Scanning Hall Probe Microscopy (SHPM)
In SHPM, a small, typically micron-sized, Hall sensor is scanned in close proximity to the sample surface (see schematics above). Mapping the Hall voltage VH as a function of location directly yields the spatial distribution of the local magnetic field. Similar to MFM, SHPM is most frequently conducted in constant height mode, where the sample plane is typically detected by tunneling current measurements (referred to as STM-tracking SHPM). Today’s state-of-the-art Hall sensors are fabricated from silicon or modulation-doped heterostructures using standard CMOS techniques, molecular beam epitaxy, or e-beam lithography. For ultra-high spatial resolution applications, the Hall bar is typically refined by focused-ion beam milling, yielding areal dimensions well below 500 nm × 500 nm.
The figures of merit of Hall sensors are sensitivity and noise. The sensitivity SHall of a Hall sensor biased with a current I is given by SHall= |VH /(I B)|= 1/(e n2D), where VH is the measured Hall voltage, B is the magnetic field experienced by the sensor, e = 1.6*10‑19 As, and n2D is the carrier density in the case of a modulation-doped Hall sensor with a two-dimensional electron gas layer, referred to as 2DEG.
Typical values for the sensitivity are 1000–2000 V/AT in a large temperature range. Together with the noise of the sensor, the sensitivity determines the minimal detectable field or field detection limit (DL) of the sensor. There are three sources of noise present in a Hall bar, which are Johnson, 1/f, and generation-recombination noise. Larger Hall sensors provide lower 1/f noise because of the larger number of charge carriers present. This typically leads to a lower DL for larger sensors, but this trend disappears at temperatures below 100 K, where heterostructure sensors are typically operated and are dominated by the thermal noise regime.
The highest-quality Hall Sensors for low temperature operation existing today are made from a GaAs/AlGaAs heterostructure, created by a molecular-beam-epitaxy (MBE) growth process. attocube currently offers this type of sensor with high and ultra-high resolution technology, yielding 400 nm and 250 nm spatial resolution. The theoretical thermodynamic noise limit of attocube’s sensors is typically 15 nT/Hz1/2 at 4 K and 80 nT/Hz1/2 at 77 K, while the experimentally attainable magnetic field resolution is limited to to the μT range in the few Hertz bandwidth for most experiments. This is due to current fluctuations in the current source, which are directly translated into voltage fluctuations because of the intrinsic voltage offsets in the Hall bar.