The bound exciton to an ionized donor impurity in semiconductor spherical quantum dot

The effects of quantum confinement on the ground state energy of a bound correlated electron-hole pair as an exciton to an hydrogenic ionized donor impurity which placed at the center of an infinite spherical microcrystal in interior dielectric medium have been investigated constitutively as a function of quantum dot size. Most of formulas and results obtained are compared for cases with and without impurity or have been checked for accuracy in a number of special case. A mathematically rigorous study confirms, in a unified and simpler manner, several results obtained earlier in the literature but not necessarily in the same contexts. Unlike the conventional procedure, the Fourier transforms have been used for evaluating three-particle integrals terms including interparticle distance rij in Hylleraas coordinates are given formulae are obtained for the Hamiltonian matrix elements of various operators arising in Hyleeraas-type variational calculations for states of arbitrary angular momenta.The integrals have been generated from Hamiltonian matrix are well suited to computer implementation. To construct an exact analytical expression for the expectation value of the Hamiltonian have been used a numerically fast and well stable algorithm for the calculation of the relevant integrals with high powers of interparticle coordinates. The optimum value of the variational parameter have been vary in the range of lambda=[0.055,0.300].The behaviors of the complexes X and D+,X are similar cause of the values of the two additional interparticle interaction integral terms I(G1) and I(G2) are completely the same by a difference opposite notation. Consequently the main inference is that injecting a donor impurity to the X complex would not change the stationary state of the system.