Quantitative Local Conductivity Imaging of Semiconductors Using Near-Field Optical Microscopy

We demonstrate contactless, nanoscale measurements of local conductivity, free carrier density, and mobility using phase-resolved infrared (IR) scattering-type near-field optical microscopy (s-SNOM). Our approach extracts quantitative conductivity information by combining analytical and finite-element methods to predict the scattered near-field amplitude and phase for specific sample geometries, without relying on bulk mobility assumptions or empirical fitting parameters. We find that the finite-dipole model (FDM) overestimates the expected near-field amplitude and phase in nonplanar or nanostructured materials, so we employ finite-element modeling to choose appropriate corrections to the FDM and account for sample geometry. The model is validated using a silicon calibration sample, and our results return the free carrier concentration expected based on the encoded dopant profile. Mobility and conductivity are also found to be in good agreement with established models for bulk silicon. This work demonstrates the potential of IR s-SNOM to perform quantitative local conductivity measurements, including the separation of free carrier density and electronic mobility, and represents a step toward the goal of quantitative carrier profiling and mobility mapping using s-SNOM.