and Loss of mid-IR Quantum Cascade

Structures

Contents4.1 Quantum Cascade Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.2 Overview on Measurement Techniques . . . . . . . . . . . . . . . . . . . . . 63

4.3 High-Performance Quantum Cascade Laser . . . . . . . . . . . . . . . . . . 66

4.3.1 Device Design and Processing . . . . . . . . . . . . . . . . . . . . . . . . 66

4.3.2 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.3.3 Correlation to Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.4 Topical Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.4.1 Empty Cavity Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.4.2 Broadband Quantum Cascade Lasers . . . . . . . . . . . . . . . . . . . . 80

4.4.3 Quantum Cascade Structures based on Quantum Dashes . . . . . . . 81

This chapter is devoted to the gain and loss analysis of quantum cascade lasers (QCLs).

Here, synchrotron infrared is used to characterise active material embedded in micron-

sized waveguide structures. The measurements are then used to test two widely-used

models. These results were recently published in [84]. In addition, the investigation of

polarisation-resolved losses in typical mid-IR waveguides is added. A short discussion of gain

55

56 Chapter 4. Gain and Loss of mid-IR Quantum Cascade Structures

investigations in advanced QCL structures with quantum dashes, as well as multi-section

broadband QCL devices, concludes this chapter.

Despite the impressive advances made in QCL research over the last decade in terms of

wavelength coverage, gain bandwidth, emission efficiency, as well as operation temperature,

the extent of quantitative methods to assess the device’s main optical properties – gain and

loss – are still underdeveloped. There is, therefore, a need for methods that deliver significant

parameters for benchmarking models and simulation tools, such as Monte Carlo, density

matrix formalism and non-equilibrium Green’s function theory.

4.1 Quantum Cascade Laser

QCLs are semiconductor heterostructures emitting light in the mid- to far-IR. Lasing is

achieved from transitions between electron subbands which are defined by the the confining

potential from quantum wells. They were first realised in 1994 by Faist et al. [59], emitting at

4.2µm. The electron states and subbands are engineered by carefully designing the quantum

well and barrier widths, their order, and the respective materials in these heterostructures.

The transition energy between the states then is purely a result of design, and opens up

the path for flexible emission throughout the mid-IR region [85]. QCLs are fully unipolar

devices, because only a single type of carrier, the electrons, undergoes transitions. As

a consequence, the band curvatures of the initial and final states is the same, as shown

in Fig. 4.1. This results in the joint density of states of QCLs being comparable to an

atomic transition. QCLs are essentially transparent below and above the transition energy

range.

In contrast to a QCL, the emission of an interband laser is mainly defined by the direct-gap

energy of the material, and thus cannot easily be engineered to specific energies [86].

Light generation in interband systems is due to the recombination of electrons and holes

in a forward biased bipolar junction. Fundamental changes of the transition energy in

an interband laser are still possible, but require laborious efforts, such as the change of

the material alloy, or the engineering of strain. Luckily, the use of a heterostructure offers

4.1. Quantum Cascade Laser 57

the possibility to slightly engineer the transition energy as well [87]. Nevertheless, the

availability of such sources in the mid-IR is limited. Most of these diode laser sources cover

the visible and near-IR range due to interband emission over the bandgap, where they have

proven energy- and cost-efficient operation. It is only the lead-salt material system, which

provides emission across the bandgap between 3 - 20µm [88], at however limited power and

reliability. On the other side, QCLs cannot reach-up to the NIR, because the quantum wells

are not deep enough to confine such high-energy transitions.

E12$+$E&$+$E1fe$$

E12$

Efe$

E&$

E$ E$

k//$ k//$

E$ E$E12$ E12$

Intersubband$ Interband$

Figure 4.1: Left panel: In the intersubband case, the electron undergoes a transition between con-

duction band states, which have the same in-plane dispersion. The joint density of states

is comparable to a typical atomic transition. Right panel: In the interband case, the

transition occurs between electrons in the conduction band and holes in the valence band

with opposite curvature of the dispersion. Adapted from [78].

The theoretical foundation of light amplification in semiconductor heterostructures dates

back to Kazarinov and Suris in the 1970s [85,89]. They described the transitions between

electron states in quantum wells of an electrically biased superlattice. A further milestone

towards the realisation of a QCL, was the first observation of an infrared transition between

quantum well states in GaAs/AlGaAs heterostructures in absorption measurements by

West and Eglash [90]. They demonstrated a large oscillator strength f of 12.2, defined


as

f =2me

~

zi j

2 E j − Ei

~, (4.1)

where me is the free-electron mass, ~ is the reduced Planck constant, zi j is the dipole matrix

element, and E j and Ei are the energies of the upper (state number j) and lower (i) quantum

well states, respectively. The dipole matrix element zi j for the case of an infinite quantum

well is defined as

zi j =Lw

π2

8i j

(i2− j2)2∝Ç

me

m∗, (4.2)

where Lw is the width of the quantum well, and m∗ is the effective mass. In the design

by West and Eglash, zi j was found to reach almost 2 nm. It is the beneficial ratio of me

m∗

in semiconductors (e.g. me

m∗u 15 for GaAs [90]) which leads to these large dipole matrix

elements and oscillator strengths. Furthermore, the oscillator strength f increases mono-

tonically for transitions between higher states in the quantum well. As shown in Chap. 5, a

direct consequence of the large dipoles are the strong non-linear coefficients in QCLs. In

addition, West and Eglash also showed that the transition energy is directly depending on the

quantum well width, which confirmed the possibility of engineering such transitions. These

characteristics, together with the proposed design of Kazarinov and Suris, were therefore

expected to lead to an efficient light-emitting device.

However, Choi et al. [91] demonstrated that the main condition for lasing, which is popula-

tion inversion between the upper and lower laser states, could only be achieved in an unstable

electrical regime along with high electric fields in such a superlattice. Intersubband light

emission between 10 - 20 meV from a superlattice was demonstrated shortly after by Helm

et al. [92], however, still at the lack of population inversion.

It was then the inclusion of graded regions with n-type doing outside of the active quantum

wells, shown in Fig. 4.2, which enabled the achievement of a population inversion and led

to the first QCL realisation in the InGaAs/AlInAs system [59]. Here, the carrier injection

and relaxation regions were properly engineered, and allowed the structure to align the

quantum well levels in an electrically stable region.

Furthermore, the technical achievement of a proper molecular beam epitaxy (MBE), shortly

shown before [93], with which accurate nm-sized layers could repeatedly be grown with


7.2. ACTIVE REGION: FUNDAMENTAL CONCEPTS 119

roughly speaking, each cell can be divided in a gain region and an injection/relaxation re-gion. The gain region is the structure that will create and maintain a population inversion

3

2

1

!32

!2!32 > !2

Active region Relaxation/Injection

a)

b)

one period

Figure 7.2: a) Schematic conduction band diagram of a quantum cascade laser [20]. Each stageof the structure consists of an active region and a relaxation/injection region. Electrons can emitup to one photon per stage. b) General philosophy of the design: The active region is a three-levelsystem. The lifetime of the 3! 2 transition has to be longer than the lifetime of level 2 to obtainpopulation inversion.

between the two levels of the laser transition. As it will be shown later, this result can beobtained using various designs. In general, the active region contains a ladder of at leastthree states (or continuum of states), such that electrons are injected in the n = 3 state andthe population inversion is maintained between the states n = 3 and n = 2. Assuming thatelectrons are exclusively injected in the n = 3 state, the population inversion requirementtranslates into the following requirement on the lifetimes

32 > 2, (7.2.1)

i.e. the total lower state lifetime 2 is shorter than the electron scattering time from the n=3to the n=2 levels.

3"

2"

1" 3"

2"

1" 3"

One"Period"

Light"Emission"

Relax8"a9on/"

Injec9on"Region"

Ac9ve"Region"

Figure 4.2: Schematic of the conduction band diagram of a QCL featuring the important wave

functions. Upon injection into the upper laser state 3, the electron undergoes a radiative

transmission down to the lower laser state 2, is extracted via state 1 and then raised in

energy for subsequent injection. Adapted from [78].

different compositions and doping levels, opened the way for the QCL realisation. Dozens of

these periodic regions are grown on top of each other (typically 35), in order to increase the

electron "recycling" and to match the height of the active region to the typical optical mode

sizes of the mid-IR. Depending on the targeted wavelength, various material compositions

are used, which mainly differ by their conduction band discontinuity ∆EC . In the following

years, various material systems, such as GaAs/AlGaAs [94], were tackled for QCL. The

lattice-matched InGaAs/AlInAs (∆EC =520 meV) on InP is widely used for emission above

5µm. When aiming for wavelengths below 5µm, thermal activation of electrons from the

the upper laser state is increased, which hampers operation at room temperature. However,

the same material system (when grown in a strain-compensated way, i.e. compressively-

strained wells and tensile-strained barriers) can provide up to ∆EC =1.2 eV, and lasing

has been reported down to 3µm [95,96]. Also, InAs/AlSb grown on InAs substrates is a

promising candidate for emission down to 3µm [97] and at 2.6µm [98]. The avoidance of

aluminum-free barriers, as shown by Nobile et al. [99], is expected to provide larger matrix

element, and thus enhanced optical gain.

Two main level designs provide the basis of most QCL high-performance operation, the

bound-to-continuum (BTC) and the two-phonon-resonance (2Ph) designs [100–103]. In

both cases, the electron injection into the upper laser state is performed by resonant


tunnelling injection [104]. However, these designs differ in the extraction technique of the

carriers from the lower subband. For the BTC, the extraction is facilitated by a series of

lower states, which define a continuum-of-states, a so-called miniband. In the second case,

the series of three lower levels, separated by the optical phonon energy, lead to a effective

carrier extraction.

In general, when defining the radiative transition in the design, there is a trade-off between

vertical and or diagonal transitions. In the first case, a maximum overlap between upper and

lower states, and hence, large oscillator strengths, a narrower gain spectrum, and a lower

threshold is achieved at the expense of an unfavourable ratio of the lifetimes. In the case of

the diagonal transition, upper and lower laser levels are separated by a thicker barrier. This

increases the lifetime of the upper laser state and results in a better population inversion, at

the expense of a reduced oscillator strength.

The design of the waveguide (WG) is important in terms of thermal optimisation. The

waveguides must allow for efficient removal of the heat created in the devices, and they

are the limiting design factor for maximum operation temperature. The best example of an

efficient waveguide, featuring low losses and efficient heat extraction, is that of the buried

heterostructure waveguide [105]. Here, after definition (i.e. etching) of the active material

to form a ridge waveguide, the side and top of the waveguide are covered with regrown InP,

which offers a high thermal conductivity. With a high doping of the dielectric layers close to

the top contact, an efficient decoupling from the lossy surface plasmon mode, the so-called

plasmon-enhanced waveguide, is achieved [106,107].

QCLs emit light with electric field polarised parallel to the growth direction of the structure,

which is termed transverse-magnetic (TM) polarisation. The polarisation condition is due to

selection rules of the intersubband transition, and was shown to be strongly obeyed [108].

For the investigation of QCLs, this means that only light of this polarisation will interact

with the intersubband transitions. This offers a convenient means of distinguishing between

intersubband and waveguide losses.

