  Here, we report the photoconducting response of field-effect transistors
based on three atomic layers of chemical vapor transport grown WSe$_2$ crystals
mechanically exfoliated onto SiO$_2$. We find that tri-layered WSe$_2$
field-effect transistors, built with the simplest possible architecture, can
display high hole mobilities ranging from 350 cm$^2$/Vs at room temperature
(saturating at a value of ~500 cm$^2$/Vs below 50 K) displaying a strong
photocurrent response which leads to exceptionally high photo responsivities up
to 7 A/W under white light illumination of the entire channel for power
densities p < 10$^2$ W/m$^2$. Under a fixed wavelength of $\lambda$ = 532 nm
and a laser spot size smaller than the conducting channel area we extract photo
responsitivities approaching 100 mA/W with concomitantly high external quantum
efficiencies up to ~ 40 % at room temperature. These values surpass values
recently reported from more complex architectures, such as graphene and
transition metal dichalcogenides based heterostructures. Also, tri-layered
WSe$_2$ photo-transistors display photo response times in the order of 10
microseconds. Our results indicate that the addition of a few atomic layers
considerably decreases the photo response times, probably by minimizing the
interaction with the substrates, while maintaining a very high
photo-responsivity.
