Electron transport in low-dimensional systems: optoelectronic device simulations

Abstract

The main topic of this thesis is the theoretical and computational investigation of the opto-electronic properties of large arrays of semiconductor quantum dots embedded in an insulator matrix. For that purpose, an electronic transport model has been formulated and implemented in a code for numerical simulations.

The relevance of this research is given by the possibility to simulate from basic design parameters, such as the device geometry and basic material constants, the electrical response of quantum dot based devices which are promising candidates to enhance and further downscaling the actual electronics.

Quantum dot properties have not analogous in the standard bulk semiconductor theory. Their electrical and optical properties are dominated by the quantum effects arising from the quantum confinement. This fact creates discrete energy level spectra and makes the electrical response of this kind of system different to the bulk.

The developed electrical transport methodology is based on rate equations within the Transfer Hamiltonian approach in the ballistic regime. A set of non-coherent rate equations can be written for a random distribution of interacting quantum dots embedded in a dielectric media and the interaction among the quantum dots and between the quantum dots and the electrodes are introduced by transition rates and capacitive couplings. The effects of the local potential are computed within the self­consistent field regime. The electrical transport model has been developed and expressed in a matrix form in order to make it extendable to larger systems. Transport through several quantum dot configurations has been studied in order to validate the model. Despite its simplicity, well-known effects are satisfactorily reproduced and explained. The results qualitatively agree with more complex theoretical approaches.

While the description of the theoretical framework is kept as general as possible, a realistic modelization of: the capacitive couplings, the transmission coefficients, the electron/hole tunneling currents and the density of states of each quantum dot have been taken into account. Creating a new simulation tool that can foster the development of quantum dot based nanosystems aiding in their design. To illustrate the kind of unique insight that these numerical simulations can provide, two specific prototypical devices, an arbitrary array and a transistor device based on quantum dots, have been simulated. To conclude, the previous developed transport model has been complete including illumination effects being able to study an design opto-electronic devices.

El proceso de miniaturización de los dispositivos eléctricos ha permitido la creación de estructuras nanométricas. A esta escala, las propiedades de los materiales difieren de las observadas a escalas macroscópicas. Se han observado fenómenos que solo pueden ser explicados mediante la mecánica quántica, como el confinamiento quántico en varias dimensiones. De esta forma, la miniaturización a escala nanométrica ha abierto las puertas a la creación de dispositivos basados en nanoestructuras cuyas propiedades y respuestas eléctricas no tienen análogo en la electrónica macroscópica.

Para poder mostrar todas las posibilidades y potencialidades de este tipo de dispositivos basados en nanoestructuras, es necesaria una descripción teórica que permita explicar a priori el comportamiento de estos. En este contexto, las simulaciones permiten entender y predecir el comportamiento experimental. Desde un punto de vista físico, se puede aprender mucho de las simulaciones si estas están basadas en parámetros físicos fundamentales de los materiales usados y de la geometría del dispositivo. Aunque se han realizado grandes progresos en el campo, aún no es posible una completa descripción de los dispositivos experimentales basada en primeros principios, es decir, mediante simulaciones atomísticas. Por lo tanto, es necesario realizar aproximaciones en los modelos teóricos relajando la precisión de los resultados obtenidos a favor de la posibilidad de simular dispositivos más parecidos a los experimentales.

El objetivo de esta tesis es servir de nexo de unión entre las simulaciones teóricas y los dispositivos opto-electrónicos fabricados experimentalmente basados en matrices de quantum dots. Se ha desarrollado un formalismo de transporte eléctrico que permite estudiar la respuesta eléctrica de estos dispositivos bajo la influencia de un potencial externo.