BOUND TO UNBOUND STATE TRANSITION OF HYDROGENIC DONORS IN SEMICONDUCTORS WITH A STATIC, SCREENED COULOMB POTENTIAL - A TRIAL ON VARIATIONALCALCULATION

The ground state energy of a hydrogenic donor in the static screened C oulomb potential for single-valley semiconductors is calculated as a f unction of the screening wavenumber q(s) by use of the variational pri nciple. We employ a more realistic variational wavefunction rather tha n a hydrogenic one in consideration of the gentle extinction of the tr ue wavefunction in the radial direction due to the strong screening. T he effective Bohr radius a I,of a screened hydrogenic donor and the av erage distance [r] of the bound electron from the positive donor atom are also obtained as a function of q(s). We obtained the result that t he critical value of q(s)a(B) for the unbound state was 1.13, compared with 1 for a hydrogenic type, with an effective Bohr radius a(B) of a n isolated hydrogenic donor. It is found that the Mott concentration i s given by N(c)(1/3)a(B) = 0.325 at q(s)a(B) = 1.13 for our calculatio n (N(c)(1/3)a(B) = 0.254 at q(s)a(B) = 1 for the hydrogenic type) if w e assume Thomas-Fermi screening and the equal concentration of free el ectrons and donors at the nonmetal-metal transition (Mott Transition) point. (C) 1997 Elsevier Science Ltd. All rights reserved.