Sensors and Actuators A 107 (2003) 261–272 Thick-film resistors on various substrates as sensing elements for strain-gauge applications Marko Hrovat a,∗ , Darko Belaviˇ c b , Andreja Benˇ can a , Janez Bernard a , Janez Holc a , Jena Cilenšek a , Walter Smetana c , Heinz Homolka c , Roland Reicher c , Leszek Golonka d , Andrzej Dziedzic d , Jaroslaw Kita d a Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia b HIPOT-R&D, d.o.o., Trubarjeva 7, SI-8310 Sentjernej, Slovenia c Vienna University of Technology, Gußhausstraße 27-27, 1040 Vienna, Austria d Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland Received 3 July 2003; accepted 13 July 2003 Abstract The characteristics of 10 kohm/sq. thick-film resistors (2041, Du Pont and 2341-B, ESL) fired on tetragonal ZrO 2 , low-temperature cofired ceramic (LTCC) and dielectric-on-steel substrates were investigated with the aim of determining the compatibility of these resistor materials, which were developed for firing on Al 2 O 3 , with other substrates. Possible interactions between the thick-film resistors and the substrates were investigated. Sheet resistivities, temperature coefficients of resistivity, noise indices and gauge factors (GFs) were measured. The results indicate that the 2041 and 3414-B thick-film resistors could be used on the evaluated substrates if an allowance is made for the increased temperature coefficient of resistivities (TCRs) of both resistor materials on the zirconia substrates and for the increased sheet resistivities and TCRs of the 3414-B resistors on the LTCC substrates. © 2003 Elsevier B.V. All rights reserved. Keywords: Thick-film resistor; Gauge factor; Microstructure; Electrical properties 1. Introduction The change in resistance of a resistor under an applied stress is partly due to deformation, i.e. the changes in the dimensions of the resistor, and partly due to alterations in the specific resistivity as a result of microstructural changes [1]. The gauge factor (GF) of a resistor is defined as the ratio of the relative change in resistance (R/R) and the strain (l/l): GF = R/R l/ l (1) Geometrical factors alone result in gauge factors of 2–2.5. Higher GF values are due to microstructural changes that alter the specific conductivity. The GF values of thick-film resistors are mostly between 3 and 15. Due to their stabil- ity, low values of the temperature coefficient of resistivity (TCR) below 100 × 10 -6 K -1 and relatively low cost, strain ∗ Corresponding author. Tel.: +386-1-477-3900; fax: +386-1-426-3126. E-mail address: marko.hrovat@ijs.si (M. Hrovat). gauges realised with thick-film technology offer advantages in some applications over both thin metal films or foils (low GF, low TCR, expensive) and semiconducting elements (high GF, high TCR, inexpensive) [2–4]. Typically, four resistors connected in a Wheatstone bridge are used. For better sensitivity (i.e. a greater change in the balance of the Wheatstone bridge), two resistors are normally under tension (an increase of resistance) and two under compres- sion (a decrease of resistance). Within the same thick-film resistor series both the GFs (which is obviously beneficial for sensing applications) and the current–noise indices in- crease with increasing sheet resistivity while the voltage response of the Wheatstone bridge decreases [5,6]. There- fore, in most cases 10 kohm/sq. resistors are used for strain sensors as a useful compromise between sensitivity and relatively low noise, and also because of their relatively low power consumption. Pressure or force sensors can be realised with resistors on deformable membranes. The thick-film resistors are printed and fired on a ceramic substrate (diaphragm), which is usu- ally based on alumina. However, sensing elements made 0924-4247/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2003.07.003