Properties ofD−centers in polar crystals

The problem of $D^{\mathrm{-}}$ centers in polar semiconductors and ionic crystals is theoretically studied under assumption of the Fröhlich electron–LO-phonon coupling. The $D^{\mathrm{-}}$ binding energy is calculated with use of the method of optimized canonical transformation, which yields an improvement of the results of Larsen [Phys. Rev. B 23, 628 (1981)]. Moreover, the present paper provides the first estimates of the average interparticle distances for the $D^{\mathrm{-}}$ state. It follows from these results that $D^{\mathrm{-}}$ centers exhibit a great variety of properties depending on the material parameters describing the electron-phonon coupling in a crystal. In nonpolar crystals, the $D^{\mathrm{-}}$ center can be treated as a simple analogue of the ${\mathrm{H}}^{\mathrm{-}}$ ion with the binding energy equal to 0.0555 of the donor rydberg. In the majority of polar crystals, the binding of $D^{\mathrm{-}}$ centers is enhanced in comparison with the nonpolar case due to the electron-phonon coupling. However, for the crystals, for which the donor potential is relatively weak and the electron-phonon coupling is of an intermediate strength, a decrease of the binding and even an instability of the $D^{\mathrm{-}}$ center is possible. A completely different behavior of $D^{\mathrm{-}}$ states has been found in the region of strong electron-phonon coupling. It has been shown for the first time that the sufficiently large Fröhlich coupling induces the negative-U properties of donor impurities, i.e., the system composed of $D^{\mathrm{-}}$ and $D^{+}$ donor centers is more stable than the two neutral donors. The present paper provides a new mechanism for the negative-U behavior of defects, which is based on the Fröhlich electron–LO-phonon interaction.