An important characteristic for efficient operation and practicability is the so-called wall plug


efficiency (WPE), which is defined as the ratio of injected electrical and extracted optical

power. Up to now, most QCLs still operate at a rather low WPE around 10-20%, which is

mainly due to the efficient non-radiative electron transition in connection with the emission

of a phonon. It was shown, that the a priori maximally achievable WPE is strongly reduced

with increasing wavelength [109]. Recently, two different approaches were reported with

higher WPEs [110]. In the first approach, presented by Bai et al. [111], the voltage drop

across the injector was minimised. Furthermore, an increased number of periods overlapped

with the optical mode due to the shorter period length and yielded a higher differential gain,

resulting in a WPE of 50%. It seems, however, ambiguous to optimise a design, which will

only ever operate at cryogenic temperatures due to heavy thermal backfilling with increased

temperature. A second approach, reported by Liu et al. [112], consisted of increasing the

coupling strength between injector and upper laser states. In this way, WPEs over 40%

have been achieved. For a real quantitation, however, the (cryogenic) cooling power should

be considered as well, which drastically lowers the above reported WPEs. Hence, a WPE

of 27% reported at room temperature in a shallow-well design by Bai et al. [113] is very

remarkable.

Power output of more than 5 W was achieved by minimising carrier losses in unwanted energy

states and in the continuum, which was achieved by implementing shallow wells and taller

barriers [113]. To allow for dense packaging and maximum portability, QCLs can be designed

to run at low power dissipation (below 1 W), which was achieved by the use of a genetic algo-

rithm for the QCL design and a low doping density [114,115].

QCls are shown to cover a spectral range throughout the mid-IR to the THz from 2.9 -

250µm [116]. In the mid-IR, they operate at room-temperature in most of that range,

which is mainly achieved by a rigorous optimisation of the waveguide structure for thermal

management, e.g. burying the waveguide in the high thermal conductivity material InP

and mounting the QCL epitaxial-side-down [105]. The operation at room-temperature in

the THz, however, is limited. After the first THz QCL by Köhler et al. [117], which ran up

to 50 K, the maximum operation temperatures of contemporary THz QCLs, which mainly

rely on a resonant-tunneling injection scheme, seems limited by Tmax ≈ ~ω/kB, as reviewed


in [118]. However, newer schemes, such as the scattering-assisted injection mechanism, are

promising for higher operation temperatures [119].

To allow for broadband spectroscopy, a wide tuneability is requested. This can be achieved

by the combination of a QCL and an external cavity setup, as shown by Luo et al. [120].

The tuning range is further extended by the use of broadband QCL design, such as the BTC

[121]. Recently, tuning over 430 cm−1 in the wavelength range between 7.6 - 11.4µm was

achieved by a QCL consisting of several periods designed for different emitting wavelengths

[122].

An easier way to achieve wavelength-tuning, at the cost of a reduced range, is the use of

a distributed feedback (DFB) laser. This type of QCL operates in single longitudinal mode

at a fixed frequency, with a high side-mode suppression ratio (SMSR). The principle of

DFB was first shown and in a laser source by Kogelnik et al. [123], who investigated laser

oscillations in a dye laser pumped by the interference pattern of two UV laser sources. The

first realisation of a semiconductor laser was soon demonstrated by Nakamura et al. [124]

for the case of an optically pumped GaAs interband laser. The first DFB-QCL was realised by

Faist et. al [125], and was soon followed by high average power DFB-QCLs [101]. With the

on-chip integration of 24 DFB-QCLs into an array, tuneability was recently demonstrated

over 220 cm−1 from 8.0 to 9.8µm. This setup however demands for a complex electrical

pumping scheme.

Using photonics crystals (PhCs) is a further means of frequency-selection. In PhCs, the

refractive index is periodically modulated, which a modulation period close to the optical

wavelength [126]. In this way, a QCL incorporating 2D optical mirrors with PhCs was

shown by Dunbar et al. [127]. Benz et al. [128] then enhanced the concept by merg-

ing the gain and PhC structure. This resulted in a further miniaturisation of the whole

structure.

Recently, QCLs were also shown to operate as a frequency comb generator in the mid-IR,

which is due to the phase-locking in a broadband QCL through the process of four-wave

mixing [12], as further introduced and explained in Chap. 5.

4.2. Overview on Measurement Techniques 63

In summary, QCL technology has achieved a mature state [116,129,130]. Today’s and future

QCLs exceed and are fully able to replace other methods for the creation of coherent mid-IR

radiation, such as the lead-salt laser introduced above, or lasers based on the discharge of

an electric current inside a gas.

4.2 Overview on Measurement Techniques

The methods for measuring the key parameters of laser sources, which are their optical gain

and loss, can be divided loosely in two main groups.

The first group comprises all the techniques that use the actual device as the only source,

i.e. by looking at threshold current densities, or internally created light. In such cases, the

determination of gain and waveguide losses is made using the measurement of the lasing

threshold current densities for samples with identical design and processing, but different

length, which is the so-called 1/L-measurement, as applied in [131]. In a similar way, these

key parameters can also be determined by measuring the threshold current densities for a

sample before and after evaporation of a coating onto the facets. These methods, however,

are susceptible to sample variations and uncertainties in facet reflectivities in the later case.

Also, they stop short of providing spectral information. The measurement of the photolu-

minescence (PL) under optical pumping, or the electroluminescence (EL) under applied

electrical bias yields information on the energy position and the width of the radiative transi-

tion(s), and on the achievable efficiency. Measurement of the EL from waveguide cavities can

be further analysed for the modulation depth of Fabry-Pérot oscillations in sub-threshold op-

eration [132], which provides a direct feedback on gain and loss in the luminescent spectral

region. However, outside that region no information can be accessed this way. Furthermore,

the use of a high-resolution spectrometer is necessary.

The second category of measurements techniques makes uses of an external light source,

whose transmission through the waveguide of a QCL is determined. The measurement of

the transmission of a Fabry-Pérot waveguide can be performed with a narrow-band light, e.g.

a HeNe laser [133]. Here, the temperature of the waveguide under investigation is changed.


The introduced variation in cavity length lead to FP oscillations. In an analogue way, the

use of the frequency chirp of a DFB-QCL can be used [134]. Here, the waveguide cavity

is kept at constant temperature, while the increase in temperature of the DFB during the

electrical pulse leads to a frequency-sweep (typ. in the order of a few cm−1) of the latter.

As a consequence, the waveguide is sampled across several FP resonances. Note, however,

that these two methods only delivers gain and loss information at the narrow-band light

energy. Furthermore, stray light has to be carefully suppressed, as it results in a decrease of

the modulation depth, and, hence, artificially high losses.

Measurements using a multi-section cavity technique [135] overcome this limitation,

but require specially processed devices, where the waveguide is cut in transverse direc-

tion to the light propagation. This cutting obviously introduces absorption and coupling

losses.

Gain and loss studies based on the transmission of externally-created broadband IR light

through broad-area waveguide QCL devices have been introduced recently. The source

employed here consists of either a globar (mid-IR) or He-lamp (NIR) [136]. Information

over the full broad spectral range (of the source) is accessible. In addition, passive structures,

such as waveguides without any embedded quantum cascade materials, can be characterised.

Furthermore, due to the fact that intersubband transition only interact with TM-polarised

light, TE-polarised light can be used for normalisation, and to characterise the material

and waveguide losses independently of the intersubband losses. Nevertheless, this method

only works reasonably well with rather broad (>20µm) waveguides to achieve sufficient

coupling for a practical transmission signal. The alignment of the source with respect to

the waveguide and their spatial stability is experimentally challenging, and quantitative

results are ambiguous, because the effective coupling efficiency of the external light into

the waveguide is difficult to estimate, and stray light introduces artifactual offsets into the

measurement. So far, the characterisation of active QC structures has only been shown

to work in CW operation. Structures under development, which are usually operated

in pulsed mode, cannot be assessed. A further variant of this method also aims for the

interpretation of the Fabry-Pérot fringes in the transmission spectrum [137]. Contrary to the

4.2. Overview on Measurement Techniques 65

above described narrow-band FP method, however, the broadband source naturally yields

broadband information. Through the analysis of the ratio of the higher-harmonics in the

Fourier transform of the spectrum, the propagation losses and the refractive index may be

independently determined.

Alternatively, time domain spectroscopy introduced recently [138,139] has been shown to

be able to resolve spectral features. Here, ultrashort IR pulses are transmitted through the

active medium. The broadband IR pulses are created by phase-matched difference frequency

(DFG) generation in a non-linear medium (e.g. a GaSe) by Ti:sapphire laser pulses with

lengths < 100 fs. The phase resolved transmission is then measured using electro-optic

sampling. This coherent detection scheme allows to measure transient phenomena with a

time-resolution below 10 fs.

The use of a synchrotron source for transmission measurement is one of the most di-

rect way to characterise high performance QCL devices, which typically involve single

transversal-mode waveguides, see Fig. 4.3. Because such waveguides feature widths well

below 10µm (which is at the diffraction limit in the mid-IR) the external IR probe source

should also be diffraction-limited, in order to maximise modal coupling, and this is one

of the key features of synchrotron IR. The technical aspects of this method were de-

scribed in detail in Chap. 2. In the following sections, its application in different cases

is given.

Transverse magnetic (TM)

Figure 4.3: Facet view on a typical mid-IR waveguide with dimensions 2 x 5µm. The active polarisa-

tion (TM) is shown as well.


4.3 High-Performance Quantum Cascade Laser

4.3.1 Device Design and Processing

In this chapter, the performed investigations of a high-performance QCL based on the

two-phonon resonance (2Ph) [140] are presented. The modelled band structure together

with the electron states are given in Fig. 4.4. Those and the dipole-matrix elements were

calculated with the self-consistent solution of the Poisson and Schrödinger equations. An

energy-dependent effective mass was employed, thereby accounting for non-parabolicity.

Light emission for the sub-threshold conditions takes place from the upper laser state

12 down to states 8-10, before concentrating for increased biases on the designed lasing

transition 12 to 10 at 8.4µm.

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Pote

ntia

l [eV

]

706050403020100

Distance [nm]

active region injector

12

13

1198

10

g

Figure 4.4: Moduli squared of the relevant wave functions and the conduction band diagram of a

period at an average field of 33 kV/cm for the QCL. The designed lasing transition is from

level 12 to 10.

The devices were processed into narrow-ridge low-loss heterostructure waveguides with

a width of 13.9µm). The waveguides were buried in iron-doped InP in order to improve

the thermal behaviour of the device, while at the same time ensuring electrical blocking

to suppress leakage currents. The measurement was performed on devices with a length

of 3 mm, which was determined to be the best trade-off between the suppression of stray

light while still guaranteeing a measurable transmission for the device without any ap-

4.3. High-Performance Quantum Cascade Laser 67

plied bias, when the optical absorption in transverse-magnetic (TM) polarisation is very

strong.

4.3.2 Measurement

The relative transmission spectra t = TT0

, which is the determined transmission T through

the device normalised with respect to the transmission T0 through a 15×8µm2 aperture with

entrance and exit optics aligned to each other, are given for TM- and TE-polarised light in

Fig. 4.5(a). The effective device temperature was 349K, and the data spans from zero bias

up to a current of I = 0.97 · Ith, with Ith being the lasing threshold current. The effective

device temperature is held constant by keeping the transmission cutoff at around 700 meV

at the InGaAs bandgap at a constant energy [136].

