  In this letter, we present a study of optimized TMR magnetic field sensors as
a function of voltage bias. The 1/f low-frequency noise is quantified by the
Hooge-like parameter {\alpha} which allows to compare the low-frequency
behavior of various TMR sensors. The sensitivity as well as the detectivity of
the sensor are characterized in the parallel state and at 0 mT. We observe that
the sensitivity shows a strong voltage dependence and the noise presents an
unexpected decrease, not anticipated by the Hooge's law. Moreover,
surprisingly, an almost stable detectivity (140-200 nT/sqrt(Hz) at 10 Hz and
15-20 nT/sqrt(Hz) at 1 kHz) as a function of the bias voltage is observed,
tending to highlight that the variation of sensitivity and noise are
correlated. Even if the I-V curves are strongly non-linear and reflect the
different symmetries of the conduction bands channels, the variations in
sensitivity and noise seems to depend mainly on the distortion of the MgO
barrier due to bias voltage. With a simple model where the normal noise and
sensitivity of the TMR sensors are modified by an element having no noise and a
parabolic conductance with voltage, we describe the behavior of noise and
sensitivity from mV to V.
