Fluoride materials have been studied for a very long time because they have a wide range of potential optical applications based on their low-energy phonons and high ionicity, which result in less absolute fundamental absorption compared with other oxide or sulfide materials.^[1–4] As an important class of fluorides, alkaline earth metal fluorides are dielectric materials, which have been widely used in microelectronic and optoelectronic devices, such as wide-gap insulating overlayers, gate dielectrics, insulators, and buffer layers in semiconductor-on-insulator structures and more advanced three-dimensional (3D) devices.^[5–8] As an important type of alkaline earth metal fluoride, calcium fluoride (CaF₂) has become the focus of the semiconductor industry with the development of UV-lithography due to its high transmittance and low absorption coefficient.^[9,10] CaF₂ can replace fused silica because it possesses a high laser-induced damage threshold and high transparency until the vacuum ultraviolet region. Therefore, it is considered as the optimal material for deep ultraviolet laser lithography techniques.^[11]

With the development of nanometer materials, inorganic nanoscale fluorides are going to play an essential role in various applications based on their unique optical, electrical, and magnetic properties. As a typical anionic conductivity material, the conductive property of CaF₂ is an interesting subject. In 1995, Puin et al. measured the conductivity of nanocrystalline CaF₂ and found that the F⁻ ionic conductivity in nanophase fluorides increases greatly, in contrast to that in the corresponding single crystalline phase.^[12] Boulfelfel et al. predicted that superionic conduction would emerge in the phase interfaces of the fluorite-to-cotunnite transition of CaF₂.^[13] Despite there being many high-pressure studies regarding the phase transitions of CaF₂,^[14–17] very few experimental and theoretical works have reported its charge transport behavior under high pressure.

In this work, we conducted a comprehensive investigation on the high-pressure electrical transport properties of CaF₂ nanocrystals by using in situ alternate-current (AC) impedance spectra measurements in a diamond anvil cell (DAC) at up to 30.0 GPa. In addition, the variations of diffusion coefficient, bulk and grain boundary resistances with pressure were also discussed.

High pressure was conducted by using a Mao–Bell-type diamond anvil cell. The culet of the diamond anvil was in diameter. A thin film of metal molybdenum was deposited on to the DAC surface and the microcircuit on the surface was utilized in the measurements of resistivity under high pressure. The fabrication process of the microcircuit on diamond anvils has been reported in the previous paper.^[18–20] The completed microcircuit and the profile of our designed DAC are shown in Fig. 1.

Fig. 1.

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	Fig. 1. (a) Completed microcircuit on diamond anvil and (b) the profile of our designed DAC. 1 is Mo, 2 is an alumina layer, 3 is an insulating layer, 4 is the sample chamber, and 5 is ruby. A and B are the contact ends of the microcircuit.

A T301 stainless steel was used as a gasket that was pre-indented into in thickness. Using a laser drilling machine, a hole was drilled at the center of the indentation with in diameter. To insure that sample and gasket, electrodes and gasket are insulated to each other, an insulating layer that mixed cubic boron nitride powder and epoxy was compressed into the indentation. Subsequently, a sample chamber of was drilled by using a laser drilling machine. The pressure was calibrated by the R1 fluorescence peak of ruby. Ruby’s R1 fluorescence peak was detected by a Renishaw in Via Raman spectrometer. To avoid additional error on the electrical transport measurements, no pressure-transmitting medium was used. By using a Solartron 1260 impedance analyzer equipped with Solartron 1296 dielectric interface, the impedance spectroscopy was measured. A voltage signal with amplitude of 1 V and frequency ranged from 0.1 Hz to 10⁷ Hz was applied to the sample. The CaF₂ nanocrystals were prepared using a liquid-solid-solution (LSS) solvothermal route, and the sample is square shaped with a mean size of length around 8±2 nm.^[21]

Figure 2 illustrates the – plots of the impedance spectra. The X-axis is the real part of impedance ( ), and the Y-axis is the imaginary part of impedance ( ).

Fig. 2.

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	Fig. 2. (color online) The – plots of impedance spectra.

To deeply analyze the impedance spectroscopy, the obtained data are usually modeled by an equivalent circuit. The ionic conduction of F⁻ can be revealed by the – plots of the impedance spectra. Figure 3 shows the – plots of CaF₂ nanocrystals.