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Tran

smis

sion

T/T

0

0.70.60.50.40.30.20.1Energy [eV]

TE

TM

Transverse-electric (TE) Transverse-magnetic (TM):

0Aup to

0.97 Ith

(a) The effective device temperature is kept at 349 K

by monitoring the bandgap onset (vertical arrow).

0.001

0.01

0.1

1

Tran

smis

sion

T/T

0

0.180.170.160.150.140.13Energy [eV]

0Aup to

0.97 Ith

(b) TM transmission spectra near the peak gain of

145 meV.

Figure 4.5: Transverse-magnetic (TM) and transverse-electric (TE) polarisation transmission spectra

for the QCL measured for increasing biases of 0 - 32.8 kV/cm

Subsequently, the peak transmission t is described with a multi-pass Fabry-Pérot (FP) model,

whose evolution is shown in Fig. 4.6. It is given by

t = c · (1− r)2 · exp(−αl) ·1

1− r2 · exp(−2αl), (4.3)


where the coupling coefficient c describes the normalisation to the reference aperture,

r = 0.27 is the mirror reflectivity at the facets, and α is the absorption over the device length

l.

r1#

Probe#x1=(1+r1)#

(1+r2)x6#=#r1r2(1+r1)#(1+r2)#exp3(+αl)#

x2=x1exp(+αl)#

(1+r1)#x4#

(1+r2)x2#=#(1+r1)#(1+r2)#exp(+αl)##x3=r2x2#x4=x3exp(+αl)#

x5=r1x4# x6=x5exp(+αl)#

x7=r2x6#

Σ#=#(1+r1)#(1+r2)#exp(+αl)#(1+x+x2+x3+…)#

!!!=!(1%r1)!(1%r2)!exp(%αl)!(1/(1%x))#

x#=#r1r2exp(+2αl)#

Figure 4.6: The multiple-paths growth of reflection and transmission in the cavity gives rise to a

geometrical series.

The total absorption α is defined a

α= α0− gm · I , (4.4)

where α0 is the total waveguide loss, gm is the linear modal gain coefficient, and I is

the applied current. The denominator on the right-hand side in Eq. 4.3 accounts for the

super-exponential increase of t when the device is operating above transparency but below

threshold, i.e. α0 ≤ gm · I . In this regime, the two constant terms c and exp(−α0l) can be

determined separately, because the super-exponential increase does not depend on c, but

only on α. In contrast, determining α0 from modeling t simply below the transparency

point, where t increases only exponentially, would require the a priori knowledge of c. This

is however difficult, because c depends on many parameters such as waveguide dimensions

and illumination of the applied optics. t is then fitted for the parameters c, α0 and gm, which

gives excellent agreement to the data, as shown in Fig. 4.7.

This data strongly supports the assumption of a linear dependence of the gain on the injection

current. The extrapolated threshold currents Ith fit well to the measured ones. In addition,

good agreement is obtained between Ith in CW mode at a given effective device temperature

TD, and the respective Ith measured under low duty-cycle pulsed conditions with the heat

sink temperature set to TD. A material gain coefficient of (8.6 ± 0.2) cm/kA is measured,

where a mode overlap factor Γ = 0.73, as calculated by 2D COMSOL simulations using


10-3

10-2

10-1

100

Tran

smis

sion

T/T

03.02.52.01.51.00.50.0

Current Density [kA/cm2]

Thre

shol

d

Tran

spa-

renc

y

Measurement Fabry-Pérot Model Fit

TE Transmission

Figure 4.7: Current dependent peak transmissions for the effective device temperature of 349K

together with the result of the three-parameter fit of the Fabry-Pérot transmission model

(full line). Vertical dashed lines indicate the obtained values for transparency and

threshold currents.

the measured lateral dimensions, is taken into account. This value is comparable to the

measured values for similar devices [141]. The current-independent total waveguide loss is

defined as

α0 = αempt yW G +Γ ·αISB, (4.5)

where αempt yW G arises from the free carrier absorption in the doped cladding layers, and αISB

are losses from intersubband transitions at zero bias [142]. This total waveguide loss α0 is

found to be (11.7 ± 0.3) cm−1.

4.3.3 Correlation to Models

The two models that go beyond semi-classical models are based on a density matrix (DM)

formalism [143, 144], and on the non-equilibrium Green’s function (NEGF) [145, 146],

respectively.

While the first method is less computationally intensive, the latter is more comprehensive

and includes scattering in k-space [147]. Usually, in order to keep the numerical load of the

NEGF within reasonable limits, the space-, energy- and momentum-resolution is decreased,

requiring a careful adaption of the input digitised potential to mimic the true structure.


In the DM simulation, scattering is included for interface roughness, LO-phonons, alloy

disorder, and ionised impurities, and the electron temperature is assumed to be the lattice

temperature. Further details of the DM simulation are discussed in [144]. For the case

of the NEGF approach, a real-space basis [146] with 1 nm grid spacing and a 2D mesh

uniformly spaced both in energy and k2 is applied. Boundary conditions and details of

numerical procedure are described in [147, 148]. The only temperature that enters this

model is the lattice temperature, however, highly non-thermal carrier distributions were

observed particularly in the lower lying subbands of the active wells. Contributions to gain

from the transitions at different ks were calculated individually and then summed up to

the total gain. The scattering mechanisms included in NEGF calculations are LO-phonon,

interface roughness, alloy disorder, ionised impurity and LA-phonon, as explained in detail

in [147], and non-parabolicity was taken into account as well.

As shown in Fig. 4.8, the prediction of ISB gain in the DM model (equal to 6.5 cm/kA) is

considerably lower than the measured value. However, as the same model also underesti-

mates the transparency current, which is the current needed to compensate the optical losses

with the intersubband gain, the predicted values of threshold are close to the experimental

ones, as pointed out in [144]. In contrast, the ISB gain of 7.9 cm/kA, as predicted by NEGF

simulation, matches reasonably well to the measurement.

25201510

50

-5-10-15

Inte

rsub

band

Gai

n [c

m-1

]

43210Current Density [kA/cm2]

Density Matrix Non-Equilibrium Green's Function Measurement

Figure 4.8: Plot of the intersubband peak gain as a function of current density, comparing the

measurements with the prediction of the non-equilibrium Green’s function and density

matrix simulations.

The absorption spectra α(ω) can be extracted from the transmission spectra T(ω). This,


however, needs extra attention, because for such a conversion to α(ω), the magnitude of

the broadband coupling c(ω) at all frequencies needs to be known. This is however not

directly accessible in this measurement. Nevertheless, in independent studies of somewhat

smaller (width ≈10µm) and undoped waveguides, i.e. with negligible TM absorption, a

similar coupling of TM and TE-polarised light for frequencies exceeding the peak gain energy

is measured, as described in Sec. 4.4.1. Also, the measured TE absorption at resonance

(0.145 eV) of 2 cm−1 for the TM-coupling appears to be an accurate measurement of the

non-resonant waveguide losses. Because TM and TE waveguide losses are anticipated to be

similar [149], the wavelength dependent coupling is normalised by taking the relation to

the TE transmission. That way, the intersubband loss and gain can be extracted from the TM

transmission for higher energies, as given in Fig. 4.9.

20

15

10

5

0

-5

-10Inte

rsub

band

Abs

orpt

ion

[cm

-1]

0.400.350.300.250.200.15Energy [eV]

0Aup to

0.97 Ith

Figure 4.9: Extracted intersubband absorption as determined by the ratio of TM and TE transmission

and by taking into account multiple passes through the cavity.

The absorption decreases considerably as soon as current flows through the (partially aligned)

cascade structure. Since many of the upper continuum states (notably the state 11 down to

7) share their dipole with the upper laser state 12, this decrease extends over almost 60 meV.

As the current is further increased, the oscillator strengths of some of these transitions

fade-out, and the continuously increasing population inversion is no longer effective, except

for the transitions 12-11 and 12-10. The absorption at zero bias predominantly arises from

the transition between the ground state levels 1 to about 5, and the non-aligned upper laser

state 12.

In Fig. 4.10, the measured spectra at 32 kV/cm are compared to the simulated intersubband


absorption for both models at an applied field of 32 kV/cm at 349 K. For the models, a clear

difference in the energy region from 0.2 - 0.32 eV is observed, while above this there is a

good agreement. The origin of the higher absorption in the NEGF simulation is the increased

occupation of injector states close to the wells of the active region. Kolek at al. [147]

showed that such states are additionally populated from lower laser subbands by currents

occurring at high-k values. The additional absorption results then from transitions between

highly occupied high-k value states in the injector. This can be seen from the lower panel

of Fig. 4.10, where the k-resolved intersubband absorption summed up to a given k-value

continues to increase up to the highest k-values. This absorption is not accounted for by

the DM model, because it assumes the thermal distribution in the subband being equal to

that of the lattice. The application of the approximation where the electron temperature

is assumed to be constant between all states, but has to satisfy a kinetic balance, does

interestingly not substantially improve the agreement in the frequency range 0.15 - 0.3 eV,

but strongly underestimates the gain, as already discussed in [144]. This is not unusual,

because it simply reflects the fact that restricting electrons to the same temperature in all

subbands can redistribute them in energy- but not in real-space. Hence, the total occupation

of injector states and ISB absorption from latter remain unchanged. On the contrary, the

NEGF approach allows for non-uniform heating of laser subbands and can account for

redistribution of carriers between active wells and the injector.

The deviation of the measured and modelled absorption below the lasing energy is discussed

in detail in Sec. 4.4.1.

As expected, the use of the DM model results in a more adequate description of the energy

levels and a very good determination of the peak gain location. This originates from the fact,

that the DM model is not bound to a discrete mesh. For the NEGF simulation, this could be

improved by using for a smaller mesh and/or a more accurate adaption of the well depths;

at the cost of high computational time.

In summary, it was shown, that the energy and real space distribution of carriers is im-

portant in the modelling of gain and absorption in a broad range. The modelling based

on the NEGF seems promising for the proper account of high-energy losses. This is espe-

4.4. Topical Research 73

20

10

0

-10

Inte

rsub

band

Abs

orpt

ion

[cm

-1]

0.600.500.400.300.200.10Energy [eV]

20

10

0

-10K-resolved NEGF (k2 in units of dk2=0.009nm-2)

1 1-4 1-6 1-2 1-8 1-10 full k

Measurement DM NEGF (full k)

Increasing k-summation -8

-6-4-20

cm-1

0.1700.1500.130

Figure 4.10: Top panel: Comparison of the modelled and the measured absorption (scaled by the

overlap factor) at a bias of 32 kV/cm. The main difference lies in the range 0.2 -

0.3 eV, where the non-equilibrium Green’s function (NEGF) model matches the higher

absorption better. Inset: The density matrix (DM) approach reproduces the gain peak

position accurately. Bottom panel: K-resolved absorption for the NEGF model at an

applied field of 32 kV/cm, given in units of dk2 = 0.009nm−2. The absorption strength

heavily depends on the amount of k-states included, which is marked by an arrow.

cially true in the case of broadband devices, such as the multi-stack QCL shown further

below.

