Abstract

Quantum Cascade Lasers (QCLs) produce coherent radiation in the mid IR to THz frequency range with applications for defense, medicine and communication. QCL operation relies on intersubband electronic transitions within confined quantum wells in superlattices of GaInAs and AlInAs on InP or GaAs substrates. While QCLs offer high efficiency, the associated large levels of heat generation cause thermal conduction within the active region to strongly influence the stability and reliability, particularly for the continuous wave (CW) or high duty-cycle mode at room temperature. With layer thicknesses in the range of 2-6 nm, phonon transport can be strongly influenced by phonon scattering and, potentially, by modifications to phonon dispersion. Previous studies have examined the thermal conductivity of as-prepared QCL structures and some coupled electro-thermal-optical models based on continuum heat conduction have been proposed. In addition, there is a wealth of prior literature on phonon scattering (and even dispersion modification) for periodic nanoscale superlattice structures. However, real QCL cores contain a distribution of well (GaInAs) and barrier (AlInAs) layer thicknesses, typically ranging between 1 nm and 4 nm, with no periodicity on length scales comparable to the phonon mean free path (MFP ≈ 2 – 5 nm; stack period ≈ 50 nm). Therefore, for the better design and optimization of QCL performance, it is crucial to make progress on a comprehensive model that can account for the aperiodic behavior in QCL superlattices. The present work develops an approximate solution to the phonon Boltzmann transport equation (BTE) accounting for both the local interface scattering and the impact of boundaries of one or more interfaces displaced from the local region. A statistical method based on phonon transition at interfaces and survival rates through the material volume is employed to develop a physics-based modeling approach for aperiodic superlattices. The goal is to develop an effective thermal conductivity model that can be applied locally within the aperiodic structure, as also to the stack as a whole in order to predict through-plane thermal transport properties of QCL active regions.