Electronic excitations and self-trapping of electrons and holes in CaSO₄

Wide-gap (E_g > 9.5 eV) CaSO₄ calcium orthosulphates (anhydrite) doped with transition or rare-earth (RE) ions in the form of single crystals or micro-grained phosphors are widely used as efficient spectral transformers of VUV radiation into a visible light with quantum yield QY > 1 as well as x-, γ- and β-dosimeters. However, the fundamental features of various electronic excitations (EE) and complex electron-hole recombination in doped or pure CaSO₄ have not been sufficiently studied. A low-temperature self-trapping of valence holes in regular lattice sites has been revealed in many binary and complex wide-gap metal oxides and halides (see, e.g. [1, 2]), while the movement of holes does not undergo freezing in MgO and Al₂O₃ even at liquid helium temperature. In some metal oxides, for instance, Sc₂O₃ (see [3] and the references therein), the motion of conduction d-electrons occurs in the form of hopping diffusion due to the corresponding four-lobe spatial character of the electron orbitals that strongly differs from the coherent motion of electrons in narrow-gap semiconductors.

Sumi theoretically analysed possible interactions of intrinsic EE (electrons, holes, and excitons) with the field of acoustic phonons in different semiconductors and wide-gap materials and built the corresponding phase diagram [4]. Later, the experimental manifestations of EE self-trapping were revealed and analysed in binary wide-gap metal oxides [3]. Several regions associated with a different interaction of electrons (e), holes (h), and excitons (e⁰) with acoustic phonons can be separated at the Sumi phase diagram. In many narrow-gap semiconductors, highly mobile e and h do not undergo self-trapping (loss of mobility) at regular lattice sites, and hydrogen-like excitons possess a large radius and high mobility. In many uni- and divalent metal halides, heavy holes undergo transition into a self-trapped state, being immobile at low temperatures, while conduction electrons preserve their mobility even after vibronic relaxation and tend to recombine with self-trapped holes partly via formation of self-trapped excitons. The third region of the phase diagram is typical of free e and h, while the sum of their deformation potentials is sufficient for the recombination formation of a self-trapped exciton (this situation is realized in Al₂O₃). Of particular interest is the diagram region that relates to the materials where e and h strongly interact with phonons and undergo self-trapping but their deformation potentials have opposite signs. In such materials, a photon in the region of band-to-band transitions creates a pair of a geminate p-hole and a d-electron, both carriers become self-trapped, and the subsequent recombination of the e and h localized at regular lattice sites not far from each other results in a typical tunnel luminescence. Manifestations of such 'excitons' have been detected in Sc₂O₃ [3], and a similar situation is expected to be realized in CaSO₄ as well (see, e.g. [5]).

Particular emphasis has been placed on the origin of a complex peak of thermally stimulated luminescence (TSL) at 50–60 K which was detected in all the investigated CaSO₄, nominally pure or doped with different RE ions, previously irradiated by 5–10 keV-electrons at 6 K [5, 6]. According to our data, the intensity of cathodoluminescence measured at the excitation of CaSO₄ by 5–10 keV-electrons (30 s excitation pulses with 60 s pauses between) significantly decreases at 70–40 K at the sample cooling down from 300 to 6 K. The ∼60 K TSL peak in CaSO₄ was tentatively attributed to the unfreezing of self-trapped conduction d-electrons [5]. However, it was convincingly shown that Ca²⁺ impurity ions serve as low-temperature hole traps (stable up to ∼60 K) in MgO:Ca single crystals electron-irradiated under the same conditions [7]. It is worth noting that neither electrons and holes nor large-radius excitons undergo self-trapping in a regular lattice of MgO crystals (see, e.g. [7]). Therefore, a further experimental and theoretical investigation of the peculiarities of electronic properties and electron-hole processes in CaSO₄ is needed.

