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High-temperature piezoelectric crystals and devices

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Abstract

Conventional piezoelectric materials such as quartz are widely used as high precision transducers and sensors based on bulk acoustic waves. However, their operation temperature is limited by the intrinsic materials properties to about 500°C. High-temperature applications are feasible by applying materials that retain their piezoelectric properties up to higher temperatures. Here, langasite (La3Ga5SiO14) and compounds of the langasite family are the most promising candidates, since they are shown to exhibit bulk acoustic waves up to at least 1400°C. The mass sensitivity of langasite resonators at elevated temperatures is about as high as that of quartz at room temperature. Factors limiting potential use of those crystals include excessive conductive and viscous losses, deviations from stoichiometry and chemical instability. Therefore, the objective of this work is to identify the related microscopic mechanisms, to correlate electromechanical properties and defect chemistry and to improve the stability of the materials by e.g. appropriate dopants. Further application examples such as resonant gas sensors are given to demonstrate the capabilities of high-temperature stable piezoelectric materials. The electromechanical properties of langasite are determined and described by a one-dimensional physical model. Key properties relevant for stable operation of resonators are found to be shear modulus, density, electrical conductivity and effective viscosity. In order to quantify their impact on frequency and dam**, a generalized Sauerbrey equation is given. Mass and charge transport in single crystalline langasite are correlated with langasite’s defect chemistry and electromechanical properties. First of all, the dominant charge carriers are identified. Undoped langasite shows predominant ionic conduction at elevated temperatures. As long as the atmosphere is nearly hydrogen-free, the transport is governed by oxygen movement. A dominant role of hydrogen is observed in hydrogenous atmospheres since the diffusion coefficient of hydrogen is orders of magnitude higher than that of oxygen. The loss in langasite is found to be governed up to about 650°C by viscoelastic dam** related to the above mentioned movement of oxygen ions. Donor do** is shown to lower the loss contribution. Above 650°C the impact of the conductivity related loss becomes pronounced. Here, lowering the conductivity results generally in decreased losses. The evaluation of langasite’s applicability is focused on map** the regimes of gas insensitive operation. The most relevant feature with respect to frequency fluctuations of resonator devices is the formation of oxygen vacancies. In nominally hydrogen free atmospheres the calculated frequency shift becomes pronounced below oxygen partial pressures of 10 − 17, 10 − 24 and 10 − 36 bar at 1000, 800 and 600°C, respectively. Water vapor is found to shift the resonance frequency at higher oxygen partial pressures. In the hydrogen containing atmospheres applied here, langasite can be regarded as a stable resonator material above 10 − 13 bar and 10 − 20 bar at 800 and 600°C, respectively. The incorporation of OH-groups determines the frequency shift.

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Notes

  1. The crystal cut designation follows [51].

  2. In [57] the electromechanical coupling K 2 = ε 2/(ec) is considered instead of ε.

  3. The situation is comparable to platinum electrodes applied here since their density is similar.

  4. The property σ B reflects the bulk conductivity of polycrystalline or single crystalline langasite. In the latter case σ B equals σ R .

  5. The amount of dopant is always given as molecular percentage of the target cation site. Strontium and praseodymium dopants refer to lanthanum. Niobium dopants are given with respect to gallium.

  6. At 800°C the curves for p O2 = 1 and 10 − 10 bar are almost identical. At 800°C and \(p_{O2} = 10^{-20}\) bar the branch for \([A_C']-[D_C^\bullet]<0\) is not shown in order to avoid confusion because of overlap** curves. It is a nearly horizontal line at \(\sigma_B \approx 6\times 10^{-3}\) S/m.

  7. The subscript of η R is skipped in this section.

  8. In both publications, the inverse resonator quality factor is used to describe the loss.

  9. The alignment of the left and right hand axis is done for data points in temperature range (2) where the viscosity dominates the loss solely (see also Fig. 37).

