In this paper, a coupled 6×6 Hamiltonian valence eigenfunction is considered using effective mass approximation. Using a trial wave function separable in z direction and x-y plane, variational calculations are presented for energies of ground state and first excited state of heavy hole exciton and binding energies in ZnO film, and for radius of exciton under a variety of thickness d of ZnO film. And the correction of energies due to quantum tunnel effect of electronic wave function with the thickness d<2.0 nm is discussed.
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