Reconstructing Local Profile of Exciton-Emission Wavelengths across a WS₂ Bubble beyond the Diffraction Limit

Air bubbles formed between layers of two-dimensional (2D) materials not only are unavoidable but also emerge as an important means of engineering their excitonic emission properties, especially as controllable quantum light sources. Measuring the actual spatially resolved optical properties across such bubbles is important for understanding excitonic physics and for device applications; however, such a measurement is challenging due to nanoscale features involved which require spatial resolution beyond the diffraction limit. Additional complexity is the involvement of multiple physical effects such as mechanical strain and dielectric environment that are difficult to disentangle. In this paper, we demonstrate an effective approach combining micro-photoluminescence measurement, atomic force microscope profile mapping, and a theoretical strain model. We succeeded in reconstructing the actual spatial profiles of the emission wavelengths beyond the diffraction limit for bubbles formed by a monolayer tungsten disulfide on boron nitride. The agreements and consistency among various approaches established the validity of our approach. In addition, our approach allows us to disentangle the effects of strain and dielectric environment and provides a general and reliable method to determine the true magnitude of wavelength changes due to the individual effects across bubbles. Importantly, we found that micro-optical measurement underestimates the red and blue shifts by almost 5 times. Our results provide important insights into strain and screening-dependent optical properties of 2D materials on the nanometer scale and contribute significantly to our understanding of excitonic emission physics as well as potential applications of bubbles in optoelectronic devices.