Funding was provided in part by DEPSCoR grant # FA9950-07-1-0519, Petroleum Research Fund Grant ACS PRF# 42747-AC10, and Air Force Office AFO Grant # FA8650-05-D-5807.

Determination and Experimental Verification of High-Temperature SAW Orientations on Langatate

Peter M. Davulis and Mauricio Pereira da Cunha Dept. of Electrical and Computer Engineering and Laboratory for Surface Science and Technology,

University of Maine, Orono, ME, 04469, U.S.A. mdacunha@eece.maine.edu

Abstract— Langatate (LGT) is a member of the langasite family of crystals appropriate for high-temperature frequency control and sensing applications. This paper identifies multiple LGT SAW orientations for use at high temperature, specifically in the 400 to 900°C range. Orientations with low sensitivity to temperature are desired for frequency control devices and many sensors, conversely large temperature sensitivity is a benefit for temperature sensors. The LGT SAW temperature behavior has been calculated along orientation searches, sweeping the Euler angles (0°, Θ, Ψ), (90°, Θ, Ψ), and (Φ, 90°, Ψ). The temperature coefficient of delay (TCD) and total frequency change over the temperature range were analyzed from 400 to 900°C. Multiple SAW orientations were found with zero-TCD between 400 and 500°C, but no orientations were identified with turn-over temperatures above 500°C. Other orientations have a low variation, −0.8%, in frequency over the range from 400 to 800°C. Additionally, temperature-sensitive orientations were identified with TCD up to 75 ppm/°C at 900°C, for use as temperature sensors at high temperature. The predictions are shown to agree with measured behavior of LGT SAW delay lines fabricated along 6 orientations in the ( 90°, 23°, Ψ) plane.

I. INTRODUCTION There is growing need for high-temperature sensors and

frequency control devices in oil and gas extraction, metal and ceramic manufacturing, aerospace, and energy generation industries [1]-[4]. Surface acoustic wave (SAW) devices can meet the demands for high-temperature survivability and wireless multi-sensor operation using substrates such as gallium orthophosphate (GaPO4) and the langasite family of crystals, including langasite (La3Ga5SiO14, LGS) and langatate (La3Ga5.5Ta0.5O14, LGT) [5]-[16]. Langatate, in particular, has a number of attractive properties for high-temperature operation: i) no phase change until the melting point at 1470°C [17], [18], ii) piezoelectric constants 2-4 times those of quartz [18], iii) higher resistivity than LGS [17], iv) demonstrated temperature-compensated SAW orientations both around room temperature and at elevated temperatures [18]-[22]. However, so far there has been very limited published on high-temperature orientation searches for LGT. In [9], [10] LGS SAW properties were calculated up to 1000°C, but the constants and temperature coefficients employed were taken from [23] and those were measured around at room temperature. Several modern high-temperature

frequency control and sensing applications require operation beyond 400°C. For example, sensors are desired for high-temperature fuel cells, which operate in the 600-1000°C range [24], and for gas turbine engines in the compressor, combustor, and exhaust engine sections, which can typically reach temperatures around 450-750°C, 900-1500°C, and 650°C, respectively [24], [25].

In this work, LGT SAW propagation properties are investigated from 400 to 900°C utilizing constants and temperature coefficients extracted at high-temperature [21]. The SAW properties are calculated according to three different orientation sweeps. The search results are used to identify orientations with either low or high sensitivity to temperature. The orientations are investigated along the Euler angles (0°, Θ, Ψ), (90°, Θ, Ψ), and (Φ, 90°, Ψ), in which 2 Euler angles are swept. Multiple zero-TCD orientations are identified between 400 and 500°C. SAW orientations with a small total frequency shift, −0.8%, between 400 and 800°C were also identified, which are anticipated to find use in sensor and frequency-control devices. Orientations with large temperature sensitivity above 400°C are uncovered and those can be utilized as temperature sensors.

The LGT material constants used and the SAW property identification targets are described in Section II. The calculation results of the SAW orientation sweeps are presented in Section III and analyzed to identify high-temperature orientations with either low or high sensitivity to temperature along different temperature ranges. Section IV details high-temperature SAW measurements that provide experimental verification of predicted LGT SAW properties. Section V concludes the paper.

II. MATERIAL CONSTANTS AND SAW PROPERTIES CALCULATIONS

In this work the LGT stiffened elastic constants from [20], [21] and the density and thermal expansion from [26] are used for the high-temperature LGT SAW predictions. The SAW electromechanical coupling (K2) predictions come from [27], [28], since the high-temperature stiffened elastic constants from [20], [21] do not separately consider the piezoelectric effects. Therefore in this paper all the reported values of K2 refer to calculations at 25°C. In [21] the authors observed that

all the fabricated SAW devices at orientations where K2 > 0.2% at room temperature operate up to at least 900°C.

