Metastability and lattice relaxation forD0andD−donor centers

Abstract

Properties of strongly localized one-electron ${(D}^{0})$ and two-electron ${(D}^{\ensuremath{-}})$ donor centers in semiconducting compounds are studied with the help of the theoretical approach, which takes into account the influence of the conduction-band states and interactions with LA and LO phonons. The eigenvalue problem has been solved for the ground states of both the centers by the variational method in the wave-vector space. The description is given of the properties of the ${D}^{0}$ and ${D}^{\ensuremath{-}}$ donor centers in GaAs under hydrostatic pressure. The calculated energy levels and pressure coefficients agree with the experimental results. Upper and lower bounds have been obtained for probabilities of radiative transitions from the extended electron states to the strongly localized ${D}^{\ensuremath{-}}$ donor states. A large reduction received for these transition probabilities has been interpreted in terms of metastability of the donor centers. It is shown that the metastable behavior of donor centers results from a large difference in a lattice deformation around the center, which occurs between the states of different electron localization. It is found that the ${D}^{\ensuremath{-}}$ center at the substitutional position in GaAs exhibits the properties that are characteristic for the $\mathrm{DX}$ center. The phonon representation of lattice vibrations has been applied to calculate the displacements from equilibrium positions of the ions surrounding the donor centers of different charge and localization. The results show that---even for the strongly localized donor state---the surrounding-lattice deformation encompasses a large number of ions. The number of ions that essentially contribute to the lattice relaxation energy is estimated to be several thousand. The present work takes into account the long-range component of the lattice deformation induced by the presence of the impurity in a crystal.