  The suppression of superconductivity by nonmagnetic disorder is investigated
systematically in the organic superconductor
$\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$. We introduce a nonmagnetic disorder arising
from molecule substitution in part with deuterated BEDT-TTF or BMDT-TTF for
BEDT-TTF molecules and molecular defects introduced by X-ray irradiation. A
quantitative evaluation of the scattering time $\tau_{\rm dHvA}$ is carried out
by de Haas-van Alphen (dHvA) effect measurement. A large reduction in $T_{\rm
c}$ with a linear dependence on $1/\tau_{\rm dHvA}$ is found in the
small-disorder region below $1/\tau_{\rm dHvA} \simeq$ 1 $\times$ 10$^{12}$
s$^{-1}$ in both the BMDT-TTF molecule-substituted and X-ray-irradiated
samples. The observed linear relation between $T_{\rm c}$ and $1/\tau_{\rm
dHvA}$ is in agreement with the Abrikosov-Gorkov (AG) formula, at least in the
small-disorder region. This observation is reasonably consistent with the
unconventional superconductivity proposed thus far for the present organic
superconductor. A deviation from the AG formula, however, is observed in the
large-disorder region above $1/\tau_{\rm dHvA} \simeq$ 1 $\times$ 10$^{12}$
s$^{-1}$, which reproduces the previous transport study (J. G. Analytis {\it et
al.}: Phys. Rev. Lett. {\bf 96} (2006) 177002). We present some interpretations
of this deviation from the viewpoints of superconductivity and the inherent
difficulties in the evaluation of scattering time.

Superconductivity;Strongly Correlated Electrons