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Donor impurities and DX centers in the ionic semiconductor CdF2 ... are a complete analog of DX centers in covalent and ionic-covalent semiconductors. The.
Donor impurities and DX centers in the ionic semiconductor CdF2 A. I. Ryskin S. I. Vavilov State Optical Institute, 199034 St. Petersburg, Russia

P. P. Fedorov A. V. Shubnikov Institute of Crystallography, Russian Academy of Sciences, 117333 Moscow, Russia

~Submitted January 22, 1997! Fiz. Tverd. Tela ~St. Petersburg! 39, 1050–1055 ~June 1997!

Group-III impurities in the wide-gap ionic crystal CdF2 are examined. After being heated in a reducing atmosphere, crystals with these impurities acquire semiconductor properties, which are determined by electrons bound in hydrogen-like orbitals near an impurity. Besides these donor states, nontransition impurities form ‘‘deep’’ states accompanied by strong lattice relaxation, i.e. they are strongly shifted along the configuration coordinate. These states are a complete analog of DX centers in covalent and ionic-covalent semiconductors. The difference of the behavior of nontransition impurities from that of transition and rare-earth impurities is analyzed. This difference is attributed to the character of the filling of their valence shells by electrons. A deep, multilevel analogy is drawn between the properties of deep centers in typical semiconductors with an appreciable fraction of a covalent bond component and in predominantly ionic crystal CdF2 with semiconductor properties. © 1997 American Institute of Physics. @S1063-7834~97!02006-6#

Among impurity centers with metastable states ~referred to below as metastable centers!, DX centers which are formed in semiconductors as a result of an additional electron being trapped on a neutral donor impurity and the accompanying radical reconstruction of the center — a displacement of the center-forming impurity or its ligand into the nearest interstitial site — have been attracting a great deal of attention for many years. Such an impurity center has two states: the two-electron ground state with C 3 v symmetry and a metastable single-electron state. In the latter state the donor electron occupies a hydrogen-like orbital centered on an impurity which has returned to the initial site ~after ionization of a C 3 v center!. These two charge states of the center are separated by a vibronic barrier. This has the effect that at a sufficiently low temperature the photoexcited carrier trapped by the ionized donor can exist in this ~metastable! state for an unlimited time, thereby making possible residual photoconductivity, which is the most characteristic property of DX centers. DX centers are of interest on account of both their unique properties and their potentially negative effect on semiconductor devices, limiting their speed of operation. These centers in principle are of interest for information science, since the photocontrolled variation of the optical properties of crystals containing them makes it possible to use such crystals as recording media. Besides the typical covalent and ionic-covalent semiconductors, DX-type metastable centers are well-known in the wide-gap, predominantly ionic crystal CdF2 , with the fluorite structure. Until recently, it was thought that these centers were similar but not identical to DX centers, differing from the latter according to electronic structure, structure, and mechanisms of photo- and thermal conversion. They were considered to be analogous on the basis of the presence of metastable centers and residual photoconductivity. Our in943

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vestigations showed that metastable centers in cadmium fluoride are true DX centers, and this conclusion is the key to further deep study of their nature and properties. In the present paper we present a general picture of the electronic structure of metastable centers in the crystal CdF2 , examine their chemical nature, and discuss their possible structure. 1. DONOR IMPURITIES IN CADMIUM FLUORIDE

After being heated in a reducing atmosphere ~hydrogen, metal vapors!, CdF2 crystals doped with group-III impurities acquire semiconductor properties as a result of the appearance of a shallow donor level associated with these impurities.1,2 The depth of this level varies for different impurities in the range 0.10–0.11 eV.3 The mechanism of the formation of a donor center can be described as follows. According to the standard conditions for growing crystals in a fluoridizing atmosphere, solid solutions of the fluorides of trivalent ions in cadmium fluoride are heterovalent solutions in which the isomorphism of the cations is realized by substitution in the cation sites in the lattice, and the excess valence of the group-III cation is compensated by additional interstitial fluorine ion ~Fig. 1!. The electrostatic interaction of a trivalent cation with this ion can result in the formation of corresponding dipoles.4,5 Such dipoles could not be found in cadmium fluoride by the method of thermally stimulated depolarization. This failure was taken to mean that nonlocal charge compensation predominates in the solid solutions Cd12x Rx F21x ~R 5 In, La, Gd!.6 Under heating in a reducing atmosphere ~additive coloring of the crystals!, interstitial F2 ions diffuse from the volume to the surface and in the process their electrons are trapped by impurity ions and occupy hydrogen-like orbitals near them, forming donor centers. The photoionization of these elec-

