  Micro- and nanomechanical resonators have emerged as promising platforms for
sensing a broad range of physical properties such as mass, force, torque,
magnetic field, and acceleration. The sensing performance relies critically on
the motional mass, the mechanical frequency, and the linewidth of the
mechanical resonator. Here, we demonstrate a hetero optomechanical crystal
(OMC) cavity based on a silicon nanobeam structure. The cavity supports phonon
lasing in a fundamental mechanical mode with a frequency of 5.91 GHz, an
effective mass of 116 fg, and a mechanical linewidth narrowing from 3.3 MHz to
5.2 kHz, while the optomechanical coupling rate of is as high as 1.9 MHz. With
this phonon laser, the on-chip sensing with a resolution of
$\delta$$\lambda$/$\lambda$ = 1.0*10-8 can be attained, which is at least two
orders of magnitude larger than that obtained with conventional silicon-based
sensors. The use of a silicon-based hetero OMC cavity that harnesses phonon
lasing could pave the way towards exciting, high-precision sensors that lend
themselves to silicon monolithic integration and offer unprecedented
sensitivity for broad physical sensing applications.
