Quantum Dot Lasers

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Quantum Dot Lasers Universidad de Sevilla Escuela Superior de Ingenieros Ingenier´ia de Telecomunicaciones Quantum Dot Lasers Candidato: Tutor en Espa˜na: Jaime P. Mora Pacheco Alejandro Carballar Tutora en Italia: Gabriella Cincotti A˜no Acad´emico: 2004/2005 Contents Introducci´on 1 0 Resumen espa˜nol 4 Resumen Capitulo 1: Conceptos Fundamentales . 4 0.1 Pozoscu´anticos................................. 5 0.2 PuntoCu´antico(QD) .............................. 7 0.2.1 DensidaddeEstados........................... 8 0.3 CristalesFot´onicos . 9 0.4 Definici´onyventajas. 12 0.5 Fabricaci´ondeQDs............................... 13 0.5.1 Elm´etodoStranski-Krastanow . 13 0.6 DOS:funci´ondedensidaddeestados . 15 0.7 EcuacionesdeestadodelQDLaser . 16 0.8 CorrienteUmbral................................. 17 0.9 Q-Switching.................................... 17 0.10VCSELs...................................... 19 Resumen Capitulo 2: L´aseres de Puntos Cu´anticos . ......... 11 I 0.11 EnsanchamientoHomog´eneo. 20 0.12 EnsanchamientoInhomog´eneo. 21 ResumenCapitulo3:EfectosNoLineales . 20 Resumen Capitulo 4: Aplicaci´on a Cristales Fot´onicos . ............ 24 Conclusiones ...................................... 27 1 Fundamental Concepts 30 1.1 PrinciplesofLasers.............................. 31 1.1.1 Populationinversion . 32 1.1.2 Threshold Conditions & Optical Gain . 34 1.2 Quantumwells .................................. 35 1.3 Quantumdot ................................... 38 1.4 DensityofStates:DOS............................. 39 1.5 ANewDevice:PhotonicCrystal . 40 2 Quantum Dot Lasers 43 2.1 QuantumDotsfabrication. 47 2.1.1 Lithography Based QD Laser Fabrication . 49 ElectronBeamLithography . 49 DryEtching................................ 50 2.1.2 Stranski-Krastanowmethod . 52 Temperature ............................... 55 Verticallystacking ............................ 56 Activated Alloy Phase Separation . 57 II Defectreductiontechnique . 58 2.2 DensityofStates:DOS............................. 60 2.3 RateEquationsofQDLaser. 64 2.4 Thresholdcurrent ................................ 70 2.5 DifferentialGain ................................. 77 2.6 Q-Switching.................................... 80 2.7 VCSELs...................................... 84 3 Non-linear Effects 88 3.1 Homogeneousbroadening . 90 3.2 Inhomogeneousbroadening . 95 3.2.1 GainandDifferentialGain . .100 3.2.2 ThresholdCurrent . .. .. .. .. .. .. .. .. .106 3.3 Cross-GainModulation . .. .. .. .. .. .. .. .. 108 4 ApplicationstoPhotonicCrystalStructures 111 Conclusions 125 Appendix 128 4.1 Appendix1:Fermi’sGoldenRule . 128 4.2 Appendix2:Smith-PurcellEffect . 131 4.3 Appendix3:MeasurementsTools . 132 4.3.1 AFM....................................132 4.3.2 TEM....................................132 III Acknowledgments 134 List of Figures 139 Bibliography 139 IV Introducci´on Este Proyecto Fin de Carrera ha sido realizado en la Universidad de Roma Tre (Roma, Italia) gracias a una beca Erasmus para el curso 2004-2005. Como proyecto realizado en el extranjero y acerca de una tecnolog´ia de ´ultima generaci´on, ha sido elaborado completamente en ingl´es, por lo que este documento pretende resumir en espa˜nol el contenido del mismo de forma breve pero explicativa. La introducci´on de la mec´anica cu´antica aplicada a los dispositivos ´opticos es uno de los mayores avances en el campo de los l´aseres semiconductores. Entre sus principales ventajas est´an la fuerte reducci´on en la corriente umbral debida a un aumento de la densidad de estados y la estabilidad del l´aser con la temperatura. Estas y otras ventajas, provienen de la discretizaci´on en el n´umero de estados permitidos para los portadores en las distintas bandas. El ´ultimo paso en lo que es la cuantizaci´on del tama˜no, que implica el pleno con- finamiento de los portadores en tres dimensiones, es el punto cu´antico o Quantum Dot (QD). La evoluci´on en cuanto al confinamiento de portadores en dispositivos semiconduc- tores puede apreciarse en la fig. 1 Los QDs fueron enunciados por primera vez como ´ultimo caso de cuantizaci´on en l´aseres semiconductores a principios de los a˜nos 80, y desde entonces, se ha recorrido un largo camino con el fin de llegar a su implementaci´on f´isica, lo cual no fue posible hasta los ´ultimos a˜nos 90. Hoy d´ia, se puede decir que el desarrollo tecnol´ogico de los QDs ha permitido comenzar a cumplir las expectativas en su d´ia anunciadas, y se puede hablar de una tecnolog´ia madura, pero ´aun en fase de desarrollo. Figure 1: Evolution of quantum confinement applied to semiconductor devices [4]. Por otra parte, hoy d´ia un nuevo tipo de dispositivos est´asiendo desarrollado y estudiado: los cristales fot´onicos. Los cristales fot´onicos o Photonic Crystals (PhC) son estructuras diel´ectricas peri´odicas caracterizadas por un ”ancho de banda fot´onico”. O lo 2 que es lo mismo, estas estructuras permiten la propagaci´on de la luz dentro de ellas s´olo para determinadas y seleccionadas frecuencias. Con esto, se consigue la propagaci´on de luz en diferentes direcciones con energ´ias