We have identified the microscopic structures for the shallow and deep donor states of Ga and In donor impurities in CdF 2 through first-principles calculations. The deep state arises from a large ͓100͔-axis atomic displacement of a donor. It has all the properties of a DX center; i.e., it is negatiyely charged and is separated from the metastable substitutional state by a large energy barrier that leads to persistent photoconductivity. [S0031-9007 (98)08097-1] PACS numbers: 61.72.Ji, 61.72.Bb, 61.72.Ww, 71.55.HtThe phenomenon of bistability in which a dopant atom has both effective-mass hydrogenic ("shallow") and highly localized deep states is well known in many III-V and II-VI zinc blende semiconductors and has been extensively studied [1,2]. Surprisingly, the same type of bistability is observed in the very-large-band-gap fluorite structure compound CdF 2 when doped with Ga or In donor impurities [3][4][5][6][7][8][9][10]. Experimental data on the absence of a paramagnetic moment for the deep center [5], a quantum yield of two electrons per photon for the deep-shallow transition [6], the bimolecular nature of the shallow center thermal decay [4,6], self-compensation, a relatively large energy barrier between the shallow and deep states [6], a large Stokes shift between thermal and optical ionization energies, persistent photoconductivity [3], photoinduced lattice shrinkage [8], and recent positron annihilation measurements [11] showing an open-volume defect occurring upon DX center formation indicate that the deep center in In-and Ga-doped CdF 2 is a negative-U center with a large lattice relaxation. The bistability of Ga in CdF 2 has aroused great interest in this material as a new type of photorefractive medium [12,13]. Optical excitation of DX centers leads to a change in the refractive index that may have potential applications in high sensitivity optical recording and provides advantages as compared to a conventional nonlinear material such as LiNbO 3 [7].The band gap of CdF 2 is about 7.8 eV and the bonding is highly ionic. The crystal structure is O 5 h ͑Fm3m͒ cubic [14]. The F atoms, by themselves, make a simple cubic structure with a lattice constant of 2.677 Å. Cadmium atoms are located at the centers of alternate F cubes so that half the cubes are filled while the other half are empty (Fig. 1a). This leads to a structure in which each F atom is tetrahedrally bonded to four Cd atoms, while each Cd atom is bonded to eight F atoms. Despite its large band gap, CdF 2 can be doped n type by the incorporation of Ga or In. The shallow effective-mass state has a binding energy of about 0.1 eV and is metastable with respect to the deep donor DX state.The DX center in zinc blende semiconductors arises mainly from large atomic displacements along antibonding directions, either at the impurity or at a nearestneighbor cation [2,15]. In the fluorite structure, a similar lattice relaxation is inhibited by the eightfold coordination of a substitutional donor on a Cd site. Originally, Langer suggested a totally symm...