Electron statistics in CdF2 semiconductor crystals with DX centers

The degree of compensation and ionization energy of two-electron DX centers in CdF₂: In and CdF₂: Ga semiconductors are determined by studying the statistical distribution of electrons localized on impurity levels. The sharp temperature dependence of the concentration of neutral donors observed in CdF₂: Ga over the temperature range T = 250–400 K is explained by a high compensation degree, K ≥ 0.996. Thus, all Ga ions introduced into a CdF₂ crystal lattice during crystal growth form shallow donor levels. However, the concentration of Ga ions that can form bistable DX centers is rather low and is close to the concentration of electrons injected into the crystal during additive coloring. In CdF₂: In crystals, the degree of compensation is smaller than that in CdF₂: Ga but is sufficiently high and the number of bistable DX centers is not limited. It is concluded that an extremely narrow impurity band forms in the CdF₂: Ga semiconductor. For a total charged-impurity concentration of ～10²⁰ cm^?3, the width of the impurity band in CdF₂: Ga is not likely to exceed ～0.02 eV.     

Optical spectra of (CdF2)0.9(InF3)0.1 semiconductor solid solutions

The differences in the optical spectra of CdF₂:In semiconductors with bistable DX centers (concentrated (CdF₂)_0.9(InF₃)_0.1 solid solutions) and “standard” samples with a lower impurity concentration used to record holograms are discussed. In contrast to the standard samples, in which complete decay of two-electron DX states and transfer of electrons to shallow donor levels may occur at low temperatures, long-term irradiation of a (CdF₂)_0.9(InF₃)_0.1 solid solution by UV or visible light leads to decay of no more than 20% deep centers. The experimental data and estimates of the statistical distribution of electrons over energy levels in this crystal give the total electron concentration, neutral donor concentration, and concentration of deep two-electron centers to be ～5 × 10¹⁸ cm^?3, ～9 × 10¹⁷ cm^?3, and more than 1 × 10²⁰ cm^?3, respectively. These estimates show that the majority of impurity ions are located in clusters and can form only deep two-electron states in CdF₂ crystals with a high indium content. In this case, In³⁺ ions in a limited concentration (In³⁺ (～9 × 10¹⁷ cm^?3) are statistically distributed in the “unperturbed” CdF₂ lattice and, as in low-concentrated samples, form DX centers, which possess both shallow hydrogen-like and deep two-electron states.     

Properties of CdF2:Ga as a medium for real-time holography

The metastable nature of the excited state of bistable Ga centers in semiconducting CdF₂ crystals allows for the use of CdF₂:Ga and CdF₂:Ga,Y crystals as materials for real-time holography over a wide range of response times (1–1000 ms). The characteristics of these materials and optimal conditions for their use are discussed in the framework of a model that describes the decay of photo-induced gratings written in them. Received: 20 November 2000 / Published online: 20 April 2001     

New class of holographic materials based on semiconductor CdF2 crystals with bistable centers: III. Mechanisms of recording and decay of holographic gratings

The mechanisms of recording and decay of holographic gratings in CdF₂ crystals with bistable gallium or indium centers are considered. The analysis of the decay kinetics allows one to determine potentialities and conditions for using these crystals both for static recording of holograms and for holography in real time. This time scale is fairly broad and covers the time range from 1 s to 10 μs or shorter. Energy characteristics of the bistable centers, namely, the binding energies of the deep and shallow levels and heights of the barriers between them, are refined.     

Microwave measurements of electrical conductivity of CdF<Subscript>2</Subscript> semiconductor crystals

The electrical conductivity of CdF₂ semiconductor crystals is measured using the microwave intracavity technique at a frequency of ～35 GHz. The crystals are activated with yttrium donor impurities and indium and gallium ions forming bistable one-electron donor impurity and two-electron DX centers. The conclusion is drawn that the concentration of electrons in the conduction band of CdF₂: Ga crystals has an anomalously high value. This confirms the results obtained in earlier NMR investigations of CdF₂ semiconductor crystals at room temperature.     

Photodielectric effect and “Configuration” modes of bistable centers in the CdF<Subscript>2</Subscript>: Ga crystal

A photoinduced increase in the real (?′) and imaginary (?″) parts of the permittivity (Δ?′ ≈ 0.23 and Δ?″ ≈ 0.10 at a frequency of 15 cm^?1) is revealed experimentally. This photodielectric effect is adequately described by the predicted configuration modes at the frequencies gv ₁ = 354 cm^?1 and gv ₂ = 123 cm^?1, which correspond to the potential-energy curves previously calculated for deep and shallow impurity states in CdF₂: Ga crystals. The dielectric contributions of these modes are determined, and the corresponding concentrations of Ga ions in deep (N ₁) and shallow (N ₂) impurity states are calculated. It is found that, unlike the CdF₂: In crystals, the changes in the quantities ?′ and ?″ before and after illumination of the CdF₂: Ga crystals are predominantly determined by the change in the contribution from the configuration mode of the shallow state, because the contribution from the configuration mode of the deep state is very small. A photoinduced decrease in the lattice reflection in the CdF₂: Ga crystals due to the change in the dielectric contribution from the impurity mode of the lattice is predicted.     