In the present study, the peculiarities of complicated electron-hole processes in pure and doped anhydrite will be considered on the basis of a comparison of the experimental data obtained for CaSO₄ doped with Gd³⁺, Tb³⁺, Dy³⁺ (see also our previous publications [5, 6, 8, 9]), Tm³⁺ rare-earth ions, and theoretical calculations of the electronic properties in a number of calcium oxides and halides [10] with a detailed consideration of CaSO₄. Results from the literature on detailed investigations of many wide-gap materials doped with RE²⁺ and RE³⁺ ions have been taken into consideration as well (see [11–13] and references therein).

Since first-principles computational modelling methods can be used to obtain fundamental information on the structural and electronic properties of solids, they can be employed for a realistic description of actual properties of various intrinsic EE in a condensed phase. One of the main aspects of the present work was, by applying the advanced DFT strategies briefly discussed further in section 3, to evaluate the details of the electronic band structure of crystalline calcium orthosulphate with a proper accuracy in order to create an adequate theoretical background for making useful interpretations of the experimental studies. Thus, in this paper we will combine our experimental research results with careful theoretical simulations to characterize the origin and key features of EE.

A set of CaSO₄:RE³⁺ (Tb³⁺, Gd³⁺, Dy³⁺, Tm³⁺) micro-grained phosphors was synthesized by the solid-state reaction route at the Institute of Physics (Tartu) with regard to the data on the crystallization and phase stability of CaSO₄ [14]. CaSO₄ (99.993), (NH₄)₂SO₄ (99.999) and TbF₃ (99.99), GdF₃ (99.99) or TmF₃ (99.99) were used as starting materials for the synthesis of phosphors with fluorine ions or calcium vacancies as main charge compensators. The phosphors were sintered in a reactor with an extra dry air atmosphere at 750 °C. The main experiments were performed at the concentration of RE³⁺ of about 1% (with respect to the Ca²⁺ ions which they substitute for), when phosphors contain both single and pair RE impurity centres. Besides RE³⁺ luminescent ions, our samples contain considerable amount of fluorine, hydrogen, and cation vacancies.

The main photoluminescence experiments were carried out at the SUPERLUMI station of HASYLAB at DESY, Hamburg (see [15] for details). The excitation spectra were normalized to equal the quantum intensities of the synchrotron radiation (3.8–20 eV) falling onto the crystal. The emission spectra of RE³⁺-related centres were recorded by a liquid nitrogen–cooled CCD detector. The spectra of cathodoluminescence (CL) were measured in the region of 1.6–11 eV (through double monochromators) at the excitation by an electron gun (2–15 keV, 100–300 nA, and 2-mm² spot) at 6–420 K. After the electron irradiation was stopped, it was possible to register the spectra of phosphorescence at 6 K and the TSL (heating rate of β = 10 K min^–1) at 6–420 K for an integral signal or a specific monochromator-selected emission (see [16] for details). A high-temperature TSL (300–800 K) of the irradiated sample was measured with β = 2 K s⁻¹ in the atmosphere of flowing nitrogen using a Harshow Model 3500 TLD Reader.

A first-principles study of the electronic properties of the CaSO₄ anhydrite structural phase (the space group Amma) was performed using the Vienna Ab-initio Simulation Package (VASP) [17]. All periodic DFT calculations were carried out at the projector-augmented wave (PAW) pseudopotential level [18, 19] employing special GW versions of the PAW potentials with 10, 6, and 6 electrons treated as valence for calcium, sulfur, and oxygen, respectively. The computational scheme involved the following parameters: a force tolerance for structural optimization and ion relaxations <0.01 eV Å⁻¹, a dense k -point mesh to sample the reciprocal space 8 × 8 × 8, and a cut-off value of the plane-wave kinetic energy 500 eV. A unit cell of CaSO₄ containing 24 atoms and a total of 256 bands was used in the electronic calculations. The theoretical modelling of the lattice relaxation and dielectric properties were done within the Perdew–Burke–Ernzerhof (PBE) implementation [20] of the generalized gradient approximation (GGA) exchange-correlation functional. The obtained values of the lattice constants—a_calc = 7.086 Å, b_calc = 7.108 Å, c_calc = 6.274 Å—agree well with the experimental data [21], a = 6.993 Å, b = 6.995 Å, c = 6.245 Å (the deviations are 1.33, 1.62, and 0.46%, respectively). Once the optimization was completed, the elements of the dielectric matrix were numerically determined using density functional perturbation theory as implemented in VASP [22]. For the calculation of the electronic density of states, a modified 'one-parameter' form [23] of PBE0 hybrid functional [24] was employed. A system-dependent fraction of the Fock exchange, 0.3708, relevant to the bulk crystalline CaSO₄ was estimated according to the algorithm of [23] as the inverse value of the calculated dielectric constant ε_∞  = 2.697.