4.4 Topical Research

4.4.1 Empty Cavity Waveguide

With this study, the experimentally much higher measured losses for energies below the

designed transition energy with respect to the ones modelled by the DM and NEGF ap-

proach are investigated. For this, the non-resonant waveguide losses are studied by inves-

tigating the TM and TE transmission through waveguide structures of a not-intentionally

doped (NID) QCL design, and of different lengths. They are undoped to suppress inter-

subband absorption in the mid-IR, while the contact layers are grown as per usual. This


allows for a direct comparison of the polarisation dependence of the waveguide absorp-

tion.

The structures consist of strained In0.635Ga0.365As/In0.335Al0.665As layers grown on low-doped

InP to a thickness of∼2µm, designed for emission at 0.29 eV. The background doping carrier

is estimated to be below 6 · 1014 cm−3. The measured polarisation-resolved transmission is

shown in Fig. 4.11.

10-324

10-224

Tran

smiss

ion

[a.u

.]

0.60.50.40.30.20.1

Energy [eV]

10-324

10-224

20

15

10

5

0Abso

rptio

n [c

m-1

]

TE 1.5mm 3mm 6mm Absorption-Fit

TM 1.5mm3.0mm6.0mmAbsorption-Fit

Model: TE Absorption TM Absorption

EmissionEnergy

Figure 4.11: Measured TM (top panel) and TE (middle) transmission of the empty cavity waveguide

structure for the three different lengths from 1.5 to 6 mm. The transmission spectra are

fitted to an absorption-model based on a ω2 dependence.

To achieve a comparable coupling strength of the SRIR into the waveguide, each sample

is carefully aligned to get maximum transmission. As expected, under application of an

electric bias, neither a change in TE- nor TM absorption is observed. This confirms that

indeed no free carriers are available to populate the electron states in the conduction

band. Below 0.25 eV for the TM and 0.20 eV for TE polarisation, the transmission decreases

strongly. For the purpose of discussion, this is attributed to free carrier absorption of

the optical modes in the doped waveguide cladding layers. The transmission is modelled

as

TP = k · e−αP l , (4.6)


with a frequency dependent effective free carrier loss

αP =α0,P

ω2

1−ΓP

, (4.7)

where p is the respective polarisation, and (1− ΓP) is the overlap of the mode with the

cladding layers, as determined from COMSOL simulations. The results are given in Fig. 4.11

for both polarisation in the upper two panels, along with the modeled losses αT M and αT E

in the lowest panel. The TM polarisation experiences higher losses than TE, although the

difference in overlap factor has been taken into account. In fact, it is obtained that the

observed losses in TM polarisation are higher than expected from literature values of free

carrier losses for the present doping levels. Hence, to investigate the importance of metal

contacts for the loss, a second series of samples with and without the top Au contact layer

was prepared.

As above, the series of transmission measurements for different cavity lengths are converted

to absorption. As shown in Fig. 4.12(a) and Fig. 4.12(b), an additional absorption of 6 cm−1 is

measured at E=160 meV for the samples capped with Au. This is attributed to the coupling of

the TM mode to the surface plasmon mode. In TE, shown in Fig. 4.12(b), the total absorption

is smaller than 2 cm−1 in the range down to 0.16 eV. Below 0.14 eV, the absorption steadily

increases, while the difference between covered and uncovered surface remains constant at

about 2.5 cm−1. The new measurements prove that the loss medium is to be located away

from the active material, presumably at the surface, where the metal, the highly doped

layers, and roughness in general are the dominant scatters.


-15

-10

-5

0

5

Abso

rptio

n [c

m-1

]

0.320.280.240.200.160.12

Energy [eV]

TM Absorption Au No Au Difference Em

issio

nEn

ergy

DFB chirp-spectroscopy TM_Au TM_noAu

(a) The difference in TM absorption increases heavily

below 0.25 eV.

-15

-10

-5

0

5

Abso

rptio

n [c

m-1

]

0.320.280.240.200.160.12

Energy [eV]

Emiss

ion

Ener

gy

TE Absorption Au No Au Difference

DFB chirp-spectroscopy TE

(b) The TE absorption is not observed to depend on

the presence of Au contacts.

Figure 4.12: Derived absorption dependence from the transmission measurent in TE and TM polarisa-

tion for samples with and without Au contacts. Also shown is the measured waveguide

loss at the emission energy using DFB chirp-spectroscopy.

The absorption strength at the emission energy is also determined using DFB chirp-spectroscopy.

Here, the transmission of a narrow-band DFB-QCL emitting at λ = 4.3µm through the

empty cavity waveguide was measured. During the application of the up to 500 ns long

electrical pulses, the temperature of the DFB-QCL increases. This leads to a shift in emission

wavelength, shown in Fig. 4.13(a) for a pulse length of 300 ns. As a consequence, the Fabry-

Pérot resonances of the empty cavity waveguide are sampled, and are used to determine

the absorption at this fixed position in energy, see Fig. 4.13(b). This results in αT M , Au =

1.8± 0.3 cm−1 and αT M , noAu = 1.3± 0.2 cm−1 for the TM polarisation. In the case of TE

polarisation, the absorption was determined as αT E = 0.2± 0.1 cm−1 irrespective of the

metal coverage. These measurements comply well to the absorption measurement shown in

Fig. 4.12(a) and Fig. 4.12(b).

To better locate the source of absorption, 1D and 2D modelling was performed using

the simulation softwares Guide and COMSOL. The relevant simulation parameters are

summarised in Table 4.1. In Fig. 4.14(a), the results for both models with and without

the top Au contact are given. Analogous to the measurements, the TE absorption is hardly

affected by the addition of the Au, and TM losses are increased by almost a factor of 2. The


4305

4307

.543

10Em

issi

on W

avel

engt

h [n

m]

450400350300250200150Time [ns]

(a) During a 300 ns long electrical pulse, the DFB

chirps over approximately 2.1 cm−1.

-300

-200

-100

0

Det

ecto

r Sig

nal [

mV

]

350300250200150

Time [ns]

120

80

40

0

Nor

mal

ized

Tran

smis

sion

[%]

TE Measurement Reference

Min Normalized Transmission Max

(b) More than 10 Fabry-Pérot oscillations are visible in

the TE measurement.

Figure 4.13: DFB chirp-spectroscopy is used to measure the absorption at the emission energy.

two simulation tools yield a similar magnitude for the absorption, however they differ in their

predicted resonances. At the resonance energies, the overlap of the optical mode with the

highly-doped contact layer leads to an increased absorption.

Table 4.1: Parameters for absorption simulations.

Layer nre f r k Thickness[µm ]

Density[cm−3]

me f f τ

[ ps ]

Au 9.6 50 0.1 0 0 0InGaAs:Si 3.46 0 0.08 1e19 0.043 0.15InP:Si 3.1 0 0.2 6e18 0.08 0.15InP:Si 3.1 0 3.8 1e16 0.08 0.15InGaAs 3.46 0 0.2 0 0.043 0.15AR 3.41 0 1.6 0 0.05 0.15InGaAs 3.46 0 0.1 0 0.043 0.15InP:Si 3.1 0 5.0 1.5e17 0.08 0.15


-25-20-15-10-50

Abso

rptio

n [c

m-1

]

0.180.160.140.120.100.08

Energy [eV]

-25-20-15-10-50

GuideNo Au Au

TM TM TE TE

COMSOLNo Au Au

TM TM TE TE

DifferencesTM Au/no AuTE to TM

(a) The modelled TM absorption (COMSOL and

Guide) for the empty cavity waveguide clearly ex-

ceeds the TE absorption (filled red), and is suscepti-

ble to the top Au layer (filled green).

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

Over

lap

Fact

or

0.300.250.200.150.10

Energy [eV]

TE no Au TE Au TM no Au TM Au

(b) The reason for the higher absorption and reso-

nance originates from the higher overlap factor of the

optical mode with the highly-doped contact layer.

Figure 4.14: Summary of modelled absorption and overlap factor.

In the case of TE polarisation, the qualitative behaviour of modelled and measured absorption

is similar, see Fig. 4.15(b). Both curves show a λ2-dependence, characteristic for free-carrier

absorption. The magnitude of the measured TE absorption however is stronger than mod-

elled. This can partly be explained by the fact that the magnitude of the modelled absorption

strongly depends on assumed doping levels and lifetimes, as shown for three doping levels

(taken within the tolerance of the InP substrate wafer).

In the case of TM polarisation, however, the shape of the absorption differs strongly between

measurement and model. A mismatch is also found in the onset of the additional absorption

for the samples with Au contacts, and the magnitudes. A tentative explanation for the

increased TM absorption could be the increased overlap of the mode with the highly doped

InGaAs layer. This could be due to the large roughness of the regrown InP layer, as can

be seen in Fig. 4.16(a) and Fig. 4.16(b). There, the two images taken by differential

interference contrast microscopy reveal a low quality regrowth. This is expected to result in

an increased field amplitude of the electric field close to the surface; and, hence, increased

losses.


-15

-10

-5

0

Abso

rptio

n [c

m-1

]

0.300.250.200.15

Energy [eV]

Doping

Guide

1.0x1019cm-3150fs

1.5x1019cm-3150fs

2.0x1019cm-3150fs

2.0x1019cm-3100fs

Au 2.0x1019cm-3100fs

Emiss

ion

Ener

gy

Measurement Au No Au

(a) Free carrier absorption cannot fully explain the

shape of the measured TM absorption.

-15

-10

-5

0

Abso

rptio

n [c

m-1

]

0.300.250.200.150.10Energy [eV]

Measurement Au No Au

Guide

1.0x1019cm-3 150fs 1.5x1019cm-3 150fs 2.0x1019cm-3 150fs 2.0x1019cm-3 100fs Em

issio

nEn

ergy

(b) In TE, the spectral behaviour of the absorption is

similar.

Figure 4.15: Summary of modelled and measured absorption for both TM and TE polarisation.

(a) Overview image. (b) Close-up of the area around the waveg-

uide.

Figure 4.16: The differential interference contrast microscopy images of the non-coated samples

using a Nomarski prism reveals a high roughness of the regrown layer.


In summary, the measured difference in TM and TE polarisation matches qualitatively

well to the modelled one. However, a strong quantitative disagreement was found for

both the onset and magnitude. Further investigations, e.g. the measurement a struc-

ture without a highly-doped InGaAs layer and its modelling, could help to clarify this

issue.

4.4.2 Broadband Quantum Cascade Lasers

A broad gain is beneficial for several applications, including e.g. trace gas detection. In light

of this, the case of a strain balanced broadband InP-based QCL based on the two-phonon

resonance (2Ph) design [101] emitting around 5µm is studied. The active region of the

structure is based on highly strained In0.66Ga0.34As/In0.36Al0.64As quantum wells and barriers.

To design a broadband emitter, the active region consists of 3 substacks emitting at different

wavelengths. The symmetric substack arrangement allows to increase the modal gain of

the structure [122]. The individual designs are optimised for light emission at 4.8, 5, and

5.5µm.

