Quantum Dot Based Light Sources for Lab-on-a-chip

Master Thesis

Quantum Dot Based LightSources for Lab-on-a-chip

Mads Brøkner Christiansen (s001612)[email protected]

Supervisor: Anders Kristensen

MIC – Department of Micro and NanotechnologyTechnical University of Denmark

1st November 2005

Abstract

This project is concerned with the use of colloidal II-VI semiconductor quantumdots as active material in lasers for lab-on-a-chip applications. Quantum dotsare interesting for lasing applications, because the emission color can be tunedby altering the diameter. The band structure and carrier decay routes arealtered by the quantum confinement in the nm sized crystals, causing the laserlevels to become depleted within pico-seconds. This makes it more complicatedto achieve population inversion. There is no fundamental barrier to quantumdot lasing, however.

The first measurements made were on CdS and ZnS capped CdSe quantumdots in TOPAS polymer. Measurements were made both on irregular volumes ofmaterial and on waveguides fabricated by a combination of UV and nanoimprintlithography. PMMA waveguides doped with rhodamine 6G were also fabricated.Strong light amplification was seen from the rhodamine samples when pumpedwith 532 nm pulses from a Nd:YAG laser, while no amplification was measuredfrom the quantum dots. The luminescence from the quantum dots was also verydifficult to detect.

Evanescent gain coupled whispering gallery mode lasers were fabricated withboth CdSe/ZnS quantum dots in hexane and rhodamine 6G in ethanol as activematerials. Using rhodamine resulted in lasing at low pump powers, but no lasingwas seen with quantum dots as active material.

The lack of succes with quantum dot lasing is attributed to aggregation ofquantum dots and too low concentrations.

Nanoimprinted DFB lasers with first order Bragg gratings were designed andfabricated from rhodamine 6G doped PMMA. Single mode lasing was achievedat low pump energy densities from the 532 nm Nd:YAG laser. The laserlinewidths were rather large, probably due to height variation of the cavities.

Resume

Dette projekt handler om brugen af kemisk fremstillede II-VI halvleder kvan-teprikker som aktivt materiale i lab-on-a-chip lasere. Kvanteprikker er inter-essante som aktivt lasermateriale, fordi emissionsbølgelængden kan bestemmesved at ændre diameteren. Bandstrukturen og henfalds-ruter for ladningsbær-erne ændres af de kvantemekaniske effekter i krystallerne, som er fa nm store.Det betyder at ladningsbærernes henfaldstid fra laser-niveauerne ma males i ps,og dette gør det mere kompliceret at opna populationsinversion. Der er dog ikkenogen fundamental barriere for at bruge kvanteprikker som lasermateriale.

De første malinger der blev foretaget var pa CdS og CdSe kvanteprikker medskaller af ZnS, opblandet i TOPAS polymer. Der blev foretaget malinger badepa irregulære klatter og pa bølgeledere, fremstillet ved en kombination af UVog nanoimprint lithografi. Der blev ogsa fremstillet rhodamin 6G dopteredePMMA bølgeledere. Der blev malt kraftig forstærkning fra rhodaminprøverne,nar de blev pumpet med 532 nm pulser fra en Nd:YAG laser, men ingen forstærkn-ing blev malt fra kvanteprikkerne. Det var ogsa svært at male den spontaneemission fra kvanteprikkerne.

Der er ogsa blevet fremstillet whispering gallery mode lasere, bade med CdSe/ZnSkvanteprikker i hexan og rhodamine 6G i ethanol som aktive materialer. Brugenaf rhodamin resulterede i laserlys ved lave pumpeeffekter, men det lykkedes ikkeat opna laserlys fra kvanteprikker.

Den manglende succes med forstærkning fra kvanteprikkerne tilskrives udfæld-ning af kvanteprik-aggregater og for lave koncentrationer.

Nanoimprintede DFB lasere med første ordens Bragg gitre blev designet og frem-stillet af rhodamin dopteret PMMA. Ved sma energitætheder i pumpepulsernefra 532 nm Nd:YAG laseren blev der genereret laserlys i en enkelt mode. Lasernesemissionslinier var dog temmelig brede, formentlig pga. højdevariationer pakaviteterne.

Preface

This thesis is submitted as partial fullfillment of the requirements for obtaininga Master of Science degree in Engineering Physics from the Technical Universityof Denmark (DTU). The project has been carried out at MIC - Department ofMicro and Nanotechnology in the period from November 1st 2004 to November1st 2005 with Anders Kristensen as supervisor.

I have been supported financially by the Oticon Foundation. Their generousityhas enabled me to visit our collaborators in Bari, Italy, to see the fabrication ofthe colloidal quantum dots used, and discuss material parameters. The grantalso makes it possible to visit international conferences, to present my resultsfrom the imprinted DFB lasers, fabricated during the last weeks of my project.

I would like to thank for the help and support of my supervisor Anders Kris-tensen. His enthusiasm and new ideas have always helped me continue work-ing, though things seemed rather hopeless at times during the project. Also, Ithank the rest of the lab-on-a-chip lasers and nanoimprint lithography group forfruitfull discussions, invaluable help with my project, and a pleasant workingenvironment. I also thank my office mates in room 119, working there is neverboring.

From the group I particularly thank Ph.D. student Søren Balslev for alwaysbeing ready to answer my questions, from his seemingly infinite amount ofknowledge on lasers, and M.Sc. student Mikkel Schøler, who, during the lastfew weeks of the project, worked hard on developing the clean room process forfabrication of the DFB laser gratings, and also for helping me measure the laserproperties, when time was constrained.

The DANCHIP staff is acknowledged for keeping the clean room in such goodcondition and for helping with processing questions. I am gratefull to HelleVendelbo Jensen for dicing my wafers with very short notice, though they weresometimes delivered late friday afternoons.

I thank M. Lucia Curri and her group in Bari, not just for supplying the quantumdot material, but also for welcoming me and my family with such hospitality.We are all very gratefull for the time they took to show us all the interestingplaces around Bari, and I learned a lot from seeing the synthesis and polymerincorporation of the quantum dots.

viii PREFACE

Last, but far from least, I thank my wife Ninette for her patience with my occa-tionally quite time consuming project, and my daughter Dicte for sleeping wellat night, soon after she was born in Februrary 2005. I also thank them both fortheir smiles, which often distracted me from my work.

Mads Brøkner ChristiansenMIC – Department of Micro and Nanotechnology

Technical University of Denmark1st November 2005

Contents

List of figures xiii

List of symbols xv

1 Introduction 11.1 Motivation and Goals . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Litterature Survey . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Colloidal Quantum Dots . . . . . . . . . . . . . . . . . . 21.2.2 Quantum Dot Lasers . . . . . . . . . . . . . . . . . . . . . 31.2.3 Dye Doped Polymer Lasers . . . . . . . . . . . . . . . . . 6

1.3 Chapter Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Theoretical Overview 92.1 Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.1 Light Amplification . . . . . . . . . . . . . . . . . . . . . 102.1.2 Laser Cavities . . . . . . . . . . . . . . . . . . . . . . . . 132.1.3 Laser Action . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 Quantum Dot Fabrication . . . . . . . . . . . . . . . . . . . . . . 172.2.1 Synthesizing the Dots . . . . . . . . . . . . . . . . . . . . 172.2.2 Size and Shape Control . . . . . . . . . . . . . . . . . . . 192.2.3 Surface Modification and Polymer Incorporation . . . . . 19

2.3 Optical properties of Quantum Dots . . . . . . . . . . . . . . . . 202.3.1 Particle in a Sphere . . . . . . . . . . . . . . . . . . . . . 202.3.2 Generalization to Quantum Dots . . . . . . . . . . . . . . 212.3.3 Further Considerations . . . . . . . . . . . . . . . . . . . . 232.3.4 Absorbtion and Emission . . . . . . . . . . . . . . . . . . 262.3.5 Quantum Dot Lasing . . . . . . . . . . . . . . . . . . . . . 28

2.4 Optical Properties of Rhodamine 6G . . . . . . . . . . . . . . . 322.4.1 Rhodamine 6G and Solvents . . . . . . . . . . . . . . . . 322.4.2 Rhodamine 6G Lasing . . . . . . . . . . . . . . . . . . . . 332.4.3 Rhodamine Bleaching . . . . . . . . . . . . . . . . . . . . 352.4.4 PMMA Incorporation . . . . . . . . . . . . . . . . . . . . 36

2.5 Nanoimprint Lithography . . . . . . . . . . . . . . . . . . . . . . 362.5.1 Nanoimprint Principle and Theory . . . . . . . . . . . . . 36

x CONTENTS

2.5.2 Stamp Anti-Stiction Coatings . . . . . . . . . . . . . . . 412.5.3 Polymers for NIL . . . . . . . . . . . . . . . . . . . . . . . 42

2.6 Waveguide Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3 Functionalized Polymer 473.1 Waveguide Design and Fabrication . . . . . . . . . . . . . . . . . 48

3.1.1 Fabrication Process . . . . . . . . . . . . . . . . . . . . . 483.1.2 Fabrication Results . . . . . . . . . . . . . . . . . . . . . . 50

3.2 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.3.1 CdS Doped TOPAS . . . . . . . . . . . . . . . . . . . . . 563.3.2 CdSe/ZnS Doped TOPAS . . . . . . . . . . . . . . . . . . 583.3.3 Rhodamine 6G Doped PMMA . . . . . . . . . . . . . . . 58

3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4 WGM Fluid Lasers 614.1 Preparation and Working Principle . . . . . . . . . . . . . . . . 614.2 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5 Imprinted DFB Laser 695.1 Design and Fabrication . . . . . . . . . . . . . . . . . . . . . . . 69

5.1.1 Fabrication Process . . . . . . . . . . . . . . . . . . . . . 725.1.2 Fabrication Results . . . . . . . . . . . . . . . . . . . . . . 73

5.2 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

6 Conclusions and Outlook 87

A MATLAB programs 95A.1 Plotting Mode Refractive Index . . . . . . . . . . . . . . . . . . . 95A.2 Plotting Bragg Reflection . . . . . . . . . . . . . . . . . . . . . . 99

B Mask Designs 103B.1 Waveguide Masks . . . . . . . . . . . . . . . . . . . . . . . . . . . 103B.2 DFB Laser Masks . . . . . . . . . . . . . . . . . . . . . . . . . . 106

C Fabrication Recipes 109C.1 CdSe/ZnS TOPAS Waveguides . . . . . . . . . . . . . . . . . . . 109C.2 Rhodamine 6G PMMA Waveguides . . . . . . . . . . . . . . . . . 112C.3 Imprinted DFB Laser . . . . . . . . . . . . . . . . . . . . . . . . 115

List of Figures

1.1 Bandgap tuning of quantum dots by size confinement . . . . . . 31.2 Tuning of emission and absorbtion by size confinement . . . . . . 31.3 Lasing from CdSe in a microcapillary tube . . . . . . . . . . . . . 41.4 CdSe quantum dot based DFB laser spectra . . . . . . . . . . . . 51.5 CdS covered microsphere laser . . . . . . . . . . . . . . . . . . . 51.6 Evenescent field WGM laser . . . . . . . . . . . . . . . . . . . . . 61.7 Holographically pumped PMMA laser . . . . . . . . . . . . . . . 71.8 PMMA:Rhod6G DFB laser . . . . . . . . . . . . . . . . . . . . . 71.9 Nanoimprinted PMMA:Rhod6G laser . . . . . . . . . . . . . . . 8

2.1 Oscillator with a positive feedback loop . . . . . . . . . . . . . . 102.2 Absorbtion, spontaneous emission, and stimulated emission . . . 112.3 A four level pumping scheme . . . . . . . . . . . . . . . . . . . . 132.4 Modes in a simple cavity . . . . . . . . . . . . . . . . . . . . . . . 142.5 Resonance spectra with different Q . . . . . . . . . . . . . . . . . 152.6 Laser starting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.7 Inversion and output as functions of pump power . . . . . . . . . 172.8 Equipment for quantum dot synthesis . . . . . . . . . . . . . . . 182.9 CdSe/ZnS core shell nanocrystal . . . . . . . . . . . . . . . . . . 192.10 Spherical Bessel functions . . . . . . . . . . . . . . . . . . . . . . 212.11 A one-dimensional Bloch function . . . . . . . . . . . . . . . . . . 222.12 Valence bands of II-VI semiconductors . . . . . . . . . . . . . . . 242.13 Quantum numbers in a quantum dot . . . . . . . . . . . . . . . . 252.14 Exciton fine structure in quantum dots . . . . . . . . . . . . . . . 252.15 Absorbtion and emission of a CdSe sample . . . . . . . . . . . . . 262.16 Absorbtion and emission of a CdS modified TOPAS sample . . . 272.17 Calculated absorbtion and emission of a CdSe sample . . . . . . 282.18 Band structure for quantum dots . . . . . . . . . . . . . . . . . . 292.19 Decay times of excitons . . . . . . . . . . . . . . . . . . . . . . . 302.20 ASE from a CdSe quantum dot sample . . . . . . . . . . . . . . . 312.21 A rhodamine 6G perchlorate molecule . . . . . . . . . . . . . . . 332.22 Electron energy bands of a laser dye . . . . . . . . . . . . . . . . 342.23 Absorbtion and emission from rhodamine 6G . . . . . . . . . . . 352.24 Thermal stability of rhodamine in PMMA . . . . . . . . . . . . . 37

xii LIST OF FIGURES

2.25 Nanoimprint lithography . . . . . . . . . . . . . . . . . . . . . . . 382.26 SEM images of nanoimprint stamp and imprinted structure . . . 382.27 Flow regimes of a thermoplastic polymer . . . . . . . . . . . . . . 392.28 Length scales important for imprint time . . . . . . . . . . . . . 402.29 The monomers of TOPAS . . . . . . . . . . . . . . . . . . . . . . 422.30 The monomer of PMMA . . . . . . . . . . . . . . . . . . . . . . . 432.31 Modes in a planar waveguide . . . . . . . . . . . . . . . . . . . . 452.32 Mode refractive indices for TOPAS and PMMA waveguides . . . 46

3.1 Fabrication of TOPAS waveguide . . . . . . . . . . . . . . . . . . 493.2 Microscope images of CdSe/ZnS quantum dot doped TOPAS

waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.3 Confocal microscope images of CdSe/ZnS quantum dot doped

TOPAS waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . 513.4 Microscope images of rhodamine 6G doped PMMA waveguides . 513.5 SEM images of CdSe/ZnS quantum dot doped TOPAS waveguides 523.6 SEM images of rhodamine 6G doped PMMA waveguides . . . . . 533.7 Optical measurement setup . . . . . . . . . . . . . . . . . . . . . 553.8 Optical measurement on waveguides . . . . . . . . . . . . . . . . 553.9 Spectrum from a CdS doped TOPAS film . . . . . . . . . . . . . 563.10 Spectrum from a CdS doped TOPAS drop . . . . . . . . . . . . . 573.11 CdS TOPAS pump power destruction . . . . . . . . . . . . . . . 573.12 CdSe TOPAS pump power destruction . . . . . . . . . . . . . . . 583.13 Spectra from rhoadmine 6G doped PMMA waveguides . . . . . . 59

4.1 Photo of a whispering gallery mode laser . . . . . . . . . . . . . . 624.2 Drawing of a whispering gallery mode laser . . . . . . . . . . . . 634.3 Intensity profile of whispering gallery modes . . . . . . . . . . . . 634.4 Optical measurement on WGM laser . . . . . . . . . . . . . . . . 644.5 Spectra from WGM laser with rhodamine 6G . . . . . . . . . . . 654.6 Spectra from WGM laser with CdSe/ZnS quantum dots . . . . . 664.7 Spectra from WGM laser with CdSe/ZnS quantum dots in higher

concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.8 Spectra from rhodamine WGM laser, measured by Moon et al. . 67

5.1 Imprinted rhodamine 6G doped PMMA DFB laser . . . . . . . . 705.2 Reflectance of DFB gratings . . . . . . . . . . . . . . . . . . . . . 715.3 Imprinted DFB laser fabrication steps a-f . . . . . . . . . . . . . 745.4 Imprinted DFB laser fabrication steps g-i . . . . . . . . . . . . . 755.5 Incomplete filling of a DFB laser imprint . . . . . . . . . . . . . . 765.6 Incomplete filling by stamp bending . . . . . . . . . . . . . . . . 765.7 SEM image of a DFB laser stamp . . . . . . . . . . . . . . . . . . 775.8 SEM image of a DFB laser . . . . . . . . . . . . . . . . . . . . . 775.9 AFM images of DFB laser gratings . . . . . . . . . . . . . . . . . 785.10 Profile scan across a DFB laser . . . . . . . . . . . . . . . . . . . 795.11 Setup for optical measurements on the DFB lasers . . . . . . . . 805.12 Laser spectra and threshold curves for 4 DFB lasers . . . . . . . 815.13 Laser spectra from identical devices . . . . . . . . . . . . . . . . 825.14 Lifetime measurements on a 195 nm pitch DFB laser . . . . . . . 835.15 Lifetime measurements on a 205 nm pitch DFB laser . . . . . . . 84

LIST OF FIGURES xiii

B.1 Waveguide wafer layout . . . . . . . . . . . . . . . . . . . . . . . 104B.2 Waveguide chip layout . . . . . . . . . . . . . . . . . . . . . . . . 104B.3 Ends of waveguides on a chip, trench layer . . . . . . . . . . . . . 105B.4 Ends of waveguides on a chip, resist layer . . . . . . . . . . . . . 105B.5 DFB laser wafer layout . . . . . . . . . . . . . . . . . . . . . . . . 106B.6 DFB laser chip layout . . . . . . . . . . . . . . . . . . . . . . . . 107B.7 End of a DFB laser . . . . . . . . . . . . . . . . . . . . . . . . . . 108B.8 Middle of a DFB laser . . . . . . . . . . . . . . . . . . . . . . . . 108

xiv LIST OF FIGURES

List of symbols

Symbol Description Unitα Loss coefficient m−1

β Protrution coverageγ Gain coefficient m−1

η Viscosity Pa · sκ Coupling coefficientλ Wavelength mρ Mass density kg m−3

φ Flux density of photons s−1 m−2

σ Transition cross section m2

τ Time constant for decay sω Angular frequency s−1

ν Frequency Hza Bragg grating corrugation depth ma Radius of a cylinder or sphere mA Area m2

D See SE Energy JF Force Nh Height mJ Quantum numberJm Quantum numberk Wavenumber m−1

l Quantum numberL Length mm Quantum numbermeff Effective electron mass kgM molecular weight u or g/mole

xvi LIST OF SYMBOLS

Symbol Description Unitna Refractive index of material an Photon density m−3

n Quantum numbern Integer numberN1 Density of unexcited molecules m−3

N2 Density of excited molecules m−3

N N2 −N1 m−3

N Quantum numberNm Quantum numberp Pressure N m−2

P See SP Power WQ Quality factor of a resonatorReff Reflection of a gratings Protrution width mS Energy level/symmetry of spherical

harmonics S,P,D....tf Imprint time st Waveguide thickness mT Temperature KTeff Transmission of a gratingw Width mW Probability per time s−1

Constant Description Valuec Vacuum speed of light 3.00 × 108 m/sh Planch’s constant 6.63 × 10−34 J·s~ Reduced Planch’s constant h/2π 1.05 × 10−34 J·sm0 Electron mass 9.1 × 10−31 kgNa Avogadro’s number 6.02 × 1023 mol−1

Chapter 1Introdu tionThis chapter serves as an introduction to both the project and the thesis. Thefirst section is concerned with the motivation and goals of the project. Thisis followed by a litterature survey, introducing colloidal quantum dots and thecurrent state-of-the-art within quantum dot lasers and dye doped polymer lasers.The final section is a chapter outline, meant as a guide for reading the thesis.

1.1 Motivation and Goals

Miniaturization of analysis systems into lab-on-a-chip systems has a number ofadvantages [1]. The systems can be made very compact, and thus portable, andthey only need a tiny specimen. Furthermore, analysis relying on diffusion canbe performed very fast in miniaturized systems, because the difusion length isshorter.

The analysis in lab-on-a-chip systems often requires light, e.g. for absorbtionmeasurements. Thus, lab-on-a-chip systems are often made of polymers suchas PMMA or TOPAS, which are cheap, transparent and can be shaped withnanoimprint lithography, which keep processing costs fairly low [2, 3]. Nanoim-print lithography and the two polymers are described in section 2.5 on page36.

Since coupling light into microchips is quite difficult and time-consuming, gen-erating the light on the chip is beneficial [4]. Lasers are particularly interesting,because of the high quality of the light. If the lasers are to be integrated, withoutintroducing a new fabrication technology, they need to be made of polymer.

So far most lab-on-a-chip lasers have been made with organic dyes, such asrhodamine 6G, as active material. Rhodamine is described in section 2.4 on page32. The advantages of the dyes are that they can be dissolved in both polymersand fluids and it is possible to find a dye with emission at any wavelength in

2 1.2 Litterature Survey

the visible spectrum. The major disadvantage is that the dyes are bleachedduring use. Colloidal semiconductor nanocrystals, also called quantum dots,are interesting as a replacement of the dyes, because their emission can betuned, they can be incorporated into polymers, and they are more resistant tobleaching.

The initial goal of the project was to investigate the use of quantum dots asactive laser material for integration into polymer lab-on-a-chip systems. Thequantum dots are chemically synthesized II-VI semiconductor crystals a fewnm in size. After a period of investigation it became clear that achieving lightamplification was not possible with the available equipment and samples. Bet-ter quantum dot samples and higher quality laser cavities or a pump laserwith shorter pulses were needed. Thus, the work turned towards fabricationof nanoimprinted laser cavities, which could be made with both rhodamine 6Gand quantum dots as active material.

1.2 Litterature Survey

This section consists of three parts. First, colloidal quantum dots and theirproperties are introduced. The next part describes some successfull experimentwith lasing from quantum dots. The final part is concerned with PMMA basedpolymer lasers, both different cavity principles and fabrication schemes.

More information on lasers, quantum dot fabrication, quantum dot optical prop-erties, and nanoimprint lithography can be found in chapter 2. This sectionassumes the reader to have a basic understanding of these things.

1.2.1 Colloidal Quantum Dots

Colloidal Quantum dots are chemically synthesized semiconductor crystals withdiameters of a few nanometers. Quantum dots with a very tight size distributioncan be fabricated using this method [5, 6]. In this project, II-VI semiconductorsare used, more specifically CdS and CdSe with a ZnS shell.

When semiconductor crystals become small enough (around 10 nm [6]), the en-ergy levels begin to separate due to quantum confinement, leading to a largerband gap, as illustrated in Fig. 1.1. As described in section 2.3 different bulkmaterial degeneracies of the electron states are lifted in quantum dots, so Fig.1.1 is very simplified. Quantum confinement makes quantum dots very inter-esting as active material in lasers, because it is possible to tune the wavelengthof the light emitted, simply by changing the quantum dot size.

Depending on material and size, quantum dots can emit light in the entirevisible spectrum. Fig. 1.2 shows absorbtion and emission spectra for 7 differentcolloidal CdSe/ZnS core-shell samples with diameters ranging from 1.9 nm to 5.2nm [5]. The samples absorb at all wavelengths shorter than a certain maximum,and the emission peak is narrow because of the tight size distribution. Thefirst absorbtion peaks are at approximately 10 nm shorter wavelengths than

1.2 Litterature Survey 3

Figure 1.1: Electron energy bands of a bulk semiconductor and a quantum dot. In quantumdots confinement of the electronic states leads to a larger bandgap. This effect can be used totune the emission color. Note that the picture is very simplified.

Figure 1.2: Absorbtion and emission spectra from CdSe/ZnS core-shell nanocrystal sampleswith core diameters from 1.9 nm (emitting blue) to 5.2 nm (emitting orange). The absorbtionspectra are broad, while the emission spectra are narrow. Picture from [5].

the corresponding emission peaks. The reason for this Stokes shift, which isimportant for lasing, is discused in section 2.3.4.

