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Scanning Hall Probe Microscopy (SHPM)
fundamentals
In SHPM, a small, typically micron-sized, Hall sensor is scanned in close
proximity to the sample surface (see schematics below). 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 modula-
tion-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 S Hall = |V H /(I B)|=
1/(e n 2D ), where VH is the measured Hall voltage, B is the magnetic field ex-
perienced by the sensor, e = 1.6*10 ‑19 As, and n 2D 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 molecu-
lar-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/Hz 1/2 at 4 K and 80 nT/Hz 1/2 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.
Hall cross (active area
250 nm or 400 nm)
STM Current
Hall voltage
I Hall
Sample
attoMICROSCOPY
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