The energy levels and the relevant dipole-matrix elements were calculated using the

self-consistent solution of the Poisson and Schrödinger equations, employing an energy-

dependent effective mass, which accounts for non-parabolicity. A transport model based on

the above density matrix formalism is used to calculate the combined gain of three stacks, as

described in [144]. In fact, the gain is first calculated individually for each stack for a com-

mon current, and then subsequently combined, as shown in Fig. 4.17(a)

For the measurement, the devices were processed as buried heterostructures with 4 - 9µm

wide waveguides. The device was cleaved to a 1.5 mm long bar. After cleaving and mounting,

both facets of the devices were AR-coated to prohibit lasing. This allows for the investigation

over the full operation regime, i.e. up to the so-called rollover point of the device, when the

electron levels become misaligned and the gain drops.

In Fig. 4.17(b), The evolution of the transmission change is shown, i.e. the ratio of pumped

and unpumped transmission, upon electrical biasing up to and above the rollover point. A


close agreement of the peak gain position is observed; however, the model overestimates the

gain bandwidth especially at the lower energy range. This could be due to inhomogeneous

alignment of substacks, or absorption of one stack in the gainy region of the other stack.

While gain simulations predicts an achievable gain bandwidth of 75 meV taking into account

a typical background loss of 5 cm−1, a possible gain only over 43 meV is determined. This

may also explain the tuning of this device in an external cavity setup, where a maximum

bandwidth of only 26 meV was shown.

30

25

20

15

10

5

0

Inte

rsub

band

Gai

n [

cm-1

]

0.320.300.280.260.240.220.20

Energy [eV]

total gain short middle long

(a) The summation of the individual modelled gain

curves (using a density matrix formalism [144])

yields the total gain.

25

20

15

10

5

0

Abso

rptio

n [c

m-1

]

0.300.280.260.240.22

Energy [eV]

19.4Vup to

22.4V

7V up to

19.4V

(b) The synchrotron measurement resolves the

injection-dependent transmission changes.

Figure 4.17: Spectral characteristics of the broadband QCL emitting around 5µm.

Given the improved performance of NEGF over the DM modelling as shown above, the range

of the bandwidth can possibly be extended using improved design tools.

4.4.3 Quantum Cascade Structures based on Quantum Dashes

Micro-spectroscopy was applied to characterise QC structures with embedded quantum

dashes (QD). QD structures provide a 3D confinement and should overcome fundamental

limits of the standard QCL based on quantum wells. In particular, they provide much

longer upper state lifetimes due to the suppression of non-radiative relaxation by phonon


emission [150]. As a consequence, lower lasing thresholds are achieved, as well as higher

wall-plug efficiencies.

In this study, the issue of injection- and extraction-efficiency was addressed in devices based

on InAs QD grown on tensile-strained Al0.64In0.36As [151]. The benefit, as compared to

the widespread InAs QDs grown on GaAs [152], lies in the potentially easier engineering

of injection- and extraction schemes to and from the QD laser states [153], which are

feasible with the well-known InGaAs/AlInAs material system. In Fig. 4.18(a), the electrically

induced changes of the synchrotron broadband transmission at 80 K are compared to

EL.

For all the investigated QD samples, it is observed that upon biasing above 15 V (when

the quantum levels become aligned), the transmission is monotonically reduced. This

can be seen in the upper panel of Fig. 4.18(a), where the difference between pumped P

and unpumped U transmission is given. For increasing applied current, P − U decreases

monotonically, which is equivalent to increasing absorption. This does not contradict the

measured increasing EL, shown in the bottom panel of Fig. 4.18(a), which is mostly a

measure of the injection in the upper state, but does not reveal information on inversion

and gain. The micro-spectroscopy, however, quantifies both injection and extraction. The

(artificial) decrease of absorption between 0.25 - 0.4 eV is attributed to the redistribution of

the charge carriers among the quantum levels, when the structure aligns. In contrast, for the

reference sample, where the QD are replaced by a quantum well with similar energy levels,

gain is clearly visible in Fig. 4.18(b).

The absence of gain in the structures based on QDs is assumed to be due to the long

extraction time from the lower laser state. This prevents the build-up of a population

inversion. An improved design of the cascade structure is necessary to allow for population

inversion in the QDashes. For this, better simulation tools to predict the QD levels will

improve the overall performance.


-0.10

-0.05

0.00

0.05

0.10

Norm

aliz

ed S

RIR

Mea

sure

men

t [a

.u.]

0.400.300.200.10Energy [eV]

1.0

0.8

0.6

0.4

0.2

0.0

Electroluminescence [a.u.]

Transmission change (P-U) 14.8V 25.3V 21V 29.1V

Electro-luminescence

24V 22V 20V 18V 15V

(a) Top panel: SRIR transmission change. Bottom

panel: Electroluminescence.

0.5

0.4

0.3

0.2

0.1

0.0

-0.1

-0.2

-0.3

Tran

smiss

ion

[a.u

.]

0.200.180.160.140.120.10Energy [eV]

U P P-U

(b) The reference sample shows gain around

120 meV.

Figure 4.18: Transmission and electroluminescence measurements of the QD and the reference

sample.

Chapter 5

Four-Wave Mixing

Contents5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.2 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.2.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.2.2 Coupled Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.3 Modelling of χ(3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.4 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

In this chapter the optical non-linearities in QCLs are investigated. Four-wave mixing (FWM)

in a mid-IR QCL is demonstrated by the simultaneous injection of two overlapping laser

pulses into its cavity, as published in [154].

5.1 Introduction

Because QCLs operate at and above room temperature in continuous wave mode with

low dissipation [114], they are used extensively in sensing applications exploiting mid-IR

spectroscopy. Recently, Hugi et al. [12] presented a QCL frequency comb, which poten-

85

86 Chapter 5. Four-Wave Mixing

tially allows for broadband multi-heterodyne spectroscopy [155] in the mid-IR using a

compact, all solid-state device. Like in the case of micro-resonators [156], the locking of the

modes needed for the generation of the comb was attributed to four-wave mixing between

neighbouring longitudinal cavity modes.

The theoretical foundation of optical non-linearities in semiconductor heterostructures

was given in the early eighties by Gurnick and de Temple [157], who predicted second-

order optical non-linearities to be 10-100 times larger in AlGaAs heterostructures with

compositional grading when compared to their bulk crystal values. Later, Tsang et al. [158]

theoretically described the second-order optical non-linearity in GaAs quantum wells in the

presence of an applied electrical field. They also predicted up to 100 times higher values

for moderate fields of up to 70 kV/cm. The large values can be well understood by the

fact that nth-order non-linearities are proportional to the product of n+ 1 dipole matrix

elements, and that the intersubband transition can be tailored to resonantly enhance the

non-linearity [159].

In the years after, the experimental evidence of the large second-order non-linearity around

10µm was demonstrated using various approaches by Feijer, Yoo et al. [160,161] and by

Rosencher, Boucaud et al. [162–165] for the GaAs/AlGaAs system. Finally, Sirtori et al. [166]

reported on the first observation of second harmonic generation on intersubband transitions

in the InGaAs/AlInAs material system, followed by a thorough investigation by Capasso

et al [167]. The possibility to engineer the second-order non-linearities in semiconductor

heterostructures in such a flexible manner is hence expected to facilitate new all-optical

types of devices such as optical parametric oscillators [168].

Third-order non-linearities are even further enhanced, because they are proportional to

the product of four dipole matrix elements [169]. In 1992, Sirtori et al. demonstrated a

coupled-quantum-well heterostructure with strong non-linearities, which allowed them to

observe third-harmonic generation [159]. Later that year, Segev et al. [170] demonstrated

the optical Kerr effect in a GaAs/AlGaAs multi-quantum-well structure, also due to the

third-order optical non-linearity. A further effect, the so-termed four-wave mixing (FWM)1

1Four-wave mixing describes the interaction between four waves in a third-order non-linear medium

5.2. Measurement 87

was shown by Walrod et al. [171] in doped quantum well systems. However, the strong

resonant absorption from the lowest populated state in these structures makes only the

near-resonant optical non-linearities practical.

In a QCL, χ (3) is anticipated to originate from both virtual transitions and the modulation of

the real population inversion. The second effect, which correlates to a time-dependent spatial

hole burning, is highly effective in QCLs because both the transport and the intersubband

scattering time, are remarkably lower than the carrier diffusion time in-plane, contrary to

the situation in interband semiconductor lasers [172].

Previous four-wave mixing investigations carried out in interband lasers also credited the

non-linearity to a moving gain grating originating from spatial hole burning [173]. In this

way, the four-wave mixing signal was heavily suppressed when the frequency offset between

pump and signal exceeded a few Gigahertz. In the case of four-wave mixing in QCLs, the

achievable bandwidth is anticipated to be higher because of the short timescales as described

above.

Recently, all-optical wavelength conversion was reported by Madéo et al. [174] in a QCL

using resonant non-linearities. An incident near-IR field, resonant to the interband transition,

enhanced the non-linearity. This resulted in a wavelength shift of the near-IR beam by the

actual emission frequency of the QCL. In this way, an efficient terahertz to near-IR conversion

is made feasible.

5.2 Measurement

5.2.1 Setup

In Fig. 5.1, an overview of the measurement setup is given. Two different laser sources

are used for the characterisation. Their beam paths are combined with a Thorlabs pellicle

beamsplitter before being coupled into and out of the investigated QCL using Ge lenses with

a focal length of 13 mm. The signals are dispersed with a grating spectrometer, detected


with an 800 MHz bandwidth Peltier-cooled MCT detector, and digitalised with a Tektronix

TDS3000B series bandwidth digital phosphor oscilloscope.

Distributed*Feedback*QCL!

DFG*(Ekspla)*

ω3!

I*Grating*

Spectrometer*ω1,!ω2,!ω3!ω1,*ω2!

MCT*Detector*

I*

AntiFReHlection*Coated*QCL!

ω2!

ω1!

Figure 5.1: Schematic of the measurement setup. The DFG pump and the DFB-QCL probe pulses

are coupled to the AR-QCL by the use of a beamsplitter and a short focal length lense.

The grating spectrometer disperses the AR-QCL output for the detection with an MCT

detector.

The pump source (ω1) is a tuneable laser system based on the difference frequency gener-

ation (DFG) between the signal and idler from an OPA pumped by a 100 ps pulse length

Nd:YAG laser, as described in Chap. 2. In particular, it provides gap-free tuning in the 4

- 5µm wavelength range with a spectral linewidth ∆ν = 0.8 cm−1. This corresponds to

approximately 5 times the Fourier-transform limited line width ∆νmin = 0.15 cm−1, where

∆νmin is defined [86] as

∆νmin =2 ln 2

π∆τ≈

0.44

∆τ(5.1)

for a Gaussian pulse with duration ∆τ = 100 ps. The contrast of the used 1 kHz DFG

pulses to the residual 83 MHz pulse train is better than 106. This eliminates any additional

saturation and/or thermal effects.

The probe laser at ω2 = ω1 + δω is a QCL with an integrated DFB grating along the

waveguide. A DFB-QCL is especially well-suited for this experiment, because it runs in single

longitudinal mode at a fixed frequency, with a high side-mode suppression ratio (SMSR).

Here, the DFB-QCL operates at a frequency of 69.7 THz with an SMSR of 25.3 dB, see Fig. 5.2.

The design is based on a 35-period strain-compensated In0.666Ga0.334As / Al0.635In0.365As

active region grown by molecular beam epitaxy with a sheet density of 1.1 · 1011 cm−2 on

n-doped InP [114]. The first-order DFB grating is etched into the InGaAs confinement layer

5.2. Measurement 89

on top of the active region. The device is processed with a standard buried heterostructure

waveguide [175].