Colloidal quantum dots are quite easy to manipulate, because the surface canbe covered in organic ligands, which makes it possible to treat them as largemolecules, and dissolve them in different solvents [6]. It is also possible toincorporate them in thin films of e.g. Poly(methyl silsesquioxane) [7] or otherpolymers such as PMMA or TOPAS [8, 9].

1.2.2 Quantum Dot Lasers

Victor I. Klimov et al. demonstrated light amplification by stimulated emissionfrom a CdSe quantum dot sample in 2000 [10]. Close packed films cast fromhexane/octane solutions were used, pumped with 100 fs laser pulses. The opticalgain was demonstrated at both 80 K and at room temperature. Fig. 2.20 on


page 31 shows a spectrum from the article, with a clear signature of amplifiedspontaneous emission (ASE).

By incorporating a close packed CdSe/ZnS film into a microcapillary tube,Klimov and his group also achieved true lasing into whispering gallery modes[11]. The refractive index of the quantum dot film is higher than that of thecapillary tube, making it possible for light to be guided inside the film, alongthe circumference, as shown in the inset of Fig. 1.3a. The main images in Fig.1.3 show ASE along the capillary tube axis and lasing in the whispering gallerymodes. The inset in Fig. 1.3b shows a piecewise linear pump/output curve,which is an indication of lasing.

In 2002 Eisler et al. reported a distributed feedback (DFB) laser [7]. Thegrating was defined by interference lithography, i.e. by exposing a photoresistfilm with two interfering UV laser beams. The grating was etched 50 nm down,into a SiO2 substrate in a reactive ion etch. A layer of heavily CdSe nanocrystaldoped Poly(methyl silsesquioxane), also called silica, was spun on the grating.This resulted in lasing when pumped with a 100 fs laser. Lasers with differentwavelengths were made by using different grating periods and different quantumdot sizes, as seen in Fig. 1.4.

The first example, to my knowledge, of CdS/ZnS core-shell nanocrystal lasingwas published in 2005 by Chan et al. [12]. Again, a doped silica film wasused. The film was spin coated in the presence of comercially available silicamicrospheres. This caused the microspheres to become covered in quantum dotdoped silica, as shown in Fig. 1.5a. When the spheres were pumped with 100 fslaser pulses, lasing was achieved into whispering gallery modes inside the dopedsilica film. A series of spectra with different pump intensities are shown in Fig.1.5b.

Kazes et al. have demonstrated lasing from CdSe quantum rods and dots inhexane solutions [13]. The cavity is shown to the left in Fig. 1.6, and treatedin more detail in section 4.1. It is an optical fiber inserted into a microcapillarytube with the active material in the region between the two. This laser relies

Figure 1.3: Lasing from CdSe quantum dots in a microcapillary tube. (a) ASE along the tube.The inset shows the setup. (b) Laser light from whispering gallery modes collected from theside of the tube. The inset shows output power as a function of pump pulse energy. Picturefrom [11].


Figure 1.4: Solid lines are laser spectra from four different DFB CdSe lasers. The dashedlines are the corresponding luminescence from the samples, when no feedback is present.Picture from [7].

Figure 1.5: (left) A flourescence microscope image of a CdS covered microsphere. (right)The laser spectra from a sphere pumped at different intensities. Pictures from [12].

on whispering gallery modes, but in contrast to the previous examples they areconfined in the optical fiber, rather than the amplifying medium. Amplificationhappens because the modes extend a short distance outside the fiber. This iscalled evanescent wave coupled gain.

The Q factor of the evanescent coupled whispering gallery cavity is very high.It has been shown to be above 107 for a similar setup with rhodamine as activematerial [14]. The high Q value of the cavity, combined with the evanescentwave gain, is probably the reasons that Kazes et al. achieved lasing in quantumdots with 5 ns pump pulses from a frequency doubled Nd:YAG laser. Laserspectra from quantum rods and a pump/output curve are shown in the rightpart of Fig. 1.6.


Figure 1.6: (left) Schematics of the setup for the fluid whispering gallery mode laser. It is anoptical fiber (blue) surrounded by active material in a fluid solution (yellow) and a microcap-illary tube (outer blue ring). The modes are confined to the central fibre and amplified throughthe evanescent field, which reaches into the fluid. Picture from [14]. (right) Laser spectrameasured with CdSe quantum rods in hexane as active material. Inset is a pump/outputcurve. The energy scale corresponds to a wavelength scale from 514 nm to 726 nm. Picturefrom [13].

1.2.3 Dye Doped Polymer Lasers

Lasing from Rhodamine 6G in PMMA was demonstrated in 1968 [15]. Sincethen, a number of different feedback schemes have been used in dye dopedPMMA thin films.

One way of getting feedback, and thus lasing, in a doped PMMA film is tointroduce periodic changes in the refractive index, thus giving a distributedfeedback effect. Because the refractive index of the PMMA film changes whenit is optically pumped, a non-permanent DFB grating can be made by pumpingthe material in lines. This has been done in a compact system by Voss et al.

[16], using a microchip pump laser and a prism, see Fig. 1.7. The prism isplaced on a dye doped film. The pump light interferes with itself inside theprism, causing the pump pattern on the film to become a series of interferencefringes. These lines give rise to the feedback. The advantages of the interferencepumping scheme is that the lasing wavelength can be tuned continuously duringoperation, simply by changing the α angle.

Another scheme is to structure the PMMA permanently by UV interferencelithography, and develop it in a solvent bath. This has been done in a couple ofvariations by Oki et Al. [17], see Fig. 1.8. Either the dye containing PMMA isstructured (Type I) or pure PMMA is structured, and then the active layer isspun on top (Type II).

The main drawback of DFB lasers relying on interference for grating definitionis, that the shape of the interference pattern can not be controlled very precisely.It is not possible to introduce a λ/4 phaseshift in the center of the laser, whichis beneficial for the feedback in the lowest order TE mode [18, 19].

A different approach to structuring is nanoimprinting or molding, where thepolymer is heated above the glass transistion temperature and shaped with a


stamp or mold. A vertically emitting laser with very good surface properties hasbeen molded by Li et Al. [20]. Nanoimprinting of a laterally emitting trapezoidlaser has been demonstrated by Nilsson et Al. [21], see Fig. 1.9. The trapezoidlaser uses total internal reflection on three sides, while the angle of incidence onthe fourth side is large enough to allow some light to escape. Both lasers aremultimode structures with relatively high threshold pump power for lasing.

Figure 1.7: A Rhodamine B doped PMMA film is pumped through a prism, resulting inan interference pattern. The pattern works as a DFB grating, because the refractive indexchanges where the film is pumped. The output wavelength can be tuned by altering the α-angle.Picture from [16].

Figure 1.8: (left) Two ways of DFB production by interference lithography. Either the dyecontaining film is structured, or the active layer is spun on a pre-prepared PMMA grating.(right) The second and third spectrum are from PMMA lasers of type I and II, respectively.The First spectrum is from a holographically pumped device like the one in Fig. 1.7. Picturesfrom [17].

8 1.3 Chapter Outline

Figure 1.9: Schematics and output from the nanoimprinted trapezoid laser. The modes arecontained on three sides by total internal reflection. Pictures from [21].

1.3 Chapter Outline

Chapter 2 is an introduction to theoretical concepts relevant to this work. Thefirst section is about the working principle of lasers, followed by a descriptionof quantum dot fabrication. The next two sections are concerned with opticalproperties of quantum dots and rhodamine 6G. The quantum dot section isquite detailed, because the theory regarding inversion of quantum dots is im-portant for this work, but also fairly complex. Rhodamine is much easier toinvert, so the rhodamine section is less detailed, but describes the basic proper-ties of rhodamine, compared to the properties of quantum dots. Nanoimprintlithography has been used for fabrication of waveguides, and thus it is naturalthat the two last sections are concerned with the theory of nanoimprinting andoptical waveguides.

Chapter 3 describes and discusses the experiments on polymer doped withquantum dots and rhodamine 6G. First, rather large drops of material were used,but later measurements were done on imprinted waveguides. The waveguideswere fabricated with a new process developed for this purpose, combining UVand nanoimprint lithography.

In Chapter 4 evanescent gain coupled whispering gallery mode lasers and re-sults measured from them are described and discussed, Fluid solutions of quan-tum dots and rhodamine 6G were used as active materials.

Chapter 5 concerns nanoimprinted DFB lasers, fabricated as a part of theproject. Design, fabrication, measurements, and results are presented and dis-cussed.

Finally, Chapter 6 concludes the report, stating the most important findings,and discussing future possibilities for demonstrating quantum dot lasing andimproving the lasers fabricated.

Chapter 2Theoreti al OverviewThis chapter gives an introduction to the theoretical background of the project.The first part is a description of lasers and their working principle. The nexttwo sections are concerned with quantum dot fabrication and optical proper-ties. Then an account of rhodamine 6G as active laser material is given, wherethe properties are compared to those of quantum dots. A sections describingnanoimprint lithography, which is the primary method used for fabrication ofpolymer structures, follows. The final section is a very brief account of thetheory of planar optical waveguides.

2.1 Lasers

This section gives an account of the basic laser principles. It is based on materialprimarily from two textbooks [22, 23].

Laser is an abbreviation for Light Amplification by Stimulated Emission of Ra-diation. A laser is a feedback coupled amplifier, working at optical frequencies,as shown in the schematic drawing in Fig. 2.1. It basically has four constituents[22]:

• An amplifier with a certain bandwidth and a gain saturation mechanism

• A positive feedback system

• A frequency-selection mechanism

• An output coupling scheme.

The oscillator system is unstable because of the positive feedback. Any smallsignal, e.g. noise, at the input port of the amplifier will be amplified and fedback to the input port to be amplified even more. This continues until theamplifier saturates, giving a steady state situation where the gain equals theloss.

10 2.1 Lasers

Figure 2.1: A laser is an oscillator, which can be drawn schematically as an amplifier in apositive feedback loop. Picture from [22].

The amplification in a laser relies on stimulated emission, which will be describedin more detail in section 2.1.1. The laser medium only amplifes at a certainwindow of wavelengths, giving part of the frequency selection. The remainingfrequency selection, feedback, and output coupling scheme comes from the lasercavity, which is basically a number of mirrors, reflecting the light in the amplifiermedium back to its starting point. Laser cavities are considered in section 2.1.2.When a laser is turned on the light in the cavity is amplified until the cavitylosses equal the amplifier gain. Laser action is described in more details insection 2.1.3.

2.1.1 Light Amplification

Laser amplification takes place through light interaction with matter. The mat-ter can for instance be molecules (such as rhodamine 6G) where electrons canbe excited between different molecular states, or semiconductor (such as CdSe),where electrons can be excited across the band gap. In this section the termmolecule will be used for the excitable part of the laser material, regardless thatthe theory applies just as well to atoms and quantum dots.

Light can interact with matter in three ways. Imagine a molecule with twoelectron energy levels and one electron, as shown in Fig. 2.2. The levels arecalled the lower (E1) and upper (E2) laser level. Fig. 2.2a shows absorbtion,where a photon, with an energy corresponding to the gap (~ω = E2 − E1),excites an electron from the lower laser level to the upper laser level. Theelectron can relax back in two radiative processes. The relaxation can happenspontaneously by the release of a photon, as shown in Fig. 2.2b. The otherpossibility is stimulated emission, shown in Fig. 2.2c. In this process a photon,again with ~ω = E2 − E1, interacts with the excited system, and causes it torelease a photon, which is identical to the one causing the transition. Becauselasers rely on amplification by stimulated emission, which makes identical copiesof photons, lasers generate monocromatic and coherent light.

It is important to note that there is a certain broadening of the lines in theenergy spectrum, so photons can interact with the material even if their en-

2.1 Lasers 11

Figure 2.2: The three ways light and matter can interact. a) Absorbtion. b) Spontaneousemission. c) Stimulated emission, where an incoming photon stimulates the release of anidentical one.

ergy is slightly different from E2 −E1. There are two kinds of broadening [23],which have different impact on the laser behaviour. In homogeneous broaden-ing all the molecules in the ensemble have their lines broadened in the sameway. There are a number of effects leading to homogeneous broadening, suchas time-energy uncertainty and the fine structure of the lower laser level. Inho-mogeneous broadening means that the molecules each have a slightly differentposition of the gain maximum. This can happen due to e.g. small differencesin molecule surroundings or by doppler shifts caused by the different velocitiesof the molecules.

A material in thermal equilibrium will never be able to amplify light, since veryfew molecules are excited to the upper laser level. The probability per time Wthat a photon is absorbed by an unexcited molecule is given by [22]

W = φσ(ω), (2.1)

where φ is the photon flux density and σ is the transition cross section, withdimension of area. Thus, the number of photons absorbed per unit time perunit volume is given by N1W , where N1 is the density of molecules in the lowerlaser level. Since the propability per time for stimulated emission to happenfor an excited atom is also given by Eq. 2.1 (with the same σ) the number of

12 2.1 Lasers

photons gained per time per unit volume (neglecting spontaneous emission) isgiven by

dn

dt= (N2 −N1)σ(ω)φ = Nσ(ω)φ, (2.2)

whereN2 is the number of excited atoms and n is the number density of photons.It is thus clear that in order for a material to amplify, it needs to have moremolecules excited to the upper laser level than the lower one. This is calledpopulation inversion.

When photons are moving through a laser material in a certain direction withflux density φ, the amplification (dφ) for an incremental movement (dz) in thez direction must be given by

dφ = Nσ(ω)φ(z)dz ⇒dφ

dz= Nσ(ω)φ(z), (2.3)

with the solution

φ(z) = φ(0)eNσ(ω)z = φ(0)eγ(ω)z, (2.4)

where γ(ω) = Nσ(ω) is called the gain coefficient.

It is necessary to transfer energy to the material, if population inversion is tobe achieved. This is called pumping, and can be done in a number of ways.In this project optical pumping with another laser has been used. The gain ofthe medium changes depending on pump power and photon flux. Larger pumppower leads to larger population inversion, and thus higher gain. Larger photonflux depletes the upper lasing level by stimulating more laser transitions. Thiseffect causes amplifier saturation.

Since a material with N2 = N1 is effectively transparent, it is impossible toachieve population inversion with pump photons of energy E2 − E1. To solvethis problem more levels must be involved. A four level pumping scheme canbe seen in Fig. 2.3. The pump excites the electrons to levels above the upperlaser level. From there they decay to the upper laser level through radiative ornon-radiative processes. After the amplification has taken place, the electronsdecay to the ground level. It is important that the upper laser level has along life-time compared to the lower laser level and the pump levels, making itpossible for electrons to accumulate in the upper laser level, and thus give thelargest possible population inversion.

A laser material needs to absorb the pump light effectively, but high absorbtionof light at the laser wavelength makes lasing more difficult. Therefore the mate-rials used have a Stokes shift between absorbtion and emission, i.e. the peak forabsorbtion of light is blue-shifted with respect to the flourescence peak. Stokesshifts in the absorbtion/emission spectra of CdS quantum dots and rhodamine6G are seen in Figs. 2.16 and 2.23, respectively. The Stokes shift is due to verydifferent reasons in the two materials. In quantum dots the transistion crosssection of the laser transition is much lower than the transistion cross section ofthe absorbing transitions. In rhodamine 6G the lower laser states are depletedvery quickly, so very few electrons are in the lower laser states, and thus veryfew molecules are able to absorb the laser light.

2.1 Lasers 13

Figure 2.3: A four level pumping scheme. Electrons are pumped to the E3 levels, from wherethey decay rapidly to the upper laser level. The lower laser level is depleted rapidly after laseremission by a transistion to the ground level. Picture from [24].

2.1.2 Laser Cavities

A laser cavity (or resonator) reflects most of the light in the laser mediumback to its own path to be amplified again. The reflection can happen on e.g.metal mirrors, dielectric interfaces, or in a medium where the refractive indexis modulated to give a Bragg type feedback.

A number of different cavity design are described in section 1.2, and more indepth describtions of the laser cavities used in this project are found in sections4.1 and 5.1.

One or more of the laser mirrors reflect less than 100% of the light, makingit possible to couple some of the light out of the laser. Similar to the gaincoefficient γ, a coefficient for cavity loss per unit length can be defined. Theloss coefficient is denoted α, and contains both the loss used for output, andloss to other mechanisms, such as scattering and absorbtion.

In order for the laser light to be amplified, it is important that the phase-shift from a roundtrip in the cavity is a multiple of 2π, otherwise the lightwill not be interferring constructively, and the feedback will not be positive.This requirement is responsible for the cavity frequency selection. This can beexemplified by considering the simplest possible cavity, two perfectly alignedmirrors, as shown in Fig. 2.4a. For the phase condition to be fulfilled it is clearthat

L = nλ

2= n

πc

ω⇔ ω = n

πc

L, (2.5)

14 2.1 Lasers

where n is an integer. Fig. 2.4b shows the frequency selection mechanisms of alaser. Lasing only happens at frequencies within the amplifier bandwidth wherethe roundtrip phaseshift in the cavity is a multiple of 2π.

Figure 2.4: (a) A simple cavity with two mirrors. The length of the cavity must be an integernumber of λ/2 for the feedback to be positive. (b) The frequency selection mechanisms ofa laser. The laser material has a certain bandwidth, and the cavity only supports certainfrequencies within that bandwidth. Pictures from [23].

It is important to note that a laser also needs a guiding mechanism perpendicularto the light propagation. The laser in Fig. 2.4 can not be realized, becausethe mirrors are required to be infinitely large in order to support plane waves.Usually curved mirrors are used, or the laser cavity is made as a dielectricwaveguide. The optical modes of a laser are the stable optical fields supportedby the cavity.

The quality factor (Q factor) of an optical resonator is a measure of the qualityof the resonance. It is defined as [25]

Q =ωE

P=

ωE

Ecα=

ω

cα, (2.6)

Where E is the energy stored in the cavity and P is the power dissipated due tolosses. The power P is rewritten by noting that the loss coefficient per lengthmust be given by cα [22]. Thus, the lower the loss in the cavity, the higher theQ factor.

Fig. 2.5 shows resonance spectra for two cavities with different Q factors. Thelower the Q factor the broader the resonance peaks. The physical reason forthe loss influence on the resonance width is found in the phase condition. If the

2.1 Lasers 15

mirrors are perfect, an optical wave with a frequency slightly detuned from theresonance frequency will stay in the cavity forever, and keep changing the phaseslightly with each round trip. This will cause the wave to interfere with itselfand be extinguished. If there is a loss the amplitude of the fed back signal is alsodiminished with each round trip, making the wave less efficient at extinguishingitself.

Figure 2.5: Resonance spectra for cavities with different Q factors. a) A cavity with infiniteQ factor. This cavity can only oscillate at the exact resonance frequencies. b) If Q is finite,the resonance peaks have a finite width. A lower Q factor gives a broader peak. Picture from[22].

It can be shown [22], that if the loss of the cavity is low, the value cα is a goodestimate of the full width at half maximum (FWHM) of the resonance peak ofa resonator like the one in Fig. 2.4a, measured in units of angular frequency.Thus, an expression for estimating the Q factor is given by

Q ≈ω

δω, (2.7)

where δω is the FWHM of the resonance peak. If the resonance peak is consid-ered symmetric around its maximum, the width in units of wavelength can befound as

δλ = 2πc

(

1

ω − δω2

−1

ω + δω2

)

=2πc

ω

(

1

1 − δω2ω

−1

1 + δω2ω

)

(2.8)

≈2πc

ω

(

1 +δω

2ω−

(

1 −δω

2ω

))

=2πcδω

ω2, (2.9)

where a taylor expansion has been performed, under the assumption that δω <<ω. It is thus noted that

λ

δλ≈

2πc

ω

ω2

2πcδω≈ Q, (2.10)

so the Q value can also be found from the peaks of a resonance spectrum as afunction of wavelength.

16 2.1 Lasers

Note that laser spectra becomes thinner than the resonance peak of the cavity,so the Q factor of the cavity can not be found from the laser spectrum usingEq.(2.10). The laser spectrum can give an upper estimate of the Q value,however.

For most laser cavities the Q value is a high number, because the optical fre-quencies are very high. A fairly good cavity has a Q value around 2000, but Qvalues close to 1010 have been reported in microsphere whispering gallery modecavities [26].

2.1.3 Laser Action

Fig. 2.6 shows what happens as an ideal laser with a homogeneously broadenedmedium is started. The moment the pump starts, the photon population in allmodes where the gain is larger than the loss starts growing. The larger opticalfield causes the gain to decrease, so that the population can grow in fewer ofthe modes . This will continue until a steady-state situation is reached, wherethe loss and gain in the central mode are equal.

Figure 2.6: Gain and mode strength when a laser starts. (a) When the pump is started theoptical power increases in all modes where the gain is larger than the loss. (b) The increasedphoton flux causes the gain to diminish, which makes it possible for fewer and fewer modesto increase their photon population, until only the central mode is growing. (c) Finally, asteady-state situation is reached, where the gain and loss of the laser mode is excactly balanced.Picture from [22].

Fig. 2.7 shows the steady-state population difference and photon flux density(i.e. output power) as a function of pumping power. The inversion wherethe gain equals the loss in the cavity is called the threshold inversion Nt. Nooscillations can initiate when the inversion is below Nt, and thus no light comesout of the laser (ideally). When pumped above threshold, oscillations will start,and light comes out of the laser. The inversion can never go above Nt in steady-state, regardless of the pump power. The reason is that the cavity loss (α) doesnot dependent on pump power, and this balances the gain (γ), which dependson only N and σ. This is called inversion clamping. A higher pump power willlead to larger output power though, because a larger optical field is required todeplete the upper laser level to Nt. The piecewise linear pump/output curve isan indication of laser action.

2.2 Quantum Dot Fabrication 17

Figure 2.7: Inversion level and output power as a function of pump power. Below thresholdno light is generated. Above threshold the output power depends on pump power, while theinversion clamps to the threshold level. The change of slope at the right curve is an indicationof laser action. Picture from [22].

Though Fig. 2.6 indicates the opposite, some lasers do lase at more than onefrequency. This can happen due to so called hole-burning. If the standing wavesin a cavity has nodes as in Fig. 2.4a, another mode with large amplitude at thesepoints may exist. These modes ”feed” on different spatially separated molecules.Thus, the gain of one mode is depleted independently of the other mode, so bothmodes can lase. The effect is called spatial hole-burning. The other effect isspectral hole-burning, which happens in inhomogeneously broadened media. Ifsome molecules amplify at a slightly different frequency than other molecules,the first molecules can be depleted independently of the others, and lasing canhappen at different frequencies. The laser materials used in this project areboth homogeneously and inhomogeneously broadened.

2.2 Quantum Dot Fabrication

The ability of quantum dot samples to amplify light depends very much onproperties such as size, surface passivation, and quantum dot surroundings [13,27]. Therefore, the synthesis and post-synthesis treatments are very important,and a section on the topics is natural to include.

The quantum dot samples for this project were synthesized by our collaboratorsM. Lucia Curri and her group at Istituto per i Processi Chimico-Fisici in Bari,Italy. I visited Bari to see how the samples were prepared, and discuss possibleimprovements in terms of e.g. quantum dot size and concentration.

Two quantum dot types were used in this project. 4 nm CdS dots passivatedwith oleic acid and 4.5 nm CdSe dots with ZnS shells. The quantum dots wererecieved in hexane or in a TOPAS/toluene solution for spin coating quantumdot doped TOPAS polymer films.

2.2.1 Synthesizing the Dots

The Cd for the quantum dots can come from different precursors, e.g. CdO orCd(CH3)2. The precursors for the other compounds are often elemental sulphuror selenium [28, 29, 30]. The idea of the synthesis is quite similar for CdSe andCdS, except that different precursors and solvents are used. The synthesis of

18 2.2 Quantum Dot Fabrication

CdS is used as example. Since this section is not intended as a recipe, butrather as an overview of the concepts used, the concentrations and volumes ofmaterials used are not included. They can be found in e.g. [28].