To understand the electronic nature of a self-trapping of carriers such as electrons or holes, we have calculated the total and partial densities of CaSO₄ states (shown in figure 1). Detailed consideration of the role of excitons in the self-trapping effect will be presented in a separate article. The narrow-width character of the outermost subbands, related to the top of the valence band and formed from the occupied oxygen 2p states, means that these states tend to be strongly localized at the ligand (SO₄)²⁻. In contrast, the combination of empty calcium 3d states dominant in the conduction band shows a broad distribution that does not play in favour of self-trapping of electrons. For this reason, we see no relevant possibilities for the localization of excited electrons on these states. Note also that due to the presence of strong hybridization between S and O orbitals, the third valence subband is essentially shifted (>4.5 eV) from the highest occupied states. The corresponding examples are illustrated in the insets of figure 1. The higher level of the localization of oxygen 2p orbitals evidently determines a limited movement of the excited p-hole corresponding to the electron transferred to the 3d levels. This reveals the channel of the self-trapping effect discussed generally in the introduction, namely, the qualitative explanation for the case of CaSO₄ appears as follows: heavy holes situated at the narrowed oxygen 2p states undergo transition into a self-trapped state being immobile at low temperatures. In view of the broad spectrum of the calcium 3d states, the mobility of hot electrons excited into the conduction band is preserved. In this context, an idea of a 'transverse' electronic mobility associated with the movement of nonequilibrium electrons across 3d states of the different calcium cations can be suggested. However, such characteristic features of electron-transfer dynamics as, for example, the coupling with the relevant lattice vibrations as well as interactions with defects can extend recombination times that in turn may both initiate a self-trapping channel for electrons and additionally support self-localization of the holes at the oxygen sites.

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The peculiarities of the calculated electronic properties of CaSO₄ single crystals can be compared with the results of the experimental investigations—first of all, with the excitation spectra for RE³⁺-centre emission measured in doped CaSO₄ phosphors using synchrotron radiation. Tm³⁺, Dy³⁺, and ¹⁵⁷Gd³⁺ (which makes up about 15% of all stable isotopes) ions have an odd number of 4f electrons. Because of the significant energy decrease caused by the coupling of two 4f electrons, these RE³⁺ act as efficient traps for conduction s-electrons. Tb³⁺ ions and the majority of Gd³⁺ stable isotopes possess an even amount of 4f electrons and, similarly to precisely investigated Ce³⁺ ions [11–13], serve as efficient traps for mobile holes. The excitation spectra for the emission of all five of these RE³⁺ ions have been measured for a set of our CaSO₄ phosphors using synchrotron radiation of 4–35 eV at 6–10 K. Within the present paper, we restrict the discussion to the narrow region of 8–16.5 eV, which contains the optical excitation of oxyanions (8 to 9.5 eV) as well as the initial stage of band-to-band transitions with the formation of valence p-holes and conduction s- or d-electrons. The onset of interband transitions (hν > 9.5 eV) was already determined from the excitation spectra of recombination phosphorescence or the creation spectra for several TSL peaks (see, e.g. [6]), while earlier E_g was estimated as about 10.5 eV [25].