0.1

1

10

100

1000

Inte

nsity

[a.

u.]

7372717069686766

Frequency ω / 2π [THz]

Figure 5.2: Typical spectrum of the DFB-QCL, which shows the side-mode suppression ratio of

23.3 dB.

The investigated mid-IR QCL amplifier is based on a single stack, strain-compensated

In0.725Ga0.275As / Al0.276In0.724As quantum well active region emitting at 4.6µm and pro-

cessed into a buried heterostructure. The structure was grown with a sheet density of

1.5 · 1011 cm−2 to a thickness of 2µm. Further details of the active region are published

elsewhere [115]. Prior to the measurement, the facets of the device was provided with a

single layer of Al2O3 anti-reflection (AR) coating.

A spectral resolution of <1 nm is achieved with a Jobin-Yvon Triax 320 grating spectrometer

with a 600 lines/mm grating. In grating spectroscopy, a monochromator is used as a

wavelength-selective element. It is based on the Czerny-Turner design. Here, a grating

mirror inside the spectrometer directs only a certain wavelength part of the light to be

measured onto an exit slit and a detector behind. By tuning the angle of the grating mirror,

this wavelength range is changed. This measurement setup is a direct technique, and does

not need any conversion from the inverse space, as does FTIR spectroscopy. However, as

only single frequencies are measured at a time, the achievable signal-to-noise ratio and

throughput is usually lower than in FTIR spectroscopy.

Different gratings are used to achieve different resolution and spectral coverage. The


Source'

Entrance'Slit'

Exit'Slit'

Rotatable'Gra2ng'

Collima2ng'Mirrors'

Detector'

Figure 5.3: Layout of a grating spectrometer based on the Czerny-Turner design. Adapted from [176].

resolution is defined by the dispersion of the grating and the widths of the in- and out-

coupling slits.

5.2.2 Coupled Waves

In the following, the evolution of an electromagnetic field E in a non-linear medium is

described based on Boyd [177] and Saleh [86]. The propagation is described by the driven

wave equation as derived from Maxwell’s equation and reads

∇2E−1

c2

∂ 2E

∂ t2 = µ0

∂ 2P

∂ t2 , (5.2)

where P is the polarisation vector. It is convenient to write P = P(1)+ PN L with the linear

(P(1)) and the non-linear (PN L) part in order to describe non-linear phenomena. The latter

reads

PN L = ε0

χ (2)E2+χ (3)E3+ . . .

(5.3)

In this way, one receives for the dependence on the non-linear part

∇2E−εr

c2

∂ 2E

∂ t2 = µ0

∂ 2PN L

∂ t2 (5.4)

for an isotropic and dispersion-less material.

Because the electric field in a QCL is polarised only along one direction, the above formulas

can be simplified to the scalar form.

5.2. Measurement 91

A set of 4 orthogonal modes in the slowly-varying envelope approximation, i.e.

E(z, t) =∑

q=1,2,3,4

ℜ

Eq(z) ei(ωq t−βqz)

=1

2

∑

q=±1,±2,±3,±4

Eq(z) ei(ωq t−βqz) (5.5)

is assumed to be a solution of Eq. 5.4 in the case of four-wave mixing, with frequencies

ω−q = −ωq, amplitudes E−q = E∗q and propagation constants β−q = −βq of the individual

fields. This situation is illustrated in Fig. 5.4.

The driven wave equation obviously needs to be fulfilled for each frequency component of the

field. This leads to a set of N coupled-wave equations of the form

dEq

dz=

iµ0

2Tβqeiβqz

∫ T

0

e−iωq t ∂2PN L

∂ t2 d t, (5.6)

where T is the integration time and βq is the propagation constant [178].

Four%Wave*Mixing*

ω3#ω1#

ω2#ω2#

ω1# ω3#

Crystal# Filter#ω4#

ω4#

Figure 5.4: General four-wave mixing.

The polarisation in the third-order then becomes

PN L(z, t) = ε0χ(3)E(z, t)3

= ε0χ(3)1

8

∑

q,r,s=±1,±2,±3,±4

Eq(z)Er(z)Es(z)e(i(ωq+ωr+ωs)t−i(βq+βr+βs)z).

(5.7)

Together with Eq. 5.6, this allows to fully describe the evolution of the amplitude for each

individual field.

5.2.3 Results

The amplified IR transmission of the QCL, used for the gain estimate, is measured by syn-

chrotron micro-spectroscopy [84]. This result is given in the bottom panel of Fig. 5.5, along

with the frequency-tuning range of the pump, probe and detected signals.


7674727068666462Frequency ω / 2π [THz]

6

4

2

0

-2

ISB

Gain

[cm

-1]

Outp

ut A

mpl

itude

s [a

.u.]

DFG

FWM-upFWM-down

DFB

Figure 5.5: A full output spectrum is given in blue colour. The purple lines show the maximum

frequency detuning for the DFG input and the respective FWM output signals. The

intersubband (ISB) gain of the AR-QCL, which was measured independently for the used

current density with SRIR micro-spectroscopy [84], is drawn in green colour.

An exemplary output spectrum is shown in Fig. 5.6(a) for a splitting δω = 2π× 0.31 THz. It

contains all the pump, probe and FWM contributions. Beneath the signals at ω1, ω2 and the

FWM signal at ω3 = 2ω1−ω2 =ω1−δω, a fourth peak is identified at ω4 = 2ω2−ω1 =

ω2 − δω. The latter is the result of the mixing of two probe and one pump photon. In

order to prevent any damage of the sensitive detector, an additional 1% transmission neutral

density filter is inserted into the beam path while the grating spectrometer is transparent at

the pump and probe frequencies.

In order to properly determine the real peak power, the measured amplitudes of DFG-

and FWM-pulses need to be corrected for the bandwidth-limited detection. This is done

by multiplying the amplitudes with a factor of 7.5, which results from the theoretical

convolution of a 100 ps pulse with an 800 MHz low-pass. In Fig. 5.6(b), the behaviour of the

FWM-signals is presented as a function of DFG input power. As expected, the FWM output

power is quadratic in the pump (DFG) P1 and linear in the probe (DFB-QCL) P2 powers,

respectively, i.e. P3 ∝

χ (3)

2P2

1 P2 (lower FWM frequency) and P4 ∝

χ (3)

2P1P2

2 (upper FWM

frequency), where χ (3) is the third-order non-linear optical susceptibility, and Pi is the mode

peak power.

Because of P1 and P2 P3 and P4, the effect of the FWM signalω4 onω3 is neglected. The be-

haviour can thus be described with degenerate four-wave mixing. Using Eq. 5.6 and Eq. 5.7,

5.2. Measurement 93

0.20

0.15

0.10

0.05

0.00De

tect

or A

mpl

itude

[V]

70.069.869.669.469.269.068.8Frequency ω / 2π [THz]

DFB-QCL x 0.01ω2

DFG x 0.01ω1

FWM-upω4

FWM-downω3

(b)$

(a)$

1.00.80.60.40.20.0

Norm

aliz

ed S

igna

l [a.

u.]

1.00.80.60.40.20.0DFG Pump Input Power [a.u.]

FWM down @ ω3 FWM up @ ω4

Figure 5.6: The measured output spectrum for a frequency detuning of δω= 2π× 0.31 THz shows

the FWM peaks at the positions required by energy conservation, i.e. ω3 = 2ω1 −ω2

and ω4 = 2ω2 −ω1. A 1% neutral density filter is present at the DFG and DFB-QCL

frequencies to protect the detector. (b) The FWM output signals as a function of input

power of the DFG confirm the expected linear and quadratic behaviour.

the amplitude A3 of the FWM-down signal is determined to

A3 =κ

g − i∆β

exp

3

2g − i∆β

z

− exp g

2z

, (5.8)

where

κ=−iµ0ε0ω

23χ(3)

16β36A2

1A2 (5.9)

gives the non-linear mixing originating from the two input fields, g is the frequency-

dependent gain, µ0 and ε0 are the permeability and permittivity, respectively, β3 is the

propagation constant at ω3, and A1 and A2 are the amplitudes of pump and probe signals,

respectively.

The phase-matching condition reads

∆β

=

2β1− β2− β3

= 0 (5.10)


and is satisfied, if

∆β l

2π, (5.11)

i.e.

∂ ng

∂ λ

(δω)2

ω20

1, (5.12)

where ng is the group refractive index [179].

For the reported low group velocity dispersion below 0.01µm−1 observed in QCLs [12,

180], and the cavity length L = 3 mm present in this experiment, this results in δω

2π× 12 THz, which is much below the frequency detunings δω applied in this work.

Hence, the group velocity dispersion ∆β in Eq. 5.8 is neglected. In the following, the

boundary conditions A3(z = 0) = 0 and the determined output fields for a δωmin = 0.21 THz

at z = L are used, i.e. E1 = 644 kV/m, E2 = 544 kV/m and E3 = 5 kV/m, as obtained

by

Ek =

r

2Ii

cε0n, (5.13)

where Ik = Pk/A gives the field intensity over a waveguide cross-section area of A=16µm2

and the peak powers are P1 = 30 mW, P2 = 21.4 mW and P3 = 0.61 mW, respectively. The

gain g present along the AR-QCL is independently determined as 5.7 cm−1, which is achieved

prior to the roll-over of the AR-QCL. This results in χ (3) = (0.9±0.2) ·10−15 m2 V−2.

5.3 Modelling of χ(3)

The third-order optical non-linearity χ (3) can be described in several ways. One approach is

the use of a power series expansion of the material response with respect to the incident

electromagnetic field and a subsequent perturbation treatment, as comprehensively shown

by Boyd [181]. As pointed out, however, this method fails under certain conditions [182],

like in the case of a saturable absorber. Here, the material parameters are a direct function

of the incident field intensity, and obviate the convergence of the power series. Also, under

resonant excitation of a system, an adequate description is not possible any more. Those

effects can be accounted for by the use of the two-level approximation, where χ (3) is

5.3. Modelling of χ(3) 95

described by the response of a two-level system (i.e. atom) to the presence of an optical

field. Its dynamical behaviour is formulated in terms of a system of equations of motion

for the inversion between the upper and the lower state population, and for the dipole

moment amplitude. A characteristic carrier relaxation T1 and dipole dephasing time T2

describe the system. The dephasing time is in general shorter than the carrier relaxation

time because electrons can be scattered to change their momentum while staying in the

same subband [183]. The derivation of an analytical expression for χ (3), which is given in

full details in [182], is sketched in the following.

For any given state ψS of a physical system, the Schrödinger equation of quantum mechanics

is fulfilled and reads

i~∂ψS

∂ t= HψS, (5.14)

where H is the Hamiltonian of the system. This equation describes the time-evolution in a

general way. The Hamiltonian is usually given by

H = H0+ V (t), (5.15)

where H0 models the unperturbed system and V (t) accounts for its interaction energy with

an external force, e.g. an electromagnetic field.

If the precise state of a system is not known and/or is not computationally feasible to follow,

the density matrix formalism can be used to provide a statistical description. It is the possibil-

ity to include effects such as the broadening of atomic transitions, which makes the density

matrix formalism so viable as compared to other approaches.