The synthesis takes place in a three neck reaction flask, as shown in Fig. 2.8.First, a reddish mixture of CdO, oleic acid, and octadecene is prepared in theflask. The oleic acid is the organic capping ligand, which is supposed to coverthe surface, while octadecene is a non-coordinating solvent, added to avoid for-mation of large CdS aggregates. The flask is stirred and heated to 300◦C. Thensulfur dissolved in octadecene is injected with a syringe, and the temperature isreduced to 250◦C. After a short period of time, the color of the solution changesto clear yellow as quantum dots begin to form. When the crystals have grownto the correct size, the heating is removed in order to stop the reaction.

Figure 2.8: (a) The fumehood in Bari, Italy, where the quantum dots for this project weresynthesized. Three reaction flasks are visible in the middle of the fumehood. (b) The CdSsynthesis happens in a three neck reaction flask with CdO, noncoordinating solvent and cap-ping ligand. At 300◦C S and non-coordinating solvent is injected rapidly, and the temperatureis decreased to 250◦C. When the quantum dots have reached the right size, the reaction isstopped by removing the heater. Picture (b) from [6].

After the solution has cooled to room temperature a mixture of chloroform(ClCH3) and methanol (CH3OH) is added, and the solution is centrifuged. Thiscauses unreacted precursors and excess oleic acid to fall to the bottom of thefluid. The upper phase is taken to another container, and a large amountof ethanol is added (at least 20 times the volume of the CdS solution). Thesolution is centrifuged again, causing the ligand covered crystals to aggregate atthe bottom. The ethanol can then be poured out, and the quantum dots can bere-dissolved in non-polar solvents such as toluene or chloroform. The ethanolprecipitation can be performed several times to remove all excess ligand.

2.2 Quantum Dot Fabrication 19

2.2.2 Size and Shape Control

The size of the quantum dots can be controlled by the concentration of thereaction solvents [30], and by changing the time from injection of sulfur tothe reaction is stopped [6]. The concentrations of the reaction solvents areimportant for the size distribution, however. If the concentration is above acertain minimum, growth of the smaller dots is favored, which causes the sizedistribution to become more narrow. This also means that care must be takenwhen increasing reaction time. After a period of time, the concentrations offree Cd and S can become small enough to favor growth of the larger dots,which causes the size distribution to broaden. If the concentrations of Cd andSe are extremely high in a CdSe synthesis, growth along a specific crystal axisis favoured. This can be used to make elongated quantum rods, rather thanquantum dots [30].

2.2.3 Surface Modification and Polymer Incorporation

After synthesis the surface of the quantum dots can be modified in order toimprove solubility or optical properties. One modification is to change thesurface ligand from oleic acid to e.g. octylamine [31]. Alternatively the quantumdots can be covered in an epitaxially grown layer of another semiconductor,making a core-shell structure, see Fig. 2.9. ZnS shells on CdSe are usuallygrown at rather low temperatures (140-220◦C [32]) and concentrations, in orderto keep the CdSe nanocrystals intact and avoid formation of ZnS particles. Thequantum dots in a solution of e.g. trioctylphosphine oxide [32] are heated, andZn and S precursors e.g. diethylzinc and bis(trimethylsilyl) sulfide [6] are addeddropwise. During growth the optical properties are monitored by taking samplesto a spectroflourometer. It is also possible to make dots where the core is CdS,covered in a layer of CdSe and an outer shell of CdS, a so-called core-well-shellstructure [33].

Figure 2.9: A ZnS shell can be grown epitaxially on a CdSe nanocrystal core. Picture from[34].

Incorporation into TOPAS polymer is done by dissolving the TOPAS in toluene,and adding a sample of highly concentrated quantum dots in toluene. Dissolvingthe TOPAS directly in the quantum dot containing toluene is difficult. Similarprocesses can incorporate quantum dots in other polymers, such as PMMA orpolystyrene [8].

20 2.3 Optical properties of Quantum Dots

2.3 Optical properties of Quantum Dots

As mentioned in section 1.2.1, quantum confinement of electronic states be-comes significant in quantum dots, making it possible to tune the band gap,and thus emission color. There are however fundamental differences in bothband structure and relaxation processes in quantum dots, compared to bulksemiconductors.

The physical reasons for the differences are rather complicated, but very im-portant to the properties of the quantum dots, especially when used as lasermaterial. Therefore this section is rather long, and requires the reader to havea reasonable understanding of quantum mechanics and solid state physics.

The section is based mostly on text material from [35, 27] for information onquantum dots, combined with a few books on quantum mechanics and solidstate physics [36, 37, 38].

2.3.1 Particle in a Sphere

The simplest quantum mechanical system resembling a quantum dot is theparticle in a sphere (the spherical polar counterpart to the cartesian particle ina box). The potential is zero within a certain distance of the origin, and infiniteeverywhere else, i.e.

V =

{

0 r ≤ a

∞ r > a(2.11)

Outside the sphere, the wavefunction has to be zero, otherwise the energy wouldbe infinite. So the difficult part is finding a solution to the Schrodinger equationinside the sphere, which goes to zero at the boundary. This is required in orderto keep the wavefunction continuous at all points.

The Hamiltonian, with a spherically symmetric potential term, commutes withthe total angular momentum operator L2 and the angular z component operatorLz. Thus, it is possible to find simultaneous eigenfunctions of the three. Thesolutions can be separated into a radial part and an angular part. The angularsolutions are the spherical harmonics, known from e.g. the hydrogenic atom.These are simultaneous eigenfunctions of L2 and Lz, see e.g. [36, 37] for moreinformation. The radial functions solving the problem in a physically acceptableway, are the spherical Bessel functions, seen in Fig. 2.10 [36]. Thus the solutionsinside the sphere can be written as

ψn,l,m = Cjl(kn,lr)Yml (θ, φ), (2.12)

where C is a normalization constant, jl is a spherical Bessel function of orderl, and Y m

l is a spherical harmonic. If the particle were completely free, thewavenumber k could be any (positive) value, but in order to fulfill the boundaryconditions it is necessary to demand that it can only take the values

kn,l =αn,l

a, (2.13)

2.3 Optical properties of Quantum Dots 21

where αn,l is the nth zero of jl. The eigenvalues of L2 and Lz are l(l+1)~2 andm~, respectively. The energy eigenvalues are [35]

En,l =~

2k2n,l

2m0=

~2α2

n,l

2m0a2. (2.14)

Thus, in this very simple model the energy levels depend inversely on a2. Thisquantum confinement effect is the physical reason that the band gap of semi-conductor quantum dots can be size-tuned, as illustrated in Fig. 1.1 on page3.

Figure 2.10: The first few spherical Bessel functions. Picture from [36].

2.3.2 Generalization to Quantum Dots

Though the particle in a sphere model contains the concept of quantum confine-ment, the resemblance to a real quantum dot is limited. Both CdS and CdSehave lattice constants in the order of 6 A, so a quantum dot with a diamter ofa few nanometers contains hundreds of atoms. The particle in a sphere modelcan be generalized to quantum dots, however.

It is necessary to assume that a quantum dot contains enough atoms to betreated as a bulk sample, when it comes to electron wavefunctions. In an infinitecrystal lattice the electron wavefunctions can be described as Bloch wavefunc-tions, which are plane waves, but modulated by the periodic potential of theatoms and also with a different mass, i.e. a Bloch wavefunction has the form[38]

ψnk(r) = eik·r unk(r), (2.15)

where unk(r) has the periodicity of the lattice and n is an index describing theband in question, see Fig. 2.11. The band structure is a plot of energy versusk.

If the conduction and valence bands of the material are considered parabolic,it is possible to define an effective mass of the carriers in the quantum dot.Since both CdSe and CdS are direct-gap semiconductors, this approximation isgood around k = 0, where the energy spacing between the bands is smallest.The effective mass is inversely proportinal to the second derivative of the band


Figure 2.11: A one-dimensional Bloch wave-function. The electron wavefunctions can betreated as plane waves (middle), though they are modulated by a function with the periodicityof the lattice (top). The Bloch wavefunction is seen in the lower graph. Picture from [38].

structure. The energy of the electrons in the conduction band and the holes inthe valence band can thus be estimated as

Eck =

~2k2

2mceff

+ Eg (2.16)

Evk = −

~2k2

2mveff

. (2.17)

The physical meaning of the effective mass is to account for the effect of thelattice on the carriers, while still being able to treat them as free plane waves,though they are infact modulated by unk(r).

If the above assumptions hold, any single particle wavefunction in the quantumdot can be written as a linear combination of Bloch wavefunctions, i.e.

ψsp =∑

k

Cnkunk(r)eik·r, (2.18)

where the coefficients Cnk ensures that the function fits with the boundaryconditions [35]. Assuming that unk are depending weakly on k, it can be movedoutside the sum, leaving the periodic parts of the solution, multiplied by anenvelope function taking care of the boundary conditions

ψsp = un0(r)∑

k

Cnkeik·r = un0(r)fsp(r). (2.19)

The un0 can be determined from the tight binding approximation as a linearcombination of atomic orbitals. The envelope functions fsp are the functions


determined in the particle in a sphere model. Thus, the energy of an electron-hole pair, also called an exciton, in a quantum dot can be approximated as

Eehp(nhlhnele) = Eg +~

2

2a2

(

α2nhlh

mveff

+α2

nele

mceff

)

−Ec. (2.20)

Apart from the terms given by the bulk band gap and the quantum confinedwavefunctions, a term (Ec) is included to take care of any coloumb interactionbetween the electron and the hole. States, when this model is used, are usuallydescribed by the quantum numbers as nhlhnele, e.g. the lowest exciton state,called the band edge exciton, is denoted 1Sh1Se.

As shown in Fig. 1.2 on page 3, the color tuning from the quantum confinementcan be rather large, though the material still plays a large role for emissionwavelength. The band gaps of bulk CdS and CdSe are 2.42 eV and 1.70 eV,respectively [39]. This corresponds to band edge emission at 547 nm and 779 nm.CdSe quantum dots with an emission wavelength of 490 nm (2.70 eV band gap)are commercially available, so in these dots the band gap has been increasedalmost 60% by quantum confinement.

2.3.3 Further Considerations

The conduction band of CdSe and CdS comes from Cd 5s orbitals. Since thesestates are spherically symmetric and non-degenerate, the parabolic band approx-imation is rather good. The valence bands are far more complicated, however.They come from the 3p and 4p S and Se orbitals, respectively, so they are bothdegenerate (threefold, excluding spin) and come from states without sphericalsymmetry.

A typical valence band structure for diamondlike semiconductors with a zinc-blende lattice can be seen in Fig. 2.12a. When considering valence band statesthe J quantum number, which gives the magnitude of the total angular momen-tum, can take the values 3/2 and 1/2, which is the l quantum number of theorbital (1 for p orbitals) ± the spin of the electron (1/2) [37]. The upper twobands A and B comes from the J = 3/2 states [35]. The bands are degenerateat k = 0, but their curvature is different. This corresponds to different effectivemasses of the particles in the bands, and thus the A and B bands are oftenreferred to as the heavy-hole (hh) or light-hole (lh) bands. The hh band hasthe numerically largest Jm quantum number of ±3/2, i.e. the largest angularmomentum projected on the z-axis, whereas the lh band has Jm = ±1/2. TheC band, with J = 1/2 is split off from the A and B bands due to spin orbitcoupling. For CdSe this splitting is 420 meV [35].

Fig. 2.12b shows a similar valence band, except that the A and B bands arealso split. This happens in crystals with a hexagonal wurtzite lattice insteadof the zinc-blende lattice. Bulk wurtzite samples are often considered zinc-blende, because the magnitude of the A-B splitting is neglegible. CdSe quantumdots have a wurtzite lattice, which causes the shape of the quantum dots tobecome slightly prolate [35]. The prolate shape enhances A-B splitting, soapproximating the band structure with that of a zinc-blende lattice is not valid.


Figure 2.12: (a) Valence band structure of a semiconductor with a zink-blende lattice. (b) Ifthe crystal structure is instead wurtzite, as in CdSe quantum dots, the upper two bands split.Picture from [35].

One approach to including the valence band complexities in quantum dot energydiagrams could be to consider each of the three valence bands independently,and combine each with the particle in a sphere envelope function. The solutionobtained fits very badly with experiments, though. This is because of mixing ofvalence band states and electron/hole exchange and Coulomb interactions.

The quantum numbers introduced thus far are presented in Fig. 2.13. Whenthe spherical potential is imposed on the crystal structure the valence bands andthe envelope functions mix, rendering all hole state quantum numbers useless,except parity and and the total angular momentum Fh. Since the conductionband states are far simpler, these problems affect this band to a much smallerextend, and thus mixing of electron states can safely be ignored.

If exchange and Coulomb interactions between electrons and holes are also in-cluded the matter complicates further, and the quantum number for the totalexciton angular momentum N becomes the important one. In bulk materialexchange is negligible, but since the hole and electron are confined to such asmall volume in a quantum dot, they overlap much more, giving exchange amore significant role, especially in smaller quantum dots.

Fig. 2.14 shows an energy level diagram for the band edge exciton of CdSe,with different effects included. On the left the simplest picture is shown, withthe band edge exciton coming from the A and B bands of a zinc-blende lattice.The band edge exciton is denoted 1S3/21Se. 1S to denote the lowest particlein a sphere state, and 3/2 to denote the the lowest energy valence band. Ifthe wurtzite lattice is included the A-B splitting gives two bands with differentprojections of the angular momentum, but still with the same magnitude ofangular momentum. In the right side of the figure, exchange dominates, andthe diagram is split in two degenerate levels, depending on the total excitonangular momentum N , which can take the values 1 or 2. Between the twolimits the band edge exciton is five fold degenerate, and the energy depends onboth N and Nm, which is the projection of N on the unique crystal axis.

CdS quantum dot states have been investigated far less than CdSe. Thus, I havebeen unable to find as detailed calculations and measurements for this material.


Figure 2.13: The quantum numbers in a quantum dot. The only good quantum numbers inthe valence band are parity and the total hole angular momentum Fh, when the combinedeffects of lattice and particle in a sphere potential is considered. If electron/hole interactionsare also included the total exciton angular momentum N must be used. Picture from [35].

Figure 2.14: Energy level diagram for the exciton fine structure. In the simplest sphericalapproximation, the band edge exciton is 8-fold degenerate. This degeneracy is split by thelattice, the prolate shape of the dots, and exchange interaction. Picture from [35].

CdS quantum dots can be grown with both wurtzite and zinc-blende lattice [40],but the crystals used in this project have all been wurtzite. I believe the theoryin this section applies as well to wurtzite CdS as CdSe quantum dots.


2.3.4 Absorbtion and Emission

Though quantum dots contain only discrete energy levels, a normal sample stillhas a continuous absorbtion band. Part of the reason is that the levels arequite densely spaced, especially deeper in the valence band, and thus normal(homogeneous) linebroadening effects cause the lines to overlap, but quantumdot samples also have a certain size distribution, which further broadens thelines (inhomogeneously). An example of an absorbtion and emission spectrum,for a CdSe quantum dot sample with effective radius of 1.9 nm, can be seen inFig. 2.15a. Fig. 2.16 shows absorbtion and luminescence of a CdS modifiedTOPAS sample prepared by our collaborators in Bari. Clearly there is a Stokesshift between absorbtion and emission. Fig. 2.15b shows more detailed featuresof the spectra, measured using photoluminescence excitation (PLE) and fluo-rescence linenarrowing (FLN). Both techniques gives better resolution, becausethey measure on a subset of the quantum dots. PLE measures emission at acertain wavelength, indicated by the upward arrow, as the excitation is scannedthrough different wavelengths. Quantum dots always emit from the lowest ex-citon level, so in PLE the absorbtion of the dots emitting at the arrow is found.FLN measures luminescence from the largest dots only, by exciting the sampleat the long wavelength side of the band edge absorbtion. In this case the FLNexcitation happens at the downward arrow.

Figure 2.15: (a) Absorption and luminescence of CdSe quantum dot with 1.9 nm radius.Note the Stokes shift. (b) FLN and PLE spectra. Picture from [41].


Figure 2.16: Absorbtion (blue) and luminescence (red) from a CdS doped TOPAS sample.The narrow peak around 420 nm is the band edge emission, whereas the broader emission atlonger wavelengths comes from defects. Picture from [9].

Fig. 2.17 shows absorbtion and emission for a single dot modelled from thesample in Fig. 2.15. The inset is an energy level diagram, compare to that tothe right of the middle on in Fig. 2.14, where both wurtzite lattice and exchangeis included. States are denoted with a number and a superscript, e.g. 1L. Thenumber indicates the Nm quantum number, and the superscript tells if the stateis from the N = 1 manifold (U) or the N = 2 manifold (L).

The band edge exciton Nm = 2 is also called the dark exciton, because it doesnot absorb photons. It can emit photons, however, so this gives rise to theStokes shift. The exciton does not absorb because photons are able to carryonly one unit of angular momentum, while the band edge exciton carries two.In order to absorb a photon, a phonon must be absorbed simultaneously, and thechance of that is negligible. Emission, generating both a photon and a phonon,is possible however, though the exciton decay time is increased for quantumdots compared to bulk material, where exchange interactions do not split theexciton levels significantly. For a long time it was believed that insufficientlypassivated surface states were responsible for the long decay time of the bandedge exciton, but it is now generally accepted that the reason is the modifiedexciton fine structure.

When quantum dots are pumped, e.g. with laser pulses, they are excited tostates above the band edge emitting state. If any population inversion is tobe achived, it is necessary that the excitons drop down to the N = 2 statesubstantially faster than the state decays due to spontaneous emission or non-radiative effects. For nanocrystals the band edge exciton usually decays on thetimescale of picoseconds to microseconds, depending on size, surface passivation,and temperature. In bulk semiconductors electrons drop very quickly (sub-ps)to the lowest conduction band state, through interactions with phonons [27].


Figure 2.17: Calculated absorbtion and emission modelled from the sample in Fig. 2.15. Theinset shows an exciton fine structure. Broad lines are optically active, while thin lines arenot. The emission from the optically inactive 2 level, which is called the dark exciton, givesrise to the Stokes shift. Picture from [41].

In quantum dots, where the energy levels are further apart, it becomes harderto fulfill the energy-momentum conservation, so the phonon assisted relaxationbecomes less effective. This is known as the ”phonon bottleneck”. Experimentsshow, however, that electrons in quantum dots can relax to the 1S state withina picosecond, through Auger interaction with holes, i.e the electron energy istransfered to a hole. A schematics of the quantum dot states are shown inFig. 2.18. Because the valence band is more complex than the conductionband, there are enough states to form a quasi-continuum of states deeper in thevalence band, so the holes can decay very quickly to the 1P3/2 state withoutinfluence from a ”phonon bottleneck”. The final decay of the hole into theemitting 1S3/2 state is inhibited to some extend, but the decay still happenswithin a picosecond even for the smallest samples [10].

2.3.5 Quantum Dot Lasing

Since the excitons drop to the emitting state much faster than the emittingstate itself decays, there is no fundamental barrier to inverting the nanocrystals.As described in Section 1.2, lasing has been demonstrated by several groups,with both CdSe and CdS samples. There are however a number of effectscomplicating the matter.

The nonradiative carrier losses, which give the relatively short lifetime of theband edge excitons, happens mostly due to two mechanisms [42]. One is surfacetrapping of carriers, where dangling bonds at the nanocrystal surface give rise


Figure 2.18: States involved in luminescence in quantum dots. After excitation the electronsdrop to the emitting states within a picosecond by Auger interaction, while the holes moveto the 1P3/2 state by phonon interactions. The final movement of the holes to the emittingstates is inhibited somewhat, but still happens within a picosecond. Picture from [27].

to fast recombination. Since the nanocrystals are very small, a substantialnumber of the atoms are at the surface, where they are able to interact withthe surroundings. Using different surface cappings, e.g. a CdSe/ZnS core-shell structure, can passivate the surface a great deal, limiting this effect to aminimum.

The other mechanism for nonradiative carrier losses is multiparticle Auger re-combination, where the energy is transferred to another particle. This effectis insignificant in bulk CdSe and CdS, but becomes important in nanocrystals.Opposite surface trapping, this is an intrinsic effect to quantum dots. TheAuger effect is enhanced in smaller quantum dots, as shown in Fig. 2.19a, andthe decay time drops substantially as more excitons are present, as seen in Fig.2.19b.

Experiments [10] have shown that gain in colloidal quantum dots can be achievedwhen the number of electron-hole pairs per dot on average, Neh, is larger than 1,


Figure 2.19: (a) Decay times for double electron hole pairs (bi-excitons) in CdSe sampleswith different radii. The decay is faster in the smaller quantum dots. (b) Decay time ofstates with different numbers of excitons in a 2.3 nm radius CdSe sample. The more excitonsthe faster they decay. Pictures from [27].

and that the gain saturates when Neh = 2. This is an indication that gain comesfrom doubly excited quantum dots, i.e. from quantum confined bi-excitons, asexpected from the fact that both the Nm = 2 and Nm = −2 states have thesame energy. Thus the gain decays as rapidly as the biexcitons, whereas normalspontaneous luminescence decays with the excitons.

The fast bi-exciton decay also explains why lasing is difficult to achieve, evenin well passivated samples. Bad surface passivation causes the flourescencequantum yield to drop, i. e. a smaller percentage of absorbed photons arereemitted. In order to keep the quantum yield high, it is important that thenon-radiative surface effects have a longer decay time than the spontaneousemission. For laser applications, moderately well passivated dots could be asgood as well passivated dots, however, since the gain time constant is so muchsmaller due to Auger recombination.

The surface can still play a large role in photoinduced absorbtion, however[27]. If surface states of excited dots can be involved in transitions at the laserfrequency, they will absorb the laser light, thus making lasing impossible, evenat the largest pump intesities. Also, the quantum dot surroundings play a rolefor photoinduced absorbtion. Different matrices of polymer or solvent givesdifferent results. In fact, quantum dots able to amplify light in close packedfilms, have been shown unable to amplify, if dissolved in hexane [10]. Later,lasing in hexane with other samples has been proven possible, however [13].

A luminescence spectrum for a close packed CdSe quantum dot film is shown inFig. 2.20. Beginning at a pump power of 8 mW, an ASE peak builds up, slightlyred-shifted with respect to the spontaneous emission peak. ASE is amplificationof spontaneous emission without feedback, so it shows a threshold behaviour, asseen in the inset. One of the reasons for the ASE redshift is that it is a resultof bi-excitons, whereas the luminescence is mostly a result of single excitons.The energy of a biexciton is lower than the energy of two single excitons. Thiscauses the redshift.

In order to demonstrate the ASE in Fig. 2.20, some important requirementshad to be fulfilled, to compete with the fast Auger decay [10]. The pump pulses


Figure 2.20: luminescence from 2.1 nm CdSe/ZnS samples pumped at different intensities.The temperature was 80 K. The energy scale from 1.8 eV to 2.4 eV corresponds to a wave-length scale from 686 nm to 514 nm. At a certain pulse energy an ASE peak develops. Theinset shows the output/pump intensities for the luminescence peak (squares) and the ASEpeak (circles). Picture from [10].

are are only 100 fs long, and thus much shorter than the bi-exciton decay time.Thus the threshold pump fluence Ep (energy per area) can be estimated byrequiring one photon pr. quantum dot [27]

Ep

~ωpσp ≈ 1 ⇔ Ep ≈

~ωp

σp, (2.21)

where the p subscripts refer to pump angular frequency and interaction crosssection for the pump light. If, on the other hand, the pump pulse is much longerthan the Auger decay time, the power required per area (Pp) can be estimatedas

Pp ≈~ωp

σpτ2, (2.22)

because the pump must supply enough power to excite the dots approximatelyevery time τ2 has passed. τ2 is the biexciton decay time constant.