As an example, figure 2 shows the excitation spectra for a steady-state luminescence of Gd³⁺ (3.97 eV) and Tb³⁺ centres (2.27 and 3.02-eV emission lines correspond to ⁵D₄ → ⁷F₅ and ⁵D₃ → ⁷F₅ electron transitions, respectively) measured in RE³⁺-doped CaSO₄ at 10 K. The efficiency of Gd³⁺-emission, measured at the background of tunnel luminescence starts to increase at E_g = 9.8 eV, and the second rise stage occurs at 11.2–12.2 eV. The green series of Tb³⁺-emission with the most intense line ⁵D₄ → ⁷F₅ dominates in CaSO₄:Tb³⁺ with a relatively large impurity concentration (∼1%) providing the presence of two-terbium centres as well. Just cooperative resonant transitions within two-terbium centres enhance the green Tb³⁺-emission [5, 8]. The excitation spectrum for the blue series of Tb³⁺-emission (the most intense line is due to the ⁵D₃ → ⁷F₅ transitions) has a shape close to that for Gd³⁺-emission, but a background connected with tunnel transitions is significantly higher.

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Note that there is a very good agreement between the DFT calculations and the results of the spectroscopy measurements. First, they agree well with respect to the calculated value of the fundamental band gap, E_g = 9.6 eV, as can be compared with the experimental estimation ∼9.8 eV shown in figure 2. Secondly, the data presented in figure 2 allow one to estimate the threshold for p − d transitions in CaSO₄ as E_p − d = 11.2 eV. This value is confirmed by analysis of the partial DOS functions, which gives the theoretical threshold of about 10.8 eV for p − d transitions. Note also that the difference in magnitude between E_g and E_pd corresponds to a region of a low density of states, predominantly of s-type, positioned at the conduction-band edge with a width of about 1.2 eV.

The CL have been also measured at the excitation of CaSO₄:RE³⁺ by 5–10 keV-electrons at 6 K. After the electron-irradiation was stopped, the intensity of RE³⁺ emission decreased by three-four orders of magnitude in 10 min. At a further phosphor heating up to 420 K with a constant rate of β = 10 K min⁻¹, the TSL of RE impurity centres emission was measured above a pedestal of tunnel luminescence. Since the first measurements [6], the most attention has been concentrated on the intense TSL peak at 50–60 K. The inset in figure 3 presents this TLS peak in CaSO₄:Gd³⁺ above a pedestal of tunnel luminescence as well as the results of its rough decomposition into two elementary components: the first weak one with a maximum at ∼37 K is characterized by the activation energy E_a = 0.017 eV and a frequency factor p₀ = 4.0 s⁻¹, the second—E_a = 0.031 eV and p₀ = 16.5 s⁻¹. The values of p₀ are significantly lower than those typical for high-temperature TSL at 400–700 K in CaSO₄ dosimetric materials (p₀ = 10¹¹–10¹³ s⁻¹). According to the presented calculations of the densities of states in CaSO₄, the self-trapping of oxygen holes can be realized at low temperatures. At T > 35 K, a small-radius hole polaron becomes mobile and via hopping diffusion comes nearer to the electron trapped at Tm³⁺, Dy³⁺, or ¹⁵⁷Gd³⁺ ion with an initially odd number of 4f electrons. As a result, the tunnel recombination of a hole polaron with an electron localized at/near RE³⁺ takes place, the energy released at recombination is spent for the excitation of RE³⁺ and the ∼55 K TSL peak is registered for a typical impurity luminescence. Specifically, a tunnel behaviour of recombination complicates the process at 35–60 K, which cannot be strictly ascribed using E_a and p₀ parameters. It is worth noting that the ∼55 K TSL peak has been detected in our x-irradiated (50 keV) CaSO₄:RE³⁺ as well. So, the peak has a bulk origin and is not mainly connected with near-surface layers.