Paramagnetic susceptibility of additively colored CdF2:In photochromic crystals

The paramagnetic susceptibility K _para of CdF₂:In crystals with metastable indium centers has been measured in darkness after photobleaching the crystals in visible light in the temperature interval 4–300 K. For crystals cooled in darkness to liquid-helium temperature K _para is wholly determined by the accompanying impurity Mn²⁺ with magnetic moment J=5/2. Illumination of the crystals leads to the appearance of an induced signal δ K _para due to the formation of centers with J=1/2. The results of the experiments indicate the absence of paramagnetism in the deep state of the indium center and its existence in the shallow (donor) state, i.e., they confirm the two-electron (negative-U) nature of the deep indium level in CdF₂. Fiz. Tverd. Tela (St. Petersburg) 39, 1205–1209 (July 1997)     

New class of holographic materials based on CdF<Subscript>2</Subscript> semiconductor crystals with bistable centers. I. Role of covalence in the formation of bistable centers

Calculations of the electronic structure of In, Ga, and Al impurity centers in a CdF₂ crystal in the cluster approximation using the method of scattered waves are made. The first two impurities form in additively colored crystals bistable centers having a ground two-electron (deep) state and a metastable hydrogen-like (shallow) state. A change in the nature of the chemical bond on doping a crystal with these impurities is traced, which consists in a considerable increase of its covalent component. A change for deep In and Ga centers is shown to be caused by the reconstruction of centers in their ground state, and a conclusion about the character of reconstruction is made. This conclusion agrees with recent calculations made for the center structure using the pseudopotential method. Conditions of formation of bistable centers in CdF 2 and their structure in different charge states are discussed.     

Relaxation processes upon photoexcitation of semiconductor CdF<Subscript>2</Subscript> by laser pulses

The microwave-cavity-based technique is used to study the processes of photoionization of electrons from donor levels to the conduction band in semiconductor CdF₂ crystals doped with Y, In, or Ga. The samples were excited by periodic pulses of Nd-laser (λ = 1.06 μm, pulse width ～10 ns) in the temperature range 6–77 K. The transient processes were detected in the absorption and dispersion modes related to variation of the imaginary and real parts of the complex permittivity ?₁ ? i?₂ induced by the light pulses. The observed signals consisted of short peak at t ～ 0, approximately 40–70 ns in length, and a long tail with a duration of ～100 ms. The short peak is likely to be related to the stay of the photoexcited carriers in the conduction band, while the long tail is associated with the processes of excitation relaxation after the electrons coming back to the donor levels of the impurity band. The weak temperature dependence of the width of the peak at t ～ 0 is explained by the tunneling mechanism of relaxation of electrons through the energy (or, probably, spatial) barrier separating the bound and free states of the carriers in the semiconductor CdF₂.     

Experimental observation of “configuration” modes of bistable centers in CdF2:In crystals

New “configuration” modes, which were predicted by us for CdF₂:In crystals, have been revealed at the frequencies ν₁ ≈ 32.4 cm^?1 and ν₂ ≈ 96.3 cm^?1 for deep and shallow impurity states, respectively. The frequencies of these oscillations exactly correspond to the potential-energy curves calculated by us for shallow and deep states of In with regard to the reduced mass M = 2m ₁ m ₂/(m ₁ + 2m ₂) of the In ion (m ₁) and two F ions (2m ₂) per primitive fluorite cell. This correspondence confirms the correct choice of the height of the potential barrier between the impurity states of In in CdF₂ (0.02 eV), which was used in the calculations. The dielectric contributions of the noted modes were determined, which made it possible to calculate the concentrations of In impurity ions in the deep (N ₁) and shallow (N ₂) states. The obtained ratio N ₂/N ₁ ≈ 2 directly indicates that photoionization of deep In centers leads to the formation of a doubled number of shallow centers and that two electrons are localized in the deep state of the In ion; such behavior is characteristic of DX centers. A photoinduced increase in the real (ε′) and imaginary (ε″) parts of the dielectric constant has been found (at a frequency of 25 cm^?1, Δε′ ≈ 0.2 and Δε″ ≈ 0.06). These changes correspond to the changes in the dielectric contributions of the configuration modes under illumination. A photoinduced decrease in the lattice reflection of CdF₂:In, related to the impurity lattice modes, has also been revealed.     