The SAW properties are calculated using the matrix method implemented with MATLAB (The MathWorks, Natick, MA, USA) [19] to sweep across three regions of Euler angles: Region A = (0°, Θ, Ψ), Region B = (90°, Θ, Ψ), and Region C = (Φ, 90°, Ψ). The LGT SAW velocity, frequency change, and TCD were calculated at 400, 500, 600, 700, 800, and 900°C over those three regions by varying two Euler angles, as indicated. These sweeps were selected because they represent cut planes with surface normals in the Y-Z, X-Z, and X-Y planes for easier wafer cutting and X-ray alignment. For the (Φ, 90°, Ψ) sweeps, Ψ was searched only from 0 to 40° because in this region K2 ≥ 0.1%. Only orientations with K2 > 0.1% at 25°C are discussed for TCD and frequency change in this work.

The LGT SAW propagation properties analysis at high temperature aimed at identifying potential orientations for three different conditions: (i) narrow temperature range of operation; (ii) large temperature range of operation (400 to 800°C); and (iii) operation of several orientations in a same plane (variation of third Euler angle, Ψ). First, SAW orientations for a narrow operation temperature range were searched for low and high TCD. Next, change in SAW frequency from 400 to 800°C is used to identify orientations for a wider range of operation temperatures. Finally, SAW cuts are investigated for multiple promising orientations in the same plane. Multiple devices on the same wafer with different orientations are useful for sensor applications [29]-[31].

III. LANGATATE SAW PROPERTIES AT HIGH TEMPERATURE

A. SAW TCD at High Temperature The calculated LGT SAW TCD for Region A, the Euler

angles (0°, Θ, Ψ), at 400°C, 600°C, and 900°C are displayed as contour plots in Fig. 1(a), 1(b), and 1(c), respectively, and are representative of the data calculated at the 6 temperatures (400, 500, 600, 700, 800, and 900°C) mentioned in Section II. The LGT SAW TCD calculated at 400°C for the Regions B, (90°, Θ, Ψ), and C (Φ, 90°, Ψ), are shown in Fig. 2 and Fig. 3, respectively.

For the three regions swept, A, B, and C, orientations with TCD=0 were only found at 400°C and none were found at 500°C or higher; however, multiple orientations have negative TCD at 400°C indicating the existence of turn-over temperatures between 400 and 500°C. In particular, LGT SAW orientations with Euler angles (90°, 40→70°, 60→75°) have 0.1 ≤ K2 ≤ 0.2% at room temperature, TCD ≈ −10 ppm/°C at 400°C and TCD ≈ 5 ppm/°C at 500°C. Therefore these orientations have TCD=0 between 400 and 500°C, the highest turnover temperatures for LGT identified in this work for orientations with K2 ≥ 0.1%.

Multiple LGT SAW orientations were found that have close to zero or zero TCD at 400°C and K2 ≥ 0.1%; their Euler angles are listed in Table I along with the respective TCD and K2.

There are also regions with higher TCD that can be useful for temperature sensing. Specifically, (0°,135→150°, 20→25°) has TCD ≈ 25ppm/°C at 400°C and K2 ≈ 0.7%. Orientations in the region (90°, 20→40°, 110→130°) have TCD between 15 and 35 ppm/°C at 400°C and 0.3% ≤ K2 ≤ 0.7%. At 900°C all the calculated orientations were found to have TCD between 40 and 75 ppm/°C.

B. SAW Frequency Change from 400 to 800°C The LGT SAW behavior for a large temperature span was

analyzed by calculating the total SAW frequency change from 400 to 800°C, Δf/f400 = (f800°C − f400°C)/ f400°C, shown in Fig. 4 for the Regions A, B, and C.

As can be seen from Fig. 4, the LGT SAW orientations in the range (90°, 55→75°, 55→80°) have the lowest temperature sensitivity from 400 to 800°C, Δf/f400 = −0.6%, among the calculated orientations with K2 ≥ 0.1%. The SAW orientations (0°, 40→90°, 40→50°) and (90°, 25→80°, 55→65°) have Δf/f400 ≈ −0.8% with 0.1% ≤ K2 ≤ 0.3%. The moderate frequency change is partly due to the fact that these orientations have turnover temperatures between 400 and 500°C.

Conversely, other LGT orientations have larger temperature dependencies. Orientations in the ranges (0°, 10→30°, 65→90°), (0°, 110→160°, 15→45°) and (90°, 15→40°, 95→140°) have Δf/f400 between −1.2% and −1.8% with 0.2% ≤ K2 ≤ 0.7%. These orientations have high TCD through out the temperature range: 15 to 40 ppm/°C at 400°C and 40 to 70 ppm/°C at 800°C.

C. SAW Plane Cuts for High-Temperature Sensor Suites Multiple regions of LGT SAW planes have been identified

as desirable for fabricating a suite of devices on the same wafer with K2 ≥ 0.2% and a variety of temperature sensitivities, useful for sensor applications. LGT planes in the range (0°, 120→140°, Ψ) contain SAW orientations with both low and high temperature-sensitivities, Δf/f400 ranging from −0.8% to −1.4%, and K2 ranging from 0.2% to 0.7%.