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According to figure 3, a pedestal of tunnel luminescence in CaSO₄:Gd³⁺ decreases to zero after a sample heating to 200 K. The TSL curve for CaSO₄:Tb³⁺ contains two intense peaks at ∼55 and ∼400 K, while the background related to tunnel processes remains even at 420 K. The emission spectrum in the region of the 55 K TSL peak contains both the green and blue series of Tb³⁺ emission (see also [5]). At the irradiation of CaSO₄:Tb³⁺, the electrons can be trapped at complex luminescence centres that contain terbium ions and different compensators. Several weak TSL peaks at 90–350 K are partially connected with a temporary trapping of becoming mobilesed self-trapped holes (hole polarons) at the existing impurity/defect-related traps. In some previous publications (see, e.g. [6]), the TSL at 100–300 K was more intense due to the higher concentration of as-synthesized imperfections in CaSO₄ phosphors prepared by the solid-state reactions from not so pure starting materials.

Figure 4 presents the spectrally integrated (3.7−1.7 eV) TSL curves measured after isodose irradiation of CaSO₄:Tm³⁺ by 10.0 or 12.5-eV photons at 295 K. The photons of 10 eV form valence p-holes and conduction s-electrons, while d-electrons are created at the excitation with 12.5-eV photons. The ratio for the TSL peak intensity is quite different for these two excitation cases. The values of a frequency factor p₀ for the TSL peaks above 300 K differ by several orders of magnitude after photocreation of s- or d-electrons. So, the distance of hopping diffusion for s- and d-electrons is rather different. In x-irradiated CaSO₄:Tm³⁺, the main TSL is detected at 400–500 K. The analysis of the initial sections of TSL, measured after repeated heating (step of 50 K and subsequent cooling down) of the irradiated sample, allowed concluding that, in contrast to low temperatures (see figure 3), there is no tunnel luminescence at T > 300 K. At high temperatures, photocreated geminate electrons and holes are separated by large distances.

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The presented experimental results are consistent with the theoretical predictions of a possible low-temperature self-trapping of oxygen p-holes, the hopping diffusion of which starts above 35 K and is accompanied by the complex ∼55 K TSL peak. In dosimetric CaSO₄:Dy³⁺, the oxygen holes formed during irradiation remain trapped near calcium vacancies up to 420 K and their structure has been thoroughly studied by the method of electron spin resonance [26]. A further investigation of extremely pure CaSO₄ a well as anhydrite doped with RE ions containing an even number of 4f electrons and serving as deep traps for p-holes still lies ahead.

The performed DFT calculation of the fundamental electronic properties of a wide-gap CaSO₄ crystal fit in many respects the experimental data obtained for CaSO₄ doped with Gd³⁺, Dy³⁺, Tm³⁺, and Tb³⁺ ions in a spectral region connected with the electron transitions from narrow outermost p-subbands of the valence band to s- and d-subbands of the conduction band. The experimental manifestations of the theoretically predicted self-trapping of p-holes have been revealed. At T > 35 K, a hopping diffusion of heavy hole polarons toward the electrons localized at/near RE³⁺ impurity ions with an initial odd number of 4f electrons takes place resulting in the excitation of a typical emission of ¹⁵⁷Gd³⁺, Dy³⁺, or Tm³⁺ impurity centres. At this point, there is no direct experimental evidence of the self-trapping of conduction d-electrons in CaSO₄. However, the migration of rather heavy d-electrons significantly differs from that of conduction s-electrons in CaSO₄ as well as from the coherent motion of conduction electrons in MgO ionic single crystals. The tunnel luminescence detected in the samples previously irradiated at 5–300 K can be considered as the manifestation of the self-trapping/trapping of oxygen holes and hopping diffusion of conduction d-electrons, which additionally complicates the kinetics of electron-hole processes in CaSO₄.

Further complex experimental investigations (including the EPR method) of CaSO₄ single crystals and ceramics, which are extremely free of electron and hole traps, are needed in an attempt to reveal the intrinsic luminescence of CaSO₄ and to prove the absence/presence of an electron self-trapping in regular lattice sites with higher certainly.

The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement n° 226716, the Estonian Research Council–Institutional Research Fundings IUT02-26 and IUT02-27 and the Estonian Science Foundation (Grant No. 8991). A. Pishtshev acknowledges also the support from the European Union through the European Regional Development Fund (Centre of Excellence 'Mesosystems: Theory and Applications,' TK114).