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.     

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     

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.     

Effective room-temperature broad-band recording of 3D dynamic holograms in CdF<Subscript>2</Subscript>:Ga crystals

Photochromic CdF₂:Ga crystals with bistable impurity centers were effectively used for the dynamic recording of holograms and readout over the visible and near IR spectral regions at spatial frequencies of up to 5000 mm^?1 at room temperature. The diffraction efficiency of the dynamic holograms was as high as 60% at maximum and exceeded 1% when the beams’ intensities were in the ratio 1:100. As one goes from the low temperatures (≤200 K) to 300 K, the peak diffraction efficiency of the dynamic holograms decreases approximately by a factor of 1.5, while the speed of their response and photosensitivity in the long-wavelength spectral region increases by more than an order of magnitude. For the sake of comparison, the dynamic holograms were recorded under the same conditions as the widely used electrooptical SBN crystals. Comparative analysis ascertained a unique combination of the useful features offered by CdF₂:Ga crystals in holography.     

Energy barrier between states of a bistable center in photochromic crystals CdF2:Ga and CdF2:In

The establishment of thermal equilibrium between photoinduced (shallow) and ground (deep) states of bistable DX centers in photochromic crystals CdF₂:In and CdF₂:Ga, which are used as real-time holographic media, is studied based on the notions of chemical kinetics. Two mechanisms of mutual transformation of shallow and deep centers—the tunnel mechanism and the mechanism with the participation of free charge carriers—are considered. Equations describing the decay of a photoinduced shallow state are obtained. These equations take into account the distribution of electrons between the photoinduced and ground states and the conduction band. Analysis of the experimental kinetic curves of the decay of photoexcited shallow centers makes it possible to determine the activation energies and barrier height for thermally activated processes of mutual transformation of shallow and deep centers. In CdF₂:In and CdF₂:Ga, this barrier, which determines the decay kinetics of holograms, lies above the bottom of the conduction band by ～10 and ～500 meV, respectively.     

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.     

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.     

Dynamic wavefront-conjugating mirror based on CdF2 crystals with bistable in centers

The wavefront reversal upon degenerate four-wave interaction in a CdF₂ crystal with bistable In centers is experimentally investigated using a pulsed ruby laser as a pump source. The reflectance and operating speed of the wavefront-conjugating mirror are measured and the quality of the reflected wave, as well as of the compensation of model phase distortions, is estimated. An operating speed of about 15 ns is obtained for such a mirror with a reflectance of up to 2% at room temperature. Compensation of model large-scale distortions yields a gain in the beam divergence of 20 and a quality of compensation of 1.05.     

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.     

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.     

A dynamic phase-conjugate mirror based on CdF<Subscript>2</Subscript> crystals with bistable centers

A four-wave phase-conjugate mirror on reflection gratings recorded in a CdF₂ crystal with bistable centers has been studied experimentally. The mirror reflectivity and speed have been measured, and the coefficient of third-order nonlinearity of this medium has been estimated. The quality of the wave reflected from the phase-conjugate mirror has been investigated in model experiments.     

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)     

On the determination of thermal ionization energy of deep centers from ESR data

It is shown that the skin effect due to thermal generation of free carriers may affect the ESR signal more than deep center depopulation. Experimental results for 0.33 eV deep Eu²⁺ donor in CdF₂ crystals are presented, to show the way in which the thermal energy of deep centers is deduced from the ESR data.     

Dynamics of the transformation of bistable centers and lattice in CdF<Subscript>2</Subscript> crystals under femtosecond pulsed photoexcitation

The kinetics of photoinduced absorption spectra of CdF₂ crystals with bistable indium and gallium centers under femtosecond pulsed excitation has been experimentally investigated. Based on the example of indium ions, it is shown that the transmission band in the absorption spectrum of deep centers is formed for 0.8–1 ps, which significantly exceeds the photon absorption time. This process is interpreted as a result of displacement of indium ion from the initial interstitial position to a site of neighboring unit cell; the displacement velocity is estimated to be 200–250 m/s, a value close to the thermal velocity of this ion at room temperature. The times characteristic of the formation of free polarons as a result of the displacement of neighboring lattice ions have been experimentally estimated for the first time at a level of 0.8–1.2 ps. The capture times of free polarons by trivalent gallium and indium ions are estimated (5 and 10 ps, respectively), as well as the corresponding cross sections (2 × 10⁻¹⁶ and 8 × 10⁻¹⁶ cm²).     

Jahn-teller chromium ions in CdF<Subscript>2</Subscript> and CaF<Subscript>2</Subscript> crystals: An EPR spectroscopic study in the frequency range 9.3–300 GHz

The bivalent chromium impurity centers in CdF₂ and CaF₂ crystals are investigated using electron paramagnetic resonance (EPR) in the frequency range 9.3–300 GHz. It is found that Cr²⁺ ions in the lattices of these crystals occupy cation positions and form [CrF₄F₄]^6? clusters whose magnetic properties at low temperatures are characterized by orthorhombic symmetry. The parameters of the electron Zeeman and ligand interactions of the Cr²⁺ ion with four fluorine ions in the nearest environment are determined. The initial splittings in the system of spin energy levels of the cluster are measured.     

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.     

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)     

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)     

Photoinduced submillimeter-wave amplitude diffraction grating in a semiconducting CdF<Subscript>2</Subscript>:Ga crystal

It is shown that exposure of an additively colored CdF₂:Ga crystal with bistable DX centers that is slowly cooled to 150 K to blue-green light through a slotted mask produces a submillimeter-wave diffraction grating, which persists for a long time at temperatures of 160–240 K. It is also shown that the diffraction grating induced in a sample is an amplitude grating. The absorption of submillimeter waves in illuminated regions of the sample is associated with the conductivity due to the transition of impurity centers to a metastable donor state. In the n-i-n-i-type conducting structure obtained, the conductivity of n-type regions at 225 K amounts to σ ′ ≈ 0.24 Ω^?1 cm^?1.     

Radiation damage and annealing in Sb implanted diamond

The predicted, but as yet unobserved, intradonor absorption spectrum of the hydrogenic-like donors in CdF₂ crystals is presented. The role of phonon coupling in these spectra is discussed. From the data on the insulator-semiconductor transition in CdPbF₂ it is concluded that the dominant factor in convertibility of CdF₂ to a semiconducting state is its electron affinity, the largest among the fluorites (x≈4 eV).