Real-space imaging of current distributions at the submicron scale using magnetic force microscopy: Inversion methodology

Abstract

We report a method, based upon magnetic force microscopy (MFM), that permits the direct imaging of current distributions with submicron resolution. Magnetic force microscopy is used to measure the curvature of the magnetic field generated by a current-carrying structure. Maximum entropy deconvolution of the MFM phase image, followed by the application of a numerical inversion procedure derived from the Biot–Savart law, yields the current distribution in the sample. Careful theoretical analysis of the spatial resolution of this method shows that the lateral resolution is noise limited to approximately one quarter of the tip height. Since tip elevations of 100 nm are typical, we anticipate that this method has a spatial resolution of tens of nanometers. The method was used to determine the current distribution in the vicinity of a (1×9) μm2 slit-like defect embedded in a 11.5-μm-wide current-carrying metallic line. Current crowding and constriction are observed in the images and are resolved at the submicron level. The observed current distributions are found to be in good agreement with finite-element calculations of the current density for equivalent lines, confirming both the fidelity and the resolution of the imaging method.