Effects of position-dependent effective mass and dielectric function of a hydrogenic donor in a quantum dot

Abstract

Ionization energies of a shallow donor in a quantum dot of GaAs, using a variational procedure within the effective mass approximation, are obtained. Calculations are presented with a constant effective mass and position-dependent effective masses along with the spatially varying dielectric function. Donor binding energies are calculated using both the approximate method ( m 0 * ) and the spatially varying electron effective mass, m * ( r ) . Dielectric quantum dots are discussed and calculations are performed with the dielectric constants of the dot ε 1 and that of the barrier material, ε 2. It is found that (i) the use of a constant effective mass (0.067 m 0) is justified for dot size ⩾ a*, where a* is the effective Bohr radius, which is about 100 Å for GaAs, in the estimation of ionization energy, (ii) the ionization energy decreases as the dot increases in both the cases of constant and variable masses, (iii) an increase of binding energy is observed when the spatially varying mass and dielectric function are included, (iv) lower binding energies are observed when the average dielectric constant is included and (v) the binding energy shows complicated behaviour when the position-dependent mass is included for the dot size ⩽ a*.