The trapping electrons have been used to explore the luminous property of the photoelectric materials.The self-trapping of an electron in a deformable lattice has been maintained interests of many scientists in the past decades.For weak electron-phonon(e-p)coupling

one expects that the electron behaves as a quasi-free particle("free polaron")and should be de-localized over all sites

whereas for very strong coupling it is conceivable that the electron is self-trapped by phonons.Various calculations for the ground-state energies of the polarons as functions of the e-p coupling strength have led to a transition from the quasi-free state to the self-trapped state.This transition phenomenon was also called "phase transition"

though it is not a real phase transition in the general sense.An electron interacts with the acoustic and optical modes of the lattice vibration in a polar crystal.However

the abrupt change of the polaron state from the quasi-free state to the self-trapping state is usually caused by the short-range acoustic interaction

i.e.the electron-longitudinal-acoustic-phonon(e-LA-p)coupling

but not by the long range longitudinal-optical(LO)-phonon interaction.It has been indicated that the acoustic polarons in three-dimensional(3D)bulk materials are difficult to be trapped in most semiconductors and Ⅲ-Ⅴ compounds

even in alkali halides.Otherwise

the e-p coupling effects would be substantially enhanced in confined structures

such as two-dimensional(2D)and one-dimensional(1D)systems

so that the self-trapping transition may be easier to be realized.Farias et al pointed out that the critical e-LA-p coupling constant of the self-trapping transition of acoustic polarons in 2D systems is a certain value and independent of the cutoff wave vector.This conclusion is doubtful in Physics.The ground state energy and effective mass of the acoustic polaron in 2D systems are calculated by using the Huybrechts-like approach in two-step according to the weak and strong e-p coupling ranges.The self-trapping of the 2D acoustic polaron is discussed.The new self-trapping transition point is determined by the intersection point of the lines of ground state energies in weak and strong coupling ranges.It is found that the critical coupling constant of the self-trapping transition of the 2D acoustic polaron shifts toward the weaker e-p coupling with the increasing cutoff wave vector.The characters of the self-trapping of the 2D acoustic polron are qualitative consistent with the previous works of surface polaron and 3D acoustic polaron.There are both the quantitative and the qualitative differences in the critical coupling constants of the self-trapping of the 2D acoustic polarons obtained in this paper and the results given by Farias et al.Our results are more intelligible than that given by Farias et al in sense of the physics.