Quantification of magnetic nanobeads with micrometer Hall sensors

This paper investigates the suitability of miniaturized semiconductor Hall devices for the quantification of magnetic nanobeads usable in biomedical applications. The analysis demonstrates the existence of conditions for which the Hall voltage signal is not proportional to bead number, focusing on the detection of a 2D array of superparamagnetic nanobeads, immobilized on the sensor surface. The study is performed by means of a numerical modeling procedure, which provides the spatial distribution of the electric potential inside the Hall plate, under the assumptions of diffusive electron transport regime and non-uniform magnetic field. We find that the proportionality of the sensor response to bead number and possibility to use micro-Hall devices as magnetic bead counters are strongly affected by the magnetostatic dipolar interactions between beads. We also observe a deviation from linearity, due to the spatial non-uniformity in the device response, which is strongly influenced by the planar position of the beads with respect to the device active area. These aspects are investigated in detail by varying external field amplitude, device dimension, bead number, interbead distance, bead vertical position and size of the area occupied by beads. The parametric analysis is performed simulating an ac-dc Hall magnetometry technique