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© 1997 American Institute of Physics

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FIG. 1. Cadmium fluoride lattice with donor impurities (A 31 ).

trons is responsible for the wide absorption band ~covering the near- and middle-IR regions of the spectrum up to ;10 m m!. 2. METASTABLE CENTERS, THEIR ELECTRONIC STRUCTURE, AND MECHANISMS OF THEIR PHOTO- AND THERMAL CONVERSION

Indium and gallium occupy a special place among group-III impurities in cadmium fluoride. Additive coloring of the crystals with these atoms results in the appearance of, besides donor states, which for these impurities are metastable ~‘‘shallow’’ centers!, also states which are strongly displaced relative to them along the configuration coordinate ~‘‘deep centers’’! ~Fig. 2!. The thermal ionization energy of these centers is only two to three times higher than that of shallow centers, i.e., it is of the order of tenths of an eV, while their optical ionization energy is very high on account of the large configurational displacement and is equal to ;2.5 eV for indium and ;3.7 eV for gallium. The photoionization absorption band for indium encompasses the UV region of the spectrum from the fundamental absorption limit

FIG. 2. Configuration diagram for a metastable center in cadmium fluoride. 944

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FIG. 3. Absorption spectrum of crystal CdF2 :In cooled to T55 K in the dark ~1! and illuminated in the UV–visible absorption band ~2!.

of crystal CdF2 (;0.2 m m) and a substantial part of the visible region; for gallium, it is shifted into the shortwavelength region of the spectrum.7,8 Light absorption in this band at a sufficiently low temperature causes the band to vanish ~photobleaching of the crystals!. This is accompanied by the appearance of an IR absorption band, indicating that deep centers are converted into shallow centers ~Fig. 3!. This process, which results in an appreciable photoinduced change in the optical constants of the crystal, was recently employed to record holographic phase gratings in CdF2 crystals with metastable centers in the region of transmission between the indicated bands.9–11 Just as in the case of DX centers in typical semiconductors, the existence of the configurational shift between the shallow and deep states of a Me center ~Me 5 In, Ga! and of a vibronic barrier separating these states gives rise to residual photoconductivity, which reflects the existence of a metastable state in equilibrium with the conduction band. In Ref. 12 a similarity was noted between the impurities under study and DX centers, but a difference between them was also postulated. The difference is that for the latter the formation of a deep state occurs when an additional electron is trapped by a neutral donor,13 while for metastable impurities in cadmium fluoride electron localization either on an inner, predominantly atomic, ns orbital ~valence state of the Me21 impurity, deep center! or in a hydrogen-like orbital near the ionized impurity ~Me31 1 e hydr , shallow center!7,8 corresponds to two states of the center. This difference was attributed to the substantially different character of the chemical bond in typical semiconductors and in cadmium fluoride. According to this concept, In and Ga centers in additively colored CdF2 crystals were regarded as an example of impurity self-trapping!,8,14,15 proposed by Toyozawa on the basis of his general theory of self-trapped states.16–18 Our investigation of photo- and thermal conversion of deep and shallow centers in CdF2 :In and CdF2 :Ga crystals showed that for these impurities as well the state of a center does indeed change as a result of a change in the charge on it. Indeed, the quantum yield for the photochemical reaction A. I. Ryskin and P. P. Fedorov