In [11] a film of close packed 2.5 nm radius CdSe quantum dots is depositedinside a microcappilary tube, and pumped with a 100 fs laser emitting at 400nm wavelength. ASE was measured at a pump pulse fluence of 1.8 µJ/mm2,corresponding to around 3.6 × 1012 photons per mm2. Fig. 2.19 shows thata high estimate for the biexciton decay time is τ2 = 100 ps. The argumentgiven after Eq. (2.22) can be used to estimate the number of photons neededto achieve ASE in the same sample with a 5 ns frequency doubled Nd:YAGpump laser. The pump pulse thus had to contain enough photons to excite thequantum dot

tpulse

τ2

= 5 ns100 ps = 50 times. This is around 1.8 × 1014 photons per

32 2.4 Optical Properties of Rhodamine 6G

mm2, corresponding to a pump fluence of 68 µJ/mm2 at 532 nm. This is ofcourse under the assumption that the absorbtion cross section of the quantumdots is approximately the same at the two wavelengths, 400 nm and 532 nm.

Another requirement for lasing with very short pump pulses, is high gain ofthe samples. This is because the time it takes to build up stimulated emissionmust be shorter than the Auger decay time. The gain buildup time is inverselyproportional to the gain magnitude, which is proportional to the density ofquantum dots. Thus, the requirement for short gain buildup time means thatthe volume fraction of quantum dots in the active material has to be above acertain minimum. For the 1.3 nm radius samples used in [10] the minimumfraction required is estimated to 0.2%, though the fraction actually used was20%.

Lasing in a CdSe/ZnS quantum dot sample in hexane with a volume fractionaround 0.5% with 5 ns pump pulses have been demonstrated [13]. The succesis believed to be due to the extremely low loss of the laser cavity used. Thethreshold pump power per area was around 100 µJ/mm2.

2.4 Optical Properties of Rhodamine 6G

Rhodamine 6G is a very commonly used organic laser dye. The properties ofrhodamine 6G are well documented in litterature, and it is used in numerousapplications. Achieving population inversion in rhodamine 6G is very easy, andsince there have not been any problems with it in this project, this sectionis shorter and less detailed than the previous section on optical properties ofquantum dots.

Understanding the basics of laser action in rhodamine 6G, how it is manipulated,and what causes bleaching is still relevant, however. It it also important tounderstand the differences between quantum dots and rhodamine 6G as activelaser material, so in this section the properties of the two materials are oftencompared.

2.4.1 Rhodamine 6G and Solvents

A molecule of rhodamine 6G perchlorate is seen in Fig. 2.21. Rhodamine 6G isan ion, and thus it is always combined with an anion. In this project perchlorate(ClO−

4 ) is the anion used, but there are other possibilities such as bromide (Br−)or chloride (Cl−). The anion can have an impact on dye efficiency in differentsolvent and on the thermal stability of the fluorescence, as seen in Fig. 2.24 [2].

In order to use rhodamine in a laser it must be dissolved in a transparentmedium, either a fluid or a solid. Since rhodamine 6G is an ion, it must bedissolved in polar fluids. Often used solvents are water, ethanol, and ethyleneglycol. In this respect quantum dots are a bit more flexible, since their surfacescan be modified to fit the solvent. Quantum dots can be dissolved in both non-polar solvent, such as toluene, and polar solvents, such as water [44], dependingon the capping molecules.

2.4 Optical Properties of Rhodamine 6G 33

Figure 2.21: A rhodamine 6G perchlorate molecule. Rhodamine 6G is a very commonly usedorganic laser dye. Picture from [43].

A number of solid state matrices have been used for rhodamine incorporation.Examples are porous glasses, silicates, and polymers [45]. It is not possibleto dissolve rhodamine in the TOPAS polymer, however [2]. The only matrixused here is PMMA because it is commonly used and can be structured withnanoimprint lithography. The PMMA used is dissolved in anisole, which isnot very polar, and thus dissolving rhodamine in it is difficult. A method forincreasing the solubility is to use an additive, such as ethanol. The process usedin this project is described in section 2.4.4.

2.4.2 Rhodamine 6G Lasing

Fig. 2.22 shows a schematic drawing of the electron energy levels. Since theenergy levels are given by the molecular structure of rhodmine 6G it is notpossible to tune the emission color, as for quantum dots. Other laser dyes exist,however, so dye lasers can cover the entire visible spectrum.

When rhodamine is pumped, the electrons are excited from the ground state,which is the lowest of the states marked S0 in Fig. 2.22, to one of the highersinglet states. From there, they quickly decay to the lowest S1 state, which ismetastable (lifetime counted in ns) [2]. Lasing (and fluorescence) happens in atransition from this level to one of the rotational and vibrational states of theS0 levels. Finally, after the laser transistion, the electron decay quickly back tothe ground state.

There is a small chance that an electron in an excited molecule moves from asinglet state to a triplet state. The time constant for this transistion is ratherlarge, around 160 ns [2]. The time constant for a transistion back to singletstates is even larger (2 µs), which means that carriers are effectively lost, oncein a triplet state. Furthermore, the triplet states absorb at the laser wavelengths,rendering laser action more difficult as carriers accumulate in the triplet states.This imposes a limitation on the time the dye can amplify.

There are two possible solutions to the triplet state loss. In large scale contin-uous wave dye lasers the rhodamine is usually dissolved in a fluid and pumpedthrough the cavity very quickly, limiting the time each molecule is used. This isnot possible in lab-on-a-chip systems, because the flow resistance in the micro-

34 2.4 Optical Properties of Rhodamine 6G

Figure 2.22: Electron levels in a laser dye such as rhodamine 6G. Each band is split inrotational (thin lines) and vibrational (thicker lines) states. Lasing happens from the lowestS1 state to one of the excited S0 states. If carriers move to the triplet states it causes problemsfor lasing. Picture from [22].

scopic channels is too large. Instead, lab-on-a-chip rhodamine lasers use pulsedpumping, allowing all molecules to decay to the ground state between the laserpulses. In this project a frequency doubled Nd:YAG pump laser has been used,because the 532 nm light it generates is very close to the absorbtion maximumof the dye, and because the 5 ns pulses are much shorter than the time constantfor decay to the triplet states.

The reason for pumping rhodamine with short pulses is different from the reasonthat fs pulses are often used to pump quantum dots. Quantum dot lasers arepulsed to compete with a non-radiative decay to the ground state, but can inprinciple be used continuously, while continuous rhodamine lasing is impossibledue to triplet loss.

Absorbtion, flourescence and gain from rhodamine 6G is shown in Fig. 2.23.There is a Stokes shift between absorbtion and emission. This comes from theenergy difference between the ground state and the vibrational and rotationalstates in the S0 band, see Fig. 2.22. The fluorescence peak is rather broad, be-cause the laser transistion can involve a number of S0 states. Opposite quantumdots, the fluorescence spectrum moves towards shorter wavelengths as the pumpincreases, because the gain is the difference between fluorescence and absorb-tion, which increases and decreases, respectively, as the pump becomes morepowerfull.

2.4 Optical Properties of Rhodamine 6G 35

Figure 2.23: (Left) Absorbtion, fluorescence, and gain from rhodamine 6G. The gain is foundby substacting emission from absorbtion. Note the Stokes shift. (Right) The gain peak shiftstowards blue as the material becomes more inverted. The reason is that the absorbtion shrinks,while the gain increases. Picture from [46].

2.4.3 Rhodamine Bleaching

The largest problem when using rhodamine 6G in lasers is bleaching of the dye,i.e. the dye becomes less efficient during use. Unlike carrier loss to tripletsbleaching is not reversible. Three processes are believed to cause the bleaching[2].

• Aggregation

• Chemical reactions involving the excited molecules

• Thermal destruction

Rhodamine molecules can aggregate in pairs or larger numbers. This causes theoptical properties to change. The tendency to aggregate depends on rhodamineconcentration, solvent or matrix material, and the anion. For example, the life-time of rhodamine 6G in PMMA has been shown to increase if a small amoungof 2-hydroxyethyl methacrylate is mixed into the PMMA chains [45]. Aggrega-tion of molecules is also enhanced during laser operation, because the materialis heated by the pump, causing the mobility of the molecules to increase.

Excited rhodamine molecules react easier with other molecules. This effect alsoleads to bleaching during operation. Reaction speed also depends on the anionand the material surrounding the molecules.

Thermal destruction is not just one process. What happens depends on theamount of energy transferred to the molecules during pumping. Thermal de-struction can be enhancement of aggregation, as mentioned, but at higher pow-ers it can also be reaction of the molecules with oxygen from the athmosphere,i.e. the molecules are burned. Thermal bleaching of PMMA films is discussedbelow.

36 2.5 Nanoimprint Lithography

2.4.4 PMMA Incorporation

The doped PMMA made during this project was prepared very similarly to theprocess described in [2]. The PMMA used was a 15 wt% 50k mixture in anisole.For more information on PMMA see section 2.5. A 20 mM ethanol/rhodamine6G perchlorate solution was prepared. The PMMA and rhodamine solutionswere combined in volumes corresponding to a final rhodamine concentrationof 2 × 10−5 moles per g dry PMMA and shaken. The PMMA was spun onglass wafers a few minutes after shaking the solution, when the small volume ofundissolved rhodamine had fallen to the bottom of the container.

The refractive index of PMMA increases with rhodamine concentration. Forthe concentration used here the effect is not very large, however [17], so it is notincluded in the calculations in this thesis.

Since the rhodamine doped PMMA is to be nanoimprinted, its optical propertiesare required to have a certain thermal stability. Fig. 2.24 shows the fluorescenceof rhodamine doped PMMA films after different periods of baking at differenttemperatures. Noting that the color scales are different in the two figures it isvery clear that rhodamine 6G perchlorate is much more stable than rhodamine6G chlorate, when incorporated into PMMA. This made perchlorate the obviouschoice in this project, since it is able to withstand temperatures up to 220◦Cfor hours without degrading.

2.5 Nanoimprint Lithography

This section descibes the basic theory of nanoimprint lithography (NIL), which isthe method used to structure the polymer films in this project. The main reasonfor using NIL in this project is that very small structures can be reproduced (sub25 nm [47]). Imprinted structures also have very smooth and vertical sidewalls,ideal for optical applications [2]. There are however other advantages, e.g. thatthe process is parallel, enabling imprint of a full wafer at the same time, andthat the often rather expensive stamp can be used several times.

2.5.1 Nanoimprint Principle and Theory

The basic idea of nanoimprint lithography is illustrated in Fig. 2.25. A polymerfilm on a hard substrate and a hard stamp is heated, until the polymer becomessoft. The stamp is then pushed into the polymer film, and the system is cooled,causing the polymer to harden in the pattern defined by the stamp. Finally,the stamp is removed. Note that there is a residual layer left under the stampprotrutions. This residual can not be removed entirely in the process. SEMimages of a stamp and the transferred pattern in a polymer film are shown inFig. 2.26

In this project the stamps have been made of silicon, patterned with standardprocessing techniques, the substrate has been pyrex glass, and the polymer hasbeen either TOPAS or PMMA (see below for polymer details). The imprintingwas done under vacuum with the pressure applied by two parallel plates. The

2.5 Nanoimprint Lithography 37

Figure 2.24: Fluorescence of rhodamine 6G doped PMMA films as a function of baking timeand baking temperature. The top film is prepared using rhodamine perchlorate, while thebottom film is prepared using rhodamine chlorate. Both scales are normalized to a samplebaked for 15 minutes at 80◦C. Perchlorate is much more stable than chlorate, which degradesaround 160◦C. Pictures from [2].


Figure 2.25: Nanoimprint Lithography. A hard stamp (red) and a polymer film (yellow) ona substrate (blue) is heated, and the stamp is pushed into the softened polymer. The stampis removed after cooling, leaving the polymer film with a pattern defined by the stamp. Aresidual layer of polymer is left under the stamp protrutions. Picture from [48].

Figure 2.26: (left) SEM image of a silicon stamp for nanoimprinting. (Right) an imprintmade with the stamp into a TOPAS polymer film, covered in 5 nm Ti and 20 nm Au. Thenegative stamp pattern is replicated very well in the polymer.

specific machine used was an EVG 520HE nanoimprinter from the EV group[49].

Obviously the polymer used in NIL is required to be thermoplastic, i.e. it mustbe possible to soften the polymer by heating it. Different deformations as afunction of temperature for a thermoplast polymer is plotted in Fig. 2.27. Thetwo important temperatures are the glass transition temperature Tg and the flowtransistion temperature Tf . Below Tg the polymer is elastic, and deformationsare recovered. Above Tg a rubber elastic regime is found, where the polymercan be deformed, but a portion of the deformation is recovered elastically. At Tf

the polymer starts behaving like a fluid, and deformations become permanent.The viscosity (resistance to flow) drops dramatically with temperature in theflow regime, it can drop orders of magnitude with a 10 K temperature increase


[50]. The optimal regime for nanoimprint is found empirically to be in the flowregime around 80 K above Tg [48, 2].

Figure 2.27: The three flow regimes of a thermoplastic polymer. Below the glass transitiontemperature Tg, the polymer is elastic, and above the flow temperature Tf , it behaves as afluid. In the temperature range between Tg and Tf the polymer is in a rubbery state, wheredeformations are both elastic and permanent. Picture from [48].

Fig. 2.28 shows a completely filled stamp in a polymer film. The stamp inthe figure has a number of line shaped protrutions with height hr, width s andlength L. L is much larger than s to make the problem as twodimensional aspossible in the figure plane. The time required for imprinting in this situationcan be estimated from the Navier-Stokes equation, see e.g. [51]. The formula isreferred to as the Stefan equation, since it was first found experimentally (for aslightly different geometry) by M. J. Stefan in 1874 [50]. The time required is

tf =ηLs3

2F

(

1

h2f

−1

h20

)

, (2.23)

where F is the force on the protrution, η is the viscosity of the polymer, and Lis the protrution length. It is noted that the imprint time depends linearly on ηand L, and has an inverse linear dependence on F . Since η changes very muchwith temperature above Tf the imprint time has an equally strong temperaturedependence. Typical values for η at different temperatures are found in tables2.1 and 2.2. Since L >> s no polymer flow is expected perpendicularly to theplane of Fig. 2.28, and thus the L dependence is simply because the pressureis proportional to F/L. The polymer has to flow to the sides of the protrution,however, and this causes the dependence on s to be very strong (cubic). Thedependence on the layer heights is 1/h2, so the imprint time goes to infinity asthe residual goes to zero.


Figure 2.28: A model for calculating the imprint time. The stamp has an array of very longprotrutions of width s, separated the distance w. The height of the film before imprinting ish0, and the residual height is hf . Picture from [52].

Eq. (2.23) can not be used without knowing the residual layer. This can befound from mass conservation, assuming an incompressible polymer. Imaginethat the stamp in Fig. 2.28 is periodic, so it contains a large number of equallyspaced protrutions. Between the dotted lines in the figure, the same volumemust be present before and after the imprint. Thus,

h0(s+ w)L = shfL+ w(hf + hr)L⇔

hf = h0 − hr

(

w

w + s

)

= h0 − hr(1 − β), (2.24)

where the protution coverage β has been introduced. β is simply the fractionof the stamp area covered with protrutions.

There are two benefits from a small protrution coverage. One is that the residualcan become thinner, because there is room for the polymer elsewhere, as seenfrom Eq. (2.24). The other benefit is that the force on the individual protrutionsis increased for a given force on the stamp. The force is given as

F = FstampApr

βA, (2.25)

where Fstamp is the force on the stamp, Apr is the total protrution area, and Ais the area of the entire stamp.

The above calculation assumes that stamp and substrate cannot be deformed.This is an idealization. If the protrution coverage varies across the stamp,the residual height will also vary. Once a high-β area is filled, it acts as onelarge protrution, and the imprint is effectively stopped for that area, since thiscorresponds to s increasing in Eq. (2.23). Thus, if the stamp must also befilled in the low-β areas it is forced to deflect. The stamp can also bend aroundprotrutions if they are large and separated by a large protrutionless area, seeFig. 5.6.

It is also possible to make imprints with protrutions taller than the polymerthickness. In this situation there is no lower limit to the residual height frommass conservation, but Eq. (2.23) still applies, with a 1/h2

f dependence onimprint time, meaning that the time required will increase progressively withthinner residual. Removing the residual completely remains impossible.


Imprint times found with Eq. (2.23) are usually very short. Calculations onimprints of 25 µm wide 300 nm tall protrution lines into 50k PMMA have beenperformed in [50]. The calculations show that for typical imprint parametersthe imprint time is within a second. Usually a few minutes are required whenactual imprints are made, so the model presented here has some limitations.The model is still good for evaluating the impact on imprint time for differentparameters, however.

Protrution width is very important for imprint time, as seen in Eq. (2.23). Ifan imprint is made with 20 µm wide protrutions, the time to imprint 1 mm

wide protrutions with the same parameters is increased 10003

203 = 125000 times.If the 20 µm imprint took 1 s the 1 mm imprint will thus take almost 35 hours.The example shows that keeping the protrutions small is very important innanoimprint lithography, but keep in mind that increasing the temperature candecrease the viscousity orders of magnitude.

2.5.2 Stamp Anti-Stiction Coatings

Since the stamp has protrutions, its surface area is larger than the surface areaof the substrate. Thus, the polymer will have a tendency to stay on the stamprather than the substrate when imprints are made. This problem is solved bytreating the sample with an anti-stiction coating (stiction is short for staticfriction [53]).

Two methods of anti-stiction have been used in this project, both are basedon coatings with fluorocarbon. The presentation here will be quite brief, andmostly describe the processes used. A more in-depth account of the subject canbe found in [3].

The method first used was deposition of a teflon-like coating with a deep reactiveion etch (DRIE) tool. The machine generates a plasma from a C4F8 gas, causinga film of polymerized nCF2 to form on the wafer. The film thickness is around5-10 nm. The exact parameters used can be found in appendix C.

The other method deposited a layer of flourocarbon chains with trichlorosilaneendgroups (F13TCS). The trichlorosilane binds covalently to the silicon surface,causing the fluorocarbon chains to form a monolayer on the stamp. The deposi-tion was done by putting the stamp in a petri dish and heating it to 250◦C on ahotplate. Then approximately 0.25 ml of F13TCS is placed next to the stamp,and the petridish is quickly covered with a lid. The F13TCS will quickly evap-orate at the elevated temperature, and start reacting with the stamp surface.After 2 hours of baking the lid is removed, and baking continues without lid for30 minutes. Finally, the stamp is allowed to cool to room temperature.

The DRIE process is very easy to perform, since everything is automated, butit has a few drawbacks. The film thickness of a few nanometers can become aproblem when imprinting very small features, and the film is not very durable.After a few imprints (3-4) the stamp must be coated again.

The dish coating (DC) technique is a bit more time consuming, but it effectivelyeliminates the problems of the DRIE process. A DC coated stamp can be usedmore than 50 times without problems [3].


2.5.3 Polymers for NIL

Polymers are materials where a number of molecules, called monomers, arebonded together to form long chains. In thermoplastic polymers the long poly-mer chains are bonded together by weak van der Waals forces. When sufficientheat is applied to the polymer the van der Waals bonds starts breaking, mak-ing it possible for the polymer chains to move independently. This causes thepolymer to behave as a fluid, which can be structured permanently by NIL.

TOPAS

TOPAS is a tradename for Thermoplastic Olefin Polymer of Amorphous Struc-ture produced, by the company Ticona [54]. TOPAS is a very good polymer forlab-on-a-chip applications. It is resistant to a large number of solvents, highlytransparent in the visible spectrum and bio-compatible [2].

TOPAS is a co-polymer, meaning that the polymer chains are made of twodifferent monomers. For TOPAS the monomers are norbonene and ethylene,both are shown in Fig. 2.29. The glass transition temperature of TOPAS canbe controlled by the amount of norbornene in the polymer macromolecules.The higher the norbornene content, the higher Tg. The TOPAS used here isgrade 8007, but other grades are available, e.g. 9506 andd 5013. The firsttwo digits in the grade number determines the weight of the molecules. Theunits are apparently only known to Ticona. The last two numbers indicate theapproximate Tg in units of 10◦C. The 8007 grade has a Tg of 75◦C

Figure 2.29: The two monomers of TOPAS. Norbornene (left) and ethylene (right). The mand n letters indicate the norbornene and ethylene contents of the chain. A higher percentageof norbornene increases the glass transition temperature. Picture from [3].

The viscosity for TOPAS 8007 at different temperatures can be seen in table2.1. The values are quite low, since all temperatures are substantially above Tg.The viscosity drops 83% as the temperature is increased from 170◦C to 200◦C.

PMMA

PMMA is an abbreviation for polymethyl methacrylate. The PMMA used hereis supplied by the MicroChem corporation [56]. Compared to TOPAS, PMMA isnot quite as transparent and much less resistant to solvents. It is bio-compatible,


Temperature Viscosity (η)◦C Pa·s170 21.6 × 103

180 9.5 × 103

200 3.6 × 103

Table 2.1: Viscosity of TOPAS grade 8007 at different temperatures. Data adapted from [55].

cheap, and used in numerous applications ranging from electron beam resist topolymer windows (often called plexiglass windows).

The monomer for PMMA is methyl methacrylate, as shown in Fig. 2.30. ThePMMA used here is called 50k PMMA, because it has a molecular weight of50000 g/mol, corresponding to around 500 MMA monomers per polymer chain[50]. 50k PMMA is a fairly low molecular weight, chosen because of its lowviscosity.

Figure 2.30: (a) Methyl methacrylate (MMA), the monomer of PMMA. (b) PMMA is achain of n MMA molecules. For the PMMA used in this project n is around 500. Picturefrom [2].

The glass transition temperature of PMMA is around 105◦C. Viscosities of111k PMMA is found for different temperatures in [57]. The viscosities for50k PMMA can be estimated from this data using the expression [2]

η50k ≈ η111k

(

M50k

M111k

)3.4

, (2.26)

Where M is the molecular weight. The viscosity data can be found in table2.2. The viscosities are generally larger than those for TOPAS, seen in table2.1. When the temperature is increased from 140◦C to 160◦C or from 160◦Cto 200◦C η drops very much. Increasing the temperature further to 220◦C doesnot make a very large difference, however.

44 2.6 Waveguide Theory

Temperature Viscosity of 111k PMMA(η) Viscosity of 50k PMMA(η)◦C Pa·s Pa·s140 4.6 × 109 3.1 × 108

160 7.1 × 107 4.7 × 106

200 1.5 × 106 1.0 × 105

220 1.4 × 106 9.3 × 104

Table 2.2: Viscosity of 111k and 50k PMMA at different temperatures. The data for 111kPMMA is adapted from [57], and the 50k data is estimated from the 111k data using Eq.(2.26).

2.6 Waveguide Theory

In this project, NIL has been used for imprinting planar optical waveguides.The waveguides are all very wide compared to the height, so they are wellapproximated as infinitely wide. This section is only a very brief resume ofwaveguide theory and parameters relevant to this project. An excellent andmore detailed account can be found in [19].

The model considered is an infinitely wide planar polymer waveguide, sur-rounded by infinite layers of air and substrate. The refractive indices of theair above the waveguide, the polymer, and the substrate are called n1, n2, andn3, respectively. n1 is the smallest refractive index.

Maxwells wave equation can be solved numerically in this structure to find sta-ble configurations of the electric and magnetic fields of the propagating waves inthe waveguide. The physically acceptable solutions are called modes. Depend-ing on thickness of the waveguide, refractive indices of the materials, and thefrequency of the light, the waveguide can support different modes. Modes arecharacterized by the polarization of the electric field, which is in the waveguideplane for transverse electric (TE) modes and perpendicular to the plane and thepropagation direction for transverse magnetic (TM) modes. The propagationof a wave along the waveguide in the z direction is descibed by solutions withthe propagation factor ei(ωt−βz).

