Machine learning for quantum cascade laser design and optimization

Abstract

Quantum cascade lasers (QCLs) are semiconductor devices that emit light in the mid-infrared and terahertz regions of the electromagnetic spectrum. Population inversion is achieved between intersubband electronic transitions in the conduction band of a multi-quantum well heterostructure formed (usually) by alternating InGaAs (well) and AlInAs (barrier) layers. The figure of merit (FoM), a measure for laser performance, the gain coefficient, and emission wavelength can be tailored based on selecting the number of layers, each layer thickness, and the applied electric field of the design.Here, a machine learning (ML) framework is developed to automatically optimize the FoM for an initial QCL design, and to find new QCL structures, based on the layer thicknesses and applied electric field. The entire design space is canvassed by ML to reveal new structures with high FoM. This thesis research focuses on the techniques used to build QCL datasets suitable for ML, the neural network optimization process used to make a ML algorithm for QCL FoM prediction, as well as the results and limitations of the algorithm to optimize an initial QCL design and predict new ones. First, a code to automatically identify the electronic state-pair transition in a QCL design that has a potential for population inversion and is suitable for machine learning has been developed. The code, building upon a Schrödinger solver, is used to build datasets consisting of the number of layers, layer thicknesses, and applied electric field of many QCL designs as inputs, and the energy difference, FoM, dipole matrix element, gain coefficient, and effective scattering time between the identified laser transition states as outputs. Designs are generated by adding a random integer material thickness to every layer of a starting QC design. Time to identify a possible laser transition in a design is reduced from six minutes to about two minutes when states in the continuum above the quantum wells are filtered out. Second, a multi-layer perceptron neural network is used on the QCL datasets. The software MATLAB is used to optimize the number of hidden layers, the number of neurons, the solver, activation function, and number of epochs needed to obtain the lowest root-mean-square error on the predicted outputs, which ranges from 16-20 eV ps Å^2 on a FoM average of 90 eV ps Å^2, or about 20%, taking anywhere from a couple of seconds to several minutes to train. The algorithm predicts QCL design FoMs very well when the designs are similar to those of the dataset. Next, this framework is applied to optimize an initial 10-layer structure. Two datasets each with 1800 random structures from two random layer thickness tolerance ranges: [-2, +3] Å and [-5, +20] Å are generated with an electric field sweep of 10-150 kV/cm in 10 kV/cm increments, predicting 27000 designs in about 36 hours using a virtual machine. Two algorithms are trained and used to predict the FoM for ~ 10^9 designs in about 8 hours on a personal computer, a significant, many orders of magnitude, increase in prediction speed when compared to building our datasets. Careful visualization of subspaces allows for identification of QC designs with high performance. For the [-2, +3] Å design space, a 1.5-fold increase in the FoM, and for the [-5, +20] Å design space, a 2-fold increase. These algorithms, furthermore, show which QCL layers should be altered, and by how much, and at what electric field these structures are best operated, to maximize the FoM in this design space, with accuracy around 16%. Finally, a genetic algorithm which uses the [-5, +20] Å ML neural network as the FoM fitness function is used to identify high FoM designs 120 times faster than when only ML is used to canvass the entire design space.