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forming shallow centers from deep centers is h '2 ~Ref. 19! and the bimolecular character of the thermal decay kinetics of shallow centers11,19 indicates that two single-electron shallow centers form when a single deep center decays and correspondingly they participate in the formation of this center. Hence it follows that the deep state of a center corresponds to the localization of two electrons on it, i.e., to its formally univalent state Me11 . It is obvious that the localization of two electrons in a single orbital is energetically unfavorable because of their Coulomb interaction, but this is compensated by the large relaxation of the lattice, which is responsible for the negative value of the Hubbard correlation energy U for a deep state. The direct proof of the negative-U nature of this state was obtained in experiments measuring the magnetic susceptibility of crystal CdF2 :In, which showed that there is no magnetic moment in the deep state of the In center and a magnetic moment ~with angular momentum J51/2, determined from the field dependence of the susceptibility! appears when the shallow state is filled as a result of photobleaching of the crystals.20,21 The experimental data mentioned above show, when taken together, that in the reduced ~additively colored! CdF2 crystal with metastable centers, which is cooled in the dark to a temperature at which shallow states are virtually unoccupied, half of the impurities are in the state Me31 , i.e., they have no valence electrons, and the other half are in the state Me11 , i.e., there are two electrons in the valence shell. In principle, all Me31 ions could be subjected to reduction in the course of the reducing chemical reaction ~additive coloring of the crystals!; in this case ~besides migration of the interstitial F2 ions!, vacancies should appear in the anion sublattice, which would correspond to a transition from anion-rich to anion-deficient solid solutions. However, this does not happen, and only half of the Me31 ions are reduced. Photobleaching of the reduced crystals results in the formation of shallow centers ~Me31 1 e hydr ) on the basis of both ions ~Me31 , Me11 ). Since the trapping of an electron, freed from a shallow center by heating, on a different shallow center ~i.e. formation of a deep center! requires that a potential barrier be overcome, trapping is possible only at a sufficiently high temperature, exceeding ;20 K for indium and ;200 K for gallium. An electron can be freed from a shallow center by IR radiation as well, but electron trapping accompanied by the formation of a deep center is, in any case, a thermally activated process.19 Therefore, the mutual transformation of metastable centers in cadmium fluoride occurs according to the reactions 2 ~ Me31 1e hydr ! 1kT→Me11 1 Me31 , Me11 1 Me31 1h n →2 ~ Me31 1e hydr!

~1!

What we have said above shows that with respect to electronic structure and photo- and thermal conversion processes Me centers in the predominantly ionic CdF2 crystal are identical to DX centers in covalent and ionic-covalent semiconductors, and this is how they should be classified. 945

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3. SPECIFIC NATURE OF NONTRANSITION AND TRANSITION (RARE-EARTH) IMPURITIES

Two obvious questions arise: Why are indium and gallium unique? Why do these elements form metastable DX centers in cadmium fluoride while other group-III impurities ~Sc, Y, La, rare-earth elements! form only shallow donor levels? The answer should be sought in the order in which the electronic shells of group-III atoms are filled. For nontransition elements of this group, the ns valence shell, whose stable state corresponds to an occupation number of 0 or 2, i.e., the valence states Me31 or Me11 , is filled. Indeed, for indium and gallium only these two charge states are known. Many investigations using diverse methods for studying the composition and structure of the compounds of these elements in the gas phase, in solutions, in melts, and in a crystalline state show that all compounds with an apparent intermediate valence contain uni- and trivalent In and Ga cations in different ratios;21–24 divalent indium is observed only in the form of a transient, short-lived state.25,26 In the series of nontransition elements Al–Ga–In–Tl the relative stability of the univalent states increases from top to bottom, so that univalent thallium is completely stable while a definite problem arises in obtaining univalent gallium, and univalent aluminum is not reliably obtained in the solid state. Since the valence state Me21 does not form for the reason given above, one electron can be localized on a Me31 ion only in a hydrogen-like orbit, whose existence is determined by the characteristics of the crystal matrix, among which, specifically, the electron affinity of its cations ~but not alone! is important. Therefore, for nontransition group-III impurities in additively colored CdF2 crystals, either the Me11 state ~ground state! or the Me31 state with an electron localized on the cations near this ion Me31 1 e hydr ~metastable state! is realized. Up to now, metastable centers have been observed in cadmium fluoride for indium and gallium. Their existence cannot be ruled out for other nontransition impurities of this group ~Tl, Al, B! as well. The maximum solubility of trifluorides of these elements can be estimated as a function of their ionic radius with the aid of a Gaussian form of empirical dependence obtained for RE trifluorides27 x50.34 exp@ 250~ r21.175! 2 # ,

~2!

where x is the mole fraction of the corresponding trifluoride in the solid solution and r is the Shannon ‘‘crystalline’’ ionic radii of the cations for coordination number 8.28 A calculation for the compound InF3 using r In 51.06 Å gives x50.175 ~17.5 mol.%!, which agrees satisfactorily with the experimental value of 0.14, determined in Ref. 29 for a temperature of 750 °C. Substituting into the relation ~2! r Tl51.12 Å, r Ga50.78 Å, and r Al50.695 Å we obtain x50.33 (33 mol.%), 0.00016 (1.6•1022 mol.%!, and 0.0000034 (3.4•1024 mol%! for Tl, Ga, and Al trifluorides, respectively ~for gallium and aluminum, the octahedral ionic radii multiplied by a correction factor of 1.03 were used!. Such low values for the last two compounds indicate the difficulty of doping CdF2 crystals with the corresponding impurities, especially aluminum. We note, however, that Eq. ~2! may be inapplicable for comparing small cations because A. I. Ryskin and P. P. Fedorov