Fig. 2.31 shows different TE solutions to the maxwell equation for a planarwaveguide. The waveguide is able to support two modes shown in situation b)and c). No physically acceptable modes exist with β outside the range betweenkn2 and kn3. For β > kn2 the electric field of the solutions become infinite,and for β < kn3 the solutions extend to infinity, and thus contain an infiniteamount of energy per width of the waveguide.

Each mode has a unique propagation constant β. The vacuum wavelength(λ) of light travelling with a given propagation constant is found as λ = 2πn

β .

Thus βλ2π gives an effective refractive index seen by the light travelling in the

mode. The fundamental mode (TE0 in Fig. 2.31) always has the largest moderefractive index, and higher order modes (TE1 and higher) have smaller andsmaller indices.

The effective refractive index of the possible modes as a function of waveguidethickness is plotted in Fig. 2.32 for PMMA and TOPAS waveguides on a pyrexsubstrate. The refractive indices used are 1.472 for the pyrex substrate and

2.6 Waveguide Theory 45

Figure 2.31: TE solutions to maxwells equations in a planar waveguide. Depending on tdifferent numbers of modes can exist for a given light frequency. In this case two modes exist(situation b) and c)). If the propagation constant β is above kn2 or below kn3 the solutionsare not physically acceptable. Picture from [19].

1 for the surrounding air. the TOPAS and PMMA indices used are 1.53 and1.49, respectively. The plots are made for a vacuum wavelength of 600 nm. Thewavelength dependence is fairly weak, and in the wavelength range importantfor this project (575 nm to 610 nm), the plots for different wavelengths canhardly be distinguished. The MATLAB files written for plotting the curves arefound in appendix A.

The number of modes increases with the difference in refractive index betweensubstrate and waveguide. Below a certain cutoff thickness no modes exist, andthus no light is guided. This is an important result for NIL of optical compo-nents, since a residual layer is acceptable, as long as it is thinner than this cutoffthickness.

46 2.6 Waveguide Theory

200 400 600 800 1000 1200 1400 1600 1800 2000

1.475

1.48

1.485

1.49

1.495

1.5

1.505

1.51

1.515

1.52

1.525

Effective refractive index for λ=600 nm modes in a TOPAS waveguide on Pyrex

TOPAS thickness /nm

mod

e re

frac

tive

inde

x0th order TE0th order TM1st order TE1st order TM2nd order TE2nd order TM

200 400 600 800 1000 1200 1400 1600 1800 20001.472

1.474

1.476

1.478

1.48

1.482

1.484

1.486

1.488

1.49Effective refractive index for λ=600 nm modes in a PMMA waveguide on Pyrex

PMMA thickness /nm

mod

e re

frac

tive

inde

x

0th order TE0th order TM1st order TE1st order TM

Figure 2.32: Calculated mode refractive index for infinitely wide planar waveguides on pyrex(n = 1.472), with air as cladding on the upper side (n = 1). The cutoff thickness forTOPAS (n = 1.53) is seen to be around 300 nm, whereas PMMA with a lower refractiveindex (n = 1.49) has to be around 600 nm thick to support even the fundamental mode.

Chapter 3Fun tionalized PolymerTwo TOPAS samples were recieved from our collaborators in Bari, Italy. Firstgrade 8007 TOPAS in toluene with oleic acid covered CdS quantum dots witha diameter of approximately 4 nm. The solution contained 0.067 g TOPASper ml toluene, and the quantum dot concentration in the solution was 1.67 ×10−7 M, meaning that each gram of dry TOPAS contains 2.5 × 10−9 moles ofquantum dots. When describing quantum dot concentration a quantum dot isconsidered a molecule, so a mole of quantum dots contains several moles of Cdand S. The other sample was again TOPAS grade 8007, but doped with 4.5nm CdSe quantum dots with ZnS shells. This time 0.05 g TOPAS were usedper ml toluene, and the concentration was 2.5× 10−5 M, giving a quantum dotconcentration in the solid TOPAS of 5 × 10−7 mol/g.

In order to test the properties of the quantum dot modified TOPAS differentexperiments were performed. Since the luminescence from the material wasrather weak, a number of spectra were taken from large drops of material onslides or in microcapillary tubes. Spin coated films were also used.

Since the quality of the edge of a film on a chip that had been sawed out wasnot believed to be very good, nor very easy to reproduce, fabrication processesfor making TOPAS and PMMA slab waveguides with smooth sidewalls were de-veloped. Unfortunately, when the process had been optimized the CdS TOPASsample had dissolved the lid of the bottle, and had become unclear and useless.Therefore only CdSe/ZnS doped TOPAS waveguides were made.

Rhodamine 6G doped PMMA waveguides with the same dimensions were fabri-cated in order to compare active material properties. The material was preparedas described in section 2.4.4. The dye concentration was 2 × 10−5 moles per gdry PMMA.

The first section of this chapter is concerned with design and fabrication of thewaveguides. The next section describes the measurements made, followed by asection on the results. Finally the results are dicussed.

48 3.1 Waveguide Design and Fabrication

3.1 Waveguide Design and Fabrication

The waveguides produced are slab waveguides on a borofloat glass substrate.Since the quantum dot doped TOPAS recieved from our collaborators had verylow viscosity, and had to be deposited by spin coating, this put a limit onthe height of the waveguides. The TOPAS layer became 600 nm high whenspun at 1500 RPM, which is close to the lowest possible spin speed. Sincepolymer moves into the stamp cavity during imprinting, the finished waveguidesare slightly thicker than 600 nm. The waveguide length was decided to be 8mm, while different widths, ranging from 50 µm to 200 µm were used. Sincethe rhodamine doped PMMA waveguides were to be used for comparison ofproperties, they were fabricated with the same dimensions.

As seen from Fig. 2.32 on page 46, the expected thickness slightly above 600nm is enough to guide light only in the fundamental TE and TM modes forboth materials, though the PMMA waveguides are rather close to the cutoffthickness.

3.1.1 Fabrication Process

Because the sidewalls needed to be steep with very small roughness, nanoimprintlithography was the obvious choice of fabrication method. Unfortunaltely, theprotrution coverage of the stamp would have to be very high, if the polymerwere to be thin enough in the entire area outside the waveguides. Thus, afabrication method using both nanoimprint and conventional UV lithographywas developed.

The fabrication of TOPAS waveguides is shown schematically in Fig. 3.1. Themask designs can be found in appendix B, and exact recipe with all parameterscan be found in appendix C. Pictures (a-c) show how the stamp is prepared.The protrution areas, which will imprint the 20 µm wide trenches around thewaveguides, are defined in an UV lithography step (a). The wafer is etched550 nm down in a reactive ion etch, using the resist as mask (b). The finishedstamp, after resist removal, is seen in picture (c).

The substrate for imprinting is a pyrex wafer with a film of functionalizedTOPAS, 600 nm thick (d). Picture (e) shows the waveguide imprint with thetrench around it. Next, the waveguides and half of the trenches are covered inphotoresist by another UV lithography step (f). The wafer is then etched in anoxygen plasma, in order to remove all the unmasked TOPAS (g). Finally, afterthe resist has been dissolved, only the waveguides are left, with a small area ofresidual layer around them (h). The residual layer should be thin enough to beunable to guide light, and since the TOPAS is removed completely from mostof the wafer, very little luminescence will come from outside the waveguides.

Since PMMA is dissolved in acetone, which is used to remove the shielding pho-toresist, the fabrication process had to be modified slightly for production ofPMMA waveguides. After imprinting, a layer of LOR (lift-off resist) is spun,prior to the photoresist spinning. Fortunately, LOR is also dissolved in pho-toresist developer, so after development (for an extended time period) only the

3.1 Waveguide Design and Fabrication 49

Figure 3.1: Fabrication process for TOPAS waveguides. The waveguides are 50-200 µm wide,8 mm long, and approximately 600 nm high. (a) The waveguide outlines on the stamp aredefined by UV lithography. (b) A reactive ion etch etches the unmasked areas down. (c) Thefinished stamp. (d) The quantum dot doped TOPAS is spun on a glass wafer. The thichnessis 600 nm. (e) The trenches are imprinted into the film. (f) The waveguide and part ofthe trench are shielded in an UV lithography step. (g) The surroundings are etched in anoxygen plasma. (h) The finished waveguide, after the resist has been stripped. Fabrication ofPMMA waveguides is similar, except that an intermediate layer of LOR resist is used underthe photoresist.


waveguides are covered in LOR and resist. Then the plasma etch proceeds aswith the TOPAS waveguides, and finally the wafer is soaked in MF-319 mi-croposit remover, which dissolves the LOR without damaging the PMMA, thuscausing the resist to fall off.

3.1.2 Fabrication Results

The first waveguides made were somewhat higher, 1200 nm, and made of pureTOPAS grade 8007. These waveguides had vertical sidewalls after the imprint,but after removal of the surroundings, the sidewalls were inclined, and the cor-ners looked rounded. The reason is that too much power was transferred to theplasma. This causes the plasma to become warmer than the glass transitiontemperature of the TOPAS. The problem was solved by lowering the power,even though it increased the etch time substantially.

Optical microscope and SEM images of the finished CdSe/ZnS doped TOPASwaveguides are seen in Figs. 3.2 and 3.5. It appears as if the pyrex substrate isvery dirty, while the waveguides also have defects, though they are far smootherthan the surroundings. The most dirty areas are those where most TOPAShas been etched away, i.e. the etched part of the trenches looks cleaner thanthe areas surrounding. Fig. 3.3 contains confocal microscope images of thewaveguides. A confocal microscope excites the sample optically, but only collectslight to the red of the excitation. This makes it possible to see flourescence. Itis clear that there is diffuse flourescence all over the waveguides, and nothing inthe plasma etched areas. There is also some fluorescence from the residual, butless than from the main waveguide. Apart from the diffuse reddish flouorescencethere are also some small very intense flourescent fields. These are quantum dotaggregates. Very few aggregates light up outside the waveguide.

It is noted that the aggregation increased with time. The first films spun wererather uniform, but after a few weeks the films contained a number of dark dots,when inspected in the microscope.

The particles seen outside the waveguides in Figs. 3.2 and 3.5 are not seen in

Figure 3.2: 50 µm wide CdSe/ZnS quantum dot doped TOPAS waveguides. (left) Normalmicroscope image. The waveguides appear well defined, but the surrounding pyrex looks dirty.(right) Dark field microscope image. The dirty areas are much easier to see. The waveguideclearly has some defects, but it is smoother than the pyrex.


Fig. 3.3. Thus, they are probably not quantum dots. Since TOPAS is quiteresistant to plasma etch, it may be unetched TOPAS, but it is also possible thatthe particles are residues from the quantum dots. The few large aggregates seenoutside the waveguides in Fig. 3.3 indicate that the semiconductor material isnot etched by the plasma (as expected), but falls of the wafer during etch or inlater processing steps.

The height profiles have been measured with a surface profiler (type Dektak 8).The waveguides are around 810 nm high, with a residual of around 370 nm. Asseen in Fig. 2.32, the waveguide are unable to support more than one TM andone TE mode. Unfortunately, the residual is also able to support guided opticalmodes. A possible explaination for the high residual is that the aggregates haveinhibited the polymer flow.

Figure 3.3: Confocal microscope images of 50 µm wide CdSe/ZnS quantum dot doped TOPASwaveguides. Fluorescence is seen from the waveguides and to a smaller extend from the resid-ual surrounding them. Quantum dot aggregates are seen at different positions in the waveg-uide. A few aggregates are also visible outside, indicating that the semiconductor material isnot etched in the plasma etch. The pictures are taken by M. L. Curri, our collaborator.

Figure 3.4: 50 µm wide Rhodamine doped PMMA waveguides. (left) Normal microscopeimage. The waveguides look clean, smooth and well defined. (right) Dark field microscopeimage. Only the PMMA areas light up, especially the thicker parts. Because the light is veryhomogeneous it is believed to be fluorescence from the rhodamine.


Figure 3.5: SEM images of 50 µm wide CdSe/ZnS quantum dot doped TOPAS waveguidescovered in 20 nm gold. The angle between the sample and the electron cannon is 35◦. Theupper picture is a closeup of a sidewall. The sidewall is well defined, but has some defects.The defects are also visible on the TOPAS planes. The lower picture shows the end of awaveguide. The defects can still be seen, but the surrounding pyrex looks far more rough.


Figure 3.6: SEM images of 50 µm wide rhodamine 6G doped PMMA waveguides coveredin 20 nm gold. The angle between the sample and the electron cannon is 35◦. The upperpicture is a closeup of a corner. The walls do not apper to be vertical, and there are a fewdefect on the PMMA, propably from undissolved rhodamine. The lower picture shows the endof a waveguide. The surrounding pyrex looks much cleaner than the quantum dot TOPASsurroundings. PMMA is damaged much easier by the electron beam, as seen in the middle ofthe picture.

54 3.2 Measurements

The rhodamine 6G doped waveguides are shown in Figs. 3.4 and 3.6. Thepyrex substrate looks much cleaner, and in the dark field microscope imageonly the PMMA lights up. Since no large light scattering centers are visible inthe PMMA, the light is probably fluorescence from the rhodamine. It can alsobe very small light scattering centers, but since the thicker parts lights up morethan the residual, the light probably comes from within the polymer rather thanthe surface. There are some defects on the surface, seen in the SEM pictures.Propably these are aggregates of undissolved rhodamine.

If the dirt around the TOPAS waveguides is indeed polymer residues, one mightexpect to see the same around the PMMA waveguides, which are etched in thesame process. However, since PMMA is substantially less resistant to plasmaetch than TOPAS, this conclusion is invalid.

The heights of the PMMA waveguides and residuals are 830 nm and 260 nm,respectively, so according to Fig. 2.32 the waveguide can sustain light modes,while the residual cannot. The sidewalls do not appear to be vertical, how-ever. The step in the process causing this has not been identified due to timeconstraints.

3.2 Measurements

All optical measurements were done at the optical table shown in Fig. 3.7. Thesetup shown is used for pumping rhodamine and CdSe/ZnS quantum dot waveg-uides with 5 ns 532 nm pulses. The light comes out of the side of the opticalparametric oscillator (OPO), from where it is guided through en attenuator tothe sample stage. The light coming from the sample on the stage is collectedwith a 200 µm diameter optical fiber and guided into a spectrometer, connectedto a computer.

The laser can also generate 355 nm pulses, and with the OPO, it is possiblegenerate light at any wavelength from 411 nm to 676 nm. Both laser and OPOare Continuum Surelite brand.

Fig. 3.8 is a closer look at the sample stage with a rhodamine doped waveguidechip. The chip is put on the stage, and pumped from above. The light iscollected from the end of the waveguides with the fiber, which is connected tothe fixed grating Avantes brand spectrometer.

The CdS quantum dots had to be pumped with wavelenths shorter than 430nm, so both light from the OPO and the frequency tripled 355 nm output of thelaser were used. Most measurements were made with 355 nm light, because thislight was brighter than the OPO light. Mirrors for 355 nm light was purchased,but did not arrive until after the CdS TOPAS had degraded, and thus themeasurements presented here are taken by putting the sample directly in frontof the laser beam, as it comes out of the OPO, and aligning the fiber to thesample. For the blue wavelenths another fixed grating spectrometer, aquiredfrom Ocean Optics, and a different fiber was used.

The energy density was measured by inserting a 1.5 mm pinhole in the pumpbeam, and let the spot from the pinhole hit a power-meter.

3.2 Measurements 55

Figure 3.7: Setup for optical measurements. The Nd:YAG pump laser is able to generatefrequency doubled (532 nm) and frequency tripled (355 nm) pulses with a duration of 5 ns.These frequencies can be coupled out of the optical parametric oscillator (OPO) at the side.A 532 nm green laser line is drawn on the photo. It is sent through an attenuator to thestage holding the samples. An optical fiber, connected to a spectrometer, is attached to aholder for measuring the light coming from the sample. At other ports of the OPO, light withwavelengths from 411-676 nm can be collected.

Figure 3.8: Closer look at the setup for measuring on the waveguides. The pump light hitsthe sample from above, and light is collected from the end of the waveguides with the opticalfiber.

56 3.3 Results

3.3 Results

3.3.1 CdS Doped TOPAS

The first spectrum from a 1200 nm thick spin coated film of CdS doped TOPASis seen in Fig. 3.9. The pump was at 355 nm with a 10 Hz repetition rate. Thelight was very weak and difficult to detect. The luminescence is seen to have itsmaximum around 460 nm.

Since the light from the thin film was very weak, drops on a glass wafer wasused instead, because this gave thicker layers. An example of a spectrum is seenin the left of Fig. 3.10. The pump is at 420 nm. This spectrum is taken a fewweeks after the one in Fig. 3.9. The light is again very weak. The spectrometerintegration time is 10 s, and still the signal is very weak and noisy. A defectband is seen, redshiftet with respect to the fluorescence peak. The defect bandappears to drop off around 545 nm, but this is because the long wavelengthlimit of the spectrometer is reached.

The right spectrum in Fig. 3.10 is also from a drop, pumped at 355 nm with 8µJ/mm2 pulses at 10 Hz repetition. The spectrum is taken a month after theprevious. Now the maximum of the light emission is in the defect band, ratherthan at the band edge fluorescence.

By measuring a spectrum at a certain pump power, increase the power for aperiod of approximately 30 s, decrease it again, and repeat the measurement, itwas possible to find the pump power where the material was damaged by thepump light. Fig. 3.11 shows two such spectra. As seen in the figure, 16 µJ/mm2

at 10 Hz repitition caused the two spectra to become different.

Figure 3.9: Fluorescence from the edge of a 1200 nm thich CdS doped TOPAS film. Thefluorescence is seen around 460 nm. The large peak at 355 nm is pump light. The x-axisshows wavelength in nm, and the y-axis shows intensity in arbitrary units.

3.3 Results 57

300 350 400 450 500 550 600

-200

0

200

400

600

800

1000

1200

Inte

nsity

/ A

. U.

Wavelength / nm

Figure 3.10: Fluorescence from CdS doped TOPAS drops on glass substrates. (left) Thisspectrum is taken with 420 nm pump light. Again, the flourescence maximum is at 460 nm,but a broader defect band is seen, redshiftet with respect to the fluorescence. The defect bandlooks like it drops off around 545 nm, because the spectrometer is unable to detect such longwavelengths properly. (right) Another spectrum from a drop taken a month after the leftspectrum. The defect luminescence is now larger than the band edge emission. This spectrumis taken with 355 nm pulses with a pulse fluence of 8 µJ/mm2.

300 350 400 450 500 550 600

-200

0

200

400

600

800

1000

1200

8 J/mm2

8 J/mm2 after 16 J/mm2

Inte

nsity

/ A

.U.

Wavelength / nm300 350 400 450 500 550 600

-200

0

200

400

600

800

1000

1200

16 J/mm2

16 J/mm2 after 40 J/mm2

Inte

nsity

/ A

.U.

Wavelength / nm

Figure 3.11: Spectra taken at the same pump power, before and after a higher pump powerhas been used. The two spectra are very close in the left plot, but in the right plot, wherehigher pump pulse energy is used, the band edge emission has dropped. Limited damage isthus inflicted by pump pulses with an energy density of 16 µJ/mm2.

58 3.3 Results

3.3.2 CdSe/ZnS Doped TOPAS

The first measurements on the TOPAS doped with CdSe quantum dots withZnS shells were on samples in microcapillary tubes with an inner diameter of140 µm. The material was sucked into the tubes by microcapillary forces andleft to dry overnight.

The luminescence was very difficult to measure, and very high pump powershad to be used. Fig. 3.12 is a pump damage curve like that in Fig. 3.11. Theband edge emission is at 618 nm, and no defect band is visible. The large peakat 532 nm is the pump light. The power needed to degrade the spectrum afterapproximately 30 s of pumping is very high, 2.6 mJ/mm2.

As shown, waveguides were made with the CdSe/ZnS doped TOPAS, but evenwhen integrating for 30 seconds with the spectrometer, no fluorescence at allwas seen.

500 550 600 650 700

0

200

400

600

Inte

nsity

/ A

.U.

Wavelength / nm

2.3 mJ/mm2

2.3 mJ/mm2 after 2.4 mJ/mm2

500 550 600 650 700

0

200

400

600 2.4 mJ/mm2

2.4 mJ/mm2 after 2.6 mJ/mm2In

tens

ity /

A.U

.

Wavelength / nm

Figure 3.12: Spectra taken at the same pump power, before and after a higher pump powerhas been used. The fluorescence is around 618 nm, and the huge peak at 532 is the pump.Note that the power is very high, counted in mJ rather than µJ. The two graphs in the leftside are practically identical, whereas the output at all wavelengths is lowered by the highpower used between the measurements in the right figure.

3.3.3 Rhodamine 6G Doped PMMA

A number of spectra from the rhodamine doped waveguides, taken at differentpump intensities, are seen in Fig. 3.13. The pump is 10 Hz 532 nm pulses,and the spectrometer has integrated for 2 seconds. A strong ASE peak, cen-tred around 590 nm, is seen at all pump powers higher than 7.9 µJ/mm2. Inthe wavelength range from 550 nm to 570 nm, the signal grows slightly withincreased pump power. This is the spontaneous emission.

3.4 Discussion 59

480 500 520 540 560 580 600 620 640 660 680 700 720

0

200

400

600

800

1000

1200

1400

Inte

nsity

/ A

.U.

Wavelength / nm

9 J/mm2

18 J/mm2

28 J/mm2

36 J/mm2

41 J/mm2

500 550 600 650 700-20

-10

0

10

20

30

40

50

60

70

80

90

100

Inte

nsity

/ A

.U.

Wavelength / nm

0.1 J/mm2

4.5 J/mm2

7.9 J/mm2

Figure 3.13: (left) Spectra from rhodamine 6G doped PMMA waveguides. ASE is seen inall spectra, and in the 550-570 nm range, a very weak spontaneous emission signal is seen.(right) When increasing from 0.1 µJ/mm2 to 4.5 µJ/mm2 the fluorescence increases in therange from 550 nm to 620 nm. As the pump is increased further to 7.9 µJ/mm2, the ASEstarts around 590 nm.

3.4 Discussion

As seen when comparing Figs. 3.9 and 3.10 the CdS quantum dots appear tohave degraded with time, during the first few weeks after they were recieved.Part of the explaination might be, that the lid, which was dissolved by the so-lution, had started to fall into the TOPAS. This can not be the whole answerhowever, since our collaborators also measured a degradation in a sample theykept in Bari. The fact that a large defect band develops indicate that somethinghas happened to the quantum dots. Either the surface passivation has brokendown, or the quantum dots have aggregated. Most likely the problem is aggre-gation, since this happened to the CdSe/ZnS doped TOPAS after a similar timeperiod.

When the CdS quantum dots break down due to high pump powers, it seemsmainly to affect the band edge emission, see Fig. 3.11. Thus, this problem ismost likely due to surface passivation problems. Another indication that thepassivation is too fragile is the low breaking fluence of 8 µJ/mm2, which is farbelow the energy necessary to change the properties of the TOPAS.

Though the concentration of quantum dots was substantially higher in the CdSedoped TOPAS than the CdS doped TOPAS, luminescence was even harder tomeasure. Nothing at all was measured from the waveguides, which are 800 nmhigh, and a very low signal was measured from the microcapillary tubes. Thematerial had a brownish color, and was unclear. As shown in Fig. 3.3, thequantum dots have aggregated.

The aggregation is undoubtedly an important part of the reason for the lowluminescence. Not only does aggregation decrease the luminescence becausethe quantum dots within the aggregate are difficult to pump, but scatteringand absorbtion of light can take place on the large aggregates, increasing theloss of the waveguide. Ultrasonic treatment of the TOPAS was tried in anattempt to dissolve the aggregates, but with little succes. Our collaborators inBari have shown that the aggregates can be removed by filtering the solution.

