  Here, Primordial Black Holes (PBHs) creation from exponential potential has
been inquired, through gravitationally raised friction emanated from the
nonminimal coupling between gravity and field derivative setup. Setting a
two-parted exponential function of inflaton field as coupling parameter, and
fine-tuning of four parameter cases of our model, we could sufficiently slow
down the inflaton owing to high friction during an ultra slow-roll phase. This
empowers us to achieve enough enhancement in the amplitude of curvature
perturbations power spectra, via numerical solving of Mukhanov-Sasaki equation.
Thereafter, we illustrate the generation of four PBHs with disparate masses in
RD era, corresponding to our four parameter cases. Two specimens of these PBHs
with stellar ${\cal O}(10)M_{\odot}$ and earth ${\cal O}(10^{-6})M_{\odot}$
masses can be appropriate to explicate the LIGO-VIRGO events, and the
ultrashort-timescale microlensing events in OGLE data, respectively. Another
two cases of PBHs have asteroid masses around ${\cal O}(10^{-13})M_{\odot}$ and
${\cal O}(10^{-15})M_{\odot}$ with abundance of $96\%$ and $95\%$ of the Dark
Matter (DM) content of the universe. Furthermore, we scrutinize the induced
Gravitational Waves (GWs) ensued from PBHs production in our model.
Subsequently, we elucidate that their contemporary density parameter spectra
$(\Omega_{\rm GW_0})$ for all predicted cases have acmes which lie in the
sensitivity scopes of the GWs detectors, thereupon the verity of our
conclusions can be verified in view of deduced data from these detectors. At
length, our numerical outcomes exhibit a power-law behavior for the spectra of
$\Omega_{\rm GW_0}$ with respect to frequency as $\Omega_{\rm GW_0} (f) \sim
(f/f_c)^{n} $ in the proximity of acmes position. As well, in the infrared
regime $f\ll f_{c}$, the log-reliant form of power index as $n=3-2/\ln(f_c/f)$
is attained.