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Acknowledgements

The contributions of the coworkers from Clausthal University of Technology, especially Dr. M. Schulz, Dr. D. Richter, J. Sauerwald and E. Ebeling, are highly acknowledged. Their experimental work and feedback helped substantially to broaden the knowledge about the high-temperature piezoelectric materials. Further, the author thanks Prof. G. Borchardt, Clausthal University of Technology, Dr. C. Rüscher, Leibniz University Hannover and Dr. H. Baumann, University of Frankfurt, for the support of the SIMS analysis, the FT-IR measurements and the gallium implantation, respectively. The tight collaboration with Prof. H.L. Tuller and Dr. H. Seh from Massachusetts Institute of Technology is one of the important driving forces of this work. Research grants from German Research Foundation (DFG) and German Government (BMBF) supported this work.

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  1. Institute of Energy Research and Physical Technologies, Clausthal University of Technology, Am Stollen 19, 38640, Goslar, Germany

    Holger Fritze

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Appendices

Appendix A: Crystal growth

Nominally undoped and doped langasite single crystals are prepared by the Institute for Crystal Growth, Berlin-Adlershof, Germany (IKZ Berlin) using the Czochralski technique [37]. Thereby, the starting powder is prepared by mixing stoichiometric amounts of La2O3, Ga2O3, and SiO2 (purity 4N). After calcination, the material is charged into a crucible and heated. Subsequently, the crystals are pulled at a rate of 1.5 mm/h under N2–2% O2. Since the crystals are grown in iridium crucibles undoped material appears transparent independent of its treatment in oxidizing or reducing atmospheres. Intentionally doped langasite single crystals are also provided by IKZ Berlin. The growth process corresponds to that described above except for the partial replacement of lanthanum or gallium by the dopants, namely strontium, praseodymium and niobium.

Appendix B: Materials data

The bulk conductivity of the resonator materials is determined by impedance spectroscopy in the frequency range from 10 to 1 MHz. The low frequency intercept of the R S C S -semicircle in the complex impedance plane represents the resistance of the parallel arrangement and is converted in the bulk conductivity σ R . Further, the dielectric constant ε R is extracted from the data. The resonance spectra of the piezoelectric resonators are determined by recording the real R and imaginary X parts of the impedance spectra in the vicinity of the resonance frequency using an high-speed network analyzer.

The fit procedure to determine the materials properties requires room-temperature data as initial values. They are taken from different publications and listed in Table 11. In addition, key values determined independently by pulse-echo measurements using the actual langasite crystals are given [69]. The high-temperature data of the piezoelectric material used for the parameter study correspond to some extend to those of langasite. The extrapolation up to 1400°C is done

  • Linearly for the dielectric constant and the piezoelectric coefficient as given for 500, 1000 and 1400°C in Table 12,

  • Parabolically for the shear modulus as given in Table 12,

  • Exponentially for the conductivity and viscosity according to \(\sigma_{\!R}\,T = \sigma_0 e^{-E_\sigma/k_B T}\) and \(\eta_R = \eta_0 e^{-E_\eta/k_B T}\) as given in Figs. 6 and 10, respectively.

Table 11 Room temperature materials constants of langasite, gallium phosphate and quartz
Full size table
Table 12 Material constants used for the parameter study at elevated temperatures
Full size table

C.1 Diffusion coefficients

1.1 16 O/18O exchange

Self-diffusion coefficients can be extracted by analysis of the movements of stable tracers within a given sample. Oxygen diffusion measurements base commonly on the exchange of the stable tracer isotope 18O with low natural abundance (0.206 at%), with that of naturally occurring 16O in the solid.

In order to prepare the samples, pre-annealing runs are performed in artificial air at the same temperature and p O2 as the subsequent diffusion runs. Thereby, the period of time is chosen to be at least four times longer than that of the tracer diffusion. After pre-annealing, the samples are temporarily moved into a cooler area of the furnace (ΔT = 250°C) to replace the gas atmosphere with 18O2 enriched gas (typically 80–90%). The samples are then exposed to the tracer at temperatures ranging from 500 up to 1000°C to achieve the 18O–16O exchange. Subsequently, the resulting concentration profiles are determined by secondary ion mass spectrometry (SIMS, Cameca IMS 3f) or secondary neutral mass spectrometry (SNMS, VG SIMS Lab).

