Effect of intersite electron-electron interaction on the concentration of ${\mathrm{D}}^{\mathrm{-}}$ ions in quantum wells

Ground-state ${\mathrm{D}}^{\mathrm{-}}$ concentrations in quantum-well structures which are lightly doped in both the barriers and wells are investigated by means of computer simulation. Correlation between electrons on different sites is found to play an important role in the formation of ${\mathrm{D}}^{\mathrm{-}}$ centers in these structures. A two-dimensional model of the system of interest is studied. Pseudo-ground-states, calculated for model systems of finite size, are argued to give estimates of ${\mathrm{D}}^{\mathrm{-}}$ concentrations for the ground states of infinite model systems accurate to within a few percent. Qualitative agreement is found with the available experimental data. A previously proposed pair model is observed to be very accurate in cases in which the binding energy of isolated barrier donors is significantly greater than that of ${\mathrm{D}}^{\mathrm{-}}$ centers in the well. An empirical formula is given for the dependence on the size of the system of the probability that a pseudo-ground-state is also an exact ground state. © 1996 The American Physical Society.