In 1970, Esaki and Tsu [5] proposed using heterostructures for applications in optoelectronics. The first suggestion to use intersubband transitions in order to create a laser was made by Kazarinov and Suris [6]. Over the past several years, solid-state lasers based on intersubband transitions in semiconductor heterostructures have proved to be very viable sources of radiation [7]. Designed by means of band structure engineering, a successfully working quantum cascade laser (QCL) has first been reported in 1994 [8]. In the following years many important milestones for semiconductor lasers were demonstrated using the semiconductor system Al0.48In0.52As/Ga0.47In0.53As/InP.
The fundamentals of these devices are not bound to a particular material system. The first demonstration of a QCL in a different material system was achieved in 1998 using GaAs/Al0.33Ga0.67As [9]. AlGaAs based heterostructures are the most widespread and developed ones among compound semiconductors. Moreover they show some significant advantages for the use of processing techniques, which are more suitable for a GaAs than an InP based device. For instance, the standard dry etching techniques, like reactive ion etching or chemically assisted ion beam etching, become more difficult to use when In compounds are present [10]. QCLs may also allow laser operation in materials traditionally considered to have poor optical properties. Indirect bandgap materials such as silicon have minimum electron and hole energies at different momentum values. For interband optical transitions, carriers change momentum through a slow, intermediate scattering process, dramatically reducing the optical emission intensity. Intersubband optical transitions, however, are independent of the relative momentum of conduction band and valence band minima and theoretical proposals for Si/SiGe quantum cascade emitters have been made [11].
However, the performance of QCLs has remarkably improved and devices have been conceived to work in a wide range of wavelengths and temperatures by considering different designs [12]. The emission wavelength has spanned the mid-infrared (MIR) to far-infrared (FIR) spectral range (3 - 190 μm) and QCLs are rapidly acquiring new applications such as free-space telecommunications [13] or chemical spectroscopy in medical applications [14]. QCLs can also be applied for radio-carbon dating and monitoring atmospheric methane levels. Since the emission frequency of intersubband lasers is determined by the design of the widths of the quantum wells and barrier layers, it can be tailored to the application. However, the commercialization of QCLs is in the early stages. For product specific optimization of emitted wavelengths and output performance, simulations of the physical processes are inevitable.
In this dissertation, we will show how the use of a Monte Carlo (MC) simulation based on a semiclasscial transport theory is a very useful approach to investigate the physics of QCL operation. To investigate charge transport and the performance in general, we developed a Monte Carlo simulator which includes the relevant scattering mechanisms such as electron-longitudinal optical phonon, acoustic and optical deformation potential, and intervalley scattering. The electron states are evaluated using a selfconsistent Schrödinger-Poisson solver. The simulator has been used to simulate the output characteristics of GaAs based QCLs in the MIR and THz region, respectively.
In Chapter 2, basic fundamentals of QCLs are described and the most important milestones and achievements are discussed. In Chapter 3, the selfconsistent Schrödinger-Poisson solver is accurately described. Special emphasis is laid on the quantum ballistic transport and the theory of open boundary value problems. Chapter 4 deals with the theoretical framework of the density matrix formulation, and the semiclassical transport model and especially the stationary charge transport governed by the Pauli master equation (PME) is presented. The ensemble Monte Carlo procedure is introduced as an efficient approach for simulating transport in QCL structures according to the given Boltzmann-like kinetic equations. The interaction mechanisms are restricted to three stages. Chapter 5 describes the scattering mechanism considered in the Monte Carlo simulator. Chapter 6 presents the simulation results obtained. In particular, current carrying states are obtained by assuming Robin boundary conditions and the presented numerical simulations show that the stationary charge transport can be well described by incorporating a reasonable concept of non-selfadjoint boundary conditions. The method has been applied to several heterostructure designs and the results obtained have been compared to other simulations and to experimental measurements. Furthermore, the developed Monte Carlo simulator is employed to study the output characteristics and special focus was laid on the study of intervalley scattering effects on the carrier dynamics. The results are analyzed with a view to optimization of QCL structures. Chapter 7 summarizes the research performed within this thesis. Furthermore, a discussion of the obtained results as well as an outlook of envisioned and necessary future work are provided.