60 3.4 Discussion

The destruction test in Fig. 3.12 is very different from that for CdS quantumdots in Fig. 3.11. First of all the pump power is substantially higher, measuredin mJ/mm2, rather than µJ/mm2. The degradation also happens in a differentway. Only the CdS band edge emission took damage, while the whole spectrum,including pump, is shifted downwards in the CdSe case. This is an indicationthat the TOPAS is breaking down, rather than the quantum dots. Thus theZnS capping seems much better than the oleic acid capping of the CdS dots.

When looking at Fig. 3.13 it is clear that rhodamine is very easy to invert.The fluorescence can be measured with a 2 second integration at a pump powerper area of 4.5 µJ/mm2. Note that the rhodamine concentration is around 40times higher than the quantum dot concentration, but even this is not enoughto explain the large difference in properties.

Chapter 4WGM Fluid LasersBecause no amplified spontaneous emission was measured from the quantumdot doped TOPAS samples, it was decided to try incorporation into high Qmicrocavities. If the cavity losses are very small, it is possible to start laseroscillations at a lower inversion level. The highest Q factors are usually obtainedin cylindrical or spherical cavities, where light is guided in whispering gallerymodes along the circumference by total internal reflection.

As mentioned in section 1.2, lasing from CdSe/ZnS quantum dots in whisperinggallery modes has been demonstrated [13]. The cavity was first introducedwith rhodamine 6G as active material [14]. The preparation of the cavity isquite simple, and the active material is used directly in a fluid solution. Bothpublished experiments used a frequency doubled Nd:YAG laser as pump.

It was decided to repeat both experiments as part of this project. The rhodamineexperiments were done to compare the cavity to those from the publications.Next, CdSe/ZnS quantum dots in hexane were used as active material. Thiswould give a very good comparison between the quantum dots available in thisproject, and those used succesfully by other groups.

4.1 Preparation and Working Principle

The laser is prepared by removing the polymer protection from an optical fiberwith a diameter of 125 µm, and inserting it into a microcapillary tube, 200µm in inner diameter, see Fig. 4.1. Removing the polymer from the fiber wasdone in three ways. Either it was burned in a lighter flame, torn off mechanicallywith a fiberstripper tool, or etched in hot sulphuric acid. Since the fiber cleaningmethod did not appear to have any impact on device performance, the strippingtool was used mostly, because it is the easiest process.

The active material was sucked into the volume between the inner wall of the

62 4.1 Preparation and Working Principle

Figure 4.1: Photo of a whispering gallery mode laser cavity. A 125 µm diameter opticalfiber is inserted into a microcapillary tube with an inner diameter of 200 µm. The activematerial, either rhodamine 6G in ethanol or CdSe/ZnS quantum dots in hexane, is suckedinto the volume between the fiber and the tube wall by capillary forces.

tube and the outer wall of the fiber by microcapillary forces. Rhodamine 6G wasdissolved in ethanol, usually in a concentration of 2 mM, but lower concentra-tions were also used. The quantum dots were dissolved in hexane. A 2.5× 10−5

M solution of 4.5 nm diameter ZnS covered CdSe dots was recieved from ourcollaborators. It was first used as recieved, but later a higher concentration wasneeded, and hexane was boiled off by placing the vial on a 100◦C hotplate. Theboiling continued until the volume was approximately a tenth of the originalvolume, i.e. a 2.5×10−4 M solution. The quantum dot solutions were sonicatedfor a few minutes before they were sucked into the laser. The lasers were usedshortly after prepared.

Fig. 4.2 is a schematic drawing of the laser seen from the end. A typical fibercladding has a refractive index around 1.46. The refractive indices of ethanoland hexane are 1.361 and 1.375, respectively, and thus light can be guidedby total internal reflection along the circumference of the fiber. Amplificationof the whispering gallery modes in the fiber can happen, even though the lasermedium is outside the fiber, because there is a certain overlap of the modes to thesurroundings. Whispering gallery modes are characterized by their polarisation,and two numbers n, which descibes the azimuthal shape of the mode, and l,which describes the radial shape of the mode [14]. the higher n or l number amode has, the higher the number of nodes around the circumference or from thecenter out, respectively. Angle averaged values of the intensity is plotted as afunction of radius for different modes in Fig. 4.3. The evanescent fields, wherethe modes are amplified, are seen at r/a values larger than 1.

A very small percentage of the light escapes in all directions perpendicular tothe fiber axis, as seen in Fig. 4.2. This constitutes the output coupling scheme.

4.1 Preparation and Working Principle 63

Figure 4.2: Schematic drawing of a whispering gallery mode laser, seen from the end. Becausethe fiber has a larger refractive index than the active material, the optical modes are confinedin the central fiber by total internal reflection. The light is amplified by evanescent wavecoupling, i.e. the optical modes extends slightly into the active material, which allows themto become amplified. The laser light comes out in all directions perpendicular to the fiber axisand tangential to the fiber.

Figure 4.3: Angle averaged intensity for whispering gallery modes in a cylindrical waveguideof radius a. The optical field extends outside the waveguide, and because the waveguide issurrounded by active material, it is possible to amplify the light in the modes. Picture from[14].

64 4.2 Measurements

Figure 4.4: Optical measurement on whispering gallery mode laser. The laser is put on thesample stage, and pumped from above. A fiber connected to a spectrometer collects the outputlight.

4.2 Measurements

Measurements are done at the optical table in Fig. 3.7 on page 55. A closer lookat the laser on the sample stage is shown in Fig. 4.4. The laser is pumped fromabove with 5 ns 532 nm pulses at 10 Hz, and the generated light is collectedwith a measurement fiber perpendicular to both pump beam and laser axis.

4.3 Results

Spectra from the whispering gallery mode laser with rhodamine 6G as activematerial are seen in Fig. 4.5. At 8 µJ/mm2 lasing is seen around 580 nm. Thepeaks are very narrow and grow much faster than the broad fluorescence peak.At the highest pump power, the spectrum also has a small bump around 625nm.

Spectra from the laser with the recieved solution of CdSe/ZnS quantum dots inhexane are seen in Fig. 4.6. No laser peaks are seen at any pump energies. The50 nm broad fluorescence peak is seen around 600 nm. It does not appear togrow for pump pulse fluences higher than 87 µJ/mm2.

Fig. 4.7 shows the spectra from the laser, where the more concentrated quantumdot solution, obtained by boiling off hexane, has been used. The fluorescenceincreases with pump powers up to around 596 µJ/mm2. The peak is seen around615 nm, despite that the quantum dots comes from the same solution as usedin Fig. 4.6, where the peak is seen around 600 nm.

4.3 Results 65

500 550 600 650 700

0

200

400

Inte

nsity

/ A

.U.

Wavelength / nm

< 8 J/mm2

8 J/mm2

72 J/mm2

565 570 575 580 585 590

0

200

400

600

800

1000

1200

1400

1600

1800

Inte

nsity

/ A

.U.

Wavelength / nm

< 8 J/mm2

8 J/mm2

72 J/mm2

FWHM: 0.138 nmQ = 580.29/0.138 = 4205

Figure 4.5: Spectra from the whispering gallery mode laser with 2 mM rhodamine 6G inethanol as active material, taken at different pump pulse energies. The integration time ofthe spectrometer is 100 ms. The lasing threshold is below 8 µJ/mm2, where the first peaksdevelop around 580 nm. The peak at 532 nm is pump laser light. (bottom) A closer lookat the peaks in the spectrum. The FWHM is found to be 0.138 nm, giving an upper limitto the cavity Q around 4200. Note that since the FWHM is very close to the spectrometerresolution the measured Q value is probably not very precise, and could quite easily be larger,if measured with a higher resolution spectrometer.

66 4.3 Results

500 550 600 650 700

0

100

200

300

400

500

600

Inte

nsity

/ A

.U.

Wavelength / nm

< 8 J/mm2

< 8 J/mm2

< 8 J/mm2

8 J/mm2

87 J/mm2

230 J/mm2

Figure 4.6: Spectra from the whispering gallery mode laser with 2.5 × 10−5 M CdSe/ZnS

quantum dots in hexane as active material, taken at different pump intensities. Integrationtime of the spectrometer is 10 s. There is no indication of lasing, but the fluorescence seemsto saturate around 87 µJ/mm2. The peak at 532 nm is pump laser light.

500 550 600 650 700

0

100

200

300

400

500

600

Inte

nsity

/ A

.U.

Wavelength / nm

135 J/mm2

270 J/mm2

437 J/mm2

596 J/mm2

700 J/mm2

Figure 4.7: Spectra from the whispering gallery mode laser with 2.5 × 10−4 M CdSe/ZnS

quantum dots in hexane as active material, taken at different pump intensities. Integrationtime of the spectrometer is 10 s. The fluorescence does not appear stronger, despite the higherconcentration, and it saturates around 596 µJ/mm2. The fluorescence peak has moved to 615nm, from the 600 nm seen in Fig. 4.6. The peak at 532 nm is pump laser light.

4.4 Discussion 67

Destructiontests similar to those in Fig. 3.12 on page 58 have been carried outwith the concentrated CdSe/ZnS solution. They showed no degradation of thematerial after pump energies of 700 µJ/mm2 had been used.

4.4 Discussion

As seen from the results in Fig. 4.5 the whispering gallery mode laser clearlyworks, and the threshold is quite low. Its properties are different from thosepresented in [14], however. Their lasing results are shown in Fig. 4.8. Thearticle states that the beam spotsize is 1 mm, and that the group of modesaround 605 nm develops at a pump energy of 200 µJ, while the group around578 nm develops at 1 mJ. This corresponds to an energy per area of 254 µJ/mm2

and 1273 µJ/mm2 for the two groups, respectively. Thus, the threshold fluencemeasured here is substantially lower, but the lasing seems to start around 580nm. As seen in Fig. 4.5, small intensity fluctuations were measured around 625nm, however.

Figure 4.8: Spectra from WGM laser in [14], where rhodamine has been used as active mate-rial. There are two groups of whispering gallery modes lasing. The group at 605 nm developsfirst, then the group at 578 nm. The modes around 555 nm are radial modes between thewalls of the tube and the fiber. The inset is from the laser with no fiber inserted. There arelasing between the tube walls, looking much like the group at 555 nm with the fiber inserted.

There can be several reasons for the differences between the results presentedhere, and those in [14]. Possibly, the refractive indices of the claddings of thetwo fibers used have been different. Further, there could be small differencesin the rhodamine concentrations. A different concentration would also impactboth refractive index of the solution and amplifying properties.

The Q factor for the group around 580 is expected to be around 2 × 105 from

68 4.4 Discussion

theoretical calculations [14]. As seen in Fig. 4.5, the upper limit to the cavity Qfound here is only 4200. The FWHM is very close to the spectrometer resolution,however, so I believe Q could be higher. I do not think it is as high as that ofthe cavities in [14], because the first peaks develop closer to the gain maximumof the dye. According to the theory presented in [14], the first peaks shoulddevelop around 605 nm, if the cavity Q is very high. The low laser thresholdsuggests a high Q, but it can also be due to higher dye concentration.

If the Q factor is indeed lower it could be due to surface roughness of the fiberor that the fiber was too close to the wall of the microcapillary tube. Tests withthree different methods of fiber cleaning did not improve the cavity properties,however, and neither did changing the orientation of the laser to vertical.

The quantum dot solutions used in the laser gave no lasing, even when pumpedsubstantially harder than the samples in [13]. This can have a number of reasons.First, if the cavity Q is too low, it may be too difficult to achieve a strong enoughinversion to compete with the losses.

Another important issue is the concentration of the quantum dots. [13] does notgive the concentration used, but the mass per volume of hexane. Consideringthat their quantum dots have the fluorescence peak around 560 nm, a goodestimate for the core size is 4 nm, when comparing to results from [6]. If theshell weight is neglected, an estimate of the concentration can thus be foundby calculating the weight of a CdSe sphere 4 nm in diameter, and then findthe number of quantum dots from the weight per volume given. This yields aconcentration estimate of 2.6 × 10−4 M.

Thus, the recieved solution was approximately 10 times as dilute as the oneused in [13]. This could easily cause the gain to become too low for lasing. Theconcentrated solution did not give any lasing either, however, but the concen-tration method with boiling the solution can have an impact on quantum dotproperties. After all, 100◦C, which is the temperature used, is a large fractionof the temperature typically used in a shell growth process.

It is interesting that the fluorescence peak from the recieved solution is around600 nm, while that of the boiled solution is 615 nm. One explaination can bethe change of quantum dot surroundings, which is known to influence the fluo-rescence properties. The quantum dots are closer together in the concentratedsolution, and so are any dirt particles. Another explaination could be that thequantum dots themselves have changed in the concentration process. It is un-likely that the cores have changed very much, since the temperature is limited,and the fluorescence does not seem to broaden, but possibly the shell propertieshave changed.

Finally, there can be other differences between the samples used here, and thosefrom [13], apart from the fact that the quantum dot sizes are different. Theremay be differences is passivation quality and the amount of reaction residues inthe hexane. It is also possible that the quantum dots have aggregated, as in theTOPAS samples.

Chapter 5Imprinted DFB LaserBecause no amplification was measured from the quantum dot samples recieved,research turned towards production af a nanoimprinted laser cavity. This wouldenable the production of polymer lasers with both rhodamine and quantum dotsas active material.

The lasers were only fabricated in rhodamine 6G doped PMMA, due to timeconstraints, and since no quantum dot doped polymer without severe aggrega-tion were availiable.

5.1 Design and Fabrication

The cavity was designed as a rhodamine 6G doped PMMA slab waveguide, withsurface corrugations acting as first order Bragg gratings. A schematic drawingof a laser device is shown in Fig. 5.1. The slab waveguide is designed to be1 mm long, 500 µm wide and approximately 700 nm high. The height of thefabricated devices ended up closer to 1 µm, however.

The corrugation depth was designed to be larger than 10 nm, which had workedin previously published experiments [17]. Since the fabrication method of thecorrugations had not been tried before, it was difficult to aim for a specificdepth, however. The final result was 40-60 nm.

Deeper currogations sound like a benefit, but that is not necessarily true. Inorder to keep the threshold low, it is important to have large feedback. Thereare however two ways of improving the feedback of a Bragg grating of this type.Either the number of currogations can be increased or the currogation depthcan be increased. Consider a Bragg grating with alternating 100 nm segmentswith n = 1.492 and n = 1.488, respectively. The grating contains 1000 periods.The blue reflectance curves in Fig. 5.2 are calculated for this grating using aT-matrix method, described in e.g. [58]. The MATLAB programs used are

70 5.1 Design and Fabrication

Figure 5.1: Schematic drawing of a nanoimprinted DFB laser. The laser is a rhodaminedoped PMMA waveguide with surface corrugations, acting as Bragg reflectors. The lasers are1 mm long, 500 µm wide, and approximately 1 µm high. The corrugations have a pitch ofeither 195 nm or 205 nm, and a depth of approximately 40 nm. In the middle og the laserthere is a λ/4 phaseshift, and on each side of it there are roughly 2500 grating periods.

found in appendix A. The two red reflectance curves show what happens ifthe modulation of the refractive index is increased, corresponding to largercorrugations, and what happens if the number of periods is increased. It isclear that the maximum reflectance is larger in both situations, but the deepercorrugations give a broader reflectance peak.

If the mirrors in a laser cavity have equal reflectance at all wavelengths the peakwidth will be defined by the loss, because it influences the amplitude of the fedback signal, as described in section 2.1.2. In a DFB grating the width of thereflectance window can be comparable to the width of the resonance peak, if themirrors reflected at all wavelengths. This can influence the width of the laserline. Making corrugations deeper can thus cause broadening of the laser line,so if a grating must be designed with a specific reflectance it is often better touse a larger number of periods than deeper corrugations.

Two different grating periods were used for the surface corrugations, 195 nmand 205 nm. The reflection wavelength of a first order Bragg grating is givenby [19]

λ = 2Λn, (5.1)

where λ is the vacuum wavelength, Λ is the grating period, and n is the effective

5.1 Design and Fabrication 71

Figure 5.2: Reflection as a function of wavelengths for Bragg gratings. The two blue spectraare the same, from a 1000 period grating made of 100 nm wide n = 1.492 and n = 1.488segments. In the upper picture the modulation of the refractive index is larger for the redcurve. In the bottom picture the number of periods is larger in the red curve. Both changesgive a larger reflectance at the central wavelength, but the curve is broadened in the upperpicture. The MATLAB code used to make the plots can be found in appendix A.


refractive index. Inserting a refractive index of 1.478, found from Fig. 2.32 onpage 46, with a 1 µm waveguide, yields laser wavelengths of 576 nm and 606nm, for the two period lengths.

In a DFB laser it is beneficial to have a phase-shift of λ/4 in the center of thelaser, in order to achieve single mode lasing at the Bragg wavelength [18]. Sincethe corrugation depth was not known very precisely, the reflection was made aslarge as possible, by maximizing the number of periods in the gratings. Thus,2564 and 2439 periods were used on either side of the central λ/4 section, forthe 195 nm pitch and 205 nm pitch lasers, respectively.

If the corrugations are considered rectangular, [19] describes how the reflectionand transmission coefficients can be found at the wavelength where the reflectionis largest. First, a coupling coefficient, κ, is found as

κ =2π2

3λ0

n22 − n2

1

n2

(a

t

)3(

1 +3(λ0/a)

2π√

n22 − n2

1

+3(λ0/a)

2

4π2(n22 − n2

1)

)

, (5.2)

where a is the corrugation height, t is the waveguide height, and n1 and n2 arethe refractive indices of the surrounding medium and the waveguide medium,respectively. The amplitude of the incident and reflected waves are called A+

and A−, respectively. For a grating of length L, starting in z = 0, they aregiven by

A+(z) = A+(0)cosh(κ(z − L))

cosh(κL)(5.3)

A−(z) = A+(0)κ

|κ|

sinh(κ(z − L))

cosh(κL). (5.4)

The fraction of power reflected (Reff ) and transmimtted (Teff ) is

Reff =

∣

∣

∣

∣

A−(0)

A+(0)

∣

∣

∣

∣

2

(5.5)

Teff =

∣

∣

∣

∣

A+(L)

A+(0)

∣

∣

∣

∣

2

. (5.6)

Using the above equations with a waveguide thickness of 1 µm, corrugationsof 40 nm, and a length of 500 µm, the gratings in the 195 nm pitch lasertransmits 2.27× 10−3 % of the light, while the 205 nm laser gratings transmits1.55×10−3 % of the light. This gives theoretical Q factors of 7×1010 and 1011,using Eq. (2.6). The actual Q is expected to be substantially lower, becausethe loss to fabrication defects and scattering is ignored in the calculations.

5.1.1 Fabrication Process

The laser is fabricated in one imprint step from a multilevel silicon stamp. Thefabrication process for the stamp is shown schematically in Figs. 5.3 and 5.4.The mask designs are found in appendix B, and the exact recipes are foundin appendix C. First, the gratings are defined in Al using an electron beam


lithography lift-off process (a). A reactive ion etch is used to etch the gratings200 nm down (b). After the aluminum is stripped, the gratings are standing onthe wafer (c). The areas outside the gratings are covered with photoresist in anormal UV lithography step (d), and another reactive ion etch is used to etch600 nm down (e). This transfers the gratings to the bottom of the cavity, whichis to form the lasers. Since the etch is not perfectly anisotropic, the corrugationsbecome smaller and more rounded. When the resist is stripped (f), the lasercavities are formed, but the protrution coverage is far too high. Thus, a 2 mmwide square covering the cavity is defined by UV lithography (g). A 2.2 µmmesa is etched, using the resist as mask (h). The finished stamp is seen in (i).Prior to imprinting the stamp was given the DC antistiction coating, describedin section 2.5.2.

The lasers are imprinted in a 680 nm thich PMMA film doped with 2 × 10−5

moles of rhodamine 6G perchlorate pr. g dry PMMA. The doped PMMA isprepared as described in section 2.4.4. After imprinting, the laser is diced alongthe edge of the mesa imprint, giving chips with a laser on a residual layer, seeFig. 5.1.

5.1.2 Fabrication Results

The first imprint was made with an 8 µm high mesa, with a piston force of20 kN for 10 minutes at 190◦C. An optical microscope image of the result isseen in Fig. 5.5. Clearly, stamp filling is incomplete. The reason is bendingof the stamp around the mesa during the imprinting, as illustrated in Fig. 5.6.Decreasing the imprint force helped to some extend, but the problem was notsolved until a new stamp with 2.2 µm mesas was made. The imprint conditionsused succesfully were 2 kN for 60 minutes at 220◦C.

A SEM image of a section of the stamp is shown in Fig. 5.7. In Fig. 5.8 theimprint is shown. The edges of the waveguide looks steep, and the grating alsoseems to be very nicely transferred.

AFM images of the imprinted gratings are seen in Fig. 5.9. Very few defectsare visible on the gratings. The depth of the two gratings are different, whenlooking at the cross sections. The 195 nm grating is 40 nm deep, and the bottomof the trenches look flat, while the ridges look rounded. The 205 nm gratingis at least 60 nm deep, and probably deeper. Most likely the AFM needle hasbeen unable to reach the bottom of the trenches, and thus the trenches do notappear to have a flat bottom.

Since the bottom of the laser currogations are defined by the top of the stampcorrugations, the pattern on the stamp probably has quite rectangular gratingprotrutions. The trenches on the stamp are pointed, however, which is mostlikely because the etch has become less effective deeper in the trenched, becausediffusion of the gases into the trenches has become less effective. This also fitsvery well with the fact that the wider trenched are deeper, because they haveinhibited the etch to a smaller extend.

Fig. 5.10 is a profilometer scan across an imprinted device, where the residualhas been scraped off a distance from the device. Though the imprint force


Figure 5.3: (a) An aluminum lift-off process is used to define the gratings. Electron beamlithography is used to define the thin lines. (b) The gratings are etched 200 nm down. (c)the Al is removed. (d) UV lithography is used to cover the areas outside the waveguide. (e)The waveguide is defined by etching 600 nm down on top of the gratings. (f) This transfersthe gratings to the bottom of the cavity. The corrugations become smaller in this step.


Figure 5.4: (g) By UV lithography a 2 by 2 mm area covering the cavity is defined. (h) A2.2 µm mesa is etched. (i) The finished stamp contains the negative of the laser on a highermesa.


Figure 5.5: Incomplete filling of a DFB laser imprint. The large central part of the imageshas not been filled. The ends of the 0.5 mm wide laser cavity is seen above and below theunfilled area, and the edge of the stamp mesa has been in the bottom left corner.

Figure 5.6: Illustration of the stamp bending, causing incomplete filling. (A) before imprintingthe stamp is flat. The mesa is seen in the central part of the stamp, with the laser cavity inthe middle. (B) As the stamp and substrate are pressed together, they bend around the mesa,causing incomplete filling in the central parts of the mesa.


Figure 5.7: A SEM image of a corner of a laser cavity on the fabricated silicon stamp. Thegrating is seen as horisontal lines. There are also vertical lines farther apart. These areprobably stitching errors from the e-beam exposure.

Figure 5.8: SEM image of the corner of an imprinted DFB laser, covered in 20 nm gold. Thepattern tansfer looks very good, both grating and stitching errors are visible. The edge of thewaveguide also looks very well defined.


Figure 5.9: AFM scans of two Bragg gratings. The top pictures are from a 195 nm pitchgrating, while the bottom pictures are from a 205 nm grating. The depth of the 195 nm gratingis around 40 nm, while the AFM needle has been unable to reach the bottom of the 205 nmgrating, which is at least 60 nm deep.


has been minimized the stamp and substrate still bends to some extend. Theproblem looks worse than it is, because the axis ranges are very different. Theresidual varies from less than 100 nm at the mesa edge to nearly 500 nm at theedge of the laser cavity. The sidewalls of the laser are approximately 400 nmhigh, but the center of the laser is elevated another 100 nm from the substratedue to bending.

Thus, the laser height ranges from approximately 900 nm to 1 µm above theresidual, according to Fig. 2.32 on page 46, the laser should thus be able tosustain a single TE and TM mode, while the residual is not guiding.

