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 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,
Hall
sensor
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.
STM Current
Hall voltage
I Hall
Sample
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