  We systematically calculate the quantum extremal surface (QES) associated
with Hawking radiation for general $D$-dimensional ($D\geq2$) asymptotically
flat (or AdS) eternal black holes using the island formula. We collect the
Hawking radiation particles by a non-gravitational bath and find that a QES
exists in the near-horizon region outside the black hole when $c\cdot G_{(D)}$
is smaller enough where $c$ is the central charge of the conformal matter and
$G_{(D)}$ the $D$-dimensional Newton constant. The locations of the QES in
these backgrounds are obtained and the late-time radiation entropy saturates
the two times of black hole entropy. Finally, we numerically check that the no
island configuration exists once $c\cdot G_{(D)}$ exceeds a certain upper bound
in two-dimensional generalized dilaton theories (GDT). When $c\cdot G_{(D)}$ is
close to the upper bound, the backreaction of the matter field on the
background can not be neglected. We also consider the conditions of existence
of the island configuration with the backreaction and prove that the upper
bound also exists for the Witten black hole and Weyl-related Witten black hole.