The case of a two-level system with lower (a) and upper (b) state is fully described by the

density matrix

ρ =

ρaa ρab

ρba ρbb

, (5.16)

where the elements ρnn denote the probability that the system is in the energy eigenstate n.

The off-diagonal elements ρnm indicate the coherence between two states n and m and, in


our case, are proportional to the electric dipole moment of the atom, which is described by

the electric dipole approximation

V (t) =−µ E(t), (5.17)

where µ = q z is the product of electric charge q and dipole matrix z.

By phenomenologically taking the decay processes into account, it then follows for a free

two-level atom without an external field (Vba = 0)

• that the population inversion relaxes to its equilibrium value with a characteristic time

T1, which is consequently termed population relaxation time, and

• that the dipole moment oscillates at a frequency ωba =Eb−Ea

~ and is damped by the

dipole dephasing time T2.

The influence of a monochromatic electromagnetic field E(t) = E e−iωt can be described

using the rotating-wave approximation. Only the off-diagonal element of the Hamiltonian V

are non-vanishing and read

Vba = V ∗ab =−µbaE e−iωt . (5.18)

The definition of the slowly varying quantity σba(t) = ρba(t) eiωt , and the introduction

of the detuning of the electromagnetic field from resonance ∆ = ω−ωab and the pop-

ulation inversion w = ρbb − ρaa allow to reframe the system of density matrix equa-

tions of motion. Using the complex amplitude p = µabσab of the dipole moment, this

yieldsdp

d t=

i∆+1

T2

p−i

~

µba

2E w,

dw

dt=−

w−w(eq)

T1+

4

~ℑ(p E∗).

(5.19)

In order to account for the presence of both a (strong) pump and (weak) probe field in the

four-wave mixing experiment, the complex amplitude of the electromagnetic field is defined

as

E = E0+ E1 e−iδωt , (5.20)

5.3. Modelling of χ(3) 97

where δω is the frequency difference of the two fields. The ansatz for the solution of Eq. 5.19

reads

p = p0+ p1 e−iδωt + p−1 eiδωt ,

w = w0+w1 e−iδωt +w−1 eiδωt ,(5.21)

where the quantities p0 and w0 represent the solution without any probe field, and the

four-wave mixing component at (w − δω) is described by p−1 and w−1. This leads

to a set of six coupled equations for the components of p and w, which can be itera-

tively solved. The third-order non-linear polarisation P of the material at the frequency

(w − δω) is given by adding up the dipole moments p−1 of all atoms, i.e. P(w − δω) =

N p−1.

By comparison, this then yields for the third-oder non-linearity

χ (3)(∆,δω) =2δN0(q · zi j)4

3ε0~3

(δω−∆− i/T2)(−δω+ 2i/T2)(∆+ i/T2)−1

(∆−δω+ i/T2) · D∗(δ), (5.22)

where δN0 is the volume population inversion per QC period.

The quantity D(δ) is defined as

D(δ) =

δω+i

T1

δω−∆+i

T2

δω+∆+i

T2

−Ω2

δω+i

T2

, (5.23)

where the Rabi-frequency is defined as

ΩR =qzi j E

~. (5.24)

Assuming the low field limit (i.e. the condition ΩRT2 1), the last term in Eq. 5.23 can be

neglected.

In order to determine χ (3), the characteristic time values are modelled by transport model

simulations based on the density matrix approach [144] and result in T1 = 0.29 ps and T2 =

0.15 ps. For the determined carrier population inversion of δN0 = 1.9 · 1015 cm−3 and the

dipole matrix element zi j = 1.6 nm, the value obtained is χ (3) = 2.5 ·10−15 m2 V−2. This


agrees reasonably well with the measurement, taking into account the uncertainties in both

the experimental and modelled parameters, and the overlap factor of the optical mode with

the active region.

5.4 Discussion and Conclusion

In Fig. 5.7(a), the spectra for the DFB-QCL and the range of DFG tuning are given along a

series of FWM-down spectra. The efficiency of the mixing from the input to the output FWM

signals was observed to be roughly -20 dB. The integrated FWM spectra, normalised to the

DFG power and the spectral gain, directly result in FWM efficiency, which is proportional

to χ (3), see Fig. 5.7(b). The determined roll-off with respect to the frequency detuning

corresponds nicely to the behaviour of Eq. 5.22 for the introduced times T1 = 0.29 ps and

T2 = 0.15 ps.

In the case of a non-coated Fabry-Pérot QCL (FP-QCL) with remaining facet reflectivities

of 27%, strong mode competitions are observed when the FP-QCL is operated near its

lasing threshold. This is shown in Fig. 5.8, where the (amplified) output power of pump,

probe, and FWM signals are given with respect to the input power of the DFG pump.

Noteworthy, the FWM-down signal is only present above a certain DFG input power. In

contrary, the FWM-up signal (quadratical dependence of the constant strong DFB field)

arises immediately. For a detailed understanding of these observations, both the reflection

from the facets and the loss modulation originating from spatial hole burning would need

to be considered. They are responsible for intensity variations in multimode operation, as

observed in [172].

Hence, the maximum possible frequency separation of δωmax = 2π× 3.05 THz, where

FWM was still observed, is determined to be more than two orders of magnitude higher

than the FP mode spacing δωmax = 2π× 15 GHz in a laser with a cavity length of 3 mm.

Combined with the measured conversion efficiency, which is above -40 dB over almost the

full examined detuning range, and thus adequate for passive FM mode-locking as reported

in [184], an important FWM mechanism was shown for enabling the mode proliferation

5.4. Discussion and Conclusion 99

0.01

0.1

1

10

FWM

Out

put [

a.u.

]

0.12 3 4 5 6 7 8 9

12 3 4 5

Frequency Detuning ω / 2π [THz]

Measured FWM Modeled FWM

10-4

10-3

10-2

10-1

100

Sign

al [

V]

7069686766656463Frequency ω / 2π [THz]

DFB x 0.01

FWM

DFG x 0.01tuning range

FWM spectra DFB-QCL DFG

(a)

(b)

Figure 5.7: (a) Combination of the output spectra of the FWM (red) for the tuning of the DFG

frequency between 69.5 and 66.7 THz (blue curves), and the DFB-QCL (green). (b) The

determined FWM output, when normalised to the DFG input power and the spectral

dependence of the AR-QCL gain, corresponds well to Eq. 5.22.

as needed for the generation of frequency comb in QCLs [12]. The assignment to the

intrinsic non-linear characteristics of QCLs will allow for novel ways to reach flexible

and ultra-fast wavelength conversion processes, which are nowadays only common at the

telecommunications wavelength of 1.5µm. Joined with the possibility of room temperature

continuous-wave operation with very low thermal dissipation [114], QCLs are prominent

candidates in the mid-IR for the use in autonomous spectroscopy and communications

applications.


806040200

Outp

ut S

igna

l [m

V]

0.300.250.200.150.100.050.00

DFG Pump Input Power [a.u.]

30

20

10

0

FWM-down threshold

FWM-down @ ω3 FWM-up @ ω4

DFB DFG

(a)

(b)

Figure 5.8: (a) The measured FWM-down signal shows a clear threshold behaviour with respect to

the DFG pump input power at constant DFB-QCL and FP-QCL pumping. This was not

observed for the FWM-up signal. (b) The decrease in the amplified DFB output originates

from the gain drain upon increased DFG input power.

Chapter 6

Conclusion

The pump-and-probe and micro-spectroscopy techniques in the infrared at the Swiss Light

Source SLS have proven to have strong potential for studies on a wide range of systems

and materials, such as semiconductor materials, quantum cascade lasers, and photocatalytic

surfaces. It was demonstrated that this synchrotron-based spectroscopy allows for the

measurement of broadband information in the energy range between 0.1 - 1.1 eV. The

high-brilliance of synchrotron IR was used to investigate samples at the diffraction-limit of

IR radiation. The achieved time-resolution of 100 ps is well suited to investigate electron

and hole carrier dynamics upon excitation with strong visible, near- or mid-infrared laser

pulses.

The optical properties of the direct interband transition in InGaAs and germanium were

studied to understand the principle of their gain build-up and lasing properties. Using

near-IR excitation, it was shown that a high direct-bandgap gain in germanium of more

than 850 cm−1 can be achieved. However, due to even stronger pumped-induced absorption

between the valence bands, no net gain could be achieved. With our understanding of

the physics in germanium, optical amplification does not seem feasible given the current

technological limits of strain and doping. Nevertheless, a high-quality doping and higher

tensile-strain seem promising for the further development of direct-bandgap lasing in

101

102 Chapter 6. Conclusion

germanium.

The chemical reaction spectroscopy of photocatalytic surfaces, decorated with TiO2 for

example, resolved and distinguished molecular absorption lines. It was shown, that the

combination of photocatalysts and plasmonic structures exhibit great potential for the

conversion of sunlight into chemical or electrical energy. The dynamic studies enabled

to follow the charging and de-charging mechanisms of the catalyst, and the injection of

electrons.

A powerful in-situ spectroscopy tool was delivered for the investigation of quantum cascade

laser devices. Their gain and absorption features were experimentally and theoretically

compared. It was found that the distribution of carriers in k-space as provided by the

non-linear Green’s function approach is necessary in order to reproduce the absorption

over the full energy range and also results in a better prediction of the differential gain

coefficient. Moreover, it was shown that the system is of great use for conceptual studies

such as the investigation of broadband as well as quantum dash cascade structures. These

results will make an impact on device qualities, as measured by higher emission efficiency,

larger bandwidth and higher operation temperatures.

The study of third-order optical non-linearities in quantum cascade lasers aimed for a better

understanding of the mode proliferation needed for a comb generation. By simultaneous

injection of two narrow-band laser sources, namely a single mode quantum cascade laser and

a broadly tuneable source, into an anti-reflection coated quantum cascade amplifier, four-

wave mixing over more than 3 THz was observed. This is more than two orders of magnitude

larger than the FP mode spacing in a typical laser cavity. Hence, this mixing mechanism was

found to be an important driving factor in mode proliferation in broadband QCLs as well

as opening up novel opportunities for ultra-fast wavelength conversion applications in the

mid-IR.

List of Abbreviations

2Ph Two-phonon resonance

ADC Analog-to-digital converter

AR Anti-reflection

CB Conduction band

CMOS Complementary metal-oxide-semiconductor

CW Continuous wave

DAQS Data acquisition system

DFB Distributed Feedback

DFG Difference frequency generation

DM Density matrix

DG Direct-bandgap

EL Electroluminescence

FCA Free-carrier absorption

FP Fabry-Pérot

FTIR Fourier-transform infrared

FWM Four-wave mixing

Ge Germanium

HH Heavy-hole

InGaAs Indium gallium arsenide

IR Infrared

JDOS Joint density of states

KTA Potassium titanyle arsenate

LH Light-hole

103

104 List of Abbreviations

LO Longitudinal optical

MBE Molecular beam epitaxy

NEGF Non-equilibrium Green’s function

NID Not-intentionally doped

OPA Optical parametric amplification

OPG Optical parametric generation

OPO Optical parametric oscillation

PCM Phase change material

PhC Photonic crystal

PIA Pump-induced absorption

PL Photoluminescence

PLL Phase-locked loop

PPLN Periodically-poled Lithium Niobate

QCL Quantum cascade laser

QD Quantum dash

RegA Regenerative amplifier

RF Radio frequency

RT Room temperature

SHG Second harmonic generation

Si Silicon

SMSR Side-mode suppression ratio

SO Split-off

SLS Swiss Light Source

TE Transverse-electric

TM Transverse-magnetic

VB Valence band

VIB Valence interband

VM Vector modulator

WG Waveguide

WPE Wall plug efficiency

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Acknowledgements

First, I would like to thank Prof. Dr. Jérôme Faist for agreeing to be the responsible faculty

member for this thesis. He was always very helpful and offered great advice concerning

the physics of quantum cascade systems. I would like to thank equally my supervisor, Dr.

