Ruchirej Yongsunthon, Doctor of Philosophy, 2002

Dissertation directed by Professor Ellen D. Williams
Department of Physics
University of Maryland, College Park

I have developed the application of Magnetic Force Microscopy (MFM) to perform current imaging with sub-micron spatial resolution. Doing so first required isolating the magnetic interaction in the MFM phase measurement from interfering signal sources and establishing methods of relative quantification that do not depend upon specific tip magnetization. This was accomplished by using a specially designed calibration standard. The accuracy of the MFM peak heights for determining relative current densities for sufficiently large (>3mm) line structures was shown to be well within 10%. The Green’s function vertical propagation of MFM data was also used to show that the MFM response is linear to within 5%. Useful instrumental tip response functions were determined for deconvolution of the MFM data.

Asymmetry in MFM peaks heights was shown to reflect spatial variation in current density across the line width, known as current crowding. Test samples were designed to reflect structures of interest in the electromigration community. MFM signatures of current behavior were empirically correlated with the defect structures. The crowding was found to be particularly strong for defect structures that have large spatial derivatives and curvatures.
Quantitative determination of the underlying current density distributions with sub-micron spatial resolution was demonstrated by inversion of MFM images and comparison with finite element calculations of the current density for the sample structures. The systematic observation of less severe and less sharp current crowding than predicted is due to incomplete recovery of the magnetic field curvature from the deconvolution procedure and to physical rounding of the structure edges. At size scales above 1mm, the combined accuracy of the deconvolution and inversion is within 10%.

Finally, a systematic study was performed using MFM signatures to determine the current crowding dependence on defect geometry. For a given type of defect, the degree of current crowding asymptotically vanishes as the defect length increases. For defects of similar lengths, the degree of crowding scales linearly with defect width. There is less crowding near defect structures where the current density changes gradually than in structures where the change is more abrupt. However, there is no consistently measurable difference in current crowding due to sharpness of corners.