A Markov Chain Monte Carlo Method for Statistically Meaningful Multi-Parameter Fits to Quantum Dot Spectroscopy Data

Optical spectroscopy is one of the most powerful tools used to understand nanostructured materials such as Quantum Dots (QDs). However, there are many parameters that influence the observed emission energies, including both the energies of confined states and many-body interactions. The situation is made even more complex by the fact that QDs are often inhomogeneous - small variations in size, shape, and composition lead to different values for every parameter in each unique nanostructure. Developing scalable quantum devices and systems that leverage the unique properties of QDs requires a method for analyzing the characterization data to extract values for the many parameters that contribute to the observed features. However, fits to too many free parameters have no scientific meaning.<br/>We develop and present a Markov Chain Monte Carlo (MCMC) method for performing statistically-meaningful fits to optical spectroscopy data of QDs. The system we use to develop our MCMC method is a vertically-stacked InAs Quantum Dot Molecule (QDM) grown on GaAs by molecular beam epitaxy. The QDM is embedded in a n-i-Schottky diode that allows the application of electric fields that tune the relative energies of the discrete states of the QDs. We analyze the photoluminescence (PL) from a single QDM as a function of applied electric field. Using the MCMC method, we simultaneously fit all experimental data to analytical expressions of the Hamiltonians for the system. The algorithm explores a range of values for each observable and, after millions of iterations, returns a histogram of values that generate an acceptable fit. We show that that MCMC approach extracts values for important physical parameters that are significantly different from those extracted using traditional methods. This approach can be extended to similar analyses of a wide range of nanostructured systems described by complex Hamiltonians.