[1]
From fig. 4(a), the Δf/ΔT is 0.05458 and -0.01253 for the dual mode respectively. For simplicity, the measured original resonant frequencies, 780.625MHz and1560.250MHz, of the FBAR at T0= 25 °C were used as f0 for the two resonant modes. From eq.(1), the TCF for the unsealed FBAR is 69.5ppm/K and -8.1ppm/K, which means FBARs can be used as a good temperature sensor, and the dual modes can be more precise than a single one. After sealed the back-trench, the TCF for the two modes is 63.3ppm/K and -10.2ppm/K respectively. The change of TCFs for the dual mode with unsealed and sealed back trench is induced by the pressure variation as the air in the sealed chamber when temperature was changed. Once the back trench is sealed, the volume of the cavity does not change very much. The membrane bending may introduce volume change, but the bending in the middle of the membrane is much less than 1mm [[] P.Seide, Int.J.Non-Linear.Mechanics. 12 (1977) 397-406. ], and the corresponding volume change is less than 10-4 which can be omitted. Therefore the isolated cavity is governed by Gay-Lussac's law [[] Information on http://en.wikipedia.org/wiki/Gay-Lussac's_law. ]
Google Scholar
[2]
where the index 1 and 2 are the temperatures and pressures of the unsealed and sealed devices respectively; and the unit of temperature is Kelvin. When the temperature changes, the pressure inside the cavity changes correspondingly as follows
Google Scholar
[3]
To a first order, the frequency shift of piezoelectric devices induced by variation on temperature is a linear relationship as shown by many piezoelectric devices [12] and by FBARs [6].The pressure coefficient of frequency (PCF) is defined as
Google Scholar
[4]
From fig. 4(a), the shift of the frequencies at different temperatures can be obtained. From fig. 4(b) and eq.(4), the PCF for the two modes is calculated to be -17.4ppm/kPa and -6.1ppm/kPa respectively. The PCF of the first mode is about five times higher than that obtained by Chiu et al [6], and an order of magnitude higher than that (-1.33 ppm·kPa-1) of the ZnO/Quartz surface acoustic wave-based pressure sensor [[] A. Talbi, F. Sarry , M. Elhakiki, L. L.Brizoual, O. Elmazria, P. Nicolay, P. Alnot, Sens. & Actuat. A 128 (2006) 78-83. ]. Even the second mode is higher than the pressure sensors reported by others, showing that the on-chip FBAR devices can be pressure sensors with very high sensitivity. Summary this paper proposed and demonstrated a dual mode single on-chip FBAR pressure and temperature sensor by utilizing the sealed back trench as the cavity isolated from the outside. FBARs exhibited a good linearity of frequency shift with temperature and pressure for the two mode peaks. By using these dual mode FBARs, it is possible to sense temperature and pressure simultaneously. This dual mode on-chip pressure sensor is simple in structure and operation, and can be fabricated at very low cost. Acknowledgments This work was supported by the NSFC and NSFC Key Program of China (No. 61150110485 & 60936002) and the Engineering and Physical Sciences Research Council (EP/F06294X/1, EP/F063865/1). References
Google Scholar