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of a decrease of the coordination number and a change in the substitution mechanism. Boron doping is apparently completely unrealistic because of its very small radius. Conversely, the solubility of thallium should be higher than that of indium. The situation is fundamentally different for transition impurities. For scandium, yttrium, and lanthanum the first electron ~after the (n21)s and (n21) p shells of the TM31 ion; TM — means transition metal! are filled! occupies the (n21)d shell and the second electron occupies the ns shell. The presence of one electron in an inner d shell, interacting weakly with the environment ~compared with the corresponding s shell!, is in principle possible. Group-III transition impurities can be in a divalent state, corresponding to the electronic configuration (n21)d 1 , at least in the calcium, strontium, and barium fluorides, which are isostructural with cadmium fluoride, and in strontium chloride.30 For these crystals, localization of an electron in a hydrogen-like orbit is energetically unfavorable and does not occur. Conversely, in cadmium fluoride the ground state is such a ~donor! state ~Tm31 1e hydr ) and the TM21 state is metastable, possibly lying in the conduction band, and has still not been observed. For the transition-group impurities under study the presence of two ‘‘additional’’ electrons in atomic shells, after additive coloring of the crystal, would correspond to the electronic configuration (n21)d 1 ns 1 , which is chemically unstable because of the presence of an unpaired s electron. Such a configuration, which could be compared with the hypothetical deep center, is evidently not realized, and these impurities form only a shallow donor state in cadmium fluoride. Just as for transition elements, for trivalent rare-earth impurities in cadmium fluoride an additional electron is localized in an energetically more favorable hydrogen-like orbital and not in a 4 f orbital. An exception is europium, which on coloring is transferred into a divalent state Eu21 ~Ref. 31 !, just like many rare-earth elements in alkalineearth metal fluoride!. Trapping of two electrons in atomic shells is impossible for trivalent rare-earth ions, since this would result in the appearance of an unstable @ # 6s 1 -configuration. These impurities, analogously to transition elements, do not form a deep state in cadmium fluoride. Hence, in our model of the nature of In and Ga centers in crystal CdF2 the metastable character of the nontransition and donor character of the transition and rare-earth impurities find a natural explanation on the basis of the most general quantum-mechanical considerations; this can be regarded as an independent ~and quite convincing! confirmation of these ideas. 4. STRUCTURE OF METASTABLE CENTERS

We shall examine one other important circumstance relating to the structure of metastable centers in cadmium fluoride. Lattice relaxation, which gives rise to a Coulombically unfavorable two-electron state of a DX center, in typical semiconductors is as a rule not completely symmetric and leads to a radical reconstruction of the center accompanied by a displacement of the impurity or its ligand out of a lattice site into an interstitial region.13,32,33 946