espec´ificas [3]. QDs introducidos en estos disposi- tivos permiten explorar nuevas aplicaciones enfocadas a un mayor control de la luz emitida. En este proyecto, se pretende estudiar el estado del arte de los Quantum Dots Lasers o l´aseres basados en puntos cu´anticos. Son estudiadas las caracter´isticas espectrales del l´aser, comportamientos din´amicos, proceso de fabricaci´on, etc. Por otra parte, se da un profundo estudio sobre la importancia de los efectos no lineales en estos l´aseres. Y para concluir, se estudia el uso de puntos cu´anticos en cristales fot´onicos en lo que es una aplicaci´on m´as pr´actica. Cabe decir que esta ´ultima parte se enmarca en un proyecto europeo de investigaci´on de la Universidad de Roma Tre, que en la fecha de partida del autor de este proyecto, estaba en espera de los par´ametros de simulaci´on que deb´ia de proveer el fabricante, con lo que los estudios realizados en el presente proyecto, se basan en simulaciones por ordenador previas. El proyecto est´aestructurado en los siguientes cap´itulos o ”chapters”: Capitulo 1: Conceptos Fundamentales. Se presentan algunos conceptos cl´asicos de • l´aseres basados en semiconductor y se introducen algunos conceptos relativos a la cuantizaci´on en dichos l´aseres. Los cristales fot´onicos tambi´en son presentados. Capitulo 2: L´aseres de Puntos Cu´anticos. El l´aser cu´antico es descrito con detalle. • Se caracteriza por su proceso de fabricaci´on, con una revisi´on de las diferentes tec- nolog´ias existentes y las ventajas y desventajas de las mismas. Tambi´en se ofrece 3 un desarrollo anal´itico de distintas caracter´isticas como la ecuaciones de estado, la densidad de estados, la corriente umbral, la ganancia ´optica, etc. La aplicaci´on fun- damental del l´aser cu´antico en los VCSELs tambi´en es recogida por su importancia en aplicaciones de telecomunicaciones. Capitulo 3: Efectos No Lineales. Se da una segunda visi´on sobre algunos conceptos • ya presentados en el cap´itulo anterior, pues ahora se tienen en cuenta los efectos no lineales. Se da un ´enfasis especial a la no-uniformidad del tama˜no del punto cu´antico como principal lastre para el buen funcionamiento de los QD lasers. Capitulo 4: Aplicaci´on a Cristales Fot´onicos. Se estudia la conveniencia de introducir • los puntos cu´anticos en PhC con el fin de controlar la emisi´on espont´anea de fotones. Otras posibles ventajas son estudiadas. De todos estos cap´itulos, se ofrecer´aa continuaci´on un breve resumen de los mismos, pudiendo encontrarse mayor informaci´on, ecuaciones y figuras, en el proyecto completo en ingl´es que se incluye tras este resumen. Las referencias bibliogr´aficas y a figuras son ´unicas en todo el documento completo (parte espa˜nola e inglesa) para facilitar el acceso a las mismas. 4 Capitulo 1:Conceptos Fundamentales En esta secci´on se da un breve repaso a algunos de los conceptos cl´asicos sobre el l´aser semiconductor, y en concreto siguiendo la estructura cl´asica de un l´aser Fabry-Perot para una mejor comprensi´on de los conceptos expuestos. El cap´itulo incluye tambi´en una breve descripci´on de la que se podr´ia llamar la tecnolog´ia previa al l´aser de puntos cu´anticos, como son los l´aseres basados en pozos cu´anticos o Quantum Well Lasers. Para concluir, se presentan los cristales fot´onicos como nuevas estructuras de gran inter´es en el campo de la electr´onica. En este resumen, se tratar´an los conceptos de Quantum Wells y Photonic Crystals o lo que es lo mismo, Pozos Cu´antincos y Cristales Fot´onicos. 0.1 Pozos cu´anticos Es conocido que en las bandas de conducci´on y de valencia de un material semiconductor, existen una serie de estados accesibles para electrones o huecos respectivamente. Esta serie 5 de estados disponible se da en un continuo, mientras que existe la posibilidad de conseguir niveles ´oestados discretos accesibles en dichas bandas mediante el confinamiento cu´antico de los portadores, usando para ellos los pozos cu´anticos. Para conseguir este confinamiento, se puede pensar en la implementacion de los po- zos cu´anticos como en una fina capa de conductor con un determinado ancho de banda prohibida, emparedada entre dos tiras de otros semiconductores con mayor separaci´on entre las bandas de conducci´on y valencia [15]. Esta es la forma m´as sencilla, como puede verse en la figura 1.2. La anchura de banda del semiconductor de en medio (al que llamare- mos material estrecho), ha de ser al menos del orden del camino medio libre del portador entre colisiones en el medio. Esto quiere decir en valores concretos, en un rango oscilante entre el medio nanometro y los 10 ´o20 nm. A su vez, tambi´en ha de ser de una anchura menor que la longitud de onda de DeBroglie, es decir, h λ = (1) p donde p es el momento del electron. Por ejemplo para el GaAs se tiene λ = 24nm. La estructura del pozo cu´antico tiene la propiedad de confinar los portadores en una regi´on muy determinada y estrecha, en la dichos portadores se comportan de forma an´aloga al cl´asico problema de la mec´anica cu´antica de la part´icula encerrada en un pozo de potencial.
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