The full set of electromechanical data of langasite
(La

Langasite (LGS, La

LGS can be used as a resonant sensor. When operated in the microbalance mode,
small mass changes of a layer with affinity to specific gas particles cause a
shift of the resonance frequency

In this work, the full set of elastic, electric and piezoelectric properties
of langasite is determined at elevated temperatures using bulk acoustic wave (BAW)
resonators of different orientations. Special attention is drawn to the
mechanical and electrical losses, which play an important role for
high-temperature applications. Subsequently, the full set of
electromechanical data is used to predict the wave velocity of SAW resonators
for two selected cuts of LGS. Their Euler angles are
(0, 138.5, 26.6

The LGS crystals for BAW resonators are provided by the Institute for Crystal Growth, Berlin Adlershof, Germany. The wafers for SAW measurements are fabricated by FOMOS-Materials, Russia, and Mitsubishi Materials Corporation, Japan.

A piezoelectric resonator operated at room temperature can be described by a one-dimensional physical model of vibration, where electrical losses are very low and thus negligible. At elevated temperatures, this description is not accurate due to, e.g., the finite electrical conductivity. In this case the elastic, dielectric and piezoelectric coefficients must be extended by imaginary parts which express the mechanical, electrical and piezoelectric losses.

The mechanical loss at elevated temperatures depends on the resonance
frequency

The elastic compliance

A perfectly insulating resonator with two parallel electrodes, excited by a
harmonic electric field

The origin of dielectric loss can be attributed to the electrical
conductivity

In analogy to the mechanical and electrical loss, the imaginary part of the
piezoelectric coefficient can be introduced. The nature of this
“piezoelectric loss” is however not clear. It may be explained by, e.g.,
jumping of lattice defects or the movement of domain walls in polycrystalline
materials

In case of piezoelectric materials, the relation between mechanical and
electrical properties is described by the piezoelectric equation

Due to the tensor symmetry and the crystal symmetry of LGS many tensor
components vanish, so that the number of independent coefficients in
Eq. (

Equation (

The determination of all components of the elastic stiffness and compliance
tensors requires different crystal cuts. The shear components of those
tensors determine two different modes of vibration. The stiffness

From Eq. (

All crystal cuts used in this work are visualized in Fig.

The crystal cuts of langasite
used to determine the full set of electromechanical data

In case of a rod, where the width

With the coupling factor, Eq. (

Solving Newton's equation of motion with

In case of a partially electroded

Under the assumption of a harmonic time dependence of an electric field,
Eq. (

Using these equations, the electric impedance of the thickness shear resonator is obtained

The face shear vibration of a

The parameters of SAW propagation, like velocity

For this purpose the equations of motion

Special test SAW devices are designed for the experimental determination of
the surface acoustic wave parameters

Delay lines of different length.

Thereby, identical input and output interdigital transducers (IDTs) with eight electrodes per electrical period are used (see Fig.

IDT with eight electrodes per period.

They can be regarded as multi-electrode transducers with double spatial
sampling. As shown in

Transfer function

During signal processing the difference between time delay of long and short
delay lines at each harmonic is obtained very precisely

The propagation losses

For the determination of the bulk properties of langasite crystals several
orientations as shown in Fig.

For the SAW measurements two cuts with Euler angles
(0, 138.5, 26.6

All samples are coated with platinum electrodes by pulsed laser deposition (PLD). The thickness of this electrodes is about 250 nm. A titanium adhesion layer of a few nanometers is applied.

The metallization of the SAW test devices is done by SAW Components Dresden GmbH using the lift-off technique. Thin Pt layers of 45 and 75 nm are deposited. A Zr film of 4 nm in thickness is taken as adhesion layer. Dewetting of the thin Pt film above that temperature determines a temperature limit for the measurements. In contrast to the BAW samples, thicker Pt layers cannot be used due to increasing reflection and scattering effects at the IDTs which distort the signal and cause additional losses.

The electric impedance at low frequencies is measured using a Solartron 1260
gain-phase analyzer to determine the electrical conductivity. The impedance
in the vicinity of the resonance frequency of all BAW resonators is acquired
using a HP 5100A network analyzer. For high-temperature measurements in
artificial air containing 20 % O

The measured impedance data are further fitted using the physical models of
the corresponding resonators in order to obtain the components of stiffness
and elastic compliance tensors. It is obvious that the number of free
parameters for the fit procedure must be much smaller than the total number
of parameters, i.e., 16 for the one-dimensional model of thickness shear
resonators. Reasonable fits can be, in general, expected if the number of
free parameters does not exceed three or four

The determination of remaining parameters is performed in several steps:

Impedance measurements of

The fit of analytically solved piezoelectric equations uses the dielectric coefficient and conductivity from step (1).

The data evaluation applied here potentially delivers unreliable absolute values due to, e.g., residual stray capacitance of the high-temperature sample holder. To overcome this problems and to verify the models, fit results are compared with preliminary pulse-echo measurements performed on the same langasite single crystal.

Two delay lines – one long and one short – are positioned on one chip. They
are connected to the same ports and are measured simultaneously. The chip is
mounted on a holder and is connected to the RF-flange of the high-temperature
furnace via two rigid coaxial cables made of steel tubes with ceramic husked
steel wires. The other side of the RF-flange is connected by standard RF
coaxial cables to the network analyzer, which measures the transfer function

A specially developed signal processing algorithm utilizing
cross-correlations, is used for the determination of the precise time delay
and for extracting SAW propagation parameters as described in detail in

The conductivity of the

Conductivity of LGS as function of temperature.

The full set of elastic stiffness
coefficients of langasite as function of temperature calculated from BAW
measurements (solid line) in comparison with the data obtained by

The piezoelectric coefficient of langasite as function of temperature.

The inverse resonant quality factor

As a result of the procedure described in Sect.

A comparison of elastic data from this work with data obtained by

As already mentioned in Sect.

The characterization of SAW devices is carried out up to about
730

Dewetted metal layer after heating
up to 800

Phase velocity of
Rayleigh waves on free surface

Comparison of our measurement results
with literature data. In case of

Coupling coefficient

The propagation loss in
[dB/

The phase velocities

Figure

The propagation loss in
[dB/

The propagation losses

The propagation loss on the metallized surface shown in
Fig.

LGS-based SAW and BAW devices exhibit an operation temperature limit caused
by the stability of the platinum electrodes. It is found, that their lifetime
drops drastically as their thickness decreases. This effect is described by,
e.g.,

Above the mentioned temperatures, de-wetting of the metal layer is observed,
as shown in Fig.

In order to compare the bulk and surface acoustic wave properties, the full
set of temperature-dependent materials data is determined using BAW
resonators and applied to calculate the phase velocity

Comparison of Rayleigh wave velocity on free
surface

A method of materials data extraction from measured data of BAW resonators is
developed for piezoelectric crystals. All components of the stiffness,
elastic compliance and piezoelectric tensors for langasite are determined in
the temperature range from 20 to 900

Based on the obtained tensor data, the phase velocity and the coupling
coefficient for SAW propagation of the crystal cuts
(0, 138.5, 26.6

Values for the velocity of SAW propagation and coupling coefficients obtained
from SAW and from BAW measurements show a good agreement. SAW devices exhibit
a local maximum of propagation loss at around 520

Thin film Pt electrodes for BAW and SAW devices limit the maximum temperature
of measurement to 900 and 730

The authors thank the German research foundation (Deutsche Forschungsgemeinschaft, DFG) for financial support and the Energy Research Center Niedersachsen. Edited by: J. Zosel Reviewed by: two anonymous referees