The 18O concentration at the surface of the sample c S is potentially lower than the concentration in the surrounding gas environment c G . Therefore, the surface exchange kinetics must be taken into consideration.

1.2 C.2 Diffusion in single crystals

The diffusion model given in [112] describes the such situations for a single diffusion mechanism. Here, the surface exchange kinetics and the bulk diffusion are expressed by k and D, respectively

$$\label{Eq:SurfEx} k\, (c_G - c_S) = D {\frac{\partial c}{\partial y}\,\vline}_{\ y=0}. $$
(73)

The measured depth profiles are fitted by a least square regression procedure based upon the diffusion solution according to Eq. 74

$$ \begin{aligned}\label{Eq:DiffO} \! \frac{c(y,t)\!-\!c_{BG}}{c_G\!-\!c_{BG}} ={}& \textrm{erfc}\!\left( {\frac{y}{2\sqrt{Dt}}} \right)\! - \exp\!\left(\!{\frac{k}{D}y + \!{\frac{k^2}{D}t}\!} \right)\notag\\ &\times\,\textrm{erfc}\!\left(\!{\frac{y}{2\sqrt{Dt}}+k\sqrt {\frac{t}{D}}}\,\right) \end{aligned} $$
(74)

where y, t and c BG are the depth, the diffusion time and the natural background 18O concentration, respectively.

1.3 C.3 Diffusion in polycrystalline materials

The analytical solution in the form of Eq. 74 cannot be applied if more than one diffusion mechanism takes place simultaneously. For example, polycrystalline samples exhibit diffusion in the volume and the grain boundaries. The common way to plot the corresponding diffusion profiles is to express the logarithm of the concentration as a function of depth to the power of 6/5. The grain boundary term is then visible as the linear part of the concentration profile, and from the slope the grain boundary diffusion coefficient can be calculated [113] when the volume diffusion coefficient is known. In this study, the analytical approach proposed in [114] is used. The linear part of the depth profile, plotted versus x 6/5 and extrapolated to x = 0, represents the contribution of grain boundaries, \(c_{GB}^{\,0}\) , approximated by

$$ c_{GB}^{\,0} = 0.9 \,c_G \lambda \, 2 \sqrt{Dt}. $$
(75)

Here, λ and D are the grain boundary length per unit area and the bulk diffusion coefficient, respectively. The grain boundary length may be extracted by processing cross sections of the specimen. Examples for diffusion profiles and cross sections of the specimen are given in [115]. A typical grain boundary length per unit area is \(\lambda = (\,0.7 {\small \pm\,}0.1)\ \mu\)m − 1.

1.4 C.4 Ion implantation

The determination of the gallium diffusion coefficients can be performed using the stable isotope 71Ga. The small difference in abundance of the gallium isotopes 69Ga and 71Ga (61 and 39 at%, respectively) requires the application of large quantities of 71Ga. Nevertheless, a poor signal resolution during analysis has to be expected.

The isotope 71Ga is implanted into the specimens at the University of Frankfurt, Germany. The tracer, extracted from a gallium arsenate plasma, is accelerated to 50 keV and focused on the surface of y-cut langasite plates. The total amount of implanted 71Ga ions is about 8 × 1016 ions/cm2. To avoid electrical charging of the surface, the samples are treated with an additional electron beam. The subsequent diffusion runs are performed in air at temperatures from 700 up to 1000°C.

71Ga is implanted by a 50 keV accelerator. Damage of the lattice in the implanted region is, therefore, expected and the evaluation of the diffusion coefficients must account for the damaged region. Fick’s second law still describes the transport. But the equation has to be solved numerically by e.g. using the Crank-Nicolson scheme [116]. Details are presented in [115].

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Fritze, H. High-temperature piezoelectric crystals and devices. J Electroceram 26, 122–161 (2011). https://doi.org/10.1007/s10832-011-9639-6

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