Figure 5.10: Surface profiler scan across a laser device, where the residual has been removeda distance from the laser. Due to stamp and substrate bending around the mesas, the deviceand residual surfaces are curved. Note that the axes represent very different distances, so thebending radius of curvature is much larger than suggested from the image.

80 5.2 Measurements

5.2 Measurements

The measurements on the DFB lasers were also made with the 532 nm pumpsetup shown in Fig. 3.7 on page 55. Fig. 5.11 is a photo of a DFB laserchip on the sample stage, also showing the fiber used for measuring the outputspectrum. A pump laser beam is drawn in the picture. The pump used was the5 ns 532 nm pulses from the Nd:YAG laser at 10 Hz repetition rate.

Figure 5.11: Setup for optical measurements on the DFB lasers. The chip is 2 mm wide, cutalong the mesa edge in front of the laser. The pump light hits the laser from above, and thelight is collected with the optical fiber.

5.3 Results

Spectra from two different 195 nm pitch and two different 205 nm pitch lasersfrom the same imprinted wafer are seen in Fig. 5.12 with their correspondingpump/output curves. All spectra have a tall main peak with a width smallerthan 0.5 nm, but the first 205 nm pitch spectrum also has a small peak veryclose to the main peak at a slightly shorter wavelength. The 195 nm pitch lasersemit at 579 nm while the 205 nm pitch lasers emit at 607 nm.

The pump/output curves all show a clear threshold behaviour. The 195 nmpitch devices have thresholds around 4 and 6 µJ/mm2, while both 205 nm pitchdevices start lasing with a pump pulse fluence around 3 µJ/mm2. There is nosignificant difference between the spectra taken with increasing pump powerand the spectra taken with decreasing pump power.

In order to assess the reproducibility of the imprint, another wafer was imprintedwith the same stamp. Again, two 195 nm pitch and two 205 nm pitch laserswere analyzed. Both spectra and threshold behaviour were very similar to thedata in Fig. 5.12. Spectra from all the devices pumped at the same fluence(10.1 µJ/mm2) are shown in Fig. 5.13.

5.3 Results 81

560 570 580 590 600 610 620

0

1000

2000

3000

4000

Inte

nsity

/ A

.U

Wavelength nm

12.0 J/mm2

= 579 nm

0 2 4 6 8 10 12 140

5000

10000

15000

20000

25000 Increasing pump power Decreasing pump power

Out

put p

ower

/ A

.U.

Pump pulse fluence / J/mm2

560 570 580 590 600 610 620

0

1000

2000

3000

4000

Inte

nsity

/ A

.U

Wavelength nm

11.0 J/mm2

= 579 nm

0 2 4 6 8 10 12 140

5000

10000

15000

20000


Out

put p

ower

/ A

.U.


560 570 580 590 600 610 620

0

1000

2000

3000

4000

Inte

nsity

/ A

.U.

Wavelength nm

11.0 J/mm2

= 607 nm

0 2 4 6 8 10 12 140

5000

10000

15000

20000

25000

30000

35000


Out

put p

ower

/ A

.U.


560 570 580 590 600 610 620

0

1000

2000

3000

4000

Inte

nsity

/ A

.U.

Wavelength nm

13.0 J/mm2

= 607 nm

0 2 4 6 8 10 12 14 160

2000

4000

6000

8000

10000

12000

14000

16000


Out

put p

ower

/ A

.U.


Figure 5.12: Laser spectra from four DFB devices, with the corresponding pump/outputcurves. All four devices are from the same imprinted wafer. The two upper spectra arefrom 195 nm pitch lasers, while the lower two are from 205 nm pitch lasers.

82 5.3 Results

570 572 574 576 578 580 582 584 586 588 590-500

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Inte

nsity

/ A

.U.

Wavelength / nm

600 602 604 606 608 610 612 614 616 618 620-500

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Inte

nsity

/ A

.U.

Wavelength / nm

Figure 5.13: (top) Spectra from 4 different 195 nm pitch lasers from two different imprintedwafers. (bottom) Similar spectra from 205 nm pitch devices. All spectra are taken with apump pulse fluence of 10.1 µJ/mm2. The red and black curves are from the devices analyzedin Fig. 5.12, while the green and blue curves are from a different wafer.

Lifetime measurements were performed on both types of lasers. The lasers werepumped at 10 Hz repetition with a pulse energy density of 8.4 µJ/mm2. Theoutput power is plotted as a function of pulse number in Figs. 5.14 and 5.15.The emitted specta are also shown. The number of pulses required to halve theoutputs are found from the fitted lines, to around 165000 and 160000 pulsesfor the 195 nm pitch and the 205 nm pitch device, respectively. The lifetimes(defined as the time to halve the output) are thus around 41

2 hours, for thepump frquency and power used in the experiments.

At the spectra in Figs. 5.14 and 5.15 it is seen that the peak moves to shorterwavelengths, as the dye bleaches.

5.3 Results 83

-100000 0 100000 200000 300000 400000 500000 600000 700000

1000

10000Datafit:

Equation: y = A1*exp(-x/t1) + y0

y0 617.31718 ±99.21856A1 5974.72274 ±99.19317t1 239009.03064 ±12508.99527

x1/2

found from t1 = 165668 pulses

Measured data Fitted data

Out

put p

ower

/ A

.U

Number of pulses

578,0 578,5 579,0 579,5 580,0

0

1000

2000

3000

4000

Inte

nsity

/ A

.U.

Wavelength / nm

Figure 5.14: (top) Output power as a function of pump pulses for a 195 nm pitch laserpumped with 5 ns 532 nm pulses with a fluence of 8.4 µJ/mm2 and a 10 Hz repetition rate.The output is halved after roughly 165000 pulses. (bottom) The spectra corresponding to thedata above. The first spectra are at the longest wavelengts. During operation the laser linebecomes smaller and shifts towards blue. The peaks appear to bundle because of digital noisefrom the limited spectrometer resolution.

84 5.3 Results

0 50000 100000 150000 200000 2500004000

5000

6000

7000

8000

9000

10000

11000

12000Datafit:

Equation: y = A1*exp(-x/t1) + y0 y0 1288.68366 ±1581.02341A1 9361.11292 ±1467.81009t1 230540.74476 ±61560.61597

x1/2

found from t1 = 159799 pulses

Measured data Fitted data

Out

put p

ower

/ A

.U.

Number of pulses

606,0 606,5 607,0 607,5 608,0

0

1000

2000

3000

4000

inte

nsity

/ A

.U.

Wavelength / nm

Figure 5.15: (top) Output power as a function of pump pulses for a 205 nm pitch laserpumped with 5 ns 532 nm pulses with a fluence of 8.4 µJ/mm2 and a 10 Hz repetition rate.The output is halved after roughly 160000 pulses. (bottom) The spectra corresponding to thedata above. The first spectra are at the longest wavelengts. During operation the laser linebecomes smaller and shifts towards blue. The peaks appear to bundle because of digital noisefrom the limited spectrometer resolution.

5.4 Discussion 85

5.4 Discussion

As shown in Figs. 5.12 and 5.13 all lasers can be operated in a single mode.Some lasers generate a clearly visible smaller peak at high pump levels, see e.g.the first spectrum in Fig. 5.12. Since the small peaks are always very close tothe main peak, they are probably due to spatial hole-burning from the standingwaves in the cavity.

The positions of the peaks are 579 nm and 607 nm, quite close to the expectedvalues of 576 and 606 nm. From the position of the peak the effective refractiveindices are calculated to 1.485 for the 195 nm pitch lasers and 1.481 for the 205nm pitch lasers. These numbers are a bit higher than expected, probably in partdue to the rhodamine doping. For a 1 µm high waveguide the mode refractiveindex of the TE0 mode is expected to be higher at 579 nm than at 607 nm.The opposite is seen here, but since the currogations have different depths, theaverage waveguide heights are probably also different.

The laser peaks have a width smaller than 0.5 nm, broader than the spectrome-ter resolution of 0.1 nm. These widths are rather large, compared e.g. to thoseof the WGM laser described in chapter 4, indicating a smaller Q factor. Thelarger width is probably due to a combination of several reasons.

There could be scattering from small rhodamine aggregates. The imprintedwaveguides were made of the same PMMA, and as seen in Fig. 3.6, there aresome indications of limited aggregation.

Since the thickness of the laser varies from 900 to 1000 nm the effective refractiveindex also varies, as seen in Fig. 2.32. This causes a difference in expected lasingwavelength of around 1 nm between the center and the edge of the laser. Thiscan also give rise to peak broadening. As seen in Fig. 5.9 there also appear tobe some small more local height variations, which might add to the effect to asmaller extend.

Further, the gratings are both quite deep and have a large number of periods.The expected reflectance is very high, as mentioned in section 5.1, so probablymost of the loss happens due to other mechanisms than transmittance throughthe gratings. Consequently, smaller currogations would probably not changethreshold behaviour much, but could give a thinner laser peak, as seen fromFig. 5.2.

The positions of the laser peaks are reproduced within 0.5 nm for nominallyidentical devices, both for devices from the same wafer and devices from differentwafers. The peak heights are different, but that is as likely to be due to differentalignment of the measuring fiber as due to differences in laser properties.

The laser threshold is also fairly well reproduced, around 3 µJ/mm2 for the 205nm pitch devices and between 4 and 6 µJ/mm2 for the 195 nm pitch devices.The cavity loss, and thus the threshold, can change substantially if there is adefect in the cavity. Peak position is a result of the feedback of the entire grating,despite that there may be a few defects, and thus it is not surprising that thepeak position is reproduced to a larger extend than the threshold fluence.

The threshold fluences of the 205 nm pitch lasers are lower than those of the

86 5.4 Discussion

195 nm pitch lasers. Part of the reason is probably more efficient gratings. Thecorrugations are deeper in the 205 nm device, but even if both devices had 40nm corrugations the 205 nm grating would be expected to reflect more light, asdescribed in section 5.1. It is also possible that the slightly longer wavelengthof the 205 nm laser is influenced less by any subwavelength defects there mightbe. It is also important to note that 579 nm is closer to the absorbtion peakof rhodamine than 607 nm. It is thus possible that the threshold difference isbecause a larger inversion is needed in the 579 nm laser to compete with largerabsorbtion.

As shown in Figs. 5.14 and 5.15, the number og pulses required to bleachthe laser dye enough to halve the output is around 160000 for both devices.This corresponds to around 41

2 hours at 10 Hz pumping, which is probablylong enough if a single use lab-on-a-chip system based on the device would bedeveloped. Another indication of the fairly good stability of the devices is seenin the pump/output curves of Fig. 5.12. There are no significant differencesbetween the data for increasing and decreasing pump power.

As the dye bleaches the laser peak shifts towards blue. Though the peaksappear to jump from higher to lower wavelengths in the figures the process ismost probably continuous. The reason that the peaks seem to bundle is digitalnoise, because the spectrometer resolution is around 0.1 nm.

Since the form of the device is not expected to change, the blueshift duringlifetime measurements must be caused by a change in index of refraction. Oneexplaination could be that the index of refraction drops as the dye bleaches.It is also possible that the index of refraction becomes smaller due to higherinversion level. As the rhodamine bleaches the gain coefficient becomes smaller,and thus the threshold inversion level of the laser has to become higher in orderto compensate.

Chapter 6Con lusions and OutlookThe primary goal of this project was to investigate the use of colloidal II-VI semi-conductor nanocrystals (quantum dots) as amplifying medium in lab-on-a-chiplasers. Quantum dots are interesting as laser medium because the confinementof electronic states in quantum dots makes the emission color size tunable.

Theory predicts that enhanced exchange interactions between holes and elec-trons in the quantum confined systems, combined with prolate shapes andwurtzite lattice, causes the energy levels of the electron-hole pairs (excitons)to become modified. The lowest energy exciton state, which gives the laser orphotoluminescence light, is called the band edge exciton. It has an angular mo-mentum larger than photons, inhibiting its ability to absorb light. This causesthe Stokes shift between absorbtion and emission spectra.

Because of degeneracy of the band edge exciton energy two electron hole pairsare required per quantum dot to achieve lasing. Unfortunately two electron-holepair states decay much faster than single electron-hole pairs by a non-radiativeAuger effect. This causes the population inversion to decay within picoseconds.The decay is faster for smaller dots. Since decay from absorbing states to theband edge exiton happens faster than the auger decay, there is no fundamentalbarrier to quantum dot lasing, which has been demonstrated by other authors.

Because a large percentage of the atoms in a quantum dot are situated at thesurface, the optical properties also depend very much on surface passivation andthe material surrounding the quantum dots.

In this project experiments were performed with two types of quantum dotsincorporated into TOPAS polymer. The first TOPAS sample used was dopedwith oleic acid capped CdS quantum dots. The luminescence of the material wasrather low, and degraded after a few weeks. Optical measurements indicate thatthe CdS quantum dot luminescence is damaged when pumped with laser lightof rather low energy density, probably because the surface passivation breaksdown. A TOPAS sample with CdSe quantum dots capped with ZnS shells were

88 Conclusions and Outlook

later recieved. This material is more resistant to pump laser pulses, probablybecause of better surface passivation.

Fabrication methods for producing PMMA and TOPAS waveguides with a com-bination of nanoimprint and UV lithography were developed. CdSe/ZnS dopedTOPAS waveguides and rhodamine 6G doped PMMA waveguides with similardimensions were produced. The rhodamine waveguides showed light ampli-fication at low thresholds, while nothing at all could be measured from theCdSe/ZnS waveguides. The lack of light from the quantum dot waveguides isprobably because of aggregation of dots, combined with low concentrations andpossibly impurities in the polymer.

The properties of CdSe/ZnS quantum dots and rhodamine 6G in fluid solutionswere compared in evanescent gain coupled whispering gallery mode lasers. Suc-cesfull results from similar lasers have been published by other authors. Whenrhodamine was used as active material, lasing started at a low pump threshold,but at a different wavelength than expected, and with larger width of the peakthan expected. This is probably because of a Q factor somewhat lower thanexpected. The low threshold indicate that Q is reasonably high, however.

When quantum dots were used in the whispering gallery mode lasers, no lasingwas achieved. Again, the reason is probably too low quantum dot concentration,and possibly also impurities and aggregates in the sample. The concentrationwas increased by boiling off solvent, but that did not result in lasing. Theluminescence peak moved with concentration, which is an indication that thesurface passivation is changed by the concentrating process.

A nanoimprinted polymer DFB laser with first order Bragg gratings were de-veloped. It was only fabricated from rhodamine doped PMMA due to timeconstraints and lack of quantum dot doped polymer. Lasers with two gratingperiods, 195 nm and 205 nm, were fabricated. They gave single mode lasing at579 nm and 607 nm, respectively. The thresholds were very low, but the lineswere rather broad, indicating a smaller Q than the whispering gallery modelasers. The thresholds were lower for the lasers emitting at 607 nm, most likelybecause the rhodamine absorbtion is smaller at this wavelength, and becausethe grating of the 607 nm laser is deeper. The broad lines are attributed tofairly deep gratings and waveguide height variations caused by stamp bendingduring imprinting.

In order to demonstrate lasing from quantum dots in the future, higher quantumdot concentrations and less aggregation is probably required. Higher quantumdot concentration will give a larger gain for the same inversion level, which isan advantage for lasing. Our collaborators in Bari have filtered some samplesthrough a teflon filter with µm sized openings. This helps very much on theaggregation problems, but has a negative influence on the concentration. It isprobably a good idea to spin coat films as soon as possible after mixing TOPASand quantum dots, since aggregation happens on a timescale of weeks.

I think the surface passivation of the CdSe/ZnS dots is good enough. It is stableto high energy pump pulses, and though the measurements made indicate thatquantum yield is lower than for rhodamine 6G, continuous wave luminescencemeasurements made in Bari seems as good as reported for the samples used byother authors.

Conclusions and Outlook 89

Since the matrix material can have an influence on lasing properties [10], it couldalso be interesting to try PMMA instead of TOPAS. Using quantum rods, ratherthan dots is also an option. Auger decay happens with a larger time constantin rods, giving a lower laser threshold when pumped with a Nd:YAG laser[13]. Core-shell-well structures have also been reported to lase more easily thanquantum dots.

Possible modifications to future measurements could be cooling the sample to80 K, which is reported to make ASE detection easier [10]. Another option isusing femtosecond pump pulses, which are shorter than the Auger decay timeconstant.

If amplification is demonstrated from quantum dot samples the developed waveg-uide fabrication method would provide means for measuring the gain magnitude.If curved waveguides were fabricated the (positive or negative) attenuation oflight guided through the waveguide could be compared for clean and dopedwaveguides, with and without pump light present. The gain could then becalculated from the data collected.

The DFB lasers have a number of good properties, but there is room for im-provement. Eliminating the height variation is very important. Instead of hav-ing large mesas the imprinted lasers could be surrounded by a 20 µm trench,and then the surroundings could be removed by plasma, as with the waveguidespresented in chapter 3. This would not only give a much shorter imprint time,but also make the protrution coverage very low, eliminating most of the stampbending. The complete removal of the surroundings could make integrationwith e.g. SU-8 components possible, if the laser was imprinted in a resistantpolymer such as TOPAS, able to survive the SU-8 processing. SU-8 is an UVphotodefinable polymer.

If the height variations are eliminated and the Q factor becomes higher, thelaser might have a loss small enough to demonstrate quantum dot lasing moreeasily. It is then straight forward to produce the lasers from a quantum dotdoped polymer.

The DFB lasers fabricated could possibly be used as they are, as light sourcesfor lab-on-a-chip systems. They only work for a few hours, however, so the chipshad to be single use. If quantum dots could be used as active material insteadof rhodamine, the lifetime could probably be improved substantially.

Instead of using the laser as a light source, it could be used as a detector ofrefractive index. The effective refractive index of the laser modes depend on theindex of material above the laser. Thus, if the laser is built into e.g. a 5 µmdeep SU-8 channel the emission color will change, depending on the refractiveindex of the fluid or gas in the channel.

90 Conclusions and Outlook

Bibliography

[1] A. Manz, N. Graber, and H. M. Widmer. Miniaturized total chemical anal-ysis systems: a novel concept for chemical sensing. Sensors and Actuators,B1:244–248, 1990.

[2] Daniel Nilsson. Polymer based miniaturized dye lasers for Lab-on-a-chip

systems. PhD thesis, Technical University of Denmark, Department ofMicro and Nanotechnology, 2005.

[3] Michael Hansen. Nanoimprinted integrated polymer optics. Master’s thesis,Technical University of Denmark, Department of Micro and Nanotechnol-ogy, 2005.

[4] E. Verpoorte. Chip vision-optics for microchips. Lab Chip, 3:42N–52N,2003.

[5] Evident Technologies Inc. Evidot specification sheet, February 2005.

[6] J. A. Hollingsworth and V. I. Klimov. Soft chemical synthesis and ma-nipulation of semiconductor nanocrystals. In V. I. Klimov, editor, Semi-

conductor and Metal Nanocrystals, Synthetic and Electronic and Optical

Properties, chapter 1. Marcel Dekker, Inc., 2004.

[7] H.-J. Eisler, V. C. Sundar, M. G. Bawendi, M. Walsh, H. I. Smith, andV. I. Klimov. Color-selective semiconductor nanocrystal laser. App. Phys.

Lett., 80(24):4614–4616, 2002.

[8] M. Tamborra, M. Striccoli, R. Comparelli, M. L. Curri, A. Petrella, andA. Agostiano. Optical properties of hybrid composites based on highlyluminescent cds nanocrystals in polymer. Nanotechnology, 15:S240–S244,2004.

[9] M. L. Curri. Presentation from napa meeting in segovia, September 2004.

[10] V. I. Klimov, A. A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth,C. A. Leatherdale, H.-J. Eisler, and M. G. Bawendi. Optical gain andstimulated emission in nanocrystal quantum dots. Science, 290:314–317,2000.

92 BIBLIOGRAPHY

[11] A. V. Malko, A. A. Mikhailovsky, M. A. Petruska, J. A. Hollingsworth,H. Htoon, M. G. Bawendi, and V. I. Klimov. From amplified spontaneousemission to microring lasing using nanocrystal quantum dot solids. Phys.

Rev. Lett., 81(7):1303–1305, 2002.

[12] Y. Chan, J. S. Steckel, P. T. Snee, J.-M. Caruge, J. M. Hodgkiss, D. G.Nocera, and M. G. Bawendi. Blue semiconductor nanocrystal laser. App.

Phys. Lett., 86(073102):1–3, 2005.

[13] M. Kazes, D. Y. Lewis, Y. Ebenstein, T. Mokari, and U. Banin. Lasing fromsemiconductor quantum rods in a cylindrical microcavity. Adv. Mater.,14(4):317–321, 2002.

[14] H.-J. Moon, Y.-T. Chough, and K. An. Cylindrical microcavity laser basedon the evanescent-wave-coupled gain. Phys. Rev. Lett., 85(15):3161–3164,2000.

[15] O. G. Peterson and B. B. Snavely. Stimulated emission from flashlampex-cited organic dyes in polymethyl methacrylate. Phys. Rev. Lett., 12(7):238–240, 1968.

[16] T. Voss, D. Scheel, and W. Shade. A microchip-laser-pumped dfb polymerdye laser. Appl. Phys. B, 73:105–109, 2001.

[17] Y. Oki, T. Yoshiura, Y. Chisaki, and M. Maeda. Fabrication of adistributed-feedback dye laser with a grating structure in its plastic waveg-uide. Appl. Optics, 41(24):5030–5035, 2002.

[18] C. Ferreira Fernandes. Single phase-shifted dfb laser diodes. Microwave

and Optical Technology Letters, 17(6):398–402, 1998.

[19] R. G. Hunsperger. Integrated Optics. Springer Verlag, fifth edition, 2002.

[20] Y. Li, M. Sasaki, and K. Hane. Fabrication an testing of solid polymerdye microcavity lasers based on pmma micromolding. Journal of Microme-

chanics and Microengineering, 11:234–238, 2001.

[21] D. Nilsson, T. Nielsen, and A. Kristensen. Solid state micro-cavity lasersfabricated by nanoimprint lithography. Review of Scientific Instruments,75(11):4481–4486, 2004.

[22] B. E. A. Saleh and M. C. Teich. Fundamentals of Photonics. John Wiley& Sons, Inc., 1991.

[23] A. E. Siegman. Lasers. University Science Books, 1986.

[24] F. L. Pedrotti and L. S. Pedrotti. Introduction to Optics. Prentice HallInternational, 1996.

[25] en.wikipedia.org/wiki/linewidth.

[26] J. K. Vahala. Optical microcavities. Nature, 424:839–846, 2003.

[27] V. I. Klimov. Charge carrier dynamics and optical gain in nanocrystalquantum dots: From fundamental photophysics to quantum dot lasing. InV. I. Klimov, editor, Semiconductor and Metal Nanocrystals, Synthetic and

Electronic and Optical Properties, chapter 5. Marcel Dekker, Inc., 2004.

BIBLIOGRAPHY 93

[28] F. Zezza, R. Comparelli, M. Striccoli, M. L. Curri, R. Tommasi, A. Agos-tiano, and M. Della Monica. High quality cds nanocrystals: Surface effects.Synthetic Metals, 139:597–600, 2003.

[29] X. Peng, M. C. Schlamp, A. V. Kadavanich, and A. P. Alivisatos. Epitaxialgrowth of highly luminescent cdse/cds core/shell nanocrystals with photo-stability and electronic accessibility. J. Am. Chem. Soc., 119:7019–7029,1997.

[30] X. Peng, L. Manna, W. Yang, J. Wickham, E. Scher, A. Kadavanich, andA. P. Alivisatos. Shape control of cdse nanocrystals. Nature, 404:59–61,2000.

[31] R. Comparelli, F. Zezza, M. Striccoli, M. L. Curri, R. Tommasi, andA. Agostiano. Improved optical properties of cds quantum dots by ligandexchange. Materials Science and Engineering C, 23:1083–1086, 2003.

