Erasmus Langer
Siegfried Selberherr
Oskar Baumgartner
Markus Bina
Hajdin Ceric
Johann Cervenka
Raffaele Coppeta
Lado Filipovic
Lidija Filipovic
Wolfgang Gös
Klaus-Tibor Grasser
Hossein Karamitaheri
Hans Kosina
Hiwa Mahmoudi
Alexander Makarov
Mahdi Moradinasab
Mihail Nedjalkov
Neophytos Neophytou
Roberto Orio
Dmitry Osintsev
Mahdi Pourfath
Florian Rudolf
Franz Schanovsky
Anderson Singulani
Zlatan Stanojevic
Viktor Sverdlov
Stanislav Tyaginov
Michael Waltl
Josef Weinbub
Yannick Wimmer
Thomas Windbacher
Wolfhard Zisser

Oskar Baumgartner
Oskar Baumgartner was born in Krems an der Donau, Austria, in 1982. He studied electrical engineering at the Technische Universität Wien, where he received the degree of Diplomingenieur in January 2007. He joined the Institute for Microelectronics in February 2007, where he is currently working on his doctoral degree. His scientific interests include the modeling and simulation of quantum transport in optical and nanoelectronic devices.

Modeling the Effects of Band Structure and Transport in Quantum Cascade Lasers and Detectors

One of the essential technologies in modern photonic systems are semiconductor heterostructures. Based on the work on intersubband devices by Kazarinov and Suris in the 1970s, the first Quantum Cascade Laser (QCL) was demonstrated by Faist et al. twenty years later. The first use of a QCL as a photo-detector was reported by Hofstetter in 2002 and since then has been refined for infrared and terahertz wavelengths leading to the modern Quantum Cascade Detectors (QCD).
Since the degrees of freedom in the design of heterostructure devices is high, the complexity of the design process becomes a challenge for the device engineer. Simulation tools are indispensable to determine the necessary adjustments of the many free parameters involved, in order to achieve the desired optical and electrical characteristics. The accuracy of the physical description needs to be in balance with the computational cost. While a fully quantum mechanical description is insightful, the computational demand often renders it impracticable for design purposes.
We developed an efficient Monte Carlo simulator in C++ as part of the Vienna Schrödinger Poisson (VSP) simulation framework. The versatility of the simulator was successfully demonstrated by the design and automatized optimization of a bi-functional QCL and QCD device [1]. The Hamiltonian includes the band edge profile of the heterostructure, thus, coherent tunneling is accounted for through the delocalized eigenstates. Transport occurs via scattering between the subbands. Due to the periodicity of the device, periodic boundaries are imposed on the Pauli-Master equation. As scattering sources we currently consider non-polar acoustic and optical phonons, and polar optical phonons as well as alloy disorder, intervalley processes and interface roughness. The incorporated model for stimulated emission and absorption of photons is essential for the description of a QCD (figure 1.).
The simulator offers huge flexibility to accurately model the device physics. For example, we can calculate the responsivity of a QCD, which relates the incoming photon flux to the detected current, for a combination of band structure models (2-band k·p, 4-band k·p, etc.) and in-plane dispersion of the transport model. For the in-plane transport treatment one can use the parabolic effective (density of states) mass as the input parameter or average it for each subband. We realized a fitting algorithm for the mass and non-parabolicity coefficient to the numerical non-parabolic subband structure determined by the Schrödinger equation. These methods enable the accurate reproduction of measurement data using our simulator (figure 2); an important property for device engineers.
This study shows that the VSP is a versatile simulator that allows quick simulation studies of QCLs and QCDs, while still accurately capturing the relevant physics.

[1] B. Schwarz et al., Appl. Phys. Lett., 101, 191109 (2012).
[2] F. Giorgetta et al., IEEE Journal of Quantum Electronics, 45, 1039 (2009).

Figure 1. The operating principle of a QCD. A ground level electron is excited to a higher state by absorbing a photon. Due to the asymmetric design, the electron relaxes in a preferred direction into the quantum well of the next cascade. This concept reduces dark current and dark current noise.

Figure 2. Calculated responsivity (solid) of the QCD compared to measurements of Giorgetta [2] (dashed); cross-plane band structure modeled with a four-band k·p Hamiltonian. The in-plane dispersion in the transport model is assumed non-parabolic with the effective mass and non-parabolicity coefficient fitted to the subband structure; inclusion of non-parabolicity has substantial effects on the responsivity.

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