Dynamic holographic joint fourier transform correlator based on a CdF2:Ga crystal

A joint Fourier transform correlator based on a bulk holographic medium—a CdF₂:Ga crystal serving a dynamic matched spatial-frequency filter—is implemented. Specific features of the correlator design are discussed. Correlatorf’s possibilities for selective recognition of objects of different type are demonstrated. Experimental data, results of mathematical modeling, and their analysis are reported. Suggestions for modifying the correlator scheme in order to improve its characteristics (operating speed, stability with respect to orientational and scale changes in objects, signal-to-noise ratio, correlation peak sharpness) are formulated.     

Photoconductivity in high purity,semiconducting CdF2

The photoconductivity spectra of high purity, semiconducting CdF₂, containing low concentrations of rare-earth donors, are interpreted in terms of a shallow trap 1260 ± 100 cm⁻¹ below the bottom of the conduction band and an excited bound state 1030 cm⁻¹ above the ground state.     

Donor impurities and DX centers in the ionic semiconductor CdF2

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. Fiz. Tverd. Tela (St. Petersburg) 39, 1050–1055 (June 1997)     

Dynamic reflection holograms in CdF2 crystals with bistable centers

The diffraction efficiency and the recording and relaxation times of dynamic reflection holograms, recorded in CdF₂ crystals with bistable centers are studied experimentally in the temperature range 20–100°C. In the model experiments which measured the quality of the wave reflected from the hologram, the dynamic wavefront distortions are demonstrated to be efficiently compensated using a holographic corrector based on these crystals. CdF₂ crystals with bistable centers are likely to be useful in solving problems of correction of laser light wavefront and image correction in observation telescopes with nonideal primary mirrors.     

Photoluminescence and tunneling charge transfer in CaF2: RE2+-CdF2 superlattices on Si(111)

The nonstationary behavior of Eu²⁺ and Sm²⁺ photoluminescence in continuously optically pumped CaF₂:RE²⁺-CdF₂superlattices was considered. The transient character of the photoluminescence is due to spontaneous electron tunneling from the excited 4f5d states into the conduction band of the adjacent CdF₂ layer. Coupled balance equations were constructed and numerically analyzed. It is shown that photoionization energies of the 4f5d states can be derived from the experimentally measured variation of the photoluminescence intensity in superlattices with CaF₂ and CdF₂ layers 10 to 20 monolayers thick.     

Thermostimulated luminescence of CdF2:Eu crystals

Using the method of fractional thermostimulated luminescence (FTSL), the temperature dependence of the mean activation energy of recombination processes in CdF₂:Eu³⁺ crystal was obtained. After thermal annealing of the crystal, thermostimulated luminescence peaks were identified. Anomalously low frequency factor (s=10⁷ s ^–1) of the recombination processes can be explained by the dependence of the resonance energy transfer probability on intercentre distance.The authors are very grateful to Dr. E. Kotomin for valuable comments and Dr. C. Paracchini for supply of CdF₂:Eu crystals.     

Recording dynamic holograms in a semiconductor crystal CdF<Subscript>2</Subscript>:In

The kinetics of decay of a phase hologram in a semiconductor CdF₂ crystal with bistable In centers is studied. Kinetic constants of the hologram decay are found, and the potential relief of the bistable center is plotted. The resolving power of the crystal is evaluated and recording of a transparency is demonstrated.     

Electronic level diagram and structure of metastable centers in CdF2:Ga and CdF2:In semiconducting crystals

A study is reported of the optical properties of wide-gap, predominantly ionic cadmium fluoride crystals in photo-and thermally stimulated transformations of metastable indium and gallium centers. An analysis of these properties leads one to a conclusion of gallium having two metastable states (two types of deep centers). The deep-center binding energies and the barriers separating the shallow (hydrogenic) and deep centers have been determined for both impurities. Configuration-coordinate diagrams are developed, and microscopic models for the deep centers are proposed. It is concluded that these centers are identical with the metastable DX centers in typical semiconducting crystals. Thus cadmium fluoride is the most ionic among the crystals where DX centers have thus far been found. The potential of using such crystals for optical information recording is discussed. Fiz. Tverd. Tela (St. Petersburg) 39, 2130–2136 (December 1997)     

Thermo-and photostimulated depolarization in self-compensated CdF2:Ga and CdF2:In crystals

A study is reported of the conductivity of CdF₂ semiconductor crystals doped by indium and gallium donor impurities and residing in a semi-isolated state. The latter results from self-compensation of the impurities, in the course of which one half of them creates two-electron DX centers, and the second is ionized. Photo-and thermostimulated depolarization of these crystals has been studied. It was shown that the observed polarization/depolarization phenomena have a nonlocal nature and are due to the charges present in these crystals changing their positions. These changes may be formally considered as charge displacement to macroscopic distances considerably in excess of the interatomic ones. The mechanisms responsible for these phenomena are discussed. Fiz. Tverd. Tela (St. Petersburg) 41, 1575–1581 (September 1999)