[32] B. O. Dabbousi, J. Rodriguez-Viejo, F. V. Mikulec, J. R. Heine, H. Mat-toussi, R. Ober, K. F. Jensen, and M. G. Bawendi. (cdse)zns core-shellquantum dots: Synthesis and characterization of a size series of highlyluminescent nanocrystallites. J. Phys. Chem. B, 101:9463–9475, 1997.

[33] J. Xu, M. Xiao, D. Battaglia, and X. Peng. Exciton radiative recombinationin spherical cds/cdse/cds quantum-well nanostructures. App. Phys. Lett.,87(043107):1–3, 2005.

[34] www.evidenttech.com.

[35] D. J. Norris. Electronic structure in semiconductor nanocrystals. In V. I.Klimov, editor, Semiconductor and Metal Nanocrystals, Synthetic and Elec-

tronic and Optical Properties, chapter 2. Marcel Dekker, Inc., 2004.

[36] B. H. Bransden and C. J. Joachain. Quantum Mechanics. Prentice Hall,second edition, 2000.

[37] L. E. Ballentine. Quantum Mechanics a modern development. World Sci-entific, 1998.

[38] S. Elliott. The Physics and Chemistry of Solids. Wiley, 1998.

[39] www.veeco.com/learning/learning lattice.asp.

[40] pubs.acs.org/cgi-bin/abstract.cgi/nalefd/2002/2/i04/abs/nl010080k.html.

[41] D. J. Norris, Al. L. Efros, M. Rosen, and M. G. Bawendi. Size dependenceof exciton fine structure in cdse quantum dots. Phys. Rev. B, 53(24):16347–16354, 1996.

[42] A. A. Mikhailovski, A. V. Malko nad J. A. Hollingsworth, M. G. Bawendi,and V. I. Klimov. Multiparticle interactions and stimulated emsiision inchemically synthesized quantum dots. Appl. Phys. Lett., 80(13):2380–2382,2002.

[43] www.sigmaaldrich.com.

[44] Evident Technologies Inc. Life sciences catalog v5, July 2005.

94 BIBLIOGRAPHY

[45] S. Singh, V.R. Kanetkar, G. Sridhar, V. Muthuswamy, and K. Raja. Solid-state polymeric dye lasers. Journal of Luminescence, 101:285–291, 2003.

[46] Morten Gersborg-Hansen. A coupled cavity micro fluidic dye ring laser.Master’s thesis, Technical University of Denmark, Department of Microand Nanotechnology, 2004.

[47] S. Y. Chou, P. R. Krauss, and P. J. Renstrom. Nanoimprint lithography.Journal of Vacuum Science Technology B, 14(6):4129–4133, 1996.

[48] L. J. Guo. Recent progress in nanoimprint technology and its applications.Journal of Applied Physics, 37:123–141, 2004.

[49] www.evgroup.com.

[50] Rasmus Haugstrup Pedersen. Nanoimprint lithography process optimiza-tion. Master’s thesis, Technical University of Denmark, Department ofMicro and Nanotechnology, 2005.

[51] Theodor Nielsen. Nanoimprint lithography. Master’s thesis, Technical Uni-versity of Denmark, Department of Micro and Nanotechnology, 2003.

[52] H. Schift and L. J. Hayderman. Nanorheology, squeeze flow in hot em-bossing of thin films. In D. J. Lochwood and C. Sotomayor Torres, ed-itors, Nanostructure science and technology, Alternative Lithography Vol-

ume. Kluwer Academic, 2003.

[53] en.wikipedia.org/wiki/stiction.

[54] www.ticona.com.

[55] T. Nielsen, D. Nilsson, F. Bundgaard, P. Shi, P. Szabo, O. Geschke, andA. Kristensen. Nanoimprint lithography in the cyclic olefin copolymer,topas, a highly uv-transparent and chemically resistant thermoplast. Jour-

nal of Vacuum Science and Technology, 22:1770–1775, 2004.

[56] www.microchem.com.

[57] H. S. Nalwa. Handbook of thin film materials, Vol. 5: Nanomaterials and

magnetic thin films. Academic Press, 2002.

[58] L. A. Coldren and S. W. Corzine. Diode Lasers and Photonic Integrated

Circuits. John Wiley & Sons, Inc., 1995.

Appendix AMATLAB programsThis appendix contains the MATLAB programs used to generate plots for thereport. Some program lines have been too long, forcing me to break them. Thesymbol ... ends the first half and starts the second half of a broken programline.

A.1 Plotting Mode Refractive Index

These MATLAB files are used to plot the graphs of mode refractive index as afunction of wavelength for planar waveguides. Only the programs for TOPASare shown , but the PMMA programs are identical, except for different refractiveindex of the polymer. The theory used can be found in [19].

The file neffplot.m calculates and plots the indices for TE and TM modes bycalling the functions findneff.m and findneffTM.m, respectively.

neffplot.m

%NEFFPLOT. Plots effective (mode) refractive index for modes in an

%infinitely wide planar TOPAS waveguide on Pyrex as a function of height.

%THE PROGRAM HANDLES 3 MODES AT MOST

%written by Mads Christiansen 20sep05

%Define wavelength (nm)

lambda=600;

%Define ranges (lengths in nanometers)

tmin=100;

tmax=2000;

96 A.1 Plotting Mode Refractive Index

% defining thichnessrange

points=1000;

tvec=linspace(tmin,tmax,points);

%initialize vectors

zeroorder=zeros(1,points);

firstorder=zeros(1,points);

secondorder=zeros(1,points);

zeroorderTM=zeros(1,points);

firstorderTM=zeros(1,points);

secondorderTM=zeros(1,points);

%calculate the neff-values

%first for TE modes

for i=1:points

neff=findneff(lambda,tvec(i));

if length(neff)==1

zeroorder(i)=neff(1);

end

if length(neff)==2

firstorder(i)=neff(1);


end

if length(neff)==3

secondorder(i)=neff(1);

firstorder(i)=neff(2);


end

end

%then for TM modes

for i=1:points

neffTM=findneffTM(lambda,tvec(i));

if length(neffTM)==1

zeroorderTM(i)=neffTM(1);

end


firstorderTM(i)=neffTM(1);


end

A.1 Plotting Mode Refractive Index 97


secondorderTM(i)=neffTM(1);

firstorderTM(i)=neffTM(2);


end

end

%And plot

plot(tvec,zeroorder,’b’,tvec,zeroorderTM,’b:’,tvec,firstorder,’r’,tvec...

...,firstorderTM,’r:’,tvec,secondorder,’g’,tvec,secondorderTM,’g:’)

axis([tmin tmax 1.472 1.53])

grid on

legend(’0th order TE’,’0th order TM’,’1st order TE’,’1st order TM’...

...,’2nd order TE’,’2nd order TM’,2)

title(’Effective refractive index for \lambda=600 nm modes in a...

... TOPAS waveguide on Pyrex’)

xlabel(’TOPAS thickness /nm’)

ylabel(’mode refractive index’)

print -djpeg neff600TOPAS.jpg

print -depsc neff600TOPAS.eps

findneff.m

function neff=findneff(lambda,thickness)

%FINDNEFF. A function for finding effective (mode) refractive

%index for TE modes in an infinitely wide planar TOPAS waveguide on Pyrex

%neff=findneff(lambda,thickness), where lengths are in nm and neff is a

%vector


t=thickness*10^-9;

k=2*pi/(lambda*10^-9);

%refractive indices of the layers

none=1;

ntwo=1.53;

nthree=1.472;

%defing the problem

betamin=nthree*k;

betamax=ntwo*k;

points=20000;

betavec=linspace(betamin,betamax,points);

h=sqrt(ntwo^2*k^2-betavec.^2);

q=sqrt(betavec.^2-none^2*k^2);

p=sqrt(betavec.^2-nthree^2*k^2);

tanvec=zeros(1,points);

98 A.1 Plotting Mode Refractive Index

othervec=zeros(1,points);

for i=1:points

tanvec(i)=tan(t*h(i));

othervec(i)=(p(i)+q(i))/(h(i)*(1-p(i)*q(i)/h(i)^2));

end

difference=abs(tanvec-othervec);

modecount=1;

%finding the solutions

possiblebetas=0;

for j=2:points-1

if ((difference(j)<difference(j+1)) & (difference(j)<difference(j-1)));

possiblebetas(modecount)=betavec(j);

modecount=modecount+1;

end

end

neff=possiblebetas*lambda*10^-9/(2*pi);

findneffTM.m

function neffTM=findneffTM(lambda,thickness)

%FINDNEFF. A function for finding effective (mode) refractive index

%for TM modes in an infinitely wide planar TOPAS waveguide on Pyrex

%neffTM=findneffTM(lambda,thickness), where lengths are in nm and neff is a

%vector


t=thickness*10^-9;

k=2*pi/(lambda*10^-9);

%refractive indices of the layers

none=1;

ntwo=1.53;

nthree=1.472;

%defing the problem

betamin=nthree*k;

betamax=ntwo*k;

points=10000;

betavec=linspace(betamin,betamax,points);

h=sqrt(ntwo^2*k^2-betavec.^2);

q=ntwo^2/none^2*sqrt(betavec.^2-none^2*k^2);

p=ntwo^2/nthree^2*sqrt(betavec.^2-nthree^2*k^2);

tanvec=zeros(1,points);

A.2 Plotting Bragg Reflection 99

othervec=zeros(1,points);

for i=1:points

tanvec(i)=tan(t*h(i));

othervec(i)=h(i)*(p(i)+q(i))/(h(i)^2-p(i)*q(i));

end

difference=abs(tanvec-othervec);

modecount=1;

%finding the solutions

possiblebetas=0;

for j=2:points-1

if ((difference(j)<difference(j+1)) & (difference(j)<difference(j-1)));

possiblebetas(modecount)=betavec(j);

modecount=modecount+1;

end

end

neffTM=possiblebetas*lambda*10^-9/(2*pi);

A.2 Plotting Bragg Reflection

MATLAB files for plotting the reflectance of Bragg gratings as a function ofwavelength. A T-matrix approach has been used, details can be found in e.g.[58].

The file GratingRefPlot.m is used to plot the data for two different modulationsof the refractive index, the data is calculated with GratingRef.m.

The files GratingRefPeriodsPlot.m and GratingRefPeriods.m are very sim-ilar, but plots for different numbers of periods instead of different index modu-lations.

GratingRefPlot.m

%A file for plotting reflection from two Bragg type mirrors

%with different corrugation depths

%Written by Mads Christiansen 25oct05

npoints=10000;

wavelengths=linspace(580e-9,620e-9,npoints);

n1a=1.492

n2a=1.488

n1b=1.495

100 A.2 Plotting Bragg Reflection

n2b=1.485

for i=1:npoints

refvec1(i)=abs(GratingRef(wavelengths(i),n1a,n2a))^2;

end

for j=1:npoints

refvec2(j)=abs(GratingRef(wavelengths(j),n1b,n2b))^2;

end

plot(wavelengths*10^9,refvec1*100,’b’,wavelengths*10^9,refvec2*100,’r’)

legend(’n_1=1.492 n_2=1.488’,’n_1=1.495 n_2=1.485’)

xlabel(’Wavelength / nm’)

ylabel(’Reflected power / %’)

print -djpeg GratingRefPlot.jpg

GratingRef.m

function Ref=GratingRef(lambda,n1,n2)

%A function for calculating reflection from a Bragg type mirror

%using the T-matrix theory

%function Ref=GratingRef(lambda,n1,n2)

%lambda is the wavelength of the light in vacuum


%lengths of the high and low segment

lh=100e-9;

ll=100e-9;

%the number of periods

periods=1000;

%propagation constants

betah=2*pi*n1/lambda;

betal=2*pi*n2/lambda;

%T-matrices

Th=[exp(i*betah*lh) 0;0 exp(-i*betah*lh) ];

Tl=[exp(i*betal*ll) 0;0 exp(-i*betal*ll) ];

smallt=2*sqrt(n1*n2)/(n1+n2);

Thl=1/smallt*[1 (n1-n2)/(n1+n2); (n1-n2)/(n1+n2) 1];

Tlh=1/smallt*[1 (-n1+n2)/(n1+n2); (-n1+n2)/(n1+n2) 1];

Tm=(Thl*Tl*Tlh*Th)^(periods);

Ref=(Tm(2,1)/Tm(1,1));

A.2 Plotting Bragg Reflection 101

GratingRefPeriodsPlot.m

%A file for plotting reflection from two Bragg type mirrors

%with different numbers of periods


npoints=10000;

wavelengths=linspace(580e-9,620e-9,npoints);

n1=1.492

n2=1.488

p1=1000

p2=2500

for i=1:npoints

refvec1(i)=abs(GratingRefPeriods(wavelengths(i),n1,n2,p1))^2;

end

for j=1:npoints

refvec2(j)=abs(GratingRefPeriods(wavelengths(j),n1,n2,p2))^2;

end

plot(wavelengths*10^9,refvec1*100,’b’,wavelengths*10^9,refvec2*100,’r’)

legend(’1000 periods’,’2500 periods’)

xlabel(’Wavelength / nm’)

ylabel(’Reflected power / %’)

print -djpeg GratingRefPeriodPlot.jpg

GratingRefPeriods.m

function Ref=GratingRefPeriods(lambda,n1,n2,periods)

%A function for calculating reflection from a Bragg type mirror

%using the T-matrix theory

%function Ref=GratingRef(lambda,n1,n2)

%lambda is the wavelength of the light in vacuum


%lengths of the high and low segment

lh=100e-9;

ll=100e-9;

%propagation constants

betah=2*pi*n1/lambda;

betal=2*pi*n2/lambda;

%T-matrices

Th=[exp(i*betah*lh) 0;0 exp(-i*betah*lh) ];

102 A.2 Plotting Bragg Reflection

Tl=[exp(i*betal*ll) 0;0 exp(-i*betal*ll) ];

smallt=2*sqrt(n1*n2)/(n1+n2);

Thl=1/smallt*[1 (n1-n2)/(n1+n2); (n1-n2)/(n1+n2) 1];

Tlh=1/smallt*[1 (-n1+n2)/(n1+n2); (-n1+n2)/(n1+n2) 1];

Tm=(Thl*Tl*Tlh*Th)^(periods);

Ref=(Tm(2,1)/Tm(1,1));

Appendix BMask DesignsThis appendix contains images of the mask designs used for fabrication of thewaveguides and DFB lasers. The masks are drawn in the CAD program L-Edit.

B.1 Waveguide Masks

104 B.1 Waveguide Masks

Figure B.1: Wafer layout for the waveguide chips. Most chips contains 8 mm long waveg-uides, with widths from 50 to 200 µm. At the bottom two very long arrays of different widthwaveguides are seen. They were intended for loss measurements.

Figure B.2: A chip with 81 50 µm wide waveguides, as indicated by the numbers. The purplelayer is for definition of the shielding photoresist.

B.1 Waveguide Masks 105

Figure B.3: The ends of some 50 µm waveguides on the stamp layout. 20 µm trenches aredefined around the waveguides.

Figure B.4: The end of the same 50 µm waveguides. The purple layer is for definition of theshielding resist. The overlap is 10 µm.

106 B.2 DFB Laser Masks

B.2 DFB Laser Masks

Figure B.5: Wafer layout for the DFB laser stamp. The mesa layer is grey, while the cavitydefinition layer is blue. The very first step in the stamp fabrication was definition of thealignmentmarks shown in green. the outer ring represents the wafer edge.

B.2 DFB Laser Masks 107

Figure B.6: DFB chip layout. Mesa layer is grey, and cavity definition layer is blue. Thenumber identifies the chip as a 195 nm pitch laser chip.

108 B.2 DFB Laser Masks

Figure B.7: A closer look at the end of a DFB laser. As in the previous images, grey ismesa and blue is cavity. In this image the lines defining the gratings are visible. There areapproximately 5000 lines on a laser.

Figure B.8: A closer look at the middle of a DFB laser. Colorcode is as the previous image.The λ/4 phaseshift in the middle of the laser is seen.

Appendix CFabri ation Re ipesThis appendix contains more detailed recipes for the CdSe/ZnS TOPAS waveg-uides, the rhodamine 6G doped PMMA waveguides, and the imprinted DFBlasers.

C.1 CdSe/ZnS TOPAS Waveguides

Stamp

Wafers

• Silicon

Standard resist

• HMDS wafers:Recipe 4: 35 min. baking time

• Spinning, SSI spinner:1.5 mu AZ5214B resistRecipe: PR1 5

• Exposure, KS Aligner:Hard contactalignment gap 30 muConstant Intensity 2exposure time: 10 s

110 C.1 CdSe/ZnS TOPAS Waveguides

• Development:60 s in NaOHDI-water rinse: 5 min (2-3 mins for 1 wafer)

Structure etch

• Reactive ion etch, RIE 1Recipe: MBC STMPTime: 2 minO2 flow: 8 sccmSF6 flow: 32 sccmRF Power: 30 WPressure: 80 mTorrEtch depth ≈ 550 nm

• Resist stripAcetone5 minUltrasound5 min. DI water rinse

Anti-stiction layer

• Teflon deposition, ASERecipe: MBCtefO2

Oxygen cleaning: 3 minO2 flow: 45 sccmCoil Power: 800 WPlaten Power: 20 W

Teflon deposition: 1 minC4F8 flow: 120 sccmCoil Power: 300 WPlaten Power: 20 W

Waveguide Fabrication

Wafers

• Borofloat glass

C.1 CdSe/ZnS TOPAS Waveguides 111

Cleaning

• Wash in Triton soap

• Standard 7up etch:Temp.: 80◦CTime: 10 minDI-water rinse: 5 min

TOPAS spinning

• Pre bake, portable hotplate:150◦C 10 min

• Spinning, Speedline manual spinner:low acceleration60s @ 1500 rpmVolume: 2 mlThickness ≈600 nm

• Post bake, portable hotplate:150◦C 10 min

Imprinting

• imprinting, EVG NILTemperature: 170 ◦CTime: 10 minPiston force: 20 kN0.5 mm graphite on each side of substrate/stamp sandwich

Masking resist

• Spinning, SSI spinner:1.5 mu AZ5214B resistRecipe: PR1 5NB

• Bakeout, Hotplate 2:Temperature: 50 ◦CTime: 20 min



112 C.2 Rhodamine 6G PMMA Waveguides

Removal of surrounding TOPAS

• Etch, Plasma asherO2 225 ml/min200 W9 h (540 min)Front inwards

• Resist stripAcetone5 min, no ultrasound5 min. DI water rinse

C.2 Rhodamine 6G PMMA Waveguides

Stamp

Wafers

• Silicon

Standard resist





Structure etch

• Reactive ion etch, RIE 1Recipe: MBC STMPTime: 2 min O2 flow: 8 sccmSF6 flow: 32 sccm

C.2 Rhodamine 6G PMMA Waveguides 113

RF Power: 30 WPressure: 80 mTorrEtch depth ≈ 550 nm

• Resist stripAcetone5 minUltrasound5 min. DI water rinse

Anti-stiction layer

• HF preparation60 s BHF5 min DI water rinse

• DC coating10 min bake in petri dish at 250◦C≈0.25 mL trichlorsilane is added, and dish is covered with lid2 h bake under lid at 250◦C30 min bake without lid at 250◦CHotplate turned off, stamp taken off at 150◦C

Waveguide Fabrication

Wafers

• Borofloat glass

Cleaning



• Dehydration:250◦C oven >12 h

Spinning

• PMMA / Rhodamine solution:15 wt% PMMA in Anisole2 ×10−5 mole Rhodamine 6G perchlorate pr g dry PMMA

114 C.2 Rhodamine 6G PMMA Waveguides

Rhodamine is first dissolved in ethanol, 2 ×10−2 mol/lPMMA is added, solution is shaken, and spun after a few minutes



Imprinting

• imprinting, EVG NILTemperature: 190 ◦CTime: 10 minPiston force: 20 kN0.5 mm graphite on each side of substrate/stamp sandwich

Masking resist

• Spinning, Speedline spinner:500 nm LOR 5B resist60 s @ 2000 RPM

• Bakeout, Portable hotplate:Temperature: 100 ◦CTime: 10 min



• Development:2 min 40 s in NaOHDI-water rinse: 5 min (2-3 mins for 1 wafer)

Removal of surrounding PMMA

• Etch, Plasma asherO2 225 ml/min200 W9 h (540 min)

C.3 Imprinted DFB Laser 115

Front inwards

• Resist strip5 min MF-3195 min. DI water rinse

C.3 Imprinted DFB Laser

Stamp

Wafers

• Silicon

Alignment mark definition





• Reactive ion etch, RIE 2:Recipe: MBC STMPTime: 1 min 40 sO2 flow: 8 sccmSF6 flow: 32 sccmRF Power: 30 WPressure: 80 mTorrEtch depth ≈ 500 nm

• Resist strip:Acetone3 min Ultrasound5 min. DI water rinse

116 C.3 Imprinted DFB Laser

Grating definition

• 7up etch:Temp.: 80◦CTime: 20 minDI-water rinse: 5 min

• Spinning, III-V spinner:110 nm ZEP-520A 3.6% resistPrespin: 500 rpm, 300 rpm/s, 5 sSpin: 1700 rpm, 500 rpm/s, 30 s

• Baking, III-IV hotplate:160◦C, 2 min

• Exposure, E-beam:220 µC/cm2, 100 kV, 6.1 nA, 12 nm grid sizeWriting time ≈24 min

• Development:60 s N5030 s IPA

• Descum, RIE2Recipe: MSCDSCUMTime: 4sN2 flow: 99 sccmO2 flow: 20 sccmRF Power: 30 WPressure: 100 mTorr

• Aluminum deposition, Alcatel:Thickness: 60 nmDeposition rate: 2 A/s

• Rough lift-off:AZ 351B developer (NaOH) thinned with DI-water 1:5, stirredTime: 10 sWater+IPA rinse

• Final lift-off:S1165 Microposit Remover 2h+Acetone+IPA rinse

• Reactive ion etch, RIE 2:Recipe: MSS BSTime: 2 min 50 sO2 flow: 24.5 sccmCHF3 flow: 10 sccmSF6 flow: 30 sccmRF Power: 20 WPressure: 36 mTorrEtch depth ≈ 200 nm


• Aluminum strip:AZ 351B developer (NaOH)Time: 30 s

Waveguide definition





• Reactive ion etch, RIE 2:Recipe: MBC STMPTime: 1 min 15 sO2 flow: 8 sccmSF6 flow: 32 sccmRF Power: 30 WPressure: 80 mTorrEtch depth ≈ 400 nm


Mesa definition




118 C.3 Imprinted DFB Laser


• Reactive ion etch, RIE 2:Recipe: MBC STMPTime: 8 minO2 flow: 8 sccmSF6 flow: 32 sccmRF Power: 30 WPressure: 80 mTorrEtch depth ≈ 2.2 µm


Anti-stiction layer

• HF preparation60 s BHF5 min DI water rinse

• DC coating, III-IV hotplate10 min bake in petri dish at 250◦C≈0.25 mL trichlorsilane is added, and dish is covered with lid2 h bake under lid at 250◦C30 min bake without lid at 250◦CHotplate turned off, stamp taken off at 150◦C

Substrate preparation

Wafers

• Borofloat glass

Cleaning



• Dehydration:250◦C oven >12 h


Spinning

• PMMA / Rhodamine solution:15 wt% PMMA in Anisole2 ×10−5 mole Rhodamine 6G perchlorate pr g dry PMMARhodamine is first dissolved in ethanol, 2 ×10−2 mol/lPMMA is added, solution is shaken and spun after a few minutes.



Imprinting

• imprinting, EVG NILTemperature: 220 ◦CTime: 60 minPiston force: 2 kNFlags and waferbow enabled0.5 mm graphite on each side of substrate/stamp sandwich

Quantum Dot Based Light Sources for Lab-on-a-chip

Documents

Transcript of Quantum Dot Based Light Sources for Lab-on-a-chip