Time–Energy Quantum Uncertainty: Quantifying the Effectiveness of Surface Defect Passivation Protocols for Low-Dimensional Semiconductors

The degree of enhancement in radiative recombination in ensembles of semiconductor nanowires after chemical treatment is quantified within a derived limit by correlating the energy released during the photoemission processes of the light-matter reaction and the effective carrier recombination lifetimes. It is argued that the usage of surface recombination velocity or surface saturation current density as passivation metrics that assess the effectiveness of surface passivation does not provide strict and universal theoretical bounds within which the degree of passivation can be confined. In this context, the model developed in this study provides a broadly applicable surface passivation metric for direct energy bandgap semiconductor materials. This is because of its reliance on the dispersion in energy and lifetime of electron-hole recombination emission at room temperature, in lieu of the mere dependence on the ratio of peak emission spectral intensities or temperature- and power-dependent photoluminescence measurements performed prior and subsequent to surface treatment. We show that the proposed quantification method, on the basis of steady-state and transient photoluminescence measurements performed entirely at room temperature, provides information about the effectiveness of surface state passivation through a comparison of the dispersion in carrier lifetimes and photon energy emissions in the nanowire ensemble before and after surface passivation. Our measure of the effectiveness of a surface passivation protocol is in essence the supremum of lower bounds one can derive on the product of Delta t and Delta E.