Fig. 3.

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	Fig. 3. (color online) The – plots of CaF2 nanocrystals at low frequency.

From Fig. 3, it can be seen that and are linear in the low frequency region, which indicates the existence of F⁻ ions diffusion at low frequency. Thus, to describe the F⁻ ions diffusion, a Warburg impedance element was added to the equivalent circuit. If the charge carriers are only F⁻ ions, the – plot in the low frequency region would be a line with 45° to the X axis such as the hollow circle plot in Fig. 4.

Fig. 4.

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	Fig. 4. (color online) The – plot of impedance spectra at 1.76 GPa. The solid square is the experimental result. The hollow circle is the result with only F− ions conduction. The continuous line is the simulated spectrum. R1 and R2 are the intercepts of the Nyquist plot on the X axis.

Thus, electron conduction and ion conduction coexist in the transport process of CaF₂ nanocrystals. We used the equivalent circuit in Fig. 5 to analyze the conduction mechanism of CaF₂ nanocrystals under high pressure.

Fig. 5.

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	Fig. 5. The equivalent circuit model for mixing conduction of electron and ion. is the grain resistance, is the grain boundary resistance, is the grain capacitance, is the grain boundary capacitance, and is the Warburg impedance.

From Fig. 4, it can be seen that the simulated spectrum well agrees with the experimental data, indicating that the equivalent circuit model we used is reasonable. It can also indicate the validity of considering that the charge carriers in CaF₂ nanocrystals include both ions and electrons.

Because F⁻ ions and electrons coexist in CaF₂ nanocrystals, it is necessary to distinguish each carrier contribution to the transport process. The transference number^[22] is usually used to describe the contribution of each type of carrier to the transport process. The F⁻ ion transference number ( ) can be expressed as

and the electron transference number ( can be expressed as

Fig. 6.

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	Fig. 6. (color online) The variation of ion and electron transference numbers with pressure.

Due to the existence of the ionic conduction, in the low frequency region and can be expressed as where is a constant, and σ is the Warburg coefficient. By linearly fitting the – curves, the Warburg coefficient under high pressure was obtained.

The ion diffusion coefficient can be expressed as where R is the ideal gas constant, T is the temperature, Fis the Faraday constant, and C is the molar concentration. We set the F⁻ ion diffusion coefficient at 0 GPa as D₀, the values of under different pressures were obtained and shown in Fig. 7(a).

Fig. 7.

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	Fig. 7. The pressure dependence of (a) diffusion coefficient, (b) grain resistance, and (c) grain boundary resistance of CaF2 nanocrystals. D0 is the diffusion coefficient at 0 GPa.

Using the equivalent circuit model (Fig. 5), the impedance spectra were fitted by the Zview2 impedance analysis software, and the grain resistance and grain boundary resistance under various pressures were obtained and shown in Fig. 7.

From Fig. 7, it can be seen that the diffusion coefficient, grain and grain boundary resistances vary abnormally at about 14.37 GPa and 20.91 GPa, corresponding to the beginning and completing of the Fm3m–Pnma structural transition.^[21] These results indicate that the electrical transport behavior has detectable changes as the phase transition occurs.

In the Fm3m and Pnma phases, the diffusion coefficient of the F⁻ ion decreases, whereas the grain resistance and the grain boundary resistance increase as the pressure rises; which indicates that both the F⁻ ions diffusion and electronic transport become more difficult under compression. In the whole pressure range, the grain resistance is larger than the grain boundary resistance, which indicates that the grain resistance has a major contribution to the total resistance and defects at grains play a dominant role in the electronic transport process.

The electrical transport properties of CaF₂ nanocrystals have been investigated by in situ impedance measurement up to 30 GPa. Each parameter changes discontinuously at about 14.37 GPa and 20.91 GPa, corresponding to the beginning and completing of CaF₂ nanocrystals phase transition under high pressure. Electron conduction and ion conduction coexist in the transport process and the electron conduction is dominant. The electron transference number of the Fm3m and Pnma phases increases with pressure increasing. As the pressure rises, the F⁻ ion diffusion and electronic transport processes in the Fm3m and Pnma phases become more difficult. Defects at grains play a dominant role in the electronic transport process.