LGT planes in the range (90°, 20→40°, Ψ) have regions in which there are SAW orientations with small temperature sensitivity, Δf/f400 = −0.8%, and others with large temperature sensitivity, Δf/f400 = −1.8%, and K2 varying between 0.2% and 0.7%. Additionally, there are a number of orientations in this range that have Δf/f400 = −1.0% and that are widely spaced over the plane, with potential for multiple measurand sensor applications.

IV. EXPERIMENTAL VERIFICATION AND DISCUSSION The SAW high-temperature properties calculated in this

work were compared to those of LGT SAW devices reported in [21] for experimental validation of the frequency and TCD predictions up to 900°C. Six SAW delay lines were fabricated along orientations (90°, 23°, Ψ) with Ψ = 0, 13, 48, 77, 119, and 123°. The interdigital transducers had periodicity given by wavelength λ = 32 μm and utilized 110-nm-thick Pt/Rh/ZrO2 electrodes [13] to enable stable high-temperature operation above 900°C.

Figure 2. Contour plot of predicted LGT SAW TCD in ppm/°C for Region B, Euler angles (90°, Θ, Ψ), at 400°C.

Figure 3. Contour plot of predicted LGT SAW TCD in ppm/°C for Region C, Euler angles (Φ, 90°, Ψ), at 400°C.

TABLE I. LGT SAW ORIENTATIONS WITH TCD ≈ 0 AT 400°C

Euler Angle Sweep (°)

Orientation Euler Angles (°)

TCD at 400°C

(ppm/°C)

K2 at 25°C (%)

(0°, Θ, Ψ) (0, 20→90, 30→50) −5 to 5 0.1 to 0.4 Region A (0, 30→130, 0→15) −5 to 5 0.1 to 0.5 (0, 110→180, 0→90) −5 to 5 0.1 to 0.4 (90°, Θ, Ψ) (90, 10→90, 40→80) −10 to 5 0.1 to 0.4 Region B (90, 0→20, 100→105) ≈0 0.1 to 0.2 (90, 0→20, 35→140) ≈0 0.1 to 0.2 (90, 0→40, 10→20) ≈0 0.1 to 0.2 (90, 0→40, 155→170) ≈0 0.1 to 0.2 (Φ, 90°, Ψ) (0→8, 90, 0→5) ≈0 0.5 Region C (0→30, 90, 28→40) ≈0 0.1 to 0.2

(a)

(b)

(c) Figure 1. Contour plots of predicted LGT SAW TCD in ppm/°C for

Region A, Euler angles (0°, Θ, Ψ): (a) at 400°C, (b) at 600°C, (c) at 900°C.

The calculated and measured SAW frequencies responses are compared in Fig. 5(a) and 5(b) at 400 and 900°C, respectively, for the six orientations identified in the previous paragraph. Along the 6 fabricated orientations the measured and predicted operation frequencies agree within experimental and prediction uncertainties in the temperature range of 400 to 900°C. The calculated SAW frequencies are within 0.85% of the measured frequencies at 400°C and within 1.6% at 900°C.

The predicted and measured TCDs on the (90°, 23°, Ψ) plane are compared in Fig. 6 at 400°C. The predicted and measured TCD agree to within the experimental and prediction uncertainty for the 6 tested SAW orientations throughout the temperature range between 400 and 900°C. The discrepancy between the predicted and measured TCD is below 4.7 ppm/°C at 400°C and less than 24.4 ppm/°C at 900°C.

The agreement between the calculated and measured SAW frequency and TCD for the 6 orientations fabricated along the (90°, 23°, Ψ) plane validates the LGT high-temperature constants and coefficients for SAW predictions at high-temperature.

V. CONCLUSIONS This work has investigated the high-temperature SAW

phase velocity, frequency change, and TCD properties behavior of LGT up to 900°C for three regions in space, namely, (0°, Θ, Ψ), (90°, Θ, Ψ), and (Φ, 90°, Ψ). New LGT SAW orientations have been identified with zero TCD between 400 and 500°C and with low TCD up to 900°C with potential applications for frequency control, sensing, and signal processing. Alternatively, temperature-sensitive orientations have been found of interest to temperature sensing.

Orientations have been identified for high-temperature applications with: i) a narrow temperature range of operation; ii) large temperature range of operation (400 to 800°C); and iii) multiple orientations in a same plane for temperature measurement and separation of the thermal effect from other measurands, as appropriate in sensor applications.

The agreement between the calculated and measured SAW frequency and TCD responses reported in the work validates the LGT constants and temperature coefficients for SAW predictions up to 900°C.

ACKNOWLEDGMENT The authors would like express their gratitude to the

personnel of the Laboratory of Surface Science and Technology (LASST) and Department of Electrical and Computer Engineering at the University of Maine for valuable technical discussion and for assisting with the equipment used in this work and with the fabrication of the devices.

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(a)

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Figure 5. Measured and predicted LGT SAW frequency for devices with λ = 32 μm: (a) along plane (90°, 23°, Ψ) at 400°C, (b) along plane

(90°, 23°, Ψ) at 900°C. Gray line: calculated frequencies, with error bars at the at angles of fabricated devices; black circle: measured

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Figure 6. LGT SAW TCD along plane (90°, 23°, Ψ) at 400°C. Gray

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