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 photodetector 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 bifunctional 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 PauliMaster equation. As scattering sources we currently consider nonpolar 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 (2band k·p, 4band k·p, etc.) and inplane dispersion of the transport model. For the inplane 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 nonparabolicity coefficient to the numerical nonparabolic 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).
