  Graphene Hall effect magnetic field sensors hold great promise for the
development of ultra-sensitive magnetometers. Their performance is frequently
analysed using the two-channel model where electron and hole conductivities are
simply added. Unfortunately, this model is unable to capture all the features
of the sensor, particularly the bias current dependence of the magnetic field
sensitivity. Here we present an advanced model that provides an in-depth
understanding of how graphene Hall sensors operate, and demonstrate its ability
to quantitatively assess their performance. First, we report the fabrication of
sensors with different qualities of graphene, with the best devices achieving
magnetic field sensitivities as high as 5000 ohms/T, outperforming the best
silicon and narrow-gap semiconductor-based sensors. Then, we examine their
performance in detail using the proposed numerical model, which combines
Boltzmann formalism, with distinct Fermi levels for electrons and holes, and a
new method for the introduction of substrate-induced electron-hole puddles.
Importantly, the dependences of magnetic field sensitivity on bias current,
disorder, substrate and Hall bar geometry are quantitatively reproduced for the
first time. In addition, the model emphasizes that the performance of devices
with widths of the order of the charge carrier diffusion length, is
significantly affected by the bias current due to the occurrence of large and
non-symmetric carrier accumulation and depletion areas near the edges of the
Hall bar. The formation of these areas induces a transverse diffusion particle
flux capable of counterbalancing the particle flux induced by the Lorentz force
when the Hall electric field cancels out in the ambipolar regime. Finally, we
discuss how sensor performance can be enhanced by Fermi velocity engineering,
paving the way for future ultra-sensitive graphene Hall effect sensors.
