  Owing to the Klein tunneling phenomenon, the permanent confinement or
localization of electrons within a graphene quantum dot is unattainable.
Nonetheless, a constant magnetic field can transiently ensnare an electron
within the quantum dot, giving rise to what are known as quasi-bound states
characterized by finite lifetimes. To prolong the retention of electrons within
the quantum dot, we introduce a mass term into the Hamiltonian, thereby
inducing an energy gap. We resolve the Dirac equation to ascertain the
eigenspinors, and by ensuring their continuity at the boundaries, we
investigate the scattering behavior. Our findings indicate that the presence of
an energy gap can extend the lifetimes of these quasi-bound states within the
quantum dot. In particular, we demonstrate that even in the absence of a
magnetic field, the scattering efficiency attains significant levels when the
energy gap gets closed to the incident energy of an electron traversing the
quantum dot. It is found that an augmentation in the electron density within
the quantum dot results in an enhancement of the electron-trapping time.
