Quantum transport in semiconductor nanostructures

By Tillmann Christoph Kubis

Purdue University



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PhD thesis of Tillmann Christoph Kubis

The main objective of this thesis is to theoretically predict the stationary charge and spin transport in mesoscopic semiconductor quantum devices in the presence of phonons and device imperfections. It is well known that the nonequilibrium Green's function method (NEGF) is a very general and all-inclusive scheme for the description of exactly this kind of transport problem. Although the NEGF formalism has been derived in the 1960's, textbooks about this formalism are still rare to find. Therefore, we introduce the NEGF formalism, its fundamental equations and approximations in the first part of this thesis. Thereby, we extract ideas of several seminal contributions on NEGF in literature and augment this by some minor derivations that are hard to find.

Although the NEGF method has often been numerically implemented on transport problems, all current work in literature is based on a significant number of approximations with often unknown influence on the results and unknown validity limits. Therefore, we avoid most of the common approximations and implement in the second part of this thesis the NEGF formalism as exact as numerically feasible. For this purpose, we derive several new scattering self-energies and introduce new self-adaptive discretizations for the Green's functions and self-energies. The most important improvements of our NEGF implementation, however, affect the momentum and energy conservation during incoherent scattering, the Pauli blocking, the current conservation within and beyond the device and the reflectionless propagation through open device boundaries. Our uncommonly accurate implementation of the NEGF method allows us to analyze and assess most of the common approximations and to unveil numerical artifacts that have plagued previous approximate implementations in literature. Furthermore, we apply our numerical implementation of the NEGF method on the stationary electron transport in THz quantum cascade lasers (QCLs) and answer several controversially discussed questions on the nature of transport in this type of nanodevices. In contrast to previous approximate approaches, we show that the nature of transport in QCLs is sensitive to the applied bias voltage and can be tuned from the coherent to the incoherent regime. We point out that the elastic scattering at rough interfaces is among the most efficient incoherent scattering mechanisms in THz-QCLs and significantly influences the laser performance. Up to now, this has been utterly underestimated in approximate studies of THz-QCLs with direct optical transitions. All current theoretical models apply periodic (or field-periodic) boundary conditions on the transport in QCLs. Our revision of the open boundary conditions allows us to consider the QCL as an open quantum devices, instead. In this way, we illustrate that charge distributions in QCLs can develop periodicities that are only commensurable or even incommensurable with the QCL periodicity. This effect leads to efficient non-radiative transitions between the laser levels and is - due to the common periodic boundary conditions - completely missed in literature. We also propose several novel THz-QCLs with larger optical gain, lower thermal load and a higher resistivity against growth imperfections.

The third part of this thesis is dedicated to the spin transport in two-dimensional semiconductor heterostructures. It is common to apply an approximate envelope function model (EFT) for the spin-orbit interaction in such devices, in spite of the well-known fact that EFT calculations typically incorrectly predict the spin-splitting in semiconductor heterostructures. For this reason, we represent the NEGF method in the EFT model as well as in a microscopic atomistic tight binding model. In the later model, the spin-orbit interaction is treated nonperturbatively going far beyond the approximate EFT model. We show that the numerically efficient EFT model yields results that qualitatively agree with predictions of the numerically very demanding microscopic model. This allows us to study the spin polarization of propagating and confined carriers in two-dimensional semiconductor devices of complex geometries. We show that the spin polarization generated by the intrinsic spin-Hall effect cannot be significantly mediated by phonons into confined states. However, we demonstrate that the interferences of partially confined carriers can significantly enhance the local spin polarization to values of almost 100%. We finally propose three and four terminal devices that act as efficient all-semiconductor non-magnetic spin polarizers.

Cite this work

Researchers should cite this work as follows:

  • T. Kubis, "Quantum transport in semiconductor nanostructures", edited by G. Abstreiter, M. C. Amann, M. Stutzmann, P. Vogl (Verein zur Foerderung des Walter Schottky Instituts der Technischen Universitaet Muenchen e.V., Garching, 2009)
  • Tillmann Christoph Kubis (2010), "Quantum transport in semiconductor nanostructures," https://nanohub.org/resources/8612.

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