Martin Franckié

Impact of interface roughness distributions on the operation of quantum cascade lasers

We study the impact of interface roughness on the operation of mid-IR and THz quantum cascade lasers. Particular emphasis is given towards the differences between the Gaussian and exponential roughness distribution functions, for which we present results from simulation packages based on nonequilibrium Greens functions and density matrices. The Gaussian distribution suppresses scattering at high momentum transfer which enhances the lifetime of the upper laser level in mid-IR lasers. For THz lasers, a broader range of scattering transitions is of relevance, which is sensitive to the entire profile of the interface fluctuations. Furthermore we discuss the implementation of interface roughness within a two band model.

Influence of interface roughness in quantum cascade lasers

We use a numerical model based on non-equilibrium Greens functions to investigate the influence of interface roughness (IFR) scattering in terahertz quantum cascade lasers. We confirm that IFR is an important phenomenon that affects both current and gain. The simulations indicate that IFR causes a leakage current that transfers electrons from the upper to the lower laser state. In certain cases, this current can greatly reduce gain. In addition, individual interfaces and their impact on the renormalized single particle energies are studied and shown to give both blue- and red-shifts of the gain spectrum.

Injection schemes in THz quantum cascade lasers under operation

The two main design schemes for Terahertz quantum cascade lasers, based on tunnelling and scattering injection, respectively, are theoretically compared. We apply our simulation package based on the non-equilibrium Green’s function technique. Our results provide a good description of the gain degradation with temperature. Thermal backfilling contributes to decrease of population inversion in both cases. However, the dropping inversion cannot account for the total reduction of gain.

Phenomenological position and energy resolving Lindblad approach to quantum kinetics

A general theoretical approach to study the quantum kinetics in a system coupled to a bath is proposed. Starting with the microscopic interaction, a Lindblad master equation is established, which goes beyond the common secular approximation. This allows for the treatment of systems, where coherences are generated by the bath couplings while avoiding the negative occupations occurring in the Bloch-Wangsness-Redfield kinetic equations. The versatility and accuracy of the approach is verified by its application to three entirely different physical systems: (i) electric transport through a double-dot system coupled to electronic reservoirs, (ii) exciton kinetics in coupled chromophores in the presence of a heat bath, and (iii) the simulation of quantum cascade lasers, where the coherent electron transport is established by scattering with phonons and impurities. (Less)

Simulating terahertz quantum cascade lasers: Trends from samples from different labs

We present a systematic comparison of the results from our non-equilibrium Greens function formalism with a large number of AlGaAs-GaAs terahertz quantum cascade lasers previously published in the literature. Employing identical material and simulation parameters for all samples, we observe that the discrepancies between measured and calculated peak currents are similar for samples from a given group. This suggests that the differences between experiment and theory are partly due to a lacking reproducibility for devices fabricated at different laboratories. Varying the interface roughness height for different devices, we find that the peak current under lasing operation hardly changes, so that differences in interface quality appear not to be the sole reason for the lacking reproducibility.

Microscopic approach to second harmonic generation in quantum cascade lasers

Second harmonic generation is analyzed from a microscopical point of view using a non-equilibrium Greens function formalism. Through this approach the complete on-state of the laser can be modeled and results are compared to experiment with good agreement. In addition, higher order current response is extracted from the calculations and together with waveguide properties, these currents provide the intensity of the second harmonic in the structure considered. This power is compared to experimental results, also with good agreement. Furthermore, our results, which contain all coherences in the system, allow to check the validity of common simplified expressions.

Simple electron-electron scattering in non-equilibrium Green's function simulations

In this work we include electron-electron interaction beyond Hartree-Fock level in our non-equilibrium Greens function approach by a crude form of GW through the Single Plasmon Pole Approximation. This is achieved by treating all conduction band electrons as a single effective band screening the Coulomb potential. We describe the corresponding self-energies in this scheme for a multi-subband system. In order to apply the formalism to heterostructures we discuss the screening and plasmon dispersion in both 2D and 3D systems. Results are shown for a four well quantum cascade laser with different doping concentration where comparisons to experimental findings can be made.

Superlattice gain in positive differential conductivity region

We analyze theoretically a superlattice structure proposed by A. Andronov et al. [JETP Lett. 102, 207 (2015)] to give Terahertz gain for an operation point with positive differential conductivity. Here we confirm the existence of gain and show that an optimized structure displays gain above 20 cm−1 at low temperatures, so that lasing may be observable. Comparing a variety of simulations, this gain is found to be strongly affected by elastic scattering. It is shown that the dephasing modifies the nature of the relevant states, so that the common analysis based on Wannier-Stark states is not reliable for a quantitative description of the gain in structures with extremely diagonal transitions.

Quantum model of gain in phonon-polariton lasers

We develop a quantum model for the calculation of the gain of phonon-polariton intersubband lasers. The polaritonic gain arizes from the interaction between the electrons confined in a quantum well structure and the phonon confined in one layer of the material. Our theoretical approach is based on expressing the crucial matter excitations (intersubband electrons and phonons) in terms of polarisation densities in second quantisation, and treating all non-resonant polarisations with an effective dielectric function. The interaction between the electronic and phononic polarizations is treated perturbatively, and gives rise to stimulated emission of polartions in the case of inverted subbands. Our model provides a complete physical insight of the system and allows to determine the phonon and photon fraction of the laser gain. Moreover, it can be applied and extended to any type of designs and material systems, offering a wide set of possibilities for the optimization of future phonon-polariton lasers.

A simple approach for electron-electron scattering in nonequilibrium Green's function simulations(Conference Presentation)

Regardless of all the success of Mid Infrared Quantum Cascade Lasers (QCLs), they still do not operate at room temperature in the THz range. The main temperature degrading mechanism for THz QCLs is not known in time of writing this abstract and it is still a topic of debate by the community [S. Khanal et al, J. Opt. 16 094001, 2014]. This is a challenge to theory and it is crucial to treat all possible scattering channels with the same mathematical footing. A summary of different methods for simulating these structures is found in [C. Jirauschek et al, Appl. Phys. Rev. 1 011307, 2014]. In this work we include and study the effects of electron-electron scattering via the Single Plasmon Pole Approximation (SPPA). In this approximation we capture both the static limit as well as dynamic effects. This gives an energy dependent (non-local in time) interaction beyond the Hartree-Fock approximation. This has been studied in a similar model with promising results [T. Schmielau and M.F. Pereira, Appl. Phys. Lett. 95 231111, 2009], and with this work we want to adapt the idea into the model described in Ref. [A. Wacker et a, IEEE Journal of Sel. Top. in Quantum Electron.,19 1200611, 2013]. We start by summarizing the theory underlying the SPPA and we show how it is implemented in the context of our formalism, by showing good agreement with the results for a four well quantum cascade laser [M. Amanti et al, New J. Phys. 11 125022, 2009].