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Two electrons in the ns valence shell of a deep center Me11 form a so-called lone pair of electrons that does not directly participate in the formation of a chemical bond. It is stereochemically active, i.e. it is directed and requires a definite space to occupy,34 which is why a deep center cannot possess the cubic symmetry characteristic for the substituted site. Therefore it can be expected, even without constructing a concrete model of a center, that even in this case the formation of a two-electron state is accompanied by reconstruction with a lowering of the symmetry of the center, which should be facilitated by the existence of interstitial sites in the fluorite structure. The conjecture that reconstruction of the center occurs also explains the very high ~exceeding 2 eV! relaxation energy of a photoionized deep center ~for gallium this energy equals about 3 eV!: Completely symmetric relaxation of the lattice is unlikely to provide, as assumed in Refs. 7 , 12 , 35, and 36 , such a high energy. For example, for F centers in the maximally ionic alkali-halide crystals the Stokes shift between the absorption and luminescence bands, which characterizes the completely symmetric relaxation accompanying a change in the state of the center, does not exceed 2.1–2.2 eV ~NaF, KF ~Ref. 37!!. High relaxation energies are achieved in the case when the change in the state of a center is accompanied by a incompletely symmetric distortion of the center. For example, for a F A center which is reoriented under excitation (F center associated with a Li ion! in KCl the Stokes shift equals ;1.7 eV, while for a F center in the same crystal the shift equals ;1.1 eV.37 We underscore in this connection that for a large relaxation of the lattice the important fact is not that the distortion of the lattice incompletely symmetric but rather the radical character of the reconstruction of the center: For a comparatively ‘‘soft’’ Jahn– Teller distortion of mercury-like ions in the same matrices the typical energies are 0.3–0.8 eV.38 We also note that the lone-pair concept employed above refers to compounds with a quite pronounced covalent component of the chemical bond in which the lone pair compensates the absent chemical bond. This concept is inapplicable to purely ionic crystals. For this reason, in contrast to cadmium fluoride, the ground state of mercury-like impurities Me11 in alkali-halide crystals ( 1 S 0 ) is spherically symmetric. Therefore, despite the different coordination of the impurity, the structure of the crystal matrix, and the quite large difference in the character of the chemical bond, the electronic structure and transformation processes of metastable centers in classical semiconductors with covalent and ioniccovalent bonds and in predominantly ionic CdF2 crystals with semiconductor properties are so similar that this justifies classifying these centers in cadmium fluoride as true DX centers, identical to their analogs in typical semiconductors. The analogy would be complete, if it were proved that the formation of a deep center is accompanied ~promoted! by an incompletely symmetric distortion of its structure. As shown in the preceding section, there is every reason to expect such a reconstruction of a center. Future experiments and calculations should confirm this conjecture. The mere presence of two charge states of the impurity ion ~Me11 and Me31 ), which differ by 2 in the number of A. I. Ryskin and P. P. Fedorov

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valence electrons ( d n52), is nontrivial for the predominantly ionic crystal CdF2 , though for classical semiconductors such states are commonplace. Besides DX centers in them ( d n52), we should mention 3d impurities for which d n can be 3 ~GaAs:Cr!. The presence of states with such radically different charge is due to a substantial hybridization of the impurity orbitals with band states. Imitating the symmetry of the atomic states, such hybridization transforms the energy scale of ionization transitions from the atomic to crystalline and thereby enables the realization of a number of valence ~charge! states in the semiconductor which for free atoms differ very strongly in energy ~see Ref. 39 !. The existence of metastable DX centers in the ionic semiconductor CdF2 shows that such hybridization of the states is characteristic for it as well. We thank P. I. Fedorov and A. S. Shcheulin for a helpful discussion of a number of questions considered in this paper as well as E. Langer for familiarizing us with the results of his early investigations on cadmium fluoride. This work is supported by the Russian Fund for Fundamental Research under Grant No. 96-02-19632. J. D. Kingsley and J. S. Prener, Phys. Rev. Lett. 8, 315 ~1962!. P. F. Weller, Inor. Chem. 4, 1545 ~1965!. 3 J. M. Langer, T. Langer, G. L. Pearson. B. Krukowska-Fulde, and U. Piekara, Phys. Status Solidi B 66, 537 ~1974!. 4 J. Corish, C. R. A. Catlow, P. W. M. Jacobs, and S. H. Ong, Phys. Rev. B 25, 6425 ~1982!. 5 I. V. Murin and W. Gunsser, Solid State Ion. 53-56, 837 ~1992!. 6 I. Kunze and P. Muller, Phys. Status Solidi A 13, 197 ~1972!. 7 U. Piekara, J. M. Langer, and B. Krukowska-Fulde, Solid State Commun. 23, 583 ~1977!. 8 J. E. Dmochowski, W. Jantsch, and J. M. Langer, Acta Phys. Pol. A 73, 247 ~1988!. 9 A. I. Ryskin, A. S. Shcheulin, B. Koziarska, J. M. Langer, A. Suchoski, I. I. Buczinskaya, P. P. Fedorov, and B. P. Sobolev, Appl. Phys. Lett. 67, 31 ~1995!. 10 B. Koziarska, J. M. Langer, A. I. Ryskin, A. S. Shcheulin, and A. Suchocki, Acta Phys. Pol. A 88, 1010 ~1995!. 11 A. S. Shcheulin, E. V. Milogliadov, A. I. Ryskin, D. I. Stasel’ko, I. I. Buchinskaia, P. P. Fedorov, and B. P. Sobolev, Opt. Spektrosk. ~in press!. 12 J. M. Langer, Rev. Solid State Sci. 4, 297 ~1990!. 1 2

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Translated by M. E. Alferieff

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