Hans Sigg, at PSI for giving me the opportunity to pursue a PhD in his research group, in the

interesting field of synchrotron-based infrared research. He was a great help in setting up

the experiments and in giving advice on how to improve the quality of the measurements.

Furthermore, I would like to thank Prof. Dr. Gottfried Strasser for agreeing to co-examine

my thesis.

I also want to express my gratitude to my colleague Dr. Lee Carroll, with whom I had the

pleasure to construct and use the pump/probe system at the infrared beam line of the SLS.

He has a great talent to teach people how to deal with physics, from which I could profit

immensely during my time at PSI. He was also a great help in reviewing this thesis. I am

especially grateful to Dr. Philippe Lerch for all his support and help in working at the beam

line, and for being more than just a colleague.

At LMN, I would like to thank Prof. Dr. Jens Gobrecht for leading such a pleasant research

institute. My particular thanks go to Stefan Stutz for his priceless support in technical ques-

tions and more. I will remember fondly my PhD colleagues Dr. Patrick Helfenstein, Richard

Geiger, Thomas Siegfried and Stefan Neuenschwander. I further thank Thomas Neiger for the

great Mac equipment and Edith Meisel for back-office support.

In my group at ETH, I would like to thank Andreas Hugi, Borislav Hinkov, Dr. Mattias Beck,

Dr. Alfredo Bismuto, Dr. Valeria Liverini, Dr. Laurent Nevou, Giancarlo Cerulo and Dr. Arun

125

126 Acknowledgements

Mohan for the collaboration and in particular for the preparation of QC samples. I also

thank Erna Hug for the administrative support at ETH.

At the SLS, I thank Dr. Daniel Treyer, Dr. Jacinto Sa, Dr. Luca Quaroni, Dennis Armstrong,

Babak Kalantari and Dr. Stephan Hunziker for the various technical and computing support

with regards to the beam line.

I would like to thank Dr. Romain Terazzi from AlpesLaser and Prof. Dr. Andrzej Kolek from

the University of Technology, Rzeszow in Poland, for the support in the simulation of QC

structures.

I would like to thank my parents, Hanni and Hans Peter Friedli, for giving me the opportu-

nity to study at the ETH Zürich and for all the moral support they gave me during the past ten

years of my studies; and my two brothers Beat und Michael Friedli.

Finally, I want to express my profound gratitude to my fiancee Doris who stood by my side

during these sometimes stressful times and showed a lot of understanding, when I stayed

over night or during weekends on beam time.

Curriculum Vitae

Personal Details

Name Peter Friedli

Born 3 Februar 1982 in Baden, Switzerland

Citizen of Lützelflüh BE, Switzerland

Email [email protected]

Education

10.2008 – 04.2013 Ph.D. research

Subject: Linear and Non-Linear Spectroscopy of Semiconductors using

Synchrotron Infrared

Laboratory of Micro- and Nanotechnology, PSI, Villigen

Quantum Optoelectronics Group, ETH Zürich

09.2008 – 01.2009 Teaching tutor

University of Applied Sciences, Windisch, Switzerland

02.2008 – 08.2008 Master Thesis

Subject: Electrical characterisation of contacts for Active Photonic Crystals

Communication Photonics Group, ETH Zürich

10.2007 – 12.2007 Internship

Bookham (Switzerland) AG, Zurich

127

128 Curriculum Vitae

07.2007 – 09.2007 Internship with the IAESTE international exchange program

Subject: Modelling of Photonic Crystals

Nanoscale Systems Integration, University of Southampton, England

09.2005 – 05.2009 Certificate of Teaching Ability

ETH, Zürich

10.2003 – 08.2008 Master of Science ETH

Electrical Engineering and Information Technology

ETH, Zürich

10.1998 – 05.2002 Matura (A-Levels)

Kantonsschule, Baden.

List of Publications

Peer-reviewed Journal Papers

As primary author

• P. Friedli, H. Sigg, B. Hinkov, A. Hugi, S. Riedi, M. Beck and J. Faist. Four-Wave Mixing

in a Quantum Cascade Laser Amplifier, Appl. Phys. Lett., vol. 102, no. 22, p. 222104,

2013.

• P. Friedli, H. Sigg, A. Wittmann, R. Terazzi, A. Kolek, M. Beck and J. Faist. Synchrotron

infrared transmission spectroscopy of a quantum cascade laser correlated to gain models.

Appl. Phys. Lett., vol. 102, no. 1, p. 012112, 2013.

As co-author

• J. Sá, G. Tagliabue, P. Friedli, J. Szlachetko, M. H. Rittmann-Frank, F. G. Santomauro,

C. J. Milne, M. Nachtegaal, and H. Sigg. Direct observation of electron excitation on Au

localized surface plasmon, submitted, 2013.

• J. Sá, P. Friedli, R. Geiger, Ph. Lerch, M. H. Rittmann-Frank, C. J. Milne, J. Szlachetko,

F. G. Santomauro, J. A. van Bokhoven, M. Chergui, M. J. Rossi and H. Sigg. Transient

mid-IR study of electron dynamics in TiO2 conduction band. Analyst, vol. 138, no. 7, p.

1966, 2013.

129

130 List of Publications

• L. Carroll, P. Friedli, S. Neuenschwander, H. Sigg, S. Cecchi, F. Isa, D. Chrastina, G.

Isella, Y. Fedoryshyn, and J. Faist. Direct-Gap Gain and Optical Absorption in Germanium

Correlated to the Density of Photoexcited Carriers, Doping, and Strain. Phys. Rev. Lett.,

vol. 109, no. 5, p. 057402, 2012.

• L. Carroll, P. Friedli, P. Lerch, J. Schneider, D. Treyer, S. Hunziker, S. Stutz, and H. Sigg.

Ultra-broadband infrared pump-probe spectroscopy using synchrotron radiation and a

tuneable pump. Rev. Sci. Instrum., vol. 82, no. 6, p. 063101, 2011.

As contributing author

• P. Lerch, L. Quaroni, J. Wambach, J. Schneider, D. B. Armstrong, D. Rossetti, F. L.

Mueller, P. Peier, V. Schlott, L. Carroll, P. Friedli, H. Sigg, S. Stutz, and M. Tran. IR

beamline at the Swiss Light Source. J. Phys.: Conf. Ser., vol. 359, p. 012003, May 2012.

• R. Kappeler, P. Kaspar, P. Friedli, and H. Jäckel. Design proposal for a low loss in-plane

active photonic crystal waveguide with vertical electrical carrier injection. Opt. Express,

vol. 20, no. 8, p. 9264, 2012.

• L. Nevou, V. Liverini, P. Friedli, F. Castellano, A. Bismuto, H. Sigg, F. Gramm, E.

Müller, and J. Faist. Current quantization in an optically driven electron pump based on

self-assembled quantum dots. Nature Phys., vol. 7, no. 5, pp. 423–427, Feb. 2011.

• P. Kaspar, R. Kappeler, P. Friedli, and H. Jäckel. Air-bridge contact fabrication for in-plane

active photonic crystal devices. Indium Phosphide & Related Materials (IPRM), 2010

International Conference on, pp. 1–4, May 2010.

Presentations

• P. Friedli, B. Hinkov, S. Riedi, A. Bismuto, A. Hugi, M. Beck, H. Sigg, J. Faist. Non-

Degenerate Four-Wave Mixing in a Quantum Cascade Laser. International Quantum

List of Publications 131

Cascade Laser Workshop and School IQCLSW, Vienna (Austria), September 2 - 6, 2012.

• P. Friedli, B. Hinkov, S. Riedi, A. Bismuto, A. Hugi, M. Beck, H. Sigg, J. Faist. Non-

Degenerate Four-Wave Mixing in a Quantum Cascade Laser. 31st International Confer-

ence on the Physics of Semiconductors ICPS, Zurich (Switzerland), July 29 - August 3,

2012.

• P. Friedli, V. Liverini, A. Hugi, Ph. Lerch, H. Sigg, J. Faist. Synchrotron Microspectroscopy

of Quantum Cascade Laser Devices based on Quantum Wells and Quantum Dashes.

Conference on Lasers and Electro-Optics CLEO, San José (California), May 6 - 11,

2012.

• P. Friedli, A. Hugi, V. Liverini, H. Sigg, Ph. Lerch, J. Faist. Broadband Gain and Loss

Characterisation of Quantum Cascade Laser based on Quantum Wells and Dashes using

Synchrotron Infrared Radiation (invited). Joint Annual Meeting of the Swiss Physical

Society and the Austrian Physical Society, Lausanne (Switzerland), June, 15.06.2011.

• P. Friedli, A. Wittmann, H. Sigg, J. Faist. Characterisaton of Quantum Cascade Laser

Devices using Synchrotron Infrared Microspectroscopy. SLS Symposium on IR Pump and

Probe, Villigen (Switzerland), October 2009.

• P. Friedli, A. Wittmann, H. Sigg, J. Faist. Upper Laser State Related Gain and Loss in High

Performance Single Mode Quantum Cascade Laser Devices. The 10th International Con-

ference on Intersubband Transitions in Quantum Wells, Montreal (Canada), September

6 - 11, 2009.

• P. Friedli, A. Wittmann, L. Carroll, H. Sigg, J. Faist. Gain/Loss Device Study of Narrow-

Ridge Buried Heterostructure Quantum Cascade Lasers Using Broadband Infrared Trans-

mission. 19th International Congress on Photonics in Europe CLEO Europe, Munich

(Germany), June 14 - 19, 2009.

132 List of Publications

Posters

• P. Friedli, H. Sigg, A. Wittmann, A. Hugi, S. Riedi, V. Liverini, J. Faist, Ph. Lerch

Synchrotron Infrared Transmission Microspectroscopy of Quantum Cascade Laser Devices

based on Quantum Wells and Quantum Dashes. 6th International Workshop on Infrared

Spectroscopy and Microscopy with Accelerator-Based Sources WIRMS, Trieste (Italy),

September 4-8, 2011.

• L. Carroll, P. Friedli, P. Lerch, J. Schneider, D. Treyer, S. Hunziker, S. Stutz, and H. Sigg.

Ultra-broadband infrared pump-probe spectroscopy using synchrotron radiation and a

tuneable pump. 6th International Workshop on Infrared Spectroscopy and Microscopy

with Accelerator-Based Sources WIRMS, Trieste (Italy), September 4-8, 2011.

• P. Friedli, H. Sigg, R. Terazzi, A. Wittmann, J. Faist. Time-resolved gain measurement of

mid-IR quantum cascade laser devices using broadband synchrotron radiation. Interna-

tional Quantum Cascade Laser Workshop and School IQCLSW, Florence (Italy), August

30 - September 3, 2010.

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